diff --git a/.ci/build_docs.sh b/.ci/build_docs.sh
new file mode 100644
index 00000000000..9a8453ba881
--- /dev/null
+++ b/.ci/build_docs.sh
@@ -0,0 +1,111 @@
+#!/bin/sh
+################################################################################
+# Title : generateDocumentationAndDeploy.sh
+# Date created : 2016/02/22
+# Notes :
+__AUTHOR__="Jeroen de Bruijn"
+# Preconditions:
+# - Packages doxygen doxygen-doc doxygen-latex doxygen-gui graphviz
+# must be installed.
+# - Doxygen configuration file must have the destination directory empty and
+# source code directory with a $(TRAVIS_BUILD_DIR) prefix.
+# - An gh-pages branch should already exist. See below for mor info on hoe to
+# create a gh-pages branch.
+#
+# Required global variables:
+# - TRAVIS_BUILD_NUMBER : The number of the current build.
+# - TRAVIS_COMMIT : The commit that the current build is testing.
+# - DOXYFILE : The Doxygen configuration file.
+# - TRAVIS_REPO_SLUG : The username / reponame for the repository.
+# - GH_REPO_TOKEN : Secure token to the github repository.
+#
+# For information on how to encrypt variables for Travis CI please go to
+# https://docs.travis-ci.com/user/environment-variables/#Encrypted-Variables
+# or https://gist.github.com/vidavidorra/7ed6166a46c537d3cbd2
+# For information on how to create a clean gh-pages branch from the master
+# branch, please go to https://gist.github.com/vidavidorra/846a2fc7dd51f4fe56a0
+#
+# This script will generate Doxygen documentation and push the documentation to
+# the gh-pages branch of a repository specified by GH_REPO_REF.
+# Before this script is used there should already be a gh-pages branch in the
+# repository.
+#
+################################################################################
+
+################################################################################
+##### Setup this script and get the current gh-pages branch. #####
+if [[ $TRAVIS_OS_NAME == "osx" ]]; then return ; fi
+
+echo 'Setting up the script...'
+# Exit with nonzero exit code if anything fails
+set -e
+
+GH_REPO_ORG=`echo $TRAVIS_REPO_SLUG | cut -d "/" -f 1`
+GH_REPO_NAME=`echo $TRAVIS_REPO_SLUG | cut -d "/" -f 2`
+GH_REPO_REF="github.com/$GH_REPO_ORG/$GH_REPO_NAME.git"
+
+# Create a clean working directory for this script.
+# Get the current gh-pages branch
+cd doc
+git clone -b gh-pages https://git@$GH_REPO_REF html
+cd html
+
+##### Configure git.
+# Set the push default to simple i.e. push only the current branch.
+git config --global push.default simple
+# Pretend to be an user called Travis CI.
+git config user.name "Travis CI"
+git config user.email "travis@travis-ci.org"
+
+# Remove everything currently in the gh-pages branch.
+# GitHub is smart enough to know which files have changed and which files have
+# stayed the same and will only update the changed files. So the gh-pages branch
+# can be safely cleaned, and it is sure that everything pushed later is the new
+# documentation.
+rm -rf *
+
+# Need to create a .nojekyll file to allow filenames starting with an underscore
+# to be seen on the gh-pages site. Therefore creating an empty .nojekyll file.
+# Presumably this is only needed when the SHORT_NAMES option in Doxygen is set
+# to NO, which it is by default. So creating the file just in case.
+echo "" > .nojekyll
+
+################################################################################
+##### Generate the Doxygen code documentation and log the output. #####
+echo 'Generating Doxygen code documentation...'
+# Redirect both stderr and stdout to the log file AND the console.
+cd ..
+
+doxygen --version
+
+doxygen $DOXYFILE 2>&1 | tee doxygen.log
+
+################################################################################
+##### Upload the documentation to the gh-pages branch of the repository. #####
+# Only upload if Doxygen successfully created the documentation.
+# Check this by verifying that the html directory and the file html/index.html
+# both exist. This is a good indication that Doxygen did it's work.
+if [ -d "html" ] && [ -f "html/index.html" ]; then
+
+ cd html
+ echo 'Uploading documentation to the gh-pages branch...'
+ # Add everything in this directory (the Doxygen code documentation) to the
+ # gh-pages branch.
+ # GitHub is smart enough to know which files have changed and which files have
+ # stayed the same and will only update the changed files.
+ git add --all
+
+ # Commit the added files with a title and description containing the Travis CI
+ # build number and the GitHub commit reference that issued this build.
+ git commit -m "Deploy code docs to GitHub Pages Travis build: ${TRAVIS_BUILD_NUMBER}" -m "Commit: ${TRAVIS_COMMIT}"
+
+ # Force push to the remote gh-pages branch.
+ # The ouput is redirected to /dev/null to hide any sensitive credential data
+ # that might otherwise be exposed.
+ git push --force "https://${GH_REPO_TOKEN}@${GH_REPO_REF}" > /dev/null 2>&1
+else
+ echo '' >&2
+ echo 'Warning: No documentation (html) files have been found!' >&2
+ echo 'Warning: Not going to push the documentation to GitHub!' >&2
+ exit 1
+fi
diff --git a/.ci/build_root.sh b/.ci/build_root.sh
new file mode 100755
index 00000000000..865eb1eec92
--- /dev/null
+++ b/.ci/build_root.sh
@@ -0,0 +1,19 @@
+pushd $DEPS_DIR
+set -evx
+
+os=$1
+if [[ $os == "osx" ]] ; then
+ wget -nv http://repo.continuum.io/miniconda/Miniconda3-latest-MacOSX-x86_64.sh -O miniconda_${os}.sh
+elif [[ $os == "linux" ]] ; then
+ wget -nv http://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda_${os}.sh
+fi
+
+bash miniconda_${os}.sh -b -p $DEPS_DIR/miniconda
+export PATH="$DEPS_DIR/miniconda/bin:$PATH"
+hash -r
+conda config --add channels conda-forge
+
+conda create --yes -n env_${os} root doxygen -c conda-forge
+
+set +evx
+popd
diff --git a/.ci/travis_linux.sh b/.ci/travis_linux.sh
new file mode 100755
index 00000000000..e63c2fbfd9d
--- /dev/null
+++ b/.ci/travis_linux.sh
@@ -0,0 +1,23 @@
+#!/bin/bash
+
+set -evx
+# from https://stackoverflow.com/questions/55342122/conda-activate-on-travis-ci
+export PATH="$DEPS_DIR/miniconda/bin:$PATH"
+. $(conda info --root)/etc/profile.d/conda.sh
+conda activate env_${TRAVIS_OS_NAME}
+
+echo -en 'travis_fold:start:script.build\\r'
+echo "Building..."
+echo "Building under OS: $TRAVIS_OS_NAME, CXX =$CXX"
+echo "Directories: DEPS_DIR=$DEPS_DIR; TRAVIS_BUILD_DIR=$TRAVIS_BUILD_DIR"
+mkdir -p build
+cd build
+cmake .. -DENABLE_INSTALL=0
+cmake --build . -- -j2
+
+set +evx
+
+cd ..
+
+./build/bin/AmpGen.exe options/example_b2kstarll.opt --CompilerWrapper::Verbose --nEvents 10000
+
diff --git a/.ci/travis_osx.sh b/.ci/travis_osx.sh
new file mode 100644
index 00000000000..069fc6f8e9c
--- /dev/null
+++ b/.ci/travis_osx.sh
@@ -0,0 +1,18 @@
+#!/bin/bash
+
+. $(conda info --root)/etc/profile.d/conda.sh
+conda activate env_${TRAVIS_OS_NAME}
+
+echo -en 'travis_fold:start:script.build\\r'
+echo "Building..."
+echo "Building under OS: $TRAVIS_OS_NAME"
+
+mkdir -p build
+cd build
+echo "CMake-ing, CXX = $CXX"
+cmake .. -DCMAKE_CXX_COMPILER=clang -DUSE_SIMD=0 -DUSE_OPENMP=0 -DUSE_MVEC=0 -DENABLE_INSTALL=0
+echo "Building ..."
+cmake --build . -- -j2
+cd ..
+echo "Running test job ..."
+./build/bin/AmpGen.exe options/example_b2kstarll.opt --CompilerWrapper::Verbose --nEvents 10000
diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
deleted file mode 100644
index eada0860293..00000000000
--- a/.gitlab-ci.yml
+++ /dev/null
@@ -1,20 +0,0 @@
-image: alpine:latest
-
-pages:
- stage: deploy
- script:
- - apk update && apk add doxygen && apk add graphviz
- - apk add ghostscript
- - mkdir build
- - cd doc
- - doxygen doxyfile
- - cd ../
- - mv build/html/ public
- - cp doc/customdoxygen.css public/
- - mkdir public/figs/
- - cp doc/figs/*.png public/figs/.
- artifacts:
- paths:
- - public
- only:
- - master
diff --git a/.travis.yml b/.travis.yml
new file mode 100644
index 00000000000..84c3110f45f
--- /dev/null
+++ b/.travis.yml
@@ -0,0 +1,51 @@
+language: cpp
+
+matrix:
+ include:
+ - os: osx
+ osx_image: xcode10.1
+ compiler: clang
+ addons:
+ homebrew:
+ packages:
+ - libomp
+ - os: linux
+ env:
+ - MATRIX_EVAL="CC=gcc-8 && CXX=g++-8"
+
+
+
+cache:
+ ccache: true
+ apt: true
+ directories:
+ - "${TRAVIS_BUILD_DIR}/deps/root"
+ - "${TRAVIS_BUILD_DIR}/deps/doxygen"
+
+# Blacklist
+branches:
+ except:
+ - gh-pages
+
+# Environment variables
+env:
+ global:
+ - GH_REPO_NAME: AmpGen
+ - DOXYFILE: $TRAVIS_BUILD_DIR/doc/doxyfile
+ - GH_REPO_REF: github.com/GooFit/AmpGen.git
+ - DEPS_DIR: "${TRAVIS_BUILD_DIR}/deps"
+
+before_install:
+ - eval "${MATRIX_EVAL}"
+ - chmod +x .ci/build_root.sh
+ - source .ci/build_root.sh ${TRAVIS_OS_NAME}
+
+# Build your code e.g. by calling make
+script:
+ - chmod +x .ci/travis_${TRAVIS_OS_NAME}.sh
+ - source .ci/travis_${TRAVIS_OS_NAME}.sh
+
+# Generate and deploy documentation
+after_success:
+ - chmod +x .ci/build_docs.sh
+ - source .ci/build_docs.sh
diff --git a/AmpGen/ASTResolver.h b/AmpGen/ASTResolver.h
index 9513347ac84..1fc44234816 100644
--- a/AmpGen/ASTResolver.h
+++ b/AmpGen/ASTResolver.h
@@ -17,54 +17,60 @@ namespace AmpGen {
class MinuitParameter;
class MinuitParameterSet;
class MinuitParameterLink;
- /// \class ASTResolver
- /// Traverses trees in IExpression::resolveDependencies()
- /// to keep track of the dependencies of the tree
- /// such as sub-trees, external parameters and the event type map.
+ /** @ingroup ExpressionEngine class ASTResolver
+ @brief (Internal) class to aide in the resolution of the dependencies of expression trees.
+
+ Traverses trees in IExpression::resolve() to keep track of the dependencies of the tree
+ such as sub-trees, external parameters and the mapping between particle kinematics and the
+ event vector.
+ */
class ASTResolver
{
public:
- ASTResolver(const std::map<std::string, size_t>& evtMap = {} , const MinuitParameterSet* mps = nullptr );
- bool hasSubExpressions() const;
- void reduceSubTrees();
- void cleanup();
- void getOrderedSubExpressions( Expression& expression, std::vector<std::pair<uint64_t,Expression>>& dependentSubexpressions );
+ ASTResolver(const std::map<std::string, unsigned>& evtMap = {} , const MinuitParameterSet* mps = nullptr );
+ std::vector<std::pair<uint64_t,Expression>> getOrderedSubExpressions( const Expression& expression);
template <class TYPE> void resolve( const TYPE& obj ){}
template <class TYPE, class ...ARGS> size_t addCacheFunction( const std::string& name, const ARGS&... args )
{
auto it = m_cacheFunctions.find(name);
if( it != m_cacheFunctions.end() ) return it->second->address();
- auto cacheFunction = std::make_shared<TYPE>(nParameters, args... );
+ auto cacheFunction = std::make_shared<TYPE>(m_nParameters, name, args... );
m_cacheFunctions[name] = cacheFunction;
- nParameters += cacheFunction->size();
- return nParameters - cacheFunction->size();
+ m_nParameters += cacheFunction->size();
+ return m_nParameters - cacheFunction->size();
}
- size_t nParams() const { return nParameters ; }
- bool enableCuda() const { return enable_cuda ; }
- bool enableCompileConstants() const { return enable_compileTimeConstants ;}
+ size_t nParams() const { return m_nParameters ; }
+ bool enableCuda() const { return m_enable_cuda ; }
+ bool enableAVX() const { return m_enable_avx; }
+ bool enableCompileConstants() const { return m_enable_compileTimeConstants ;}
+ void setEnableAVX(){ m_enable_avx = true ; }
std::map<std::string, std::shared_ptr<CacheTransfer>> cacheFunctions() const;
void addResolvedParameter(const IExpression* param, const std::string& thing);
void addResolvedParameter(const IExpression* param, const size_t& address, const size_t& arg=0);
std::string resolvedParameter( const IExpression* param ) const;
+
+ void clear();
+ std::map<const IExpression*, std::string> parameters() const { return m_resolvedParameters; }
private:
- std::map<const IExpression* , std::string> m_resolvedParameters;
- std::map<std::string, std::shared_ptr<CacheTransfer>> m_cacheFunctions;
- std::map<std::string, size_t> evtMap; /// event specification
- std::map<std::string, std::string> parameterMapping; /// Mapping of parameters to compile parameters
- const MinuitParameterSet* mps; /// Set of MinuitParameters
- std::map<const SubTree*, uint64_t> tempTrees; /// temporary store of sub-trees for performing cse reduction
- std::map<uint64_t, Expression> subTrees; /// Unordered sub-trees
- unsigned int nParameters; /// Number of parameters
- bool enable_cuda; /// flag to generate CUDA code <<experimental>>
- bool enable_compileTimeConstants; /// flag to enable compile time constants <<experimental>>
-
+ std::map<const IExpression*, std::string> m_resolvedParameters; /// Map of parameters that have been resolved
+ std::map<std::string, std::shared_ptr<CacheTransfer>> m_cacheFunctions; /// Container of functions for calculating function cache
+ std::map<std::string, unsigned> m_evtMap; /// Event specification
+ std::map<std::string, std::string> m_parameterMapping; /// Mapping of parameters to compile parameters
+ const MinuitParameterSet* m_mps; /// Set of MinuitParameters
+ std::map<const IExpression*, const SubTree*> m_tempTrees; /// temporary store of sub-trees for performing cse reduction
+ unsigned int m_nParameters; /// Number of parameters
+ bool m_enable_cuda {false}; /// flag to generate CUDA code <<experimental>>
+ bool m_enable_compileTimeConstants {false}; /// flag to enable compile time constants <<experimental>>
+ bool m_enable_avx {false}; /// flag to generate code using AVX instructions <<experimental>>
+ bool m_check_hashes {false}; /// flag to check that hashes are unique
};
template <> void ASTResolver::resolve<Parameter>( const Parameter& obj );
template <> void ASTResolver::resolve<SubTree> ( const SubTree & obj );
template <> void ASTResolver::resolve<Spline> ( const Spline & obj );
template <> void ASTResolver::resolve<MinuitParameterLink>( const MinuitParameterLink& obj );
+ template <> void ASTResolver::resolve<LambdaExpression>( const LambdaExpression& obj);
}
diff --git a/AmpGen/AddCPConjugate.h b/AmpGen/AddCPConjugate.h
new file mode 100644
index 00000000000..40bb9011540
--- /dev/null
+++ b/AmpGen/AddCPConjugate.h
@@ -0,0 +1,6 @@
+
+namespace AmpGen {
+ class MinuitParameterSet;
+
+ void AddCPConjugate(MinuitParameterSet&);
+}
diff --git a/AmpGen/AmplitudeRules.h b/AmpGen/AmplitudeRules.h
index a3b53f6c6fa..57e30519d34 100644
--- a/AmpGen/AmplitudeRules.h
+++ b/AmpGen/AmplitudeRules.h
@@ -13,105 +13,120 @@
#include "AmpGen/CompiledExpression.h"
#include "AmpGen/Event.h"
#include "AmpGen/Particle.h"
+#include "AmpGen/ExpressionParser.h"
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+#endif
namespace AmpGen
{
- class AmplitudeRules;
class MinuitParameter;
+ class MinuitExpression;
class MinuitParameterSet;
- class CouplingConstant;
- class AmplitudeRule
+ class Coupling
{
public:
- AmplitudeRule( const std::string& reName, const std::map<std::string, MinuitParameter*>& mapping );
+ Coupling(MinuitParameter* re, MinuitParameter* im);
+ Coupling(MinuitExpression* expression);
std::string name() const { return m_name; }
std::string head() const { return m_particle.name(); }
std::string prefix() const { return m_prefix; }
EventType eventType() const;
- friend class CouplingConstant;
- friend class AmplitudeRules;
-
+ MinuitParameter* x() const { return m_re; }
+ MinuitParameter* y() const { return m_im; }
+ complex_t operator()() const;
+ Expression to_expression() const;
+ const Particle& particle() const { return m_particle ; }
+ bool isCartesian() const { return m_isCartesian; }
private:
- std::string m_prefix;
- std::string m_name;
- MinuitParameter* m_re;
- MinuitParameter* m_im;
- bool m_isGood;
- Particle m_particle;
+ std::string m_prefix = {""};
+ std::string m_name = {""};
+ MinuitParameter* m_re = {nullptr};
+ MinuitParameter* m_im = {nullptr};
+ MinuitExpression* m_expr = {nullptr};
+ Particle m_particle;
+ bool m_isCartesian = {true};
+ double m_sf = {1};
};
- class AmplitudeRules
- {
- public:
- AmplitudeRules() = default;
- AmplitudeRules( const MinuitParameterSet& mps );
- std::vector<AmplitudeRule> rulesForDecay(const std::string& head, const std::string& prefix="");
- bool hasDecay( const std::string& head );
- std::map<std::string, std::vector<AmplitudeRule>> rules();
- std::vector<std::pair<Particle, CouplingConstant>> getMatchingRules(
- const EventType& type, const std::string& prefix );
- std::vector<AmplitudeRule> processesThatProduce(const Particle& particle) const;
- private:
- std::map<std::string, std::vector<AmplitudeRule>> m_rules;
- };
-
- class CouplingConstant
+ class TotalCoupling
{
public:
- CouplingConstant() = default;
- CouplingConstant( const CouplingConstant& other, const AmplitudeRule& pA);
- CouplingConstant( const AmplitudeRule& pA);
+ TotalCoupling() = default;
+ TotalCoupling( const TotalCoupling& other, const Coupling& pA);
+ TotalCoupling( const Coupling& pA);
std::complex<double> operator()() const;
Expression to_expression() const;
void print() const;
- std::pair<MinuitParameter*, MinuitParameter*> operator[]( const size_t& index ) { return couplings[index]; }
+ Coupling operator[]( const size_t& index ) { return couplings[index]; }
bool isFixed() const;
bool contains( const std::string& name ) const;
- void changeSign();
- std::vector<std::pair<MinuitParameter*, MinuitParameter*>> couplings;
+ size_t size() const { return couplings.size(); }
+ std::vector<Coupling>::const_iterator begin() const { return couplings.begin() ; }
+ std::vector<Coupling>::const_iterator end() const { return couplings.end() ; }
+ private:
+ std::vector<Coupling> couplings;
+ };
+
+ class AmplitudeRules
+ {
+ public:
+ AmplitudeRules() = default;
+ AmplitudeRules( const MinuitParameterSet& mps );
+ std::vector<Coupling> rulesForDecay(const std::string& head, const std::string& prefix="");
+ bool hasDecay( const std::string& head );
+ const std::map<std::string, std::vector<Coupling>>& rules() const;
+ std::vector<std::pair<Particle, TotalCoupling>> getMatchingRules(
+ const EventType& type, const std::string& prefix="" );
+ std::vector<Coupling> processesThatProduce(const Particle& particle) const;
private:
- bool isCartesian = {true};
- double sf = {1};
+ std::map<std::string, std::vector<Coupling>> m_rules;
};
- template <class RT> struct TransitionMatrix
+ template <class RT> struct TransitionMatrix : public CompiledExpression<RT(const real_t*, const float_v*)>
{
+ using amp_type = CompiledExpression<RT(const real_t*, const float_v*)>;
TransitionMatrix() = default;
TransitionMatrix(const Particle& dt,
- const CouplingConstant& coupling,
- const CompiledExpression<RT, const real_t*, const real_t*> & pdf) :
+ const TotalCoupling& coupling,
+ const amp_type& amp) :
+ amp_type(amp),
decayTree(dt),
- coupling(coupling),
- pdf(pdf) {}
+ coupling(coupling) {}
- TransitionMatrix(Particle& dt,
- const CouplingConstant& coupling,
+ TransitionMatrix(const Particle& dt,
+ const TotalCoupling& coupling,
const MinuitParameterSet& mps,
- const std::map<std::string,size_t>& evtFormat,
+ const std::map<std::string, unsigned>& evtFormat,
const bool& debugThis=false) :
+ amp_type(Particle(dt).getExpression(debugThis ? &db : nullptr ), dt.decayDescriptor(), evtFormat, db, &mps ),
decayTree(dt),
- coupling(coupling)
- {
- DebugSymbols db;
- auto expression = dt.getExpression(debugThis ? &db : nullptr);
- pdf = CompiledExpression<RT,const real_t*, const real_t*>
- (expression, dt.decayDescriptor(), evtFormat, debugThis ? db : DebugSymbols(), &mps );
- }
+ coupling(coupling) {}
- const RT operator()(const Event& event) const { return pdf(event.address() ); }
+ #if ENABLE_AVX
+ const RT operator()(const Event& event) const { return amp_type::operator()(EventListSIMD::makeEvent(event).data()); }
+ void debug( const Event& event ) const { amp_type::debug(EventListSIMD::makeEvent(event).data() ) ; }
+
+ #else
+ const RT operator()(const Event& event) const { return amp_type::operator()(event.address()) ; }
+ void debug( const Event& event ) const { amp_type::debug(event.address()) ; }
+ #endif
+ template <class... arg_types> auto operator()(arg_types... args ) const { return amp_type::operator()(args...) ; }
+
+ const RT operator()(const float_v* t) const { return amp_type::operator()(t) ; }
+ void debug( const float_v* t ) const { amp_type::debug(t) ; }
const std::string decayDescriptor() const { return decayTree.decayDescriptor() ; }
Particle decayTree;
- CouplingConstant coupling;
+ TotalCoupling coupling;
complex_t coefficient;
- CompiledExpression<RT,const real_t*,const real_t*> pdf;
- size_t addressData = {999};
+ DebugSymbols db;
+ bool workToDo = {false};
};
- template <class RT>
- std::vector<size_t> processIndex(const std::vector<TransitionMatrix<RT>>& tm, const std::string& label)
+ template <class RT> std::vector<size_t> processIndex(const std::vector<TransitionMatrix<RT>>& tm, const std::string& label)
{
std::vector<size_t> indices;
for ( size_t i = 0; i < tm.size(); ++i ) {
@@ -120,8 +135,7 @@ namespace AmpGen
return indices;
}
- template <class RT>
- size_t findIndex(const std::vector<TransitionMatrix<RT>>& tm, const std::string& decayDescriptor)
+ template <class RT> size_t findIndex(const std::vector<TransitionMatrix<RT>>& tm, const std::string& decayDescriptor)
{
for ( size_t i = 0; i < tm.size(); ++i ) {
if ( tm[i].decayDescriptor() == decayDescriptor ) return i;
@@ -139,7 +153,54 @@ namespace AmpGen
}
return rt;
}
+
+ template <> struct TransitionMatrix<void> : public CompiledExpression<void(complex_v*, const size_t&, const real_t*, const float_v*)>
+ {
+ using amp_type = CompiledExpression<void(complex_v*, const size_t&, const real_t*, const float_v*)>;
+ TransitionMatrix() = default;
+ TransitionMatrix(const Particle& dt,
+ const TotalCoupling& coupling,
+ const amp_type& amp) :
+ amp_type(amp),
+ decayTree(dt),
+ coupling(coupling) {}
+
+ TransitionMatrix(const Particle& dt,
+ const TotalCoupling& coupling,
+ const MinuitParameterSet& mps,
+ const std::map<std::string, unsigned>& evtFormat,
+ const bool& debugThis=false) :
+ amp_type(Particle(dt).getExpression(debugThis ? &db : nullptr ), dt.decayDescriptor(), evtFormat, db, &mps ),
+ decayTree(dt),
+ coupling(coupling)
+ { use_rto();}
+
+ const std::vector<complex_v> operator()(const Event& event) const
+ {
+ std::vector<complex_v> rt(size);
+ #if ENABLE_AVX
+ amp_type::operator()(rt.data(), 1, externBuffer().data(), EventListSIMD::makeEvent(event).data());
+ #else
+ amp_type::operator()(rt.data(), 1, externBuffer().data(), event.address());
+ #endif
+ return rt;
+ }
+ template <class... arg_types> auto operator()(arg_types... args ) const { return amp_type::operator()(args...) ; }
+ #if ENABLE_AVX
+ void debug( const Event& event ) const { amp_type::debug(EventListSIMD::makeEvent(event).data() ) ; }
+ #else
+ void debug( const Event& event ) const { amp_type::debug(event.address()) ; }
+ #endif
+ const std::string decayDescriptor() const { return decayTree.decayDescriptor() ; }
+ Particle decayTree;
+ TotalCoupling coupling;
+ complex_t coefficient;
+ DebugSymbols db;
+ bool workToDo = {false};
+ unsigned size = {0};
+ };
+
} // namespace AmpGen
#endif
diff --git a/AmpGen/ArgumentPack.h b/AmpGen/ArgumentPack.h
index 90b66758d0f..a9e745a7750 100644
--- a/AmpGen/ArgumentPack.h
+++ b/AmpGen/ArgumentPack.h
@@ -7,94 +7,94 @@
#include <string>
#include <vector>
-
namespace AmpGen
{
+ #define DECLARE_ARGUMENT(X, Y) \
+ struct X : public AmpGen::Argument<Y> { \
+ template<class Z> \
+ explicit X(Z val = Z()) : AmpGen::Argument<Y>(val){} \
+ X() : AmpGen::Argument<Y>(){} \
+ }
+ /** @class IArgument
+ @brief Virtual base class for arguments
+ Named arguments to functions (python-style) are given a virtual base class such
+ that they can be stored into an argument pack. Relies on runtime polymorphism
+ and should be kept away from any code that has to be fast.
+ */
struct IArgument {
- virtual ~IArgument() = default;
+ virtual ~IArgument() = default;
};
+
/** @class Argument
- Structure to flexibly pass blocks of "Named" parameters to functions, to
- approximate the behaviour of python's named arguments.
- Typical usage is for constructors with variable arguments, such as
- to read data from the disk. The interface for the user is typically
- \code{cpp}
- EventList events("files.root",
- type,
- GetGenPDF(true),
- WeightBranch("eventWeight"),
- Branches({"K_PX","K_PY",...}));
- \endcode
- Internally these arguments are used to construct an ArgumentPack, and then read out
- using getArg<TYPE>, so for this example:
- \code{cpp}
- auto pdfSize = args.getArg<CacheSize>().val;
- auto filter = args.getArg<Filter>().val;
- auto getGenPdf = args.getArg<GetGenPdf>(true).val;
- auto weightBranch = args.getArg<WeightBranch>().val;
- auto branches = args.getArg<Branches>().val;
- auto applySym = args.getArg<ApplySym>().val;
- auto entryList = args.getArg<EntryList>().val;
- \endcode
- @tparam: TYPE type of the argument, such as a string, a number, a bool etc.
- */
- template <class TYPE> struct Argument : public IArgument
+ @brief Structure to pass "named" parameters to functions.
+ Structure to flexibly pass blocks of "Named" parameters to functions, to
+ approximate the behaviour of Python's named arguments.
+ Typical usage is for constructors with variable arguments, such as
+ to read data from the disk. The interface for the user is typically
+ \code{cpp}
+ EventList events("files.root",
+ type,
+ GetGenPDF(true),
+ WeightBranch("eventWeight"),
+ Branches({"K_PX","K_PY",...}));
+ \endcode
+ Internally these arguments are used to construct an ArgumentPack, and then read out
+ using getArg<TYPE>, so for this example:
+ \code{cpp}
+ auto pdfSize = args.getArg<CacheSize>().val;
+ auto filter = args.getArg<Filter>().val;
+ auto getGenPdf = args.getArg<GetGenPdf>(true).val;
+ auto weightBranch = args.getArg<WeightBranch>().val;
+ auto branches = args.getArg<Branches>().val;
+ auto applySym = args.getArg<ApplySym>().val;
+ auto entryList = args.getArg<EntryList>().val;
+ \endcode
+ @tparam TYPE Type of the argument, such as a string, a number, a bool etc.
+ */
+ template <typename TYPE>
+ struct Argument : public IArgument
{
- Argument( const TYPE& x = TYPE() ) : val( x ) {}
+ template <typename T>
+ explicit Argument( T x ) : val(x) {}
+ Argument() = default;
operator TYPE() const { return val; }
- TYPE val;
- };
-
- template <class TYPE> struct ArgumentPtr : public IArgument
- {
- ArgumentPtr( TYPE* x = nullptr ) : val( x ) {}
- TYPE* val;
- };
-
- struct File : public IArgument
- {
- std::string name;
- std::ios_base::openmode mode;
- File( const std::string& name = "", const std::ios_base::openmode& mode = std::ios_base::in )
- : name( name ), mode( mode ){};
+ TYPE val = { TYPE() };
};
+ /** @class ArgumentPack
+ @brief Container for a set of arguments
+ Contains a set of arguments packed from a variadic constructor, that can
+ then be unpacked in the call site of the function where the named arguments
+ are required, as per the description in Argument.
+ */
class ArgumentPack
{
public:
- template <class... ARGS>
- ArgumentPack( const ARGS&... args )
+ template <typename... ARGS>
+ explicit ArgumentPack( const ARGS&... args )
{
std::tuple<ARGS...> argTuple( args... );
- for_each( argTuple, [this]( auto& f ) { m_parameters.emplace_back( makeShared( f ) ); } );
+ for_each(argTuple, [this](const auto& f){ this->addArgument(f) ; } );
}
- template <class ARG>
- ARG getArg( const ARG& default_argument = ARG() ) const
+ template <typename arg_type> arg_type* get() const
+ {
+ for( const auto& param : m_parameters )
{
- for ( auto& param : m_parameters ) {
- auto ptr = dynamic_cast<ARG*>( param.get() );
- if ( ptr != nullptr ) return *ptr;
- }
- return default_argument;
+ auto ptr = dynamic_cast<arg_type*>(param.get());
+ if( ptr != nullptr ) return ptr;
}
+ return nullptr;
+ }
+ template <typename arg_type, typename default_arg_type=arg_type>
+ arg_type getArg( const default_arg_type& default_argument = default_arg_type() ) const
+ {
+ auto p = get<arg_type>();
+ return p == nullptr ? arg_type(default_argument) : *p;
+ }
private:
std::vector<std::shared_ptr<IArgument>> m_parameters;
+ template <typename T> void addArgument( const T& f ){ m_parameters.emplace_back( std::make_shared<T>(f) ) ; }
};
-#define DECLARE_ARGUMENT( X, Y ) \
- struct X : public AmpGen::Argument<Y> { \
- X( const Y& val = Y() ) : AmpGen::Argument<Y>( val ){}; \
- }
-
-#define DECLARE_ARGUMENT_PTR( X, Y ) \
- struct X : public AmpGen::ArgumentPtr<Y> { \
- X( Y* val = nullptr ) : AmpGen::ArgumentPtr<Y>( val ){}; \
- }
-
-#define DECLARE_ARGUMENT_DEFAULT( X, Y, Z ) \
- struct X : public AmpGen::Argument<Y> { \
- X( const Y& val = Z ) : AmpGen::Argument<Y>( val ){}; \
- }
-
} // namespace AmpGen
#endif
diff --git a/AmpGen/Array.h b/AmpGen/Array.h
index 92aeae0310e..312cd465e08 100644
--- a/AmpGen/Array.h
+++ b/AmpGen/Array.h
@@ -15,22 +15,27 @@
namespace AmpGen
{
class ASTResolver;
-
+
+ /** @ingroup ExpressionEngine class Array
+ @brief Expression for a fixed size array of values.
+ Expression for an array, i.e. a set of values with an index.
+ Can be used to return an expression from the array, which is resolved at (second) compile time.
+ */
class Array : public IExpression
{
public:
Array( const Expression& top, const size_t& size, const Expression& address = 0 );
std::string to_string(const ASTResolver* resolver=nullptr) const override ;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
operator Expression();
complex_t operator()() const override;
Expression operator[]( const Expression& address ) const;
Expression top() const { return m_top ; }
-
+ unsigned size() const { return m_size; }
private:
Expression m_top;
Expression m_address;
- size_t m_size;
+ unsigned m_size;
};
} // namespace AmpGen
diff --git a/AmpGen/BinDT.h b/AmpGen/BinDT.h
index 20b00c73ecb..386c55a6cad 100644
--- a/AmpGen/BinDT.h
+++ b/AmpGen/BinDT.h
@@ -15,31 +15,23 @@
#include <vector>
#include "AmpGen/ArgumentPack.h"
-#include "AmpGen/EventList.h"
#include "AmpGen/MsgService.h"
#include "AmpGen/Types.h"
+#include "AmpGen/EventList.h"
namespace AmpGen
{
class Event;
- #define PACKET_SIZE 22
DECLARE_ARGUMENT(MaxDepth, size_t );
DECLARE_ARGUMENT(MinEvents, size_t );
DECLARE_ARGUMENT(Dim, size_t );
- DECLARE_ARGUMENT_PTR( Stream, std::ifstream );
- DECLARE_ARGUMENT_DEFAULT( Functor, std::function<std::vector<real_t>( const Event& )>, nullptr );
+ DECLARE_ARGUMENT(Functor, std::function<std::vector<real_t>( const Event& )>);
+ DECLARE_ARGUMENT(File, std::string);
class BinDT
{
public:
- struct AddressCompressor
- {
- AddressCompressor() = default;
- uint32_t operator[]( const void* ptr );
- uint32_t counter = {0};
- std::map<const void*, uint32_t> elements;
- };
class EndNode;
class INode
@@ -77,7 +69,9 @@ namespace AmpGen
void serialize( std::ostream& stream ) const override;
void setChildren( std::shared_ptr<INode> l, std::shared_ptr<INode> r );
void visit( const std::function<void(INode*)>& visit_function ) override;
+
friend class BinDT;
+
private :
std::shared_ptr<INode> m_left;
std::shared_ptr<INode> m_right;
@@ -95,62 +89,65 @@ namespace AmpGen
{
m_top = makeNodes( addr );
}
- template <class... ARGS>
- BinDT( const EventList& events, const ARGS&... args ) : BinDT( ArgumentPack( args... ) )
+ template <class... ARGS> BinDT( const EventList& events, const ARGS&... args ) : BinDT(ArgumentPack(args...) )
+ {
+ m_top = makeNodes( events.begin(), events.end() );
+ }
+ template <class iterator_type,
+ class... ARGS> BinDT( const iterator_type& begin,
+ const iterator_type& end, const ARGS&... args ) : BinDT(ArgumentPack( args... ) )
{
- std::vector<double> data( m_dim * events.size() );
- std::vector<double*> addresses( events.size() );
- size_t counter = 0;
- for ( auto& evt : events ) {
- auto val = m_functors( evt );
- for ( unsigned int i = 0; i < m_dim; ++i ) data[m_dim * counter + i] = val[i];
- addresses[counter] = &( data[m_dim * counter] );
- counter++;
- }
- INFO( "Making nodes" );
- m_top = makeNodes( addresses );
+ m_top = makeNodes(begin, end );
}
- BinDT( const ArgumentPack& args );
+ explicit BinDT( const ArgumentPack& args );
+ BinDT( const EventList& events, const ArgumentPack& args );
BinDT() = default;
std::shared_ptr<INode> top() { return m_top; }
- double nnUniformity( std::vector<double*> evts, const unsigned int& index ) const;
unsigned int getBinNumber( const Event& evt ) const;
unsigned int getBinNumber( const double* evt ) const;
unsigned int getBin( const Event& evt ) const;
unsigned int getBin( const double* evt ) const;
unsigned int size() const;
void readFromStream( std::istream& stream );
- void readFromBinary( std::ifstream& stream );
void serialize( std::ofstream& output );
void serialize( const std::string& filename );
- void writeToBinary( std::ofstream& file );
- void setQueueOrdering( const std::vector<size_t>& queueOrdering ){ m_queueOrdering = queueOrdering ; }
+ void setQueueOrdering( const std::vector<unsigned>& queueOrdering ){ m_queueOrdering = queueOrdering ; }
std::vector<std::shared_ptr<EndNode>>& nodes() { return m_endNodes; }
const std::vector<std::shared_ptr<EndNode>>& const_nodes() const { return m_endNodes; }
std::vector<std::shared_ptr<EndNode>>::iterator begin() { return m_endNodes.begin(); }
std::vector<std::shared_ptr<EndNode>>::iterator end() { return m_endNodes.end(); }
std::function<std::vector<double>( const Event& )> makeDefaultFunctors();
- void refreshQueue( const std::vector<double*>& evts, std::queue<unsigned int>& indexQueue,
- const unsigned int& depth );
- std::shared_ptr<INode> makeNodes( std::vector<double*> evts, std::queue<unsigned int> indexQueue,
- const unsigned int& depth );
- std::shared_ptr<INode> makeNodes( std::vector<double*> evts );
- std::shared_ptr<INode> makeNodes( std::vector<double*> source, std::vector<double*> target );
-
- std::shared_ptr<INode> makeNodes( std::vector<double*> source, std::vector<double*> target,
- std::queue<unsigned int> indexQueue, const unsigned int& depth );
- void setFunctor( const std::function<std::vector<double>( const Event& )>& functors ) { m_functors = functors; }
-
+ void refreshQueue(const std::vector<double*>&, std::queue<unsigned>&, const unsigned&);
+ template <class iterator_type>
+ std::shared_ptr<INode> makeNodes(const iterator_type& begin, const iterator_type& end)
+ {
+ std::vector<double> data( m_dim * (end-begin) );
+ std::vector<double*> addresses( end-begin );
+ size_t counter = 0;
+ for ( auto evt = begin; evt != end; ++evt )
+ {
+ auto val = m_functors( *evt );
+ for ( unsigned int i = 0; i < m_dim; ++i ) data[m_dim * counter + i] = val[i];
+ addresses[counter] = &( data[m_dim * counter] );
+ counter++;
+ }
+ return makeNodes( addresses );
+ }
+ std::shared_ptr<INode> makeNodes(const std::vector<double*>&, std::queue<unsigned>, const unsigned&);
+ std::shared_ptr<INode> makeNodes(const std::vector<double*>&);
+ std::shared_ptr<INode> makeNodes(const std::vector<double*>&, const std::vector<double*>&);
+ std::shared_ptr<INode> makeNodes(std::vector<double*>, std::vector<double*>, std::queue<unsigned>, const unsigned&);
+ void setFunctor(const std::function<std::vector<double>( const Event& )>& functors) { m_functors = functors; }
private:
- std::shared_ptr<INode> m_top;
- unsigned int m_dim;
- std::vector<std::shared_ptr<EndNode>> m_endNodes;
- std::function<std::vector<double>( const Event& )> m_functors;
- unsigned int m_minEvents;
- unsigned int m_maxDepth;
- std::vector<size_t> m_queueOrdering;
+ std::shared_ptr<INode> m_top = {nullptr};
+ unsigned m_dim = {0};
+ unsigned m_minEvents = {0};
+ unsigned m_maxDepth = {0};
+ std::vector<unsigned> m_queueOrdering = {};
+ std::vector<std::shared_ptr<EndNode>> m_endNodes = {};
+ std::function<std::vector<double>(const Event&)> m_functors = {};
double getBestPost(const std::vector<double*>& source, const std::vector<double*>& target, int index, bool verbose = false );
};
diff --git a/AmpGen/CacheTransfer.h b/AmpGen/CacheTransfer.h
index 5be2ef201fa..67bcd1e0f95 100644
--- a/AmpGen/CacheTransfer.h
+++ b/AmpGen/CacheTransfer.h
@@ -3,41 +3,60 @@
#include <vector>
#include <cstddef>
+#include <string>
+#include <functional>
namespace AmpGen
{
class CompiledExpressionBase;
class MinuitParameter;
+ class LambdaExpression;
class CacheTransfer
{
- protected:
- unsigned int m_address;
- double m_value;
- size_t m_size;
public:
CacheTransfer();
- CacheTransfer( const unsigned int& address, const double& value, const size_t& size=1);
+ CacheTransfer( const size_t& address, const std::string& name, const double& value=0, const size_t& size=1);
virtual ~CacheTransfer() = default;
+
+ size_t address() const { return m_address ; }
+
virtual void transfer( CompiledExpressionBase* destination );
- virtual void print() const;
- virtual unsigned int address() const { return m_address ; }
- virtual unsigned int size() const { return m_size ; }
+ virtual void print() const;
+ virtual size_t size() const { return m_size ; }
+
+ protected:
+ size_t m_address = {0};
+ size_t m_size = {0};
+ double m_value = {0};
+ std::string m_name = {""};
};
class ParameterTransfer : public CacheTransfer
{
- protected:
- unsigned int m_address;
- AmpGen::MinuitParameter* m_source;
-
- public:
- ParameterTransfer( const unsigned int& address, AmpGen::MinuitParameter* source );
- virtual ~ParameterTransfer() = default;
- void transfer( CompiledExpressionBase* destination ) override;
- void print() const override;
- unsigned int address() const override { return m_address ; }
- unsigned int size() const override { return 1 ; }
+ public:
+ ParameterTransfer( const size_t& address, const std::string& name, MinuitParameter* source );
+ virtual ~ParameterTransfer() = default;
+
+ size_t size() const override { return 1 ; }
+
+ void transfer( CompiledExpressionBase* destination ) override;
+ void print() const override;
+
+ protected:
+ MinuitParameter* m_source = {nullptr};
+ };
+ class LambdaTransfer : public CacheTransfer
+ {
+ public:
+ LambdaTransfer( const size_t& address, const std::string& name, const LambdaExpression* source );
+
+ size_t size() const override { return 1 ; }
+
+ void transfer( CompiledExpressionBase* destination ) override;
+ void print() const override;
+
+ std::function<double(void)> m_function;
};
} // namespace AmpGen
diff --git a/AmpGen/Chi2Estimator.h b/AmpGen/Chi2Estimator.h
index 9102cbdb7dc..ea92e4d09de 100644
--- a/AmpGen/Chi2Estimator.h
+++ b/AmpGen/Chi2Estimator.h
@@ -7,24 +7,38 @@
#include "AmpGen/BinDT.h"
+#if ENABLE_AVX
+#include "AmpGen/EventListSIMD.h"
+#else
+#include "AmpGen/EventList.h"
+#endif
+
+
namespace AmpGen
{
- class EventList;
class EventType;
class Event;
class Chi2Estimator
{
- public:
- Chi2Estimator( const EventList& dataEvents, const EventList& mcEvents,
- const std::function<double( const Event& )>& fcn, const unsigned int& minEvents = 10 );
+ #if ENABLE_AVX
+ typedef EventListSIMD EventList_type;
+ #else
+ typedef EventList EventList_type;
+ #endif
+ public:
+ template <typename... argument_types>
+ Chi2Estimator( const EventList_type& dataEvents, const EventList_type& mcEvents,
+ const std::function<double( const Event& )>& fcn,
+ const argument_types&... args ) : m_binning(dataEvents.begin(), dataEvents.end(), ArgumentPack(args...) )
+ {
+ doChi2(dataEvents, mcEvents, fcn);
+ }
- Chi2Estimator( const EventList& dataEvents, const EventList& mcEvents,
- const std::function<double( const Event& )>& fcn, const std::string& filename );
double chi2() const;
double nBins() const;
void writeBinningToFile( const std::string& filename );
- void doChi2( const EventList& dataEvents, const EventList& mcEvents,
+ void doChi2( const EventList_type& dataEvents, const EventList_type& mcEvents,
const std::function<double( const Event& )>& fcn );
private:
double m_chi2;
diff --git a/AmpGen/CoherenceFactor.h b/AmpGen/CoherenceFactor.h
deleted file mode 100644
index de7638f058b..00000000000
--- a/AmpGen/CoherenceFactor.h
+++ /dev/null
@@ -1,196 +0,0 @@
-#ifndef AMPGEN_COHERENCEFACTOR_H
-#define AMPGEN_COHERENCEFACTOR_H
-#include <stddef.h>
-#include <array>
-#include <cmath>
-#include <complex>
-#include <functional>
-#include <map>
-#include <string>
-#include <vector>
-
-#include "AmpGen/BinDT.h"
-#include "AmpGen/EventList.h"
-#include "AmpGen/EventType.h"
-#include "AmpGen/CoherentSum.h"
-#include "AmpGen/Integrator.h"
-#include "AmpGen/MsgService.h"
-#include "AmpGen/Utilities.h"
-#include "AmpGen/Types.h"
-
-namespace AmpGen
-{
- class Event;
-
- struct CoherenceEvent {
- std::array<real_t, 5> values;
- complex_t amp1;
- complex_t amp2;
- real_t weight;
- uint64_t flag;
- };
-
- struct CoherenceCalculator {
- CoherentSum* m_pdf1;
- CoherentSum* m_pdf2;
- Bilinears R;
- Bilinears N1;
- Bilinears N2;
- real_t rTransform;
- real_t phiTransform;
- CoherenceCalculator() = default;
- CoherenceCalculator( CoherentSum* pdf1, CoherentSum* pdf2 )
- : m_pdf1( pdf1 )
- , m_pdf2( pdf2 )
- , R( m_pdf1->size(), m_pdf2->size() )
- , N1( m_pdf1->size(), m_pdf1->size() )
- , N2( m_pdf2->size(), m_pdf2->size() )
- , rTransform( 1 )
- , phiTransform( 0 )
- {
- }
-
- void setTransform( const real_t& rT, const real_t& pT )
- {
- rTransform = rT;
- phiTransform = pT;
- }
- real_t getN2() const
- {
- real_t accN2 = 0;
- for ( unsigned int i = 0; i < m_pdf2->size(); ++i ) {
- accN2 += std::norm( ( *m_pdf2 )[i].coefficient ) * std::abs( N2.get( i, i ) );
- for ( unsigned int j = i + 1; j < m_pdf2->size(); ++j ) {
- accN2 +=
- 2 * std::real( ( *m_pdf2 )[i].coefficient * std::conj( ( *m_pdf2 )[j].coefficient ) * N2.get( i, j ) );
- }
- }
- return accN2;
- }
-
- real_t getN1() const
- {
- real_t accN1 = 0;
- for ( unsigned int i = 0; i < m_pdf1->size(); ++i ) {
- accN1 += std::norm( ( *m_pdf1 )[i].coefficient ) * std::abs( N1.get( i, i ) );
- for ( unsigned int j = i + 1; j < m_pdf1->size(); ++j ) {
- accN1 +=
- 2 * std::real( ( *m_pdf1 )[i].coefficient * std::conj( ( *m_pdf1 )[j].coefficient ) * N1.get( i, j ) );
- }
- }
- return accN1 * rTransform * rTransform;
- }
-
- complex_t getVal()
- {
- complex_t accR( 0, 0 );
- m_pdf1->transferParameters();
- m_pdf2->transferParameters();
- for ( unsigned int i = 0; i < m_pdf1->size(); ++i ) {
- for ( unsigned int j = 0; j < m_pdf2->size(); ++j ) {
- accR += ( *m_pdf1 )[i].coefficient * std::conj( ( *m_pdf2 )[j].coefficient ) * R.get( i, j );
- }
- }
- return complex_t( cos( phiTransform ), sin( phiTransform ) ) * rTransform * accR /
- sqrt( getN1() * getN2() );
- }
- };
-
- struct HadronicParameters {
-
- HadronicParameters( const real_t& _R, const real_t& _d, const real_t& k1 );
- HadronicParameters( const real_t& _R, const real_t& _d, const real_t& k1, const real_t& k2 );
- HadronicParameters() : n1( 0 ), n2( 0 ), wt(0), coherence( 0, 0 ), nFills( 0 ), id( 0 ), binID( 0 ) {}
-
- real_t n1;
- real_t n2;
- real_t wt;
- complex_t coherence;
- unsigned int nFills;
- unsigned int id;
- unsigned int binID;
- real_t I1() const { return n1 / wt ; }
- real_t I2() const { return n2 / wt ; }
- real_t d() const { return std::arg( coherence ); }
- real_t R() const { return std::abs( getCoherence() ); }
- real_t r() const { return sqrt( n1 / n2 ); }
- complex_t getCoherence() const { return coherence / ( wt * sqrt( I1() * I2() ) ) ; }
- void scale_p1( const real_t& sf );
- void scale_p2( const real_t& sf );
- void rotate( const real_t& angle );
- void clear();
-
- void add( const complex_t& f1, const complex_t& f2, const real_t& weight = 1 );
-
- HadronicParameters operator+=( const HadronicParameters& other );
- HadronicParameters operator-=( const HadronicParameters& other );
-
- std::string to_string() const;
- };
-
- HadronicParameters operator+( const HadronicParameters& a, const HadronicParameters& b );
- class CoherenceFactor
- {
- private:
- HadronicParameters m_global;
- real_t m_globalPhase;
- real_t m_globalR;
- CoherentSum* m_pdf1;
- CoherentSum* m_pdf2;
- BinDT m_voxels;
- std::vector<HadronicParameters> m_paramsPerVoxel;
- std::map<unsigned int, unsigned int> m_nodeID2Bin;
- unsigned int m_nBins;
-
- CoherenceCalculator m_calc;
- EventList* m_data;
- EventType m_type;
-
- void MakeEventDeltaPlots(const std::vector<CoherenceEvent>& events );
- public:
- BinDT& getDT() { return m_voxels; }
- real_t phase();
- real_t getR();
- std::vector<size_t> getNumberOfEventsInEachBin( const EventList& events ) const;
- HadronicParameters calculateGlobalCoherence( EventList* data = nullptr );
- void writeToFile( const std::string& filename );
-
- HadronicParameters getVal() const;
- CoherenceFactor( const std::string& filename );
- CoherenceFactor();
- CoherenceFactor( CoherentSum* pdf1, CoherentSum* pdf2, EventList* data = nullptr );
-
- CoherenceFactor( CoherentSum* pdf1, CoherentSum* pdf2, const EventType& type );
-
- void makeCoherentMapping( const unsigned int& nBins,
- const std::function<std::vector<real_t>( const Event& )>& functors = nullptr,
- const size_t& maxDepth = 20, const size_t& minPop = 50,
- const std::function<uint64_t( const Event& )>& flagFunctor = nullptr,
- const bool& refreshEvents = true );
- void makeCoherentMapping( const unsigned int& nBins, const BinDT& binDT );
-
- void groupByStrongPhase( const std::vector<CoherenceEvent>& coherenceEvents = {}, const bool& recalculateVoxels =true );
-
- void readBinsFromFile( const std::string& binName ); ///
- unsigned int getBinNumber( const Event& event ) const;
- real_t operator()();
- void testCoherenceFactor() const;
-
- std::vector<HadronicParameters> getCoherenceFactors() const;
- std::vector<HadronicParameters> getCoherenceFactorsFast() const;
- std::vector<HadronicParameters> coherenceFactorsPerVoxel() const { return m_paramsPerVoxel; }
-
- void calculateNorms();
- void calculateCoherenceFactorsPerVoxel();
- void calculateCoherenceFactorsPerVoxel( const std::vector<CoherenceEvent>& dtEvents );
-
- void setGlobals( const real_t& globalPhase, const real_t& globalR )
- {
- m_globalR = globalR;
- m_globalPhase = globalPhase;
- }
- void setBinOfNode( const unsigned int& nodeID, const unsigned int& bin ) { m_nodeID2Bin[nodeID] = bin; }
- };
-} // namespace AmpGen
-
-#endif
diff --git a/AmpGen/CoherentSum.h b/AmpGen/CoherentSum.h
index 6321ac1ec65..22863b73f68 100644
--- a/AmpGen/CoherentSum.h
+++ b/AmpGen/CoherentSum.h
@@ -1,5 +1,5 @@
-#ifndef AMPGEN_FASTCOHERENTSUM_H
-#define AMPGEN_FASTCOHERENTSUM_H
+#ifndef AMPGEN_COHERENTSUM_H
+#define AMPGEN_COHERENTSUM_H
#include <memory.h>
#include <stddef.h>
@@ -13,90 +13,118 @@
#include "AmpGen/AmplitudeRules.h"
#include "AmpGen/CompiledExpression.h"
#include "AmpGen/EventList.h"
+#include "AmpGen/EventListSIMD.h"
#include "AmpGen/EventType.h"
#include "AmpGen/Integrator.h"
#include "AmpGen/Types.h"
#include "AmpGen/Event.h"
-
+#include "AmpGen/Projection.h"
+#include "AmpGen/MinuitParameter.h"
+#include "AmpGen/Store.h"
+#include "AmpGen/KeyedFunctors.h"
namespace AmpGen
{
class LinearErrorPropagator;
- class MinuitParameter;
class MinuitParameterSet;
class FitFraction;
class Particle;
+ /** @class CoherentSum
+ @brief A coherent sum of amplitudes
+
+ An coherent sum of resonant contributions, where at a position in phase-space @f$\psi@f$,
+ the (unnormalised) probability density is given by
+ @f[
+ \mathcal{P}(\psi) = \left| \sum_{i} g_i \mathcal{A}_i(\psi) \right|^2,
+ @f]
+ where @f$\mathcal{P}(\psi)@f$ is the probability, @f$g_i@f$ is the coupling to an isobar channel,
+ and @f$\mathcal{A}_i(\psi)@f$ is the amplitude of the ith channel.
+ */
class CoherentSum
{
public:
+ #if ENABLE_AVX
+ using EventList_type = EventListSIMD;
+ #else
+ using EventList_type = EventList;
+ #endif
CoherentSum();
CoherentSum( const EventType& type, const AmpGen::MinuitParameterSet& mps, const std::string& prefix = "" );
virtual ~CoherentSum() = default;
- AmplitudeRules protoAmplitudes() { return m_protoAmplitudes; }
+ AmplitudeRules protoAmplitudes() { return m_rules; }
std::string prefix() const { return m_prefix; }
- TransitionMatrix<complex_t> operator[]( const size_t& index ) { return m_matrixElements[index]; }
- const TransitionMatrix<complex_t> operator[]( const size_t& index ) const { return m_matrixElements[index]; }
- size_t size() const { return m_matrixElements.size(); }
-
- real_t getWeight() const { return m_weight; }
- real_t operator()( const Event& evt ) const { return prob( evt ); }
- real_t prob( const Event& evt ) const { return m_weight * std::norm( getVal( evt ) ) / m_norm; }
- real_t prob_unnormalised( const Event& evt ) const { return std::norm( getVal( evt ) ); }
- real_t norm( const Bilinears& norms ) const;
+ auto operator[]( const size_t& index ) { return m_matrixElements[index]; }
+ auto operator[]( const size_t& index ) const { return m_matrixElements[index]; }
+ size_t size() const { return m_matrixElements.size(); }
+ real_t getWeight() const { return m_weight; }
+ real_t norm( const Bilinears& norms ) const;
real_t norm() const;
real_t getNorm( const Bilinears& normalisations );
- real_t get_norm() const { return m_norm ; }
- complex_t norm( const unsigned int& x, const unsigned int& y ) const;
+ complex_t norm( const size_t& x, const size_t& y ) const;
complex_t getVal( const Event& evt ) const;
- complex_t getVal( const Event& evt, const std::vector<unsigned int>& cacheAddresses ) const;
- complex_t getValNoCache( const Event& evt ) const;
-
+ complex_t getValNoCache( const Event& evt ) const;
+
void transferParameters();
void prepare();
void printVal( const Event& evt );
- void updateNorms( const std::vector<unsigned int>& changedPdfIndices );
- void setWeight( const double& weight ) { m_weight = weight; }
- void setWeight( MinuitParameter* param ) { m_weightParam = param; }
+ void updateNorms();
+ void setWeight( MinuitProxy param ) { m_weight = param; }
void makeTotalExpression();
void reset( bool resetEvents = false );
- void setEvents( EventList& list );
- void setMC( EventList& sim );
- void PConjugate();
+ void setEvents( const EventList_type& list );
+ void setMC( const EventList_type& sim );
+ #if ENABLE_AVX
+ void setEvents( const EventList& list) {
+ WARNING("Setting events from a AoS container, will need to make a copy");
+ m_ownEvents = true; setEvents( *(new EventListSIMD(list)) ) ; }
+ void setMC ( const EventList& list) {
+ WARNING("Setting integration events from a AoS container, will need to make a copy");
+ setMC( *(new EventListSIMD(list)) ) ; }
+ double operator()(const double*, const unsigned) const;
+ #endif
+
+ float_v operator()(const float_v*, const unsigned) const;
+ real_t operator()(const Event& evt ) const { return m_weight*std::norm(getVal(evt))/m_norm; }
+
void debug( const Event& evt, const std::string& nameMustContain="");
void generateSourceCode( const std::string& fname, const double& normalisation = 1, bool add_mt = false );
- void resync();
- std::vector<unsigned int> cacheAddresses( const EventList& evts ) const;
std::vector<FitFraction> fitFractions( const LinearErrorPropagator& linProp );
- std::vector<TransitionMatrix<complex_t>> matrixElements() const { return m_matrixElements; }
+ auto matrixElements() const { return m_matrixElements; }
std::map<std::string, std::vector<unsigned int>> getGroupedAmplitudes();
Bilinears norms() const { return m_normalisations ; }
-
+
+ std::function<real_t(const Event&)> evaluator(const EventList_type* = nullptr) const;
+ KeyedFunctors<double(Event)> componentEvaluator(const EventList_type* = nullptr) const;
+ EventType eventType() const { return m_evtType; }
protected:
- std::vector<TransitionMatrix<complex_t>> m_matrixElements; ///< Vector of (expanded) matrix elements
- Bilinears m_normalisations; ///< Normalisation integrals
- AmplitudeRules m_protoAmplitudes; ///< Proto amplitudes from user rule-set
- Integrator<10> m_integrator; ///< Integral dispatch tool (with default unroll = 10)
- TransitionMatrix<complex_t> m_total; ///< Total Matrix Element
- EventList* m_events = {nullptr}; ///< Data events to evaluate PDF on
- EventType m_evtType; ///< Final state for this amplitude
- MinuitParameter* m_weightParam = {nullptr}; ///< Weight parameter (i.e. the normalised yield)
- size_t m_prepareCalls = {0}; ///< Number of times prepare has been called
- size_t m_lastPrint = {0}; ///< Last time verbose PDF info was printed
- size_t m_printFreq = {0}; ///< Frequency to print verbose PDF info
- double m_weight = {1}; ///< Weight number (i.e. the normalised yield)
- double m_norm = {0}; ///< Normalisation integral
- bool m_isConstant = {false}; ///< Flag for a constant PDF
- bool m_dbThis = {false}; ///< Flag to generate amplitude level debugging
- bool m_verbosity = {false}; ///< Flag for verbose printing
- std::string m_objCache = {""}; ///< Directory that contains (cached) amplitude objects
- std::string m_prefix = {""}; ///< Prefix for matrix elements
- void addMatrixElement( std::pair<Particle, CouplingConstant>& particleWithCoupling, const MinuitParameterSet& mps );
- bool isFixedPDF(const MinuitParameterSet& mps) const;
+ std::vector<TransitionMatrix<complex_v>> m_matrixElements; ///< Vector of matrix elements
+ Bilinears m_normalisations; ///< Normalisation integrals
+ AmplitudeRules m_rules; ///< Ruleset for the selected transition.
+
+ Integrator m_integrator; ///< Tool to calculate integrals
+ const EventList_type* m_events = {nullptr}; ///< Data events to evaluate PDF on
+ Store<complex_v, Alignment::AoS> m_cache; ///< Store of intermediate values for the PDF calculation
+
+ bool m_ownEvents = {false}; ///< Flag as to whether events are owned by this PDF or not
+ EventType m_evtType; ///< Final state for this amplitude
+ size_t m_prepareCalls = {0}; ///< Number of times prepare has been called
+ size_t m_lastPrint = {0}; ///< Last time verbose PDF info was printed
+ size_t m_printFreq = {0}; ///< Frequency to print verbose PDF info
+ MinuitProxy m_weight = {nullptr, 1}; ///< Weight (i.e. the normalised yield)
+ double m_norm = {1}; ///< Normalisation integral
+ bool m_isConstant = {false}; ///< Flag for a constant PDF
+ bool m_dbThis = {false}; ///< Flag to generate amplitude level debugging
+ bool m_verbosity = {false}; ///< Flag for verbose printing
+ std::string m_objCache = {""}; ///< Directory that contains (cached) amplitude objects
+ std::string m_prefix = {""}; ///< Prefix for matrix elements
+ const MinuitParameterSet* m_mps = {nullptr};
+
+ void addMatrixElement( std::pair<Particle, TotalCoupling>& particleWithCoupling, const MinuitParameterSet& mps );
};
} // namespace AmpGen
diff --git a/AmpGen/CompiledExpression.h b/AmpGen/CompiledExpression.h
index 94f0e08dfea..cff94a74e8d 100644
--- a/AmpGen/CompiledExpression.h
+++ b/AmpGen/CompiledExpression.h
@@ -9,231 +9,265 @@
#include "AmpGen/MsgService.h"
#include "AmpGen/Utilities.h"
#include "AmpGen/Types.h"
-
+#include "AmpGen/simd/utils.h"
+#include "AmpGen/Tensor.h"
+#include "AmpGen/ArgumentPack.h"
#include <cxxabi.h>
#include <dlfcn.h>
#include <vector>
+#include <map>
namespace AmpGen
{
/* @class CompiledExpression
- @tparam RETURN_TYPE The type that is returned this compiled expression,
+ @tparam ret_type The type that is returned this compiled expression,
usually this is a std::complex<double>,
but in principal support also exists for computing coupled channel propagators
(i.e. returning array types) */
+
+
+
+ namespace detail {
+ template <typename T> struct size_of { static constexpr unsigned value = sizeof(T); };
+ template <> struct size_of<void> { static constexpr unsigned value = 0; } ;
+ }
+ DECLARE_ARGUMENT(disableBatch, bool);
+
+ template <typename ret_type, typename... arg_types> class CompiledExpression;
+
- template <class RETURN_TYPE, class... ARGS>
- class CompiledExpression : public CompiledExpressionBase
- {
-
- private:
- DynamicFCN<RETURN_TYPE( ARGS... )> m_fcn;
- DynamicFCN<std::vector<std::pair<std::string,
- std::complex<double>>>( ARGS... )> m_fdb;
- std::vector<real_t> m_externals;
- bool m_hasExternalsChanged;
-
- public:
-
- CompiledExpression( const Expression& expression,
- const std::string& name,
- const std::map<std::string, size_t>& evtMapping =
- std::map<std::string, size_t>(),
- const DebugSymbols& db = {},
- const MinuitParameterSet* mps = nullptr )
- : CompiledExpressionBase( expression, name, db, evtMapping ),
- m_hasExternalsChanged( false )
+ template <typename ret_type, typename... arg_types>
+ class CompiledExpression<ret_type(arg_types...)> : public CompiledExpressionBase
{
- resolve(mps);
- }
- CompiledExpression( const std::string& name = "" ) : CompiledExpressionBase( name ) {};
- std::vector<real_t> externBuffer() const { return m_externals ; }
- std::string returnTypename() const override { return typeof<RETURN_TYPE>(); }
- std::string fcnSignature() const override
- {
- std::string signature;
- auto argTypes = typelist<ARGS...>();
- for( unsigned int i = 0 ; i < argTypes.size(); ++i )
- {
- signature += argTypes[i] + " x"+std::to_string(i) ;
- if( i != argTypes.size() - 1 ) signature += ", ";
- }
- return signature;
- }
- std::string args() const override
- {
- std::string signature;
- auto argTypes = typelist<ARGS...>();
- for( unsigned int i = 0 ; i < argTypes.size(); ++i )
- {
- signature += " x"+std::to_string(i) ;
- if( i != argTypes.size() - 1 ) signature += ", ";
- }
- return signature;
- }
+ private:
+ DynamicFCN<ret_type( arg_types... )> m_fcn;
+ DynamicFCN<void( const size_t&, const size_t&, const size_t&, ret_type*, arg_types... )> m_batchFcn;
+ DynamicFCN<std::vector<std::pair<std::string, complex_v>>(arg_types...)> m_fdb;
+ std::vector<real_t> m_externals = {};
+ bool m_hasExternalsChanged = {false};
+
+ public:
+ typedef ret_type return_type;
+ unsigned m_outputSize = {0};
- void resolve( const MinuitParameterSet* mps=nullptr )
- {
- CompiledExpressionBase::resolve(mps);
- }
- void setExternals( const std::vector<double>& external ) { m_externals = external; }
+ template <typename... namedArgs>
+ CompiledExpression( const Expression& expression, const std::string& name, const namedArgs&... args ) : CompiledExpressionBase(expression, name)
+ {
+ const MinuitParameterSet* mps = nullptr;
+ auto process_argument = [this, &mps]( const auto& arg ) mutable
+ {
+ if constexpr( std::is_convertible<decltype(arg), DebugSymbols>::value ) this->m_db = arg;
+ else if constexpr( std::is_convertible<decltype(arg), std::map<std::string, unsigned>>::value ) this->m_evtMap = arg;
+ else if constexpr( std::is_convertible<decltype(arg), MinuitParameterSet*>::value ) mps = arg;
+ else if constexpr( std::is_convertible<decltype(arg), const MinuitParameterSet*>::value ) mps = arg;
+ else if constexpr( std::is_convertible<decltype(arg), MinuitParameterSet>::value ) mps = &arg;
+ else if constexpr( std::is_convertible<decltype(arg), disableBatch>::value ) {
+ WARNING("Disabling bulk evaluation: did you do this on purpose?");
+ m_disableBatch = true;
+ }
+ else ERROR("Unrecognised argument: " << type_string(arg) );
+ };
+ for_each( std::tuple<const namedArgs&...>(args...), process_argument);
+ resolve(mps);
+ if constexpr(std::is_same<ret_type,void>::value )
+ {
+ typedef typename std::remove_pointer<zeroType<arg_types...>>::type zt;
+ m_outputSize = detail::size_of<zt>::value;
+ DEBUG( "one element: " << m_outputSize << type_string<zt>() );
+ if( is<TensorExpression>(expression) ) m_outputSize *= cast<TensorExpression>(expression).tensor().size();
+ }
+ else m_outputSize = detail::size_of<ret_type>::value;
+ }
- unsigned int getNParams() const { return m_externals.size(); }
-
- void print() const override
- {
- INFO( "Name = " << name() );
- INFO( "Hash = " << hash() );
- INFO( "IsReady? = " << isReady() << " IsLinked? " << (m_fcn.isLinked() ) );
- INFO( "args = ["<< vectorToString( m_externals, ", ") <<"]");
- for( auto& c : m_cacheTransfers ){ c->print() ; }
- }
+ CompiledExpression( const std::string& name = "" ) : CompiledExpressionBase( name ) { m_outputSize = detail::size_of<ret_type>::value; };
+ std::vector<real_t> externBuffer() const { return m_externals ; }
+ std::string returnTypename() const override { return type_string<ret_type>(); }
+ std::string fcnSignature() const override
+ {
+ return CompiledExpressionBase::fcnSignature(typelist<arg_types...>(), use_rto());
+ }
+ bool use_rto() const override {
+ return std::is_same<ret_type, void>::value;
+ }
+ std::string args() const override
+ {
+ std::string signature;
+ auto argTypes = typelist<arg_types...>();
+ for( unsigned int i = 0 ; i < argTypes.size(); ++i )
+ {
+ signature += " x"+std::to_string(i) ;
+ if( i != argTypes.size() - 1 ) signature += ", ";
+ }
+ return signature;
+ }
- void setExternal( const double& value, const unsigned int& address ) override
- {
- DEBUG( "Setting external " << address << " / " << m_externals.size() << " to value = " << value << " ; current = " << m_externals[address] );
- if ( m_externals[address] == value ) return;
- m_externals[address] = value;
- m_hasExternalsChanged = true;
- }
- void resizeExternalCache(const size_t& N ) override {
- if( m_externals.size() < N ){
- m_externals.resize(N);
- }
- }
- bool hasExternalsChanged() { return m_hasExternalsChanged; }
- void resetExternals() { m_hasExternalsChanged = false; }
+ void resolve( const MinuitParameterSet* mps=nullptr )
+ {
+ CompiledExpressionBase::resolve(mps);
+ }
+ void setExternals( const std::vector<double>& external ) { m_externals = external; }
- Expression& expression() { return m_obj; }
- void compileDetails( std::ostream& stream ) const
- {
- stream << "extern \"C\" int " << progName() << "_pSize () {\n"
- << " return " << m_externals.size() << ";\n";
- stream << "}\n";
-
- stream << "extern \"C\" double " << progName() << "_pVal (int n) {\n";
- for ( size_t i = 0; i < m_externals.size(); i++ )
- stream << " if(n == " << i << ") return " << m_externals.at( i ) << ";\n";
- stream << " return 0;\n}\n";
- }
+ unsigned int getNParams() const { return m_externals.size(); }
- void compileWithParameters( std::ostream& stream ) const
- {
- DEBUG( "Compiling " << name() << " = " << hash() );
- // Avoid a warning about std::complex not being C compatible (it is)
- stream << "#pragma clang diagnostic push\n"
- << "#pragma clang diagnostic ignored \"-Wreturn-type-c-linkage\"\n";
- stream << "extern \"C\" " << returnTypename() << " " << progName() << "_wParams"
- << "( const double*__restrict__ E ){" << std::endl;
- stream << " double externalParameters [] = {";
- if ( m_externals.size() != 0 ) {
- for ( unsigned int i = 0; i < m_externals.size() - 1; ++i ) {
- stream << m_externals[i] << ", " ;
- }
- stream << m_externals[m_externals.size() - 1] << " }; " << std::endl;
- } else stream << "0};" << std::endl;
- stream << " return " << progName() << "( externalParameters, E ); // E is P \n}\n";
- stream << "#pragma clang diagnostic pop\n\n" << std::endl;
- }
+ void print() const override
+ {
+ INFO( "Name = " << name() );
+ INFO( "Hash = " << hash() );
+ INFO( "IsReady? = " << isReady() << " IsLinked? " << (m_fcn.isLinked() ) );
+ INFO( "args = ["<< vectorToString( m_externals, ", ") <<"]");
+ std::vector<const CacheTransfer*> ordered_cache_functors;
+ for( const auto& c : m_cacheTransfers ) ordered_cache_functors.push_back( c.get() );
+ std::sort( ordered_cache_functors.begin(),
+ ordered_cache_functors.end(),
+ [](auto& c1, auto& c2 ) { return c1->address() < c2->address() ; } );
+ for( auto& c : ordered_cache_functors ) c->print() ;
+ }
- bool isReady() const override { return (m_readyFlag != nullptr && m_readyFlag->get() ) && m_fcn.isLinked(); }
- bool isLinked() const { return m_fcn.isLinked() ; }
- size_t returnTypeSize() const override { return sizeof( RETURN_TYPE ); }
-
- template < class T >
- RETURN_TYPE operator()( const T* event ) const
- {
- return m_fcn( (const double*)( &( m_externals[0] ) ), event );
- }
- RETURN_TYPE operator()( const ARGS&... args ) const
- {
- return m_fcn( args... );
- }
+ void setExternal( const double& value, const unsigned int& address ) override
+ {
+ DEBUG( "Setting external " << address << " / " << m_externals.size() << " to value = " << value << " ; current = " << m_externals[address] );
+ if ( m_externals[address] == value ) return;
+ m_externals[address] = value;
+ m_hasExternalsChanged = true;
+ }
+ void resizeExternalCache(const size_t& N ) override
+ {
+ if( m_externals.size() < N ) m_externals.resize(N);
+ }
+ bool hasExternalsChanged() { return m_hasExternalsChanged; }
+ void resetExternals() { m_hasExternalsChanged = false; }
+
+ Expression& expression() { return m_obj; }
+
+ void compileDetails( std::ostream& stream ) const
+ {
+ stream << "extern \"C\" int " << progName() << "_pSize () {\n"
+ << " return " << m_externals.size() << ";\n";
+ stream << "}\n";
+
+ stream << "extern \"C\" double " << progName() << "_pVal (int n) {\n";
+ for ( size_t i = 0; i < m_externals.size(); i++ )
+ stream << " if(n == " << i << ") return " << m_externals.at( i ) << ";\n";
+ stream << " return 0;\n}\n";
+ }
+ void compileBatch( std::ostream& stream ) const override
+ {
+ stream << "#include <omp.h>\n";
+ stream << "extern \"C\" void " << progName()
+ << "_batch(";
+ stream << " const size_t& N, "
+ << " const size_t& eventSize, "
+ << " const size_t& cacheSize, ";
+ stream << type_string<ret_type>() << " * rt, ";
+ stream << CompiledExpressionBase::fcnSignature(typelist<arg_types...>(), use_rto(), false) << ") {\n";
+ #if USE_OPENMP
+ stream << "#pragma omp parallel for\n";
+ #endif
+ stream << "for( size_t i = 0; i < N/" << utils::size<float_v>::value << "; ++i ){\n";
+ if( use_rto() ) stream << progName() + "( r + cacheSize * i, s, x0, x1 + i * eventSize);";
+ else stream << " rt[cacheSize*i] = " << progName() + "( x0, x1 + i * eventSize);";
+ stream << "}\n}";
+ }
+
+ void compileWithParameters( std::ostream& stream ) const
+ {
+ DEBUG( "Compiling " << name() << " = " << hash() );
+ stream << "extern \"C\" " << returnTypename() << " " << progName() << "_wParams"
+ << "( const double*__restrict__ E ){" << std::endl;
+ stream << " double externalParameters [] = {" <<
+ (m_externals.size() == 0 ? "0" : vectorToString(m_externals,", ", [](auto& line){ return std::to_string(line); }) ) <<"};\n" ;
+ stream << " return " << progName() << "( externalParameters, E ); // E is P \n}\n";
+ }
- void debug( const double* event ) const
+ bool isReady() const override { return m_fcn.isLinked(); }
+ bool isLinked() const { return m_fcn.isLinked() ; }
+
+ unsigned returnTypeSize() const override { return m_outputSize; }
+
+ template < typename T >
+ ret_type operator()( const T* event ) const
+ {
+ return m_fcn( m_externals.data(), event );
+ }
+ ret_type operator()( const arg_types&... args ) const
+ {
+ return m_fcn( args... );
+ }
+ template <typename... batch_arg_types> void batch( batch_arg_types... args ) const {
+ m_batchFcn(args...);
+ }
+
+ template < typename T> void debug( const T* event ) const
+ {
+ if ( !m_fcn.isLinked() ) {
+ FATAL( "Function " << name() << " not linked" );
+ }
+ if ( !m_fdb.isLinked() ) {
+ FATAL( "Function" << name() << " debugging symbols not linked" );
+ }
+ std::vector<std::pair<std::string, complex_v>> debug_results;
+ if constexpr(std::is_same<void, ret_type>::value) debug_results = m_fdb( nullptr, 0, &( m_externals[0] ), event );
+ else debug_results = m_fdb( &(m_externals[0]), event);
+ for( auto& debug_result : debug_results ){
+ auto val = debug_result.second;
+ auto label = debug_result.first;
+ if( utils::all_of(val.real(), -999.) ) std::cout << bold_on << std::setw(50) << std::left << label << bold_off << std::endl;
+ else if( utils::all_of(val.imag(), 0.) ) std::cout << " " << std::setw(50) << std::left << label << " = " << val.real() << std::endl;
+ else
+ std::cout << " " << std::setw(50) << std::left << label << " = " << val << std::endl;
+ }
+ }
+
+ bool link( void* handle ) override
+ {
+ const std::string symbol = progName() ;
+ bool status = true;
+ status &= m_fcn.set(handle, symbol, true);
+ status &= m_db.size() == 0 || m_fdb.set(handle, symbol + "_DB");
+ if( !m_disableBatch ) status &= m_batchFcn.set(handle, symbol + "_batch");
+ return status;
+ }
+ bool link( const std::string& handle ) override
+ {
+ return link( dlopen( handle.c_str(), RTLD_NOW ) );
+ };
+ std::string arg_type(const unsigned& i ) const override
+ {
+ return typelist<arg_types...>()[i];
+ }
+ };
+
+ template <typename return_type>
+ CompiledExpression<void(return_type*, const double*, const double*)>
+ make_rto_expression( const Expression& expression, const std::string& name , const bool& verbose=false)
{
- if ( !m_fcn.isLinked() ) {
- ERROR( "Function " << name() << " not linked" );
- }
- if ( !m_fdb.isLinked() ) {
- ERROR( "Function" << name() << " debugging symbols not linked" );
- }
- auto debug_results = m_fdb( &( m_externals[0] ), event );
- for( auto& debug_result : debug_results ){
- auto val = debug_result.second;
- auto label = debug_result.first;
- if( std::real(val) == -999. ) std::cout << bold_on << std::setw(50) << std::left << label << bold_off << std::endl;
- else if( std::imag(val) == 0 ) std::cout << " " << std::setw(50) << std::left << label << " = " << std::real(val) << std::endl;
- else std::cout << " " << std::setw(50) << std::left << label << " = " << val << std::endl;
- }
+ CompiledExpression<void(return_type*, const double*, const double*)> rt(expression,name);
+ rt.compile();
+ rt.prepare();
+ return rt;
}
- bool link( void* handle ) override
+ template <typename return_type> CompiledExpression<return_type(const double*, const double*)>
+ make_expression( const Expression& expression, const std::string& name , const bool& verbose=false)
{
- const std::string symbol = progName() ;
- if ( m_fcn.set( handle, symbol ) == 0 ) {
- ERROR( dlerror() );
- ERROR( name() << " (symbol = " << symbol << ") linking fails" );
- return false;
- }
- if ( m_db.size() ==0 ) return true;
- if ( m_fdb.set( handle, progName() + "_DB" ) == 0 ) {
- ERROR( "Linking of " << name() << " symbol = " << symbol << ") for debugging fails" );
- return false;
- }
- return true;
+ CompiledExpression<return_type(const double*, const double*)> rt(expression,name);
+ rt.compile();
+ rt.prepare();
+ return rt;
}
- bool link( const std::string& handle ) override
+ template <typename return_type, typename arg1 = double, typename arg2 =double, typename... arg_types>
+ CompiledExpression<return_type(const arg1*, const arg2*)>
+ make_expression( const Expression& expression,
+ const std::string& name,
+ const arg_types&... args)
{
- DEBUG( "Linking " << name() << ( m_db.size() !=0 ? " (debugging)" : "" ) << " hash = " << hash() );
- const std::string symbol = progName();
- if ( m_fcn.set( handle, symbol ) == 0 ) {
- ERROR( "Function not linked: " << name() << " (sym="<< symbol << ")" );
- return false;
- }
- if ( m_db.size() ==0 ) return true;
- const std::string dbsymbol = symbol + "_DB";
- if ( m_fdb.set( handle, dbsymbol ) == 0 ) {
- ERROR( "Linking of " << name() << " symbol = " << dbsymbol << ")" );
- return false;
- }
- return true;
+ CompiledExpression<return_type(const arg1*, const arg2*)> rt(expression,name,args...);
+ rt.compile();
+ rt.prepare();
+ return rt;
}
- };
-
- template <class RT>
- CompiledExpression<RT, const double*, const double*>
- make_expression( const Expression& expression, const std::string& name , const bool& verbose=false)
- {
- CompiledExpression<RT,const double*, const double*> rt(expression,name);
- rt.compile("", true);
- rt.prepare();
- return rt;
- }
- template <class RT>
- CompiledExpression<RT, const double*, const double*>
- make_expression( const Expression& expression,
- const std::string& name,
- const MinuitParameterSet& mps )
- {
- CompiledExpression<RT,const double*, const double*> rt(expression,name,{},{},&mps);
- rt.compile("", true);
- rt.prepare();
- return rt;
- }
- template <class RT>
- CompiledExpression<RT, const double*, const double*>
- make_expression( const Expression& expression,
- const std::string& name,
- const std::map<std::string, size_t> & evtMap,
- const MinuitParameterSet& mps )
- {
- CompiledExpression<RT,const double*, const double*> rt(expression,name,evtMap,{},&mps);
- rt.compile("", true);
- rt.prepare();
- return rt;
- }
+
} // namespace AmpGen
diff --git a/AmpGen/CompiledExpressionBase.h b/AmpGen/CompiledExpressionBase.h
index 5051ae3b5bd..7cace4fda1e 100644
--- a/AmpGen/CompiledExpressionBase.h
+++ b/AmpGen/CompiledExpressionBase.h
@@ -18,10 +18,9 @@ namespace AmpGen
class CacheTransfer;
std::string programatic_name( std::string s );
-
+ class ASTResolver;
class MinuitParameter;
class MinuitParameterSet;
- class ASTResolver;
/** @class CompiledExpressionBase
* Base class for compiled expressions, i.e. expressions that are (almost) ready to be evaluated.
@@ -31,44 +30,49 @@ namespace AmpGen
*/
class CompiledExpressionBase
{
- protected:
- Expression m_obj;
- std::string m_name;
- std::string m_progName;
- DebugSymbols m_db;
- std::map<std::string, size_t> m_evtMap;
- std::shared_future<bool>* m_readyFlag = {nullptr};
- std::vector<std::pair<uint64_t, Expression>> m_dependentSubexpressions;
- std::vector<std::pair<uint64_t, Expression>> m_debugSubexpressions;
- std::vector<std::shared_ptr<CacheTransfer>> m_cacheTransfers;
- ASTResolver* m_resolver = {nullptr};
public:
+ CompiledExpressionBase();
+ CompiledExpressionBase( const std::string& name );
CompiledExpressionBase( const Expression& expression,
const std::string& name,
const DebugSymbols& db=DebugSymbols(),
- const std::map<std::string,size_t>& evtMapping = {} );
- CompiledExpressionBase( const std::string& name );
- CompiledExpressionBase() = default;
+ const std::map<std::string, unsigned>& evtMapping = {} );
void resolve(const MinuitParameterSet* mps = nullptr);
void prepare();
- void compile(const std::string& fname="", const bool& wait = false );
+ void compile(const std::string& fname="");
+ virtual void compileBatch( std::ostream& stream ) const = 0;
void to_stream( std::ostream& stream ) const;
unsigned int hash() const;
std::string name() const;
std::string progName() const;
- virtual bool link( void* handle ) = 0;
- virtual bool link( const std::string& handle ) = 0;
- virtual void setExternal( const double& value, const unsigned int& address ) = 0;
- virtual void resizeExternalCache( const size_t& N ) = 0;
+ virtual bool link( void*) = 0;
+ virtual bool link( const std::string&) = 0;
+ virtual void setExternal(const double&, const unsigned&) = 0;
+ virtual void resizeExternalCache(const size_t&) = 0;
virtual bool isReady() const = 0;
virtual std::string returnTypename() const = 0;
virtual std::string fcnSignature() const = 0;
virtual std::string args() const = 0;
virtual void print() const = 0;
- virtual ~CompiledExpressionBase() = default;
- virtual size_t returnTypeSize() const = 0;
-
+ virtual ~CompiledExpressionBase();
+ virtual unsigned returnTypeSize() const = 0;
+ static std::string fcnSignature(const std::vector<std::string>&, bool=false, bool=true);
+ virtual bool use_rto() const = 0;
+ Expression expression() const { return m_obj; }
+ virtual std::string arg_type( const unsigned& counter) const =0;
+ protected:
+ Expression m_obj;
+ std::string m_name;
+ std::string m_progName;
+ DebugSymbols m_db;
+ std::map<std::string, unsigned> m_evtMap;
+ std::vector<std::pair<uint64_t, Expression>> m_dependentSubexpressions;
+ std::vector<std::pair<uint64_t, Expression>> m_debugSubexpressions;
+ std::vector<std::shared_ptr<CacheTransfer>> m_cacheTransfers;
+ std::shared_ptr<ASTResolver> m_resolver;
+ std::vector<std::string> m_additionalHeaders;
+ bool m_disableBatch = {false};
private:
void addDebug( std::ostream& stream ) const;
void addDependentExpressions( std::ostream& stream, size_t& sizeOfStream ) const;
diff --git a/AmpGen/CompilerWrapper.h b/AmpGen/CompilerWrapper.h
index 258a80952de..a7f20be2439 100644
--- a/AmpGen/CompilerWrapper.h
+++ b/AmpGen/CompilerWrapper.h
@@ -14,18 +14,21 @@ namespace AmpGen
class CompilerWrapper
{
public:
- CompilerWrapper( const bool& verbose=false);
+ explicit CompilerWrapper( const bool& verbose=false);
void generateSource( const CompiledExpressionBase& expression, const std::string& fname);
bool compile( CompiledExpressionBase& expression, const std::string& fname="");
bool compile( std::vector<CompiledExpressionBase*>& expression, const std::string& fname="");
void compileSource(const std::string& fname, const std::string& oname );
void setVerbose() { m_verbose = true ; }
void preamble(std::ostream& os ) const ;
+ void addHeader(const std::string& include ) { m_includes.push_back(include); }
+
private:
- std::vector<std::string> m_includes;
+ std::vector<std::string> m_includes = {"array","complex","math.h","vector"};
bool m_verbose;
std::string m_cxx;
std::string generateFilename();
+ bool isClang() const;
};
} // namespace AmpGen
#endif
diff --git a/AmpGen/CoupledChannel.h b/AmpGen/CoupledChannel.h
index e72e1e8a68d..f9837963538 100644
--- a/AmpGen/CoupledChannel.h
+++ b/AmpGen/CoupledChannel.h
@@ -2,5 +2,11 @@
#include "AmpGen/Particle.h"
namespace AmpGen {
+
+ namespace Lineshape {
+ /** @ingroup Lineshapes class CoupledChannel
+ @brief Description of a resonance that decays to multiple two and three-body final states. */
+ DECLARE_LINESHAPE( CoupledChannel );
+ }
Expression phaseSpace(const Expression& s, const Particle& p, const size_t& l);
}
diff --git a/AmpGen/DalitzIntegrator.h b/AmpGen/DalitzIntegrator.h
index 31c09622e26..06bbdb144df 100644
--- a/AmpGen/DalitzIntegrator.h
+++ b/AmpGen/DalitzIntegrator.h
@@ -32,18 +32,8 @@ namespace AmpGen
DalitzIntegrator( const double& s0, const double& s1, const double& s2, const double& s3);
- template <class FCN>
- double integrate( FCN fcn, const double& s) const
- {
- double event[12];
- for(size_t i = 0; i < 12; ++i) event[i] = 0;
- TF2 f( "fcn", [&]( double* x, double* p ) {
- sqCo pos = {x[0], x[1]};
- setEvent( pos, event, s);
- return J(pos, s) * std::real( fcn(event) ); }, 0, 1, 0, 1, 0 );
- return integrate_internal(f) / s;
- }
-
+ template <class FCN> double integrate( FCN fcn, const double& s) const;
+
template <class FCN> double integrate( FCN fcn ) const
{
return integrate( fcn, m_s0 );
@@ -80,6 +70,18 @@ namespace AmpGen
double integrate_internal( TF2& fcn ) const ;
};
+ template <class FCN>
+ double DalitzIntegrator::integrate( FCN fcn, const double& s) const
+ {
+ double event[12];
+ for(size_t i = 0; i < 12; ++i) event[i] = 0;
+ TF2 f( "fcn", [&]( double* x, double* p ) {
+ sqCo pos = {x[0], x[1]};
+ setEvent( pos, event, s);
+ return J(pos, s) * std::real( fcn(event) ); }, 0, 1, 0, 1, 0 );
+ return integrate_internal(f) / s;
+ }
+
} // namespace AmpGen
#endif
diff --git a/AmpGen/DiracMatrices.h b/AmpGen/DiracMatrices.h
index 69ce55aaf25..a754899a3e7 100644
--- a/AmpGen/DiracMatrices.h
+++ b/AmpGen/DiracMatrices.h
@@ -8,11 +8,14 @@
namespace AmpGen
{
- extern const Expression I;
- extern const Expression Z;
- extern const std::array<Tensor,5> Gamma;
- extern const std::array<Tensor,3> Sigma;
- extern const std::array<Tensor,3> S03;
+ extern const Expression I; // Imaginary unit
+ extern const Expression Z; // Zero
+ extern const std::array<Tensor,5> Gamma; // Gamma matrices, orderered weirdly due to ROOT convention, so Gamma[{0,1,2}] = gamma[{1,2,3}] and Gamma[3] = gamma[0]
+ // where gamma are the gamma matrices in the more conventional ordering.
+ extern const std::array<Tensor,3> Sigma; // The pauli matrices
+ extern const std::array<Tensor,3> Sigma4; // The pauli matrices acting on bispinors
+ extern const std::array<Tensor,3> SO3; // basis elements for the vector reprsentation of SO(3)
+ extern const std::array<Tensor,8> SU3; // basis elements for the vector representation of SU(3), i.e. the Gell-Mann matrices
} // namespace AmpGen
#endif
diff --git a/AmpGen/DynamicFCN.h b/AmpGen/DynamicFCN.h
index d8758b29c90..59157e5c7b7 100644
--- a/AmpGen/DynamicFCN.h
+++ b/AmpGen/DynamicFCN.h
@@ -50,11 +50,12 @@ namespace AmpGen
}
return set(m_handle,name);
}
- bool set( void* handle, const std::string& name )
+ bool set( void* handle, const std::string& name, bool isFatal = false)
{
m_fcn = (RETURN_TYPE( * )( IN_TYPES... ))dlsym( handle, name.c_str() );
if ( m_fcn == nullptr ) {
- ERROR( dlerror() );
+ if( !isFatal ) ERROR( "Failed to link: " << name << " error: " << dlerror() );
+ else FATAL("Failed to link: " << name << " error: " << dlerror() );
return false;
}
return true;
diff --git a/AmpGen/ErrorPropagator.h b/AmpGen/ErrorPropagator.h
index 7470162c0dc..1178c74badb 100644
--- a/AmpGen/ErrorPropagator.h
+++ b/AmpGen/ErrorPropagator.h
@@ -27,99 +27,34 @@ class TRandom3;
namespace AmpGen
{
class MinuitParameterSet;
- /// \class LinearErrorPropagator
- /// Propagates uncertainties on functors using either a MinuitParameterSet (thus assuming a diagonal covariance matrix)
- /// or with a set of parameters and a covariance matrix (i.e. the product of a fit).
- /// Can be used for calculating the uncertainties on observables such as Fit fractions,
- /// or for producing uncertainty bands in predictions on figures.
- /// Usage is
-
+ /** @class LinearErrorPropagator
+ Propagates uncertainties on functors using either a MinuitParameterSet (thus assuming a diagonal covariance matrix)
+ or with a set of parameters and a covariance matrix (i.e. the product of a fit).
+ Can be used for calculating the uncertainties on observables such as Fit fractions,
+ or for producing uncertainty bands in predictions on figures.
+ Usage is
+ */
class LinearErrorPropagator
{
public:
///< Constructor for LinearErrorPropagator taking a vector of free parameters, assumes a diagonal covariance matrix taking the parameter uncertainties.
- LinearErrorPropagator( const std::vector<MinuitParameter*>& params );
+ explicit LinearErrorPropagator( const std::vector<MinuitParameter*>& params );
///< Constructor for LinearErrorPropagator, taking a MinuitParameterSet as argument, assumes a diagonal coviarance matrix using the uncertainties on parameters.
- LinearErrorPropagator( const MinuitParameterSet& params );
-
+ explicit LinearErrorPropagator( const MinuitParameterSet& params );
///< Constructor for LinearErrorPropagator, taking a covariance matrix and a vector parameters
- LinearErrorPropagator( const TMatrixD& reducedCovarianceMatrix,
- const std::vector<MinuitParameter*>& params );
+ LinearErrorPropagator( const TMatrixD& reducedCovarianceMatrix, const std::vector<MinuitParameter*>& params );
///< Calculates the uncertainty on functor fcn.
template <class FCN> double operator()( FCN fcn ) const
{
- return getError( fcn );
+ return getError( std::function<double(void)>(fcn) );
}
///< Calculates the error on functor fcn (should take no arguments and return a double).
- template <class FCN> double getError( FCN fcn ) const
- {
- unsigned int N = m_cov.GetNrows();
- TVectorD errorVec( N );
- for ( unsigned int i = 0; i < N; ++i ) {
- DEBUG( "Perturbing parameter: [" << m_parameters[i]->name() << "] " << startingValue << " by "
- << sqrt( m_cov( i, i ) ) << " " << m_parameters[i] );
- errorVec(i) = derivative(fcn,i);
- fcn();
- }
- return sqrt( errorVec * ( m_cov * errorVec ) );
- }
-
- ///< Calculate the uncertainties on a functor that returns an array of doubles of size RANK, used for propagating the uncertainties on figures.
- template <size_t RANK, class FCN> std::array<double, RANK> getVectorError( FCN fcn ) const
- {
- unsigned int N = m_cov.GetNrows();
- std::array<TVectorD, RANK> errorVec;
- for ( unsigned int i = 0; i < RANK; ++i ) errorVec[i].ResizeTo( N );
- for ( unsigned int i = 0; i < N; ++i ) {
- double startingValue = m_parameters[i]->mean();
- double error = sqrt( m_cov( i, i ) );
- double min = m_parameters[i]->mean() - error;
- double max = m_parameters[i]->mean() + error;
- DEBUG( "Perturbing parameter: " << m_parameters[i]->name() << " -> [" << min << ", " << max << "]" );
-
- m_parameters[i]->setCurrentFitVal( max );
- auto plus_variation = fcn();
- m_parameters[i]->setCurrentFitVal( min );
- auto minus_variation = fcn();
- m_parameters[i]->setCurrentFitVal( startingValue );
- for ( size_t j = 0; j < RANK; ++j ) {
- errorVec[j]( i ) = ( plus_variation[j] - minus_variation[j] ) / ( 2 * error );
- }
- }
- fcn();
- std::array<double, RANK> rt;
- for ( unsigned int j = 0; j < RANK; ++j ) rt[j] = sqrt( errorVec[j] * ( m_cov * errorVec[j] ) );
- return rt;
- }
+ double getError( const std::function<double(void)>& fcn ) const;
///< Calculate the uncertainties on a functor that returns a vector of size RANK.
- template <class FCN> std::vector<double> getVectorError( FCN fcn, size_t RANK ) const
- {
- unsigned int N = m_cov.GetNrows();
- std::vector<TVectorD> errorVec( RANK, TVectorD( N ) );
- for ( unsigned int i = 0; i < N; ++i ) {
- double startingValue = m_parameters[i]->mean();
- double error = sqrt( m_cov( i, i ) );
- double min = m_parameters[i]->mean() - error;
- double max = m_parameters[i]->mean() + error;
- DEBUG( "Perturbing parameter: " << m_parameters[i]->name() << " -> [" << min << ", " << max << "]" );
-
- m_parameters[i]->setCurrentFitVal( max );
- auto plus_variation = fcn();
- m_parameters[i]->setCurrentFitVal( min );
- auto minus_variation = fcn();
- m_parameters[i]->setCurrentFitVal( startingValue );
- for ( size_t j = 0; j < RANK; ++j ) {
- errorVec[j]( i ) = ( plus_variation[j] - minus_variation[j] ) / ( 2 * error );
- }
- }
- fcn();
- std::vector<double> rt( RANK, 0 );
- for ( unsigned int j = 0; j < RANK; ++j ) rt[j] = sqrt( errorVec[j] * ( m_cov * errorVec[j] ) );
- return rt;
- }
+ std::vector<double> getVectorError( const std::function<std::vector<double>(void)>& fcn, size_t RANK ) const;
/// Calculate the variance-covariance matrix of functor set functions.
std::vector<double> combinationWeights( const std::vector<std::function<double(void)>>& functions );
diff --git a/AmpGen/Event.h b/AmpGen/Event.h
index 36c269c7404..5e420599f1b 100644
--- a/AmpGen/Event.h
+++ b/AmpGen/Event.h
@@ -13,63 +13,53 @@ namespace AmpGen {
/** @class Event
@brief Encapsulates the final state particles of a single event
- Encapsulates the final state particles of a single event, or candidate in the language of proton-proton collisions. Typically will store (i) the event kinematics, i.e. four-momenta, (ii). a cache of complex numbers that contain intermediate calculations of the amplitude, (iii). the weight of the given event/candidate, (iv). The probability that the event was generated with, in the case of a simulated event */
+ Encapsulates the final state particles of a single event, or candidate in the language of proton-proton collisions. Typically will store (i) the event kinematics, i.e. four-momenta, (ii). the weight of the given event/candidate, (iii). The probability that the event was generated with, in the case of a simulated event */
class Event {
public:
+ Event () = default;
+ Event( const unsigned& N );
+ Event( const real_t* data, const unsigned& N );
- Event( const size_t& N, const size_t& cacheSize=0 );
- Event( const real_t* data, const size_t& N, const size_t& cacheSize=0);
-
- void set( const size_t& i, const std::vector<real_t>& p );
- void set( const size_t& i, const real_t* p );
+ void set( const unsigned& i, const std::vector<real_t>& p );
+ void set( const unsigned& i, const real_t* p );
void set( const real_t* evt );
- void set( const size_t& i, const real_t& p ) ;
+ void set( const unsigned& i, const real_t& p ) ;
void swap( const unsigned int& i , const unsigned int& j );
- void setCache(const complex_t& value, const size_t& pos) ;
- template <size_t N> void setCache( const std::array<complex_t,N>& value, const size_t& pos )
- {
- std::memmove( m_cache.data() + pos, value.data(), sizeof(std::array<complex_t,N>) );
- }
- void setCache( const std::vector<complex_t>& value, const size_t& pos );
- void resizeCache( const unsigned int& new_size );
- size_t size() const { return m_event.size(); }
-
- real_t* pWeight() { return &(m_weight); }
- real_t* pGenPdf() { return &m_genPdf; }
- const real_t* address(const unsigned int ref=0 ) const { return &(m_event[ref]); }
- real_t* address(const unsigned int& ref=0) { return &(m_event[ref]); }
+ unsigned size() const { return m_event.size(); }
- unsigned int cacheSize() const { return m_cache.size(); }
- real_t weight() const { return m_weight; }
- real_t genPdf() const { return m_genPdf; }
- real_t operator[](const unsigned int& i) const { return m_event[i]; }
- real_t& operator[](const unsigned int& i) { return m_event[i]; }
- operator const real_t*() const { return &(m_event[0]); }
- operator real_t*() { return &(m_event[0]); }
+ real_t* pWeight() { return &(m_weight); }
+ real_t* pGenPdf() { return &m_genPdf; }
+ const real_t* address(const unsigned& ref=0) const { return &(m_event[ref]); }
+ real_t* address(const unsigned& ref=0) { return &(m_event[ref]); }
- const complex_t& getCache(const unsigned int& pos) const { return m_cache[pos]; }
- const complex_t* getCachePtr(const unsigned int& pos=0) const { return &(m_cache[0]) + pos; }
+ real_t weight() const { return m_weight; }
+ real_t genPdf() const { return m_genPdf; }
+ real_t operator[](const unsigned& i) const { return m_event[i]; }
+ real_t& operator[](const unsigned& i) { return m_event[i]; }
+ operator const real_t*() const { return &(m_event[0]); }
+ operator real_t*() { return &(m_event[0]); }
void setWeight( const real_t& weight ){ m_weight = weight ; }
void setGenPdf( const real_t& genPdf ){ m_genPdf = genPdf ; }
void extendEvent(const real_t& value) { m_event.push_back( value ); }
void print() const;
- void printCache() const;
-
- real_t s( const size_t& index) const ;
- real_t s( const size_t& index1, const size_t& index2 ) const ;
- real_t s( const size_t& index1, const size_t& index2, const size_t& index3 ) const;
- real_t s( const std::vector<size_t>& indices ) const ;
+ // void printCache() const;
+ void setIndex(const unsigned& index){ m_index = index; }
+ unsigned index() const { return m_index; }
+ real_t s( const unsigned& index) const ;
+ real_t s( const unsigned& index1, const unsigned& index2 ) const ;
+ real_t s( const unsigned& index1, const unsigned& index2, const unsigned& index3 ) const;
+ real_t s( const std::vector<unsigned>& indices ) const ;
+ void reorder( const std::vector<unsigned>& addresses);
private:
std::vector<real_t> m_event;
- std::vector<complex_t> m_cache;
real_t m_genPdf = {1};
real_t m_weight = {1};
-
- inline real_t get(const size_t& index ) const { return m_event[index]; };
+ unsigned m_index = {0};
+ inline real_t get(const unsigned& index ) const { return m_event[index]; };
};
}
diff --git a/AmpGen/EventList.h b/AmpGen/EventList.h
index c0800963a5e..8495845e2dc 100644
--- a/AmpGen/EventList.h
+++ b/AmpGen/EventList.h
@@ -7,6 +7,8 @@
#include "AmpGen/Event.h"
#include "AmpGen/Projection.h"
#include "AmpGen/Utilities.h"
+#include "AmpGen/MetaUtils.h"
+#include "AmpGen/Units.h"
#include <chrono>
#include <functional>
@@ -18,31 +20,33 @@
#include <TH2D.h>
#include <TTree.h>
-#ifdef __USE_OPENMP__
-#include <omp.h>
+#ifdef _OPENMP
+ #include <omp.h>
#endif
namespace AmpGen
{
- DECLARE_ARGUMENT_DEFAULT( Bins, size_t, 100 );
-
+ namespace PlotOptions { DECLARE_ARGUMENT(Bins, size_t); }
class CompiledExpressionBase;
class EventList
{
private:
std::vector<Event> m_data = {};
EventType m_eventType = {};
- std::map<uint64_t, unsigned int> m_pdfIndex = {};
std::map<std::string, unsigned int> m_extensions = {};
- double m_norm = {0};
- size_t m_lastCachePosition = {0};
+
public:
+ typedef Event value_type;
EventList() = default;
EventList( const EventType& type );
template < class ... ARGS > EventList( const std::string& fname, const EventType& evtType, const ARGS&... args ) : EventList(evtType)
{
loadFromFile( fname, ArgumentPack(args...) );
}
+ template < class ... ARGS > EventList( const std::string& fname, const ARGS&... args ) : EventList()
+ {
+ loadFromFile( fname, ArgumentPack(args...) );
+ }
template < class ... ARGS > EventList( const std::vector<std::string>& fname, const EventType& evtType, const ARGS&... args ) : EventList(evtType)
{
for( auto& f : fname ) loadFromFile( f, ArgumentPack(args...) );
@@ -51,8 +55,7 @@ namespace AmpGen
{
loadFromTree( tree, ArgumentPack(args...) );
}
-
- void resetCache();
+ const EventList& store() const { return *this;}
std::vector<Event>::reverse_iterator rbegin() { return m_data.rbegin(); }
std::vector<Event>::reverse_iterator rend() { return m_data.rend(); }
std::vector<Event>::iterator begin() { return m_data.begin(); }
@@ -66,118 +69,95 @@ namespace AmpGen
EventType eventType() const { return m_eventType; }
const Event& at( const size_t& pos ) const { return m_data[pos]; }
size_t size() const { return m_data.size(); }
+ size_t aligned_size() const { return m_data.size() ; }
+ size_t nBlocks() const { return m_data.size() ; }
double integral() const;
- double norm();
-
- void reserve( const size_t& size ) { m_data.reserve( size ); }
- void push_back( const Event& evt ) { m_data.push_back( evt ); }
+ const double* block(const unsigned pos) const { return m_data[pos].address(); }
+ real_t weight( const size_t& pos) const { return m_data[pos].weight(); }
+ real_t genPDF( const size_t& pos) const { return m_data[pos].genPdf(); }
+ unsigned key(const std::string& key) const
+ {
+ auto it = m_extensions.find(key);
+ if( it == m_extensions.end() ) return m_data[0].size() - 1;
+ return it->second;
+ }
+ void reserve( const size_t& size );
+ void resize ( const size_t& size );
+ void push_back( const Event& evt );
+ void emplace_back( const Event& evt);
void setEventType( const EventType& type ) { m_eventType = type; }
void add( const EventList& evts );
void loadFromTree( TTree* tree, const ArgumentPack& args );
void loadFromFile( const std::string& fname, const ArgumentPack& args );
- void printCacheInfo( const unsigned int& nEvt = 0 );
void clear();
- void erase( const std::vector<Event>::iterator& begin, const std::vector<Event>::iterator& end );
-
- TTree* tree( const std::string& name, const std::vector<std::string>& extraBranches = {} );
-
- size_t getCacheIndex( const CompiledExpressionBase& PDF, bool& status ) const;
- size_t getCacheIndex( const CompiledExpressionBase& PDF ) const;
- template <class T>
- size_t registerExpression(const T& expression, const size_t& size_of=0)
- {
- auto key = FNV1a_hash( expression.name() );
- auto pdfIndex = m_pdfIndex.find( key );
- if ( pdfIndex != m_pdfIndex.end() ) {
- return pdfIndex->second;
- } else {
- size_t size = m_lastCachePosition;
- size_t expression_size = size_of == 0 ?
- expression.returnTypeSize() / sizeof(complex_t) : size_of;
- if ( size >= at( 0 ).cacheSize() ) {
- WARNING("Cache index " << size << " exceeds cache size = "
- << at(0).cacheSize() << " resizing to "
- << size + expression_size );
-
- for (auto& evt : *this) evt.resizeCache( size + expression_size );
- }
- m_pdfIndex[key] = m_lastCachePosition;
- m_lastCachePosition += expression_size;
- return size;
- }
- }
-
- template <class FUNCTOR>
- unsigned int extendEvent( const std::string& name, FUNCTOR func )
+ void setWeight( const unsigned int& pos, const double& w, const double&g=+1)
{
- unsigned int index = this->begin()->size();
- for ( auto& evt : *this ) evt.extendEvent(func(evt));
- m_extensions[name] = index;
- return index;
- }
-
- template <class FCN>
- void updateCache( const FCN& fcn, const size_t& index )
- {
- #pragma omp parallel for
- for ( unsigned int i = 0; i < size(); ++i ) {
- ( *this )[i].setCache(fcn(getEvent(i)), index);
- }
+ m_data[pos].setWeight(w);
+ m_data[pos].setGenPdf(g);
}
+ void erase( const std::vector<Event>::iterator& begin, const std::vector<Event>::iterator& end );
- TH2D* makeProjection( const Projection2D& projection, const ArgumentPack& args );
+ TTree* tree( const std::string& name, const std::vector<std::string>& extraBranches = {} ) const;
+
+ TH1D* makeProjection(const Projection& projection , const ArgumentPack& args = ArgumentPack()) const;
+ TH2D* makeProjection(const Projection2D& projection, const ArgumentPack& args = ArgumentPack()) const;
std::vector<TH1D*> makeProjections( const std::vector<Projection>& projections, const ArgumentPack& args );
- template <class... ARGS>
- std::vector<TH1D*> makeDefaultProjections( const ARGS&... args )
+ template <class... ARGS> std::vector<TH1D*> makeDefaultProjections( const ARGS&... args )
{
auto argPack = ArgumentPack( args... );
- size_t nBins = argPack.getArg<Bins>(100);
+ size_t nBins = argPack.getArg<PlotOptions::Bins>(100);
auto proj = eventType().defaultProjections(nBins);
return makeProjections( proj , argPack );
}
- template <class... ARGS>
- std::vector<TH1D*> makeProjections( const std::vector<Projection>& projections, const ARGS&... args )
+
+ template <typename... ARGS> std::vector<TH1D*> makeProjections( const std::vector<Projection>& projections, const ARGS&... args )
{
return makeProjections( projections, ArgumentPack( args... ) );
}
- template <class... ARGS>
- TH1D* makeProjection( const Projection& projection, const ARGS&... args )
+
+ template <typename... ARGS,
+ typename = std::enable_if_t< ! std::is_same<zeroType<ARGS...>, ArgumentPack>::value > >
+ TH1D* makeProjection( const Projection& projection, const ARGS&... args ) const
{
return makeProjection( projection, ArgumentPack(args...) );
}
- TH1D* makeProjection( const Projection& projection, const ArgumentPack& args );
-
- template <class... ARGS>
+
+ template <typename... ARGS,
+ typename = std::enable_if_t< ! std::is_same<zeroType<ARGS...>, ArgumentPack>::value > >
TH2D* makeProjection( const Projection2D& projection, const ARGS&... args )
{
return makeProjection( projection, ArgumentPack(args...) );
}
- template <class FCN>
- EventList& transform( FCN&& fcn )
+
+ template <typename functor> EventList& transform( functor&& fcn )
{
for ( auto& event : m_data ) fcn( event );
return *this;
}
- template <class FCN>
- void filter( FCN&& fcn ){
- size_t currentSize = size();
+
+ template <typename functor> void filter( functor&& fcn )
+ {
+ unsigned currentSize = size();
m_data.erase( std::remove_if( m_data.begin(), m_data.end(), fcn ) , m_data.end() );
- INFO("Filter removes: " << currentSize - size() << " / " << currentSize << " events");
+ INFO("Filter retains " << size() << " / " << currentSize << " events");
+ }
+
+ template <typename functor> unsigned count( functor&& fcn ) const
+ {
+ return std::count_if( std::begin(*this), std::end(*this), fcn );
}
- };
- DECLARE_ARGUMENT( LineColor, int );
- DECLARE_ARGUMENT( DrawStyle, std::string );
- DECLARE_ARGUMENT( Selection, std::function<bool( const Event& )> );
- DECLARE_ARGUMENT( WeightFunction, std::function<double( const Event& ) > );
- DECLARE_ARGUMENT( Branches, std::vector<std::string> );
- DECLARE_ARGUMENT( EntryList, std::vector<size_t> );
- DECLARE_ARGUMENT_DEFAULT(GetGenPdf, bool, false );
- DECLARE_ARGUMENT_DEFAULT(CacheSize, size_t , 0 );
- DECLARE_ARGUMENT_DEFAULT(Filter, std::string , "");
- DECLARE_ARGUMENT_DEFAULT(WeightBranch, std::string, "" );
- DECLARE_ARGUMENT_DEFAULT(ApplySym, bool, 0 );
- DECLARE_ARGUMENT_DEFAULT(Prefix, std::string, "" );
+ };
+ DECLARE_ARGUMENT(Branches, std::vector<std::string>); /// Branch names containing kinematic information
+ DECLARE_ARGUMENT(ExtraBranches, std::vector<std::string>); /// additional information about the event to include
+ DECLARE_ARGUMENT(IdBranches, std::vector<std::string>); /// Branches containing PID information, used if the names of particles are incorrect (looking at you, DTF)
+ DECLARE_ARGUMENT(EntryList, std::vector<size_t>);
+ DECLARE_ARGUMENT(GetGenPdf, bool);
+ DECLARE_ARGUMENT(Filter, std::string);
+ DECLARE_ARGUMENT(WeightBranch, std::string);
+ DECLARE_ARGUMENT(ApplySym, bool);
+ DECLARE_ARGUMENT(WeightFunction, std::function<double( const Event& )>);
+ DECLARE_ARGUMENT(InputUnits, AmpGen::Units);
} // namespace AmpGen
#endif
diff --git a/AmpGen/EventListSIMD.h b/AmpGen/EventListSIMD.h
new file mode 100644
index 00000000000..487f7898cef
--- /dev/null
+++ b/AmpGen/EventListSIMD.h
@@ -0,0 +1,148 @@
+#ifndef AMPGEN_EVENTLIST2_H
+#define AMPGEN_EVENTLIST2_H
+
+#include "AmpGen/ArgumentPack.h"
+#include "AmpGen/EventType.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/Event.h"
+#include "AmpGen/Projection.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/MetaUtils.h"
+#include "AmpGen/EventList.h"
+#include <chrono>
+#include <functional>
+#include <numeric>
+#include <cstddef>
+#include <algorithm>
+
+#include <TH1D.h>
+#include <TH2D.h>
+#include <TTree.h>
+
+#ifdef _OPENMP
+ #include <omp.h>
+#endif
+
+#include "AmpGen/simd/iterator.h"
+#include "AmpGen/simd/utils.h"
+#include "AmpGen/Store.h"
+
+namespace AmpGen
+{
+ class CompiledExpressionBase;
+ class EventListSIMD
+ {
+ private:
+ Store<float_v, Alignment::AoS> m_data {};
+ std::vector<float_v> m_weights {};
+ std::vector<float_v> m_genPDF {};
+ EventType m_eventType {};
+ public:
+ typedef Event value_type;
+ EventListSIMD() = default;
+ EventListSIMD( const EventType& type );
+ template < class ... ARGS > EventListSIMD( const std::string& fname, const EventType& evtType, const ARGS&... args ) : EventListSIMD(evtType)
+ {
+ loadFromFile( fname, ArgumentPack(args...) );
+ }
+ template < class ... ARGS > EventListSIMD( const std::string& fname, const ARGS&... args ) : EventListSIMD()
+ {
+ loadFromFile( fname, ArgumentPack(args...) );
+ }
+ template < class ... ARGS > EventListSIMD( const std::vector<std::string>& fname, const EventType& evtType, const ARGS&... args ) : EventListSIMD(evtType)
+ {
+ for( auto& f : fname ) loadFromFile( f, ArgumentPack(args...) );
+ }
+ template < class ... ARGS > EventListSIMD( TTree* tree, const EventType& evtType, const ARGS&... args ) : EventListSIMD(evtType)
+ {
+ loadFromTree( tree, ArgumentPack(args...) );
+ }
+ EventListSIMD( const EventList& other );
+ const float_v* data() const { return m_data.data(); }
+ operator Store<float_v, Alignment::AoS> () const { return m_data ; }
+ const auto& store() const { return m_data; }
+ const Event at(const unsigned& p) const { return EventListSIMD::operator[](p) ; }
+ const float_v* block(const unsigned& p) const { return m_data.data() + p * m_data.nFields(); }
+ float_v* block(const unsigned& p) { return m_data.data() + p * m_data.nFields(); }
+ float_v weight(const unsigned& p) const { return m_weights[p]; }
+ float_v genPDF(const unsigned& p) const { return m_genPDF[p]; }
+
+ void setWeight( const unsigned& block, const float_v& w, const float_v& g=1.f)
+ {
+ m_weights[block] = w;
+ m_genPDF[block] = g;
+ }
+ void resize( const unsigned nEvents )
+ {
+ m_data = Store<float_v, Alignment::AoS>( nEvents, m_eventType.eventSize() );
+ m_weights.resize( aligned_size(), 1.f);
+ m_genPDF.resize( aligned_size(), 1.f );
+ }
+ const Event operator[]( const size_t&) const;
+ std::array<Event, utils::size<float_v>::value> scatter(unsigned) const;
+ void gather(const std::array<Event, utils::size<float_v>::value>&, unsigned);
+ auto begin() const { return make_scatter_iterator<utils::size<float_v>::value>(0,this); }
+ auto end() const { return make_scatter_iterator<utils::size<float_v>::value>(size(), (const EventListSIMD*)(nullptr) ); }
+ auto begin() { return make_scatter_iterator<utils::size<float_v>::value, true>(0, this); }
+ auto end() { return make_scatter_iterator<utils::size<float_v>::value, true>(size(), (EventListSIMD*)(nullptr) ); }
+ EventType eventType() const { return m_eventType; }
+ size_t aligned_size() const { return m_data.aligned_size(); }
+ double integral() const;
+ size_t eventSize() const { return m_data.nFields(); }
+ size_t size() const { return m_data.size(); }
+ size_t nBlocks() const { return m_data.nBlocks(); }
+ void setEventType( const EventType& type ) { m_eventType = type; }
+ void add( const EventListSIMD& evts );
+ void loadFromTree( TTree* tree, const ArgumentPack& args );
+ void loadFromFile( const std::string& fname, const ArgumentPack& args );
+ void clear();
+
+ TTree* tree( const std::string& name, const std::vector<std::string>& extraBranches = {} ) const;
+
+
+ TH1D* makeProjection(const Projection& projection , const ArgumentPack& args = ArgumentPack()) const;
+ TH2D* makeProjection(const Projection2D& projection, const ArgumentPack& args = ArgumentPack()) const;
+ std::vector<TH1D*> makeProjections( const std::vector<Projection>& projections, const ArgumentPack& args );
+
+ template <class... ARGS> std::vector<TH1D*> makeDefaultProjections( const ARGS&... args )
+ {
+ auto argPack = ArgumentPack( args... );
+ size_t nBins = argPack.getArg<PlotOptions::Bins>(100);
+ auto proj = eventType().defaultProjections(nBins);
+ return makeProjections( proj , argPack );
+ }
+
+ template <typename... ARGS> std::vector<TH1D*> makeProjections( const std::vector<Projection>& projections, const ARGS&... args )
+ {
+ return makeProjections( projections, ArgumentPack( args... ) );
+ }
+
+ template <typename... ARGS,
+ typename = std::enable_if_t< ! std::is_same<zeroType<ARGS...>, ArgumentPack>::value > >
+ TH1D* makeProjection( const Projection& projection, const ARGS&... args ) const
+ {
+ return makeProjection( projection, ArgumentPack(args...) );
+ }
+
+ template <typename... ARGS,
+ typename = std::enable_if_t< ! std::is_same<zeroType<ARGS...>, ArgumentPack>::value > >
+ TH2D* makeProjection( const Projection2D& projection, const ARGS&... args )
+ {
+ return makeProjection( projection, ArgumentPack(args...) );
+ }
+
+ template <typename functor> EventListSIMD& transform( functor&& fcn )
+ {
+ for ( auto& event : *this ) fcn( event );
+ return *this;
+ }
+ static std::vector<float_v> makeEvent( const Event& event )
+ {
+ std::vector<float_v> rt( event.size() );
+ for( unsigned i = 0 ; i != event.size(); ++i ) rt[i] = event[i];
+ return rt;
+ }
+ };
+
+} // namespace AmpGen
+#endif
diff --git a/AmpGen/EventType.h b/AmpGen/EventType.h
index 21ec4cb6ec4..191cf35f976 100644
--- a/AmpGen/EventType.h
+++ b/AmpGen/EventType.h
@@ -9,57 +9,78 @@
namespace AmpGen
{
- class Projection;
- class Event;
+ class Projection;
+ class Event;
/**@class EventType
- * Deals with final state configuration of events,
- * specifically dealing with the ordering of particles in trees.
+ Deals with final state configuration of events,
+ specifically dealing with the ordering of particles in trees.
*/
+ class EventType;
+ std::ostream& operator<<( std::ostream& os, const EventType& type );
class EventType
{
- private:
- std::string m_mother; ///< name of decaying particle
- double m_motherMass; ///< mass of decaying particle
- std::vector<std::string> m_particleNames; ///< names of decay products
- std::vector<std::string> m_particleNamesPickled; ///< names of decay product pickled for ROOT
- std::vector<double> m_particleMasses; ///< masses of decay products
- bool m_timeDependent;
- std::vector<std::string> m_eventTypeExtensions; ///< extended event data
- std::pair<size_t, size_t> m_dim; ///< Rank of the relevant transition matrix
- public:
- EventType() = default;
- EventType( const std::vector<std::string>&, const bool& isTD = false );
- std::map<std::string, size_t> getEventFormat( const bool& outputNames = false ) const;
-
- std::pair<double, double> minmax( const std::vector<size_t>& indices, bool isGeV = false ) const;
- std::vector<std::vector<unsigned int>> getBosePairs() const;
- std::vector<double> masses() const;
- std::string mother() const;
- double mass( const size_t& index ) const;
- double motherMass() const;
- std::vector<std::string> finalStates() const;
- bool isTimeDependent() const;
- size_t eventSize() const;
- size_t size() const;
- size_t dof() const;
- std::string operator[]( const size_t& index ) const;
+ public:
+ /// Default constructor
+ EventType() = default;
+
+ /// Takes a list of particles, beginning with the head of the decay and
+ /// then then final state particles, and a flag as to whether to include time dependence.
+ EventType( const std::vector<std::string>&, const bool& isTD = false );
+
+ /// Returns the CP-conjugated event type. Can also require that only the initial/
+ /// final state is conjugated. By default, conjugates both.
+ EventType conj( const bool& headOnly = 0, const bool& dontConjHead = 0 ) const;
+
+ /// Returns the event format, that matches between expressions and the names used in Particle.
+ std::map<std::string, unsigned> getEventFormat( const bool& outputNames = false ) const;
+
+ /// Counts the number of particles in this event type with
+ /// the same name as the index'th name.
+ std::pair<unsigned,unsigned> count(const unsigned& index) const;
+ std::pair<double, double> minmax( const std::vector<unsigned>& indices) const;
+ std::vector<double> masses() const;
+ std::string mother() const;
+ double mass( const unsigned& index ) const;
+ double motherMass() const;
+ std::vector<std::string> finalStates() const;
+ bool isTimeDependent() const;
+ unsigned eventSize() const;
+ unsigned size() const;
+ unsigned dof() const;
+ std::string operator[]( const unsigned& index ) const;
+ std::string decayDescriptor() const;
+ std::string label( const unsigned& index, bool isRoot = true ) const;
+ std::string label( const std::vector<unsigned>& index, bool isRoot = true ) const;
+ std::vector<Projection> defaultProjections(const unsigned& nBins=100) const;
+ Projection projection(const unsigned& nBins, const std::vector<unsigned>& indices, const std::string& observable = "mass2") const;
- std::string label( const size_t& index, bool isRoot = true ) const;
- std::string label( const std::vector<size_t>& index, bool isRoot = true ) const;
- std::vector<Projection> defaultProjections(const size_t& nBins) const;
- Projection projection(const size_t& nBins, const std::vector<size_t>& indices) const;
+ bool operator==( const EventType& other ) const;
+ bool has( const std::string& name ) const;
- bool operator==( const EventType& other ) const;
- bool has( const std::string& name ) const;
- EventType conj( const bool& headOnly = 0, const bool& dontConjHead = 0 ) const;
-
- void setMotherMass( const double& mass ){ m_motherMass = mass ; }
- void extendEventType( const std::string& branch );
- std::function<void( Event& )> symmetriser() const;
- std::pair<size_t, size_t> dim() const; ///< calculates the number of spin indices accociated with the initial and final state, i.e. the rank of the relevant transition matrix.
+ void extendEventType( const std::string& branch );
+
+ /// Functor to randomly symmetrise data of this event type, using the Fisher-Yates shuffle.
+ std::function<void( Event& )> symmetriser() const;
+ std::function<bool( Event&, const std::vector<int>& ids)> automaticOrdering() const;
+
+ /// Calculates the number of spin indices associated with the initial and final state, i.e. the rank of the relevant transition matrix.
+ std::pair<unsigned, unsigned> dim() const;
+
+ friend std::ostream& AmpGen::operator<<( std::ostream& os, const EventType& type );
+
+ private:
+ std::string m_mother; ///< name of decaying particle
+ double m_motherMass; ///< mass of decaying particle
+ std::vector<std::string> m_particleNames; ///< names of decay products
+ std::vector<std::string> m_particleNamesPickled; ///< names of decay product pickled for ROOT
+ std::vector<double> m_particleMasses; ///< masses of decay products
+ std::vector<bool> m_ignore; ///< Flag to ignore particle when reading events, for invisible or tags
+ bool m_timeDependent; ///< Flag to include a decay time as the last element in the event vector
+ std::vector<std::string> m_eventTypeExtensions; ///< extended event data
+ std::pair<unsigned, unsigned> m_dim; ///< Rank of the relevant transition matrix
+ bool m_alt_part_names; ///< alternative naming in ouput tree (e.g. Xi- pi+ pi+ becomes Xim pip0 pip1 rather than _1_Xi# _2_pi~ _3_pi~)
};
- std::ostream& operator<<( std::ostream& os, const EventType& type );
} // namespace AmpGen
#endif
diff --git a/AmpGen/Expression.h b/AmpGen/Expression.h
index 9198ff061b8..f48312d89f2 100644
--- a/AmpGen/Expression.h
+++ b/AmpGen/Expression.h
@@ -57,12 +57,17 @@
complex_t X::operator()() const { return F( m_expression() ); } \
std::string X::to_string(const ASTResolver* resolver) const { return std::string(#F)+"("+ m_expression.to_string(resolver)+")";}
+#define DEFINE_UNARY_OPERATOR_NO_RESOLVER( X, F ) \
+ X::X( const AmpGen::Expression& expression) : IUnaryExpression(expression) {} \
+ X::operator Expression() const { return Expression( std::make_shared<X>(*this) ) ; } \
+ complex_t X::operator()() const { return F( m_expression() ); }
+
/// @ingroup ExpressionEngine macro DECLARE_UNARY_OPERATOR
/// Macro to declare a unary operator, \ref ExpressionEngine "see IUnaryExpression"
#define DECLARE_UNARY_OPERATOR( X ) \
class X : public IUnaryExpression { \
public: \
- X( const Expression& other ); \
+ explicit X( const Expression& other ); \
virtual std::string to_string(const ASTResolver* resolver=nullptr) const override; \
virtual Expression d() const override; \
operator Expression() const; \
@@ -114,7 +119,7 @@ namespace AmpGen
/// Resolve the dependencies of a tree using an ASTResolver,
/// which keeps track of parameters, dependent sub-trees, etc.
/// \param resolver resolver object to use
- virtual void resolve( ASTResolver& resolver ) = 0;
+ virtual void resolve( ASTResolver& resolver ) const = 0;
/// virtual descructor
virtual ~IExpression() = default;
/// Evaluate the expression using the tree,
@@ -134,11 +139,11 @@ namespace AmpGen
~Expression() = default;
std::string to_string(const ASTResolver* resolver=nullptr) const;
IExpression* get() const;
- void resolve( ASTResolver& resolver );
- Expression operator+=( const Expression& other ) const;
- Expression operator*=( const Expression& other ) const;
- Expression operator-=( const Expression& other ) const;
- Expression operator/=( const Expression& other ) const;
+ void resolve( ASTResolver& resolver ) const;
+ Expression operator+=( const Expression& other );
+ Expression operator*=( const Expression& other );
+ Expression operator-=( const Expression& other );
+ Expression operator/=( const Expression& other );
Expression operator-() const;
complex_t operator()() const;
@@ -157,7 +162,7 @@ namespace AmpGen
Constant( const complex_t& value ) : m_value(value) {}
std::string to_string(const ASTResolver* resolver=nullptr) const override;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
operator Expression() const;
complex_t operator()() const override { return m_value; }
private:
@@ -173,13 +178,12 @@ namespace AmpGen
such as cache states, but this currently requires manually specifying the argument ordering. */
class Parameter : public IExpression {
public:
- Parameter( const std::string& name = "",
- const double& defaultValue = 0 ,
- const bool& resolved = false,
- const unsigned int& fromArg = 0 );
+ Parameter(const std::string& name = "",
+ const double& defaultValue = 0 ,
+ const bool& resolved = false);
std::string to_string(const ASTResolver* resolver = nullptr) const override;
- void resolve( ASTResolver& resolver ) override;
- operator Expression() const;
+ void resolve( ASTResolver& resolver ) const override;
+ virtual operator Expression() const;
complex_t operator()() const override { return complex_t( m_defaultValue, 0 ); }
std::string name() const { return m_name; }
const double& defaultValue() const { return m_defaultValue ; }
@@ -189,9 +193,34 @@ namespace AmpGen
std::string m_name;
double m_defaultValue;
bool m_resolved;
- unsigned int m_fromArg;
};
+ class ComplexParameter : public IExpression {
+ public:
+ ComplexParameter( const Parameter& real, const Parameter& imag );
+ std::string to_string(const ASTResolver* resolver = nullptr ) const override;
+ void resolve( ASTResolver& resolver ) const override;
+ operator Expression() const ;
+ complex_t operator()() const override;
+ private:
+ Parameter m_real;
+ Parameter m_imag;
+ };
+ /** @ingroup ExpressionEngine class LambdaExpression
+ @brief Parameter that the value of which is given by some arbitrary C++ function
+ */
+ class LambdaExpression : public IExpression {
+ public:
+ template <typename function_type>
+ LambdaExpression( const function_type& function) : m_function(function), m_name(type_string<function_type>()) {}
+ std::string to_string(const ASTResolver* resolver = nullptr) const override;
+ void resolve( ASTResolver& resolver) const override;
+ operator Expression() const;
+ complex_t operator()() const override;
+ std::function<double(void)> m_function;
+ std::string m_name;
+ };
+
/** @ingroup ExpressionEngine class Ternary
@brief Evaluates the ternary operator.
@@ -199,12 +228,14 @@ namespace AmpGen
\code{.cpp}
return a ? b : c
\endcode */
- struct Ternary : public IExpression {
+ class Ternary : public IExpression {
+ public:
Ternary( const Expression& cond, const Expression& v1, const Expression& v2 );
std::string to_string(const ASTResolver* resolver = nullptr ) const override;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
operator Expression() const ;
complex_t operator()() const override { return std::real(m_cond()) ? m_v1() : m_v2(); }
+ private:
Expression m_cond;
Expression m_v1;
Expression m_v2;
@@ -214,11 +245,12 @@ namespace AmpGen
struct SubTree : public IExpression {
SubTree( const Expression& other ) ;
std::string to_string(const ASTResolver* resolver = nullptr ) const override ;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
operator Expression() const ;
complex_t operator()() const override { return m_expression(); }
uint64_t key() const;
void setKey( const size_t& new_key );
+ Expression expression() const { return m_expression; }
Expression m_expression;
uint64_t m_key;
};
@@ -226,7 +258,7 @@ namespace AmpGen
struct Function : public IExpression {
Function( const std::string& name, const std::vector<Expression>& args ) ;
std::string to_string(const ASTResolver* resolver = nullptr ) const override ;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
operator Expression() const ;
complex_t operator()() const override { return 0; }
std::string m_name;
@@ -238,7 +270,7 @@ namespace AmpGen
class IBinaryExpression : public IExpression {
public:
IBinaryExpression( const Expression& l, const Expression& r ) : lval( l ), rval( r ){};
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
complex_t operator()() const override = 0;
Expression l() const { return lval ; }
Expression r() const { return rval ; }
@@ -278,10 +310,22 @@ namespace AmpGen
/// @ingroup ExpressionEngine class GreaterThan
/// @brief Binary expression that returns \f$l > r\f$
DECLARE_BINARY_OPERATOR( GreaterThan );
+
+ /// @ingroup ExpressionEngine class LessThanEqualTo
+ /// @brief Binary expression that returns \f$l < r\f$
+ DECLARE_BINARY_OPERATOR( LessThanEqualTo );
+ /// @ingroup ExpressionEngine class GreaterThanEqualTo
+ /// @brief Binary expression that returns \f$l > r\f$
+ DECLARE_BINARY_OPERATOR( GreaterThanEqualTo );
+
/// @ingroup ExpressionEngine class And
/// @brief Binary expression that returns \f$l \wedge r\f$
DECLARE_BINARY_OPERATOR( And );
+
+ /// @ingroup ExpressionEngine class Or
+ /// @brief Binary expression that returns \f$l \wedge r\f$
+ DECLARE_BINARY_OPERATOR( Or );
DECLARE_BINARY_OPERATOR( Equal );
DECLARE_BINARY_OPERATOR( ATan2 );
@@ -290,7 +334,7 @@ namespace AmpGen
class IUnaryExpression : public IExpression {
public:
IUnaryExpression( const Expression& other ) : m_expression( other ){};
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
complex_t operator()() const override = 0;
virtual Expression d() const = 0;
Expression arg() const { return m_expression ;}
@@ -348,7 +392,6 @@ namespace AmpGen
/// @ingroup ExpressionEngine struct ACos
/// @brief Unary expression that returns \f$\cos^{-1}(z)\f$
DECLARE_UNARY_OPERATOR( ACos );
-
/// @ingroup ExpressionEngine struct ATan
/// @brief Unary expression that returns \f$\tan^{-1}(z)\f$
DECLARE_UNARY_OPERATOR( ATan );
@@ -363,6 +406,8 @@ namespace AmpGen
Expression operator<( const Expression& A, const Expression& B );
Expression operator>( const Expression& A, const Expression& B );
+ Expression operator<=( const Expression& A, const Expression& B );
+ Expression operator>=( const Expression& A, const Expression& B );
Expression operator+( const Expression& A, const Expression& B );
Expression operator-( const Expression& A, const Expression& B );
@@ -388,6 +433,7 @@ namespace AmpGen
Expression operator/( const T& A, const Expression& B ){ return Constant(A) / B; }
Expression operator&&( const Expression& A, const Expression& B );
+ Expression operator||( const Expression& A, const Expression& B );
Expression operator==( const Expression& A, const Expression& B );
Expression operator==( const Expression& A, const double& B );
Expression operator==( const double& A, const Expression& B );
@@ -412,7 +458,6 @@ namespace AmpGen
Expression exp( const Expression& expression );
Expression log( const Expression& expression );
Expression atan2( const Expression& y, const Expression& x);
-
}
template < class T > bool is( const Expression& expression ){
diff --git a/AmpGen/ExpressionParser.h b/AmpGen/ExpressionParser.h
index 5f18e924dc0..6becfbf086d 100644
--- a/AmpGen/ExpressionParser.h
+++ b/AmpGen/ExpressionParser.h
@@ -1,4 +1,5 @@
#ifndef AMPGEN_EXPRESSIONPARSER_H
+#define AMPGEN_EXPRESSIONPARSER_H 1
#include <complex>
#include <functional>
@@ -9,31 +10,36 @@
#include "AmpGen/Expression.h"
#include "AmpGen/Types.h"
+#include "AmpGen/enum.h"
namespace AmpGen
{
class ASTResolver;
class MinuitParameter;
class MinuitParameterSet;
-
+
+ declare_enum(coordinateType, cartesian, polar)
+ declare_enum(angType, deg, rad)
+
class MinuitParameterLink : public IExpression {
public:
- MinuitParameterLink( MinuitParameter* param ) ;
+ explicit MinuitParameterLink( MinuitParameter* param ) ;
std::string to_string(const ASTResolver* resolver=nullptr) const override ;
- void resolve( ASTResolver& resolver ) override ;
+ void resolve( ASTResolver& resolver ) const override ;
complex_t operator()() const override ;
operator Expression() const ;
std::string name() const;
+ const MinuitParameter& param() const;
private:
MinuitParameter* m_parameter;
};
class ExpressionPack : public IExpression {
public:
- ExpressionPack( const std::vector<Expression>& expressions ){ m_expressions = expressions ; }
+ explicit ExpressionPack( const std::vector<Expression>& expressions ): m_expressions(expressions) {}
ExpressionPack( const Expression& A, const Expression& B );
std::string to_string(const ASTResolver* resolver=nullptr) const override;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
complex_t operator()() const override;
operator Expression() const ;
private:
@@ -60,27 +66,30 @@ namespace AmpGen
}
void add_binary( const std::string& name, binaryFCN op ) { m_binaryFunctions.emplace_back( name, op ); }
- void setMPS( MinuitParameterSet* mps ) { m_mps = mps; }
- static Expression Parse( const std::string& str );
+ static Expression parse( const std::string& str, const MinuitParameterSet* mps=nullptr );
+ static Expression parse(std::vector<std::string>::const_iterator begin,
+ std::vector<std::string>::const_iterator end ,
+ const MinuitParameterSet* mps = nullptr );
static ExpressionParser* gExpressionParser;
static ExpressionParser* getMe()
{
if ( !gExpressionParser ) gExpressionParser = new ExpressionParser();
return gExpressionParser;
}
-
private:
ExpressionParser();
- Expression processEndPoint( const std::string& name );
- Expression parseTokens( const std::vector<std::string>& tokens );
+ Expression processEndPoint( const std::string& name, const MinuitParameterSet* mps = nullptr );
+ Expression parseTokens( std::vector<std::string>::const_iterator begin, std::vector<std::string>::const_iterator end , const MinuitParameterSet* mps = nullptr );
void processBinaryOperators( std::vector<std::string>& opCodes, std::vector<Expression>& expressions );
void processUnaryOperators( std::vector<std::string>& opCodes, std::vector<Expression>& expressions );
- MinuitParameterSet* m_mps;
std::map<std::string, unaryFCN> m_unaryFunctions;
std::vector<std::pair<std::string, binaryFCN>> m_binaryFunctions;
+ bool m_isCartesian = {true};
+ double m_sf = {1};
+
};
} // namespace AmpGen
diff --git a/AmpGen/Factory.h b/AmpGen/Factory.h
index 0a76926c6e4..3323914be87 100644
--- a/AmpGen/Factory.h
+++ b/AmpGen/Factory.h
@@ -34,7 +34,7 @@ namespace AmpGen
auto ptrToStatic = getMe();
auto raw_base = ptrToStatic->m_terms.find( type );
if ( raw_base == ptrToStatic->m_terms.end() ) {
- if ( !quiet ) ERROR( type << " not found in Factory<" << typeof<TYPE>() << typeof<KEY_TYPE>() << " >" );
+ if ( !quiet ) ERROR( type << " not found in Factory<" << type_string<TYPE>() << type_string<KEY_TYPE>() << " >" );
return nullptr;
}
auto objectToReturn = raw_base->second->create();
diff --git a/AmpGen/FastDT.h b/AmpGen/FastDT.h
index 37158765c53..14f2953e4ae 100644
--- a/AmpGen/FastDT.h
+++ b/AmpGen/FastDT.h
@@ -24,14 +24,14 @@ namespace AmpGen {
{
public:
struct Node {
- unsigned int index;
- int left;
- int right;
- double cutValue;
+ unsigned index;
+ unsigned left;
+ unsigned right;
+ double cutValue;
Node(){};
- Node(const unsigned int& index,
- const int& left,
- const int& right,
+ Node(const unsigned& index,
+ const unsigned& left,
+ const unsigned& right,
const double& cutValue) : index(index), left(left), right(right), cutValue(cutValue) {};
};
FastDT() = default;
@@ -41,8 +41,8 @@ namespace AmpGen {
std::vector<Node> m_nodes;
std::function<std::vector<double>(const Event&)> m_functors;
std::queue<size_t> m_queueOrdering;
- size_t m_dim;
- size_t m_minEvents;
+ size_t m_dim = {0};
+ size_t m_minEvents = {0};
size_t m_maxDepth = {0};
int m_endNodeCounter = {0};
int makeNodes(std::vector<double*>& evts, std::queue<size_t> indexQueue, const size_t& depth);
diff --git a/AmpGen/FitFraction.h b/AmpGen/FitFraction.h
index 29142f17bdc..88efd3af8c5 100644
--- a/AmpGen/FitFraction.h
+++ b/AmpGen/FitFraction.h
@@ -7,17 +7,17 @@
#include <algorithm>
#include "AmpGen/Types.h"
#include "AmpGen/ErrorPropagator.h"
+#include "AmpGen/AmplitudeRules.h"
namespace AmpGen
{
class EventType;
class Particle;
-
class FitFraction
{
public:
- FitFraction(const std::string& line, const AmpGen::EventType& evtType);
+ FitFraction(const std::string& line);
FitFraction(const std::string& name, const double& frac, const double& err);
FitFraction() = default;
@@ -25,13 +25,13 @@ namespace AmpGen
double val() const;
double err() const;
std::string name() const;
- std::shared_ptr<Particle> particle() const;
private:
std::string m_name;
double m_value;
double m_error;
};
+
bool operator <(const FitFraction& lhs, const FitFraction& rhs);
bool operator >(const FitFraction& lhs, const FitFraction& rhs);
bool operator ==(const FitFraction& lhs, const FitFraction& rhs);
@@ -60,7 +60,8 @@ namespace AmpGen
pdf(pdf),
normSet(normSet),
recalculateIntegrals(recalculateIntegrals) {}
- std::vector<double> operator()(){
+ std::vector<double> operator()()
+ {
if ( recalculateIntegrals ) pdf->prepare();
else pdf->transferParameters();
std::vector<double> rv;
@@ -82,14 +83,14 @@ namespace AmpGen
}
return std::real(sum);
}
- real_t getVal( const size_t& index ) const {
+ real_t getVal( const size_t& index, const bool& getImaginaryPart = false) const {
complex_t sum = 0;
for ( auto& i : calculators[index].i ) {
for ( auto& j : calculators[index].j ) {
sum += (*pdf)[i].coefficient * std::conj( (*pdf)[j].coefficient ) * ( j >= i ? pdf->norm(i, j) : std::conj(pdf->norm(j,i)) );
}
}
- return std::real(sum) / norm();
+ return (getImaginaryPart ? std::imag(sum) : std::real(sum) ) / norm();
}
std::vector<FitFraction> operator()(const std::string& name, const LinearErrorPropagator& linProp )
{
diff --git a/AmpGen/FitResult.h b/AmpGen/FitResult.h
index a518679836c..932eab0f979 100644
--- a/AmpGen/FitResult.h
+++ b/AmpGen/FitResult.h
@@ -2,8 +2,8 @@
#define AMPGEN_FITRESULT_H
#include "TMatrixD.h"
+#include "TClass.h"
-#include "AmpGen/EventType.h"
#include "AmpGen/FitFraction.h"
#include "AmpGen/MinuitParameter.h"
#include "AmpGen/Utilities.h"
@@ -15,75 +15,64 @@ namespace AmpGen
class FitResult
{
- private:
- double m_chi2;
- double m_LL;
- double m_nBins;
- double m_nParam;
- int m_status;
- EventType m_eventType;
- std::map<std::string, double> m_observables;
- std::vector<FitFraction> m_fitFractions;
- TMatrixD m_covarianceMatrix;
- std::shared_ptr<MinuitParameterSet> m_mps;
- bool m_fitted;
- std::map<std::string, unsigned int> m_covMapping;
-
- std::string getLastLine( std::ifstream& in ) const;
- void addToParameters( const std::string& line );
- void addToObservables( const std::string& line );
- void setFitQuality( const std::string& line );
-
public:
- FitResult( const FitResult& other );
+ ~FitResult(){};
+ FitResult();
+ explicit FitResult( const FitResult& other );
+ explicit FitResult( const std::string& filename );
+ explicit FitResult( const Minimiser& mini );
+ FitResult( MinuitParameterSet& mps, const TMatrixD& covMini );
void addObservable( const std::string& name, const double& F );
- FitResult( const Minimiser& mini );
- FitResult( const MinuitParameterSet& mps, const TMatrixD& covMini );
-
- FitResult( const std::string& filename, const EventType& evtType = EventType() );
- FitResult() : m_chi2( 0 ), m_LL( -999 ), m_nBins( 0 ), m_nParam( 0 ), m_status( -1 ), m_fitted( 0 ) {}
-
- bool readFile( const std::string& fname );
+ void addChi2( const double& chi2, const double& nBins );
+ void addFractions( const std::vector<FitFraction>& fractions );
+ void addFraction( const std::string& name, const double& frac, const double& err );
+ void setCov( const size_t& x, const size_t& y, const double& F );
void writeToFile( const std::string& fname );
+ void clearFitFractions();
- double chi2() const { return m_chi2; }
- double LL() const { return m_LL; }
- int status() const { return m_status; }
- int nParam() const { return m_nParam; }
- int nBins() const { return m_nBins; }
+ bool readFile( const std::string& fname );
- EventType eventType() const { return m_eventType; }
- std::map<std::string, double> observables() const { return m_observables; }
- std::vector<FitFraction> fitFractions() const { return m_fitFractions; }
- std::shared_ptr<MinuitParameterSet> mps() const { return m_mps; }
+ double chi2() const;
+ double LL() const;
+ double dof() const;
+ double cov(const size_t& x, const size_t& y ) const;
+ double cov(const std::string& x, const std::string& y ) const;
+ double correlation( const std::string& x, const std::string& y ) const;
+
+ int status() const;
+ int nParam() const;
+ int nBins() const;
- double dof() const { return m_nBins - m_nParam - 1; }
- std::vector<MinuitParameter*> getParameters() const;
- std::vector<FitFraction> getFitFractions() const { return m_fitFractions; }
- MinuitParameterSet* MPS() const { return &( *m_mps ); }
- TMatrixD cov() const { return m_covarianceMatrix; }
- double cov( const size_t& x, const size_t& y ) const { return m_covarianceMatrix( x, y ); }
+ std::map<std::string, double> observables() const;
+ MinuitParameterSet* mps() const;
+ std::vector<FitFraction> fitFractions() const;
+ std::vector<MinuitParameter*> parameters() const;
+ std::vector<MinuitParameter*> floating(const bool& extended = false) const;
+ TMatrixD cov() const;
+
void print() const;
- std::vector<MinuitParameter*> getFloating( const bool& extended = false ) const;
TMatrixD getReducedCovariance( const bool& extended = false ) const;
LinearErrorPropagator getErrorPropagator( const bool& extended = false ) const;
- void addChi2( const double& chi2, const double& nBins );
- void addFractions( const std::vector<FitFraction>& fractions );
- void addFraction( const std::string& name, const double& frac, const double& err )
- {
- m_fitFractions.emplace_back( name, frac, err );
- }
- void clearFitFractions() { m_fitFractions.clear(); }
- void setCov( const size_t& x, const size_t& y, const double& F ) { m_covarianceMatrix( x, y ) = F; }
- double correlation( const std::string& x, const std::string& y )
- {
- auto ix = m_covMapping[x];
- auto iy = m_covMapping[y];
- return m_covarianceMatrix( ix, iy ) / sqrt( m_covarianceMatrix( ix, ix ) * m_covarianceMatrix( iy, iy ) );
- }
+
+ private:
+ MinuitParameterSet* m_mps = {nullptr};
+ double m_chi2 = {0};
+ double m_LL = {-999};
+ double m_nBins = {0};
+ double m_nParam = {0};
+ int m_status = {-1};
+ bool m_fitted = {false};
+ std::map<std::string, double> m_observables;
+ std::vector<FitFraction> m_fitFractions;
+ TMatrixD m_covarianceMatrix;
+ std::map<std::string, unsigned int> m_covMapping;
+
+ void addToParameters( const std::string& line );
+ void addToObservables( const std::string& line );
+ void setFitQuality( const std::string& line );
};
} // namespace AmpGen
diff --git a/AmpGen/Generator.h b/AmpGen/Generator.h
index 9f146fd8e2e..dc0fa9c0718 100644
--- a/AmpGen/Generator.h
+++ b/AmpGen/Generator.h
@@ -5,148 +5,172 @@
#include "AmpGen/EventType.h"
#include "AmpGen/PhaseSpace.h"
#include "AmpGen/Utilities.h"
+#include "AmpGen/ProfileClock.h"
+#include "AmpGen/ProgressBar.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/MetaUtils.h"
namespace AmpGen
{
- template <class PHASESPACE = PhaseSpace>
- class Generator
- {
- private:
- EventType m_eventType;
- PHASESPACE m_gps;
- unsigned int m_generatorBlock = {5000000};
- TRandom* m_rnd = {gRandom};
- bool m_normalise = {true};
-
- public:
- template <class... ARGS>
- Generator( const ARGS&... args )
- : m_gps(args...)
- {
- m_eventType = m_gps.eventType();
- setRandom( m_rnd );
- }
- PHASESPACE phsp() { return m_gps; }
- void setRandom( TRandom* rand )
- {
- m_rnd = rand;
- m_gps.setRandom( m_rnd );
- }
- void fillEventListPhaseSpace( EventList& list, const unsigned int& N, unsigned int cacheSize = 0 )
- {
- fillEventListPhaseSpace( list, N, cacheSize, []( const Event& evt ) { return 1; } );
- }
- void setBlockSize( const size_t& blockSize ) { m_generatorBlock = blockSize; }
- void setNormFlag( const bool& normSetting ) { m_normalise = normSetting; }
-
- template <class HARD_CUT>
- void fillEventListPhaseSpace( EventList& list, const unsigned int& N, const unsigned int& cacheSize, HARD_CUT cut )
+ template <typename phaseSpace_t = PhaseSpace, typename eventListInternal_t = EventList>
+ class Generator
{
- unsigned int rejected = 0;
- #ifdef DEBUGLEVEL
- auto t_start = std::chrono::high_resolution_clock::now();
- #endif
- list.reserve( N );
- while( list.size() < N ){
- Event newEvent = m_gps.makeEvent( cacheSize );
- newEvent.setWeight( 1 );
- if ( cut( newEvent ) ) list.push_back( newEvent );
- else rejected ++;
- }
- #ifdef DEBUGLEVEL
- auto t_end = std::chrono::high_resolution_clock::now();
- double time = std::chrono::duration<double, std::milli>( t_end - t_start ).count();
- #endif
- DEBUG( "Stage 1 efficiency = " << 100. * list.size() / ( list.size() + rejected ) << "%, yield = " << list.size()
- << " time = " << time );
- }
- template <class PDF>
- void fillEventList( PDF& pdf, EventList& list, const unsigned int& N )
- {
- fillEventList( pdf, list, N, []( const Event& evt ) { return 1; } );
- }
+ private:
+ EventType m_eventType;
+ phaseSpace_t m_gps;
+ size_t m_generatorBlock = {5000000};
+ TRandom* m_rnd = {gRandom};
+ bool m_normalise = {true};
- template <class PDF, class HARD_CUT>
- void fillEventList( PDF& pdf, EventList& list, const unsigned int& N, HARD_CUT cut )
- {
- if ( m_rnd == nullptr ) {
- ERROR( "Random generator not set!" );
- return;
- }
- double normalisationConstant = m_normalise ? 0 : 1;
- unsigned int size0 = list.size();
- auto tStartTotal = std::chrono::high_resolution_clock::now();
- pdf.reset( true );
- while ( list.size() - size0 < N ) {
- auto t_start = std::chrono::high_resolution_clock::now();
- EventList mc( m_eventType );
- fillEventListPhaseSpace( mc, m_generatorBlock, pdf.size(), cut );
-
- pdf.setEvents( mc );
- pdf.prepare();
+ public:
+ template <typename... ARGS> explicit Generator( const ARGS&... args ) : m_gps(args...)
+ {
+ m_eventType = m_gps.eventType();
+ if( m_rnd != gRandom ) setRandom( m_rnd );
+ DEBUG("Creating generator, using: " << type_string<phaseSpace_t>() << " and internal store type: " << type_string<eventListInternal_t>() );
+ }
+
+ phaseSpace_t phsp() { return m_gps; }
+
+ void setRandom( TRandom* rand )
+ {
+ m_rnd = rand;
+ m_gps.setRandom( m_rnd );
+ }
+ void setBlockSize( const size_t& blockSize ) { m_generatorBlock = blockSize; }
+ void setNormFlag( const bool& normSetting ) { m_normalise = normSetting; }
- if ( normalisationConstant == 0 ) {
- double max = 0;
- for ( auto& evt : mc ) {
- double value = pdf.prob_unnormalised( evt );
+ template <typename cut_t=std::nullptr_t> void fillEventListPhaseSpace( eventListInternal_t& events, const size_t& N, [[maybe_unused]] cut_t cut = nullptr)
+ {
+ events.resize(N);
+ auto it = events.begin();
+ while( it != events.end() )
+ {
+ *it = m_gps.makeEvent();
+ if constexpr( ! std::is_same<cut_t, std::nullptr_t>::value )
+ {
+ if( ! cut(*it ) ) continue;
+ }
+ if constexpr( std::is_same<eventListInternal_t, EventList>::value ) it->setIndex( it - events.begin() );
+ ++it;
+ }
+ }
+ template <typename eventList_t, typename pdf_t> void fillEventList( pdf_t& pdf, eventList_t& list, const size_t& N )
+ {
+ fillEventList( pdf, list, N, nullptr);
+ }
+ template <typename pdf_t> double getMax(const pdf_t& pdf, const eventListInternal_t& events) const
+ {
+ auto max = 0.;
+ for ( const auto& evt : events )
+ {
+ auto value = pdf(evt) / evt.genPdf();
if ( value > max ) max = value;
}
- normalisationConstant = max * 1.5;
- INFO( "Setting normalisation constant = " << normalisationConstant );
+ DEBUG( "Returning normalisation constant = " << max * 1.5 );
+ return max;
}
- unsigned int previousSize = list.size();
- for ( auto& evt : mc ) {
- double value = pdf.prob_unnormalised( evt );
- if ( value > normalisationConstant ) {
- WARNING( "PDF value exceeds norm value: " << value << " " << normalisationConstant );
- }
- if ( value > normalisationConstant * m_rnd->Rndm() ) {
- evt.setGenPdf( value );
- list.push_back( evt );
+ template <typename eventList_t, typename pdf_t, typename cut_t> void fillEventList( pdf_t& pdf, eventList_t& list, const size_t& N, cut_t cut )
+ {
+ if ( m_rnd == nullptr )
+ {
+ ERROR( "Random generator not set!" );
+ return;
}
- if ( list.size() - size0 == N ) break;
+ double maxProb = m_normalise ? 0 : 1;
+ auto size0 = list.size();
+ double totalGenerated = 0;
+ pdf.reset( true );
+ ProgressBar pb(60, detail::trimmedString(__PRETTY_FUNCTION__) );
+ ProfileClock t_phsp, t_eval, t_acceptReject, t_total;
+ std::vector<bool> efficiencyReport(m_generatorBlock,false);
+ bool accept_all = NamedParameter<bool>("AcceptAll",false);
+ eventListInternal_t mc( m_eventType );
+ while ( list.size() - size0 < N ) {
+ t_phsp.start();
+ fillEventListPhaseSpace(mc, m_generatorBlock, cut);
+ t_phsp.stop();
+ t_eval.start();
+ pdf.setEvents( mc );
+ pdf.prepare();
+ maxProb = maxProb == 0 ? 1.5 * getMax(pdf, mc) : maxProb;
+ auto previousSize = list.size();
+ #ifdef _OPENMP
+ #pragma omp parallel for
+ #endif
+ for ( size_t block=0; block < mc.nBlocks(); ++block )
+ mc.setWeight(block, 1.0, pdf(mc.block(block), block) / mc.genPDF(block));
+ t_eval.stop();
+ t_acceptReject.start();
+ totalGenerated += mc.size();
+ for(const auto& event : mc)
+ {
+ if ( event.genPdf() > maxProb ) {
+ std::cout << std::endl;
+ WARNING( "PDF value exceeds norm value: " << event.genPdf() << " > " << maxProb );
+// pdf.debug( event );
+ }
+ if ( accept_all || event.genPdf() > maxProb * m_rnd->Rndm() ){
+ list.push_back(event);
+ efficiencyReport[event.index()] = true;
+ }
+ else efficiencyReport[event.index()] = false;
+ if ( list.size() - size0 == N ) break;
+ }
+ t_acceptReject.stop();
+
+ // m_gps.provideEfficiencyReport( efficiencyReport );
+ double efficiency = 100. * ( list.size() - previousSize ) / (double)m_generatorBlock;
+ pb.print( double(list.size()) / double(N), " ε[gen] = " + mysprintf("%.4f",efficiency) + "% , " + std::to_string(int(t_total.count()/1000.)) + " seconds" );
+ if ( list.size() == previousSize ) {
+ ERROR( "No events generated, PDF: " << type_string<pdf_t>() << " is likely to be malformed" );
+ break;
+ }
+ }
+ pb.finish();
+ t_total.stop();
+ INFO("Generated " << N << " events in " << t_total << " ms");
+ INFO("Generating phase space : " << t_phsp << " ms");
+ INFO("Evaluating PDF : " << t_eval << " ms");
+ INFO("Accept/reject : " << t_acceptReject << " ms");
+ INFO("Efficiency = " << double(N) * 100. / totalGenerated << " %");
}
- auto t_end = std::chrono::high_resolution_clock::now();
- // double time = std::chrono::duration<double, std::milli>(t_end-t_stage2).count() ;
- double timeTotal = std::chrono::duration<double, std::milli>( t_end - t_start ).count();
- INFO( "Generator Efficiency = " << 100. * ( list.size() - previousSize ) / (double)m_generatorBlock
- << "% integrated yield = " << list.size() << ", time = " << timeTotal << "ms" );
- if ( list.size() == previousSize ) {
- ERROR( "No events generated, PDF: " << typeof<PDF>() << " is likely to be malformed" );
- break;
+ template <typename pdf_t, typename = typename std::enable_if<!std::is_integral<pdf_t>::value>::type>
+ EventList generate(pdf_t& pdf, const size_t& nEvents )
+ {
+ EventList evts( m_eventType );
+ fillEventList( pdf, evts, nEvents );
+ return evts;
+ }
+ EventList generate(const size_t& nEvents)
+ {
+ EventList evts( m_eventType );
+ fillEventListPhaseSpace( evts, nEvents);
+ return evts;
}
- }
- double time =
- std::chrono::duration<double, std::milli>( std::chrono::high_resolution_clock::now() - tStartTotal ).count();
- INFO( "Generated " << N << " events in " << time << " ms" );
- }
- template <class PDF>
- EventList generate( PDF& pdf, const unsigned int& nEvents )
- {
- EventList evts( m_eventType );
- fillEventList( pdf, evts, nEvents );
- return evts;
- }
- EventList generate( const unsigned int& nEvents, const size_t& cacheSize=0 )
- {
- EventList evts( m_eventType );
- fillEventListPhaseSpace( evts, nEvents, cacheSize );
- return evts;
- }
+ };
- };
- template <class FCN>
- class PDFWrapper {
- FCN m_fcn;
+ template <class FCN> class PDFWrapper
+ {
public:
- void prepare(){};
- void setEvents( AmpGen::EventList& evts ){};
- double prob_unnormalised( const AmpGen::Event& evt ) const { return m_fcn(evt); }
- PDFWrapper( const FCN& fcn ) : m_fcn(fcn) {}
- size_t size() const { return 0; }
- void reset( const bool& flag = false ){};
+ void prepare(){};
+ void setEvents( AmpGen::EventList& /*evts*/ ){};
+ double prob_unnormalised( const AmpGen::Event& evt ) const { return m_fcn(evt); }
+ explicit PDFWrapper( const FCN& fcn ) : m_fcn(fcn) {}
+ size_t size() const { return 0; }
+ void reset( const bool& /*flag*/ = false ){};
+
+ private:
+ FCN m_fcn;
};
+
+ template <class FCN> PDFWrapper<FCN> make_pdf(const FCN& fcn){ return PDFWrapper<FCN>(fcn) ; }
+
+ /** @function PyGenerate
+
+ Wrapper around the a phase space generator from a stringy event type to be used with python / numpy.
+ */
extern "C" void PyGenerate( const char* eventType, double* out, const unsigned int size );
} // namespace AmpGen
#endif
diff --git a/AmpGen/IncoherentSum.h b/AmpGen/IncoherentSum.h
index c4c32bb6b16..589c6760057 100644
--- a/AmpGen/IncoherentSum.h
+++ b/AmpGen/IncoherentSum.h
@@ -1,5 +1,5 @@
-#ifndef AMPGEN_FASTINCOHERENTSUM_H
-#define AMPGEN_FASTINCOHERENTSUM_H
+#ifndef AMPGEN_INCOHERENTSUM_H
+#define AMPGEN_INCOHERENTSUM_H
#include <complex>
#include <iomanip>
@@ -19,22 +19,47 @@ namespace AmpGen
class FitFraction;
class LinearErrorPropagator;
class MinuitParameterSet;
-
+
+ /** @class IncoherentSum
+ @brief An incoherent sum of resonances, traditionally considered as an approximate background model.
+ An incoherent sum of resonant contributions, where at a positiion in phase-space @f$\psi@f$,
+ the (unnormalised) probability density is given by
+ @f[
+ \mathcal{P}(\psi) = \sum_{i} \left| g_i \mathcal{A}_i(\psi) \right|^2,
+ @f]
+ where @f$\mathcal{P}(\psi)@f$ is the probability, @f$g_i@f$ is the coupling to an isobar channel,
+ and @f$\mathcal{A}_i(\psi)@f$ is the amplitude of the ith channel.
+ I dont know whats going on?
+ */
class IncoherentSum : public CoherentSum
{
public:
- IncoherentSum( const EventType& finalStates, const AmpGen::MinuitParameterSet& mps, const std::string& prefix = "Inco" );
+ /** Constructs an incoherentSum from the type of event this is expected to describe,
+ and a set of parameters that are expected to be able to describe it.
+ @param eventType The type of event that this PDF should describe
+ @param mps The parameter set of couplings, masses, etc.
+ @param prefix Prefix required for the ``head'' decays for this event type. */
+ IncoherentSum(const EventType& eventType, const AmpGen::MinuitParameterSet& mps, const std::string& prefix = "Inco");
+
+ /// Evaluates the normalised probability for an event.
+ real_t prob( const Event& evt ) const;
+ real_t operator()(const Event& evt) const { return prob(evt) ; }
- double getVal( const Event& evt ) const;
- double operator()( const Event& evt ) const;
- double prob( const Event& evt ) const;
- double prob_unnormalised( const Event& evt ) const;
- void prepare();
- double norm() const;
+ /// Calculates the unnormalised probability for an event.
+ real_t prob_unnormalised( const Event& evt ) const;
+
+ /** Returns the normalisation for this PDF, given by
+ @f[
+ \mathcal{N} = \int d\psi \varepsilon(\psi) \mathcal{P}(\psi) \approx \sum_i \frac{\mathcal{P}(\psi_i)}{\mathcal{P}^\prime(\psi_i)}
+ @f]
+ where the sum is over a simulated sample, generated with PDF @f$\mathcal{P}^\prime(\psi)@f$. */
+ real_t norm() const;
complex_t norm(const size_t& i, const size_t& j){ return i==j ? m_normalisations.get(i, 0) : 0; }
complex_t norm(const size_t& i) { return m_normalisations.get(i, 0); }
- double norm( const Bilinears& norms ) const;
+ real_t norm( const Bilinears& norms ) const;
std::vector<FitFraction> fitFractions( const LinearErrorPropagator& linProp );
+
+ void prepare();
};
} // namespace AmpGen
diff --git a/AmpGen/Integrator.h b/AmpGen/Integrator.h
index b9e4f5b024e..df48b7a763d 100644
--- a/AmpGen/Integrator.h
+++ b/AmpGen/Integrator.h
@@ -5,15 +5,74 @@
#include "AmpGen/EventList.h"
#include <array>
#include <complex>
-
-/*
- * Calculates Bilinears A_i A_j^* integrated over the phase-space.
- * Integrates in blocks of (i,j) such that integrals can be queued and evaluated in blocks
- * to optimise cache throughput.
- */
+#include "AmpGen/simd/utils.h"
+#include "AmpGen/Store.h"
+#include "AmpGen/EventListSIMD.h"
+#include "AmpGen/EventList.h"
namespace AmpGen
-{
+{
+ class Integrator
+ {
+ struct QueuedIntegral
+ {
+ QueuedIntegral() = default;
+ QueuedIntegral(complex_t* result, const unsigned& i, const unsigned& j)
+ : result(result), i(i), j(j) {}
+ complex_t* result = {nullptr};
+ unsigned i = {0};
+ unsigned j = {0};
+ };
+ public:
+ Integrator() = default;
+
+ template <typename EventList_type, typename T> Integrator( const EventList_type* events, const std::vector<T>& expressions ={}, const size_t& size_of =0) : m_events(events)
+ {
+ if( events == nullptr ) {
+ WARNING("No events specified, returning");
+ return;
+ }
+ m_cache = Store<complex_v, Alignment::SoA>(events->size(), expressions);
+ m_weight.resize( events->nBlocks() );
+ float_v norm_acc = 0.;
+ for( size_t i = 0 ; i < events->nBlocks(); ++i )
+ {
+ m_weight[i] = events->weight(i) / events->genPDF(i);
+ norm_acc += m_weight[i];
+ }
+ m_norm = utils::sum_elements(norm_acc);
+ }
+
+ bool isReady() const;
+ void queueIntegral( complex_t* result, const unsigned& i, const unsigned& j );
+ void flush();
+
+ template <class return_type> return_type get( const unsigned& index, const unsigned& evt ) const ;
+ template <class T> unsigned getCacheIndex( const T& t ) const { return m_cache.find(t) ; }
+ double norm() const { return m_norm; }
+
+ template <class T> void updateCache(const T& expression)
+ {
+ #if ENABLE_AVX
+ if( m_events != nullptr ) m_cache.update( static_cast<const EventListSIMD*>(m_events)->store(), expression );
+ #else
+ if( m_events != nullptr ) m_cache.update( static_cast<const EventList*>(m_events)->store(), expression );
+ #endif
+ }
+ template <class T> const T* events() const { return static_cast<const T*>(m_events) ; }
+
+ const Store<complex_v, Alignment::SoA>& cache() const { return m_cache; }
+ private:
+ static constexpr size_t N = {8}; ///unroll factor
+ size_t m_counter = {0}; ///
+ std::array<QueuedIntegral, N> m_integrals;
+ const void* m_events = {nullptr};
+ std::vector<float_v> m_weight;
+ Store<complex_v, Alignment::SoA> m_cache;
+ double m_norm = {0};
+ void integrateBlock();
+ };
+
class Bilinears
{
private:
@@ -25,9 +84,8 @@ namespace AmpGen
public:
Bilinears( const size_t& r = 0, const size_t& c = 0 );
complex_t get(const size_t& x, const size_t& y) const;
- template <class T>
- complex_t get(const size_t& x, const size_t& y, T* integ = nullptr, const size_t& kx=0, const size_t& ky=0){
- if( integ != nullptr ) integ->queueIntegral(kx, ky, &norms[x*cols+y]);
+ complex_t get(const size_t& x, const size_t& y, Integrator* integ = nullptr, const size_t& kx=0, const size_t& ky=0){
+ if( integ != nullptr ) integ->queueIntegral(&norms[x*cols+y], kx, ky );
/// will return the wrong answer for now, but queues for later..
return norms[x*cols+y];
}
@@ -40,232 +98,5 @@ namespace AmpGen
void resize(const size_t& r, const size_t& c = 1 );
};
- template <class TYPE = complex_t>
- struct Integral {
- typedef std::function<void(TYPE)> TransferFCN;
- size_t i = {0};
- size_t j = {0};
- TransferFCN transfer;
- Integral() = default;
- Integral(const size_t& i, const size_t& j, TransferFCN t) : i(i), j(j), transfer(t) {}
- };
-
- template <size_t NROLL = 10>
- class Integrator
- {
- private:
- typedef const complex_t& arg;
- typedef std::function<void(arg)> TransferFCN;
- size_t m_counter = {0};
- std::array<Integral<arg>, NROLL> m_integrals;
- EventList* m_events = {nullptr};
- void calculate()
- {
- integrateBlock();
- m_counter = 0;
- }
- void integrateBlock()
- {
- real_t re[NROLL] = {0};
- real_t im[NROLL] = {0};
- #pragma omp parallel for reduction( +: re, im )
- for ( size_t i = 0; i < m_events->size(); ++i ) {
- auto& evt = ( *m_events )[i];
- real_t w = evt.weight() / evt.genPdf();
- for ( size_t roll = 0; roll < NROLL; ++roll ) {
- auto c = evt.getCache(m_integrals[roll].i) * std::conj(evt.getCache(m_integrals[roll].j));
- re[roll] += w * std::real(c);
- im[roll] += w * std::imag(c);
- }
- }
- real_t nv = m_events->norm();
- for ( size_t j = 0; j < m_counter; ++j )
- m_integrals[j].transfer( complex_t( re[j], im[j] ) / nv );
- }
- public:
- Integrator( EventList* events = nullptr ) : m_events( events ){}
-
- double sampleNorm() { return m_events->norm(); }
- bool isReady() const { return m_events != nullptr ; }
- const EventList& events() const { return *m_events ; }
- template <class T1, class T2>
- void addIntegral( const T1& f1, const T2& f2, const TransferFCN& tFunc )
- {
- addIntegralKeyed( m_events->getCacheIndex(f1), m_events->getCacheIndex(f2), tFunc );
- }
- void queueIntegral(const size_t& i, const size_t& j, complex_t* result){
- addIntegralKeyed(i, j, [result](arg& val){ *result = val ; } );
- }
- void queueIntegral(const size_t& c1,
- const size_t& c2,
- const size_t& i,
- const size_t& j,
- Bilinears* out,
- const bool& sim = true )
- {
- if( out->workToDo(i,j) ){
- if( sim )
- addIntegralKeyed( c1, c2, [out,i,j]( arg& val ){
- out->set(i,j,val);
- if( i != j ) out->set(j,i, std::conj(val) ); } );
- else
- addIntegralKeyed( c1, c2, [out,i,j]( arg& val ){ out->set(i,j,val); } );
- }
- }
- void addIntegralKeyed( const size_t& c1, const size_t& c2, const TransferFCN& tFunc )
- {
- m_integrals[m_counter++] = Integral<arg>(c1,c2,tFunc);
- if ( m_counter == NROLL ) calculate();
- }
-
- void flush()
- {
- if ( m_counter == 0 ) return;
- calculate();
- }
- template <class EXPRESSION>
- void prepareExpression( const EXPRESSION& expression, const size_t& size_of = 0 )
- {
- if( m_events == nullptr ) return;
- auto index = m_events->registerExpression( expression , size_of );
- m_events->updateCache( expression, index );
- }
- };
-
- template <size_t NBINS = 100, size_t NROLL = 10>
- class BinnedIntegrator
- {
- private:
- typedef const std::vector<std::complex<double>>& arg;
- typedef std::function<void( arg )> TransferFCN;
-
- size_t m_counter = {0};
- std::vector<unsigned int> m_view = {0};
- std::vector<size_t> m_slice = {0};
- std::array<Integral<arg>, NROLL> m_integrals;
- EventList* m_events = {nullptr};
- void calculate()
- {
- integrateBlock();
- m_counter = 0;
- }
- void integrateBlock()
- {
- double re[( NBINS + 1 ) * NROLL] = {0};
- double im[( NBINS + 1 ) * NROLL] = {0};
- auto ij = [&]( const Event& evt, const unsigned int& i, const unsigned int& j ) {
- return evt.getCache( i ) * std::conj( evt.getCache( j ) );
- };
- if ( m_slice.size() == 0 ) {
- #pragma omp parallel for reduction( + : re, im )
- for ( unsigned int i = 0; i < m_events->size(); ++i ) {
- auto& evt = ( *m_events )[i];
- size_t binNo = m_view[i];
- double w = evt.weight() / evt.genPdf();
- for ( unsigned int roll = 0; roll < NROLL; ++roll ) {
- auto c = ij( evt, m_integrals[roll].i, m_integrals[roll].j );
- DEBUG( "pos = " << roll * NBINS + binNo << " val = " << w * c );
- re[roll * NBINS + binNo] += w * std::real( c );
- im[roll * NBINS + binNo] += w * std::imag( c );
- }
- }
- } else {
- #pragma omp parallel for reduction( + : re, im )
- for ( unsigned int i = 0; i < m_slice.size(); ++i ) {
- auto& evt = ( *m_events )[m_slice[i]];
- size_t binNo = m_view[i];
- double w = evt.weight() / evt.genPdf();
- for ( unsigned int roll = 0; roll < NROLL; ++roll ) {
- auto c = ij( evt, m_integrals[roll].i, m_integrals[roll].j );
- re[roll * NBINS + binNo] += w * std::real( c );
- im[roll * NBINS + binNo] += w * std::imag( c );
- }
- }
- }
- double nv = m_events->norm();
- for ( size_t thisIntegral = 0; thisIntegral < m_counter; ++thisIntegral ) {
- std::vector<std::complex<double>> tmpBins( NBINS );
- size_t offset = thisIntegral * NBINS;
- for ( size_t nBin = 0; nBin < NBINS; ++nBin )
- tmpBins[nBin] = std::complex<double>( re[offset + nBin], im[offset + nBin] ) / nv;
- m_integrals[thisIntegral].transfer( tmpBins );
- }
- }
- public:
- BinnedIntegrator( EventList* events = nullptr ) : m_events( events ) {}
- void setView( const std::function<size_t( const Event& )>& binNumber )
- {
- if ( m_slice.size() == 0 ) {
- if ( m_view.size() != m_events->size() ) m_view.resize( m_events->size() );
- for ( unsigned int i = 0; i < m_events->size(); ++i ) {
-
- m_view[i] = binNumber( ( *m_events )[i] );
-
- if ( m_view[i] >= NBINS ) {
- m_view[i] = NBINS;
- WARNING( "Event " << m_slice[i] << " bin number = " << m_view[i] << " is out of range!" );
- }
- }
- } else {
- if ( m_view.size() != m_slice.size() ) m_view.resize( m_slice.size() );
- for ( unsigned int i = 0; i < m_slice.size(); ++i ) {
- m_view[i] = binNumber( ( *m_events )[m_slice[i]] );
- if ( m_view[i] >= NBINS ) {
- m_view[i] = NBINS;
- WARNING( "Event " << m_slice[i] << " bin number = " << m_view[i] << " is out of range!" );
- }
- }
- }
- }
- void setSlice( const std::function<bool( const Event& )>& sliceFunction )
- {
- if ( m_slice.size() != 0 ) m_slice.clear();
- for ( unsigned int i = 0; i < m_events->size(); ++i )
- if ( sliceFunction( ( *m_events )[i] ) ) m_slice.push_back( i );
- }
-
- template <class T1, class T2>
- void addIntegral( const T1& f1, const T2& f2, const TransferFCN& tFunc )
- {
- m_integrals[m_counter++] = Integral<arg>( m_events->getCacheIndex( f1 ), m_events->getCacheIndex( f2 ), tFunc );
- if ( m_counter == NROLL ) calculate();
- }
- void flush()
- {
- if ( m_counter == 0 ) return;
- calculate();
- }
- template <class FCN>
- void update( FCN& fcn, std::array<Bilinears, NBINS>& normalisations )
- {
- auto mE = fcn.matrixElements();
- auto size = mE.size();
- std::vector<size_t> toUpdate;
- std::vector<size_t> integralHasChanged( size * size );
- for ( size_t x = 0; x < size; ++x ) {
- auto& pdf = mE[x].pdf;
- pdf.prepare();
- if ( !pdf.hasExternalsChanged() ) continue;
- m_events->updateCache( pdf, m_events->getCacheIndex( pdf ) );
- toUpdate.push_back( x );
- }
- for ( auto& i : toUpdate ) {
- DEBUG( "Updating: " << mE[i].decayTree->uniqueString() );
- for ( unsigned int j = 0; j < size; ++j ) {
- if ( integralHasChanged[i * size + j] ) continue;
- integralHasChanged[i * size + j] = true;
- integralHasChanged[j * size + i] = true;
-
- addIntegral( mE[i].pdf, mE[j].pdf,
- [i, j, &normalisations]( const auto& val ) {
- for ( unsigned int bin = 0; bin < NBINS; ++bin ) {
- normalisations[bin].set( i, j, val[bin] );
- if ( i != j ) normalisations[bin].set( j, i, std::conj( val[bin] ) );
- }
- } );
- }
- }
- }
- };
} // namespace AmpGen
#endif
diff --git a/AmpGen/KeyedFunctors.h b/AmpGen/KeyedFunctors.h
new file mode 100644
index 00000000000..c1c9fa7654a
--- /dev/null
+++ b/AmpGen/KeyedFunctors.h
@@ -0,0 +1,31 @@
+#ifndef AMPGEN_LITESPAN_H
+#define AMPGEN_LITESPAN_H
+
+#include "AmpGen/MsgService.h"
+#include "AmpGen/Utilities.h"
+
+namespace AmpGen {
+ template <typename return_type, typename ...arg_types> struct KeyedFunctors;
+
+ template <typename return_type, typename ...arg_types> struct KeyedFunctors <return_type(arg_types...)>
+ {
+ std::vector<std::function<return_type(arg_types...)> > functors;
+ std::vector<std::string> keys;
+ std::vector<std::string> titles;
+ template <typename functor_type> void add(const functor_type& functor, const std::string& key, const std::string& title="")
+ {
+ functors.push_back(functor);
+ keys.push_back(key);
+ titles.push_back(title);
+ }
+ std::vector<return_type> operator()( arg_types... arg ) const
+ {
+ std::vector<return_type> rt;
+ for( auto& f : functors ) rt.push_back( f(arg...) );
+ return rt;
+ }
+ };
+
+}
+
+#endif
diff --git a/AmpGen/Kinematics.h b/AmpGen/Kinematics.h
index 6385fe8230e..a86ebb8e6e4 100644
--- a/AmpGen/Kinematics.h
+++ b/AmpGen/Kinematics.h
@@ -23,15 +23,15 @@ namespace AmpGen
*/
class HelicityCosine {
public:
- HelicityCosine(const std::vector<size_t>& p1, const std::vector<size_t>& p2,
- const std::vector<size_t>& pR);
+ HelicityCosine(const std::vector<unsigned>& p1, const std::vector<unsigned>& p2,
+ const std::vector<unsigned>& pR);
- HelicityCosine(const size_t& i, const size_t& j, const std::vector<size_t>& pR);
+ HelicityCosine(const unsigned& i, const unsigned& j, const std::vector<unsigned>& pR);
double operator()( std::vector<Event>::iterator evt ) const;
double operator()( const Event& evt ) const;
private:
- std::vector<size_t> _i, _j, _pR;
+ std::vector<unsigned> _i, _j, _pR;
};
/** @ingroup Kin class MomentumTransfer
@@ -39,13 +39,13 @@ namespace AmpGen
*/
class MomentumTransfer {
public:
- MomentumTransfer( const std::vector<size_t>& _p1, const std::vector<size_t>& _p2 );
+ MomentumTransfer( const std::vector<unsigned>& _p1, const std::vector<unsigned>& _p2 );
double operator()( const Event& evt ) const;
private:
double Q2( const double& s, const double& s1, const double& s2 ) const;
- std::vector<size_t> p1;
- std::vector<size_t> p2;
- std::vector<size_t> s;
+ std::vector<unsigned> p1;
+ std::vector<unsigned> p2;
+ std::vector<unsigned> s;
};
/** @ingroup Kin function acoplanarity
@@ -79,12 +79,12 @@ namespace AmpGen
/** @ingroup Kin function pFromEvent
@brief Helper function to extract a TLorentzVector of the ith decay product from an AmpGen::Event.
*/
- TLorentzVector pFromEvent( const Event& evt, const size_t& ref );
+ TLorentzVector pFromEvent( const Event& evt, const unsigned& ref );
/** @ingroup Kin function pFromEvent
@brief Helper function to extract a TLorentzVector of the sum of {2} decay product from an AmpGen::Event.
*/
- TLorentzVector pFromEvent( const Event& evt, const std::vector<size_t>& ref );
+ TLorentzVector pFromEvent( const Event& evt, const std::vector<unsigned>& ref );
} // namespace AmpGen
#endif
diff --git a/AmpGen/Lineshapes.h b/AmpGen/Lineshapes.h
index 9d4648251ce..9c36c384e74 100644
--- a/AmpGen/Lineshapes.h
+++ b/AmpGen/Lineshapes.h
@@ -10,6 +10,8 @@
#include "AmpGen/Factory.h"
#include "AmpGen/MsgService.h"
#include "AmpGen/Tensor.h"
+#include "AmpGen/Particle.h"
+
/**
@defgroup Lineshapes Lineshapes
@brief Lineshapes are semi-empirical complex functions for describing the propagation and decay of short-lived resonances.
@@ -39,7 +41,7 @@
*/
#define DECLARE_LINESHAPE( X ) \
- class X : public AmpGen::ILineshape { \
+ class X : public AmpGen::Lineshape::Base { \
static std::string _id; \
public: \
X(){ DEBUG("Constructing lineshape") ;} \
@@ -47,50 +49,36 @@
const AmpGen::Expression& s2, const std::string& particleName, \
const unsigned int& L, const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions = 0) const override; \
- AmpGen::Expression get(const AmpGen::Expression& s, const std::vector<AmpGen::Tensor>& p, \
- const std::string& particleName, \
- const unsigned int& L, const std::string& lineshapeModifier, \
+ AmpGen::Expression get(const AmpGen::Particle& p, \
+ const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions = nullptr ) const override; \
}
#define DEFINE_LINESHAPE( X ) \
- REGISTER_WITH_KEY( ILineshape, Lineshape::X, #X, std::string ); \
- AmpGen::Expression Lineshape::X::get( const AmpGen::Expression& s, const std::vector<AmpGen::Tensor>& p, \
- const std::string& particleName, \
- const unsigned int& L, const std::string& lineshapeModifier, \
+ REGISTER_WITH_KEY( Lineshape::Base, Lineshape::X, #X, std::string ); \
+ AmpGen::Expression Lineshape::X::get( const AmpGen::Particle& p, \
+ const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions ) const { return \
- get(s, dot(p[0],p[0]), dot(p[1],p[1]), \
- particleName, L, lineshapeModifier, dbexpressions) ;} \
+ get(p.massSq(), p.daughter(0)->massSq(), p.daughter(1)->massSq(), \
+ p.name(), p.L(), lineshapeModifier, dbexpressions) ;} \
AmpGen::Expression Lineshape::X::get( const AmpGen::Expression& s, const AmpGen::Expression& s1, \
const AmpGen::Expression& s2, const std::string& particleName, \
const unsigned int& L, const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions ) const
#define DEFINE_GENERIC_SHAPE( X ) \
- REGISTER_WITH_KEY( ILineshape, Lineshape::X, #X, std::string ); \
+ REGISTER_WITH_KEY( Lineshape::Base, Lineshape::X, #X, std::string ); \
AmpGen::Expression Lineshape::X::get( const AmpGen::Expression& s, const AmpGen::Expression& s1, \
const AmpGen::Expression& s2, const std::string& particleName, \
const unsigned int& L, const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions ) const { return 0;} \
- AmpGen::Expression Lineshape::X::get( const AmpGen::Expression& s, const std::vector<AmpGen::Tensor>& p, \
- const std::string& particleName, \
- const unsigned int& L, const std::string& lineshapeModifier, \
+ AmpGen::Expression Lineshape::X::get( const AmpGen::Particle& p, \
+ const std::string& lineshapeModifier, \
AmpGen::DebugSymbols* dbexpressions ) const
namespace AmpGen
{
- class ILineshape {
- public:
- virtual ~ILineshape() = default;
- virtual Expression get( const Expression& s, const Expression& s1, const Expression& s2,
- const std::string& particleName, const unsigned int& L,
- const std::string& lineshapeModifier, DebugSymbols* dbexpressions = nullptr ) const = 0;
-
- virtual Expression get( const Expression& s, const std::vector<AmpGen::Tensor>& p, const std::string& particleName,
- const unsigned int& L, const std::string& lineshapeModifier,
- AmpGen::DebugSymbols* dbexpressions = nullptr ) const = 0;
- ILineshape* create() { return this; }
- };
+ class Particle; // forward definitions
/** @ingroup Lineshapes namespace Lineshape
Namespace that contains all lineshapes, i.e. propagators for describing amplitudes and phases for resonances (and nonresonant) contributions to a total amplitude.
@@ -98,16 +86,27 @@ namespace AmpGen
namespace Lineshape
{
- class Factory : public AmpGen::Factory<ILineshape>
+ class Base {
+ public:
+ virtual ~Base() = default;
+ virtual Expression get( const Expression& s, const Expression& s1, const Expression& s2,
+ const std::string& particleName, const unsigned& L,
+ const std::string& lineshapeModifier, DebugSymbols* dbexpressions = nullptr ) const = 0;
+ virtual Expression get( const AmpGen::Particle& p,
+ const std::string& lineshapeModifier,
+ AmpGen::DebugSymbols* dbexpressions = nullptr ) const = 0;
+ Base* create() { return this; }
+ };
+
+ class Factory : public AmpGen::Factory<Lineshape::Base>
{
public:
static Expression get(const std::string& lineshape, const Expression& s, const Expression& s1,
- const Expression& s2, const std::string& particleName, const unsigned int& L,
+ const Expression& s2, const std::string& particleName, const unsigned& L,
std::vector<std::pair<std::string, Expression>>* dbexpressions = nullptr );
static Expression get(const std::string& lineshape,
- const Expression& s,
- const std::vector<Tensor>& p, const std::string& particleName,
- const unsigned int& L, AmpGen::DebugSymbols* dbexpressions );
+ const Particle& p,
+ AmpGen::DebugSymbols* dbexpressions );
static bool isLineshape( const std::string& lineshape );
};
@@ -134,7 +133,7 @@ namespace AmpGen
@f$r@f$ | <EM>particleName_</EM>radius | Hadronic radius for Blatt-Weisskopf form-factor (defaults to 1.5GeV for light resonances, 3.5GeV for charm)
<EM> BL </EM> : Use Blatt-Weisskopf factors normalised at @f$ \sqrt{s}=m @f$ (by default, normalised at @f$\sqrt{s}=0@f$)
- \image html BW_combined.png "Modulus and phase of the Relativistic Breit-Wigner propagator, for @f$l={0,4}@f$, using the mass and nominal width of the @f$\rho@f$ meson"
+ \image html BW_combined.png "Modulus and phase of the Relativistic Breit-Wigner propagator, for orbital momentum up-to four, using the mass and nominal width of the rho meson."
*/
DECLARE_LINESHAPE( BW );
@@ -152,7 +151,16 @@ namespace AmpGen
@f$\Gamma_0@f$ | <EM>particleName_</EM>width | Breit-Wigner width, defined as the width of resonance at the Breit-Wigner mass
*/
DECLARE_LINESHAPE( SBW );
- /// Non-relativistic Breit-Wigner lineshape
+
+ /** @ingroup Lineshapes class NonRelBW
+ @brief Nonrelativistic Breit-Wigner lineshape
+
+ Non-relativistic Breit-Wigner lineshape, given by
+
+ @f[
+ \mathcal{A}(s) = \sqrt{ \frac{ \Gamma_0 }{ 2 \pi } } \left( \sqrt{s} - m_0 - i \Gamma_0 /2 \right)^{-1}
+ @f]
+ */
DECLARE_LINESHAPE( NonRelBW );
/** @ingroup Lineshapes class GounarisSakurai
@@ -180,8 +188,90 @@ namespace AmpGen
*/
DECLARE_LINESHAPE( GounarisSakurai );
- /// Description of the \f$ K\pi \f$ S-wave, based on the fits to scattering data.
+ /** @ingroup Lineshapes class LASS
+ @brief Description of the @f$ K\pi @f$ S-wave, based on the fits to scattering data.
+ The LASS parameterisation of the @f$ K\pi @f$ S-wave is derived from fits to ~ elastic @f$ K \pi @f$ scattering data, which is approximately up to the @f$ K \eta^\prime @f$ threshold.
+ In this regime, unitarity implies that phases, rather than amplitudes should be summed.
+ In this context, a slow varying nonresonant phase,
+ @f[
+ \tan(\phi_{NR}) = \frac{2 a q}{2 + arq^2},
+ @f]
+ where @f$a, r@f$ are parameters determined from scattering data, is added to the phase shift of a Breit-Wigner,
+ @f[
+ \tan(\phi_{BW}) = \frac{m\Gamma(s)}{m^2 -s },
+ @f]
+ normally associated to the @f$ K^*(1430)^{0} @f$ resonance.
+ The total amplitude is therefore:
+ @f[
+ \mathcal{A}(s) = \frac{2 a \sqrt{s} }{ 2 + arq^2 - 2iaq} + \frac{2+arq^2 + 2iaq}{2+arq^2 - 2iaq }\mathcal{A}_{BW}(s) = \mathcal{A}_{NR}(s) + \mathcal{A}^{\prime}_{BW}(s).
+ @f]
+ As this expression somewhat resembles the sum of a Breit-Wigner with a slowly varying nonresonant component, the two parts are sometimes split apart with an additional production amplitude placed on one or the other.
+ These can be accessed separately using the modifiers LASS.BW and LASS.NR, and given independent coupling constants. From the user interface:
+ \code{.cpp}
+ K*(1430)bar0[LASS.NR]{K-,pi+} 0 2.0 0.1 0 -90 0.1
+ K*(1430)bar0[LASS.BW]{K-,pi+} 0 1.5 0.1 0 20 0.1
+ \endcode
+ Corresponds to the overall lineshape:
+ @f[
+ \mathcal{A}(s)
+ = \left(\texttt{K*(1430)bar0[LASS.NR]{K-,pi+}}\right) \mathcal{A}_{NR}(s) +
+ \left(\texttt{K*(1430)bar0[LASS.BW]{K-,pi+}}\right) \mathcal{A}^{\prime}_{BW}(s)
+ = 2.0 e^{-90^\mathrm{o}} \mathcal{A}_{NR}(s) + 1.5 e^{-20^\mathrm{o}} \mathcal{A}^{\prime}_{BW}(s).
+ @f]
+ An alternative way to introduce a different coupling between the two components is to fix one coupling and to introduce an additional production coupling.
+ In the user interface, this might for example in @f$ D^{0} \to K^{-} \pi^{+} \pi^{0} @f$ decays:
+ \code{.cpp}
+ D0{K*(1430)bar0,pi0} 0 1.3 0.0 0 15 0.1
+ K*(1430)bar0[LASS.NR]{K-,pi+} 0 2.0 0.1 0 -90 0.1
+ K*(1430)bar0[LASS.BW]{K-,pi+} 2 1.0 0.0 0 0 0.0
+ \endcode
+ Then the lineshape with production couplings will be:
+ @f[
+ \mathcal{A}(s)
+ = \left(\texttt{D0{K*(1430)bar0,pi0}}\right)\left(
+ = \left(\texttt{K*(1430)bar0[LASS.NR]{K-,pi+}}\right) \mathcal{A}_{NR}(s) +
+ \mathcal{A}^{\prime}_{BW}(s) \right)
+ = 1.3 e^{15^\mathrm{o}} \left( 2.0 e^{-90^\mathrm{o}} \mathcal{A}_{NR}(s) + \mathcal{A}^{\prime}_{BW}(s) \right).
+ @f]
+
+ Parameter | User name | Description
+ -----------------------|--------------------------------------|------------------------------------------------------------------------
+ @f$m@f$ | <EM>particleName_</EM>mass | Breit-Wigner mass of the resonant component, defined as energy at which the self-energy of the resonance is purely imaginary (defaults to value in PDG) <br>
+ @f$\Gamma_0@f$ | <EM>particleName_</EM>width | Breit-Wigner width of the resonant component, defined as the width of resonance at the Breit-Wigner mass <br>
+ @f$a@f$ | LASS::a | Scattering length of the nonresonant component, defaults to @f$2.07\mathrm{G\kern -0.1em eV}^{-1}@f$
+ @f$r@f$ | LASS::r | Effective interaction length of the nonresonant component, defaults to @f$3.32\mathrm{G\kern -0.1em eV}^{-1}@f$
+ */
DECLARE_LINESHAPE( LASS );
+ /** @ingroup Lineshapes class GLASS
+ @brief Generalised description of the @f$ K\pi@f$ S-wave, taken from BABAR / BELLE analysis of @f$ D^{0} \to K_{S}^{0} \pi^{+} \pi^{-} @f$ https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.112012
+
+ Alternative parameterisation of the @f$ K \pi @f$ S-wave taken from the BABAR/BELLE analysis of @f$ D^{0} \to K_{S}^{0} \pi^{+} \pi^{-} @f$ https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.112012.
+ It introduces four additional parameters, two amplitudes and two phases, and is written
+ @f[
+ \mathcal{A}(s) = R\sin\delta_R e^{i(\delta_R + 2\delta_F)} + F\sin\delta_F e^{i\delta_F}
+ @f]
+ where
+ @f[
+ \delta_R = \phi_R + \tan^{-1}\left(\frac{m\Gamma(s)}{m^2 -s }\right)
+ @f]
+ and
+ @f[
+ \delta_F = \phi_F + \tan^{-1}\left(\frac{2 a q}{2 + arq^2}\right),
+ @f]
+ that is, the 'resonant' and 'nonresonant' phases of the LASS formulation with additional 'proudction' phases @f$ \phi_R @f$ and @f$\phi_F @f$, and production couplings @f$R, F@f$. One of the production couplings can typically be fixed to 1, normally the resonant coupling, @f$R @f$.
+
+ Parameter | Interface parameter name | Description
+ -----------------------|--------------------------------------|------------------------------------------------------------------------
+ @f$m@f$ | <EM>particleName_</EM>mass | Breit-Wigner mass of the resonant component, defined as energy at which the self-energy of the resonance is purely imaginary (defaults to value in PDG) <br>
+ @f$\Gamma_0@f$ | <EM>particleName_</EM>width | Breit-Wigner width of the resonant component, defined as the width of resonance at the Breit-Wigner mass <br>
+ @f$a@f$ | <EM>particleName</EM>::GLASS::a | Scattering length of the nonresonant component, defaults to @f$2.07\mathrm{G\kern -0.1em eV}^{-1}@f$
+ @f$r@f$ | <EM>particleName</EM>::GLASS::r | Effective interaction length of the nonresonant component, defaults to @f$3.32\mathrm{G\kern -0.1em eV}^{-1}@f$
+ @f$\phi_R@f$ | <EM>particleName</EM>::GLASS::phiR | Additional production phase of the resonant component, defaults to @f$0^{\mathrm{o}}@f$, measured in degrees.
+ @f$\phi_F@f$ | <EM>particleName</EM>::GLASS::phiF | Additional production phase of the nonresonant component, defaults to @f$0^{\mathrm{o}}@f$, measured in degrees.
+ @f$R@f$ | <EM>particleName</EM>::GLASS::R | Additional production coupling of the resonant component, defaults to @f$1@f$.
+ @f$F@f$ | <EM>particleName</EM>::GLASS::F | Additional production coupling of the nonresonant component, defaults to @f$1@f$.
+ */
+ DECLARE_LINESHAPE(GLASS);
/** @ingroup Lineshapes class Flatte
@brief Lineshape to describe resonances with coupled channels such as @f$f_{0}(980)^{0} / a_{0}(980) @f$.
@@ -195,11 +285,11 @@ namespace AmpGen
@f]
where the running width is given by
@f[
- \Gamma(s) = g_{\pi\pi} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\pi}^2) + \frac{g_{KK}}{g_{\pi\pi}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right)
+ \Gamma(s) = \frac{ g_{\pi\pi} }{s} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\pi}^2) + \frac{g_{KK}}{g_{\pi\pi}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right)
@f]
or
@f[
- \Gamma(s) = g_{\pi\eta} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\eta}^2) + \frac{g_{KK}}{g_{\pi\eta}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right)
+ \Gamma(s) = \frac{ g_{\pi\eta}}{s} \left( \Lambda^{1/2}(s,m_{\pi}^2,m_{\eta}^2) + \frac{g_{KK}}{g_{\pi\eta}} \Lambda^{1/2}(s,m_K^2, m_K^2) \right)
@f]
for the @f$f_0(980)^{0}@f$ and the @f$a_0(980)^{0}@f$, respectively.
@@ -215,14 +305,14 @@ namespace AmpGen
/** @ingroup Lineshapes class Gaussian
@brief Gaussian shape for (relatively) long lived states that are limited by experimental resolution, rather than natural width.
- @detail The gaussian lineshape has the form
+ The gaussian lineshape has the form
@f[
\mathcal{A}(s) = e^{ -(s-\mu)^2 / 2\sigma^2 },
@f]
which is potentially useful for fitting very long-lived contributions that are essentially limited by the experimental resolution,
rather than the natural lifetime. This type of parameterisation will assess contributions from interference incorrectly.
- Parameter | User name | Description
+ Parameter | Interface parameter name | Description
-----------------------|--------------------------------------|------------------------------------------------------------------------
@f$\mu@f$ | <EM>lineshapeModifier</EM>_mean | Mean of the gaussian distribution.
@f$\sigma@f$ | <EM>lineshapeModifier</EM>_sigma | Width of the gaussian distribution.
@@ -232,23 +322,13 @@ namespace AmpGen
/** @ingroup Lineshapes class Poly
* @brief Polynominal shape \f$ \mathcal{A}(s) = \sum^n_i c_i s^{i} \f$ where the sum is to lineshapeModifier::Degree, and the free parameters of the shape are lineshapeModifier_ci
*/
+ DECLARE_LINESHAPE( PolyNR );
+
+ /** @ingroup Lineshapes class PolyNR
+ * @brief Polynominal shape \f$ \mathcal{A}(s) = \sqrt{ \sum_{ij} c_{ij} s^{i} (s^\prime)^{j} } \f$ where the sum is to lineshapeModifier::Degree, and the free parameters of the shape are lineshapeModifier_cij
+ */
DECLARE_LINESHAPE( Poly );
- /** @ingroup Lineshapes class kMatrix
- @brief Anisovich-Sarantsev Isoscalar K-matrix from https://arxiv.org/abs/hep-ph/0204328
-
- Describes the isoscalar @f$ \pi\pi, KK, 4\pi \eta\eta, \eta\eta^\prime@f$ S-wave in terms of a five-by-five K-matrix and corresponding P-vector couplings.
- Includes a large number of parameters that can be fixed from the above publication.
- These parameters can be found in the options directory, which in turn can be includes in the fit by adding
-
- \code{cpp}
- Import $AMPGENROOT/options/kMatrix.opt
- \endcode
-
- to the user configuration file.
- */
- DECLARE_LINESHAPE( kMatrix );
-
/** @ingroup Lineshapes class FOCUS
* @brief K matrix amplitudes used for I=1/2 and I=3/2 in the description of the \f$ K\pi \f$ S-wave in the analysis of @f$ D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}@f$ https://arxiv.org/abs/0705.2248
*/
@@ -257,17 +337,6 @@ namespace AmpGen
/// I=1/2 and I=3/2 K Matrices used in the description of the \f$ K\pi\f$ S-wave in the analysis of @f$\eta_{c}\rightarrow K^{+} K^{-} \pi^{0}@f$ https://arxiv.org/abs/1701.04881
DECLARE_LINESHAPE( PALANO );
- /** @ingroup Lineshapes class ObelixRho
- * @brief Amplitude to describe the vector-isovector system, otherwise known as the @f$ \rho @f$ mesons. WARNING untested.
-
- Vector-Isovector amplitude @f$(I=1, J=1)@f$ using a K-matrix to describe the @f$\pi\pi, KK, \pi\pi\pi\pi @f$ channels using three poles, commonly associated with
- the @f$ \rho(770), \rho(1450), \rho(1900) @f$ resonances.
- */
- DECLARE_LINESHAPE( ObelixRho );
-
- /// K matrix to describe \f$K_1(1270) / K_1(1400)\f$. WARNING incompleted.
- DECLARE_LINESHAPE( AxialKaon );
-
/** @ingroup Lineshapes class kMatrixSimple
@brief Simple and flexible K matrix that implements a variable number of scalar channels and poles.
Flexible K matrix implementation that accepts a variable number of scalar channels and pole terms.
@@ -286,7 +355,7 @@ namespace AmpGen
@f]
where @f$a_n@f$ is the value of the function evaluated at the @f$ n @f$ knot and the other polynomial coefficients are determined by imposing continuity and
differentiability.
- Parameter | User name | Description
+ Parameter | Interface parameter name | Description
-----------------------|--------------------------------------|------------------------------------------------------------------------
@f$\mathcal{R}(a_j)@f$ | <EM>particleName</EM>::Spline::Re::j | The real value of the lineshape evaluated at the @f$ j @f$th knot.
@f$\mathcal{I}(a_j)@f$ | <EM>particleName</EM>::Spline::Im::j | The imaginary value of the lineshape evaluated at the @f$ j @f$th knot.
@@ -301,10 +370,6 @@ namespace AmpGen
DECLARE_LINESHAPE( DecaySpline );
DECLARE_LINESHAPE( InelasticSpline );
- /** @ingroup Lineshapes class CoupledChannel
- @brief Description of a resonance that decays to multiple two and three-body final states.
- */
- DECLARE_LINESHAPE( CoupledChannel );
/** @ingroup Lineshapes class GenericKmatrix
@brief Implementation of a generic K-matrix
*/
@@ -323,6 +388,19 @@ namespace AmpGen
*/
DECLARE_LINESHAPE( EtaDalitz );
+ /** @ingroup Lineshapes class TD
+ @brief (Linear) time dependence
+
+ ''Lineshape'' that gives a linear time-dependence for use in time-dependent generation / fitting.
+ @f[
+ \mathcal{A}(t) = \frac{t}{2\tau},
+ @f]
+ where @f$\tau@f$ is the proper decay time.
+
+ */
+ DECLARE_LINESHAPE( TD );
+
+ DECLARE_LINESHAPE( Photon );
} // namespace Lineshape
Expression Q2( const Expression& Msq, const Expression& M1sq, const Expression& M2sq );
@@ -338,11 +416,10 @@ namespace AmpGen
Expression pol( const AmpGen::Expression& X, const std::vector<Expression>& p );
- std::vector<Expression> parameterVector( const std::string& name, const unsigned int& nParam );
+ std::vector<Expression> parameterVector(const std::string& name, const size_t& nParam);
Expression width( const Expression& s, const Expression& s1, const Expression& s2, const Expression& mass,
const Expression& width, const Expression& radius, unsigned int L,
DebugSymbols* dbexpressions = nullptr );
-
} // namespace AmpGen
#endif
diff --git a/AmpGen/MetaUtils.h b/AmpGen/MetaUtils.h
index 4d436d436fb..3c985be4daa 100644
--- a/AmpGen/MetaUtils.h
+++ b/AmpGen/MetaUtils.h
@@ -6,14 +6,16 @@
#include <vector>
#include <string>
#include <cxxabi.h>
+#include <algorithm>
namespace AmpGen
{
- /** Utility classes for (library) compile-level metaprogramming, such as identifying the types of
- * arguments for generating source code, compile-time unrolling of tuples and loops, and identifying if a class can be constructed in different ways.
+ /** Utility classes for compile-time metaprogramming, such as identifying the types of
+ arguments for generating source code, compile-time unrolling of tuples and loops,
+ and identifying if a class can be constructed in different ways.
*/
-
- template <class TYPE> std::string typeof()
+
+ template <class TYPE> std::string type_string()
{
int status = 0;
std::string name = abi::__cxa_demangle( typeid( TYPE ).name(), nullptr, nullptr, &status );
@@ -23,22 +25,40 @@ namespace AmpGen
return name;
}
- template <class TYPE> std::string typeof( TYPE t ) { return typeof<TYPE>(); }
+ template <class TYPE> std::string type_string( const TYPE& t ) { return type_string<TYPE>(); }
+
+ namespace detail {
+ template<typename T, typename... args> struct zeroType { typedef T type; };
+ }
+ template<int N, typename... args> using nthType = typename std::tuple_element<N, std::tuple<args...>>::type;
+
+ template<typename... args> using zeroType = typename detail::zeroType<args...>::type;
template <std::size_t I = 0, typename FuncT, typename... Tp>
- typename std::enable_if<I == sizeof...( Tp ), void>::type
+ typename std::enable_if_t<I == sizeof...( Tp ), void>
for_each( std::tuple<Tp...>&, FuncT ){}
template <std::size_t I = 0, typename FuncT, typename... Tp>
- inline typename std::enable_if < I<sizeof...( Tp ), void>::type for_each( std::tuple<Tp...>& t, FuncT f )
+ inline typename std::enable_if_t< I<sizeof...( Tp ), void> for_each( std::tuple<Tp...>& t, FuncT f )
{
f( std::get<I>( t ) );
for_each<I + 1, FuncT, Tp...>( t, f );
}
+ template <typename iterator, typename... transform_types>
+ void for_each_sequence( iterator begin, iterator end, transform_types... transforms)
+ {
+ for_each( std::tuple<transform_types...>(transforms...), [&](auto& transform){ std::for_each( begin, end, transform ); } );
+ }
+
+ template <std::size_t I = 0, typename FuncT, typename... Tp>
+ typename std::enable_if_t<I == sizeof...( Tp ), void>
+ for_each( const std::tuple<Tp...>&, FuncT ){}
- template <class TYPE> std::shared_ptr<TYPE> makeShared( const TYPE& obj )
+ template <std::size_t I = 0, typename FuncT, typename... Tp>
+ inline typename std::enable_if_t< I<sizeof...( Tp ), void> for_each( const std::tuple<Tp...>& t, FuncT f )
{
- return std::make_shared<TYPE>( obj );
+ f( std::get<I>( t ) );
+ for_each<I + 1, FuncT, Tp...>( t, f );
}
template <typename R,
@@ -69,21 +89,33 @@ namespace AmpGen
{
return std::is_constructible<T,R...>::value && (false == std::is_same<T, R...>::value);
}
+
template <typename arg=void, typename... args> std::vector<std::string> typelist()
{
std::vector< std::string > rt;
- if( typeof<arg>() != "void" ) {
- rt.emplace_back( typeof<arg>() );
+ if( type_string<arg>() != "void" ) {
+ rt.emplace_back( type_string<arg>() );
auto rtp = typelist<args...>();
- for( auto& r : rtp ) rt.emplace_back( r );
+ std::copy( rtp.begin(), rtp.end(), std::back_inserter(rt) );
}
return rt;
}
template <typename> struct isTuple: std::false_type {};
-
template <typename ...T> struct isTuple<std::tuple<T...>>: std::true_type {};
+ template <typename> struct isVector : std::false_type {};
+ template <typename T> struct isVector<std::vector<T>> : std::true_type {};
+
+
+ #define def_has_function(function_name) \
+ template <typename T> \
+ struct has_##function_name { \
+ template<typename U> static auto test(int) -> decltype(std::declval<U>().function_name() == 1, std::true_type()); \
+ template<typename> static std::false_type test(...); \
+ static constexpr bool value = std::is_same<decltype(test<T>(0)), std::true_type>::value; \
+ }
+
} // namespace AmpGen
#endif
diff --git a/AmpGen/Minimiser.h b/AmpGen/Minimiser.h
index 815235b1e28..736380d6588 100644
--- a/AmpGen/Minimiser.h
+++ b/AmpGen/Minimiser.h
@@ -9,15 +9,18 @@
#include <vector>
#include "TMatrixTSym.h"
+#include "AmpGen/MetaUtils.h"
+/** @cond PRIVATE */
namespace ROOT
{
- namespace Math
+ namespace Minuit2
{
- class Minimizer;
+ class Minuit2Minimizer;
}
}
class TGraph;
+/** @endcode */
namespace AmpGen
{
@@ -28,14 +31,24 @@ namespace AmpGen
class Minimiser
{
+ private:
+ def_has_function(getVal);
+
public:
- template <class TYPE>
+ template <typename TYPE> void setFunction( TYPE& fcn )
+ {
+ if constexpr( has_getVal<TYPE>::value ) m_theFunction = [&fcn]() { return fcn.getVal(); };
+ else m_theFunction = fcn;
+ }
+
+ template <typename TYPE>
Minimiser(TYPE& fitFunction, MinuitParameterSet* mps) :
m_parSet(mps)
{
- m_theFunction = [&fitFunction]() { return fitFunction.getVal(); };
+ setFunction(fitFunction);
prepare();
}
+
Minimiser(std::function<double(void)>& fitFunction, MinuitParameterSet* mps) :
m_parSet(mps),
m_theFunction(fitFunction)
@@ -46,11 +59,9 @@ namespace AmpGen
unsigned int nPars() const;
void prepare();
+ void gradientTest();
bool doFit();
- void GradientTest();
-
TGraph* scan( MinuitParameter* param, const double& min, const double& max, const double& step );
-
void addExtendedTerm( IExtendLikelihood* term );
TMatrixTSym<double> covMatrix() const;
TMatrixTSym<double> covMatrixFull() const;
@@ -58,21 +69,19 @@ namespace AmpGen
double FCN() const;
MinuitParameterSet* parSet() const;
int status() const;
- ROOT::Math::Minimizer* minimiserInternal();
-
+ ROOT::Minuit2::Minuit2Minimizer* minimiserInternal();
private:
- void print( const double& LL );
- MinuitParameterSet* m_parSet = {nullptr};
+ MinuitParameterSet* m_parSet = {nullptr};
std::function<double(void)> m_theFunction;
- ROOT::Math::Minimizer* m_minimiser = {nullptr};
- std::vector<double> m_covMatrix = {0};
- std::vector<unsigned int> m_mapping;
+ ROOT::Minuit2::Minuit2Minimizer* m_minimiser = {nullptr};
+ std::vector<double> m_covMatrix = {0};
+ std::vector<unsigned> m_mapping = {};
+ int m_status = {0};
+ unsigned m_nParams = {0};
+ unsigned m_printLevel = {0};
+ double m_ll_zero = {0};
+ bool m_normalise = {false};
std::vector<IExtendLikelihood*> m_extendedTerms;
- int m_status = {0};
- unsigned int m_nParams = {0};
- unsigned int m_lastPrint = {0};
- unsigned int m_printLevel = {0};
-
};
} // namespace AmpGen
#endif
diff --git a/AmpGen/MinuitExpression.h b/AmpGen/MinuitExpression.h
index 377dd01de6d..159abc5e0d8 100644
--- a/AmpGen/MinuitExpression.h
+++ b/AmpGen/MinuitExpression.h
@@ -14,20 +14,16 @@ namespace AmpGen
class MinuitExpression : public MinuitParameter
{
+ public:
+ MinuitExpression(const std::vector<std::string>& tokens, MinuitParameterSet* mps );
+ MinuitExpression(const std::string& name, const Expression& expression);
+ double mean() const override;
+ complex_t getVal() const;
+ Expression expression() const { return m_expression; }
+ operator double() const override;
+ ~MinuitExpression() override;
private:
Expression m_expression;
- bool m_isGood;
-
- public:
- MinuitExpression( const std::vector<std::string>& tokens, MinuitParameterSet* mps );
-
- double getVal() const { return std::real( m_expression() ); }
- operator double() const override { return getVal(); }
-
- ~MinuitExpression() override = default;
-
- double mean() const override { return getVal(); }
- bool isGood() const { return m_isGood; }
};
} // namespace AmpGen
diff --git a/AmpGen/MinuitParameter.h b/AmpGen/MinuitParameter.h
index 0aa2c51d678..7d79369bd0d 100644
--- a/AmpGen/MinuitParameter.h
+++ b/AmpGen/MinuitParameter.h
@@ -5,23 +5,25 @@
#include <iostream>
#include <string>
+#include "AmpGen/enum.h"
namespace AmpGen
{
class MinuitParameterSet;
-
+ declare_enum( Flag, Free, Hide, Fix, CompileTimeConstant)
class MinuitParameter
{
public:
- enum Flag { Float, Hide, Fix, CompileTimeConstant };
-
+
MinuitParameter() = default;
- MinuitParameter(const std::string& name, const Flag& iFixInit, const double& mean, const double& step,
+ MinuitParameter(const std::string& name, const Flag& flag, const double& mean, const double& step,
+ const double& min = 0, const double& max = 0 );
+ MinuitParameter(const std::string& name, const double& mean, const double& step,
const double& min = 0, const double& max = 0 );
- Flag iFixInit() const;
- bool hidden() const;
- bool fixed();
+ Flag flag() const;
+ bool isFixed() const;
+ bool isFree() const;
const std::string& name() const;
double meanInit() const;
@@ -33,7 +35,7 @@ namespace AmpGen
double errNeg() const;
double* vp() { return &m_meanResult ; }
- void setInit( const double& init );
+ void setInit( const double& init, const double& step=-1 );
void setStepInit( const double& si );
void setFree() ;
void scaleStep( const double& sf );
@@ -42,7 +44,6 @@ namespace AmpGen
void setLimits( const double& min, const double& max );
void setResult( double fitMean, double fitErr, double fitErrPos, double fitErrNeg );
void resetToInit();
- void print( std::ostream& os = std::cout ) const;
void setName( const std::string& name );
virtual double mean() const;
virtual operator double() const { return m_meanResult; }
@@ -50,7 +51,7 @@ namespace AmpGen
friend class MinuitParameterSet;
private:
- Flag m_iFixInit;
+ Flag m_flag;
std::string m_name;
double m_meanInit;
double m_stepInit;
@@ -64,18 +65,18 @@ namespace AmpGen
class MinuitProxy
{
- double m_value;
- MinuitParameter* m_parameter;
-
public:
- void update() { m_value = m_parameter->mean(); }
+ void update() { if(m_parameter != nullptr ) m_value = m_parameter->mean(); }
MinuitParameter* ptr() { return m_parameter; }
- operator double() const { return m_parameter->mean(); }
- double getFast() const { return m_value ; }
- MinuitProxy( MinuitParameter* param = nullptr ) : m_parameter( param ) { if( m_parameter != nullptr ) update(); }
+ operator double() const { return m_value; }
+ MinuitProxy(MinuitParameter* param = nullptr, const double& value=0) : m_parameter(param), m_value(value) { update(); }
MinuitParameter* operator->() { return m_parameter; }
const MinuitParameter* operator->() const { return m_parameter; }
+ private:
+ MinuitParameter* m_parameter{nullptr};
+ double m_value;
};
+ std::ostream& operator<<( std::ostream& os, const MinuitParameter& type );
} // namespace AmpGen
#endif
diff --git a/AmpGen/MinuitParameterSet.h b/AmpGen/MinuitParameterSet.h
index 272b556c7fc..13b79a00caf 100644
--- a/AmpGen/MinuitParameterSet.h
+++ b/AmpGen/MinuitParameterSet.h
@@ -17,69 +17,53 @@ namespace AmpGen
class MinuitParameterSet
{
public:
+ typedef std::vector<MinuitParameter*>::iterator iterator;
+ typedef std::vector<MinuitParameter*>::const_iterator const_iterator;
+
MinuitParameterSet();
- MinuitParameterSet( const MinuitParameterSet& other );
- ~MinuitParameterSet();
+ explicit MinuitParameterSet(const std::vector<MinuitParameter*>& params );
- MinuitParameterSet getFloating();
+ MinuitParameterSet( const MinuitParameterSet& other ) = delete;
+ ~MinuitParameterSet(); // = default;
+
+ // MinuitParameterSet getFloating();
bool add( MinuitParameter* parPtr );
- MinuitParameter* add( const std::string& name, const unsigned int& flag, const double& mean, const double& sigma,
- const double& min = 0, const double& max = 0 );
+ MinuitParameter* add(const std::string& name, const Flag& flag, const double& mean, const double& sigma, const double& min = 0, const double& max = 0 );
bool unregister( MinuitParameter* patPtr );
- MinuitParameter* addOrGet( const std::string& name, const unsigned int& flag, const double& mean,
- const double& sigma, const double& min = 0, const double& max = 0 );
+ MinuitParameter* addOrGet(const std::string& name, const Flag& flag, const double& mean,
+ const double& sigma, const double& min = 0, const double& max = 0 );
void loadFromStream();
void loadFromFile( const std::string& name );
void resetToInit();
- unsigned int size() const;
-
- MinuitParameter* getParPtr( unsigned int i ) const;
-
- std::map<std::string, MinuitParameter*>& map() { return _keyAccess; }
- const std::map<std::string, MinuitParameter*>& const_map() const { return _keyAccess; }
- std::vector<MinuitParameter*>::const_iterator cbegin() const { return _parPtrList.cbegin(); }
- std::vector<MinuitParameter*>::const_iterator cend() const { return _parPtrList.cend(); }
-
- std::vector<MinuitParameter*> parPtrs() { return _parPtrList; }
- std::vector<MinuitParameter*>::iterator begin() { return _parPtrList.begin(); }
- std::vector<MinuitParameter*>::iterator end() { return _parPtrList.end(); }
- std::vector<MinuitParameter*>::const_iterator begin() const { return _parPtrList.cbegin(); }
- std::vector<MinuitParameter*>::const_iterator end() const { return _parPtrList.cend(); }
-
- void deleteListAndObjects();
- void deleteListKeepObjects();
-
void print( std::ostream& os = std::cout ) const;
void printVariable( std::ostream& os = std::cout ) const;
-
void set( const MinuitParameterSet& mps );
+ bool rename(const std::string& name, const std::string& new_name);
+ unsigned int size() const;
+
+ const_iterator cbegin() const;
+ const_iterator cend() const;
+ iterator begin();
+ iterator end();
+ const_iterator begin() const;
+ const_iterator end() const;
+
MinuitParameter* at( const std::string& key );
+ MinuitParameter* at( const size_t& index ) const;
MinuitParameter* operator[]( const std::string& key );
MinuitParameter* operator[]( const std::string& key ) const;
- MinuitParameter* operator[]( const unsigned int& key );
- MinuitParameter* find( const std::string& key ) const
- {
- auto it = _keyAccess.find(key);
- return it == _keyAccess.end() ? nullptr : it->second;
- }
- double operator()( const std::string& name )
- {
- if ( _keyAccess.find( name ) == _keyAccess.end() ) {
- std::cout << "Cannot find parameter " << name << std::endl;
- }
- return _keyAccess[name]->mean();
- }
+ MinuitParameter* operator[]( const size_t& key );
+ MinuitParameter* find( const std::string& key ) const;
+ double operator()( const std::string& name );
private:
void tryParameter( const std::vector<std::string>& line );
void tryAlias( const std::vector<std::string>& line );
- std::vector<MinuitParameter*> _parPtrList;
- std::vector<MinuitExpression*> _aliasList;
- std::map<std::string, MinuitParameter*> _keyAccess;
bool addToEnd( MinuitParameter* parPtr );
-
+
+ std::vector<MinuitParameter*> m_parameters;
+ std::map<std::string, MinuitParameter*> m_keyAccess;
};
-
} // namespace AmpGen
#endif
//
diff --git a/AmpGen/MsgService.h b/AmpGen/MsgService.h
index 6e00b5d814e..3d91b75d63f 100644
--- a/AmpGen/MsgService.h
+++ b/AmpGen/MsgService.h
@@ -1,90 +1,97 @@
#ifndef AMPGEN_MSGSERVICE_H
#define AMPGEN_MSGSERVICE_H
-/*
- MsgService Header
- -Defines coloured and organised output macro streams using __PRETTY_FUNCTION__
- INFO() - info level messages, always displayed
- ERROR() - error level messages, always displayed
- FATAL() - error message that throws the process, always displayed
- WARNING() - warning level messages, can be switched with the WARNINGLEVEL flag
- DEBUG() - debug level messages, can be switched with the DEBUGLEVEL flag
- */
+/** @defgroup msgService Messaging and logging
+ MsgService Header
+ Defines coloured and organised output macro streams using __PRETTY_FUNCTION__
+ INFO() - info level messages, always displayed
+ ERROR() - error level messages, always displayed
+ FATAL() - error message that throws the process, always displayed
+ WARNING() - warning level messages, can be switched with the WARNINGLEVEL flag
+ DEBUG() - debug level messages, can be switched with the DEBUGLEVEL flag
+ */
#include <iomanip>
#include <iostream>
#include <string>
+#include <type_traits>
#define WARNINGLEVEL 1
-//#define DEBUGLEVEL 0
-//#define TRACELEVEL 0
-#define FCNNAMELENGTH 45
-inline std::string trimmedString( std::string thing, const unsigned int& length = FCNNAMELENGTH )
-{
- size_t pos2=0;
- do {
- pos2 = thing.find( "AmpGen::" );
- if ( pos2 != std::string::npos ) thing = thing.replace( pos2, 8, "" );
- } while( pos2 != std::string::npos );
-
- pos2 = thing.find( "std::" );
- if ( pos2 != std::string::npos ) thing.replace( pos2, 5, "" );
-
- pos2 = thing.find( "virtual " );
- if ( pos2 != std::string::npos ) thing = thing.replace( pos2, 8, "" );
-
- size_t pos = thing.find( "(" );
-
- if ( pos != std::string::npos ) {
- return pos < length ? thing.substr( 0, pos ) : thing.substr( 0, length );
+namespace AmpGen {
+ namespace detail {
+ constexpr static int FCNNAMELENGTH = 45;
+
+ inline std::string trimmedString( std::string thing, const unsigned int& length = FCNNAMELENGTH )
+ {
+ size_t pos2=0;
+ do {
+ pos2 = thing.find( "AmpGen::" );
+ if ( pos2 != std::string::npos ) thing = thing.replace( pos2, 8, "" );
+ } while( pos2 != std::string::npos );
+
+ pos2 = thing.find( "std::" );
+ if ( pos2 != std::string::npos ) thing.replace( pos2, 5, "" );
+
+ pos2 = thing.find( "virtual " );
+ if ( pos2 != std::string::npos ) thing = thing.replace( pos2, 8, "" );
+
+ size_t pos = thing.find( "(" );
+
+ if ( pos != std::string::npos ) {
+ return pos < length ? thing.substr( 0, pos ) : thing.substr( 0, length );
+ }
+ return thing.size() < length ? thing : thing.substr( 0, length ) + "...";
+ }
+ inline std::ostream& labelled_stream(const std::string& function_name)
+ {
+ return std::cout << "\033[2;34m" << std::left << std::setw(FCNNAMELENGTH) << trimmedString(function_name) << " INFO " << "\033[0m";
+ }
+ template <typename T> struct debug_type : std::false_type {};
}
- return thing.size() < length ? thing : thing.substr( 0, length ) + "...";
- if ( thing.size() < length ) return thing;
}
+#define ENABLE_DEBUG(X) \
+ namespace AmpGen { namespace detail { template <> struct debug_type <X> : std::true_type {}; } }
-#ifdef DEBUGLEVEL
-#define DEBUG( X ) \
- std::cout << "\033[2;32m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " DEBUG " \
-<< "\033[0m" << X << std::endl
-#else
-#define DEBUG( X )
-#endif
+/// @ingroup msgService macro DEBUG
+/// Used for printing verbose debugging messages, only if DEBUGLEVEL is defined.
+#define DEBUG( X ) { \
+ if constexpr( AmpGen::detail::debug_type<typename std::decay<decltype(*this)>::type>::value ) { \
+ std::cout << "\033[2;32m" << std::left << std::setw( AmpGen::detail::FCNNAMELENGTH ) << AmpGen::detail::trimmedString(__PRETTY_FUNCTION__) \
+ << " DEBUG " \
+ << "\033[0m" << X << " " << std::endl; } }
-#define INFO( X ) \
- std::cout << "\033[2;34m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " INFO " \
-<< "\033[0m" << X << std::endl
+/// @ingroup msgService macro INFO
+/// Used for printing information messages, and will always be printed.
+#define INFO( X ) \
+ AmpGen::detail::labelled_stream(__PRETTY_FUNCTION__) << X << std::endl
+/// @ingroup msgService macro ERROR
+/// Used for printing errors messages, and will always be printed.
#define ERROR( X ) \
- std::cout << "\033[1;31m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " ERROR " \
-<< "\033[0m" << X << std::endl
+ std::cout << "\033[1;31m" << std::left << std::setw( AmpGen::detail::FCNNAMELENGTH ) << AmpGen::detail::trimmedString( __PRETTY_FUNCTION__ ) \
+ << " ERROR " \
+ << "\033[0m" << X << std::endl
+/// @ingroup msgService macro FATAL
+/// Used for printing fatal errors messages, and will always be printed and will terminate the process afterwards.
#define FATAL( X ) \
- { std::cout << "\033[1;31m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " FATAL " \
-<< "\033[0m" << X << std::endl; \
-throw std::runtime_error( trimmedString( __PRETTY_FUNCTION__)+ " FATAL" ) ;}
+{ std::cout << "\033[1;31m" << std::left << std::setw( AmpGen::detail::FCNNAMELENGTH ) << AmpGen::detail::trimmedString( __PRETTY_FUNCTION__ ) \
+ << " FATAL " \
+ << "\033[0m" << X << std::endl; \
+ throw std::runtime_error( AmpGen::detail::trimmedString( __PRETTY_FUNCTION__)+ " FATAL" ) ;}
+
+/// @ingroup msgService macro FATAL
+/// Used for printing warning messages, can be switched off using WARNINGLEVEL. These messages are often harmless, but sometimes not!
#ifdef WARNINGLEVEL
#define WARNING( X ) \
- std::cout << "\033[1;35m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " WARNING " \
-<< "\033[0m" << X << std::endl
+ std::cout << "\033[1;35m" << std::left << std::setw( AmpGen::detail::FCNNAMELENGTH ) << AmpGen::detail::trimmedString( __PRETTY_FUNCTION__ ) \
+ << " WARNING " \
+ << "\033[0m" << X << std::endl
#else
#define WARNING( X )
#endif
-#ifdef TRACELEVEL
-#define TRACE( X ) \
- std::cout << "\033[1;36m" << std::left << std::setw( FCNNAMELENGTH ) << trimmedString( __PRETTY_FUNCTION__ ) \
-<< " TRACE " \
-<< "\033[0m" << X << std::endl
-#else
-#define TRACE( X )
-#endif
-
#endif
diff --git a/AmpGen/NamedParameter.h b/AmpGen/NamedParameter.h
index 18b993f5eb0..8c5a1264385 100644
--- a/AmpGen/NamedParameter.h
+++ b/AmpGen/NamedParameter.h
@@ -12,6 +12,7 @@
#include <vector>
#include <iomanip>
#include <map>
+#include <cstring>
#include "AmpGen/MsgService.h"
#include "AmpGen/OptionsParser.h"
@@ -20,13 +21,20 @@
namespace AmpGen
{
+ /** @class NamedParameter
+ @brief A parameter with value specified by the user at runtime, either in an options file or via the command line
+
+ Stores a vector of values for a parameter.
+ @tparam T the type of this named parameter, i.e. strings, or numbers or bools etc.
+
+ */
template <class T>
class NamedParameter
{
protected:
- std::string m_name;
- std::string m_helpString;
- std::vector<T> m_valueArray;
+ std::string m_name; /// < Name of this parameter
+ std::string m_helpString; /// < The helper string for this parameter, printed if the flag --help is used.
+ std::vector<T> m_valueArray; /// < The value (array) of this parameter.
bool setFromOptionsParser()
{
@@ -59,29 +67,6 @@ namespace AmpGen
if ( OptionsParser::printHelp() ) help(def);
DEBUG( *this );
}
- /*
- template <class... ARGS>
- NamedParameter( const std::string& name, const T& def, const ARGS&... args ) :
- m_name(name)
- {
- setVal( def );
- setFromOptionsParser();
- auto arg_pack = ArgumentPack(args...);
- auto acceptedValues = arg_pack.getArg<AcceptedValues<T>>().val;
- m_helpString = arg_pack.getArg<HelpString>().val;
-
- if( acceptedValues.size() != 0 ){
- bool isAcceptedValue = false;
- for( auto& v : acceptedValues ) if( m_valueArray[0] == v ) isAcceptedValue = true;
- if( !isAcceptedValue ){
- ERROR( "Argument: " << name << " is not in [" << italic_on << vectorToString( acceptedValues, ", ") << italic_off <<"]" );
- }
- }
- if ( OptionsParser::printHelp() ) help(def);
- DEBUG( *this );
- }
- */
-
NamedParameter(const std::string& name, const std::vector<T>& defVec, const std::string& helpString="")
: m_name(name),
m_helpString(helpString)
@@ -90,10 +75,8 @@ namespace AmpGen
setFromOptionsParser();
if ( OptionsParser::printHelp() ) help( defVec.size() > 0 ? defVec[0] : T() );
}
-
void help(const T& def){
- std::map< std::string, std::string > aliases;
- std::string type = typeof<T>();
+ std::string type = type_string<T>();
if( type == "std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> >" ) type = "string";
std::cout << " " << bold_on << std::left << std::setw(27) << m_name << bold_off
<< std::setw(20) << "[" + type + "]" ;
@@ -123,6 +106,8 @@ namespace AmpGen
operator T() const { return getVal(); }
operator T() { return getVal(); }
+ template <class G> bool operator==(const G& other) const { return getVal() == other; }
+ template <class G> bool operator!=(const G& other) const { return getVal() != other; }
const std::vector<T>& getVector() const { return m_valueArray; }
void setVal( const T& val, int i = 0 )
@@ -163,24 +148,30 @@ namespace AmpGen
return return_container;
}
};
- template <class T>
- std::ostream& operator<<( std::ostream& os, const NamedParameter<T>& np );
-
- std::string optionalHelpString(const std::string& header, const std::vector<std::pair<std::string, std::string>>& args);
+ template <typename T> std::ostream& operator<<( std::ostream& os, const NamedParameter<T>& np );
+ template <typename ...T> std::string optionalHelpString(const std::string& header, const T&... args);
}
-
template <typename T>
std::ostream& AmpGen::operator<<( std::ostream& os, const AmpGen::NamedParameter<T>& np )
{
os << np.name() ;
for ( size_t i = 0; i < np.size(); i++ ) {
if( i == 0 ) os << " = ";
- os << np.getVal( i );
+ os << np.getVal(i);
if ( i != np.size() ) os << " ";
}
return os;
}
+template <typename ...T> std::string AmpGen::optionalHelpString(const std::string& header, const T&... args )
+{
+ std::stringstream rt;
+ rt << header;
+ for_each( std::make_tuple(args...), [&rt](const auto& f) mutable {
+ rt << "\n\033[3m " << f.first << "\033[0m: " << f.second;
+ });
+ return rt.str();
+}
+
#endif
-//
diff --git a/AmpGen/OptionsParser.h b/AmpGen/OptionsParser.h
index c1bd3449a15..ec9dc04832d 100644
--- a/AmpGen/OptionsParser.h
+++ b/AmpGen/OptionsParser.h
@@ -6,6 +6,7 @@
#include <map>
#include <string>
#include <utility>
+#include <functional>
namespace AmpGen
{
@@ -17,26 +18,29 @@ namespace AmpGen
static OptionsParser* getMe();
static bool printHelp();
- static void setArgs( int argc, char** argv );
+ static void setArgs( int argc, char** argv, const std::string& description="" );
static void setArg( const std::string& arg );
+ void setQuiet();
void addArg( const std::string& arg );
- void setCommandLineArgs( int argc, char** argv );
+ void setCommandLineArgs( int argc, char** argv, const std::string& description ="");
void import( const std::string& fName );
iterator find( const std::string& name );
iterator begin();
iterator end();
const_iterator begin() const;
const_iterator end() const;
-
private:
std::map<std::string,std::vector<std::string>> m_parsedLines;
- bool m_printHelp;
+ std::map<std::string, std::function<void(std::vector<std::string>)> > m_keywords;
+ bool m_printHelp = {false};
+ bool m_quiet = {false};
static OptionsParser* gOptionsParser;
OptionsParser();
bool ignoreThisLine( const std::string& line );
void readStream( std::istream& is );
std::vector<std::string> makeParsedStrings( const std::string& line, int& braceDepth ) const;
+ void addArg(const std::vector<std::string>& tokens );
};
} // namespace AmpGen
#endif
diff --git a/AmpGen/Pade.h b/AmpGen/Pade.h
new file mode 100644
index 00000000000..2b3c7d90d3d
--- /dev/null
+++ b/AmpGen/Pade.h
@@ -0,0 +1,56 @@
+#ifndef AMPGEN_PADE_H
+#define AMPGEN_PADE_H
+
+#include <array>
+#include <functional>
+#include <vector>
+
+namespace AmpGen {
+ enum Strategy { linear, quadratic, cubic, quartic };
+ namespace detail {
+ std::vector<double> solve_pade(const std::function<double(const double&)>& fcn,
+ const double& min,
+ const double& max,
+ const unsigned& N,
+ const Strategy& strat = Strategy::linear);
+ }
+
+ template <unsigned N, class T = double> class Pade
+ {
+ public:
+ Pade(const std::function<double(const double&)>& fcn,
+ const double& min,
+ const double& max,
+ const Strategy& strat = Strategy::linear) :
+ m_function(fcn), min(min),max(max)
+ {
+ auto r = detail::solve_pade(fcn, min, max, N, strat );
+ for(unsigned i = 0; i <= N; ++i ) co_f[i] = r[i];
+ for(unsigned i = 0; i < N; ++i ) co_g[i] = r[i+(N+1)];
+ range = 1./(max-min);
+ }
+ T operator()(const T& s)
+ {
+ T x = (s-min)*range;
+ T f = 0;
+ T g = 1;
+ T acc = 1;
+ for(unsigned i = 0; i < N; ++i){
+ f += co_f[i] * acc;
+ acc *= x;
+ g += co_g[i] * acc;
+ }
+ return (f + co_f[N]*acc)/g;
+ }
+
+ private:
+ std::function<double(const double&)> m_function;
+ std::array<T, N+1> co_f;
+ std::array<T, N> co_g;
+ T min;
+ T max;
+ T range;
+ };
+}
+
+#endif
diff --git a/AmpGen/Particle.h b/AmpGen/Particle.h
index 2b0306fc9da..4b9fc065585 100644
--- a/AmpGen/Particle.h
+++ b/AmpGen/Particle.h
@@ -26,7 +26,8 @@ namespace stdx {
#include "AmpGen/Expression.h"
#include "AmpGen/Tensor.h"
#include "AmpGen/QuarkContent.h"
-
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/enum.h"
namespace AmpGen
{
/** @class Particle
@@ -61,18 +62,19 @@ namespace AmpGen
These will be denoted by the use of [] braces, so for example
\code{cpp}
- Delta(1232)++{p+,pi+}
- Delta(1232)++[D]{p+,pi+}
+ a(1)(1260)+{rho(770)0,pi+}
+ a(1)(1260)+[D]{rho(770)0,pi+}
\endcode
- correspond to the S-wave and D-wave decays of the @f$\Delta(1232)^{++}@f$ baryon.
+ correspond to the S-wave and D-wave decays of the @f$a(1)(1260)^{+}@f$ meson.
As a rule, the lowest orbital state permitted by the relevant conservation laws of the decay is
used if the orbital state is not specified, so the conservation of angular momentum,
and the conservation of parity if the decay proceeds via the strong or electromagnetic force.
The modifier syntax is also used to specify a different choice of lineshape for the resonance.
For example, a common parameterisation for the @f$\rho(770)@f$ meson is the Gounaris-Sakurai propagator,
- which accounts for dispersive corrections to the @f$I=1@f$ dipion scattering. In this example
+ which accounts for dispersive corrections to the @f$I=1@f$ dipion system.
+ In this example
\code{cpp}
rho(770)0[GounarisSakurai]{pi+,pi-}
@@ -93,168 +95,172 @@ namespace AmpGen
Similar to other components of AmpGen, Particles will rarely be constructed in the C++ context,
and will instead be instantiated dynamically at runtime from a user supplied options file. */
class ParticleProperties;
- //struct zFrame {
- // /// Frame where parent is at rest, particle 0 is along the z-axis
- // Tensor operator(const std::vector<size_t>& indices)() const
- // {
- //
- // }
- //};
+
+ declare_enum( spinFormalism, Covariant, Canonical )
+ declare_enum( spinBasis , Dirac , Weyl )
class Particle
{
- private:
- const ParticleProperties* m_props; ///< Particle Properties from the PDG
- std::string m_name = {""}; ///< Name of the particle
- std::string m_lineshape = {"BW"}; ///< Propagator to use
- std::string m_uniqueString = {""}; ///< Unique string of particle tree
- int m_parity = {0}; ///< Intrinsic parity of particle
- int m_polState = {0}; ///< polarisation state
- unsigned int m_index = {999}; ///< Index, for constructing four-momenta
- unsigned int m_originalIndex = {999}; ///< Starting index, used in Bose-symmetrisation
- unsigned int m_orbital = {0}; ///< Orbital angular momentum between daughters
- unsigned int m_spinConfigurationNumber = {0}; ///< Spin configuration quantum number 'S'
- unsigned int m_minL = {0}; ///< Minimum orbital angular momentum
- bool m_isHead = {true}; ///< Flag that particle is head of decay chain
- bool m_isStateGood = {true}; ///< Flag to check the decay is well-formed
- bool m_usesDefaultLineshape = {false}; ///< Flag to check if default shape is used
- std::vector<std::shared_ptr<Particle>> m_daughters; ///< Array of daughter particles
- std::vector<std::string> m_modifiers; ///< Additional modifiers for amplitude
- std::string m_spinFormalism = {""}; ///< Spin formalism to use for this particle (global)
- std::string m_spinBasis = {""}; ///< Basis to use for external polarisations (global)
- std::string m_defaultModifier = {""}; ///< Default Modifier to use (global)
-
- void pdgLookup(); ///< Lookup information from the PDG database (using ParticlePropertiesList)
- bool hasModifier( const std::string& modifier ) const; ///< Check if this particle has a given modifier
- std::string modifierString() const; ///< Re-generate modifier string used to create particle
- std::string makeUniqueString(); ///< Generate the decay descriptor for this decay.
- void sortDaughters(); ///< Recursively order the particle's decay products.
public:
- /// @constructor default constructor
+ /// Default Constructor
Particle();
- /// @constructor Constructor that takes a pair of other particles (i.e. this particle's decay products) as arguments and looks up the properties of this particle using the particle name.
+ /// Constructor that takes a pair of other particles (i.e. this particle's decay products) as arguments and looks up the properties of this particle using the particle name.
Particle( const std::string& name, const Particle& p1, const Particle& p2 );
- /// @constructor Constructor that takes a pair of other particles (i.e. this particle's decay products) as arguments and looks up the properties of this particle using the PDG MC ID.
+ /// Constructor that takes a pair of other particles (i.e. this particle's decay products) as arguments and looks up the properties of this particle using the PDG MC ID.
Particle( const int& pdg_id, const Particle& p1, const Particle& p2 );
- /// @constructor Constructor by name and with an index to match to the event type
+ /// Constructor by name and with an index to match to the event type
Particle( const std::string& name, const unsigned int& index );
- /// @constructor Constructor that takes a decay descriptor as an argument and a list of final state particles to match to the event type. Constructs the entire decay tree.
+ /// Constructor that takes a decay descriptor as an argument and a list of final state particles to match to the event type. Constructs the entire decay tree.
Particle( const std::string& decayString, const std::vector<std::string>& finalStates = {}, const bool& orderDaughters = true );
+ /// (Quasi) Constructor that returns the (quasi)CP conjugated amplitude. The full behaviour of the amplitude is made more complicated by the ordering convention.
+ Particle conj(bool invertHead = true, bool reorder = true);
+
+ /// CP conjugate this particle //
+
+ void conjThis();
+
+ static bool isValidDecayDescriptor( const std::string& decayDescriptor );
+ /// Set the orbital quantum number 'L' for this decay.
void setOrbital( const unsigned int& orbital );
+
+ /// Set the lineshape for the decay of this particle.
void setLineshape( const std::string& lineshape );
+
+ /// Set the index'th daughter of this to particle.
void setDaughter( const Particle& particle, const unsigned int& index );
- void setTop( bool state = true );
+
+ /// Set the parent particle for this particle
+ void setParent( const Particle* particle );
+
+ /// Set the index of this particle, i.e. where it is positioned in the event data structure.
void setIndex( const unsigned int& index, const bool& setOri = false );
+ /// Remove all of the decay products of this particle
+ void clearDecayProducts();
+
+ /// Add some modifier to the particle, such as a lineshape or a different spin state
void addModifier( const std::string& mod );
+
+ /// Parse some set of modifiers, delimited with semicolons.
void parseModifier( const std::string& mod );
+
+ /// Set some particle ordering of the decay products of this particle, mostly used internally by the symmetrisation
void setOrdering( const std::vector<size_t>& ordering );
+
+ /// Set the particle name
+ void setName(const std::string& name);
+
+ /// Add a decay product
void addDaughter( const std::shared_ptr<Particle>& particle );
+
+ /// Set the polarisation state of this particle, which is twice the projection of the spin along the quantisation axis.
void setPolarisationState( const int& state );
- std::pair<size_t,size_t> orbitalRange( const bool& converseParity = true ) const; ///< Range of possible orbital angular momenta between decay products
+ void setPolarisationState( const std::vector<int>& state);
+
+ /// Returns the range of orbital angular momentum between the decay products
+ std::pair<size_t,size_t> orbitalRange( const bool& converseParity = true ) const;
+
+ /// Returns the set of possible spin-orbit couplings allowed by conservation of angular momentum, and if specified parity
std::vector<std::pair<double,double>> spinOrbitCouplings( const bool& conserveParity = true ) const;
+
+ /// Return the additional optional attribute keyed by variable key
stdx::optional<std::string> attribute(const std::string& key) const;
+
+ /// Return the particleProperties object for this particle
const ParticleProperties* props() const;
- QuarkContent quarks() const;
- QuarkContent daughterQuarks() const;
- int parity() const;
- int finalStateParity() const;
- int polState() const;
- int conjugate( bool invertHead = false , bool reorder = true);
- double mass() const;
- double spin() const;
- double S() const;
- bool isHead() const;
- bool isWeakDecay() const;
- bool isStateGood() const;
- bool isStable() const;
- bool isQuasiStable() const;
- bool conservesParity( unsigned int L = 0 ) const;
- bool checkExists() const;
-
- unsigned int orbital() const;
- unsigned int index() const;
- unsigned int originalIndex() const;
-
- /// @function Name of the decaying particle.
- std::string name() const;
-
- /// @function Name of the propagator to use for the decay of this particle.
- std::string lineshape() const;
-
- /// @function Name of the (spin)vertex to use for the decay of this particle
- std::string vertexName() const;
-
- /// @function The unique string (i.e. decay descriptor) that identifies this decay /
- /// can be parsed to generate the decay tree.
- std::string uniqueString() const;
- /// @function The descriptor that describes this decay /
- /// that can be parsed to generate the decay tree and uniquely identify it.
- std::string decayDescriptor() const;
+ QuarkContent quarks() const; ///< Return the quarks of this particle
+
+ QuarkContent daughterQuarks() const; ///< Returns the quark content of the sum of the decay products of this particle
+
+ int parity() const; ///< Returns the parity of this particle
+ int finalStateParity() const; ///< Returns the parity of the final state of this particle
+
+ int polState() const; ///< Returns the polarisation state, i.e. twice the projection of the spin along the quantisation axis, of this particle.
+ int CP() const; ///< Returns the CP of this decay.
+ int C() const; ///< Returns the C quantum number for this decay
+ double mass() const; ///< Returns the (PDG) mass of the particle
+ double spin() const; ///< Returns the spin of the particle
+ double S() const; ///< Returns the spin configuration of the decay products of the particle
+ unsigned L() const; ///< Returns the orbital angular
+
+ bool isHead() const; ///< Returns whether if this particle is the head of the decay, i.e. has no parent
+ bool isWeakDecay() const; ///< Returns whether is this particle decays weakly or not
+ bool isStateGood() const; ///< Returns whether this particle, and its decays have been configured correctly
+ bool isStable() const; ///< Check whether this particle is stable, has any decay products.
+ bool isQuasiStable() const; ///< Check whether the particle is quasi-stable, i.e. may have some appreciable flight distance
+ bool conservesParity( unsigned int L = 0 ) const; ///< Check whether the decay of this particle with angular momentum L conserves parity or not
+
+ unsigned index() const; ///< Returns the current index of the particle in event data structure. Can differ from the original index due to symmetrisation
+ unsigned originalIndex() const; ///< Returns the original index of the particle
+ std::string name() const; ///< Name of the decaying particle.
+ std::string lineshape() const; ///< Name of the propagator to use for the decay of this particle.
+
+ std::string uniqueString() const; ///< Returns the unique string (i.e. decay descriptor) that identifies this decay, which can be parsed to generate the decay tree.
+ std::string decayDescriptor() const;///< Returns the unique string (i.e. decay descriptor) that identifies this decay, which can be parsed to generate the decay tree.
- /// @function The string that describes the spin/orbital topology of this decay,
+ /// The string that describes the spin/orbital topology of this decay,
/// i.e. replacing specific particle names with their spins.
std::string topologicalString() const;
- /// @function The string that describes the spin/orbit configuration of this decay.
+ /// The string that describes the spin/orbit configuration of this decay.
std::string orbitalString() const;
- /// @function Decay descriptor formatted as LaTeX for this decay.
+ /// Decay descriptor formatted as LaTeX for this decay.
std::string texLabel( const bool& printHead = false, const bool& recurse=true ) const;
- /// @function Returns the ``quasi'' CP Quantum number for this decay
- int quasiCP() const;
-
- /// @function Return the eventType for this decay (i.e. the initial and final state particles)
+ /// Return the eventType for this decay (i.e. the initial and final state particles)
EventType eventType() const;
- /// @function Returns the indexth decay product of this particle
+ /// Returns the indexth decay product of this particle
std::shared_ptr<Particle> daughter( const size_t& index );
- /// @function Returns in indexth decay product of this particle (as constant)
+ /// Returns in indexth decay product of this particle (as constant)
std::shared_ptr<Particle> daughter( const size_t& index ) const;
+
+ /// Returns in indexth decay product of this particle (as constant)
+ std::shared_ptr<Particle> daughter(const std::string& name, const int& maxDepth=-1) const;
- /// @function Vector of decay products of this particle
+ /// Vector of decay products of this particle
std::vector<std::shared_ptr<Particle>> daughters() const;
- /// @function Get orderings of the final state that are identical to each other, i.e. those that only differ by exchanging identical particles.
+ /// Get orderings of the final state that are identical to each other, i.e. those that only differ by exchanging identical particles.
std::vector<std::vector<size_t>> identicalDaughterOrderings() const;
- /// @function Returns the final state particles for this decay process.
+ /// Returns the final state particles for this decay process.
std::vector<std::shared_ptr<Particle>> getFinalStateParticles( const bool& sort = true ) const;
- /// @function Calculate the particle tree only including quasi-stable processes,
+ /// Calculate the particle tree only including quasi-stable processes,
/// i.e. only includes states with lifetimes > ParticleProperties::qsThreshold (default ~ 1 KeV )
Particle quasiStableTree() const;
- /// @function Calculates the momentum sum of the decay products
+ /// Calculates the momentum sum of the decay products
Tensor P() const;
- /// @function Calculates the momentum difference between the decay products (only well defined for quasi two-body processes )
+ /// Calculates the momentum difference between the decay products (only well defined for quasi two-body processes )
Tensor Q() const;
- /// @function Calculates the spin tensor or generalised current for this particle
+ /// Calculates the spin tensor or generalised current for this particle
Tensor spinTensor( DebugSymbols* db = nullptr ) const;
- /// @function Calculates the polarisation vector / spinor etc. of this particle, used for the initial/final state particles
+ /// Calculates the polarisation vector / spinor etc. of this particle, used for the initial/final state particles
Tensor externalSpinTensor(const int& polState, DebugSymbols* db = nullptr) const;
- /// @function Calculates the invariant mass-squared of the mass of this particle
+ /// Calculates the invariant mass-squared of the mass of this particle
Expression massSq() const;
- /// @function Calculates the lineshape / propagator for this particle.
+ /// Calculates the lineshape / propagator for this particle.
Expression propagator( DebugSymbols* db = nullptr ) const;
- /// @function Calculates the total expression for this particle, including symmetrisation and the current polarisation state
- Expression getExpression( DebugSymbols* db = nullptr, const unsigned int& index = 0 );
+ /// Calculates the total expression for this particle, including symmetrisation and the current polarisation state
+ Expression getExpression( DebugSymbols* db = nullptr, const std::vector<int>& = {} );
- /// @function Calculate the transition matrix for this decay
+ /// Calculate the transition matrix for this decay
Tensor transitionMatrix( DebugSymbols* db = nullptr );
bool operator<( const Particle& other );
bool operator>( const Particle& other );
@@ -267,9 +273,44 @@ namespace AmpGen
DifferentOrbital = ( 1<<3 ),
DifferentPolarisation = ( 1<<4 )
};
- /// @function matches Check the matching between two decay chains, according to the MatchState enum.
+ /// matches Check the matching between two decay chains, according to the MatchState enum.
unsigned int matches( const Particle& other ) const;
+ std::string makeUniqueString(); ///< Generate the decay descriptor for this decay.
+
+ private:
+ std::string m_name = {""}; ///< Name of the particle
+ const ParticleProperties* m_props = {nullptr}; ///< Particle Properties from the PDG
+ std::string m_lineshape = {"BW"}; ///< Propagator to use
+ std::string m_uniqueString = {""}; ///< Unique string of particle tree
+ int m_parity = {0}; ///< Intrinsic parity of particle
+ int m_polState = {0}; ///< Projection of the spin along the quantisation axis, i.e. 'z'
+ unsigned m_index = {999}; ///< Index, for constructing four-momenta
+ unsigned m_originalIndex = {999}; ///< Starting index, used in Bose-symmetrisation
+ unsigned m_orbital = {0}; ///< Orbital angular momentum between daughters
+ unsigned m_spinConfigurationNumber = {0}; ///< Spin configuration quantum number 'S'
+ unsigned m_minL = {0}; ///< Minimum orbital angular momentum
+ bool m_usesDefaultLineshape = {false}; ///< Flag to check if default shape is used
+ bool m_isStateGood = {true}; ///< Flag to check the decay is well-formed
+ std::vector<std::shared_ptr<Particle>> m_daughters; ///< Array of daughter particles
+ std::vector<std::string> m_modifiers; ///< Additional modifiers for amplitude
+ const Particle* m_parent = {nullptr}; ///< Pointer to the parent particle of this particle
+ void pdgLookup(); ///< Lookup information from the PDG database (using ParticlePropertiesList)
+ bool hasModifier( const std::string& modifier ) const; ///< Check if this particle has a given modifier
+ std::string modifierString() const; ///< Re-generate modifier string used to create particle
+ void sortDaughters(); ///< Recursively order the particle's decay products.
+
+ NamedParameter<spinFormalism> m_spinFormalism = {"Particle::SpinFormalism" ,spinFormalism::Covariant,
+ optionalHelpString("Formalism to use for spin calculations",
+ std::make_pair("Covariant", "[default] Covariant Tensor, based on Rarita-Schwinger constraints on the allowed covariant wavefunctions.")
+ , std::make_pair("Canonical", "Canonical formulation, based on rotational properties of wavefunctions, i.e. Wigner D-matrices and Clebsch-Gordan for (L,S) expansion.") ) };
+
+ NamedParameter<spinBasis> m_spinBasis = {"Particle::SpinBasis", spinBasis::Dirac,
+ optionalHelpString("Basis to use for calculating external polarisation tensors / spinors.",
+ std::make_pair("Dirac", "[default] Quantises along the z-axis")
+ , std::make_pair("Weyl", "Quantises along the direction of motion") )};
+ NamedParameter<std::string> m_defaultModifier = {"Particle::DefaultModifier","", "Default modifier to use for lineshapes, for example to use normalised vs unnormalised Blatt-Weisskopf factors."};
};
+ std::ostream& operator<<( std::ostream& os, const Particle& particle );
} // namespace AmpGen
#endif
diff --git a/AmpGen/ParticleProperties.h b/AmpGen/ParticleProperties.h
index 02766797f00..df8e000bfe3 100644
--- a/AmpGen/ParticleProperties.h
+++ b/AmpGen/ParticleProperties.h
@@ -11,96 +11,103 @@
namespace AmpGen
{
- class ParticleProperties
- {
- private:
- double m_mass; ///< mass [MeV]
- double m_mErrPlus; ///< +ve mass error [MeV]
- double m_mErrMinus; ///< -ve mass error [MeV]
- double m_width; ///< width [MeV]
- double m_wErrPlus; ///< +ve width error [MeV]
- double m_wErrMinus; ///< -ve width error [MeV]
- double m_Radius; ///< hadronic radius
- int m_Gparity; ///< G-parity
- int m_Parity; ///< Parity
- int m_Cparity; ///< Charge 'parity'
- int m_pdgID; ///< PDG id
- int m_Rexist; ///< likelihood of existence, baryons only
- int m_charge; ///< electrical charge
- int m_twoSpin; ///< twice the spin
- std::string m_Isospin; ///< isospin
- std::string m_JtotalSpin; ///< total spin
- std::string m_name; ///< particle name
- std::string m_quarks; ///< quark string
- std::string m_texName; ///< latex label of particle
- std::string m_chargeString; ///< string for particle charge
- char m_Aformat; ///< anti-particle format character
- char m_status; ///< status (estalished or not etc)
- QuarkContent m_netQuarkContent;
- bool m_isValid;
-
- void setRadius();
+ /** @class ParticleProperties
+ @brief Class that contains the PDG properties (mass, width, charges, etc.) for a single particle species,
+
+ Stores the information for a single particle species, the mass, the width, spin, various charges.
+ The data is typically loaded from ParticlePropertiesList, which loads from the PDG provided
+ \code{cpp}
+ mass_width.cvs
+ \endcode
+ See that more details.
+ */
- void antiQuarks();
- void antiQuarkContent();
- void antiCharge();
- int chargeFromString( const std::string& ch, bool& status ) const;
- public:
- double mass() const { return m_mass * MeV; } ///< returns mass of particle in MeV
- double mErrPlus() const { return m_mErrPlus * MeV; } ///< returns +ve uncertainty on particle mass in MeV
- double mErrMinus() const { return m_mErrMinus * MeV; } ///< returns -ve uncertainty on particle mass in MeV
- double width() const { return m_width * MeV; } ///< returns width of particle in MeV
- double wErrPlus() const { return m_wErrPlus * MeV; } ///< returns +ve uncertainty on particle width in MeV
- double wErrMinus() const { return m_wErrMinus * MeV; } ///< returns -ve uncertainty on particle width in MeV
- double radius() const;
+ class ParticleProperties
+ {
+ public:
+ explicit ParticleProperties( const std::string& pdg_string = "" ); ///< Constructor from a string formatted by the PDG convention.
+ double mass() const { return m_mass * MeV; } ///< Returns mass of particle in MeV
+ double mErrPlus() const { return m_mErrPlus * MeV; } ///< Returns +ve uncertainty on particle mass in MeV
+ double mErrMinus() const { return m_mErrMinus * MeV; } ///< Returns -ve uncertainty on particle mass in MeV
+ double width() const { return m_width * MeV; } ///< Returns width of particle in MeV
+ double wErrPlus() const { return m_wErrPlus * MeV; } ///< Returns +ve uncertainty on particle width in MeV
+ double wErrMinus() const { return m_wErrMinus * MeV; } ///< Returns -ve uncertainty on particle width in MeV
+ double radius() const; ///< Returns the effective interaction radius of the particle, i.e. for the Blatt-Weisskopf factors
+ double lifetime() const; ///< Returns the lifetime of the particle in ns
- int G() const { return m_Gparity; }
- int P() const { return m_Parity; }
- int C() const { return m_Cparity; }
- int R() const { return m_Rexist; }
- int pdgID() const { return m_pdgID; }
- int twoSpin() const { return m_twoSpin ; }
- std::string I() const { return m_Isospin; }
- std::string J() const { return m_JtotalSpin; }
- int charge() const { return m_charge; }
- std::string label() const { return m_texName; }
- std::string quarks() const { return m_quarks; }
- std::string name() const;
- std::string chargeString() const { return m_chargeString; }
- std::string spinName() const;
+ int G() const { return m_Gparity; } ///< Returns the G-parity of the particle
+ int P() const { return m_parity; } ///< Returns the parity of the particle
+ int C() const { return m_Cparity; } ///< Returns the C-parity of the particle
+ int R() const { return m_Rexist; } ///< Returns the R-parity of the particle
+ int pdgID() const { return m_pdgID; } ///< Returns the PDG id of the particle.
+ int twoSpin() const { return m_twoSpin; } ///< Returns twice the spin of the particle
+ int charge() const { return m_charge; } ///< Returns the (electrical) charge of the particle
+ char S() const { return m_status; } ///< Returns the existence status of the particle, i.e. whether it is confirmed by multiple experiments
+ std::string I() const { return m_isospin; } ///< Returns the isospin of the particle as a string.
+ std::string J() const;
+ std::string label() const { return m_texName; } ///< Returns the LaTeX formatted label for the particle
+ std::string name() const; ///< Returns the particle name
+ std::string spinName() const; ///< Returns the name of the particles spin.
+ bool isValid() const { return m_isValid; } ///< Check if the particle properties have been configured correctly
+ bool hasDistinctAnti() const; ///< Check if the particle has a distinct antiparticle
+ bool isNonResonant() const; ///< Check is this is a nonresonant `quasi-particle'
+ bool isFermion() const; ///< Check if the particle is a fermion, i.e. if the spin 1/2, 3/2, ...
+ bool isBoson() const; ///< Check if the particle is a boson, i.e. if the spin 0, 1, 2...
+ bool isNeutrino() const; ///< Check if the particle is a neutrino
- char S() const { return m_status; }
- void setLabel( const std::string& label ) { m_texName = label; }
- void setName( const std::string& name ) { m_name = name; }
- const QuarkContent& netQuarkContent() const { return m_netQuarkContent; }
-
- bool isValid() const { return m_isValid; }
+ bool isPhoton() const; ///< Check if the particle is a photon
+ void setProperty(const std::string& key, const std::string& value); ///< set a propery of a particle by key
+ const QuarkContent& quarkContent() const { return m_quarkContent; } ///< Returns the particle's quark content
- bool hasDistinctAnti() const;
- bool barred() const;
- bool isItsOwnAnti() const { return !hasDistinctAnti(); }
+ void setLabel( const std::string& label ) { m_texName = label; } ///< Set the LaTeX label of the particle
+ void setName( const std::string& name ) {
+ m_customName = true;
+ m_name = name; } ///< Set the name of the particle
- ParticleProperties( const std::string& pdg_string = "" );
+ void print( std::ostream& out = std::cout ) const;
- void print( std::ostream& out = std::cout ) const;
+ bool operator==( const ParticleProperties& rhs ) const;
+ bool operator< ( const ParticleProperties& rhs ) const;
+ bool operator> ( const ParticleProperties& rhs ) const;
+ bool operator<=( const ParticleProperties& rhs ) const;
+ bool operator>=( const ParticleProperties& rhs ) const;
- bool operator==( const ParticleProperties& rhs ) const;
- bool operator< ( const ParticleProperties& rhs ) const;
- bool operator> ( const ParticleProperties& rhs ) const;
- bool operator<=( const ParticleProperties& rhs ) const;
- bool operator>=( const ParticleProperties& rhs ) const;
+ bool antiThis(); ///< Change this particle to its antiparticle
+ ParticleProperties anti() const; ///< Return the antiparticle of this particle
- bool antiThis();
- ParticleProperties anti() const;
+ static const ParticleProperties* get( const std::string& name, const bool& quiet=false );
- bool isNonResonant() const;
- bool isFermion() const ;
- bool isBoson() const;
- static const ParticleProperties* get( const std::string& name, const bool& quiet=false );
+ private:
+ double m_mass{0}; ///< mass [GeV]
+ double m_mErrPlus{0}; ///< +ve mass error [GeV]
+ double m_mErrMinus{0}; ///< -ve mass error [GeV]
+ double m_width{0}; ///< width [GeV]
+ double m_wErrPlus{0}; ///< +ve width error [GeV]
+ double m_wErrMinus{0}; ///< -ve width error [GeV]
+ double m_radius{0}; ///< hadronic radius
+ int m_Gparity{0}; ///< G-parity
+ int m_parity{0}; ///< Parity
+ int m_Cparity{0}; ///< Charge 'parity'
+ int m_pdgID{0}; ///< PDG id
+ int m_Rexist{0}; ///< likelihood of existence, baryons only
+ int m_charge{0}; ///< electrical charge
+ int m_twoSpin{0}; ///< twice the spin
+ std::string m_isospin{""}; ///< isospin
+ std::string m_name{""}; ///< particle name
+ std::string m_texName{""}; ///< latex label of particle
+ std::string m_chargeString{""}; ///< string for particle charge
+ char m_Aformat; ///< anti-particle format character
+ char m_status; ///< status (estalished or not etc)
+ QuarkContent m_quarkContent; ///< The quark content of the state (uD, uud etc.)
+ bool m_isValid; ///< Flag to check whether the ParticleProperties have configured correctly
+ bool m_customName = {false}; ///< Flag to make custom name
+ void antiQuarks();
+ void antiCharge();
+ int chargeFromString( const std::string& ch, bool& status ) const;
};
-} // namespace AmpGen
-std::ostream& operator<<( std::ostream& out, const AmpGen::ParticleProperties& pp );
+ std::ostream& operator<<( std::ostream& out, const AmpGen::ParticleProperties& pp );
+}
#endif
//
diff --git a/AmpGen/ParticlePropertiesList.h b/AmpGen/ParticlePropertiesList.h
index 0256ff3ca4d..289ccd8343d 100644
--- a/AmpGen/ParticlePropertiesList.h
+++ b/AmpGen/ParticlePropertiesList.h
@@ -24,7 +24,7 @@ namespace AmpGen
std::map<int, ParticleProperties*> m_byID;
double m_quasiStableThreshold;
- ParticlePropertiesList( const std::string& fname_in = "mass_width.csv" );
+ explicit ParticlePropertiesList( const std::string& fname_in = "mass_width.csv" );
protected:
const std::vector<std::string> dirList() const;
@@ -48,6 +48,7 @@ namespace AmpGen
void print( std::ostream& out = std::cout ) const;
bool readLatexLabels( const std::string& name );
void makeMappings();
+ void addParticle(const std::vector<std::string>& properties );
};
std::ostream& operator<<( std::ostream& out, const ParticlePropertiesList& ppl );
} // namespace AmpGen
diff --git a/AmpGen/PhaseSpace.h b/AmpGen/PhaseSpace.h
index 090badfc489..2d3f37257d6 100644
--- a/AmpGen/PhaseSpace.h
+++ b/AmpGen/PhaseSpace.h
@@ -10,38 +10,39 @@
namespace AmpGen
{
- /**@class PhaseSpace
- * Phase-space generator taken from the ROOT routine, from Rene Brun and Valerio Filippini,
- * which was originally based on the GENBOD routine of CERNLIB with
- * modifications such that unweighted events are generated,
- * which saves a large amount of CPU. Further modified to remove the dependencies on TLorentzVector
- * and to only use the AmpGen::Event classes, and to add the option to include a time dependence.
+ /** @class PhaseSpace
+ Phase-space generator taken from the ROOT routine, from Rene Brun and Valerio Filippini,
+ which was originally based on the GENBOD routine of CERNLIB with
+ modifications such that unweighted events are generated,
+ which saves a large amount of CPU. Further modified to remove the dependencies on TLorentzVector
+ and to only use the AmpGen::Event classes, and to add the option to include a time dependence.
*/
+ class Particle;
class PhaseSpace
{
public:
- PhaseSpace() = default;
- PhaseSpace( const EventType& type, TRandom* rand = gRandom );
- ~PhaseSpace() = default;
+ PhaseSpace() = default; ///< Empty constructor
+ explicit PhaseSpace(const EventType& type, TRandom* rand = gRandom); ///< Construct a phase space generator from an EventType
+ explicit PhaseSpace(const Particle& type, TRandom* rand = gRandom); ///< Construct a phase space generator from a Particle
- bool setDecay( const double& m0, const std::vector<double>& mass );
- void setRandom( TRandom* rand ) { m_rand = rand; }
- size_t size() const { return m_nt; }
- AmpGen::Event makeEvent( const size_t& cacheSize = 0 );
- AmpGen::EventType eventType() const;
+ bool setDecay( const double& m0, const std::vector<double>& mass ); ///< Set the parameters of this phase space generator
+ void setRandom( TRandom* rand ) { m_rand = rand; } ///< Set the random number used by this phase space generator
+ size_t size() const { return m_nt; } ///< Return the number of decay products
+ Event makeEvent(); ///< Make an event in this phase space.
+ EventType eventType() const; ///< Returns the EventType that this phase space is generating
+ void provideEfficiencyReport(const std::vector<bool>& report){}
private:
- unsigned int m_nt = {0}; // number of decay particles
- double m_mass[18] = {0}; // masses of particles
- double m_teCmTm = {0}; // total energy in the C.M. minus the total mass
- double m_wtMax = {0}; // maximum weight
- double m_decayTime = {0}; // decay time
- TRandom* m_rand = {nullptr}; // Random number generator
- EventType m_type; // EventType to generate
+ size_t m_nt = {0}; ///< Number of particles in the final state
+ double m_mass[18] = {0}; ///< Masses of particles in the final state
+ double m_teCmTm = {0}; ///< Total energy in the rest frame minus the total mass
+ double m_wtMax = {0}; ///< Maximum weight of an event
+ double m_decayTime = {0}; ///< Proper decay time of the particle
+ TRandom* m_rand = {nullptr}; ///< Random number generator
+ EventType m_type; ///< EventType to generate
- double rndm() { return m_rand->Rndm(); }
- double q(double a, double b, double c) const;
+ double q(double a, double b, double c) const; ///< Breakup momentum of a particle with mass a decaying to decay products with masses b and c.
};
} // namespace AmpGen
#endif
diff --git a/AmpGen/Plots.h b/AmpGen/Plots.h
deleted file mode 100644
index 7135c708329..00000000000
--- a/AmpGen/Plots.h
+++ /dev/null
@@ -1,103 +0,0 @@
-#ifndef AMPGEN_PLOTS_H
-#define AMPGEN_PLOTS_H
-#include "AmpGen/ErrorPropagator.h"
-#include "AmpGen/EventList.h"
-#include "AmpGen/CoherentSum.h"
-#include "AmpGen/IncoherentSum.h"
-#include "AmpGen/Integrator.h"
-#include "AmpGen/MinuitParameterSet.h"
-#include "AmpGen/Projection.h"
-#include "AmpGen/Utilities.h"
-#include "AmpGen/EventList.h"
-
-#include "TFile.h"
-#include "TH1D.h"
-#include "TH2D.h"
-#include <chrono>
-
-namespace AmpGen
-{
- void perAmplitudePlot(const EventList& evts, const Projection& projection, const CoherentSum& pdf);
-
- template <size_t NBINS, size_t NROLLS>
- std::array<Bilinears, NBINS> getNorms( CoherentSum& fcn, BinnedIntegrator<NBINS, NROLLS>& bid )
- {
-
- std::array<Bilinears, NBINS> normalisations;
- for ( unsigned int i = 0; i < NBINS; ++i ) normalisations[i] = Bilinears( fcn.size(), fcn.size() );
-
- for ( unsigned int i = 0; i < fcn.size(); ++i ) {
- for ( unsigned int j = i; j < fcn.size(); ++j ) {
- bid.addIntegral( fcn[i].pdf, fcn[j].pdf, [i, j, &normalisations]( const auto& val ) {
- for ( unsigned int bin = 0; bin < NBINS; ++bin ) {
- normalisations[bin].set( i, j, val[bin] );
- if ( i != j ) normalisations[bin].set( j, i, std::conj( val[bin] ) );
- }
- } );
- }
- }
- bid.flush();
- return normalisations;
- }
-
- template <size_t NBINS, size_t NROLLS>
- std::array<Bilinears, NBINS> getNorms( IncoherentSum& fcn, BinnedIntegrator<NBINS, NROLLS>& bid )
- {
- std::array<Bilinears, NBINS> normalisations;
- for ( unsigned int i = 0; i < NBINS; ++i ) normalisations[i] = Bilinears( fcn.size(), fcn.size() );
- for ( unsigned int i = 0; i < fcn.size(); ++i ) {
- bid.addIntegral( fcn[i].pdf, fcn[i].pdf, [i, &normalisations]( const auto& val ) {
- for ( unsigned int bin = 0; bin < NBINS; ++bin ) normalisations[bin].set( i, 0, val[bin] );
- } );
- }
- bid.flush();
- return normalisations;
- }
-
- template <size_t NBINS, class FCN>
- TH1D* plotWithError( EventList& events, FCN& fcn, const Projection& projection, const std::string& prefix,
- LinearErrorPropagator& linProp, const std::function<bool( const Event& )>& selection = nullptr )
- {
- BinnedIntegrator<NBINS, 10> bid( &events );
- if ( selection != nullptr ) bid.setSlice( selection );
- bid.setView( projection.binFunctor() );
- TH1D* plot = projection.plot();
- plot->SetName( ( prefix + plot->GetName() ).c_str() );
- auto normalisations = getNorms<NBINS>( fcn, bid );
-
- auto vectorBinFunctor = [&normalisations, &fcn, &bid] {
- fcn.transferParameters();
- bid.update( fcn, normalisations );
- std::array<double, NBINS> values;
- double total = 0;
- for ( size_t bin = 0; bin < NBINS; ++bin ) {
- values[bin] = fcn.norm( normalisations[bin] );
- total += values[bin];
- }
- for ( size_t bin = 0; bin < NBINS; ++bin ) values[bin] /= total;
- return values;
- };
- auto values = vectorBinFunctor();
- auto errors = linProp.getVectorError<NBINS>( vectorBinFunctor );
- for ( size_t bin = 0; bin < NBINS; ++bin ) {
- plot->SetBinContent( bin + 1, values[bin] );
- plot->SetBinError( bin + 1, errors[bin] );
- }
- return plot;
- }
-
-
- template <size_t NBINS, class FCN>
- std::vector<TH1D*> bandPlot( EventList& events, const std::string& prefix, FCN& fcn, LinearErrorPropagator& linProp )
- {
- std::vector<TH1D*> plots;
- auto axes = events.eventType().defaultProjections( NBINS );
- for ( auto& proj : axes ) {
- INFO( "Making plot:" << proj.name() );
- plots.push_back( plotWithError<NBINS>( events, fcn, proj, prefix, linProp ) );
- }
- return plots;
- }
-} // namespace AmpGen
-
-#endif
diff --git a/AmpGen/PolarisedSum.h b/AmpGen/PolarisedSum.h
index e9f7cf9225e..c6aec002e18 100644
--- a/AmpGen/PolarisedSum.h
+++ b/AmpGen/PolarisedSum.h
@@ -19,13 +19,14 @@
#include "AmpGen/CoherentSum.h"
#include "AmpGen/Expression.h"
#include "AmpGen/Tensor.h"
+#include "AmpGen/MinuitParameter.h"
+
#include "TMatrixD.h"
namespace AmpGen
{
class LinearErrorPropagator;
- class MinuitParameter;
class MinuitParameterSet;
class FitFraction;
class Event;
@@ -35,53 +36,68 @@ namespace AmpGen
class PolarisedSum
{
public:
- PolarisedSum( const EventType& eventType, AmpGen::MinuitParameterSet& mps, const std::string& prefix="" );
+ #if ENABLE_AVX
+ using EventList_type = EventListSIMD;
+ #else
+ using EventList_type = EventList;
+ #endif
+
+ PolarisedSum() = default;
+ PolarisedSum(const EventType&, MinuitParameterSet&, const std::vector<MinuitProxy>& = {});
void prepare();
- void setEvents( AmpGen::EventList& events );
- void setMC( AmpGen::EventList& events );
- void reset( const bool& flag = false );
- void debug(const AmpGen::Event& event );
+ void setEvents(EventList_type&);
+ void setMC(EventList_type&);
+ #if ENABLE_AVX
+ void setEvents(EventList& evts){ m_ownEvents = true; setEvents( *new EventList_type(evts)) ; };
+ void setMC(EventList& evts){ setMC( *new EventList_type(evts)) ; };
+ double operator()(const double*, const unsigned) const;
+ #endif
+ float_v operator()(const float_v*, const unsigned) const;
+ real_t operator()(const Event& evt) const;
+ void reset(const bool& = false);
+ void debug(const Event&);
void debug_norm();
- void setWeight( MinuitParameter* param );
+ void setWeight(MinuitProxy);
double getWeight() const;
- void calculateNorms(const std::vector<bool>& hasChanged);
- void generateSourceCode( const std::string& fname, const double& normalisation = 1, bool add_mt = false );
- void build_probunnormalised();
- Expression probExpression( const Tensor& T_matrix, const std::vector<Expression>& p ) const;
- size_t size() const ;
+ void updateNorms();
+ void generateSourceCode(const std::string&, const double& = 1, bool = false);
+ Expression probExpression(const Tensor&, const std::vector<Expression>&, DebugSymbols* = nullptr) const;
+ size_t size() const;
real_t norm() const;
- complex_t norm(const size_t& i, const size_t& j, Integrator<18>* integ = nullptr );
- real_t operator()(const AmpGen::Event& event) const { return prob_unnormalised(event) ;}
- real_t prob_unnormalised( const AmpGen::Event& evt ) const;
- real_t prob(const AmpGen::Event& evt ) const ;
- real_t getValNoCache( const AmpGen::Event& evt ) ;
- std::vector<FitFraction> fitFractions( const LinearErrorPropagator& prop );
- std::vector<TransitionMatrix<std::vector<complex_t>>> matrixElements() const;
+ complex_t norm(const size_t&, const size_t&, Integrator* = nullptr);
+ real_t getValNoCache(const Event&) const;
+ std::vector<FitFraction> fitFractions(const LinearErrorPropagator&);
+ std::vector<TransitionMatrix<void>> matrixElements() const;
void transferParameters();
- Tensor transitionMatrix();
- TransitionMatrix<std::vector<complex_t>> operator[](const size_t& i) const { return m_matrixElements[i] ; }
-
+ Tensor transitionMatrix() const;
+ const TransitionMatrix<void>& operator[](const size_t& i) const { return m_matrixElements[i] ; }
+ std::function<real_t(const Event&)> evaluator(const EventList_type* = nullptr) const;
+ KeyedFunctors<double(Event)> componentEvaluator(const EventList_type* = nullptr) const;
+ EventType eventType() const{ return m_eventType; }
private:
size_t m_nCalls = {0};
real_t m_norm = {1};
- EventList* m_events = {nullptr};
- MinuitParameter* m_weightParam = {nullptr};
- const MinuitParameterSet* m_mps = {nullptr};
- double m_weight = {1};
+ EventList_type* m_events = {nullptr};
+ Store<complex_v, Alignment::AoS> m_cache = {};
+ Store<float_v , Alignment::SoA> m_pdfCache = {};
+ bool m_ownEvents = {false};
+ MinuitParameterSet* m_mps = {nullptr};
+ MinuitProxy m_weight = {nullptr,1};
std::vector<MinuitProxy> m_pVector = {};
bool m_verbosity = {0};
- Integrator<18> m_integrator;
+ bool m_debug = {0};
+ Integrator m_integrator;
std::vector<Bilinears> m_norms;
- std::vector<std::vector<int>> m_polStates;
EventType m_eventType;
std::string m_prefix = "";
- std::vector<complex_t> m_psi;
+ std::vector<complex_t> m_rho;
std::vector<size_t> m_integIndex;
- std::vector<TransitionMatrix<std::vector<complex_t>>> m_matrixElements;
- CompiledExpression<real_t, const real_t*, const complex_t*> m_probExpression;
AmplitudeRules m_rules;
- std::vector<std::vector<int>> polarisationOuterProduct( const std::vector<std::vector<int>>& A, const std::vector<int>& B ) const;
- std::vector<int> polarisations( const std::string& name ) const ;
+ std::pair<unsigned, unsigned> m_dim;
+ std::vector<TransitionMatrix<void>> m_matrixElements;
+ CompiledExpression<float_v(const real_t*, const complex_v*)> m_probExpression;
+ std::vector<std::vector<int>> indexProduct(const std::vector<std::vector<int>>&, const std::vector<int>&) const;
+ std::vector<int> polarisations(const std::string&) const ;
};
} // namespace AmpGen
diff --git a/AmpGen/ProfileClock.h b/AmpGen/ProfileClock.h
index 008b834cad1..8810c325663 100644
--- a/AmpGen/ProfileClock.h
+++ b/AmpGen/ProfileClock.h
@@ -1,24 +1,67 @@
#ifndef AMPGEN_PROFILECLOCK_H
#define AMPGEN_PROFILECLOCK_H 1
#include <chrono>
+#include <math.h>
#include "AmpGen/MsgService.h"
#include "AmpGen/Utilities.h"
namespace AmpGen{
struct ProfileClock {
- std::chrono::time_point<std::chrono::high_resolution_clock> t_start;
- std::chrono::time_point<std::chrono::high_resolution_clock> t_end;
- ProfileClock() : t_start( std::chrono::high_resolution_clock::now()) {}
- void stop(){ t_end = std::chrono::high_resolution_clock::now() ; }
- operator double() const { return std::chrono::duration<double, std::milli>( t_end - t_start ).count() ; } ;
+ std::chrono::time_point<std::chrono::high_resolution_clock> t_start;
+ std::chrono::time_point<std::chrono::high_resolution_clock> t_end;
+ double t_duration = {0};
+
+ ProfileClock() : t_start(std::chrono::high_resolution_clock::now()) {}
+ void stop()
+ {
+ t_end = std::chrono::high_resolution_clock::now() ;
+ t_duration += std::chrono::duration<double, std::milli>( t_end - t_start ).count();
+ }
+ double count() const
+ {
+ auto now = std::chrono::high_resolution_clock::now() ;
+ return std::chrono::duration<double, std::milli>(now - t_start ).count();
+ }
+ void start(){ t_start = std::chrono::high_resolution_clock::now() ; }
+ operator double() const { return t_duration; } ;
};
template <int N, class FCN>
- double Profile( const FCN& fcn ){
+ double Profile( const FCN& fcn, const std::string& name ="" ){
ProfileClock t;
for( size_t i = 0 ; i < N; ++i ) fcn();
t.stop();
- INFO( typeof<FCN>() << " " << t/double(N) << "[ms] per iteration" );
+ INFO( (name == "" ? type_string<FCN>() : name ) << " " << t/double(N) << "[ms] per iteration" );
+ return t;
+ }
+ template <int N, class FCN>
+ double ProfileWithStat( const FCN& fcn, const std::string& name ="" ){
+ double t = 0;
+ double t2 = 0;
+ double tmin = 1e9;
+ double tmax = 0;
+ for( size_t i = 0 ; i < N; ++i ){
+ ProfileClock pi;
+ fcn();
+ pi.stop();
+ t += pi;
+ t2 += pi*pi;
+ tmin = pi < tmin ? pi : tmin;
+ tmax = pi > tmax ? pi : tmax;
+ }
+ t /= double(N);
+ t2 = std::sqrt( t2 / double(N) - t*t);
+ INFO( (name == "" ? type_string<FCN>() : name ) << " " << t << " ± " << t2 << "[ms] per iteration << [" << tmin << ", " << tmax << "]" );
+ return t;
+ }
+
+ template <int N, class FCN>
+ double Profile2( const FCN& fcn ){
+ ProfileClock t;
+ auto z = 0 ;
+ for( size_t i = 0 ; i < N; ++i ) z += fcn();
+ t.stop();
+ INFO( type_string<FCN>() << " " << t/double(N) << "[ms] per iteration; " << z );
return t;
}
}
diff --git a/AmpGen/ProgressBar.h b/AmpGen/ProgressBar.h
new file mode 100644
index 00000000000..258fe5f9202
--- /dev/null
+++ b/AmpGen/ProgressBar.h
@@ -0,0 +1,21 @@
+#ifndef AMPGEN_PROGRESSBAR_H
+#define AMPGEN_PROGRESSBAR_H
+
+#include <string>
+namespace AmpGen {
+ class ProgressBar {
+ public:
+ ProgressBar(const size_t& width, const std::string& context);
+ ~ProgressBar();
+ void print(const double& percentage, const std::string& message="");
+ void finish();
+ private:
+ size_t m_width;
+ int m_lastPercent;
+ std::string m_context;
+ std::string m_lastMessage = {""};
+ bool m_finished = {false};
+ };
+}
+
+#endif
diff --git a/AmpGen/Projection.h b/AmpGen/Projection.h
index ad77e66c683..ce91ffb9e1e 100644
--- a/AmpGen/Projection.h
+++ b/AmpGen/Projection.h
@@ -8,43 +8,67 @@
#include "TH1D.h"
#include "TH2D.h"
-#include "AmpGen/Event.h"
+#include "THStack.h"
-class TH1D;
-class TH2D;
+#include "AmpGen/ArgumentPack.h"
+#include "AmpGen/Types.h"
+#include "AmpGen/KeyedFunctors.h"
namespace AmpGen
{
class Projection2D;
class Event;
+ class EventList;
class Projection
{
- friend class Projection2D;
- private:
- std::function<double( const Event& )> m_func;
- std::string m_name;
- std::string m_xAxisTitle;
- std::string m_units;
- size_t m_nBins;
- double m_min;
- double m_max;
- double m_width;
+ using keyedFunctors = KeyedFunctors<double(Event)>;
public:
- const std::string name() const ;
- double operator()( const Event& evt ) const ;
- template <class FCN>
+ Projection();
+ template <class FCN>
Projection( const FCN& fcn, const std::string& name,
const std::string& xAxisTitle, const size_t& nBins, const double& min, const double& max,
const std::string& units = "" ) : Projection( std::function< double( const Event& )>( fcn ), name, xAxisTitle, nBins, min, max, units ) {}
- Projection( const std::function<double( const Event& )>& fcn, const std::string& name,
- const std::string& xAxisTitle, const size_t& nBins, const double& min, const double& max,
- const std::string& units = "" );
+ Projection( const std::function<double( const Event& )>& fcn, const std::string& name,
+ const std::string& xAxisTitle, const size_t& nBins, const double& min, const double& max,
+ const std::string& units = "" );
+ const std::string name() const;
+ template <class eventlist_type, class... ARGS> TH1D* operator()(const eventlist_type& evts, const ARGS... args) const
+ {
+ return projInternal(evts, ArgumentPack(args...) );
+ }
+ template <class eventlist_type, class... ARGS> std::tuple<std::vector<TH1D*>, THStack*> operator()(const eventlist_type& evts,
+ const keyedFunctors& weightFunction, const ARGS... args ) const
+ {
+ return projInternal(evts, weightFunction, ArgumentPack(args...) );
+ }
+
+ double operator()( const Event& evt ) const;
+
+ TH1D* plot(const std::string& prefix="") const;
- TH1D* plot(const std::string& prefix="") const;
+ std::function<int( const Event& evt )> binFunctor() const;
+ void setRange( const double& min, const double& max )
+ {
+ m_min = min;
+ m_max = max;
+ m_width = (m_max-m_min)/double(m_nBins);
+ }
- std::function<size_t( const Event& evt )> binFunctor() const;
- void setRange( const double& min, const double& max ){ m_min = (min); m_max = (max) ; }
+ friend class Projection2D;
+ /// private:
+ template <class eventlist_type>
+ TH1D* projInternal(const eventlist_type&, const ArgumentPack&) const;
+ template <class eventlist_type>
+ std::tuple<std::vector<TH1D*>, THStack*> projInternal(const eventlist_type&, const keyedFunctors&, const ArgumentPack&) const;
+ std::function<double( const Event& )> m_func;
+ std::string m_name = {""};
+ std::string m_xAxisTitle = {""};
+ std::string m_units = {""};
+ size_t m_nBins = {0};
+ double m_min = {0};
+ double m_max = {0};
+ double m_width = {0};
};
class Projection2D
@@ -60,7 +84,15 @@ namespace AmpGen
std::pair<double, double> operator()( const Event& evt ) const;
};
-
+ namespace PlotOptions {
+ DECLARE_ARGUMENT(LineColor , int);
+ DECLARE_ARGUMENT(DrawStyle , std::string);
+ DECLARE_ARGUMENT(Selection , std::function<bool( const Event& )>);
+ DECLARE_ARGUMENT(Prefix , std::string);
+ DECLARE_ARGUMENT(Norm , double);
+ DECLARE_ARGUMENT(AddTo , THStack*);
+ DECLARE_ARGUMENT(AutoWrite , bool);
+ }
} // namespace AmpGen
#endif
diff --git a/AmpGen/QuarkContent.h b/AmpGen/QuarkContent.h
index 17d4feb7ab7..061750ba6df 100644
--- a/AmpGen/QuarkContent.h
+++ b/AmpGen/QuarkContent.h
@@ -17,9 +17,8 @@ namespace AmpGen
std::array<int, 6> m_quarks;
public:
QuarkState();
- QuarkState( const std::string& str );
+ explicit QuarkState( const std::string& str );
void antiThis();
- void initFromString( const std::string& str );
char nameFromPosition( int i ) const;
int positionFromName( char c ) const;
bool isVacuum() const;
@@ -28,8 +27,9 @@ namespace AmpGen
QuarkState& operator-=( const QuarkState& rhs );
QuarkState operator+ ( const QuarkState& rhs ) const;
QuarkState operator- ( const QuarkState& rhs ) const;
- bool operator==( const QuarkState& rhs ) const;
- int operator[]( const size_t& index ) const;
+ bool operator==( const QuarkState& rhs ) const;
+ bool operator!=( const QuarkState& rhs ) const;
+ int operator[]( const size_t& index ) const;
};
class QuarkContent
@@ -38,9 +38,8 @@ namespace AmpGen
std::vector<QuarkState> m_quarks;
public:
QuarkContent();
- QuarkContent( const std::string& str ){ initFromString(str); }
+ explicit QuarkContent( const std::string& str );
void antiThis();
- void initFromString( const std::string& str );
void print( std::ostream& os = std::cout ) const;
size_t size() const;
bool compatible( const QuarkContent& other ) const;
@@ -50,8 +49,8 @@ namespace AmpGen
QuarkContent operator- ( const QuarkContent& rhs ) const;
bool operator==( const QuarkContent& rhs ) const;
bool operator!=( const QuarkContent& rhs ) const;
- QuarkState operator[]( const size_t& index) const;
- std::vector<QuarkState> quarks() const;
+ QuarkState operator[]( const size_t& index) const;
+ const std::vector<QuarkState>& quarks() const;
};
std::ostream& operator<<( std::ostream& st, const QuarkState& qc );
std::ostream& operator<<( std::ostream& st, const QuarkContent& qc );
diff --git a/AmpGen/RecursivePhaseSpace.h b/AmpGen/RecursivePhaseSpace.h
index 073a21ae7d7..bf71534a906 100644
--- a/AmpGen/RecursivePhaseSpace.h
+++ b/AmpGen/RecursivePhaseSpace.h
@@ -21,35 +21,43 @@ namespace AmpGen
{
class Particle;
class Event;
-
+ /** @class RecursivePhaseSpace
+ @brief Generator of events with more complex topologies.
+ @decription Generates events in the phase space of a decay with one-or-more quasistable products
+ that are further decayed, where these quasistable products are suitably long-lived
+ that their propagators can be assumed to be delta-functions, i.e. particles such as
+ @f$ \Lambda^0 , {K_\rm{S}}^0 @f$ etc. Such a process has a natural factorisation into
+ each of these steps. For each of the decays of a quasistable particle, the PhaseSpace
+ generator is used, which is itself based heavily on TGenPhaseSpace.
+ */
class RecursivePhaseSpace
{
private:
struct Node
{
- std::string name;
- int sink = {-1};
+ std::string name = {""};
+ int sink = {-1};
std::shared_ptr<RecursivePhaseSpace> decayProds = {nullptr};
- Node( const std::string& _name ) : name( _name ) {};
+ explicit Node( const std::string& _name ) : name( _name ) {};
};
public:
- RecursivePhaseSpace(const EventType& type);
+ explicit RecursivePhaseSpace(const EventType& type);
RecursivePhaseSpace(const Particle& decayChain, const EventType& type, TRandom* rndm = gRandom);
std::vector<Node*> getFinalStates();
void print( const size_t& offset = 0 ) const;
void setRandom( TRandom* rand );
- AmpGen::Event makeEvent( const size_t& cacheSize = 0 );
+ Event makeEvent();
size_t size() const;
EventType eventType() const ;
+ void provideEfficiencyReport(const std::vector<bool>& report){}
private:
PhaseSpace m_phsp;
- unsigned int m_totalSize;
- std::string m_name;
+ unsigned m_totalSize = {0};
+ std::string m_name = {""};
EventType m_eventType;
std::vector<Node> m_nodes;
-
};
} // namespace AmpGen
diff --git a/AmpGen/SimPDF.h b/AmpGen/SimPDF.h
index ba46838a76b..ad47ef00d64 100644
--- a/AmpGen/SimPDF.h
+++ b/AmpGen/SimPDF.h
@@ -7,23 +7,25 @@ namespace AmpGen
{
class SimFit
{
- std::vector<std::function<double( void )>> m_pdfs;
+ public:
+ SimFit() = default;
+ double getVal()
+ {
+ double LL = 0;
+ for ( auto& pdf : m_pdfs ) LL += pdf();
+ return LL;
+ }
- public:
- SimFit() {}
- double getVal()
- {
- double LL = 0;
- for ( auto& pdf : m_pdfs ) LL += pdf();
- return LL;
- }
+ template <class PDF>
+ void add( PDF& pdf )
+ {
+ INFO( "Adding " << &pdf << " to sim fit" );
+ m_pdfs.emplace_back( [&pdf]() -> double { return pdf.getVal(); } );
+ }
+
+ private:
+ std::vector<std::function<double( void )>> m_pdfs;
- template <class PDF>
- void add( PDF& pdf )
- {
- INFO( "Adding " << &pdf << " to sim fit" );
- m_pdfs.emplace_back( [&pdf]() -> double { return pdf.getVal(); } );
- }
};
} // namespace AmpGen
diff --git a/AmpGen/Simplify.h b/AmpGen/Simplify.h
index 5ecdc59be87..882d081ac9f 100644
--- a/AmpGen/Simplify.h
+++ b/AmpGen/Simplify.h
@@ -8,6 +8,9 @@
#include "AmpGen/Expression.h"
namespace AmpGen {
+
+ Expression Simplify(const Expression& expression );
+
class NormalOrderedExpression {
public:
struct Term {
@@ -31,7 +34,6 @@ namespace AmpGen {
std::vector<Term> m_terms;
bool m_expandSubTrees;
};
- Expression Simplify(const Expression& expression );
}
#endif
diff --git a/AmpGen/Spline.h b/AmpGen/Spline.h
index bed74747e21..3556e80b823 100644
--- a/AmpGen/Spline.h
+++ b/AmpGen/Spline.h
@@ -12,7 +12,6 @@
#include "AmpGen/Expression.h"
#include "AmpGen/CacheTransfer.h"
#include "AmpGen/Types.h"
-#include "TMatrixDUtilsfwd.h"
#include "TMatrixTBase.h"
#include "TMatrixD.h"
@@ -24,54 +23,50 @@ namespace AmpGen{
class SplineTransfer : public CacheTransfer
{
- private:
- TMatrixD m_transferMatrix;
- std::vector<AmpGen::MinuitParameter*> m_parameters;
- unsigned int m_nKnots;
- double m_min;
- double m_max;
- unsigned int m_address;
+ public:
+ SplineTransfer();
+ SplineTransfer( const SplineTransfer& other );
+ SplineTransfer( const size_t& address, const std::string& name, const unsigned int& N, const double& min, const double& max );
+ void transfer( CompiledExpressionBase* destination ) override;
+ bool isConfigured();
+ void set( const unsigned int& N, AmpGen::MinuitParameter* f );
+ void set( const unsigned int& N, const double& value );
+ void print() const override;
+ size_t size() const override { return 2*m_nKnots; }
- public:
- SplineTransfer();
- SplineTransfer( const SplineTransfer& other );
- SplineTransfer( const unsigned int& address, const unsigned int& N, const double& min, const double& max );
- void transfer( CompiledExpressionBase* destination ) override;
+ private:
+ TMatrixD m_transferMatrix;
+ std::vector<AmpGen::MinuitParameter*> m_parameters;
+ size_t m_nKnots;
+ double m_min;
+ double m_max;
+ };
- bool isConfigured();
+ class Spline : public IExpression {
+ public:
+ Spline( const std::string& name,
+ const size_t& nKnots,
+ const double& min,
+ const double& max );
- void set( const unsigned int& N, AmpGen::MinuitParameter* f );
- void set( const unsigned int& N, const double& value );
+ Spline( const Spline& spline, const Expression& x, DebugSymbols* db =nullptr );
+ void resolve( ASTResolver& resolver ) const override ;
+ std::string to_string(const ASTResolver* resolver=nullptr) const override;
+ operator Expression() ;
+ complex_t operator()() const override ;
+ Expression operator()( const Expression& x, DebugSymbols* db);
+ Expression eval(DebugSymbols* db=nullptr) const ;
- void setAddress( const unsigned int& address );
- void print() const override;
- unsigned int address() const override { return m_address ; }
- unsigned int size() const override { return 2*m_nKnots ; }
- };
-
- struct Spline : public IExpression {
- Array m_points;
- std::string m_name;
- size_t m_nKnots;
- double m_min;
- double m_max;
- Expression m_x;
- Expression m_eval;
- Spline( const std::string& name,
- const size_t& nKnots,
- const double& min,
- const double& max );
-
- Spline( const Spline& spline, const Expression& x );
- void resolve( ASTResolver& resolver ) override ;
- std::string to_string(const ASTResolver* resolver=nullptr) const override;
- operator Expression() ;
- complex_t operator()() const override ;
- Expression operator()( const Expression& x );
- Expression eval() const ;
+ Array m_points;
+ std::string m_name;
+ size_t m_nKnots;
+ double m_min;
+ double m_max;
+ Expression m_x;
+ Expression m_eval;
};
Expression getSpline( const std::string& name, const AmpGen::Expression& x, const std::string& arrayName,
- AmpGen::DebugSymbols* dbexpressions = nullptr, const bool& continueSpline = false );
+ AmpGen::DebugSymbols* dbexpressions = nullptr, const bool& continueSpline = false );
}
#endif
diff --git a/AmpGen/Store.h b/AmpGen/Store.h
new file mode 100644
index 00000000000..7c7e0ffe2df
--- /dev/null
+++ b/AmpGen/Store.h
@@ -0,0 +1,178 @@
+#ifndef AMPGEN_STORE_H
+#define AMPGEN_STORE_H
+
+#include "AmpGen/simd/utils.h"
+#include "AmpGen/EventList.h"
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+
+namespace AmpGen {
+
+ enum Alignment {
+ SoA, AoS
+ };
+
+ template <typename stored_type, Alignment align = SoA> class Store
+ {
+ public:
+ Store( const size_t& nEntries=0, const size_t& nFields=0) :
+ m_nEntries(nEntries),
+ m_nBlocks(utils::aligned_size<stored_type>( nEntries ) / utils::size<stored_type>::value ),
+ m_nFields(nFields),
+ m_store(m_nBlocks * m_nFields) {}
+
+ template <typename functor_type>
+ void addFunctor( const functor_type& functor )
+ {
+ if( m_index.count(functor.name()) == 0 )
+ {
+ auto vsize = functor.returnTypeSize() / sizeof(stored_type);
+ DEBUG("Registering: " << functor.name() << " field = " << m_nFields << " " << functor.returnTypeSize() << " / " << sizeof(stored_type) );
+ m_index[ functor.name() ] = std::make_pair(m_nFields, vsize);
+ m_nFields += vsize;
+ }
+ }
+ template <typename functor_type> void allocate( const size_t& nEntries, const std::vector<functor_type>& functors)
+ {
+ for(const auto& functor : functors) addFunctor( functor );
+ m_nEntries = nEntries;
+ m_nBlocks = utils::aligned_size<stored_type>(nEntries)/utils::size<stored_type>::value;
+ m_store.resize(m_nBlocks * m_nFields);
+ }
+ template <typename functor_type, typename = typename std::enable_if<!std::is_integral<functor_type>::value>::type >
+ void allocate( const size_t& nEntries, const functor_type& functor)
+ {
+ addFunctor(functor);
+ m_nEntries = nEntries;
+ m_nBlocks = utils::aligned_size<stored_type>(nEntries)/utils::size<stored_type>::value;
+ m_store.resize(m_nBlocks * m_nFields);
+ }
+
+ template <typename functor_type> Store( const size_t& nEntries, const std::vector<functor_type>& functors)
+ {
+ allocate(nEntries, functors);
+ }
+ template <typename functor_type, typename = typename std::enable_if<!std::is_integral<functor_type>::value>::type>
+ Store( const size_t& nEntries, const functor_type& functor)
+ {
+ allocate( nEntries, {functor});
+ }
+
+ inline stored_type operator[]( const size_t& index ) const { return m_store[index]; }
+ inline stored_type& operator[]( const size_t& index ) { return m_store[index]; }
+ template <typename T> unsigned find( const T& t ) const { return m_index.find( t.name() )->second.first; }
+
+ inline size_t size() const { return m_nEntries; }
+ inline size_t nBlocks() const { return m_nBlocks; }
+ inline size_t nFields() const { return m_nFields; }
+ inline size_t aligned_size() const { return m_nBlocks * utils::size<stored_type>::value ; }
+ inline const stored_type& operator()(const size_t& index, const size_t& field) const
+ {
+ if constexpr( align == Alignment::SoA ) return m_store[ field * m_nBlocks + index] ;
+ else return m_store[index*m_nFields+field];
+ }
+ template <typename return_type>
+ inline const return_type get(const size_t& index, const size_t& field ) const
+ {
+ return utils::at( operator()( index / utils::size<stored_type>::value, field ), index % utils::size<stored_type>::value );
+ }
+ inline const stored_type* data() const { return m_store.data(); }
+ inline stored_type* data() { return m_store.data() ;}
+ inline stored_type& operator()(const size_t& index, const size_t& field)
+ {
+ if constexpr( align == Alignment::SoA ) return m_store[ field * m_nBlocks + index] ;
+ else return m_store[index*m_nFields+field];
+ }
+
+ void resize(const size_t& nEntries, const size_t& nFields )
+ {
+ m_nEntries = nEntries;
+ m_nBlocks = utils::aligned_size<stored_type>(nEntries)/utils::size<stored_type>::value;
+ m_nFields = nFields;
+ m_store.resize(m_nBlocks * m_nFields);
+ m_index.clear();
+ }
+ void clear() { m_store.clear(); m_index.clear() ; }
+ void store( const size_t& event0, const size_t& index0, const stored_type* item, const unsigned N = 1 )
+ {
+ if constexpr( align == Alignment::AoS )
+ std::memcpy( &(*this)(event0, index0) , item, N * sizeof( stored_type ) );
+ else
+ {
+ for( unsigned i = 0 ; i != N ; ++i ) (*this)(event0, index0 +i ) = item[i];
+ }
+ }
+
+ template <typename functor_type, typename input_type> void update(const Store<input_type, Alignment::AoS>& is, const functor_type& fcn)
+ {
+ auto f = m_index.find( fcn.name() );
+ if( f == m_index.end() ) FATAL("Expression: " << fcn.name() << " is not registed");
+ auto [p0, s] = f->second;
+ DEBUG("Updating: " << fcn.name() << " index = " << p0 << " size_of = " << s << " on store: " << is.size() << " blocks = " << is.nBlocks() << " fields = " << is.nFields () );
+ if constexpr( align == Alignment::AoS )
+ {
+ if constexpr( std::is_same< typename functor_type::return_type, void >::value )
+ fcn.batch(aligned_size(), is.nFields(), m_nFields, nullptr, m_store.data() + p0, 1, fcn.externBuffer().data(), is.data());
+ if constexpr( ! std::is_same< typename functor_type::return_type, void >::value )
+ fcn.batch(aligned_size(), is.nFields(), m_nFields , m_store.data() + p0 , fcn.externBuffer().data(), is.data());
+ }
+ else
+ {
+ if constexpr( std::is_same< typename functor_type::return_type, void >::value)
+ fcn.batch(aligned_size(), is.nFields(), 1, nullptr, m_store.data() + p0*m_nBlocks, m_nBlocks, fcn.externBuffer().data(), is.data() );
+ else
+ fcn.batch(aligned_size(), is.nFields(), 1 , m_store.data() + p0*m_nBlocks , fcn.externBuffer().data(), is.data() );
+ }
+ }
+ template <typename functor_type> void update( const EventList& events, const functor_type& fcn )
+ {
+ auto f = m_index.find( fcn.name() );
+ if( f == m_index.end() ) FATAL("Expression: " << fcn.name() << " is not registed");
+ //auto& [p0, s] = f->second; /// bug in the C++ standard. Such fun.
+ auto p0 = f->second.first;
+ auto s = f->second.second;
+ DEBUG("Updating: " << fcn.name() << " index = " << p0 << " size_of = " << s << " on store: " << size() << " blocks = " << nBlocks() << " fields = " << nFields () );
+
+ if constexpr( std::is_same< typename functor_type::return_type, void >::value )
+ {
+
+ #ifdef _OPENMP
+ #pragma omp parallel for
+ #endif
+ for ( size_t evt = 0; evt < events.size(); ++evt )
+ {
+ std::vector<stored_type> buffer(s);
+ fcn(buffer.data(), 1, fcn.externBuffer().data(), events[evt].address() );
+ store(evt, p0, buffer.data(), s );
+ }
+ }
+ else {
+ #ifdef _OPENMP
+ #pragma omp parallel for
+ #endif
+ for ( size_t evt = 0; evt < events.size(); ++evt )
+ {
+ auto tmp = fcn( events[evt].address() );
+ store( evt, p0, &tmp, s);
+ }
+ }
+ }
+
+ private:
+ size_t m_nEntries{0}; /// Number of entries, i.e. number of events
+ size_t m_nBlocks {0}; /// Number of blocks, i.e. number of entries aligned to the size, divided by block size.
+ size_t m_nFields {0}; /// Number of fields per entry
+ std::vector<stored_type> m_store;
+ std::map<std::string, std::pair<unsigned, unsigned>> m_index;
+ };
+}
+#if DEBUG_LEVEL ==1
+using aos_store = AmpGen::Store<AmpGen::complex_v, AmpGen::Alignment::AoS>;
+using soa_store = AmpGen::Store<AmpGen::complex_v, AmpGen::Alignment::SoA>;
+
+ENABLE_DEBUG(aos_store)
+ENABLE_DEBUG(soa_store)
+#endif
+
+#endif
diff --git a/AmpGen/SumPDF.h b/AmpGen/SumPDF.h
index 2cdcea39e62..832d5d68860 100644
--- a/AmpGen/SumPDF.h
+++ b/AmpGen/SumPDF.h
@@ -1,74 +1,159 @@
#ifndef AMPGEN_SUMPDF_H
#define AMPGEN_SUMPDF_H
-#include "AmpGen/EventList.h"
#include "AmpGen/IExtendLikelihood.h"
#include "AmpGen/MetaUtils.h"
#include "AmpGen/MsgService.h"
#include "AmpGen/ProfileClock.h"
-
+#include "AmpGen/KeyedFunctors.h"
#include <tuple>
-/* A SumPDF is the log-likelihood of the form
- -2*LL(event) = -2*log( Sum( i, P_i(event) ) )
- Where P_i are some probability density functions
- The sum is variadically unrolled at compile time, i.e. the wrapper
- is the same for 1..N pdfs. The unrolling should be properly inlined,
- hence N can be reasonably large with out afflicting either
- compile time or binary size.
- */
+
+#if ENABLE_AVX
+ #include "AmpGen/simd/utils.h"
+#endif
namespace AmpGen
{
- template <class... TYPES>
+ class EventList;
+ class EventListSIMD;
+ /** @class SumPDF
+ @brief A pdf that contains one or more terms.
+
+ A pdf with a probability of the form
+ @f[
+ P(\psi) = \sum_{j} \mathcal{P}_j (\psi),
+ @f]
+ where @f$ \mathcal{P}_j(\psi) @f$ are some normalised probability density functions
+ as a function of position in the phase space @f$ \psi @f$
+ , and the sum is over the different terms, typically a signal term and then a number of background terms.
+ The pdf is also equipped with a log-likelihood of the form:
+ @f[
+ -2 \mathcal{L} = - 2 \sum_{i} \log \left( \sum_{j} \mathcal{P}_j \left(\psi_i\right) \right)
+ @f]
+ and the sum over @f$ i @f$ is over some dataset.
+ This combined functionality is largely historical and the two roles should be separated at some point in the future.
+ The sum is variadically unrolled at compile time, i.e. the wrapper
+ is the same for 1..N pdfs. The unrolling should be properly inlined,
+ hence N can be reasonably large with out afflicting either
+ compile time or binary size. It isn't primarily used as PDF, as its primary function is
+ as a likelihood via function getVal().
+ Typically constructed using either the make_pdf helper function or make_likelihood helper function. */
+ template <class eventListType, class... pdfTypes>
class SumPDF
{
+ private:
+ typedef typename eventListType::value_type eventValueType; ///< The value type stored in the eventListType
+ std::tuple<pdfTypes...> m_pdfs; ///< The tuple of probability density functions
+ const eventListType* m_events = {nullptr}; ///< The event list to evaluate likelihoods on
+
public:
- SumPDF( const TYPES&... _pdfs ) : m_pdfs( std::tuple<TYPES...>( _pdfs... ) ) {}
- std::tuple<TYPES...> m_pdfs;
- EventList* m_events;
+ /// Default Constructor
+ SumPDF() = default;
+
+ /// Constructor from a set of PDF functions
+ SumPDF( const pdfTypes&... pdfs ) : m_pdfs( std::tuple<pdfTypes...>( pdfs... ) ) {}
+
+ /// Returns negative twice the log-likelihood for this PDF and the given dataset.
- std::tuple<TYPES...> pdfs() const { return m_pdfs; }
-
double getVal()
{
-// ProfileClock pc;
- double LL = 0;
- for_each( m_pdfs, []( auto& f ) { f.prepare(); } );
-// pc.stop();
-// ProfileClock eval;
- #pragma omp parallel for reduction( +: LL )
- for ( unsigned int i = 0; i < m_events->size(); ++i ) {
- auto prob = ((*this))(( *m_events)[i] );
- LL += log(prob);
+ if constexpr( std::is_same<eventListType,EventList>::value )
+ {
+ double LL = 0;
+ for_each( m_pdfs, []( auto& f ) { f.prepare(); } );
+ #pragma omp parallel for reduction( +: LL )
+ for ( unsigned int i = 0; i < m_events->size(); ++i ) {
+ auto prob = ((*this))(( *m_events)[i] );
+ auto w = (*m_events)[i].weight();
+ LL += w*log(prob);
+ }
+ return -2 * LL;
}
-// eval.stop();
-// std::cout << "t [prepare] = " << pc << "; t[eval] = " << eval << "ms" << std::endl;
- return -2 * LL;
+ #if ENABLE_AVX
+ if constexpr( std::is_same<eventListType, EventListSIMD>::value )
+ {
+ float_v LL = 0.f;
+ for_each( m_pdfs, []( auto& f ) { f.prepare(); } );
+ #pragma omp parallel for reduction( +: LL )
+ for ( size_t block = 0; block < m_events->nBlocks(); ++block )
+ {
+ LL += m_events->weight(block) * AVX::log(this->operator()(m_events->block(block), block));
+ }
+ return -2 * utils::sum_elements(LL);
+ }
+ #endif
+ }
+ /// Returns the probability for the given event.
+ float_v operator()( const float_v* evt , const unsigned block)
+ {
+ float_v prob = 0.f;
+ for_each( this->m_pdfs, [&prob, &evt,block]( const auto& f ) { prob += f(evt, block); } );
+ return prob;
}
- double operator()( const Event& evt )
+ /// Returns the probability for the given event.
+ double operator()( const eventValueType& evt )
{
double prob = 0;
- for_each( this->m_pdfs, [&prob, &evt]( auto& f ) { prob += f.prob( evt ); } );
+ for_each( this->m_pdfs, [&prob, &evt]( const auto& f ) { prob += f(evt); } );
return prob;
}
- void setEvents( EventList& events )
+
+ /// Sets the events to be summed over in the likelihood
+ void setEvents( eventListType& events )
{
m_events = &events;
for_each( m_pdfs, [&events]( auto& f ) { f.setEvents( events ); } );
}
- template <class FCN>
- void forEach( const FCN& fcn )
- {
- for_each( m_pdfs, fcn );
+ /// Returns the number of PDFs contained by this function
+ std::size_t nPDFs() const { return sizeof...(pdfTypes); }
+
+ /// Returns the tuple of PDFs used by this function
+ std::tuple<pdfTypes...> pdfs() const { return m_pdfs; }
+
+ std::function<double(const eventValueType&)> evaluator(const eventListType* events) const
+ {
+ std::vector<double> values( events->size() );
+ for_each( this->m_pdfs, [events, &values](const auto& pdf ) mutable {
+ auto eval = pdf.evaluator(events);
+ for( unsigned i = 0; i != events->size(); ++i ) values[i] += eval( events->at(i) );
+ } );
+ return arrayToFunctor<double, typename eventListType::value_type>(values);
+ }
+ KeyedFunctors<double(eventValueType)> componentEvaluator(const eventListType* events) const
+ {
+ KeyedFunctors<double(eventValueType)> view;
+ for_each( this->m_pdfs, [&view, &events]( const auto& pdf) mutable {
+ auto eval = pdf.evaluator(events);
+ view.add([eval](const auto& event){ return eval(event) ; } , type_string(pdf), "" );
+ } );
+ return view;
}
- std::size_t nPDFs() { return sizeof...( TYPES ); }
};
- template <class... PDFS>
- auto make_pdf( PDFS&&... pdfs )
+ /** @function make_pdf
+
+ Usage is
+ \code{cpp}
+ auto pdf = make_pdf( signal, bkg1, ... );
+ \endcode
+ which returns a PDF that is the sum of the signal and bkg1 etc. The sum is also equipped with a likelihood, which can be used by setting
+ the data for the PDF.
+ Therefore, named SumPDF, it is useful to use this function to get a likelihood for a PDF containing a single term (i.e. signal or background only).
+ */
+ template <class eventListType = EventList, class... pdfTypes>
+ auto make_pdf( pdfTypes&&... pdfs )
+ {
+ //return SumPDF<eventListType, pdfTypes...>( std::forward<pdfTypes>( pdfs )... );
+ return SumPDF<eventListType, pdfTypes...>( pdfs... );
+ }
+
+ template <class eventListType = EventList, class... pdfTypes>
+ auto make_likelihood( eventListType& events, pdfTypes&&... pdfs )
{
- return SumPDF<PDFS...>( std::forward<PDFS>( pdfs )... );
+ auto rt = SumPDF<eventListType, pdfTypes...>( std::forward<pdfTypes>( pdfs )... );
+ rt.setEvents(events);
+ return rt;
}
} // namespace AmpGen
diff --git a/AmpGen/Tensor.h b/AmpGen/Tensor.h
index f79646e9c1e..d5a13ca827a 100644
--- a/AmpGen/Tensor.h
+++ b/AmpGen/Tensor.h
@@ -15,11 +15,11 @@
#include "AmpGen/Types.h"
#define ADD_DEBUG_TENSOR( X, Y ) \
- if ( Y != nullptr ) for( size_t i = 0 ; i < X.size(); ++i ) \
- Y->emplace_back( std::string(#X) + Tensor::coordinates_to_string( X.coords(i) ) , X[i] );
+ if ( Y != nullptr ) for( unsigned i = 0 ; i < Tensor(X).size(); ++i ) \
+ Y->emplace_back( std::string(#X) + Tensor::coordinates_to_string( Tensor(X).coords(i) ) , Tensor(X)[i] );
#define ADD_DEBUG_TENSOR_NAMED( X, Y, Z ) \
- if ( Y != nullptr ) for( size_t i = 0 ; i < X.size(); ++i ) \
+ if ( Y != nullptr ) for( unsigned i = 0 ; i < X.size(); ++i ) \
Y->emplace_back( Z + Tensor::coordinates_to_string( X.coords(i) ) , X[i] );
namespace AmpGen
@@ -34,52 +34,51 @@ namespace AmpGen
private:
std::shared_ptr<int> m_ptr;
bool m_isUpper;
- std::string name;
public:
bool operator==( const Tensor::Index& other ) const { return m_ptr.get() == other.m_ptr.get(); }
bool operator!=( const Tensor::Index& other ) const { return m_ptr.get() != other.m_ptr.get(); }
bool isUpper() const { return m_isUpper; };
- Index( bool isUpper = false ) : m_ptr( new int() ), m_isUpper( isUpper ) {}
+ explicit Index( bool isUpper = false ) : m_ptr( new int() ), m_isUpper( isUpper ) {}
Index( const std::shared_ptr<int>& index, bool isUpper = false ) : m_ptr( index ), m_isUpper( isUpper ) {}
Index operator-() const { return Index( m_ptr, !m_isUpper ); }
friend std::ostream& operator <<( std::ostream& out, const Index& index );
};
Tensor();
- Tensor(const std::vector<Expression>& elements);
- Tensor(const std::vector<size_t>& dim);
+ explicit Tensor(const std::vector<Expression>& elements);
+ explicit Tensor(const std::vector<unsigned>& dim);
template <class TYPE> Tensor(const std::initializer_list<TYPE>& elements,
- const std::vector<size_t>& dim) : m_dim(dim)
+ const std::vector<unsigned>& dim) : m_dim(dim)
{
setupCoordinates();
for ( auto& x : elements ) append( x );
}
template <class TYPE> Tensor(const std::vector<TYPE>& elements,
- const std::vector<size_t>& dim) : m_dim(dim)
+ const std::vector<unsigned>& dim) : m_dim(dim)
{
setupCoordinates();
for ( auto& x : elements ) append( x );
}
/// Low level access of elements, either by coordinates or by index ///
- Expression& operator[]( const size_t& i );
- Expression& operator[]( const std::vector<size_t>& co );
- const Expression& operator[]( const size_t& i ) const;
- const Expression& operator[]( const std::vector<size_t>& co ) const;
+ Expression& operator[]( const unsigned& i );
+ Expression& operator[]( const std::vector<unsigned>& co );
+ const Expression& operator[]( const unsigned& i ) const;
+ const Expression& operator[]( const std::vector<unsigned>& co ) const;
- Expression get( const size_t& co );
- Expression get( const size_t& co ) const;
- Expression get( const std::vector<size_t>& _co ) const;
+ Expression get( const unsigned& co );
+ Expression get( const unsigned& co ) const;
+ Expression get( const std::vector<unsigned>& _co ) const;
/// TensorProxy access to class members
/// High level access is done via these commands, i.e. () operators
- Expression& operator()( const size_t& a ) { return Tensor::operator[]( {a} ) ; }
- Expression& operator()( const size_t& a, const size_t& b) { return Tensor::operator[]( {a,b} ) ; }
- const Expression operator()( const size_t& a ) const { return Tensor::operator[]( {a} ) ; }
- const Expression& operator()( const size_t& a, const size_t& b) const { return Tensor::operator[]( {a,b} ) ; }
+ Expression& operator()( const unsigned& a ) { return Tensor::operator[]( {a} ) ; }
+ Expression& operator()( const unsigned& a, const unsigned& b) { return Tensor::operator[]( {a,b} ) ; }
+ const Expression operator()( const unsigned& a ) const { return Tensor::operator[]( {a} ) ; }
+ const Expression& operator()( const unsigned& a, const unsigned& b) const { return Tensor::operator[]( {a,b} ) ; }
TensorProxy operator()( const Tensor::Index& a ) const;
TensorProxy operator()( const Tensor::Index& a, const Tensor::Index& b ) const;
@@ -91,57 +90,54 @@ namespace AmpGen
Tensor operator-() const;
void st(const bool simplify=false);
-
bool rankMatches( const Tensor& other );
- void imposeSymmetry( size_t indexA, size_t indexB);
- void imposeSymmetry( std::vector<size_t> indices );
+ void imposeSymmetry( unsigned indexA, unsigned indexB);
+ void imposeSymmetry( std::vector<unsigned> indices );
Tensor Invert() const;
std::string to_string(const ASTResolver* resolver=nullptr) const ;
- int metricSgn( const std::vector<size_t>& coordinates ) const;
- int metricSgn( const size_t& index ) const;
+ int metricSgn( const std::vector<unsigned>& coordinates ) const;
+ int metricSgn( const unsigned& index ) const;
void append( const Expression& expression );
void append( const real_t& value );
void append( const complex_t& value );
void append( const std::string& value );
void setupCoordinates();
- size_t nDim() const;
- size_t rank() const;
- size_t size() const;
- size_t index( const std::vector<size_t>& _co ) const;
- size_t symmetrisedIndex( const std::vector<size_t>& _co ) const;
- size_t nElements() const;
+ unsigned nDim() const;
+ unsigned rank() const;
+ unsigned size() const;
+ unsigned index( const std::vector<unsigned>& _co ) const;
+ unsigned symmetrisedIndex( const std::vector<unsigned>& _co ) const;
+ unsigned nElements() const;
- const std::vector<size_t> coords( const size_t& index ) const;
- const std::vector<size_t>& dims() const { return m_dim; }
+ const std::vector<unsigned> coords( const unsigned& index ) const;
+ const std::vector<unsigned>& dims() const { return m_dim; }
const std::string dimString() const ;
void print(const bool& eval = false) const;
- const std::vector<size_t>& uniqueElements() const {
- return m_uniqueElements;
- }
+ const std::vector<unsigned>& uniqueElements() const { return m_uniqueElements; }
void operator+=( const Tensor& rhs );
void operator-=( const Tensor& rhs );
Tensor conjugate() const;
- static std::vector<size_t> index_to_coordinates( const size_t& index, const std::vector<size_t>& dim );
- static size_t coordinates_to_index( const std::vector<size_t>& coords, const std::vector<size_t>& dim );
- static std::string coordinates_to_string( const std::vector<size_t >& coordinates );
+ static std::vector<unsigned> index_to_coordinates( const unsigned& index, const std::vector<unsigned>& dim );
+ static unsigned coordinates_to_index( const std::vector<unsigned>& coords, const std::vector<unsigned>& dim );
+ static std::string coordinates_to_string( const std::vector<unsigned >& coordinates );
template <class... ARGS>
- static std::vector<size_t> dim( const ARGS&... args ){
- std::vector<size_t> rt;
+ static std::vector<unsigned> dim( const ARGS&... args ){
+ std::vector<unsigned> rt;
auto up = std::tuple<ARGS...>(args...);
- for_each(up, [&rt]( auto& f ) { rt.emplace_back(f); } );
+ for_each(up, [&rt]( const unsigned& f ) { rt.emplace_back(f); } );
return rt;
- }
+ }
private:
- std::vector<size_t> m_dim;
- std::vector<size_t> m_symmetrisedCoordinates;
- std::vector<size_t> m_uniqueElements;
+ std::vector<unsigned> m_dim;
+ std::vector<unsigned> m_symmetrisedCoordinates;
+ std::vector<unsigned> m_uniqueElements;
std::vector<Expression> m_elements;
};
@@ -173,39 +169,39 @@ namespace AmpGen
public:
TensorExpression( const Tensor& tensor );
std::string to_string(const ASTResolver* resolver) const override;
- void resolve( ASTResolver& resolver ) override;
+ void resolve( ASTResolver& resolver ) const override;
complex_t operator()() const override;
operator Expression() const;
-
+ Tensor tensor() const { return m_tensor;}
private:
Tensor m_tensor;
};
- Tensor operator+( const Tensor& t1, const Tensor& t2 );
- Tensor operator-( const Tensor& t1, const Tensor& t2 );
- Tensor operator/( const Tensor& t1, const Expression& t2 );
- Tensor operator*( const Expression& t1, const Tensor& t2 );
- Tensor operator*( const Tensor& t1, const Expression& t2 );
+ Tensor operator+(const Tensor&, const Tensor&);
+ Tensor operator-(const Tensor&, const Tensor&);
+ Tensor operator/(const Tensor&, const Expression&);
+ Tensor operator*(const Expression&, const Tensor&);
+ Tensor operator*(const Tensor&, const Expression&);
- Tensor operator/( const Tensor& t1, const double& t2 );
- Tensor operator*( const double& t1, const Tensor& t2 );
- Tensor operator*( const Tensor& t1, const double& t2 );
+ Tensor operator/(const Tensor&, const double&);
+ Tensor operator*(const double&, const Tensor&);
+ Tensor operator*(const Tensor&, const double&);
- TensorProxy operator*( const TensorProxy& t1, const TensorProxy& t2 );
- TensorProxy operator+( const TensorProxy& t1, const TensorProxy& t2 );
- TensorProxy operator-( const TensorProxy& t1, const TensorProxy& t2 );
+ TensorProxy operator*(const TensorProxy&, const TensorProxy&);
+ TensorProxy operator+(const TensorProxy&, const TensorProxy&);
+ TensorProxy operator-(const TensorProxy&, const TensorProxy&);
- TensorProxy operator/( const TensorProxy& t1, const Expression& t2 );
- TensorProxy operator*( const Expression& t1, const TensorProxy& t2 );
- TensorProxy operator*( const TensorProxy& t1, const Expression& t2 );
+ TensorProxy operator/(const TensorProxy&, const Expression& );
+ TensorProxy operator*(const Expression& , const TensorProxy&);
+ TensorProxy operator*(const TensorProxy&, const Expression& );
- TensorProxy operator/( const TensorProxy& t1, const double& t2 );
- TensorProxy operator*( const double& t1, const TensorProxy& t2 );
- TensorProxy operator*( const TensorProxy& t1, const double& t2 );
+ TensorProxy operator/(const TensorProxy&, const double&);
+ TensorProxy operator*(const double& , const TensorProxy&);
+ TensorProxy operator*(const TensorProxy&, const double&);
- Tensor Identity( const size_t& rank = 4 );
+ Tensor Identity( const unsigned& rank = 4 );
- const Tensor LeviCivita( const size_t& rank = 4);
+ const Tensor LeviCivita( const unsigned& rank = 4);
Expression dot( const Tensor& A, const Tensor& B );
std::ostream& operator <<( std::ostream& out, const Tensor::Index& index );
diff --git a/AmpGen/ThreadPool.h b/AmpGen/ThreadPool.h
index 7604c971ddb..589a06e1422 100644
--- a/AmpGen/ThreadPool.h
+++ b/AmpGen/ThreadPool.h
@@ -3,8 +3,8 @@
/* @class ThreadPool ThreadPool.h AmpGen/ThreadPool.h
* Thread pool implementation taken from https://github.com/progschj/ThreadPool
- * Modified to allow explicit clearing of queues.
- * A single static thread pool exists that can be used as a sceduler.
+ * Modified to allow explicit clearing of queues, and to make
+ * the constructor explicit
*
* Copyright (c) 2012 Jakob Progsch, Václav Zeman
*
@@ -48,27 +48,12 @@ namespace AmpGen
class ThreadPool
{
public:
- static size_t nThreads;
-
+ explicit ThreadPool(const size_t& nt);
~ThreadPool();
-
- template <class F, class... Args> static auto schedule( F&& f, Args&&... args ) -> std::future<typename std::result_of<F( Args... )>::type>
- {
- return getMe()->enqueue( f, args... );
- }
-
template<class F, class... Args> auto enqueue(F&& f, Args&&... args) -> std::future<typename std::result_of<F(Args...)>::type>;
-
- ThreadPool(const size_t& nt);
void waitForStoppedThreads();
+
private:
- static ThreadPool* gThreadPool;
- static ThreadPool* getMe()
- {
- if ( !gThreadPool )
- gThreadPool = new ThreadPool(ThreadPool::nThreads);
- return gThreadPool;
- }
std::vector<std::thread> m_workers;
std::queue<std::function<void()>> m_tasks;
std::mutex m_queue_mutex;
diff --git a/AmpGen/ThreeBodyCalculators.h b/AmpGen/ThreeBodyCalculators.h
index 4ff024ede6a..d7b24724dd4 100644
--- a/AmpGen/ThreeBodyCalculators.h
+++ b/AmpGen/ThreeBodyCalculators.h
@@ -10,7 +10,6 @@ class TGraph;
namespace AmpGen
{
-
class MinuitParameterSet;
class ThreeBodyCalculator
@@ -19,12 +18,12 @@ namespace AmpGen
struct PartialWidth {
CoherentSum fcs;
DalitzIntegrator integrator;
- CompiledExpression< std::complex<double>, const real_t*, const real_t* > totalWidth;
+ CompiledExpression<complex_t(const real_t*, const real_t*) > totalWidth;
EventType type;
- std::vector<CompiledExpression< std::complex<double>, const real_t*, const real_t*>> partialWidths;
+ std::vector<CompiledExpression< complex_t(const real_t*, const real_t*)>> partialWidths;
double getWidth( const double& m );
PartialWidth( const EventType& type, MinuitParameterSet& mps );
- Expression spinAverageMatrixElement( const std::vector<TransitionMatrix<std::complex<double>>>& elements,
+ Expression spinAverageMatrixElement( const std::vector<std::pair<Particle, TotalCoupling> >& elements,
DebugSymbols* msym );
};
Expression calculateSAME( const std::string& particle );
diff --git a/AmpGen/Transform.h b/AmpGen/Transform.h
index 576e56e987c..1c703a7b056 100644
--- a/AmpGen/Transform.h
+++ b/AmpGen/Transform.h
@@ -41,13 +41,16 @@ namespace AmpGen {
class TransformSequence
{
public:
- TransformSequence() = default;
+ TransformSequence();
+ TransformSequence( const Transform& transform );
+ TransformSequence( const TransformSequence& t1, const TransformSequence& t2);
+ TransformSequence( const Transform& t1, const Transform& t2);
TransformSequence inverse() const;
- Tensor operator()( const Transform::Representation& repr ) const;
+ Tensor operator()( const Transform::Representation& repr ) const ;
Tensor operator()( const Tensor& tensor,
const Transform::Representation& repr=Transform::Representation::Vector ) const;
- void add( const Transform& transform );
- void add( const TransformSequence& transform );
+ void push_back( const Transform& transform );
+ void push_back( const TransformSequence& transform );
void stepThrough( const Tensor& tensor,
const Transform::Representation& repr = Transform::Representation::Vector );
@@ -58,9 +61,14 @@ namespace AmpGen {
std::vector<Transform>::const_iterator end() const { return m_transforms.cend(); }
std::vector<Transform>::iterator begin() { return m_transforms.begin(); }
std::vector<Transform>::iterator end() { return m_transforms.end(); }
+ unsigned size() const { return m_transforms.size(); }
+
private:
+ void buildCache();
std::vector<Transform> m_transforms;
+ std::array<Tensor,3> m_cache;
};
+
}
#endif
diff --git a/AmpGen/TreePhaseSpace.h b/AmpGen/TreePhaseSpace.h
new file mode 100644
index 00000000000..3c708882f5d
--- /dev/null
+++ b/AmpGen/TreePhaseSpace.h
@@ -0,0 +1,100 @@
+#ifndef AMPGEN_TREEPHASESPACE_H
+#define AMPGEN_TREEPHASESPACE_H
+
+#include <memory.h>
+#include <stddef.h>
+#include <algorithm>
+#include <memory>
+#include <ostream>
+#include <string>
+#include <vector>
+#include <utility>
+#include <random>
+
+#include "AmpGen/EventType.h"
+#include "AmpGen/PhaseSpace.h"
+#include "AmpGen/Particle.h"
+
+#include <TRandom3.h>
+#include <TLorentzVector.h>
+
+namespace AmpGen
+{
+ class Particle;
+ class Event;
+ /** @class TreePhaseSpace
+ @brief Generator of events where the phase space is decomposed into a series of subtrees.
+ @decription Generates events using the decomposition of the phase space
+ into a series of two-body phase spaces, where the invariant mass of the two-body space
+ can be generated according to, for example, a simplified Breit-Wigner model.
+ This can then be used to generate a more complex model using accept-reject, which
+ allows for a much more efficient generation of narrow peaks.
+
+ Currently, each of the available channels is given the same weight relative to phase space,
+ ideally feedback could be given from the generator phase to focus on the more efficient channels,
+ i.e. those that have larger contributions to the full amplitude.
+ */
+ class TreePhaseSpace
+ {
+
+ public:
+ struct Vertex
+ {
+ enum Type { BW, Flat, Stable, QuasiStable};
+ Vertex() = default;
+ Vertex(const Particle& particle, const double& min);
+ Vertex(const Particle& particle, const double& min, const double& max);
+ double p() const;
+ double weight() const;
+ double genPdf(const Event& event) const;
+ void generate();
+ void print(const unsigned& offset = 0) const;
+ void place(Event& event);
+ Event event(const unsigned& eventSize);
+ void generateFullEvent();
+ void setRhoMax();
+ void setRandom(TRandom3* rnd);
+ static Vertex make(const Particle& particle, Vertex* parent = nullptr);
+ Particle particle;
+ double min = {0};
+ double max = {0};
+ double phiMin = {0};
+ double phiMax = {0};
+ Type type = {Type::BW};
+ unsigned index = {999};
+ double bwMass = {0};
+ double bwWidth = {0};
+ double s = {0};
+ std::shared_ptr<Vertex> left = {nullptr};
+ std::shared_ptr<Vertex> right = {nullptr};
+ TRandom3* rand = {nullptr};
+ std::vector<unsigned> indices;
+ TLorentzVector mom;
+ bool isMultiBody = {false};
+ PhaseSpace phsp; /// multibody phase to resort to for non two-body decomposition;
+ };
+
+ explicit TreePhaseSpace(const EventType& type);
+ TreePhaseSpace(const Particle& decayChain, const EventType& type, TRandom* rndm = nullptr );
+ TreePhaseSpace(const std::vector<Particle>& decayChains, const EventType& type, TRandom* rndm = nullptr);
+
+ void setRandom( TRandom* rand );
+ Event makeEvent();
+ size_t size() const;
+ EventType eventType() const ;
+ double genPdf( const Event& event) const ;
+ const Vertex& operator[](const unsigned i) const { return m_top[i]; }
+
+ void provideEfficiencyReport(const std::vector<bool>& report);
+ private:
+ std::vector<Vertex> m_top;
+ TRandom3* m_rand = {nullptr};
+ EventType m_type; ///< EventType to generate
+ std::discrete_distribution<> m_dice; ///<
+ std::vector<double> m_weights;
+ std::vector<unsigned> m_generatorRecord;
+ std::mt19937 m_gen;
+ };
+} // namespace AmpGen
+
+#endif
diff --git a/AmpGen/TreeReader.h b/AmpGen/TreeReader.h
index a71f97d752d..86bea94c1e7 100644
--- a/AmpGen/TreeReader.h
+++ b/AmpGen/TreeReader.h
@@ -5,115 +5,106 @@
#include "TLeaf.h"
#include "TTree.h"
#include <vector>
-
+#include "AmpGen/MetaUtils.h"
namespace AmpGen
{
- template <class OutputType>
- class TreeReader
- {
- private:
- struct IReadBranch {
- std::string name;
- IReadBranch( const std::string& name = "" ) : name( name ) {}
- virtual void* address() const = 0;
- virtual void transfer() = 0;
- virtual ~IReadBranch() = default;
- };
-
- template <class InputType> struct ReadBranch : public IReadBranch {
- InputType thing;
- OutputType* output;
- void* address() const override { return (void*)&thing; }
- ReadBranch( const std::string& name, OutputType* outputBranch ) : IReadBranch( name ), output( outputBranch ) {}
- void transfer() override { *output = thing; }
- };
-
- template <class InputType> struct ReinterpretBranch : public IReadBranch {
- InputType thing;
- OutputType* output;
- void* address() const override { return (void*)&thing; }
- ReinterpretBranch( const std::string& name, OutputType* outputBranch ) : IReadBranch( name ), output( outputBranch ) {}
- void transfer() override { *output = reinterpret_cast<OutputType>(thing); }
- };
-
- struct Branch {
- OutputType* value;
- Branch() : value( new OutputType() ) {}
- ~Branch() { delete value; }
- operator OutputType() const { return *value; }
- operator OutputType&() { return *value; }
- OutputType* operator&() { return value; }
- };
+ class TreeReader
+ {
+ private:
+ struct IReadBranch {
+ std::string name;
+ IReadBranch( const std::string& name = "" ) : name( name ) {}
+ virtual void* address() const = 0;
+ virtual void transfer() = 0;
+ virtual ~IReadBranch() = default;
+ };
- struct Iterator {
- size_t m_position;
- TreeReader* m_parent;
- Iterator( const size_t& pos, TreeReader* parent ) : m_position( pos ), m_parent( parent ) {}
- Iterator& operator++()
- {
- m_position++;
- m_parent->getEntry( m_position );
- return *this;
- }
- bool operator==( const Iterator& rhs ) const { return m_position == rhs.m_position; }
- bool operator!=( const Iterator& rhs ) const { return m_position != rhs.m_position; }
- size_t operator*() const { return m_position; }
- };
- TTree* tree;
- bool ready;
- std::vector<IReadBranch*> branches;
+ template <class InputType, class OutputType> struct ReadBranch : public IReadBranch
+ {
+ InputType thing;
+ OutputType* output;
+ void* address() const override { return (void*)&thing; }
+ ReadBranch( const std::string& name, OutputType* outputBranch ) : IReadBranch( name ), output( outputBranch ) {}
+ void transfer() override { *output = thing; }
+ };
- public:
- TreeReader( TTree* tree ) : tree( tree ) {}
- void setBranch( const std::string& name, OutputType* ptr )
+ template <class InputType, class OutputType> struct ReinterpretBranch : public IReadBranch
+ {
+ InputType thing;
+ OutputType* output;
+ void* address() const override { return (void*)&thing; }
+ ReinterpretBranch( const std::string& name, OutputType* outputBranch ) : IReadBranch( name ), output( outputBranch ) {}
+ void transfer() override { *output = reinterpret_cast<OutputType>(thing); }
+ };
+ struct Iterator {
+ size_t m_position;
+ TreeReader* m_parent;
+ Iterator( const size_t& pos, TreeReader* parent ) : m_position( pos ), m_parent( parent ) {}
+ Iterator& operator++()
{
- IReadBranch* new_branch = nullptr;
- TLeaf* leaf = tree->GetLeaf( name.c_str() );
- if( leaf == nullptr ){
- ERROR( "Leaf: " << name << " not found");
- return;
- }
- std::string branchType = leaf->GetTypeName();
- if( branchType == "Double_t" ) new_branch = new ReadBranch<Double_t>( name, ptr );
- if( branchType == "Float_t" ) new_branch = new ReadBranch<Float_t>( name, ptr );
- if( branchType == "Bool_t" ) new_branch = new ReadBranch<Bool_t>( name, ptr );
- if( branchType == "Int_t" ) new_branch = new ReadBranch<Int_t>( name, ptr );
- if( branchType == "UInt_t" ) new_branch = new ReadBranch<UInt_t>( name, ptr );
- if( branchType == "ULong64_t") new_branch = new ReadBranch<ULong64_t>( name, ptr );
- if( new_branch == nullptr ){
- ERROR( "Branch type:" << branchType << " not recognised" );
- return;
- }
- ready = false;
- branches.push_back( new_branch );
+ m_position++;
+ m_parent->getEntry( m_position );
+ return *this;
}
- Branch bind( const std::string& name )
- {
- Branch rt;
- setBranch( name, &rt );
- return rt;
+ bool operator==( const Iterator& rhs ) const { return m_position == rhs.m_position; }
+ bool operator!=( const Iterator& rhs ) const { return m_position != rhs.m_position; }
+ size_t operator*() const { return m_position; }
+ unsigned pos() const { return m_position; }
+ };
+ TTree* m_tree = {nullptr};
+ bool m_ready = {false};
+ std::vector<IReadBranch*> m_branches = {};
+ std::vector<size_t> m_entryList = {};
+ public:
+ template <class OutputType> struct Proxy
+ {
+ OutputType* data;
+ Proxy() : data( new OutputType() ) {}
+ operator OutputType() const { return *data; }
+ ~Proxy(){ delete data ; }
+ };
+ explicit TreeReader( TTree* tree );
+ template <typename OutputType> Proxy<OutputType> make_proxy( const std::string& name )
+ {
+ Proxy<OutputType> rt;
+ setBranch( name, rt.data );
+ return rt;
+ }
+ template <typename OutputType> void setBranch( const std::string& name, OutputType& thing ) {
+ setBranch(name,&thing) ; }
+ template <typename OutputType> void setBranch( const std::string& name, OutputType* ptr )
+ {
+ IReadBranch* new_branch = nullptr;
+ TLeaf* leaf = m_tree->GetLeaf( name.c_str() );
+ if( leaf == nullptr ){
+ ERROR( "Leaf: " << name << " not found");
+ return;
}
- void getEntry( const unsigned int& entry )
- {
- if ( !ready ) prepare();
- tree->GetEntry( entry );
- for ( auto& branch : branches ) branch->transfer();
- }
- void prepare()
- {
- for ( auto& branch : branches ) {
- tree->SetBranchStatus( branch->name.c_str(), "1" );
- tree->SetBranchAddress( branch->name.c_str(), branch->address() );
- }
- ready = true;
- }
- ~TreeReader()
- {
- for ( auto& branch : branches ) delete branch;
+ std::string branchType = leaf->GetTypeName();
+ if( branchType == "Double_t" ) new_branch = new ReadBranch<Double_t , OutputType>( name, ptr );
+ if( branchType == "Float_t" ) new_branch = new ReadBranch<Float_t , OutputType>( name, ptr );
+ if( branchType == "Bool_t" ) new_branch = new ReadBranch<Bool_t , OutputType>( name, ptr );
+ if( branchType == "Int_t" ) new_branch = new ReadBranch<Int_t , OutputType>( name, ptr );
+ if( branchType == "UInt_t" ) new_branch = new ReadBranch<UInt_t , OutputType>( name, ptr );
+ if( branchType == "ULong64_t") new_branch = new ReadBranch<ULong64_t, OutputType>( name, ptr );
+ if( new_branch == nullptr ){
+ ERROR( "Branch type:" << branchType << " not recognised" );
+ return;
}
- Iterator begin() { return Iterator( 0, this ); }
- Iterator end() { return Iterator( tree->GetEntries(), this ); }
- };
+ DEBUG("Making branch with properties: [name = " << name << ", input type = " << branchType << " output type = " << type_string<OutputType>() << "]" );
+ m_ready = false;
+ m_branches.push_back( new_branch );
+ }
+ void setEntryList( const std::vector<size_t>& entryList );
+ void unsetEntryList();
+ void getEntry( const unsigned int& entry );
+ void prepare();
+ size_t nEntries() const;
+ ~TreeReader();
+ Iterator begin();
+ Iterator end();
+ };
+// ENABLE_DEBUG(TreeReader);
} // namespace AmpGen
#endif
diff --git a/AmpGen/Units.h b/AmpGen/Units.h
index fc9db3fddd2..00b40c2ccf5 100644
--- a/AmpGen/Units.h
+++ b/AmpGen/Units.h
@@ -1,10 +1,25 @@
#ifndef AMPGEN_UNITS_H
#define AMPGEN_UNITS_H 1
+#include "AmpGen/enum.h"
namespace AmpGen {
+
static const double TeV = 1000;
static const double GeV = 1;
static const double MeV = 0.001;
static const double KeV = 0.001*0.001;
+ static const double eV = 0.001*0.001*0.001;
+
+ static const double ms = 1000*1000;
+ static const double us = 1000;
+ static const double ns = 1;
+ static const double ps = 0.001;
+ static const double fs = 0.001*0.001;
+
+ static const double mm = 1.0;
+ static const double um = 0.001;
+ static const double nm = 0.001*0.001;
+ declare_enum( Units, TeV, GeV, MeV, KeV, eV, ms, us, ns, ps, fs )
+ double to_double(const Units& unit );
}
#endif
diff --git a/AmpGen/Utilities.h b/AmpGen/Utilities.h
index 90d8f335854..213591f10a9 100644
--- a/AmpGen/Utilities.h
+++ b/AmpGen/Utilities.h
@@ -12,52 +12,38 @@
#include <typeinfo>
#include <vector>
#include <future>
+#ifdef _OPENMP
#include <omp.h>
+#endif
#include "AmpGen/MsgService.h"
#include "AmpGen/MetaUtils.h"
-namespace AmpGen {
- template <class T>
- static bool isIn( const std::vector<T>& container, const T& obj )
- {
- for ( auto& it : container )
- if ( obj == it ) return true;
- return false;
- }
-
- template <class T, class B, class F>
- static bool isIn( const std::vector<T>& container, const B& obj, F f )
- {
- for ( auto& it : container )
- if ( f( it, obj ) ) return true;
- return false;
- }
- template <class T>
- std::string vectorToString( const std::vector<T>& obj, const std::string& delim = "" )
+namespace AmpGen {
+ template <typename iterator_type,
+ typename functor_type>
+ std::string vectorToString( iterator_type begin,
+ iterator_type end,
+ const std::string& delim,
+ functor_type fcn )
{
- std::string returnValue;
std::stringstream ss;
- if( obj.size() == 0 ) return "";
- for ( unsigned int i = 0 ; i < obj.size()-1; ++i )
- ss << obj[i] << delim;
- ss << obj[obj.size()-1];
+ if( begin == end ) return "";
+ for ( auto it = begin; it != end-1; ++it)
+ ss << fcn(*it) << delim;
+ ss << fcn(*(end-1));
return ss.str();
}
- template <class T, class F>
- std::string vectorToString( const std::vector<T>& obj, const std::string& delim="", const F& functor =[](auto& f){ return f ; } )
+ template <typename container_type,
+ typename vtype = typename container_type::value_type,
+ typename functor_type = std::function<vtype(const vtype&)> >
+ std::string vectorToString( const container_type& obj, const std::string& delim = "", const functor_type& f = [](const auto& arg){ return arg; })
{
- std::string returnValue;
- std::stringstream ss;
- if( obj.size() == 0 ) return "";
- for ( unsigned int i = 0 ; i < obj.size()-1; ++i )
- ss << functor(obj[i]) << delim;
- ss << functor(obj[obj.size()-1]);
- return ss.str();
+ return vectorToString( std::begin(obj), std::end(obj), delim, f);
}
- template <class T> std::vector<std::vector<T>> nCr( const T& n, const T& r )
+ template <typename T> std::vector<std::vector<T>> nCr( const T& n, const T& r )
{
std::vector<bool> mask( n );
std::vector<std::vector<T>> combinations;
@@ -82,6 +68,7 @@ namespace AmpGen {
size_t find_next_of( const std::string& input, const std::vector<std::string>& patterns, const size_t& begin = 0 );
std::string replaceAll( const std::string& input, const std::string& toReplace, const std::string& replaceWith );
+ std::string replaceAll( const std::string& input, const std::vector<std::pair<std::string, std::string>>& rules );
unsigned int FNV1a_hash( const std::string& toHash );
@@ -96,13 +83,13 @@ namespace AmpGen {
std::string numberWithError( const double& number, const double& error, const unsigned int& nDigits );
- template <class RETURN_TYPE>
- RETURN_TYPE lexical_cast( const std::string& word, bool& status )
+ template <typename return_type>
+ return_type lexical_cast( const std::string& word, bool& status )
{
- WARNING( "Only use specialised versions of this template (word = " << word << ", type = " << AmpGen::typeof<RETURN_TYPE>()
+ WARNING( "Only use specialised versions of this template (word = " << word << ", type = " << AmpGen::type_string<return_type>()
<< ") " );
status = 0;
- return RETURN_TYPE();
+ return return_type();
}
template <class ...ARGS>
@@ -111,7 +98,7 @@ namespace AmpGen {
auto size = std::snprintf(nullptr, 0, format.c_str(), std::forward<ARGS>(args)...);
std::string output(size+1,'\0');
std::sprintf(&output[0],format.c_str(), std::forward<ARGS>(args)...);
- return output;
+ return output.substr(0, output.size()-1);
}
@@ -124,13 +111,14 @@ namespace AmpGen {
template <> unsigned long int lexical_cast( const std::string& word, bool& status );
template <> long int lexical_cast( const std::string& word, bool& status );
- template <class FCN>
- void processFile( const std::string& filename, FCN&& toDo, const char ignoreLinesThatBeginWith = '#' )
+ template <typename functor_type>
+ void processFile( const std::string& filename, functor_type&& toDo, const char ignoreLinesThatBeginWith = '#' )
{
std::string tmp;
std::ifstream inFile( filename.c_str() );
while ( inFile.good() ) {
std::getline( inFile, tmp );
+ tmp.erase( std::remove_if( tmp.begin(), tmp.end(), [](const char c){ return c == '\r'; }), tmp.end() );
if ( tmp.size() == 0 || tmp[0] == ignoreLinesThatBeginWith ) continue;
toDo( tmp );
}
@@ -169,12 +157,19 @@ namespace AmpGen {
{
auto total = init;
auto size = end-begin;
+ #ifdef _OPENMP
#pragma omp parallel for reduction( +: total )
+ #endif
for( int it = 0; it < size; ++it ){
total += f(*(begin+it));
}
return total;
}
+ template <typename return_type, typename contained_type> std::function<return_type(const contained_type&)>
+ arrayToFunctor( const std::vector<return_type>& values)
+ {
+ return [values](const contained_type& event) -> return_type {return *(values.data() + event.index()); };
+ }
template<class iterator>
void parallel_sort(iterator begin,
@@ -191,14 +186,14 @@ namespace AmpGen {
bool isDir( const std::string& fname );
bool fileExists( const std::string& name );
- std::vector<std::string> getListOfFiles( const std::string& directory, std::string patternString = "" );
+ std::vector<std::string> getListOfFiles(const std::string& directory, const std::string& patternString = "");
void printSplash();
void printReleaseNotes(const std::string& fname);
std::string ltrim( std::string s );
std::string rtrim( std::string s );
- std::string trim( std::string s );
+ std::string trim( const std::string& s );
std::string expandGlobals( std::string path );
std::ostream& bold_on( std::ostream& );
diff --git a/AmpGen/Version.h.in b/AmpGen/Version.h.in
index 9adbb1f3413..d80b4640bbf 100644
--- a/AmpGen/Version.h.in
+++ b/AmpGen/Version.h.in
@@ -1,2 +1,3 @@
-#define AMPGEN_VERSION_MAJOR @AmpGen_VERSION_MAJOR@
-#define AMPGEN_VERSION_MINOR @AmpGen_VERSION_MINOR@
+#define AMPGEN_MAJOR_VERSION @AmpGen_VERSION_MAJOR@
+#define AMPGEN_MINOR_VERSION @AmpGen_VERSION_MINOR@
+
diff --git a/AmpGen/Vertex.h b/AmpGen/Vertex.h
index fb2cd7636c3..b78b8a7def8 100644
--- a/AmpGen/Vertex.h
+++ b/AmpGen/Vertex.h
@@ -24,31 +24,31 @@
* Macro to declare a vertex
*/
#define DECLARE_VERTEX(NAME) \
- struct NAME : public VertexBase { \
+ struct NAME : public Base { \
NAME(){ DEBUG("Constructing vertex"); } \
- virtual Tensor operator()( const Tensor& P, const Tensor& Q, const Tensor& V1, const Tensor& V2, DebugSymbols* db = 0 ) override; \
+ virtual Tensor operator()(const Tensor& P, const Tensor& Q, const Tensor& V1, const Tensor& V2, DebugSymbols* db = 0 ) override; \
static std::string _id; \
}
#define DEFINE_VERTEX(VERTEX) \
- REGISTER_WITH_KEY( Vertex::VertexBase, Vertex::VERTEX, #VERTEX, std::string ); \
+ REGISTER_WITH_KEY( Vertex::Base, Vertex::VERTEX, #VERTEX, std::string ); \
Tensor Vertex::VERTEX::operator()( const Tensor& P, const Tensor& Q, const Tensor& V1, const Tensor& V2, DebugSymbols* db )
namespace AmpGen
{
/** @ingroup Vertices namespace Vertex
- Namespace that contains the base class for vertices, VertexBase, as well as the implementations
+ Namespace that contains the base class for vertices, Vertex::Base, as well as the implementations
of specific spin couplings and some helper functions such as the orbital operators.
*/
namespace Vertex
{
- /** @ingroup Vertices class VertexBase
+ /** @ingroup Vertices class Base
@brief Base class for all spin vertices.
Virtual base class from which all the other vertices derive, in essence this is
just a named function pointer that can create a pointer to itself, i.e. such
that it can be constructed using a Factory.
*/
- struct VertexBase {
+ struct Base {
/** Calculate the generalised current for this decay process, as a function of:
@param P The momentum of the decaying particle
@@ -64,8 +64,8 @@ namespace AmpGen
const AmpGen::Tensor& V2,
AmpGen::DebugSymbols* db = nullptr ) = 0;
- virtual ~VertexBase() = default;
- VertexBase* create() { return this; }
+ virtual ~Base() = default;
+ Base* create() { return this; }
};
/// \ingroup Vertices class S_SS_S
/// \brief \f$ S = S_1 S_2 \f$
@@ -119,6 +119,11 @@ namespace AmpGen
DECLARE_VERTEX( V_VS_D );
DECLARE_VERTEX( V_TS_P );
DECLARE_VERTEX( V_TS_D );
+
+ DECLARE_VERTEX( V_VV_P );
+ DECLARE_VERTEX( V_VV_P1 );
+ DECLARE_VERTEX( V_VV_P2 );
+ DECLARE_VERTEX( V_VV_S );
DECLARE_VERTEX( T_VS_D );
DECLARE_VERTEX( T_VS_P );
@@ -138,6 +143,12 @@ namespace AmpGen
DECLARE_VERTEX( f_Vf_P2 );
DECLARE_VERTEX( f_Vf_P3 );
+ DECLARE_VERTEX( f_fS_SL );
+ DECLARE_VERTEX( f_fS_SR );
+
+ DECLARE_VERTEX( f_Vf_SL );
+ DECLARE_VERTEX( f_Vf_SR );
+
DECLARE_VERTEX( f_Vf_D );
DECLARE_VERTEX( f_Vf_D1 );
@@ -151,9 +162,11 @@ namespace AmpGen
DECLARE_VERTEX( S_ff_S );
DECLARE_VERTEX( S_ff_S1 );
- DECLARE_VERTEX( V_ff_P );
- DECLARE_VERTEX( V_ff_P1 );
- class Factory : public AmpGen::Factory<Vertex::VertexBase>
+ DECLARE_VERTEX( V_ff_S );
+ DECLARE_VERTEX( V_ff_S1 );
+ DECLARE_VERTEX( V_ff_PL );
+ DECLARE_VERTEX( V_ff_PR );
+ class Factory : public AmpGen::Factory<Vertex::Base>
{
public:
static Tensor getSpinFactor( const Tensor& P, const Tensor& Q, const Tensor& V1, const Tensor& V2,
@@ -164,14 +177,43 @@ namespace AmpGen
};
} // namespace Vertex
- /// \ingroup Vertices function Orbital_PWave
- /// Helper function that computes the L=1 orbital momentum operator, i.e.
- /// \f$ L_{\mu} = q_{\mu} - \frac{p_{\nu}q^{\nu} p_{\mu} }{ p_{\alpha} p^{\alpha}} \f$
- Tensor Orbital_PWave( const Tensor& A, const Tensor& B );
- Tensor Orbital_DWave( const Tensor& A, const Tensor& B );
- Tensor Spin1Projector( const Tensor& A );
- Tensor Spin2Projector( const Tensor& A );
-
+ /** @ingroup Vertices function Orbital_PWave
+ @brief Helper function that computes the @f$L=1@f$ orbital momentum operator.
+ Helper function that computes the @f$L=1@f$ orbital momentum operator, which is given by
+ @f[ L_{\mu} = q_{\mu} - p_{\mu} \frac{p_{\nu}q^{\nu}}{ p^2 }, @f]
+ where @f$ p @f$ is total momentum and @f$ q @f$ is the momentum difference between
+ the two particles in the state.
+ */
+ Tensor Orbital_PWave(const Tensor& p, const Tensor& q);
+
+ /** @ingroup Vertices function Orbital_DWave
+ @brief Helper function that computes the @f$L=2@f$ orbital momentum operator.
+ Helper function that computes the @f$L=2@f$ orbital momentum operator, which is given by
+ @f[ L_{\mu\nu} = L_{\mu}L_{\nu} - \frac{L^2}{3} S_{\mu\nu}, @f]
+ where @f$ L_{\mu} @f$ is the Orbital_PWave operator and @f$ S_{\mu\nu} @f$ is the
+ Spin1Projector. */
+ Tensor Orbital_DWave(const Tensor& p, const Tensor& q);
+
+ /** @ingroup Vertices function Spin1Projector
+ @brief Helper function that computes the projection operator onto a spin one state.
+ Helper function that projects some lorentz object onto the momentum @f$p_\mu @f$ of state,
+ and is given by
+ @f[ S_{\mu\nu} = g_{\mu\nu} - \frac{p_{\mu}p_{\nu}}{p^2}. @f] */
+ Tensor Spin1Projector(const Tensor& p);
+
+ /** @ingroup Vertices function Spin2Projector
+ @brief Helper function that computes the projection operator onto a spin one state.
+ Helper function that projects some lorentz object onto the momentum @f$p_\mu @f$ of state,
+ and is given by
+ @f[ S_{\mu\nu\alpha\beta} = \frac{1}{2}\left( S_{\mu\alpha} S_{\nu\beta} + S_{\mu\beta}S_{\nu\alpha} \right) - \frac{1}{3} S_{\mu\nu} S_{\alpha\beta}, @f]
+ where @f$ S_{\mu\nu} @f$ is the spin-one projection operator (see Spin1Projector). */
+ Tensor Spin2Projector(const Tensor& p);
+
+ /** @ingroup Vertices function Spin1hProjector
+ @brief Helper function that projects a spinor.
+ Helper function that projects out a spin-half state
+ @f[ S_{ab} = \frac{1}{2m}\left( {p\!\!\!/} + m I \right) @f]
+ */
Tensor Spin1hProjector( const Tensor& B );
Tensor Spin3hProjector( const Tensor& A );
diff --git a/AmpGen/Wigner.h b/AmpGen/Wigner.h
index be44e8a08b5..01a3792ec63 100644
--- a/AmpGen/Wigner.h
+++ b/AmpGen/Wigner.h
@@ -6,50 +6,55 @@
#include "AmpGen/Transform.h"
namespace AmpGen {
-class Particle;
+ class Particle;
+ using TransformCache = std::map<std::string, TransformSequence>;
Expression wigner_d( const Expression& cb, const double& j, const double& m, const double& n );
- Expression wigner_D( const Tensor& P, const double& J, const double& lA, const double& lB, DebugSymbols* db , const std::string& name = "");
-
+ Expression wigner_D( const std::pair<Expression, Expression>& P, const double& J, const double& lA, const double& lB, DebugSymbols* db);
/** @ingroup Vertices function CG
Calculates the Clebsch-Gordan coefficient for (j1 m1 j2 m2 | J M), the expansion
coefficients in
*/
double CG( const double& j1,
- const double& m1,
- const double& j2,
- const double& m2,
- const double& J,
- const double& M );
+ const double& m1,
+ const double& j2,
+ const double& m2,
+ const double& J,
+ const double& M );
- /** @ingroup Vertices function helicityTransformMatrix
- Generates a helicity transform tensor (matrix) that aligns tensor P (four-vector) to the +/- ve z-axis, then boosts to the rest frame.
+ /** @ingroup Vertices function wickTransform
+ Generates a wick transform sequence that aligns tensor P (four-vector) to the +/- ve z-axis, then boosts to the rest frame.
The mass may be seperately specified. The parameter ve specifies whether the initial Euler rotation is to the +/- z-axis.
In the case where ve =-1, a second rotation is applied about the x-axis that aligns P to the +ve z-axis.
This ensures that singly and doubly primed helicity frames remain orthonormal.
*/
- TransformSequence helicityTransformMatrix( const Tensor& P, const Expression& M, const int& ve =1, const bool& handleZeroCase = false );
-
- Expression helicityAmplitude( const Particle& particle, const TransformSequence& parentFrame, const double& Mz, DebugSymbols* db , const int sgn=1);
+ TransformSequence wickTransform(const Tensor& P, const Particle& p, const int& ve =1, DebugSymbols* db = nullptr );
+ Expression helicityAmplitude(const Particle& particle,
+ const TransformSequence& parentFrame,
+ const double& Mz,
+ DebugSymbols* db ,
+ const int sgn=1,
+ TransformCache* cacheptr = nullptr);
Tensor basisSpinor(const int& polState, const int& id);
+ Tensor basisVector(const int& polState);
struct LS {
- double factor;
- double cg1;
- double cg2;
- double p;
- double m1;
- double m2;
+ double factor = {1};
+ double cg1 = {0};
+ double cg2 = {0};
+ double p = {0};
+ double m1 = {0};
+ double m2 = {0};
};
-
+
std::vector<LS> calculate_recoupling_constants(
- const double& J,
- const double& M,
- const double& L,
- const double& S,
- const double& j1,
- const double& j2 );
+ const double& J,
+ const double& M,
+ const double& L,
+ const double& S,
+ const double& j1,
+ const double& j2 );
}
#endif
diff --git a/AmpGen/enum.h b/AmpGen/enum.h
new file mode 100644
index 00000000000..ba526c714b1
--- /dev/null
+++ b/AmpGen/enum.h
@@ -0,0 +1,71 @@
+#ifndef AMPGEN_ENUM_H
+#define AMPGEN_ENUM_H 1
+#include "AmpGen/MsgService.h"
+#include "AmpGen/Utilities.h"
+
+#define declare_enum(name, ...) \
+enum class name {__VA_ARGS__, Invalid}; \
+template <> name parse(const std::string& word); \
+template <> std::string to_string( const name& enumItem ); \
+std::ostream& operator<<( std::ostream& os, const name& np);
+
+#define complete_enum(name, ...) \
+template <> name parse(const std::string& word){ constexpr auto args = #__VA_ARGS__; return AmpGen::detail::parse<name>(word, args); } \
+template <> std::string to_string( const name& enumItem ){ constexpr auto args = #__VA_ARGS__; return AmpGen::detail::to_string<name>(enumItem, args) ; } \
+template <> name lexical_cast(const std::string& word, bool& /*status*/){ return parse<name>(word); } \
+std::ostream& operator<<(std::ostream& os, const name& np){ return os << to_string<name>(np);}
+
+#define make_enum(name, ...) \
+enum class name {__VA_ARGS__, Invalid}; \
+template <> name parse(const std::string& word){ constexpr auto args = #__VA_ARGS__; return AmpGen::detail::parse<name>(word, args); } \
+template <> std::string to_string( const name& enumItem ){ constexpr auto args = #__VA_ARGS__; return AmpGen::detail::to_string<name>(enumItem, args) ; } \
+template <> name lexical_cast(const std::string& word, bool& /*status*/){ return parse<name>(word); } \
+std::ostream& operator<<(std::ostream& os, const name& np){ return os << to_string<name>(np);}
+
+namespace AmpGen {
+ template <class T> T parse( const std::string& word ){ return T(); }
+ template <class T> std::string to_string( const T& enumItem ){ return ""; }
+
+ namespace detail {
+ template <class T> T parse(const std::string& word, const char* args)
+ {
+ char* p;
+ auto number = strtoul( word.c_str(), &p, 10 );
+ if( *p == 0 ) return T(number);
+ unsigned counter = 0;
+ unsigned begin = 0;
+ unsigned end = 0;
+ auto compare = [](const char* word, const char* otherWord, const unsigned& nChar)
+ {
+ for( size_t x = 0; x != nChar ; ++x) if( word[x] != otherWord[x] ) return false;
+ return true;
+ };
+ bool found = false;
+ while( args[begin] != '\0' )
+ {
+ while( args[begin] == ' ' ) begin++;
+ for( end=begin; args[end] != '\0'; end++ ) if( args[end] == ',' ) break;
+ if( compare( word.c_str(), args + begin , end-begin ) ) { found = true; break; }
+ begin = end+1;
+ counter++;
+ if( args[end] == '\0' ) break;
+ }
+ if(!found) return T::Invalid;
+ return T(counter);
+ }
+ template <class T> std::string to_string(const T& enumItem, const char* args)
+ {
+ unsigned counter = 0;
+ unsigned sBegin = 0;
+ unsigned sLength = 0;
+ for( ; args[sBegin] != '\0' && counter != unsigned(enumItem); sBegin++ )
+ {
+ if( args[sBegin] == ',' ) counter++;
+ }
+ while( args[sBegin] == ' ') sBegin++;
+ for(; args[sLength + sBegin] != '\0' ; ++sLength ) if( args[sBegin + sLength] == ',') break;
+ return std::string(args).substr(sBegin, sLength);
+ }
+ }
+}
+#endif
diff --git a/AmpGen/gsl_wrapper.h b/AmpGen/gsl_wrapper.h
new file mode 100644
index 00000000000..57228b24f7f
--- /dev/null
+++ b/AmpGen/gsl_wrapper.h
@@ -0,0 +1,56 @@
+
+#include <gsl/gsl_integration.h>
+
+namespace AmpGen {
+ template <typename function_type> double integrate_1d( const function_type& fcn, const double& min, const double& max, gsl_integration_workspace* ws = nullptr)
+ {
+ gsl_integration_workspace* w = (ws == nullptr) ? gsl_integration_workspace_alloc (1000) : ws;
+ double result = 0;
+ double error = 0;
+ gsl_function F;
+ F.function = [](double x, void* p) -> double { return (*static_cast<function_type*>(p))(x); };
+ F.params = const_cast<function_type*>(&fcn);
+ gsl_integration_qags (&F, min, max, 0, 1e-5, 1000, w, &result, &error);
+ if( ws == nullptr ) gsl_integration_workspace_free (w);
+ return result;
+ }
+ template <typename function_type> double integrate_1d_inf( const function_type& fcn, gsl_integration_workspace* ws = nullptr)
+ {
+ gsl_integration_workspace* w = (ws == nullptr) ? gsl_integration_workspace_alloc (1000) : ws;
+ double result = 0;
+ double error = 0;
+ gsl_function F;
+ F.function = [](double x, void* p) -> double { return (*static_cast<function_type*>(p))(x); };
+ F.params = const_cast<function_type*>(&fcn);
+ gsl_integration_qagi(&F, 0, 1e-5, 1000, w, &result, &error);
+ if( ws == nullptr ) gsl_integration_workspace_free (w);
+ std::cout << result << " +/- " << error << std::endl;
+ return result;
+ }
+
+
+ template <typename function_type> double integrate_2d( const function_type& fcn, const double& x1, const double& x2, const double& y1, const double& y2)
+ {
+ gsl_integration_workspace* w1 = gsl_integration_workspace_alloc (1000);
+ auto outer = [fcn, &x1, &x2, &w1](const double& y)
+ {
+ auto inner = [fcn, &y](const double& x){ return fcn(x,y); };
+ return integrate_1d(inner, x1,x2, w1);
+ };
+ auto r = integrate_1d( outer, y1, y2);
+ gsl_integration_workspace_free (w1);
+ return r;
+ }
+ template <typename function_type> double integrate_1d_cauchy( const function_type& fcn, const double& x0, const double& min, const double& max, gsl_integration_workspace* ws = nullptr)
+ {
+ gsl_integration_workspace* w = (ws == nullptr) ? gsl_integration_workspace_alloc (1000) : ws;
+ double result = 0;
+ double error = 0;
+ gsl_function F;
+ F.function = [](double x, void* p) -> double { return (*static_cast<function_type*>(p))(x); };
+ F.params = const_cast<function_type*>(&fcn);
+ gsl_integration_qawc(&F, min, max, x0, 0, 1e-5, 1000, w, &result, &error);
+ if( ws == nullptr ) gsl_integration_workspace_free (w);
+ return result;
+ }
+}
diff --git a/AmpGen/kMatrix.h b/AmpGen/kMatrix.h
index ae4165af1fc..06d9b763e5e 100644
--- a/AmpGen/kMatrix.h
+++ b/AmpGen/kMatrix.h
@@ -3,26 +3,54 @@
#include "AmpGen/Expression.h"
#include "AmpGen/Tensor.h"
+#include "AmpGen/Lineshapes.h"
namespace AmpGen
{
+ namespace Lineshape {
+
+ /** @ingroup Lineshapes class kMatrix
+ @brief Anisovich-Sarantsev Isoscalar K-matrix from https://arxiv.org/abs/hep-ph/0204328
+
+ Describes the isoscalar @f$ \pi\pi, KK, 4\pi \eta\eta, \eta\eta^\prime@f$ S-wave in terms of a five-by-five K-matrix and corresponding P-vector couplings.
+ Includes a large number of parameters that can be fixed from the above publication.
+ These parameters can be found in the options directory, which in turn can be includes in the fit by adding
+
+ \code{cpp}
+ Import $AMPGENROOT/options/kMatrix.opt
+ \endcode
+
+ to the user configuration file.
+ */
+ DECLARE_LINESHAPE( kMatrix );
+ }
+
struct poleConfig {
Expression s;
+ Expression gamma;
+ std::string type;
std::vector<Expression> couplings;
std::vector<Expression> bl_factors;
- poleConfig(const Expression& s, const std::vector<Expression>& c = {})
- : s(s), couplings(c), bl_factors(c.size(), 1){};
+ poleConfig(const Expression& s, const std::vector<Expression>& c = {}, const Expression& g = 0, const std::string& type = "")
+ : s(s), gamma(g), couplings(c), bl_factors(c.size(), 1), type(type){};
void add(const Expression& coupling, const Expression& bl_factor = 1)
{
couplings.push_back( coupling );
bl_factors.push_back( bl_factor );
}
- const Expression coupling(const size_t& i) const { return couplings[i] * bl_factors[i]; }
- const Expression g(const size_t& i) const { return couplings[i]; }
+ const Expression coupling(const unsigned& i) const { return couplings[i] * bl_factors[i]; }
+ const Expression g(const unsigned& i) const { return couplings[i]; }
+
+ const Expression pole(const Expression& this_s) const {
+ Expression I = Constant(0,1);
+ if(type=="ACCMOR") return fcn::sqrt(s) - fcn::sqrt(this_s); //Implements K-Matrix definition from https://arxiv.org/pdf/0909.2171v1.pdf
+ return s - this_s - I * s * gamma;
+ }
+
};
- Tensor constructKMatrix(const Expression& s, const size_t& nChannels,
+ Tensor constructKMatrix(const Expression& s, const unsigned& nChannels,
const std::vector<poleConfig>& poleConfigs);
Expression phsp_twoBody( const Expression& s, const double& m0, const double& m1 );
@@ -32,9 +60,7 @@ namespace AmpGen
std::vector<Parameter> paramVector( const std::string& name, const unsigned int& nParam );
- Tensor getPropagator(const Tensor& kMatrix, const std::vector<Expression>& phaseSpace);
-
-
+ Tensor getPropagator(const Tensor& kMatrix, const std::vector<Expression>& phaseSpace, DebugSymbols* db=nullptr);
} // namespace AmpGen
#endif /* end of include guard: AMPGEN_KMATRIX_H */
diff --git a/AmpGen/simd/avx2d_types.h b/AmpGen/simd/avx2d_types.h
new file mode 100644
index 00000000000..e3e0349d7fb
--- /dev/null
+++ b/AmpGen/simd/avx2d_types.h
@@ -0,0 +1,217 @@
+#ifndef AMPGEN_AVXd_TYPES
+#define AMPGEN_AVXd_TYPES 1
+
+#include <immintrin.h>
+#include <array>
+#include <iostream>
+#include <complex>
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+#include <math.h>
+
+#if USE_MVEC
+extern "C" void _ZGVdN4vvv_sincos(__m256d x, __m256i ptrs, __m256i ptrc);
+#endif
+
+#if USE_MVEC
+#define libmvec_alias( function_name) \
+ extern "C" __m256d _ZGVcN4v_##function_name(__m256d x); \
+ inline real_v function_name( const real_v& v ){ return _ZGVcN4v_##function_name (v) ; }
+#else
+#define libmvec_alias( F ) \
+ inline real_v F( const real_v& v ){ auto arr = v.to_array(); return real_v( std::F(arr[0]), std::F(arr[1]), std::F(arr[2]), std::F(arr[3])) ; }
+#endif
+
+namespace AmpGen {
+ namespace AVX2d {
+
+ struct real_v {
+ __m256d data;
+ static constexpr unsigned size = 4;
+ typedef double scalar_type;
+ real_v() = default;
+ real_v(__m256d data ) : data(data) {}
+ real_v(const double& f ) : data( _mm256_set1_pd( f )) {}
+ real_v(const double& x0, const double& x1, const double& x2, const double& x3 )
+ {
+ data = _mm256_set_pd(x3,x2,x1,x0);
+ }
+ real_v(const double* f ) : data( _mm256_loadu_pd( f ) ) {}
+ real_v(const std::array<double,4> f ) : data( _mm256_loadu_pd( f.data() ) ) {}
+ void store( double* ptr ) const { _mm256_storeu_pd( ptr, data ); }
+ std::array<double, 4> to_array() const { std::array<double, 4> b; store( &b[0] ); return b; }
+ double at(const unsigned i) const { return to_array()[i] ; }
+ operator __m256d() const { return data ; }
+ };
+
+ inline real_v operator+( const real_v& lhs, const real_v& rhs ) { return _mm256_add_pd(lhs, rhs); }
+ inline real_v operator-( const real_v& lhs, const real_v& rhs ) { return _mm256_sub_pd(lhs, rhs); }
+ inline real_v operator*( const real_v& lhs, const real_v& rhs ) { return _mm256_mul_pd(lhs, rhs); }
+ inline real_v operator/( const real_v& lhs, const real_v& rhs ) { return _mm256_div_pd(lhs, rhs); }
+ inline real_v operator-( const real_v& x ) { return -1.f * x; }
+ inline real_v operator&( const real_v& lhs, const real_v& rhs ) { return _mm256_and_pd( lhs, rhs ); }
+ inline real_v operator|( const real_v& lhs, const real_v& rhs ) { return _mm256_or_pd( lhs, rhs ); }
+ inline real_v operator^( const real_v& lhs, const real_v& rhs ) { return _mm256_xor_pd( lhs, rhs ); }
+ inline real_v operator+=(real_v& lhs, const real_v& rhs ){ lhs = lhs + rhs; return lhs; }
+ inline real_v operator-=(real_v& lhs, const real_v& rhs ){ lhs = lhs - rhs; return lhs; }
+ inline real_v operator*=(real_v& lhs, const real_v& rhs ){ lhs = lhs * rhs; return lhs; }
+ inline real_v operator/=(real_v& lhs, const real_v& rhs ){ lhs = lhs / rhs; return lhs; }
+ inline real_v operator&&( const real_v& lhs, const real_v& rhs ) { return _mm256_and_pd( lhs, rhs ); }
+ inline real_v operator||( const real_v& lhs, const real_v& rhs ) { return _mm256_or_pd( lhs, rhs ); }
+ inline real_v operator!( const real_v& x ) { return x ^ _mm256_castsi256_pd( _mm256_set1_epi32( -1 ) ); }
+ inline real_v operator<( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_pd( lhs, rhs, _CMP_LT_OS ); }
+ inline real_v operator>( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_pd( lhs, rhs, _CMP_GT_OS ); }
+ inline real_v operator<=( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_pd( lhs, rhs, _CMP_LE_OS ); }
+ inline real_v operator>=( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_pd( lhs, rhs, _CMP_GE_OS ); }
+ inline real_v operator==( const real_v& lhs, const real_v& rhs ){ return _mm256_cmp_pd( lhs, rhs, _CMP_EQ_OS ); }
+ inline real_v sqrt( const real_v& v ) { return _mm256_sqrt_pd(v); }
+ inline real_v abs ( const real_v& v ) { return _mm256_andnot_pd(_mm256_set1_pd(-0.), v); }
+ libmvec_alias( sin )
+ libmvec_alias( cos )
+ libmvec_alias( exp )
+ libmvec_alias( log )
+ //inline real_v log( const real_v& v ){ auto arr = v.to_array(); return real_v( std::log(arr[0]), std::log(arr[1]), std::log(arr[2]), std::log(arr[3])) ; }
+ inline void sincos( const real_v& v, real_v& s, real_v& c )
+ {
+#if USE_MVEC
+ __m256i sp = _mm256_add_epi64(_mm256_set1_epi64x((uint64_t)&s),_mm256_set_epi64x(24,16,8,0));
+ __m256i cp = _mm256_add_epi64(_mm256_set1_epi64x((uint64_t)&c),_mm256_set_epi64x(24,16,8,0));
+ _ZGVdN4vvv_sincos(v,sp,cp);
+#else
+ s = sin(v);
+ c = cos(v);
+#endif
+ }
+ inline std::pair<real_v, real_v> sincos( const real_v& v )
+ {
+ std::pair<real_v, real_v> rt;
+ sincos( v, rt.first, rt.second );
+ return rt;
+ }
+ inline real_v tan( const real_v& v )
+ {
+ auto [s,c] = sincos( v );
+ return s / c ;
+ }
+
+ inline real_v select(const real_v& mask, const real_v& a, const real_v& b ) { return _mm256_blendv_pd( b, a, mask ); }
+ inline real_v select(const bool& mask , const real_v& a, const real_v& b ) { return mask ? a : b; }
+ inline real_v sign ( const real_v& v){ return select( v > 0., +1., -1. ); }
+ inline real_v atan2( const real_v& y, const real_v& x ){
+ std::array<double, 4> bx{x.to_array()}, by{y.to_array()};
+ return real_v (
+ std::atan2( by[0], bx[0])
+ , std::atan2( by[1], bx[1])
+ , std::atan2( by[2], bx[2])
+ , std::atan2( by[3], bx[3]) );
+ }
+ inline __m256i udouble_to_uint( const real_v& x )
+ {
+ auto xr = _mm256_round_pd(x, _MM_FROUND_TO_NEG_INF);
+ // based on: https://stackoverflow.com/questions/41144668/how-to-efficiently-perform-double-int64-conversions-with-sse-avx
+ return _mm256_sub_epi64(_mm256_castpd_si256(_mm256_add_pd(xr, _mm256_set1_pd(0x0018000000000000))),
+ _mm256_castpd_si256(_mm256_set1_pd(0x0018000000000000)));
+ }
+ inline real_v gather( const double* base_addr, const real_v& offsets)
+ {
+ return _mm256_i64gather_pd(base_addr, udouble_to_uint(offsets),sizeof(double));
+ }
+
+ inline real_v fmadd( const real_v& a, const real_v& b, const real_v& c )
+ {
+ return _mm256_fmadd_pd(a, b, c);
+ }
+ inline real_v remainder( const real_v& a, const real_v& b ){ return a - real_v(_mm256_round_pd(a/b, _MM_FROUND_TO_NEG_INF)) * b; }
+ inline real_v fmod( const real_v& a, const real_v& b )
+ {
+ auto r = remainder( abs(a), abs(b) );
+ return select( a > 0., r, -r );
+ }
+
+ struct complex_v {
+ real_v re;
+ real_v im;
+ typedef std::complex<double> scalar_type;
+ static constexpr unsigned size = 4;
+
+ real_v real() const { return re; }
+ real_v imag() const { return im; }
+ real_v norm() const { return re*re + im *im ; }
+ complex_v() = default;
+ complex_v( const real_v& re, const real_v& im) : re(re), im(im) {}
+ complex_v( const float& re, const float& im) : re(re), im(im) {}
+ complex_v( const std::complex<double>& f ) : re( f.real() ), im( f.imag() ) {}
+ complex_v( const std::complex<float>& f ) : re( f.real() ), im( f.imag() ) {}
+ complex_v( const std::complex<double>* arr ) :
+ re ( arr[0].real(), arr[1].real(), arr[2].real(), arr[3].real() ),
+ im ( arr[0].imag(), arr[1].imag(), arr[2].imag(), arr[3].imag() ){}
+ explicit complex_v( const real_v& arg ) : re(arg) {};
+ explicit complex_v( const double& arg ) : re(arg) {};
+ const std::complex<double> at(const unsigned i) const { return std::complex<float>(re.to_array()[i], im.to_array()[i]) ; }
+ void store( double* sre, double* sim ){ re.store(sre); im.store(sim); }
+ void store( scalar_type* r ) const {
+ auto re_arr = re.to_array();
+ auto im_arr = im.to_array();
+ for( unsigned i = 0 ; i != re_arr.size(); ++i ) r[i] = scalar_type( re_arr[i], im_arr[i] );
+ }
+ auto to_array() const
+ {
+ std::array<scalar_type, 4> rt;
+ store( rt.data() );
+ return rt;
+ }
+ };
+
+ inline std::ostream& operator<<( std::ostream& os, const real_v& obj ) {
+ auto buffer = obj.to_array();
+ for( unsigned i = 0 ; i != 4; ++i ) os << buffer[i] << " ";
+ return os;
+ }
+ inline real_v real(const complex_v& arg ){ return arg.re ; }
+ inline real_v imag(const complex_v& arg ){ return arg.im ; }
+ inline complex_v conj(const complex_v& arg ){ return complex_v(arg.re, -arg.im) ; }
+ inline real_v conj(const real_v& arg ){ return arg ; }
+ inline complex_v operator+( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re + rhs, lhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re - rhs, lhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re*rhs, lhs.im*rhs); }
+ inline complex_v operator/( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re/rhs, lhs.im/rhs); }
+ inline complex_v operator+( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs + rhs.re, rhs.im); }
+ inline complex_v operator-( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs - rhs.re, - rhs.im); }
+ inline complex_v operator*( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs*rhs.re, lhs*rhs.im); }
+ inline complex_v operator/( const real_v& lhs, const complex_v& rhs ) { return complex_v( lhs * rhs.re , -lhs *rhs.im) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator+( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re + rhs.re, lhs.im + rhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re - rhs.re, lhs.im - rhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re - lhs.im*rhs.im, lhs.re*rhs.im + lhs.im*rhs.re); }
+ inline complex_v operator/( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re + lhs.im*rhs.im, -lhs.re*rhs.im + lhs.im*rhs.re) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator-( const complex_v& x ) { return -1.f * x; }
+ inline real_v abs( const complex_v& v ) { return sqrt( v.re * v.re + v.im * v.im ) ; }
+ inline real_v norm( const complex_v& v ) { return ( v.re * v.re + v.im * v.im ) ; }
+ inline complex_v select(const real_v& mask, const complex_v& a, const complex_v& b ) { return complex_v( select(mask, a.re, b.re), select(mask, a.im, b.im ) ) ; }
+ inline complex_v select(const real_v& mask, const real_v& a, const complex_v& b ) { return complex_v( select(mask, a , b.re), select(mask, 0.f, b.im) ); }
+ inline complex_v select(const real_v& mask, const complex_v& a, const real_v& b ) { return complex_v( select(mask, a.re, b ) , select(mask, a.im, 0.f) ); }
+ inline complex_v select(const bool& mask , const complex_v& a, const complex_v& b ) { return mask ? a : b; }
+ inline complex_v exp( const complex_v& v ){
+ auto [s,c] = sincos( v.im);
+ return exp(v.re) * complex_v(c, s);
+ }
+ inline complex_v sqrt( const complex_v& v )
+ {
+ auto r = abs(v);
+ return complex_v ( sqrt( 0.5 * (r + v.re) ), sign(v.im) * sqrt( 0.5*( r - v.re ) ) );
+ }
+ inline complex_v log( const complex_v& v )
+ {
+ return complex_v( 0.5 * log( v.norm() ) , atan2(v.im, v.re) );
+ }
+
+ inline std::ostream& operator<<( std::ostream& os, const complex_v& obj ) { return os << "( "<< obj.re << ") (" << obj.im << ")"; }
+ #pragma omp declare reduction(+: real_v: \
+ omp_out = omp_out + omp_in)
+ #pragma omp declare reduction(+: complex_v: \
+ omp_out = omp_out + omp_in)
+
+ }
+}
+
+#endif
diff --git a/AmpGen/simd/avx2f_types.h b/AmpGen/simd/avx2f_types.h
new file mode 100644
index 00000000000..66a91df9431
--- /dev/null
+++ b/AmpGen/simd/avx2f_types.h
@@ -0,0 +1,204 @@
+#ifndef AMPGEN_AVX_TYPES
+#define AMPGEN_AVX_TYPES 1
+
+#include <immintrin.h>
+#include <array>
+#include <iostream>
+#include <complex>
+#include <omp.h>
+
+#if USE_MVEC
+extern "C" void _ZGVdN8vvv_sincos(__m256 x, __m256i ptrs, __m256i ptrc);
+#endif
+
+#if USE_MVEC
+#define libmvec_alias( function_name) \
+ extern "C" __m256 _ZGVcN8v_##function_name(__m256 x); \
+ inline real_v function_name( const real_v& v ){ return _ZGVcN8v_##function_name (v) ; }
+#else
+#define libmvec_alias( F ) \
+ inline real_v F( const real_v& v ){ auto arr = v.to_array(); return real_v( \
+ std::F(arr[0]), std::F(arr[1]), std::F(arr[2]), std::F(arr[3]), \
+ std::F(arr[4]), std::F(arr[5]), std::F(arr[6]), std::F(arr[7]) ) ; }
+#endif
+
+namespace AmpGen {
+ namespace AVX2f {
+ struct real_v {
+ __m256 data;
+ static constexpr unsigned size = 8 ;
+ typedef float scalar_type;
+ real_v() = default;
+ real_v(__m256 data ) : data(data) {}
+ real_v(const float& f ) : data( _mm256_set1_ps(f) ) {}
+ real_v(const double& f ) : data( _mm256_set1_ps( float(f) )) {}
+ real_v(const float* f ) : data( _mm256_loadu_ps( f ) ) {}
+ real_v(const float& x0, const float& x1, const float& x2, const float& x3,
+ const float& x4, const float& x5, const float& x6, const float& x7)
+ {
+ data = _mm256_set_ps(x7,x6,x5,x4,x3,x2,x1,x0);
+ }
+
+ void store( float* ptr ) const { _mm256_storeu_ps( ptr, data ); }
+ std::array<float, 8> to_array() const { std::array<float, 8> b; store( &b[0] ); return b; }
+ float at(const unsigned i) const { return to_array()[i] ; }
+ operator __m256() const { return data ; }
+ };
+
+ inline real_v operator+( const real_v& lhs, const real_v& rhs ) { return _mm256_add_ps(lhs, rhs); }
+ inline real_v operator-( const real_v& lhs, const real_v& rhs ) { return _mm256_sub_ps(lhs, rhs); }
+ inline real_v operator*( const real_v& lhs, const real_v& rhs ) { return _mm256_mul_ps(lhs, rhs); }
+ inline real_v operator/( const real_v& lhs, const real_v& rhs ) { return _mm256_div_ps(lhs, rhs); }
+ inline real_v operator-( const real_v& x ) { return -1.f * x; }
+ inline real_v operator&( const real_v& lhs, const real_v& rhs ) { return _mm256_and_ps( lhs, rhs ); }
+ inline real_v operator|( const real_v& lhs, const real_v& rhs ) { return _mm256_or_ps( lhs, rhs ); }
+ inline real_v operator^( const real_v& lhs, const real_v& rhs ) { return _mm256_xor_ps( lhs, rhs ); }
+ inline real_v operator+=(real_v& lhs, const real_v& rhs ){ lhs = lhs + rhs; return lhs; }
+ inline real_v operator-=(real_v& lhs, const real_v& rhs ){ lhs = lhs - rhs; return lhs; }
+ inline real_v operator*=(real_v& lhs, const real_v& rhs ){ lhs = lhs * rhs; return lhs; }
+ inline real_v operator/=(real_v& lhs, const real_v& rhs ){ lhs = lhs / rhs; return lhs; }
+ inline real_v operator&&( const real_v& lhs, const real_v& rhs ) { return _mm256_and_ps( lhs, rhs ); }
+ inline real_v operator||( const real_v& lhs, const real_v& rhs ) { return _mm256_or_ps( lhs, rhs ); }
+ inline real_v operator!( const real_v& x ) { return x ^ _mm256_castsi256_ps( _mm256_set1_epi32( -1 ) ); }
+ inline real_v operator<( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_ps( lhs, rhs, _CMP_LT_OS ); }
+ inline real_v operator>( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_ps( lhs, rhs, _CMP_GT_OS ); }
+ inline real_v operator<( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_ps( lhs, rhs, _CMP_LE_OS ); }
+ inline real_v operator>( const real_v& lhs, const real_v& rhs ) { return _mm256_cmp_ps( lhs, rhs, _CMP_GE_OS ); }
+ inline real_v operator==( const real_v& lhs, const real_v& rhs ){ return _mm256_cmp_ps( lhs, rhs, _CMP_EQ_OS ); }
+ inline real_v sqrt( const real_v& v ) { return _mm256_sqrt_ps(v); }
+ libmvec_alias(sin)
+ libmvec_alias(cos)
+ libmvec_alias(exp)
+ libmvec_alias(log)
+
+ inline void sincos( const real_v& v, real_v& s, real_v& c )
+ {
+#if USE_MVEC
+ __m256i sp = _mm256_add_epi64(_mm256_set1_epi32x((uint64_t)&s),_mm256_set_epi32x(28,24,20,16,12,8,4,0));
+ __m256i cp = _mm256_add_epi64(_mm256_set1_epi32x((uint64_t)&c),_mm256_set_epi32x(28,24,20,16,12,8,4,0));
+ _ZGVdN8vvv_sincos(v,sp,cp);
+#else
+ s = sin(v);
+ c = cos(v);
+#endif
+ }
+ inline std::pair<real_v, real_v> sincos( const real_v& v )
+ {
+ std::pair<real_v, real_v> rt;
+ sincos( v, rt.first, rt.second );
+ return rt;
+ }
+ inline real_v tan( const real_v& v )
+ {
+ auto [s,c] = sincos( v );
+ return s / c ;
+ }
+
+
+
+ inline real_v abs ( const real_v& v ) { return v & _mm256_castsi256_ps( _mm256_set1_epi32( 0x7FFFFFFF ) ); }
+ inline real_v select(const real_v& mask, const real_v& a, const real_v& b ) { return _mm256_blendv_ps( b, a, mask ); }
+ inline real_v select(const bool& mask , const real_v& a, const real_v& b ) { return mask ? a : b; }
+ inline real_v atan2( const real_v& y, const real_v& x ){
+ std::array<float, 8> bx{x.to_array()}, by{y.to_array()}, rt;
+ for( unsigned i = 0 ; i != 8 ; ++i ) rt[i] = std::atan2( by[i] , bx[i] );
+ return real_v (rt.data() );
+ }
+// inline real_v gather( const double* base_addr, const real_v& offsets)
+// {
+// auto addr_avx =_mm256_cvtps_epi32(offsets);
+// std::array<uint32_t, 8> addr;
+// _mm256_storeu_ps( addr.data(), _mm256_cvtps_epi32(offsets) );
+// return real_v(
+// base_addr[addr[0]], base_addr[addr[1]],base_addr[addr[2]],base_addr[addr[3]],
+// base_addr[addr[4]], base_addr[addr[5]],base_addr[addr[6]],base_addr[addr[7]] );
+//
+// //return _mm256_i32gather_ps(base_addr, _mm256_cvtps_epi32(offsets),sizeof(double));
+// }
+
+ inline real_v fmadd( const real_v& a, const real_v& b, const real_v& c )
+ {
+ return _mm256_fmadd_ps(a, b, c);
+ }
+ inline real_v remainder( const real_v& a, const real_v& b ){ return a - real_v(_mm256_round_ps(a/b, _MM_FROUND_TO_NEG_INF)) * b; }
+ inline real_v fmod( const real_v& a, const real_v& b )
+ {
+ auto r = remainder( abs(a), abs(b) );
+ return select( a > 0., r, -r );
+ }
+ struct complex_v {
+ real_v re;
+ real_v im;
+ typedef std::complex<float> scalar_type;
+ static constexpr unsigned size = 8 ;
+
+ real_v real() const { return re; }
+ real_v imag() const { return im; }
+ real_v norm() const { return re*re + im *im ; }
+ complex_v() = default;
+ complex_v( const real_v& re, const real_v& im) : re(re), im(im) {}
+ complex_v( const float& re, const float& im) : re(re), im(im) {}
+ complex_v( const std::complex<double>& f ) : re( f.real() ), im( f.imag() ) {}
+ complex_v( const std::complex<float>& f ) : re( f.real() ), im( f.imag() ) {}
+
+ const std::complex<float> at(const unsigned i) const { return std::complex<float>(re.to_array()[i], im.to_array()[i]) ; }
+ void store( float* sre, float* sim ) const { re.store(sre); im.store(sim); }
+ void store( std::complex<float>* r ) const {
+ auto re_arr = re.to_array();
+ auto im_arr = im.to_array();
+ for( unsigned i = 0 ; i != re_arr.size(); ++i ) r[i] = std::complex<float>( re_arr[i], im_arr[i] );
+ }
+ auto to_array() const
+ {
+ std::array<scalar_type, 8> rt;
+ store( rt.data() );
+ return rt;
+ }
+ };
+
+ inline std::ostream& operator<<( std::ostream& os, const real_v& obj ) {
+ auto buffer = obj.to_array();
+ for( unsigned i = 0 ; i != 8; ++i ) os << buffer[i] << " ";
+ return os;
+ }
+ inline real_v real(const complex_v& arg ){ return arg.re ; }
+ inline real_v imag(const complex_v& arg ){ return arg.im ; }
+ inline complex_v conj(const complex_v& arg ){ return complex_v(arg.re, -arg.im) ; }
+ inline real_v conj(const real_v& arg ){ return arg ; }
+ inline complex_v operator+( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re + rhs, lhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re - rhs, lhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re*rhs, lhs.im*rhs); }
+ inline complex_v operator/( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re/rhs, lhs.im/rhs); }
+ inline complex_v operator+( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs + rhs.re, rhs.im); }
+ inline complex_v operator-( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs - rhs.re, - rhs.im); }
+ inline complex_v operator*( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs*rhs.re, lhs*rhs.im); }
+ inline complex_v operator/( const real_v& lhs, const complex_v& rhs ) { return complex_v( lhs * rhs.re , -lhs *rhs.im) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator+( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re + rhs.re, lhs.im + rhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re - rhs.re, lhs.im - rhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re - lhs.im*rhs.im, lhs.re*rhs.im + lhs.im*rhs.re); }
+ inline complex_v operator/( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re + lhs.im*rhs.im, -lhs.re*rhs.im + lhs.im*rhs.re) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator-( const complex_v& x ) { return -1.f * x; }
+ inline real_v abs( const complex_v& v ) { return sqrt( v.re * v.re + v.im * v.im ) ; }
+ inline real_v norm( const complex_v& v ) { return ( v.re * v.re + v.im * v.im ) ; }
+ inline complex_v select(const real_v& mask, const complex_v& a, const complex_v& b ) { return complex_v( _mm256_blendv_ps( b.re, a.re, mask ), _mm256_blendv_ps( b.im, a.im, mask ) ); }
+ inline complex_v select(const real_v& mask, const real_v& a, const complex_v& b ) { return complex_v( _mm256_blendv_ps( b.re, a , mask ), _mm256_blendv_ps( b.im, real_v(0.f), mask ) ); }
+ inline complex_v select(const real_v& mask, const complex_v& a, const real_v& b ) { return complex_v( _mm256_blendv_ps( b, a.re, mask ), _mm256_blendv_ps( real_v(0.f), a.im, mask ) ); }
+ inline complex_v select(const bool& mask , const complex_v& a, const complex_v& b ) { return mask ? a : b; }
+ inline complex_v exp( const complex_v& v ){
+ auto [s,c] = sincos( v.im );
+ return exp( v.re ) * complex_v(c, s);
+ }
+ inline complex_v log( const complex_v& v )
+ {
+ return complex_v( 0.5 * log( v.norm() ) , atan2(v.im, v.re) );
+ }
+ inline std::ostream& operator<<( std::ostream& os, const complex_v& obj ) { return os << "( "<< obj.re << ") (" << obj.im << ")"; }
+ #pragma omp declare reduction(+: real_v: \
+ omp_out = omp_out + omp_in)
+ #pragma omp declare reduction(+: complex_v: \
+ omp_out = omp_out + omp_in)
+
+ }
+}
+
+#endif
diff --git a/AmpGen/simd/avx512d_types.h b/AmpGen/simd/avx512d_types.h
new file mode 100644
index 00000000000..36d9695af77
--- /dev/null
+++ b/AmpGen/simd/avx512d_types.h
@@ -0,0 +1,213 @@
+#ifndef AMPGEN_AVXd_TYPES
+#define AMPGEN_AVXd_TYPES 1
+
+#include <immintrin.h>
+#include <array>
+#include <iostream>
+#include <complex>
+#include <omp.h>
+
+namespace AmpGen {
+ namespace AVX512d {
+ #define stl_fallback( x ) \
+ inline real_v x( const real_v& v ){ auto a = v.to_array(); return real_v( std::x(a[0]), std::x(a[1]), std::x(a[2]), std::x(a[3]), std::x(a[4]), std::x(a[5]), std::x(a[6]), std::x(a[7]) ) ; }
+
+ struct real_v {
+ __m512d data;
+ static constexpr unsigned size = 8;
+ typedef double scalar_type;
+ real_v() = default;
+ real_v(__m512d data ) : data(data) {}
+ real_v(const double& f ) : data( _mm512_set1_pd( f )) {}
+ real_v(
+ const double& x0, const double& x1, const double& x2, const double& x3,
+ const double& x4, const double& x5, const double& x6, const double& x7)
+ {
+ double tmp[8] = {x0,x1,x2,x3,x4,x5,x6,x7};
+ data = _mm512_loadu_pd(tmp);
+ }
+ real_v(const double* f ) : data( _mm512_loadu_pd( f ) ) {}
+ void store( double* ptr ) const { _mm512_storeu_pd( ptr, data ); }
+ std::array<double, 8> to_array() const { std::array<double, 8> b; store( &b[0] ); return b; }
+ double at(const unsigned i) const { return to_array()[i] ; }
+ operator __m512d() const { return data ; }
+ };
+
+ inline real_v operator+( const real_v& lhs, const real_v& rhs ) { return _mm512_add_pd(lhs, rhs); }
+ inline real_v operator-( const real_v& lhs, const real_v& rhs ) { return _mm512_sub_pd(lhs, rhs); }
+ inline real_v operator*( const real_v& lhs, const real_v& rhs ) { return _mm512_mul_pd(lhs, rhs); }
+ inline real_v operator/( const real_v& lhs, const real_v& rhs ) { return _mm512_div_pd(lhs, rhs); }
+ inline real_v operator-( const real_v& x ) { return -1.f * x; }
+ inline real_v operator&( const real_v& lhs, const real_v& rhs ) { return _mm512_and_pd( lhs, rhs ); }
+ inline real_v operator|( const real_v& lhs, const real_v& rhs ) { return _mm512_or_pd( lhs, rhs ); }
+ inline real_v operator^( const real_v& lhs, const real_v& rhs ) { return _mm512_xor_pd( lhs, rhs ); }
+ inline real_v operator+=(real_v& lhs, const real_v& rhs ){ lhs = lhs + rhs; return lhs; }
+ inline real_v operator-=(real_v& lhs, const real_v& rhs ){ lhs = lhs - rhs; return lhs; }
+ inline real_v operator*=(real_v& lhs, const real_v& rhs ){ lhs = lhs * rhs; return lhs; }
+ inline real_v operator/=(real_v& lhs, const real_v& rhs ){ lhs = lhs / rhs; return lhs; }
+ inline real_v operator&&( const real_v& lhs, const real_v& rhs ) { return _mm512_and_pd( lhs, rhs ); }
+ inline real_v operator||( const real_v& lhs, const real_v& rhs ) { return _mm512_or_pd( lhs, rhs ); }
+ inline real_v operator!( const real_v& x ) { return x ^ _mm512_castsi512_pd( _mm512_set1_epi32( -1 ) ); }
+ inline __mmask8 operator<( const real_v& lhs, const real_v& rhs ) { return _mm512_cmp_pd_mask( lhs, rhs, _CMP_LT_OS ); }
+ inline __mmask8 operator>( const real_v& lhs, const real_v& rhs ) { return _mm512_cmp_pd_mask( lhs, rhs, _CMP_GT_OS ); }
+ inline __mmask8 operator==( const real_v& lhs, const real_v& rhs ){ return _mm512_cmp_pd_mask( lhs, rhs, _CMP_EQ_OS ); }
+ inline real_v sqrt( const real_v& v ) { return _mm512_sqrt_pd(v); }
+ inline real_v abs ( const real_v& v ) { return _mm512_andnot_pd(_mm512_set1_pd(-0.), v); }
+ // inline real_v sin( const real_v& v ) { return sin512_pd(v) ; }
+ // inline real_v cos( const real_v& v ) { return cos512_pd(v) ; }
+ // inline real_v tan( const real_v& v ) { real_v s; real_v c; sincos512_pd(v, (__m512*)&s, (__m512*)&c) ; return s/c; }
+ // inline real_v exp( const real_v& v ) { return exp512_ps(v) ; }
+ inline real_v select(const __mmask8& mask, const real_v& a, const real_v& b ) { return _mm512_mask_mov_pd( b, mask, a ); }
+ inline real_v select(const bool& mask , const real_v& a, const real_v& b ) { return mask ? a : b; }
+ inline real_v sign ( const real_v& v){ return select( v > 0., +1., -1. ); }
+ inline real_v atan2( const real_v& y, const real_v& x ){
+ std::array<double, 8> bx{x.to_array()}, by{y.to_array()};
+ return real_v (
+ std::atan2(by[0], bx[0]) , std::atan2( by[1], bx[1]), std::atan2( by[2], bx[2]), std::atan2( by[3], bx[3]) ,
+ std::atan2(by[4], bx[4]) , std::atan2( by[5], bx[5]), std::atan2( by[6], bx[6]), std::atan2( by[7], bx[7]) );
+ }
+ inline __m512i double_to_int( const real_v& x )
+ {
+ auto xr = _mm512_roundscale_pd(x, _MM_FROUND_TO_ZERO);
+ // based on: https://stackoverflow.com/questions/41144668/how-to-efficiently-perform-double-int64-conversions-with-sse-avx
+ return _mm512_sub_epi64(_mm512_castpd_si512(_mm512_add_pd(xr, _mm512_set1_pd(0x0018000000000000))),
+ _mm512_castpd_si512(_mm512_set1_pd(0x0018000000000000)));
+ }
+ inline real_v gather( const double* base_addr, const real_v& offsets)
+ {
+ return _mm512_i64gather_pd(double_to_int(offsets), base_addr, sizeof(double));
+ }
+
+ inline void frexp(const real_v& value, real_v& mant, real_v& exponent)
+ {
+ auto arg_as_int = _mm512_castpd_si512(value);
+ static const real_v offset(4503599627370496.0 + 1022.0); // 2^52 + 1022.0
+ static const __m512i pow2_52_i = _mm512_set1_epi64(0x4330000000000000); // *reinterpret_cast<const uint64_t*>(&pow2_52_d);
+ auto b = _mm512_srl_epi64(arg_as_int, _mm_cvtsi32_si128(52));
+ auto c = _mm512_or_si512( b , pow2_52_i);
+ exponent = real_v( _mm512_castsi512_pd(c) ) - offset;
+ mant = _mm512_castsi512_pd(_mm512_or_si512(_mm512_and_si512 (arg_as_int, _mm512_set1_epi64(0x000FFFFFFFFFFFFFll) ), _mm512_set1_epi64(0x3FE0000000000000ll)));
+ }
+
+ inline real_v fmadd( const real_v& a, const real_v& b, const real_v& c )
+ {
+ return _mm512_fmadd_pd(a, b, c);
+ }
+ inline real_v log(const real_v& arg)
+ {
+ static const real_v corr = 0.693147180559945286226764;
+ static const real_v CL15 = 0.148197055177935105296783;
+ static const real_v CL13 = 0.153108178020442575739679;
+ static const real_v CL11 = 0.181837339521549679055568;
+ static const real_v CL9 = 0.22222194152736701733275;
+ static const real_v CL7 = 0.285714288030134544449368;
+ static const real_v CL5 = 0.399999999989941956712869;
+ static const real_v CL3 = 0.666666666666685503450651;
+ static const real_v CL1 = 2.0;
+ real_v mant, exponent;
+ frexp(arg, mant, exponent);
+ auto x = (mant - 1.) / (mant + 1.);
+ auto x2 = x * x;
+ auto p = fmadd(CL15, x2, CL13);
+ p = fmadd(p, x2, CL11);
+ p = fmadd(p, x2, CL9);
+ p = fmadd(p, x2, CL7);
+ p = fmadd(p, x2, CL5);
+ p = fmadd(p, x2, CL3);
+ p = fmadd(p, x2, CL1);
+ p = fmadd(p, x, corr * exponent);
+ return p;
+ }
+ stl_fallback( exp )
+ stl_fallback( tan )
+ stl_fallback( sin )
+ stl_fallback( cos )
+ inline real_v remainder( const real_v& a, const real_v& b ){ return a - real_v(_mm512_roundscale_pd(a/b, _MM_FROUND_TO_NEG_INF)) * b; }
+ inline real_v fmod( const real_v& a, const real_v& b )
+ {
+ auto r = remainder( abs(a), abs(b) );
+ return select( a > 0., r, -r );
+ }
+
+ struct complex_v {
+ real_v re;
+ real_v im;
+ static constexpr unsigned size = 8;
+ typedef std::complex<double> scalar_type;
+
+ real_v real() const { return re; }
+ real_v imag() const { return im; }
+ real_v norm() const { return re*re + im *im ; }
+ complex_v() = default;
+ complex_v( const real_v& re, const real_v& im) : re(re), im(im) {}
+ complex_v( const float& re, const float& im) : re(re), im(im) {}
+ complex_v( const std::complex<double>& f ) : re( f.real() ), im( f.imag() ) {}
+ complex_v( const std::complex<float>& f ) : re( f.real() ), im( f.imag() ) {}
+ explicit complex_v( const real_v& arg ) : re(arg) {};
+ explicit complex_v( const double& arg ) : re(arg) {};
+ const std::complex<double> at(const unsigned i) const { return std::complex<float>(re.to_array()[i], im.to_array()[i]) ; }
+ void store( double* sre, double* sim ){ re.store(sre); im.store(sim); }
+ void store( scalar_type* r ) const {
+ auto re_arr = re.to_array();
+ auto im_arr = im.to_array();
+ for( unsigned i = 0 ; i != re_arr.size(); ++i ) r[i] = scalar_type( re_arr[i], im_arr[i] );
+ }
+ auto to_array() const
+ {
+ std::array<scalar_type, 8> rt;
+ store( rt.data() );
+ return rt;
+ }
+ };
+
+ inline std::ostream& operator<<( std::ostream& os, const real_v& obj ) {
+ auto buffer = obj.to_array();
+ for( unsigned i = 0 ; i != 8; ++i ) os << buffer[i] << " ";
+ return os;
+ }
+ inline real_v real(const complex_v& arg ){ return arg.re ; }
+ inline real_v imag(const complex_v& arg ){ return arg.im ; }
+ inline complex_v conj(const complex_v& arg ){ return complex_v(arg.re, -arg.im) ; }
+ inline real_v conj(const real_v& arg ){ return arg ; }
+ inline complex_v operator+( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re + rhs, lhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re - rhs, lhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re*rhs, lhs.im*rhs); }
+ inline complex_v operator/( const complex_v& lhs, const real_v& rhs ) { return complex_v(lhs.re/rhs, lhs.im/rhs); }
+ inline complex_v operator+( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs + rhs.re, rhs.im); }
+ inline complex_v operator-( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs - rhs.re, - rhs.im); }
+ inline complex_v operator*( const real_v& lhs, const complex_v& rhs ) { return complex_v(lhs*rhs.re, lhs*rhs.im); }
+ inline complex_v operator/( const real_v& lhs, const complex_v& rhs ) { return complex_v( lhs * rhs.re , -lhs *rhs.im) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator+( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re + rhs.re, lhs.im + rhs.im); }
+ inline complex_v operator-( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re - rhs.re, lhs.im - rhs.im); }
+ inline complex_v operator*( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re - lhs.im*rhs.im, lhs.re*rhs.im + lhs.im*rhs.re); }
+ inline complex_v operator/( const complex_v& lhs, const complex_v& rhs ) { return complex_v(lhs.re*rhs.re + lhs.im*rhs.im, -lhs.re*rhs.im + lhs.im*rhs.re) / (rhs.re * rhs.re + rhs.im * rhs.im ); }
+ inline complex_v operator-( const complex_v& x ) { return -1.f * x; }
+ inline real_v abs( const complex_v& v ) { return sqrt( v.re * v.re + v.im * v.im ) ; }
+ inline real_v norm( const complex_v& v ) { return ( v.re * v.re + v.im * v.im ) ; }
+ inline complex_v select(const __mmask8& mask, const complex_v& a, const complex_v& b ) { return complex_v( select(mask, a.re, b.re), select(mask, a.im, b.im ) ) ; }
+ inline complex_v select(const __mmask8& mask, const real_v& a, const complex_v& b ) { return complex_v( select(mask, a , b.re), select(mask, 0.f, b.im) ); }
+ inline complex_v select(const __mmask8& mask, const complex_v& a, const real_v& b ) { return complex_v( select(mask, a.re, b ) , select(mask, a.im, 0.f) ); }
+ inline complex_v select(const bool& mask , const complex_v& a, const complex_v& b ) { return mask ? a : b; }
+ inline complex_v exp( const complex_v& v ){
+ return exp( v.re) * complex_v( cos( v.im ), sin( v.im ) );
+ }
+ inline complex_v sqrt( const complex_v& v )
+ {
+ auto r = abs(v);
+ return complex_v ( sqrt( 0.5 * (r + v.re) ), sign(v.im) * sqrt( 0.5*( r - v.re ) ) );
+ }
+ inline complex_v log( const complex_v& v )
+ {
+ return complex_v( log( v.re ) , atan2(v.im, v.re) );
+ }
+
+ inline std::ostream& operator<<( std::ostream& os, const complex_v& obj ) { return os << "( "<< obj.re << ") (" << obj.im << ")"; }
+ #pragma omp declare reduction(+: real_v: \
+ omp_out = omp_out + omp_in)
+ #pragma omp declare reduction(+: complex_v: \
+ omp_out = omp_out + omp_in)
+
+ }
+}
+
+#endif
diff --git a/AmpGen/simd/iterator.h b/AmpGen/simd/iterator.h
new file mode 100644
index 00000000000..3949a0a44ea
--- /dev/null
+++ b/AmpGen/simd/iterator.h
@@ -0,0 +1,45 @@
+#include <array>
+
+namespace AmpGen {
+ template <class stored_type, class store_type, unsigned simd_size, bool modifiable> class scatter_iterator
+ {
+ store_type* m_store;
+ std::array<stored_type, simd_size> m_buffer;
+ size_t m_pos{0};
+ public:
+ int pos() const { return m_pos ; }
+ scatter_iterator( const size_t& pos, store_type* store ) :
+ m_store(store),
+ m_pos(pos) {
+ if( m_store != nullptr && pos < m_store->aligned_size()) m_buffer = m_store->scatter(pos / simd_size );
+ }
+ stored_type* operator->() const { return &( m_buffer )[m_pos % simd_size]; }
+ stored_type operator*() const { return m_buffer [m_pos % simd_size]; }
+ stored_type& operator*() { return m_buffer [m_pos % simd_size]; }
+ scatter_iterator& operator++()
+ {
+ m_pos++;
+ if ( m_pos % simd_size == 0 )
+ {
+ if constexpr(modifiable == true ) m_store->gather(m_buffer, (m_pos-1) / simd_size);
+ m_buffer = m_store->scatter( m_pos );
+ }
+ return *this;
+ }
+ ~scatter_iterator()
+ {
+ if constexpr(modifiable == true)
+ {
+ if(m_store != nullptr && m_pos % simd_size != 0 ){
+ m_store->gather(m_buffer, m_pos/simd_size);
+ }
+ }
+ }
+ bool operator==( const scatter_iterator& rhs ) const { return m_pos == rhs.m_pos ; }
+ bool operator!=( const scatter_iterator& rhs ) const { return m_pos != rhs.m_pos ; }
+ friend int operator-( const scatter_iterator& lhs, const scatter_iterator& rhs) { return lhs.pos() - rhs.pos() ; }
+ };
+ template<unsigned simd_size, bool modifiable = false, class store_type>
+ auto make_scatter_iterator( const unsigned& pos, store_type* store) {
+ return scatter_iterator<typename store_type::value_type, store_type, simd_size, modifiable>(pos, store) ; }
+}
diff --git a/AmpGen/simd/utils.h b/AmpGen/simd/utils.h
new file mode 100644
index 00000000000..12c0ecf6c51
--- /dev/null
+++ b/AmpGen/simd/utils.h
@@ -0,0 +1,112 @@
+#ifndef AMPGEN_SIMD_UTILS_H
+#define AMPGEN_SIMD_UTILS_H
+
+#include <array>
+#include <complex>
+
+#if ENABLE_AVX512
+ #include "AmpGen/simd/avx512d_types.h"
+#elif ENABLE_AVX2d
+ #include "AmpGen/simd/avx2d_types.h"
+#elif ENABLE_AVX2f
+ #include "AmpGen/simd/avx2f_types.h"
+#endif
+
+
+
+namespace AmpGen {
+#if ENABLE_AVX512
+ namespace AVX = AVX512d;
+#elif ENABLE_AVX2d
+ namespace AVX = AVX2d;
+#elif ENABLE_AVX2f
+ namespace AVX = AVX2f;
+#endif
+
+#if ENABLE_AVX
+ using float_v = AVX::real_v;
+ using complex_v = AVX::complex_v;
+#else
+ using float_v = double;
+ using complex_v = std::complex<double>;
+#endif
+
+ namespace utils {
+
+ template <class T> struct is_vector_type : std::false_type {};
+ template <class T> struct size { static constexpr unsigned value = 1; } ;
+#if ENABLE_AVX
+ template <> struct is_vector_type <AVX::complex_v> : std::true_type {};
+ template <> struct is_vector_type <AVX::real_v > : std::true_type {};
+ template <> struct size <AVX::complex_v>{ static constexpr unsigned value = AVX::complex_v::size; };
+ template <> struct size <AVX::real_v> { static constexpr unsigned value = AVX::complex_v::size; };
+#endif
+ template <class simd_type, class container_type, class functor_type> simd_type gather(
+ const container_type& container, const functor_type& functor, unsigned offset=0, typename simd_type::scalar_type df =0.)
+ {
+ std::array<typename simd_type::scalar_type, simd_type::size> rv;
+ if( df == 0. )
+ for( unsigned k = 0 ; k != simd_type::size; ++k ) rv[k] = offset + k < container.size() ? functor(container[offset+k]) : functor(container[container.size()-1]);
+ else
+ for( unsigned k = 0 ; k != simd_type::size; ++k ) rv[k] = offset + k < container.size() ? functor(container[offset+k]) : df;
+ return simd_type( rv.data() );
+ }
+
+ template <class simd_type> size_t aligned_size( const size_t& unaligned_size ) {
+ return size<simd_type>::value * unsigned ( 1 + (unaligned_size -1 ) / size<simd_type>::value );
+ }
+ template <class simd_type> auto sum_elements( const simd_type& obj )
+ {
+ if constexpr ( is_vector_type<simd_type>::value )
+ {
+ auto arr = obj.to_array();
+ auto rt = arr[0];
+ for( unsigned i = 1 ; i != size<simd_type>::value; ++i ) rt = rt + arr[i];
+ return rt;
+ }
+ else return obj;
+ }
+ template <class simd_type, class value_type> bool all_of( const simd_type& obj, const value_type& v )
+ {
+ if constexpr( size<simd_type>::value == 1 ) return obj == v;
+ if constexpr( size<simd_type>::value == 4 ) return _mm256_movemask_pd( obj == v ) == 0xF;
+ if constexpr( size<simd_type>::value == 8 ) return _mm256_movemask_ps( obj == v ) == 0xFF;
+ return false;
+ }
+ template <class simd_type> bool all_of( const simd_type& obj)
+ {
+ if constexpr( ! is_vector_type<simd_type>::value ) return obj;
+ else return _mm256_movemask_pd( obj ) == 0xF;
+ }
+ template <unsigned p=0, class vtype> auto get( vtype v )
+ {
+ if constexpr ( is_vector_type<vtype>::value ) return v.at(p);
+ if constexpr ( ! is_vector_type<vtype>::value ) return v;
+ }
+ template < class vtype> auto at( vtype v, const unsigned p=0 )
+ {
+ if constexpr ( is_vector_type<vtype>::value ) return v.at(p);
+ if constexpr ( ! is_vector_type<vtype>::value ) return v;
+ }
+ template <class ctype> auto norm( const ctype& v )
+ {
+ #if ENABLE_AVX
+ if constexpr( is_vector_type<ctype>::value ) return AVX::norm(v);
+ #endif
+ if constexpr( ! is_vector_type<ctype>::value ) return std::norm(v);
+ }
+ template <class type, class store_type> void store( store_type* container, const type& v)
+ {
+ if constexpr( is_vector_type<type>::value )
+ {
+ auto arr = v.to_array();
+ for( unsigned k = 0 ; k != utils::size<type>::value; ++k ) container[k] = arr[k];
+ }
+ else {
+ *container = v;
+ }
+ }
+ }
+}
+
+#endif
diff --git a/AmpGenConfig.cmake.in b/AmpGenConfig.cmake.in
new file mode 100644
index 00000000000..01d34c5eeec
--- /dev/null
+++ b/AmpGenConfig.cmake.in
@@ -0,0 +1,18 @@
+# - Config file for the AmpGen package
+# It defines the following variables
+# AMPGEN_INCLUDE_DIRS - include directories for AmpGen
+# AMPGEN_LIBRARIES - libraries to link against
+# AMPGEN_EXECUTABLE - the bar executable
+
+# Compute paths
+get_filename_component(AMPGEN_CMAKE_DIR "${CMAKE_CURRENT_LIST_FILE}" PATH)
+set(AMPGEN_INCLUDE_DIRS "@PROJECT_SOURCE_DIR@")
+set(USE_OPENMP "@USE_OPENMP@")
+# Our library dependencies (contains definitions for IMPORTED targets)
+if(NOT TARGET AmpGen AND NOT AmpGen_BINARY_DIR)
+ include("@CMAKE_BINARY_DIR@/AmpGenTargets.cmake")
+endif()
+
+# These are IMPORTED targets created by FooBarTargets.cmake
+set(AMPGEN_LIBRARIES AmpGen)
+
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 63017dab540..1cea6e70ded 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -2,33 +2,281 @@
# Package: AmpGen
################################################################################
-# Support standalone build
-if(COMMAND gaudi_subdir)
- gaudi_subdir(AmpGen v1r1)
-
- find_package(ROOT COMPONENTS RIO Hist Matrix Graf Minuit2 Tree MathMore MathCore Physics)
- find_package(TBB REQUIRED)
- find_package(GSL REQUIRED)
- include_directories(${CMAKE_CURRENT_SOURCE_DIR})
-
- set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp -Wno-unused-parameter -ldl")
- set(AmpGen_VERSION_MAJOR "1")
- set(AmpGen_VERSION_MINOR "1")
- set(AMPGEN_CXX ${CMAKE_CXX_COMPILER} CACHE FILEPATH "This should be the path to compiler (use which c++ for macOS)" )
- configure_file ("${CMAKE_CURRENT_SOURCE_DIR}/AmpGen/Version.h.in" "${CMAKE_CURRENT_SOURCE_DIR}/AmpGen/Version.h")
- gaudi_add_library(AmpGen
- src/*.cpp
- src/Lineshapes/*.cpp
- NO_PUBLIC_HEADERS
- INCLUDE_DIRS ROOT
- LINK_LIBRARIES ROOT TBB GSL)
- target_compile_definitions(AmpGen PUBLIC "AMPGEN_CXX=\"${AMPGEN_CXX}\"")
- foreach(app Generator Fitter ConvertToSourceCode)
- gaudi_add_executable(${app} apps/${app}.cpp
- LINK_LIBRARIES AmpGen)
- endforeach()
+cmake_minimum_required(VERSION 3.9...3.15)
+
+if(${CMAKE_VERSION} VERSION_LESS 3.12)
+ cmake_policy(VERSION ${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION})
+endif()
+
+project(AmpGen LANGUAGES CXX VERSION 2.1)
+
+set(AMPGEN_CXX ${CMAKE_CXX_COMPILER} CACHE FILEPATH "This should be the path to compiler (use which c++ for macOS)" )
+
+file(TO_CMAKE_PATH "${PROJECT_BINARY_DIR}/CMakeLists.txt" LOC_PATH)
+if(EXISTS "${LOC_PATH}")
+ message(FATAL_ERROR "You cannot build in a source directory (or any directory with a CMakeLists.txt file). Please make a build subdirectory. Feel free to remove CMakeCache.txt and CMakeFiles.")
+endif()
+
+file(GLOB_RECURSE AMPGEN_SRC src/*)
+file(GLOB_RECURSE AMPGEN_HDR AmpGen/*)
+
+set(CMAKE_CXX_STANDARD "17" CACHE STRING "CMAKE_CXX_STANDARD")
+set(USE_SIMD "AVX2d" CACHE STRING "USE_SIMD") # AVX instruction set + precision to use
+set(USE_OPENMP TRUE CACHE BOOL "USE_OPENMP") # flag to use openmp for threading
+set(USE_MVEC TRUE CACHE BOOL "USE_MVEC") # flag to use vector math library mvec
+set(ENABLE_FITTING TRUE CACHE BOOL "ENABLE_FITTING") # flag to enable fitting (requires Minuit2)
+set(ENABLE_TESTS TRUE CACHE BOOL "ENABLE_TESTS") # flag to build unit tests
+set(BUILTIN_GSL TRUE CACHE BOOL "BUILTIN_GSL") # flag to use ROOT's builtin GSL
+set(ENABLE_INSTALL TRUE CACHE BOOL "ENABLE_INSTALL") # flag to enable installs (switched off to make Travis happier)
+set(CMAKE_CXX_EXTENSIONS OFF)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
+set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin")
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_BINARY_DIR}/bin")
+set(CMAKE_RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_BINARY_DIR}/bin")
+set(CMAKE_TEST_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin/test")
+
+include(CMakeDependentOption)
+include(CMakePrintHelpers)
+include(GNUInstallDirs)
+
+option(AMPGEN_DEBUG "AmpGen Debug printout")
+option(AMPGEN_TRACE "AmpGen Trace printout")
+
+configure_file ("${PROJECT_SOURCE_DIR}/AmpGen/Version.h.in" "${CMAKE_BINARY_DIR}/AmpGenVersion.h")
+
+add_library(${PROJECT_NAME} SHARED ${AMPGEN_SRC} ${AMPGEN_HDR})
+add_library(${PROJECT_NAME}::${PROJECT_NAME} ALIAS ${PROJECT_NAME})
+
+if(NOT DEFINED ROOT_LIBRARIES)
+ if(DEFINED ENV{ROOTSYS})
+ list(APPEND CMAKE_MODULE_PATH "$ENV{ROOTSYS}/etc/cmake/")
+ endif()
+ find_package(ROOT COMPONENTS Matrix MathMore MathCore Gpad Tree Graf)
+else()
+ string( REPLACE ":" " " ROOT_LIBRARIES ${ROOT_LIBRARIES})
+ separate_arguments(ROOT_LIBRARIES)
+endif()
+
+if( NOT BUILTIN_GSL OR DEFINED GSL_LIBRARIES )
+ if( NOT DEFINED GSL_LIBRARIES )
+ find_package(GSL)
+ else()
+ string( REPLACE ":" " " GSL_LIBRARIES ${GSL_LIBRARIES})
+ separate_arguments(GSL_LIBRARIES)
+ endif()
+endif()
+
+if( USE_OPENMP )
+ find_package(OpenMP)
+endif()
+
+# Default build type from the Kitware Blog
+set(default_build_type "Release")
+if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
+ message(STATUS "Setting build type to '${default_build_type}' as none was specified.")
+ set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE
+ STRING "Choose the type of build." FORCE)
+ # Set the possible values of build type for cmake-gui
+ set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS
+ "Debug" "Release" "MinSizeRel" "RelWithDebInfo")
+endif()
+
+target_include_directories(AmpGen PUBLIC $<BUILD_INTERFACE:${${PROJECT_NAME}_SOURCE_DIR}> $<BUILD_INTERFACE:${CMAKE_BINARY_DIR}> )
+
+target_include_directories(AmpGen PUBLIC ${ROOT_INCLUDE_DIRS} )
+
+target_link_libraries(AmpGen PUBLIC -lm "${ROOT_LIBRARIES}" ${CMAKE_DL_LIBS} "${GSL_LIBRARIES}" )
+
+find_library(libmvec mvec)
+
+if ( USE_MVEC AND libmvec )
+ message( STATUS "Using libmvec for vectorised math operations")
+ target_link_libraries(AmpGen PUBLIC mvec)
+ target_compile_definitions(AmpGen PUBLIC "USE_MVEC=1")
+else()
+ message( STATUS "Warning: libmvec not found, with use scalar math where necessary.")
+ target_compile_definitions(AmpGen PUBLIC "USE_MVEC=0")
+endif()
+
+if( ENABLE_FITTING )
+ if( ( NOT TARGET ROOT::Minuit2 AND NOT TARGET Minuit2 ) OR "${extern_minuit2}" )
+ message( STATUS "Use external Minuit2")
+ add_subdirectory("extern/Minuit2")
+ set_target_properties(Minuit2 PROPERTIES FOLDER extern)
+ target_compile_options(Minuit2 PUBLIC -fPIC -Wno-suggest-override)
+ set_target_properties(Minuit2Math PROPERTIES FOLDER extern)
+ add_library(ROOT::Minuit2 ALIAS Minuit2)
+ target_include_directories( AmpGen PUBLIC "${CMAKE_SOURCE_DIR}/extern/Minuit2/inc/")
+ else()
+ message( STATUS "Use ROOT::Minuit2")
+ endif()
+ if ( TARGET Minuit2 AND NOT TARGET ROOT::Minuit2 )
+ find_package( ROOT CONFIG REQUIRED COMPONENTS Minuit2)
+ add_library(ROOT::Minuit2 ALIAS Minuit2)
+ endif()
+ target_link_libraries(AmpGen PUBLIC ROOT::Minuit2 )
+else()
+ message(STATUS "Disable fitting")
+endif()
+
+
+if( USE_OPENMP )
+ target_compile_definitions(AmpGen PUBLIC "USE_OPENMP=1")
+ if(OpenMP_FOUND OR OpenMP_CXX_FOUND)
+ if(NOT TARGET OpenMP::OpenMP_CXX)
+ add_library(OpenMP::OpenMP_CXX IMPORTED INTERFACE)
+ set_property(TARGET OpenMP::OpenMP_CXX PROPERTY INTERFACE_COMPILE_OPTIONS ${OpenMP_CXX_FLAGS})
+ set_property(TARGET OpenMP::OpenMP_CXX PROPERTY INTERFACE_LINK_LIBRARIES ${OpenMP_CXX_FLAGS})
+ if(CMAKE_VERSION VERSION_LESS 3.4)
+ set_property(TARGET OpenMP::OpenMP_CXX APPEND PROPERTY INTERFACE_LINK_LIBRARIES -pthread)
+ else()
+ find_package(Threads REQUIRED)
+ set_property(TARGET OpenMP::OpenMP_CXX APPEND PROPERTY INTERFACE_LINK_LIBRARIES Threads::Threads)
+ endif()
+ endif()
+ target_link_libraries(AmpGen PUBLIC OpenMP::OpenMP_CXX)
+ else()
+ message(STATUS "OpenMP not found for CXX, you might have forgotten lb-run ROOT bash or CXX=`which g++` in CERN stack")
+ endif()
+else()
+ target_compile_definitions(AmpGen PUBLIC "USE_OPENMP=0")
+endif()
+
+if( DEFINED TBB_LIBRARIES )
+ target_link_libraries(AmpGen PUBLIC ${TBB_LIBRARIES})
+endif()
+
+# Default to XROOTD only if on CMT system. Can be overridden with -DAMPGEN_XROOTD=ON
+if(DEFINED ENV{CMTCONFIG})
+ set(AMPGEN_XROOTD_DEFAULT ON)
+else()
+ set(AMPGEN_XROOTD_DEFAULT OFF)
+endif()
+
+cmake_dependent_option(AMPGEN_XROOTD "Turn on XROOTD discovery" ON "AMPGEN_XROOTD_DEFAULT" OFF)
+
+if(AMPGEN_XROOTD)
+ find_library(XROOTD_LIB NAMES libXrdCl.so
+ HINTS "/cvmfs/lhcb.cern.ch/lib/lcg/releases/LCG_89/xrootd/4.6.0/$ENV{CMTCONFIG}/lib64")
+ target_link_libraries(AmpGen PUBLIC ${XROOTD_LIB})
+endif()
+
+target_compile_definitions(AmpGen PRIVATE
+ "AMPGENROOT_CMAKE=\"${CMAKE_BINARY_DIR}/bin\""
+ "AMPGENROOT=\"${PROJECT_SOURCE_DIR}\""
+ "AMPGEN_CXX=\"${AMPGEN_CXX}\""
+ $<$<BOOL:${AMPGEN_DEBUG}>:DEBUGLEVEL=1>
+ $<$<BOOL:${AMPGEN_TRACE}>:TRACELEVEL=1>)
+
+
+target_compile_options(AmpGen
+ INTERFACE
+ -Wall -Wextra -Wpedantic -g3
+ -Wno-unused-parameter
+ -Wno-unknown-pragmas
+ $<$<CONFIG:Release>:-O3>)
+
+if ( ${USE_SIMD} MATCHES "AVX2d" )
+ message(STATUS "Enabling AVX2 [double precision]")
+ target_compile_definitions(AmpGen PUBLIC "ENABLE_AVX=1" "ENABLE_AVX2d=1")
+ target_compile_options(AmpGen PUBLIC -march=native -ftree-vectorize -mavx2 -ffast-math -DHAVE_AVX2_INSTRUCTIONS)
+elseif ( ${USE_SIMD} MATCHES "AVX2f" )
+ message(STATUS "Enabling AVX2 [single precision]")
+ target_compile_definitions(AmpGen PUBLIC "ENABLE_AVX=1" "ENABLE_AVX2f=1")
+ target_compile_options(AmpGen PUBLIC -march=native -ftree-vectorize -mavx2 -ffast-math -DHAVE_AVX2_INSTRUCTIONS)
+elseif ( ${USE_SIMD} MATCHES "AVX512d" )
+ message(STATUS "Enabling AVX2 [double precision]")
+ target_compile_definitions(AmpGen PUBLIC "ENABLE_AVX=1" "ENABLE_AVX512=1")
+ target_compile_options(AmpGen PUBLIC -march=native -ftree-vectorize -mavx512f -ffast-math -DHAVE_AVX512_INSTRUCTIONS)
+else()
+ target_compile_definitions(AmpGen PUBLIC "ENABLE_AVX=0")
+ target_compile_options(AmpGen PUBLIC -march=x86-64)
+ message(STATUS "SIMD disabled, resorting to scalar build : ${USE_SIMD}")
+endif()
+
+if(${CMAKE_CXX_COMPILER_ID} MATCHES "AppleClang" OR
+ ${CMAKE_CXX_COMPILER_ID} MATCHES "Clang" )
+ target_compile_options(AmpGen PUBLIC -mfma)
+endif()
+
+if("${CMAKE_CXX_COMPILER_ID}" MATCHES "AppleClang" )
+ target_link_libraries(AmpGen PUBLIC stdc++ )
+ message(STATUS "Using OSX specific flags: -lm -lstdc++ -lSystem")
+ set (CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -lm -lstdc++ -lSystem")
+elseif ("${CMAKE_CXX_COMPILER_ID}" MATCHES "Clang")
+ target_link_libraries(AmpGen PUBLIC stdc++)
+ set (CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -lm -lstdc++")
else()
- cmake_minimum_required(VERSION 3.3)
- project(AmpGen LANGUAGES CXX VERSION 1.1)
- include(Standalone.cmake)
+ target_compile_options(AmpGen PUBLIC -Wno-suggest-override)
+endif()
+
+# build the applications and examples
+
+file(GLOB_RECURSE applications apps/*.cpp examples/*.cpp )
+foreach( file ${applications} )
+ get_filename_component( Executable ${file} NAME_WE )
+ add_executable(${Executable}.exe ${file})
+ target_compile_options(${Executable}.exe PUBLIC -g3 -Ofast)
+ target_link_libraries(${Executable}.exe PUBLIC AmpGen )
+ target_include_directories(${Executable}.exe PRIVATE ${ROOT_INCLUDE_DIRS})
+endforeach()
+
+# symlink the options files (so as there is the mass_width etc.) to the build directory, and also the release notes
+file(GLOB_RECURSE options_files options/*.*)
+execute_process(COMMAND ${CMAKE_COMMAND} -E make_directory "${CMAKE_BINARY_DIR}/bin")
+foreach(file ${options_files})
+ get_filename_component(OptionFile "${file}" NAME)
+ execute_process(COMMAND ${CMAKE_COMMAND} -E create_symlink "${file}" "${CMAKE_BINARY_DIR}/bin/${OptionFile}")
+endforeach()
+execute_process(COMMAND ${CMAKE_COMMAND} -E create_symlink "${CMAKE_SOURCE_DIR}/doc/release.notes" "${CMAKE_BINARY_DIR}/bin/release.notes")
+
+if( ENABLE_TESTS )
+ enable_testing()
+ set(Boost_NO_BOOST_CMAKE ON)
+ add_subdirectory(test)
+endif()
+
+
+# stuff related to export, install and version tagging
+
+include(CMakePackageConfigHelpers)
+write_basic_package_version_file(${CMAKE_CURRENT_BINARY_DIR}/AmpGenVersion.cmake VERSION ${PACKAGE_VERSION} COMPATIBILITY AnyNewerVersion)
+
+set(INCLUDE_INSTALL_DIR ${CMAKE_INSTALL_INCLUDEDIR})
+set(LIB_INSTALL_DIR ${CMAKE_INSTALL_LIBDIR})
+set(DATA_INSTALL_DIR ${CMAKE_INSTALL_DATADIR}/AmpGen)
+
+configure_package_config_file(AmpGenConfig.cmake.in
+ ${CMAKE_CURRENT_BINARY_DIR}/AmpGenConfig.cmake
+ INSTALL_DESTINATION ${CMAKE_INSTALL_DATADIR}/AmpGen/cmake
+ PATH_VARS INCLUDE_INSTALL_DIR LIB_INSTALL_DIR DATA_INSTALL_DIR
+ )
+
+if( ENABLE_INSTALL )
+ install( FILES ${CMAKE_CURRENT_BINARY_DIR}/AmpGenConfig.cmake
+ ${CMAKE_CURRENT_BINARY_DIR}/AmpGenVersion.cmake
+ DESTINATION ${CMAKE_INSTALL_DATADIR}/AmpGen/cmake)
+
+ install(
+ TARGETS ${PROJECT_NAME}
+ EXPORT AmpGenTargets
+ LIBRARY DESTINATION lib
+ PUBLIC_HEADER DESTINATION AmpGen
+ )
+
+ install(
+ TARGETS AmpGen.exe
+ DESTINATION bin
+ )
+
+ install(EXPORT "AmpGenTargets"
+ NAMESPACE "AmpGen::"
+ DESTINATION ${CMAKE_INSTALL_DATADIR}/AmpGen/cmake
+ )
+
+ export( TARGETS AmpGen NAMESPACE AmpGen:: FILE AmpGenTargets.cmake )
+ set(CMAKE_EXPORT_PACKAGE_REGISTRY ON)
+ export(PACKAGE AmpGen)
endif()
diff --git a/README.md b/README.md
index d6277d15b6e..75c5c8cee01 100644
--- a/README.md
+++ b/README.md
@@ -1,61 +1,66 @@
+
+
+[![Build Status][travis-badge]][travis-link]
+[![License: LGPL v3][license-badge]](./LICENSE)
+
<p align="center">
- <img src="https://gitlab.com/tevans1260/AmpGen/raw/master/doc/figs/logo.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/logo.png">
</p>
AmpGen is a library and set of applications for fitting and generating multi-body particle decays using the isobar model.
It developed out of the MINT project used in the fitting of three and four-body pseudoscalar decays by the CLEO-c and LHCb colloborations. The library can handle the fitting and generation of a wide variety of final states, including those involving fermions and photons, as well as polarised initial states.
-Source code for the evaluation of amplitudes is dynamically generated by a custom engine, JIT compiled and dynamically linked to the user programme at runtime, which results in high flexibility and performance.
+Source code for the evaluation of amplitudes is dynamically generated by a custom engine, JIT compiled and dynamically linked to the user programme at runtime, which results in high flexibility and performance.
-## Table of Contents
+## Table of Contents
* [Getting Started](#getting-started)
* [Applications](#applications)
* [Examples](#examples)
* [Advanced](#advanced)
-* [API documentation](https://tevans1260.gitlab.io/AmpGen/)
+* [API documentation](https://goofit.github.io/AmpGen/)
* [Acknowledgements](#acknowledgements)
## Getting started
-
### Installation
#### Getting the source
Clone with git
```
-git clone http://gitlab.com/tevans1260/AmpGen.git --recursive
+git clone http://github.com/GooFit/AmpGen/ --recursive
```
-There is at the time of writing only a master branch (FIXME)
+
##### Build requirements:
-* cmake >= 3.11.0
-* C++ compiler with CXX standard >= 14 (gcc >= 4.9.3, clang ~ 5).
+* cmake >= 3.11.0
+* C++ compiler with CXX standard >= 14 (gcc >= 4.9.3, clang ~ 5).
Defaults to Cxx17 (enable cxx14 with cmake flag `-DCMAKE_CXX_STANDARD=14` )
* ROOT >= 6 with MathMore
- To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dmathmore=ON` when configuring the installation of ROOT.
+ To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dmathmore=ON` when configuring the installation of ROOT.
##### Optional:
-* boost >= 1.67.0 for unit tests
-* xROOTd for network file access
+* boost >= 1.67.0 for unit tests
+* xROOTd for network file access
* OpenMP for multithreading
-* ROOT >= 6 with MathMore and Minuit2 enabled. The external version of Minuit2 provided as an external package of GooFit is used if the ROOT version is not unavailable.
- To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dminuit2=ON -Dmathmore=ON` when configuring the installation of ROOT.
+* ROOT >= 6 with MathMore and Minuit2 enabled. The external version of Minuit2 provided as an external package of GooFit is used if the ROOT version is not unavailable.
+ To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dminuit2=ON -Dmathmore=ON` when configuring the installation of ROOT.
#### Building
-The configuration of the AmpGen build is performed by cmake.
-It is recommended to use a build directory to keep the source tree clean.
+The configuration of the AmpGen build is performed by cmake.
+It is recommended to use a build directory to keep the source tree clean.
```shell
mkdir build
cd build
cmake ..
-make
+make
+make install #optional#
```
This will build the shared library, several standalone test applications, and a set of unit tests.
#### Usage with ROOT
-The library can be used interactively in conjunction with the ROOT C++ interpreter by adding the following lines
-to the users root login script
+The library can be used interactively in conjunction with the ROOT C++ interpreter by adding the following lines
+to the users root login script
-```
+```c++
gSystem->Load("path_to_ampgen/build/lib/libAmpGen.so");
gROOT->ProcessLine(".include path_to_ampgen");
```
@@ -64,159 +69,245 @@ You can also build AmpGen with LLVM. The only change you might want when using A
is to specifically specify the location of the build tool for AmpGen's JIT:
```shell
--DAMPGEN_CXX=$(which c++)
+-DAMPGEN_CXX=\$(which c++)
```
-##### CentOS7
+##### LXPLUS
-In order to build stand-alone on CentOS7, you will need a valid development environment; the following line will work:
+A valid development environment is required to build the library on LXPLUS and similar. The easiest way to provide this is via cvmfs views where available, as this provides the necessary versions of gcc in addition to the ROOT libraries in a coherent manner, which can be used as
-```shell
-lb-run ROOT $SHELL
+````
+source /cvmfs/sft.cern.ch/lcg/views/setupViews.sh LCG_94python3 x86_64-centos7-gcc8-opt
+````
+
+The LCG versions and binary tag may need to be updated over time.
+
+Several examples of usages of the library are included in apps and examples directories and are built alongside the library. All standalone programs can accept both options files and command line arguments. Also supported is the `--help` option to print instructions for key arguments to the program.
+
+#### Using SIMD instructions.
+
+AmpGen (v > 2.0) can be setup to generate vectorised code for faster evaluation of amplitudes / computation of integrals on compatible hardware. Such extensions can be enabled by setting the providing the flag
+```
+-DUSE_SIMD=AVX2d
```
-Several examples of usages of the library are included in the apps directory and are
-built alongside the library.
-All standalone programs can accept both options files and command line arguments.
-They also support `--help` to print help for key arguments to the program.
-This will also run the program, as arguments can be defined throughout each of the programs rather than all defined at the beginning.
+to cmake. This tells AmpGen that code should be generated using the AVX2 instruction set using double precision. Single precision is also supported, but not recommended for fitting. The support for SIMD instructions is often limited on batch systems, and therefore it is often useful to also have a build with these instruction switched off, which can be done using
-### Options files and decay descriptors
+```
+-DUSE_SIMD=0
+```
+
+### Options files and decay descriptors
-Options files will generally contain the description of one or more particle decays,
-as well as other settings such as input/output locations, global flags such as
-whether complex numbers should be interpreted as cartesian or polar, and other parameters
-such as the masses and widths of particles is these differ from those given in the PDG.
-
-A minimal example options file for the generator application could contain:
+Options files will generally contain the description of one or more particle decays, as well as other settings such as input/output locations, global flags such as whether complex numbers should be interpreted as cartesian or polar, and other parameters such as the masses and widths of particles is these differ from those given in the PDG.
+
+A minimal example options file for the generator application could contain:
```
EventType D0 K+ pi- pi- pi+
-# Real / Amplitude | Imaginary / Phase
+# Real / Amplitude | Imaginary / Phase
# Fix? Value Step | Fix? Value Step
D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 1 0 2 0 0
```
-The EventType specifies the initial and final states requested by the user.
-This gives the ordering of particles used in input data, in output code, and used in internal computations.
-This also defines how the amplitude source code must be interfaced with external packages, i.e. MC generators such as EvtGen.
+The EventType specifies the initial and final states requested by the user. This gives the ordering of particles used in input data, in output code, and used in internal computations. This also defines how the amplitude source code must be interfaced with external packages, i.e. MC generators such as EvtGen.
The decay products of a particle are enclosed within curly braces, for example
```
K*(892)0{K+,pi-}
```
-describes an excited vector kaon decaying into a charged kaon and pion.
-For more details about the API for describing particle decays, see [AmpGen::Particle](https://tevans1260.gitlab.io/AmpGen/de/dd7/class_amp_gen_1_1_particle.html).
-The other numbers on the lines that describe the decays parameterise the coupling to this channel,
-either in terms of real and imaginary parts or an amplitude and a phase.
-Each parameter is specified in terms of three numbers: the _fix_ flag, the initial value, and the step size.
-The possible options for the _fix_ flag are:
+describes an excited vector kaon decaying into a charged kaon and pion. For more details about the API for describing particle decays, see [AmpGen::Particle](https://goofit.github.io/AmpGen/de/dd7/class_amp_gen_1_1_particle.html) The other numbers on the lines that describe the decays parameterise the coupling to this channel,
+either in terms of real and imaginary parts or an amplitude and a phase. Each parameter is specified in terms of three numbers: the _fix_ flag, the initial value, and the step size.
+The possible options for the _fix_ flag are:
+
* Free (fix=0) and a step size of not 0.
* Fixed (fix=2, for historical reasons)
-* Compile-Time-Constant (fix=3) which indicates that the parameter should be treated as a (JIT) compile time constant, which in some cases allows for more aggressive optimisations to be performed.
+* Compile-Time-Constant (fix=3) which indicates that the parameter should be treated as a (JIT) compile time constant, which in some cases allows for more aggressive optimisations to be performed.
-These options can be used in the Generator application, which is described below.
+These options can be used in the AmpGen application, which is described below.
Decays can either be specified fully inline, as above, or split into multiple steps, which is useful for treating the so called _cascade_ decays, an example of which is shown below.
```
D0{K(1)(1270)+,pi-} 0 1 0.1 0 0 0.1
-
+Type
K(1)(1270)+{rho(770)0{pi+,pi-},K+} 2 1 0 2 0 0
K(1)(1270)+{K*(892)0{K+,pi-},pi+} 0 1 0.1 0 0 0.1
```
-The production/decay couplings of the K(1270) resonance are now defined in terms of the coupling to the rho(770),K+ channel,
-which can be useful in making comparisons between different production modes of a resonance.
-Additional care must be taken in such a case to not introduce redundant degrees of freedom.
+The production/decay couplings of the <img src="doc/figs/tex/fig0.svg" style="height:2ex;margin-bottom:+1ex" /> resonance are now defined in terms of the coupling to the <img src="doc/figs/tex/fig1.svg" style="height:2ex;margin-bottom:+1ex" /> channel, which can be useful in making comparisons between different production modes of a resonance. Additional care must be taken in such a case so as not to introduce redundant degrees of freedom.
-Configuration can be split over multiple files by the using _Import_ keyword, for example, to import the parameters for the isoscalar K-matrix, the line
+Configuration can be split over multiple files by the using _Import_ keyword, for example, to import the parameters for the parameters associated with the isoscalar K-matrix, the line
```
-Import $AMPGENROOT/options/kMatrix.opt
+Import \$AMPGENROOT/options/kMatrix.opt
```
-can be added to options file. Multiple user configuration files can also be specified by including multiple files on the command line.
+
+can be added to options file. Multiple user configuration files can also be specified by including multiple files on the command line.
+
+#### PDF Types
+
+AmpGen supports several different types of probability density functions (PDFs), which are detailed in this section.
+
+##### CoherentSum
+
+The most common type of PDF is the CoherentSum. In this case, the total amplitude is given by the sum of amplitudes, weighted by complex coefficients. At a position in the phase space <img src="doc/figs/tex/fig2.svg" height=2ex margin-bottom=1ex /> , the transition amplitude <img src="doc/figs/tex/fig3.svg" style="height:2ex;margin-bottom:+1ex" /> is given by:
+
+ <img src="doc/figs/tex/fig4.svg" style="height:2ex;margin-bottom:+1ex" />
+
+and the corresponding probability density is proportional to <img src="doc/figs/tex/fig5.svg" style="height:2ex;margin-bottom:+1ex" /> . The CoherentSum is the default amplitude in many cases, and is used to describe the decay of a single, (pseudo)scalar particle to two or more (pseudo)scalar decay products.
+
+##### PolarisedSum
+
+The initial and/or final state(s) may also carry spin, in which case the spin states must also be summed. The transition matrix can be written in the isobar model as
+
+ <img src="doc/figs/tex/fig6.svg" style="height:2ex;margin-bottom:+1ex" /> ,
+
+where <img src="doc/figs/tex/fig7.svg" style="height:2ex;margin-bottom:+1ex" /> and <img src="doc/figs/tex/fig8.svg" style="height:2ex;margin-bottom:+1ex" /> label the initial and final states, respectively. As these states are in principal observables, the indices related to spin must be summed incoherently. The probability density function in this case is therefore given by
+
+ <img src="doc/figs/tex/fig9.svg" style="height:2ex;margin-bottom:+1ex" /> ,
+
+where <img src="doc/figs/tex/fig10.svg" style="height:2ex;margin-bottom:+1ex" /> is the relevant density matrix for the initial state, which is given by 1 for a scalar initial state. For a spin- <img src="doc/figs/tex/fig11.svg" style="height:2ex;margin-bottom:+1ex" /> state, the density matrix can be parameterised in terms of a polarisation vector <img src="doc/figs/tex/fig12.svg" style="height:2ex;margin-bottom:+1ex" /> and the Pauli matrices <img src="doc/figs/tex/fig13.svg" style="height:2ex;margin-bottom:+1ex" /> , and is given by:
+
+ <img src="doc/figs/tex/fig14.svg" style="height:2ex;margin-bottom:+1ex" />
+
+For a spin-1 initial state, the density matrix is parameterised in terms of the Gell-Mann matrices, <img src="doc/figs/tex/fig15.svg" style="height:2ex;margin-bottom:+1ex" /> , as
+
+ <img src="doc/figs/tex/fig16.svg" style="height:2ex;margin-bottom:+1ex" /> ,
+
+where now the polarisation 'vector' <img src="doc/figs/tex/fig17.svg" style="height:2ex;margin-bottom:+1ex" /> has 8 components.
+
+##### IncoherentSum
+
+An alternative model is the IncoherentSum, which may be useful to describe the probability density of a background contribution that contains incoherent sources with several different resonances. Generally, such models are only useful for relatively small backgrounds in relatively pure samples, as in general background contributions cannot be described with such a simple parameterisation. In this case, the probability is given by an incoherent sum of amplitudes:
+
+ <img src="doc/figs/tex/fig18.svg" style="height:2ex;margin-bottom:+1ex" />
## Applications
-This section details the prebuilt command line applications that use the AmpGen library for some common functionality, such as generating Toy Monte Carlo samples
-and debugging amplitudes.
+
+This section details the prebuilt command line applications that use the AmpGen library for some common functionality, such as generating Toy Monte Carlo samples and debugging amplitudes.
### Table of contents
-* [Generator](#generator)
+* [AmpGen](#AmpGen)
* [Debugger](#debugger)
-* [ConvertToSourceCode](#converttosourcecode)
+* [LibDiff](#LibDiff)
+* [DataConverter](#DataConverter)
-### Generator
+### AmpGen
-The standalone generator for models can be used as
+The standalone generator (named AmpGen) is used as:
```shell
-Generator MyOpts.opt --nEvents=10000 --Output=output.root
+AmpGen.exe MyOpts.opt --nEvents=10000 --Output=output.root
```
-Which generates 10000 events of the model described in MyOpts.opt and saves them to output.root.
-The output should include a tree (DalitzEventList) of candidates with the full four-vectors, as well as one- and two-dimensional projections, an example of which is shown below:
+where MyOpts.opt contains the options described in the previous section that describe the decay the user wishes to generate, and the optional arguments `nEvents` and `Output` given the number of events requested and the output file, respectively. The full list of application specific arguments can be obtained by:
-
+```bash
+AmpGen.exe --help
+```
-In particular, the tree indicates the way in which data is by default loaded into the _Event_ / _EventList_ class.
+The output includes a tree (DalitzEventList) of candidates with the full four-vectors, as well as one- and two-dimensional projections, an example of which is shown below:
-### Debugger
+<p align="center">
+ <img src="doc/figs/k3pi_s01.svg" width=300 >
+</p>
-The debugger application is a tool for producing verbose information debugging for amplitudes and models. It is used on an options file as
-```
-./Debugger MyOpts.opt
+Several models for different <img src="doc/figs/tex/fig19.svg" style="height:2ex;margin-bottom:+1ex" /> decays published by the LHCb collaboration are included in the options directory, in addition to several other decay modes to demonstrate different features. These options often do not include EventTypes so as they can be included as part of a larger decay chain if required. For example, to generate <img src="doc/figs/tex/fig20.svg" style="height:2ex;margin-bottom:+1ex" /> toy <img src="doc/figs/tex/fig21.svg" style="height:2ex;margin-bottom:+1ex" /> decays, the type of the events requested must also be specified:
+
+```shell
+AmpGen.exe options/D02Kpipipi.opt --EventType "D0 K- pi+ pi+ pi-" --nEvents 1000000
```
-which calculates each amplitude at a randomly generated point in phase space, as well as calculating the total amplitude accounting for complex
-couplings. Also computed is the amplitude for the P conjugate event. A more useful application is the _verbose_ debugging mode which can be
-activated by
+
+The standalone generator can also be used to only produce the source code that evaluates the amplitude, to be used by other generators such as EvtGen. In this case, the PDF is automatically normalised such that <img src="doc/figs/tex/fig22.svg" style="height:2ex;margin-bottom:+1ex" /> . The code can be generated and compiled into a shared library as follows
+```shell
+AmpGen.exe MyOpts.opt --Output=MyModel.cpp --SourceOnly
+g++ -Ofast -shared -rdynamic --std=c++14 -fPIC MyModel.cpp -o MyModel.so
```
-./Debugger MyOpts.opt --CoherentSum::Debug
+Decays can also be specified entirely on the command line in order to quickly study the distributions of different decay modes. For example, to generate a sample of 10000 <img src="doc/figs/tex/fig23.svg" style="height:2ex;margin-bottom:+1ex" /> decays,
+
+```shell
+AmpGen.exe --Decay "Lambda(b)0{p+,K*(892)bar-{K-,pi0}}" --nEvents 10000 --Type PolarisedSum
```
-which produces a large number of intermediate steps in the calculation of each amplitude, which are added to the calculation using the
-ADD_DEBUG and ADD_DEBUG_TENSOR macros in the code generation. For example, in src/Lineshapes/BW.cpp.
-### ConvertToSourceCode
+The flag `Type` is used to specify that the initial and/or final states includes at least one particle carrying spin, and thus polarisation must be taken into account. The output is both the full event kinematics, as well as projections of the different invariant masses shown below:
+
+<p align="center">
+<div>
+<img src="doc/figs/lb2pKpi_s01.svg" width=300/>
+<img src="doc/figs/lb2pKpi_s02.svg" width=300 />
+</div>
+</p>
+
+#### Phase space generators
+
+Generating events consists of two phases. Firstly, the kinematics of candidates are generated according to some distribution, by default uniform in the phase space. The target distribution, <img src="doc/figs/tex/fig24.svg" style="height:2ex;margin-bottom:+1ex" /> , is then obtained using the accept-reject method. A candidate generated at position <img src="doc/figs/tex/fig25.svg" style="height:2ex;margin-bottom:+1ex" /> in the phase space is retained on the condition that
+
+ <img src="doc/figs/tex/fig26.svg" style="height:2ex;margin-bottom:+1ex" /> ,
+
+where <img src="doc/figs/tex/fig27.svg" style="height:2ex;margin-bottom:+1ex" /> is the largest possible value of <img src="doc/figs/tex/fig28.svg" style="height:2ex;margin-bottom:+1ex" /> , and <img src="doc/figs/tex/fig29.svg" style="height:2ex;margin-bottom:+1ex" /> is a random number uniformly drawn between 0 and 1.
+
+ The generation can be made more efficient by making the first step produce candidates that are distributed more closely to the full distribution than the uniform phase space. In particular, this is relevant for producing very narrow structures such as the <img src="doc/figs/tex/fig30.svg" style="height:2ex;margin-bottom:+1ex" /> resonance efficiently. To use this option, the flag `PhaseSpace` should be set to the value `TreePhaseSpace`. For example, to generate a sample of <img src="doc/figs/tex/fig31.svg" style="height:2ex;margin-bottom:+1ex" /> <img src="doc/figs/tex/fig32.svg" style="height:2ex;margin-bottom:+1ex" /> decays:
-This produces source code to evaluate the PDF, and normalises for use with other generators such as EvtGen, i.e. P(max) < 1. This can be used as
```shell
-./ConvertToSourceCode MyOpts.opt --Output=MyFile.cpp
+AmpGen.exe --Decay "Lambda(b)0{J/psi0{mu+,mu-},Lambda(1405)0{p+,pi-}}" --nEvents 1000000 --Type PolarisedSum --PhaseSpace TreePhaseSpace
```
-This can then be a compiled to a shared library using
-```shell
-g++ -Ofast -shared -rdynamic --std=c++14 -fPIC MyFile.cpp -o MyFile.so
+
+Two example projections are shown below, of the dimuon invariant mass with essentially no width, which would be virtually impossible to generate with a uniform distribution and the naive accept-reject method, and the combined mass of the dimuon with the proton from the <img src="doc/figs/tex/fig33.svg" style="height:2ex;margin-bottom:+1ex" /> decay:
+
+<p align="center">
+<div>
+<img src="doc/figs/lb2jspiL_s01.svg" width=300 />
+<img src="doc/figs/lb2jspiL_s012.svg" width=300 />
+</div>
+</p>
+
+### Debugger
+
+The debugger application is a tool for producing verbose information debugging for amplitudes and models. It is used on an options file as
+
```
+Debugger.exe MyOpts.opt
+```
+which calculates each amplitude at a randomly generated point in phase space, as well as calculating the total amplitude accounting for complex couplings.
+
+A more useful application is the _verbose_ debugging mode which can be activated by
+
+```
+Debugger.exe MyOpts.opt --CoherentSum::Debug
+```
+which produces a large number of intermediate steps in the calculation of each amplitude, which are added to the calculation using the ADD_DEBUG and ADD_DEBUG_TENSOR macros in the code generation. For example, in src/Lineshapes/BW.cpp.
+If the model is a PolarisedSum, i.e. handles spin in the initial/final state, the flag PolarisedSum::Debug should be used instead of CoherentSum::Debug.
+
+### LibDiff
+### DataConvertor
## Examples
### SignalOnlyFitter
-An example fitter is provided in _examples/SignalOnlyFitter.cpp_, which as the name suggests only has a single signal component in the fit.
-The free parameters of the fit are specified in the same way as the Generator,
-with the additional relevant slots being _DataSample_ which specifies the signal sample to fit,
-which is presumed to already have the selection applied, and _Branches_ which takes a list of branch names,
-and defaults to the format used by the Generator etc. More details can be found with
-```
-SignalOnlyFitter --help
+An example fitter is provided in _examples/SignalOnlyFitter.cpp_, which as the name suggests only has a single signal component in the fit. The free parameters of the fit are specified in the same way as the Generator, with the additional relevant slots being _DataSample_ which specifies the signal sample to fit, which is presumed to already have the selection applied, and _Branches_ which takes a list of branch names, and defaults to the format used by the Generator. More details can be found with
+```shell
+SignalOnlyFitter.exe --help
```
For example, the fitter can be used to fit a toy MC sample generated by the generator by running:
-```
-Generator MyOpts.opt --nEvents 100000
-SignalOnlyFitter MyOpts.opt --DataSample Generate_Output.root
+```shell
+AmpGen.exe MyOpts.opt --nEvents 100000
+SignalOnlyFitter.exe MyOpts.opt --DataSample Generate_Output.root
```
-## Advanced
+## Advanced
-This section contains miscellaneous details on more advanced functionality, including using python bindings and alternative parameterisation of the spin factors.
+This section contains miscellaneous details on more advanced functionality, including using python bindings and alternative parameterisations of the spin factors.
### Table of contents
* [Python Bindings](#python-bindings)
* [Particle Properties and Lineshape parameters](#particle-properties-and-lineshape-parameters)
* [Fit parameters and expressions](#fit-parameters-and-expressions)
* [Spin Formalisms](#spin-formalisms)
-
+* [Quasiparticles](#quasiparticles)
### Python Bindings
Models built into a shared library can be used in python using the following flags into ConvertToSourceCode:
-```shell
-./ConvertToSourceCode MyOpts.opt --Output=MyFile.cpp --OutputEvents=events.csv --IncludePythonBindings
+```shell
+./AmpGen.exe MyOpts.opt --Output=MyFile.cpp --SourceOnly --OutputEvents=events.csv --IncludePythonBindings
```
-where normalisation events are also output for testing purposes in events.csv.
+where normalisation events are also output for testing purposes in events.csv.
This can then be used with the python bindings in ampgen.py:
```python
from ampgen import FixedLib
@@ -232,51 +323,46 @@ fcn2 = data.apply(model.FCN, axis=1)
```
### Particle Properties and Lineshape parameters
-The particles available and their default properties can be found in *options/mass\_width.csv* using the MC format of the 2008 PDG.
-Additional pseudoparticles, such as nonresonant states and terms for use in conjunction with K-matrices are defined by *options/MintDalitzSpecialParticles.csv*.
-Any additional user defined particles should be added here.
-For the default lineshape (the relavistic Breit-Wigner or BW), there are three parameters: The mass, the width and the Blatt-Weisskopf radius.
-These default to their PDG values, but can be overridden in the options file with parameters: *particleName*\_mass, *particleName*\_width, *particleName*\_radius.
-So if the K(1270)+ mass was allowed to vary, the line:
+The particles available and their default properties can be found in *options/mass\_width.csv* using the MC format of the 2008 PDG. Additional pseudoparticles, such as nonresonant states and terms for use in conjunction with K-matrices are defined by *options/MintDalitzSpecialParticles.csv*. Any additional user defined particles should be added here. For the default lineshape (the relavistic Breit-Wigner or BW), there are three parameters: The mass, the width and the Blatt-Weisskopf radius. These default to their PDG values, but can be overridden in the options file with parameters: *particleName*\_mass, *particleName*\_width, *particleName*\_radius. To vary the mass of the <img src="doc/figs/tex/fig34.svg" style="height:2ex;margin-bottom:+1ex" /> meson, the line:
```
-K(1270)+_mass 0 1.270 0.01
+K(1)(1270)+_mass 0 1.270 0.01
```
-could be added to the user configuration.
-Other lineshapes may define other parameters, for example channel couplings or pole masses in the case of the K-matrices, which can be set or varied in a similar manner.
+could be added to the user configuration.
+Other lineshapes may define other parameters, for example channel couplings or pole masses in the case of the K-matrices, can be set or varied in a similar manner.
### Fit parameters and expressions
-Parameters can either be specified by three parameters, in the case of a scalar parameter such as a mass or a width, or with six parameters in the case of a complex parameter such as a coupling.
-Upper and lower bounds on parameters can also be set by specifying a parameter with five parameters or ten parameters for a scalar or complex, respectively.
-For example, if we wished to vary the K(1)(1270)+ mass in the above example, but restricting the allowed values in the range \[0.0,2.0\] GeV:
+Parameters can either be specified by three parameters, in the case of a scalar parameter such as a mass or a width, or with six parameters in the case of a complex parameter such as a coupling.
+Upper and lower bounds on parameters can also be set by specifying a parameter with five parameters or ten parameters for a scalar or complex, respectively.
+For example, if we wished to vary the mass of the <img src="doc/figs/tex/fig35.svg" style="height:2ex;margin-bottom:+1ex" /> meson in the above example, but restricting the allowed values in the range <img src="doc/figs/tex/fig36.svg" style="height:2ex;margin-bottom:+1ex" /> :
```
K(1)(1270)+_mass 0 1.27 0.01 0.0 2.0
```
-(Scalar) parameters can also be related to each other via simple expressions, although the implementation of this is rather unreliable so should be used with caution.
-Suppose for example we have K(1)(1270)+ and K(1)(1270)bar- in the same fit (for example, for D-\>KKpipi)
-The properties of one can be allowed to vary, for example the K(1)(1270)+, and the other fixed to the same value, using:
+Parameters can also be related to each other via expressions,
+Suppose for example we have <img src="doc/figs/tex/fig37.svg" style="height:2ex;margin-bottom:+1ex" /> and <img src="doc/figs/tex/fig38.svg" style="height:2ex;margin-bottom:+1ex" /> in the same fit (for example, in <img src="doc/figs/tex/fig39.svg" style="height:2ex;margin-bottom:+1ex" /> )
+The properties of one can be allowed to vary, for example the <img src="doc/figs/tex/fig40.svg" style="height:2ex;margin-bottom:+1ex" /> , and the other fixed to the same value, using:
```
-K(1)(1270)+_mass 0 1.27 0.01 0.0 2.0
-K(1)(1270)bar-_mass = K(1)(1270)+_mass
+K(1)(1270)+_mass 0 1.27 0.01 0.0 2.0
+K(1)(1270)bar-_mass = K(1)(1270)+_mass
```
-Due to the abundance of **odd** glyphs such as brackets and +/- in parameter names, parameter expressions are white space delimited and somewhat sensitive to bracket usage.
+Parameter expressions are whitespace delimited due to the abundance of **odd** glyphs such as brackets and +/- in the names of parameters.
+Expressions support the binary operations <img src="doc/figs/tex/fig41.svg" style="height:2ex;margin-bottom:+1ex" /> , as well as common unary functions such as sqrt, trigonometric functions etc.
### Spin Formalisms
-AmpGen implements both the covariant tensor (or Rarita-Schwinger) and canonical helicity formalism for describing the angular momentum component of decays.
-Both formalisms refer to states of well-defined orbital angular momentum, as opposed to the helicity states, as the states with well-defined orbital angular momentum have a straightforward parity and momentum dependences.
-The default formalism is the covariant tensor formalism, but this can be switched to the canonical formalism changing the flag
+AmpGen implements both the covariant tensor (or Rarita-Schwinger) and canonical helicity formalism for describing the angular momentum component of decays.
+Both formalisms refer to states of well-defined orbital angular momentum, as opposed to the helicity states, as the states with well-defined orbital angular momentum have a straightforward parity and momentum dependences.
+The default formalism is the covariant tensor formalism, but this can be switched to the canonical formalism changing the flag
```
-Particle::SpinFormalism Canonical ## default = Covariant
+Particle::SpinFormalism Canonical
```
-in the options file.
-The spin formalism for an individual decay chain can be specified by changing the attribute SpinFormalism in the decay descriptor. For example,
+in the options file.
+The spin formalism for an individual decay chain can be specified by changing the attribute SpinFormalism in the decay descriptor. For example,
```
D0[SpinFormalism=Canonical]{K*(892)bar0,rho(770)0}
```
-selects the S-wave of the K*, rho system. The user can also specify systems of helicity couplings in the canonical formalism, using the attribute _helAmp_.
-For example, suppose the transversity amplitudes were used rather than the canonical, then the user can specify
+selects the S-wave of the <img src="doc/figs/tex/fig42.svg" style="height:2ex;margin-bottom:+1ex" /> system. The user can also specify systems of helicity couplings in the canonical formalism, using the attribute _helAmp_. For example, suppose the transversity amplitudes were used rather than the canonical, then the user can specify
```
D0[SpinFormalism=Canonical;helAmp=Long]{K*(892)bar0,rho(770)0}
D0[SpinFormalism=Canonical;helAmp=t1]{K*(892)bar0,rho(770)0}
@@ -298,17 +384,42 @@ t2 {
-0.707106781 -1 -1
}
```
-That is specified as sets of three numbers, firstly the coupling, and then the two particle helicities. So in this example, the longitudinal amplitude is the 00 helicity state, while the two transverse amplitudes and the sum and difference of the two other helicity amplitudes.
+That is specified as sets of three numbers, firstly the coupling, and then the two particle helicities. So in this example, the longitudinal amplitude is the <img src="doc/figs/tex/fig43.svg" style="height:2ex;margin-bottom:+1ex" /> helicity state, while the two transverse amplitudes and the sum and difference of the two other helicity amplitudes.
+
+### Quasiparticles
+Quasiparticles are fictional decaying particles that can be implemented in the decay chain for a variety of different purposes. The original use case was to group some amplitudes with the same quantum numbers with couplings that want to be factorised.
+For example, for the <img src="doc/figs/tex/fig44.svg" style="height:2ex;margin-bottom:+1ex" /> <img src="doc/figs/tex/fig45.svg" style="height:2ex;margin-bottom:+1ex" /> -wave, the K matrix description may be used. The coupling from the initial state may be written as
+
+```
+D0{K0S0,NonResS0} ...
+```
+The quasiparticle _NonResS0_ can then be decayed to the final state via the K matrix lineshape(s)
+```
+NonResS0[kMatrix.pole.0]{pi+,pi-} ...
+NonResS0[kMatrix.pole.1]{pi+,pi-} ...
+...
+```
+where each of the .X is one of the terms of the (pole) production vector.
+In this example, an equivalent formulation would be
+```
+D0{K0S0,NonResS0[kMatrix.pole.0]{pi+,pi-}} ...
+D0{K0S0,NonResS0[kMatrix.pole.1]{pi+,pi-}} ...
+...
+```
## Acknowledgements
The development of this software has been supported by the National Science Foundation under grant PHY-1414736 and through a subcontract under Cooperative Agreement OAC-1836650. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the developers and do not necessarily reflect the views of the National Science Foundation.
<p align="center">
<div>
- <img src="https://gitlab.com/tevans1260/AmpGen/raw/master/doc/figs/UC_ID_PrimaryBlackRed.png">
- <img src="https://gitlab.com/tevans1260/AmpGen/raw/master/doc/figs/Iris-hep-3-regular-complete.png">
- <img src="https://gitlab.com/tevans1260/AmpGen/raw/master/doc/figs/NSF_4-Color_bitmap_Logo.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/UC_ID_PrimaryBlackRed.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/Iris-hep-3-regular-complete.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/NSF_4-Color_bitmap_Logo.png">
</div>
</p>
+[travis-badge]: https://travis-ci.org/GooFit/AmpGen.svg?branch=master
+[license-badge]: https://img.shields.io/badge/License-GPL%20v2-blue.svg
+[travis-link]: https://travis-ci.org/GooFit/AmpGen
+
diff --git a/README.tex.md b/README.tex.md
new file mode 100644
index 00000000000..4ebda4aca94
--- /dev/null
+++ b/README.tex.md
@@ -0,0 +1,427 @@
+
+
+[![Build Status][travis-badge]][travis-link]
+[![License: LGPL v3][license-badge]](./LICENSE)
+
+<p align="center">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/logo.png">
+</p>
+AmpGen is a library and set of applications for fitting and generating multi-body particle decays using the isobar model.
+It developed out of the MINT project used in the fitting of three and four-body pseudoscalar decays by the CLEO-c and LHCb colloborations. The library can handle the fitting and generation of a wide variety of final states, including those involving fermions and photons, as well as polarised initial states.
+
+Source code for the evaluation of amplitudes is dynamically generated by a custom engine, JIT compiled and dynamically linked to the user programme at runtime, which results in high flexibility and performance.
+
+## Table of Contents
+* [Getting Started](#getting-started)
+* [Applications](#applications)
+* [Examples](#examples)
+* [Advanced](#advanced)
+* [API documentation](https://goofit.github.io/AmpGen/)
+* [Acknowledgements](#acknowledgements)
+
+## Getting started
+### Installation
+#### Getting the source
+Clone with git
+```
+git clone http://github.com/GooFit/AmpGen/ --recursive
+```
+
+
+##### Build requirements:
+* cmake >= 3.11.0
+* C++ compiler with CXX standard >= 14 (gcc >= 4.9.3, clang ~ 5).
+ Defaults to Cxx17 (enable cxx14 with cmake flag `-DCMAKE_CXX_STANDARD=14` )
+* ROOT >= 6 with MathMore
+ To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dmathmore=ON` when configuring the installation of ROOT.
+
+##### Optional:
+* boost >= 1.67.0 for unit tests
+* xROOTd for network file access
+* OpenMP for multithreading
+* ROOT >= 6 with MathMore and Minuit2 enabled. The external version of Minuit2 provided as an external package of GooFit is used if the ROOT version is not unavailable.
+ To (re)configure root with these options, use the additional command line options `-Dcxx14 -Dminuit2=ON -Dmathmore=ON` when configuring the installation of ROOT.
+
+#### Building
+The configuration of the AmpGen build is performed by cmake.
+It is recommended to use a build directory to keep the source tree clean.
+
+```shell
+mkdir build
+cd build
+cmake ..
+make
+make install #optional#
+```
+This will build the shared library, several standalone test applications, and a set of unit tests.
+
+#### Usage with ROOT
+
+The library can be used interactively in conjunction with the ROOT C++ interpreter by adding the following lines
+to the users root login script
+
+```c++
+ gSystem->Load("path_to_ampgen/build/lib/libAmpGen.so");
+ gROOT->ProcessLine(".include path_to_ampgen");
+```
+##### LLVM
+You can also build AmpGen with LLVM. The only change you might want when using Apple LLVM
+is to specifically specify the location of the build tool for AmpGen's JIT:
+
+```shell
+-DAMPGEN_CXX=\$(which c++)
+```
+
+##### LXPLUS
+
+A valid development environment is required to build the library on LXPLUS and similar. The easiest way to provide this is via cvmfs views where available, as this provides the necessary versions of gcc in addition to the ROOT libraries in a coherent manner, which can be used as
+
+````
+source /cvmfs/sft.cern.ch/lcg/views/setupViews.sh LCG_94python3 x86_64-centos7-gcc8-opt
+````
+
+The LCG versions and binary tag may need to be updated over time.
+
+Several examples of usages of the library are included in apps and examples directories and are built alongside the library. All standalone programs can accept both options files and command line arguments. Also supported is the `--help` option to print instructions for key arguments to the program.
+
+#### Using SIMD instructions.
+
+AmpGen (v > 2.0) can be setup to generate vectorised code for faster evaluation of amplitudes / computation of integrals on compatible hardware. Such extensions can be enabled by setting the providing the flag
+```
+-DUSE_SIMD=AVX2d
+```
+to cmake. This tells AmpGen that code should be generated using the AVX2 instruction set using double precision. Single precision is also supported, but not recommended for fitting. The support for SIMD instructions is often limited on batch systems, and therefore it is often useful to also have a build with these instruction switched off, which can be done using
+
+```
+-DUSE_SIMD=0
+```
+
+### Options files and decay descriptors
+
+Options files will generally contain the description of one or more particle decays, as well as other settings such as input/output locations, global flags such as whether complex numbers should be interpreted as cartesian or polar, and other parameters such as the masses and widths of particles is these differ from those given in the PDG.
+
+A minimal example options file for the generator application could contain:
+```
+EventType D0 K+ pi- pi- pi+
+# Real / Amplitude | Imaginary / Phase
+# Fix? Value Step | Fix? Value Step
+D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 1 0 2 0 0
+```
+The EventType specifies the initial and final states requested by the user. This gives the ordering of particles used in input data, in output code, and used in internal computations. This also defines how the amplitude source code must be interfaced with external packages, i.e. MC generators such as EvtGen.
+
+The decay products of a particle are enclosed within curly braces, for example
+```
+K*(892)0{K+,pi-}
+```
+describes an excited vector kaon decaying into a charged kaon and pion. For more details about the API for describing particle decays, see [AmpGen::Particle](https://goofit.github.io/AmpGen/de/dd7/class_amp_gen_1_1_particle.html) The other numbers on the lines that describe the decays parameterise the coupling to this channel,
+either in terms of real and imaginary parts or an amplitude and a phase. Each parameter is specified in terms of three numbers: the _fix_ flag, the initial value, and the step size.
+The possible options for the _fix_ flag are:
+
+* Free (fix=0) and a step size of not 0.
+* Fixed (fix=2, for historical reasons)
+* Compile-Time-Constant (fix=3) which indicates that the parameter should be treated as a (JIT) compile time constant, which in some cases allows for more aggressive optimisations to be performed.
+
+These options can be used in the AmpGen application, which is described below.
+
+Decays can either be specified fully inline, as above, or split into multiple steps, which is useful for treating the so called _cascade_ decays, an example of which is shown below.
+```
+D0{K(1)(1270)+,pi-} 0 1 0.1 0 0 0.1
+Type
+K(1)(1270)+{rho(770)0{pi+,pi-},K+} 2 1 0 2 0 0
+K(1)(1270)+{K*(892)0{K+,pi-},pi+} 0 1 0.1 0 0 0.1
+```
+The production/decay couplings of the $K_1(1270)^+$ resonance are now defined in terms of the coupling to the $\rho(770)^0 K^+$ channel, which can be useful in making comparisons between different production modes of a resonance. Additional care must be taken in such a case so as not to introduce redundant degrees of freedom.
+
+Configuration can be split over multiple files by the using _Import_ keyword, for example, to import the parameters for the parameters associated with the isoscalar K-matrix, the line
+```
+Import \$AMPGENROOT/options/kMatrix.opt
+```
+
+can be added to options file. Multiple user configuration files can also be specified by including multiple files on the command line.
+
+#### PDF Types
+
+AmpGen supports several different types of probability density functions (PDFs), which are detailed in this section.
+
+##### CoherentSum
+
+The most common type of PDF is the CoherentSum. In this case, the total amplitude is given by the sum of amplitudes, weighted by complex coefficients. At a position in the phase space $\mathbf{x}$, the transition amplitude $\mathcal{T}$ is given by:
+
+$\mathcal{T}(\mathbf{x}) = \sum_{k} g_k A_k (\mathbf{x})$
+
+and the corresponding probability density is proportional to $\mathcal{P}(\mathbf{x})\propto \left|\mathcal{T}(\mathbf{x})\right|^2$. The CoherentSum is the default amplitude in many cases, and is used to describe the decay of a single, (pseudo)scalar particle to two or more (pseudo)scalar decay products.
+
+##### PolarisedSum
+
+The initial and/or final state(s) may also carry spin, in which case the spin states must also be summed. The transition matrix can be written in the isobar model as
+
+$\mathcal{T}_{if} = \sum_k g_k \mathcal{T}^{k}_{if}(\mathbf{x})$,
+
+where $i$ and $f$ label the initial and final states, respectively. As these states are in principal observables, the indices related to spin must be summed incoherently. The probability density function in this case is therefore given by
+
+$\mathcal{P}(\mathbf{x}) = \sum_{if} \hat{\rho}_{ij} T_{if}(\mathbf{x}) T^{*}_{jf}(\mathbf{x}) $,
+
+where $\hat{\rho}$ is the relevant density matrix for the initial state, which is given by 1 for a scalar initial state. For a spin-$\frac{1}{2}$ state, the density matrix can be parameterised in terms of a polarisation vector $p_i$ and the Pauli matrices $\sigma_i$, and is given by:
+
+$\hat{\rho} = I + \sigma_i p_i$
+
+For a spin-1 initial state, the density matrix is parameterised in terms of the Gell-Mann matrices, $\lambda_k$, as
+
+$\hat{\rho} = I + \lambda_k p_k$,
+
+where now the polarisation 'vector' $p_k$ has 8 components.
+
+##### IncoherentSum
+
+An alternative model is the IncoherentSum, which may be useful to describe the probability density of a background contribution that contains incoherent sources with several different resonances. Generally, such models are only useful for relatively small backgrounds in relatively pure samples, as in general background contributions cannot be described with such a simple parameterisation. In this case, the probability is given by an incoherent sum of amplitudes:
+
+$\mathcal{P}(\mathbf{x}) = \sum_k g_k^2 \left| A_k \right|^2 $
+
+## Applications
+
+This section details the prebuilt command line applications that use the AmpGen library for some common functionality, such as generating Toy Monte Carlo samples and debugging amplitudes.
+
+### Table of contents
+* [AmpGen](#AmpGen)
+* [Debugger](#debugger)
+* [LibDiff](#LibDiff)
+* [DataConverter](#DataConverter)
+
+### AmpGen
+
+The standalone generator (named AmpGen) is used as:
+
+```shell
+AmpGen.exe MyOpts.opt --nEvents=10000 --Output=output.root
+```
+
+where MyOpts.opt contains the options described in the previous section that describe the decay the user wishes to generate, and the optional arguments `nEvents` and `Output` given the number of events requested and the output file, respectively. The full list of application specific arguments can be obtained by:
+
+```bash
+AmpGen.exe --help
+```
+
+The output includes a tree (DalitzEventList) of candidates with the full four-vectors, as well as one- and two-dimensional projections, an example of which is shown below:
+
+<p align="center">
+ <img src="doc/figs/k3pi_s01.svg" width=300>
+</p>
+
+
+Several models for different $D^0$ decays published by the LHCb collaboration are included in the options directory, in addition to several other decay modes to demonstrate different features. These options often do not include EventTypes so as they can be included as part of a larger decay chain if required. For example, to generate $10^6$ toy $\Dz\to\Km\pip\pip\pim$ decays, the type of the events requested must also be specified:
+
+```shell
+AmpGen.exe options/D02Kpipipi.opt --EventType "D0 K- pi+ pi+ pi-" --nEvents 1000000
+```
+
+The standalone generator can also be used to only produce the source code that evaluates the amplitude, to be used by other generators such as EvtGen. In this case, the PDF is automatically normalised such that $\mathcal{P}_{\text{max}} < 1$ . The code can be generated and compiled into a shared library as follows
+```shell
+AmpGen.exe MyOpts.opt --Output=MyModel.cpp --SourceOnly
+g++ -Ofast -shared -rdynamic --std=c++14 -fPIC MyModel.cpp -o MyModel.so
+```
+Decays can also be specified entirely on the command line in order to quickly study the distributions of different decay modes. For example, to generate a sample of 10000 $\Lambda_b \to p K^{*-}$ decays,
+
+```shell
+AmpGen.exe --Decay "Lambda(b)0{p+,K*(892)bar-{K-,pi0}}" --nEvents 10000 --Type PolarisedSum
+```
+
+The flag `Type` is used to specify that the initial and/or final states includes at least one particle carrying spin, and thus polarisation must be taken into account. The output is both the full event kinematics, as well as projections of the different invariant masses shown below:
+
+<p align="center">
+<div>
+<img src="doc/figs/lb2pKpi_s01.svg" width=300 />
+<img src="doc/figs/lb2pKpi_s02.svg" width=300 />
+</div>
+</p>
+
+
+#### Phase space generators
+
+Generating events consists of two phases. Firstly, the kinematics of candidates are generated according to some distribution, by default uniform in the phase space. The target distribution, $\mathcal{P}(\mathbf{x})$ , is then obtained using the accept-reject method. A candidate generated at position $\mathbf{x}$ in the phase space is retained on the condition that
+
+ $\mathcal{P}(\mathbf{x}) > \mathcal{P}_{\text{max}} \times \texttt{Uniform}(0,1) $,
+
+where $\mathcal{P}_{\text{max}}$ is the largest possible value of $\mathcal{P}(\mathbf{x})$ , and $\texttt{Uniform}(0,1)$ is a random number uniformly drawn between 0 and 1.
+
+ The generation can be made more efficient by making the first step produce candidates that are distributed more closely to the full distribution than the uniform phase space. In particular, this is relevant for producing very narrow structures such as the $J/\psi$ resonance efficiently. To use this option, the flag `PhaseSpace` should be set to the value `TreePhaseSpace`. For example, to generate a sample of $10^6$ $\Lambda_b^0 \to J/\psi \left[\mu^+\mu^-\right]\Lambda(1405)^0 \left[p^+ \pi^-\right]$ decays:
+
+```shell
+AmpGen.exe --Decay "Lambda(b)0{J/psi0{mu+,mu-},Lambda(1405)0{p+,pi-}}" --nEvents 1000000 --Type PolarisedSum --PhaseSpace TreePhaseSpace
+```
+
+Two example projections are shown below, of the dimuon invariant mass with essentially no width, which would be virtually impossible to generate with a uniform distribution and the naive accept-reject method, and the combined mass of the dimuon with the proton from the $\Lambda(1405)^0$ decay:
+
+<p align="center">
+<div>
+<img src="doc/figs/lb2jspiL_s01.svg" width=300 />
+<img src="doc/figs/lb2jspiL_s012.svg" width=300 />
+</div>
+</p>
+
+
+### Debugger
+
+The debugger application is a tool for producing verbose information debugging for amplitudes and models. It is used on an options file as
+
+```
+Debugger.exe MyOpts.opt
+```
+which calculates each amplitude at a randomly generated point in phase space, as well as calculating the total amplitude accounting for complex couplings.
+
+A more useful application is the _verbose_ debugging mode which can be activated by
+
+```
+Debugger.exe MyOpts.opt --CoherentSum::Debug
+```
+which produces a large number of intermediate steps in the calculation of each amplitude, which are added to the calculation using the ADD_DEBUG and ADD_DEBUG_TENSOR macros in the code generation. For example, in src/Lineshapes/BW.cpp.
+If the model is a PolarisedSum, i.e. handles spin in the initial/final state, the flag PolarisedSum::Debug should be used instead of CoherentSum::Debug.
+
+### LibDiff
+
+### DataConvertor
+
+## Examples
+
+### SignalOnlyFitter
+
+An example fitter is provided in _examples/SignalOnlyFitter.cpp_, which as the name suggests only has a single signal component in the fit. The free parameters of the fit are specified in the same way as the Generator, with the additional relevant slots being _DataSample_ which specifies the signal sample to fit, which is presumed to already have the selection applied, and _Branches_ which takes a list of branch names, and defaults to the format used by the Generator. More details can be found with
+```shell
+SignalOnlyFitter.exe --help
+```
+For example, the fitter can be used to fit a toy MC sample generated by the generator by running:
+```shell
+AmpGen.exe MyOpts.opt --nEvents 100000
+SignalOnlyFitter.exe MyOpts.opt --DataSample Generate_Output.root
+```
+
+## Advanced
+
+This section contains miscellaneous details on more advanced functionality, including using python bindings and alternative parameterisations of the spin factors.
+
+### Table of contents
+* [Python Bindings](#python-bindings)
+* [Particle Properties and Lineshape parameters](#particle-properties-and-lineshape-parameters)
+* [Fit parameters and expressions](#fit-parameters-and-expressions)
+* [Spin Formalisms](#spin-formalisms)
+* [Quasiparticles](#quasiparticles)
+
+### Python Bindings
+Models built into a shared library can be used in python using the following flags into ConvertToSourceCode:
+```shell
+./AmpGen.exe MyOpts.opt --Output=MyFile.cpp --SourceOnly --OutputEvents=events.csv --IncludePythonBindings
+```
+where normalisation events are also output for testing purposes in events.csv.
+This can then be used with the python bindings in ampgen.py:
+```python
+from ampgen import FixedLib
+model = FixedLib('MyModel.so')
+print(model.matrix_elements[0]) # Print first matrix element
+
+import pandas as pd
+data = pd.read_csv('events.csv', nrows=100_000)
+fcn1 = model.FCN_all(data)
+
+# or, a bit slower, but just to show flexibility:
+fcn2 = data.apply(model.FCN, axis=1)
+```
+
+### Particle Properties and Lineshape parameters
+The particles available and their default properties can be found in *options/mass\_width.csv* using the MC format of the 2008 PDG. Additional pseudoparticles, such as nonresonant states and terms for use in conjunction with K-matrices are defined by *options/MintDalitzSpecialParticles.csv*. Any additional user defined particles should be added here. For the default lineshape (the relavistic Breit-Wigner or BW), there are three parameters: The mass, the width and the Blatt-Weisskopf radius. These default to their PDG values, but can be overridden in the options file with parameters: *particleName*\_mass, *particleName*\_width, *particleName*\_radius. To vary the mass of the $K_1(1270)^+$ meson, the line:
+```
+K(1)(1270)+_mass 0 1.270 0.01
+```
+could be added to the user configuration.
+Other lineshapes may define other parameters, for example channel couplings or pole masses in the case of the K-matrices, can be set or varied in a similar manner.
+
+### Fit parameters and expressions
+
+Parameters can either be specified by three parameters, in the case of a scalar parameter such as a mass or a width, or with six parameters in the case of a complex parameter such as a coupling.
+Upper and lower bounds on parameters can also be set by specifying a parameter with five parameters or ten parameters for a scalar or complex, respectively.
+For example, if we wished to vary the mass of the $K_1(1270)^+$ meson in the above example, but restricting the allowed values in the range $[0.0,2.0]\,\mathrm{GeV}$:
+```
+K(1)(1270)+_mass 0 1.27 0.01 0.0 2.0
+```
+
+Parameters can also be related to each other via expressions,
+Suppose for example we have $K_1(1270)^+$ and $K_1(1270)^-$ in the same fit (for example, in $D^0 \to K^- K^+ \pi^- \pi^+$)
+The properties of one can be allowed to vary, for example the $K_1(1270)^+$, and the other fixed to the same value, using:
+```
+K(1)(1270)+_mass 0 1.27 0.01 0.0 2.0
+K(1)(1270)bar-_mass = K(1)(1270)+_mass
+```
+Parameter expressions are whitespace delimited due to the abundance of **odd** glyphs such as brackets and +/- in the names of parameters.
+Expressions support the binary operations $(+,-,/,* )$, as well as common unary functions such as sqrt, trigonometric functions etc.
+
+### Spin Formalisms
+
+AmpGen implements both the covariant tensor (or Rarita-Schwinger) and canonical helicity formalism for describing the angular momentum component of decays.
+Both formalisms refer to states of well-defined orbital angular momentum, as opposed to the helicity states, as the states with well-defined orbital angular momentum have a straightforward parity and momentum dependences.
+The default formalism is the covariant tensor formalism, but this can be switched to the canonical formalism changing the flag
+```
+Particle::SpinFormalism Canonical
+```
+in the options file.
+The spin formalism for an individual decay chain can be specified by changing the attribute SpinFormalism in the decay descriptor. For example,
+```
+D0[SpinFormalism=Canonical]{K*(892)bar0,rho(770)0}
+```
+selects the S-wave of the $K^* \rho$ system. The user can also specify systems of helicity couplings in the canonical formalism, using the attribute _helAmp_. For example, suppose the transversity amplitudes were used rather than the canonical, then the user can specify
+```
+D0[SpinFormalism=Canonical;helAmp=Long]{K*(892)bar0,rho(770)0}
+D0[SpinFormalism=Canonical;helAmp=t1]{K*(892)bar0,rho(770)0}
+D0[SpinFormalism=Canonical;helAmp=t2]{K*(892)bar0,rho(770)0}
+```
+For the longitudinal and two transverse amplitudes. These must then be defined by the user in terms of the helicity amplitudes in the following structure:
+```
+Long {
+ 1.0 0 0
+}
+
+t1 {
+ 0.707106781 +1 +1
+ 0.707106781 -1 -1
+}
+
+t2 {
+ 0.707106781 +1 +1
+ -0.707106781 -1 -1
+}
+```
+That is specified as sets of three numbers, firstly the coupling, and then the two particle helicities. So in this example, the longitudinal amplitude is the $00$ helicity state, while the two transverse amplitudes and the sum and difference of the two other helicity amplitudes.
+
+### Quasiparticles
+
+Quasiparticles are fictional decaying particles that can be implemented in the decay chain for a variety of different purposes. The original use case was to group some amplitudes with the same quantum numbers with couplings that want to be factorised.
+For example, for the $I=0$ $S$-wave, the K matrix description may be used. The coupling from the initial state may be written as
+
+```
+D0{K0S0,NonResS0} ...
+```
+The quasiparticle _NonResS0_ can then be decayed to the final state via the K matrix lineshape(s)
+```
+NonResS0[kMatrix.pole.0]{pi+,pi-} ...
+NonResS0[kMatrix.pole.1]{pi+,pi-} ...
+...
+```
+where each of the .X is one of the terms of the (pole) production vector.
+In this example, an equivalent formulation would be
+```
+D0{K0S0,NonResS0[kMatrix.pole.0]{pi+,pi-}} ...
+D0{K0S0,NonResS0[kMatrix.pole.1]{pi+,pi-}} ...
+...
+```
+
+## Acknowledgements
+The development of this software has been supported by the National Science Foundation under grant PHY-1414736 and through a subcontract under Cooperative Agreement OAC-1836650. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the developers and do not necessarily reflect the views of the National Science Foundation.
+
+<p align="center">
+ <div>
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/UC_ID_PrimaryBlackRed.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/Iris-hep-3-regular-complete.png">
+ <img src="https://github.com/GooFit/AmpGen/raw/master/doc/figs/NSF_4-Color_bitmap_Logo.png">
+ </div>
+</p>
+
+[travis-badge]: https://travis-ci.org/GooFit/AmpGen.svg?branch=master
+[license-badge]: https://img.shields.io/badge/License-GPL%20v2-blue.svg
+[travis-link]: https://travis-ci.org/GooFit/AmpGen
diff --git a/Standalone.cmake b/Standalone.cmake
deleted file mode 100644
index e3b6e0ecad2..00000000000
--- a/Standalone.cmake
+++ /dev/null
@@ -1,180 +0,0 @@
-set(AMPGEN_CXX ${CMAKE_CXX_COMPILER} CACHE FILEPATH "This should be the path to compiler (use which c++ for macOS)" )
-
-file(GLOB_RECURSE AMPGEN_SRC src/*)
-file(GLOB_RECURSE AMPGEN_HDR AmpGen/*)
-
-
-if( NOT "${CMAKE_CXX_STANDARD}" )
- set(CMAKE_CXX_STANDARD 14)
-endif()
-
-set(CMAKE_CXX_EXTENSIONS OFF)
-set(CMAKE_CXX_STANDARD_REQUIRED ON)
-set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
-set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib")
-set(CMAKE_RUNTIME_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin")
-set(CMAKE_RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_BINARY_DIR}/bin")
-set(CMAKE_RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_BINARY_DIR}/bin")
-set(CMAKE_TEST_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin/test")
-
-include(CMakeDependentOption)
-include(CMakePrintHelpers)
-
-option(AMPGEN_DEBUG "AmpGen Debug printout")
-option(AMPGEN_TRACE "AmpGen Trace printout")
-
-configure_file ("${PROJECT_SOURCE_DIR}/AmpGen/Version.h.in" "${PROJECT_SOURCE_DIR}/AmpGen/Version.h")
-
-add_library(AmpGen SHARED ${AMPGEN_SRC} ${AMPGEN_HDR})
-
-if(DEFINED ENV{ROOTSYS})
- list(APPEND CMAKE_MODULE_PATH "$ENV{ROOTSYS}/etc/cmake/")
-endif()
-
-find_package(ROOT CONFIG REQUIRED COMPONENTS Matrix MathMore MathCore Gpad Tree Graf)
-find_package(OpenMP)
-
-cmake_print_variables(CMAKE_SOURCE_DIR)
-
-# Default build type from the Kitware Blog
-set(default_build_type "Release")
-if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
- message(STATUS "Setting build type to '${default_build_type}' as none was specified.")
- set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE
- STRING "Choose the type of build." FORCE)
- # Set the possible values of build type for cmake-gui
- set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS
- "Debug" "Release" "MinSizeRel" "RelWithDebInfo")
-endif()
-
-message( STATUS "ROOT_INCLUDE_DIRS = ${ROOT_INCLUDE_DIRS}")
-
-target_include_directories(AmpGen PUBLIC "${CMAKE_SOURCE_DIR}")
-
-target_include_directories(AmpGen SYSTEM PUBLIC "${ROOT_INCLUDE_DIRS}")
-
-target_link_libraries(AmpGen PUBLIC ${ROOT_LIBRARIES} ${CMAKE_DL_LIBS})
-
-if( ( NOT TARGET ROOT::Minuit2 AND NOT TARGET Minuit2 ) OR "${extern_minuit2}" )
- message( STATUS "Use external Minuit2")
- add_subdirectory("extern/Minuit2")
- set_target_properties(Minuit2 PROPERTIES FOLDER extern)
- target_compile_options(Minuit2 PUBLIC -fPIC -Wno-suggest-override)
- set_target_properties(Minuit2Math PROPERTIES FOLDER extern)
- add_library(ROOT::Minuit2 ALIAS Minuit2)
- target_include_directories( AmpGen PUBLIC "${CMAKE_SOURCE_DIR}/extern/Minuit2/inc/")
-else()
- message( STATUS "Use ROOT::Minuit2")
-endif()
-if ( TARGET Minuit2 AND NOT TARGET ROOT::Minuit2 )
- find_package( ROOT CONFIG REQUIRED COMPONENTS Minuit2)
- add_library(ROOT::Minuit2 ALIAS Minuit2)
-endif()
-
-target_link_libraries(AmpGen PUBLIC ROOT::Minuit2 )
-
-
-if(OpenMP_FOUND OR OpenMP_CXX_FOUND)
- if(NOT TARGET OpenMP::OpenMP_CXX)
- add_library(OpenMP::OpenMP_CXX IMPORTED INTERFACE)
- set_property(TARGET OpenMP::OpenMP_CXX PROPERTY INTERFACE_COMPILE_OPTIONS ${OpenMP_CXX_FLAGS})
- set_property(TARGET OpenMP::OpenMP_CXX PROPERTY INTERFACE_LINK_LIBRARIES ${OpenMP_CXX_FLAGS})
- if(CMAKE_VERSION VERSION_LESS 3.4)
- set_property(TARGET OpenMP::OpenMP_CXX APPEND PROPERTY INTERFACE_LINK_LIBRARIES -pthread)
- else()
- find_package(Threads REQUIRED)
- set_property(TARGET OpenMP::OpenMP_CXX APPEND PROPERTY INTERFACE_LINK_LIBRARIES Threads::Threads)
- endif()
- endif()
- target_link_libraries(AmpGen PUBLIC OpenMP::OpenMP_CXX)
-else()
- message(STATUS "OpenMP not found for CXX, you might have forgotten lb-run ROOT bash or CXX=`which g++` in CERN stack")
-endif()
-
-# Default to XROOTD only if on CMT system. Can be overridden with -DAMPGEN_XROOTD=ON
-if(DEFINED ENV{CMTCONFIG})
- set(AMPGEN_XROOTD_DEFAULT ON)
-else()
- set(AMPGEN_XROOTD_DEFAULT OFF)
-endif()
-
-cmake_dependent_option(AMPGEN_XROOTD "Turn on XROOTD discovery" ON "AMPGEN_XROOTD_DEFAULT" OFF)
-
-if(AMPGEN_XROOTD)
- find_library(XROOTD_LIB NAMES libXrdCl.so
- HINTS "/cvmfs/lhcb.cern.ch/lib/lcg/releases/LCG_89/xrootd/4.6.0/$ENV{CMTCONFIG}/lib64")
- target_link_libraries(AmpGen PUBLIC ${XROOTD_LIB})
-endif()
-
-target_compile_definitions(AmpGen
- PUBLIC
- "AMPGENROOT_CMAKE=\"${CMAKE_BINARY_DIR}/bin\""
- "AMPGEN_CXX=\"${AMPGEN_CXX}\""
- $<$<BOOL:${AMPGEN_DEBUG}>:DEBUGLEVEL=1>
- $<$<BOOL:${AMPGEN_TRACE}>:TRACELEVEL=1>)
-
-target_compile_options(AmpGen
- PUBLIC
- -Wall -Wextra -Wpedantic -g3
- -Wno-unused-parameter
- -Wno-unknown-pragmas
- -Wnon-virtual-dtor
- -Woverloaded-virtual
- $<$<CONFIG:Release>:-Ofast>)
-
-if ("${CMAKE_CXX_COMPILER_ID}" MATCHES "Clang")
- set (CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -lm -lstdc++")
-else()
- target_compile_options(AmpGen PUBLIC -Wsuggest-override)
-endif()
-
-file(GLOB_RECURSE applications apps/*.cpp )
-file(GLOB_RECURSE examples examples/*.cpp )
-
-foreach( file ${applications} )
- get_filename_component( Executable ${file} NAME_WE )
- cmake_print_variables(Executable)
- add_executable(${Executable} ${file})
- target_compile_options(${Executable} PUBLIC -g3 -Ofast)
- target_link_libraries(${Executable} PUBLIC AmpGen)
-endforeach()
-
-foreach( file ${examples} )
- get_filename_component( Executable ${file} NAME_WE )
- cmake_print_variables(Executable)
- add_executable(${Executable} ${file})
- target_link_libraries(${Executable} PUBLIC AmpGen)
-endforeach()
-
-file(GLOB_RECURSE options_files options/*.*)
-execute_process(COMMAND ${CMAKE_COMMAND} -E make_directory "${CMAKE_BINARY_DIR}/bin")
-foreach(file ${options_files})
- get_filename_component(OptionFile "${file}" NAME)
- cmake_print_variables(OptionFile)
- execute_process(COMMAND ${CMAKE_COMMAND} -E create_symlink "${file}" "${CMAKE_BINARY_DIR}/bin/${OptionFile}")
-endforeach()
-
-enable_testing()
-find_package(Boost 1.67.0 COMPONENTS unit_test_framework)
-if ( Boost_FOUND )
- include_directories (${Boost_INCLUDE_DIRS})
-
- file(GLOB TEST_SRCS RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} test/*.cpp)
-
- foreach(testSrc ${TEST_SRCS})
- get_filename_component(testName ${testSrc} NAME_WE)
- add_executable(${testName} ${testSrc})
- set_target_properties(${testName}
- PROPERTIES
- RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_TEST_OUTPUT_DIRECTORY}"
- RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_TEST_OUTPUT_DIRECTORY}"
- RUNTIME_OUTPUT_DIRECTORY "${CMAKE_TEST_OUTPUT_DIRECTORY}"
- EXECUTABLE_OUTPUT_DIRECTORY "${CMAKE_TEST_OUTPUT_DIRECTORY}"
- )
- target_link_libraries(${testName} ${Boost_LIBRARIES} AmpGen)
- add_test(NAME ${testName} WORKING_DIRECTORY ${CMAKE_TEST_OUTPUT_DIRECTORY} COMMAND ${CMAKE_TEST_OUTPUT_DIRECTORY}/${testName} )
- endforeach(testSrc)
-else()
- message( WARNING "Warning: Boost (version >=1.67.0) required to build unit tests\n")
-endif()
-
diff --git a/apps/AmpGen.cpp b/apps/AmpGen.cpp
new file mode 100644
index 00000000000..85d62204891
--- /dev/null
+++ b/apps/AmpGen.cpp
@@ -0,0 +1,289 @@
+#include <Rtypes.h>
+#include <TH1.h>
+#include <dlfcn.h>
+#include <memory>
+#include <string>
+
+#include "TFile.h"
+#include "TRandom3.h"
+#include "TTree.h"
+
+#ifdef _OPENMP
+#include <omp.h>
+#include <thread>
+#endif
+
+#include "AmpGen/DynamicFCN.h"
+#include "AmpGen/EventList.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/Particle.h"
+#include "AmpGen/RecursivePhaseSpace.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/EventType.h"
+#include "AmpGen/CoherentSum.h"
+#include "AmpGen/Generator.h"
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/PolarisedSum.h"
+#include "AmpGen/OptionsParser.h"
+#include "AmpGen/TreePhaseSpace.h"
+#include "AmpGen/enum.h"
+#include "AmpGen/ParticlePropertiesList.h"
+#include "AmpGen/AddCPConjugate.h"
+
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_t = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_t = AmpGen::EventList;
+#endif
+
+using namespace AmpGen;
+
+namespace AmpGen {
+ make_enum(pdfTypes, CoherentSum, PolarisedSum, FixedLib)
+ make_enum(phspTypes, PhaseSpace, RecursivePhaseSpace, TreePhaseSpace)
+}
+
+struct FixedLibPDF
+{
+ void* lib = {nullptr};
+ DynamicFCN<double( const double*, int )> PDF;
+ void debug( const Event& event) {};
+ void prepare(){};
+ void setEvents( AmpGen::EventList& evts ){};
+ void setEvents( AmpGen::EventListSIMD& evts ){};
+ double operator()( const AmpGen::Event& evt ) const { return PDF( evt, 1 ); }
+ double operator()( const double* evt, const unsigned& index )
+ {
+ return PDF(evt, 1 );
+ }
+ FixedLibPDF( const std::string& lib )
+ {
+ void* handle = dlopen( lib.c_str(), RTLD_NOW );
+ if ( handle == nullptr ) ERROR( dlerror() );
+ PDF = DynamicFCN<double( const double*, int )>( handle, "FCN" );
+ }
+ size_t size() { return 0; }
+ void reset( const bool& flag = false ){};
+};
+
+template <class T> void generateSource(T& pdf, const std::string& sourceFile, MinuitParameterSet& mps)
+{
+ bool normalise = NamedParameter<bool>("Normalise",true);
+ double safetyFactor = NamedParameter<double>( "SafetyFactor", 3 );
+ int seed = NamedParameter<int>("Seed", 1);
+ size_t nEvents = NamedParameter<size_t>( "NormEvents", 1000000 );
+
+ TRandom3 rnd(seed);
+
+ Generator<PhaseSpace> phsp(pdf.eventType());
+ phsp.setRandom(&rnd);
+ EventList normEvents = phsp.generate(nEvents);
+ if constexpr( std::is_same<T, CoherentSum>::value ) pdf.prepare();
+
+ double norm = 1;
+ if( normalise ){
+ double pMax = 0;
+ for ( auto& evt : normEvents )
+ {
+ if constexpr ( std::is_same<T, PolarisedSum>::value )
+ {
+ double px, py, pz;
+ rnd.Sphere(px,py,pz, rnd.Uniform(0,1));
+ mps["Px"]->setCurrentFitVal(px);
+ mps["Py"]->setCurrentFitVal(py);
+ mps["Pz"]->setCurrentFitVal(pz);
+ pdf.transferParameters();
+ }
+ double n = 0;
+ if constexpr ( std::is_same<T, CoherentSum>::value ) n = std::norm( pdf.getValNoCache(evt) );
+ if constexpr ( std::is_same<T, PolarisedSum>::value ) n = pdf.getValNoCache(evt);
+ if ( n > pMax ) pMax = n;
+ }
+ norm = pMax * safetyFactor ;
+ INFO( "Making binary with " << pMax << " x safety factor = " << safetyFactor );
+ }
+ mps.resetToInit();
+ pdf.generateSourceCode( sourceFile, norm, true );
+}
+
+
+template <typename pdf_t> Particle getTopology(const pdf_t& pdf)
+{
+ if constexpr( std::is_same<pdf_t, FixedLibPDF>::value )
+ {
+ FATAL("Cannot deduce decay topology from a compiled library, check generator options");
+ }
+ else return pdf.matrixElements()[0].decayTree.quasiStableTree();
+}
+
+template <typename pdf_t> std::vector<Particle> getDecayChains( const pdf_t& pdf )
+{
+ if constexpr( std::is_same<pdf_t, FixedLibPDF>::value )
+ {
+ FATAL("Cannot deduce decay topology from a compiled library, check generator options");
+ }
+ else {
+ std::vector<Particle> channels;
+ for( auto& chain : pdf.matrixElements() ) channels.push_back( chain.decayTree );
+ return channels;
+ }
+}
+
+
+template <typename pdf_t> void generateEvents( EventList& events
+ , pdf_t& pdf
+ , const phspTypes& phsp_type
+ , const size_t& nEvents
+ , const size_t& blockSize
+ , TRandom* rndm
+ , const bool& normalise = true )
+{
+ if constexpr( std::is_same<pdf_t, FixedLibPDF>::value )
+ {
+ Generator<PhaseSpace, EventList> signalGenerator(events.eventType(), rndm);
+ signalGenerator.setBlockSize(blockSize);
+ signalGenerator.setNormFlag(normalise);
+ signalGenerator.fillEventList(pdf, events, nEvents );
+ }
+ else {
+ if( phsp_type == phspTypes::PhaseSpace )
+ {
+ Generator<PhaseSpace, EventList_t> signalGenerator(events.eventType(), rndm);
+ signalGenerator.setBlockSize(blockSize);
+ signalGenerator.setNormFlag(normalise);
+ signalGenerator.fillEventList(pdf, events, nEvents );
+ }
+ else if( phsp_type == phspTypes::RecursivePhaseSpace )
+ {
+ Generator<RecursivePhaseSpace, EventList_t> signalGenerator( getTopology(pdf), events.eventType(), rndm );
+ signalGenerator.setBlockSize(blockSize);
+ signalGenerator.setNormFlag(normalise);
+ signalGenerator.fillEventList(pdf, events, nEvents);
+ }
+ else if( phsp_type == phspTypes::TreePhaseSpace )
+ {
+ Generator<TreePhaseSpace, EventList_t> signalGenerator(getDecayChains(pdf), events.eventType(), rndm);
+ signalGenerator.setBlockSize(blockSize);
+ signalGenerator.setNormFlag(normalise);
+ signalGenerator.fillEventList(pdf, events, nEvents );
+ }
+ else {
+ FATAL("Phase space configuration: " << phsp_type << " is not supported");
+ }
+ }
+}
+
+
+
+int main( int argc, char** argv )
+{
+ OptionsParser::setArgs( argc, argv );
+
+ size_t nEvents = NamedParameter<size_t> ("nEvents" , 1, "Total number of events to generate" );
+ size_t blockSize = NamedParameter<size_t> ("BlockSize", 5000000, "Number of events to generate per block" );
+ int seed = NamedParameter<int> ("Seed" , 0, "Random seed used in event Generation. Should always be set for pseudoexperiment generation." );
+ std::string outfile = NamedParameter<std::string>("Output" , "Generate_Output.root" , "Name of output file" );
+ auto pdfType = NamedParameter<pdfTypes>( "Type", pdfTypes::CoherentSum, optionalHelpString("Type of PDF to use:",
+ std::make_pair(pdfTypes::CoherentSum , "Describes decays of a (pseudo)scalar particle to N pseudoscalars")
+ , std::make_pair(pdfTypes::PolarisedSum, "Describes the decay of a particle with spin to N particles carrying spin.")
+ , std::make_pair(pdfTypes::FixedLib , "PDF to describe a decay from a precompiled library, such as those provided to GAUSS.") ) );
+ auto phspType = NamedParameter<phspTypes>( "PhaseSpace", phspTypes::PhaseSpace, optionalHelpString("Phase-space generator to use:",
+ std::make_pair(phspTypes::PhaseSpace , "Phase space generation based on Raubold-Lynch algorithm (recommended).\0")
+ , std::make_pair(phspTypes::TreePhaseSpace , "Divides the phase-space into a series of quasi two-body phase-spaces for efficiently generating narrow states.\0")
+ , std::make_pair(phspTypes::RecursivePhaseSpace, "Includes possible quasi-stable particles and the phase spaces of their decay products, such as Λ baryons.\0") ) );
+ std::string lib = NamedParameter<std::string>("Library","","Name of library to use for a fixed library generation");
+ size_t nBins = NamedParameter<size_t> ("nBins" ,100, "Number of bins for monitoring plots." );
+ bool sourceOnly = NamedParameter<bool> ("SourceOnly",false, "Flag to only generate the source code, but not produce any events");
+ bool poissonVaryYield = NamedParameter<bool> ("PoissonYield",false, "Vary the number of events generated by a poisson distribution");
+#ifdef _OPENMP
+ unsigned int concurentThreadsSupported = std::thread::hardware_concurrency();
+ unsigned int nCores = NamedParameter<unsigned int>( "nCores", concurentThreadsSupported, "Number of cores to use (OpenMP only)" );
+ omp_set_num_threads( nCores );
+ omp_set_dynamic( 0 );
+ #endif
+
+ TRandom3 rand;
+ rand.SetSeed( seed + 934534 );
+
+ if( poissonVaryYield ) nEvents = rand.Poisson( nEvents );
+ MinuitParameterSet MPS;
+ MPS.loadFromStream();
+
+ EventType eventType;
+ std::string decay = NamedParameter<std::string>("Decay","","Single decay written on the command line");
+ if( decay != "" )
+ {
+ Particle p(decay);
+ eventType = p.eventType();
+ MPS.add(p.decayDescriptor()+"_Re", Flag::Fix, 1., 0);
+ MPS.add(p.decayDescriptor()+"_Im", Flag::Fix, 0., 0);
+ }
+ else eventType = EventType( NamedParameter<std::string>( "EventType" , "", "EventType to generate, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector(),
+ NamedParameter<bool>( "GenerateTimeDependent", false , "Flag to include possible time dependence of the amplitude") );
+
+ bool conj = NamedParameter<bool>("Conj",false, "Flag to generate the CP conjugate amplitude under the assumption of CP conservation");
+ bool add_cp_conjugate = NamedParameter<bool>("AddConj",false, "Flag to add all of the CP conjugate amplitudes, under the assumption of CP conservation");
+ if ( conj ) eventType = eventType.conj();
+ if( conj || add_cp_conjugate ) AddCPConjugate(MPS);
+
+ if( OptionsParser::printHelp() ) return 0;
+
+ INFO("Writing output: " << outfile );
+ #ifdef _OPENMP
+ INFO("Using: " << nCores << " / " << concurentThreadsSupported << " threads" );
+ #endif
+
+ if( sourceOnly )
+ {
+ if ( pdfType == pdfTypes::CoherentSum )
+ {
+ CoherentSum pdf( eventType, MPS);
+ generateSource(pdf, outfile, MPS);
+ }
+ else if ( pdfType == pdfTypes::PolarisedSum )
+ {
+ PolarisedSum pdf(eventType, MPS);
+ generateSource(pdf, outfile, MPS);
+ }
+ return 0;
+ }
+ INFO("Generating time-dependence? " << eventType.isTimeDependent() );
+ EventList accepted( eventType );
+
+ INFO("Generating events with type = " << eventType );
+
+ if ( pdfType == pdfTypes::CoherentSum ){
+ CoherentSum pdf( eventType, MPS);
+ generateEvents(accepted, pdf, phspType , nEvents, blockSize, &rand );
+ }
+ else if ( pdfType == pdfTypes::PolarisedSum ){
+ PolarisedSum pdf(eventType, MPS);
+ generateEvents( accepted, pdf, phspType, nEvents, blockSize, &rand );
+ }
+ else if ( pdfType == pdfTypes::FixedLib ){
+ FixedLibPDF pdf(lib);
+ generateEvents( accepted, pdf, phspType, nEvents, blockSize, &rand, false );
+ }
+ else {
+ FATAL("Did not recognise configuration: " << pdfType );
+ }
+ if( accepted.size() == 0 ) return -1;
+ TFile* f = TFile::Open( outfile.c_str(), "RECREATE" );
+ accepted.tree( "DalitzEventList" )->Write();
+ auto plots = accepted.makeDefaultProjections(PlotOptions::Bins(nBins), PlotOptions::LineColor(kBlack));
+ for ( auto& plot : plots ) plot->Write();
+ if( NamedParameter<bool>("plots_2d",true) == true ){
+ auto proj = eventType.defaultProjections(nBins);
+ for( size_t i = 0 ; i < proj.size(); ++i ){
+ for( size_t j = i+1 ; j < proj.size(); ++j ){
+ accepted.makeProjection( Projection2D(proj[i], proj[j]), PlotOptions::LineColor(kBlack) )->Write();
+ }
+ }
+ }
+ INFO( "Writing output file " );
+
+ f->Close();
+}
diff --git a/apps/ConvertToSourceCode.cpp b/apps/ConvertToSourceCode.cpp
deleted file mode 100644
index 72783952716..00000000000
--- a/apps/ConvertToSourceCode.cpp
+++ /dev/null
@@ -1,139 +0,0 @@
-#include <complex>
-#include <fstream>
-#include <string>
-#include <vector>
-
-#include "AmpGen/EventList.h"
-#include "AmpGen/EventType.h"
-#include "AmpGen/CoherentSum.h"
-#include "AmpGen/PolarisedSum.h"
-#include "AmpGen/Generator.h"
-#include "AmpGen/MinuitParameterSet.h"
-#include "AmpGen/NamedParameter.h"
-#include "AmpGen/PhaseSpace.h"
-#include "AmpGen/Utilities.h"
-#include "AmpGen/ThreadPool.h"
-#include "AmpGen/Particle.h"
-#include "TRandom3.h"
-
-using namespace AmpGen;
-
-template <class T>
-void create_integration_tests(T& pdf,
- const EventType& type,
- const MinuitParameterSet& mps,
- const std::vector<Event>& testEvents,
- const std::string& sourceFile)
-{
- auto stringify = [](const std::string arg ){ return "\"" + arg + "\"" ; };
- std::ofstream unit_tests;
- unit_tests.open(split( sourceFile, '.')[0] + "_test.cpp");
- unit_tests << "#define BOOST_TEST_DYN_LINK" << std::endl;
- unit_tests << "#define BOOST_TEST_MODULE amp" << std::endl;
- unit_tests << "#include <boost/test/included/unit_test.hpp>" << std::endl;
- unit_tests << "#include \"AmpGen/Particle.h\"" << std::endl;
- unit_tests << "#include \"AmpGen/CompiledExpression.h\"" << std::endl;
- unit_tests << "#include \"AmpGen/EventType.h\"" << std::endl;
- unit_tests << "#include \"AmpGen/MinuitParameterSet.h\"" << std::endl;
- unit_tests << "#include \"AmpGen/OptionsParser.h\"" << std::endl;
- unit_tests << "using namespace AmpGen;" << std::endl;
-
- unit_tests << "void setupOptions(){" << std::endl;
- for( auto& p : *OptionsParser::getMe() )
- {
- unit_tests << " OptionsParser::setArg( \"" << vectorToString(p.second," ") <<"\");"<< std::endl;
- }
- unit_tests << "\n}\n" << std::endl;
-
- for( auto& mE : pdf.matrixElements() ){
- auto value = mE.pdf(testEvents[0].address());
- unit_tests << "BOOST_AUTO_TEST_CASE( " << mE.pdf.progName() + "_test){" << std::endl;
- unit_tests << " EventType type({" << stringify(type.mother()) << ", " << vectorToString( type.finalStates(), ", ", stringify ) << "});" << std::endl;
- unit_tests << " Particle p("<<stringify(mE.decayDescriptor()) << ", type.finalStates());" << std::endl;
- unit_tests << " setupOptions();" << std::endl;
- unit_tests << " MinuitParameterSet mps; mps.loadFromStream();" << std::endl;
-
- unit_tests << " double event[] = {"<< std::setprecision(15) ;
- for( size_t i = 0 ; i < testEvents[0].size() -1; ++i) unit_tests << testEvents[0][i] << ", ";
- unit_tests << testEvents[0][testEvents[0].size()-1];
- unit_tests << "};" << std::endl;
- unit_tests << " auto expr = make_expression<complex_t>(p.getExpression(), p.decayDescriptor(), type.getEventFormat(), mps);" << std::endl;
- unit_tests << " auto eval = expr(event);" << std::endl;
- unit_tests << " BOOST_TEST( std::real(eval) == " << std::real(value)<< ", boost::test_tools::tolerance(1e-6)) ;" << std::endl;
- unit_tests << " BOOST_TEST( std::imag(eval) == " << std::imag(value)<< ", boost::test_tools::tolerance(1e-6)) ;" << std::endl;
- unit_tests << "}\n\n";
- }
- unit_tests.close();
-}
-
-
-template <class T> void generate_source(T& pdf, EventList& normEvents, const std::string& sourceFile, MinuitParameterSet& mps, const double& sf)
-{
- bool normalise = NamedParameter<bool>("Normalise",true);
- std::string type = NamedParameter<std::string>( "Type", "CoherentSum" );
-
- double norm = 1;
- if( normalise ){
- double pMax = 0 ;
- pdf.setEvents( normEvents );
- pdf.prepare();
- for ( auto& evt : normEvents ) {
- if( type == "PolarisedSum" ){
- double px, py, pz;
- gRandom->Sphere(px,py,pz, gRandom->Uniform(0,1));
- mps["Px"]->setCurrentFitVal(px);
- mps["Py"]->setCurrentFitVal(py);
- mps["Pz"]->setCurrentFitVal(pz);
- pdf.transferParameters();
- }
- double n = pdf.prob_unnormalised( evt );
- if ( n > pMax ) pMax = n;
- }
- norm = pMax * sf ;
- INFO( "Making binary with " << pMax << " x safety factor = " << sf );
- }
- mps.resetToInit();
- pdf.generateSourceCode( sourceFile, norm, true );
-}
-
-int main( int argc, char** argv )
-{
- OptionsParser::setArgs( argc, argv );
- std::vector<std::string> oEventType = NamedParameter<std::string>( "EventType" ).getVector();
- std::string sourceFile = NamedParameter<std::string>( "Output" , "output.cpp" );
- std::string type = NamedParameter<std::string>( "Type", "CoherentSum" );
- std::string outputPS = NamedParameter<std::string>( "OutputEvents", "" );
- unsigned int NormEvents = NamedParameter<unsigned int>( "NormEvents", 1000000 );
- double safetyFactor = NamedParameter<double>( "SafefyFactor", 3 );
-
- EventType eventType( oEventType );
-
- AmpGen::MinuitParameterSet MPS; //
- MPS.loadFromStream();
- Generator<PhaseSpace> phsp( eventType );
- TRandom3 rnd;
-
- gRandom = &rnd;
- phsp.setRandom( &rnd );
-
- EventList phspEvents( oEventType );
- phsp.fillEventListPhaseSpace( phspEvents, NormEvents );
-
- if( type == "CoherentSum" ){
- CoherentSum sig( eventType, MPS, "" );
- generate_source( sig, phspEvents, sourceFile, MPS, safetyFactor );
- create_integration_tests(sig, eventType, MPS, {phspEvents[15]}, sourceFile );
- }
- if( type == "PolarisedSum" ){
- PolarisedSum sig( eventType, MPS );
- generate_source( sig, phspEvents, sourceFile, MPS, safetyFactor );
- }
- if ( outputPS != "" ) {
- std::ofstream ofile( outputPS );
- ofile << "0x,0y,0z,0t,1x,1y,1z,1t,2x,2y,2z,2t,3x,3y,3z,3t\n";
- for ( auto& event : phspEvents ) {
- for ( size_t i = 0; i < event.size(); i++ ) ofile << ( i == 0 ? "" : "," ) << event[i];
- ofile << "\n";
- }
- }
-}
diff --git a/apps/DataConverter.cpp b/apps/DataConverter.cpp
index 815e824599e..bde9ca91297 100644
--- a/apps/DataConverter.cpp
+++ b/apps/DataConverter.cpp
@@ -18,7 +18,7 @@
#include "AmpGen/NamedParameter.h"
#include "AmpGen/Utilities.h"
#include "AmpGen/Projection.h"
-
+#include "AmpGen/TreeReader.h"
#include "TEventList.h"
#include "TFile.h"
#include "TH1.h"
@@ -36,11 +36,10 @@ void invertParity( Event& event, const size_t& nParticles=0)
}
}
-
int main( int argc, char* argv[] )
{
OptionsParser::setArgs( argc, argv );
- std::string inputFilename = NamedParameter<std::string>("Input" , "", "Input ROOT file" );
+ std::string inputFilename = NamedParameter<std::string>("Input" , "", "Input ROOT file(s)" );
std::string treeName = NamedParameter<std::string>("Tree" , "", "Input ROOT tree." );
std::string outputFilename = NamedParameter<std::string>("Output" , "", "Output ROOT file" );
std::string pdfLibrary = NamedParameter<std::string>("PdfLibrary", "", "PDF Library that used to generate this sample for MC reweighting (MC only)" );
@@ -49,10 +48,15 @@ int main( int argc, char* argv[] )
std::vector<std::string> particles = NamedParameter<std::string>("ParticleNames" , std::vector<std::string>() ).getVector();
std::vector<std::string> monitorBranches = NamedParameter<std::string>("Monitors" , std::vector<std::string>() ).getVector();
std::vector<std::string> branchFormat = NamedParameter<std::string>("BranchFormat" , std::vector<std::string>() ).getVector();
- bool usePIDCalib = NamedParameter<bool>("usePIDCalib" , false );
- bool rejectMultipleCandidates = NamedParameter<bool>("rejectMultipleCandidates", true );
- std::string cuts = vectorToString( NamedParameter<std::string>("Cut","").getVector() , " && ");
+ std::vector<std::string> friends = NamedParameter<std::string>("Friends" , std::vector<std::string>() ).getVector();
+ std::vector<std::string> idBranches = NamedParameter<std::string>("IdBranches" , std::vector<std::string>() ).getVector();
+ bool usePIDCalib = NamedParameter<bool>("usePIDCalib" , false);
+ bool rejectMultipleCandidates = NamedParameter<bool>("rejectMultipleCandidates", true );
+ auto cuts = NamedParameter<std::string>("Cut","").getVector();
EventType evtType( NamedParameter<std::string>( "EventType" ).getVector() );
+
+ std::vector<std::string> branches;
+ for( auto& particle : particles ) for(auto& bf : branchFormat) branches.push_back( mysprintf(bf, particle.c_str()));
INFO( "Reading file " << inputFilename );
INFO( "Outputting file: " << outputFilename);
@@ -61,8 +65,11 @@ int main( int argc, char* argv[] )
TTree* in_tree = (TTree*)f->Get( treeName.c_str() );
in_tree->SetBranchStatus( "*", 1 );
+ for( auto& frie : friends ){
+ auto tokens = split( frie, ':');
+ in_tree->AddFriend( tokens[1].c_str(), tokens[0].c_str() );
+ }
- INFO( "Using cut = " << cuts );
if(inputFilename == "") FATAL("No input specified in options" );
if(treeName == "") FATAL("No tree specified in options" );
@@ -71,19 +78,16 @@ int main( int argc, char* argv[] )
if(in_tree == nullptr ) FATAL(treeName + " not found" );
INFO( "Got tree " << inputFilename << ":" << treeName );
-
- in_tree->Draw( ">>elist", cuts.c_str() );
+ std::string cut = "";
+ for( auto& i : cuts ) cut += i;
+ INFO( "Using cut = " << cut );
+
+ in_tree->Draw( ">>elist", cut.c_str() );
TEventList* elist = (TEventList*)gDirectory->Get( "elist" );
INFO( "Total efficiency = " << elist->GetN() / (double)in_tree->GetEntries() );
std::vector<size_t> eventsToTake;
- std::vector<std::string> branches;
- for( auto& particle : particles ) {
- for(size_t i = 0 ; i < 4; ++i ) branches.push_back( mysprintf(branchFormat[i], particle.c_str()));
- }
- for(auto& branch : monitorBranches) branches.push_back( branch );
-
if ( rejectMultipleCandidates ) {
ULong64_t totCandidate;
ULong64_t eventNumber;
@@ -125,7 +129,13 @@ int main( int argc, char* argv[] )
}
}
- EventList evts( in_tree, evtType, Branches(branches), EntryList(eventsToTake), GetGenPdf(false));
+ EventList evts( in_tree, evtType, Branches(branches),
+ EntryList(eventsToTake),
+ GetGenPdf(false),
+ ApplySym(true) ,
+ ExtraBranches(monitorBranches),
+ IdBranches(idBranches),
+ InputUnits(Units::MeV) );
INFO( "Branches = ["<< vectorToString(branches, ", " ) << "]" );
@@ -133,14 +143,14 @@ int main( int argc, char* argv[] )
INFO("Constructing eventList");
if ( motherID != "" ) {
+ bool neg = motherID[0] == '-';
INFO( "Converting " << evtType.mother() << " " << eventsToTake.size() << " " << evts.size() );
- in_tree->SetBranchStatus( "*", 0 );
+ TreeReader tr( in_tree );
int id = 0;
- in_tree->SetBranchStatus( motherID.c_str() );
- in_tree->SetBranchAddress( motherID.c_str(), &id );
+ tr.setBranch( neg ? motherID.substr(1, motherID.size() -1 ) : motherID, & id );
for ( unsigned int i = 0; i < eventsToTake.size(); ++i ) {
- in_tree->GetEntry( eventsToTake[i] );
- if ( id < 0 ) invertParity( evts[i] , evtType.size() );
+ tr.getEntry(eventsToTake[i] );
+ if ( neg ? id > 0 : id < 0 ) invertParity( evts[i] , evtType.size() );
}
}
@@ -177,18 +187,11 @@ int main( int argc, char* argv[] )
evts[i].setWeight( weight );
}
}
- evts.transform( [=](auto& event){ for( size_t i = 0 ; i < 4*evtType.size(); ++i ) event[i] /= 1000. ; } );
-
if ( pdfLibrary != "" ) {
INFO( "Setting generator level PDF from " << pdfLibrary );
- void* handle = dlopen( pdfLibrary.c_str(), RTLD_NOW );
- if ( handle == nullptr ) dlerror();
-
- DynamicFCN<double( const double*, const int& )> fcn( handle, "FCN" );
+ DynamicFCN<double( const double*, const int& )> fcn( pdfLibrary, "FCN" );
for ( unsigned int i = 0; i < evts.size(); ++i ) {
- if ( i % 500000 == 0 ) {
- INFO( "Set for " << i << " events" );
- }
+ if ( i % 500000 == 0 ) INFO( "Set for " << i << " events" );
evts[i].setGenPdf( fcn( (const real_t*)(evts[i]), 1 ) );
}
}
@@ -202,10 +205,15 @@ int main( int argc, char* argv[] )
INFO("Closing file...");
outputFile->Close();
TFile* outputPlotFile = TFile::Open( plotsName.c_str(), "RECREATE" );
- auto plots = evts.makeDefaultProjections();
- for ( auto& plot : plots ) {
- INFO( "Writing plot " << plot->GetName() << " to file" );
- plot->Write();
+ auto projections = evtType.defaultProjections();
+ for ( auto& p : projections ) {
+ p( evts ) -> Write();
+ // p( evts, WeightFunction([](auto& evt){ return 1; }), PlotOptions::Prefix("noweight") )->Write();
+ }
+ for( unsigned i = 0 ; i != evtType.size(); ++i )
+ {
+ Projection p( [i](auto& event){ return sqrt( event.s(i) ); }, "m_"+std::to_string(i), "m_"+std::to_string(i), 100, 0, 2.5 );
+ p(evts)->Write();
}
outputPlotFile->Close();
}
diff --git a/apps/Debugger.cpp b/apps/Debugger.cpp
index 411d1dc3fb7..35f65cccd0e 100644
--- a/apps/Debugger.cpp
+++ b/apps/Debugger.cpp
@@ -20,6 +20,7 @@
#include "AmpGen/ParticlePropertiesList.h"
#include "AmpGen/Utilities.h"
#include "TRandom3.h"
+#include "AmpGen/AddCPConjugate.h"
#ifdef _OPENMP
#include <omp.h>
@@ -33,6 +34,7 @@
#include "AmpGen/NamedParameter.h"
#include "AmpGen/PolarisedSum.h"
+
using namespace AmpGen;
void invertParity( Event& event, const size_t& nParticles)
@@ -45,71 +47,21 @@ void invertParity( Event& event, const size_t& nParticles)
}
}
-int invert_parameter( AmpGen::MinuitParameter* param, MinuitParameterSet& mps )
-{
- const std::string name = param->name();
- size_t pos = 0;
- std::string prefix = "";
- std::string new_name = name;
- int sgn = 1;
- if ( name.find( "::" ) != std::string::npos ) {
- pos = name.find( "::" );
- auto props = AmpGen::ParticlePropertiesList::get( name.substr( 0, pos ), true );
- if ( props != nullptr ) new_name = props->anti().name() + name.substr( pos );
- } else {
- auto tokens = split( name, '_' );
- std::string reOrIm = *tokens.rbegin();
- std::string prefix = "";
- std::string name = tokens[0];
- if ( tokens.size() == 3 ) {
- prefix = tokens[0];
- name = tokens[1];
- }
- if ( reOrIm == "Re" || reOrIm == "Im" ) {
- std::vector<std::string> final_state_ordering;
- AmpGen::Particle test( name, final_state_ordering );
- sgn = test.conjugate( true );
- if ( reOrIm == "Re" ) sgn = 1;
- new_name = ( prefix != "" ? prefix + "_" : "" ) + test.uniqueString() + "_" + reOrIm;
- } else if ( tokens.size() == 2 ) {
- auto props = AmpGen::ParticlePropertiesList::get( name );
- if ( props != nullptr ) new_name = props->anti().name() + "_" + tokens[1];
- }
- }
- DEBUG( param->name() << " → " << new_name << " sgn = " << sgn );
- mps.map().erase( param->name() );
- param->setName( new_name );
- mps.map().emplace( param->name(), param );
- if ( sgn == -1 ) param->setCurrentFitVal( param->mean() + M_PI );
- return sgn;
-}
-
-template <class MatrixElements> void print( const Event& event, const MatrixElements& matrixElements, bool verbose )
-{
- for ( auto& mE : matrixElements ) {
- INFO( mE.decayDescriptor() << " " << mE.coupling() );
- auto terms = mE.coupling.couplings;
- if ( verbose ) {
- for ( auto& term : terms ) {
- INFO( "--> " << term.first->name() << " = (" << term.first->mean() * cos( term.second->mean() ) << " + i " << term.first->mean() * sin( term.second->mean() ) << ")" );
- }
- mE.pdf.debug( event );
- }
- }
-}
-
template < class FCN > void debug( FCN& sig, EventList& accepted, bool verbose, TRandom3* rndm, MinuitParameterSet& mps ){
INFO("Debugging: ");
+ unsigned eventToDebug = 0;
sig.setEvents( accepted );
sig.prepare();
- sig.debug( accepted[0] );
- accepted[0].print();
- if( verbose ) print( accepted[0], sig.matrixElements(), verbose );
- invertParity(accepted[0], accepted.eventType().size() );
- accepted[0].print();
+ sig.debug( accepted[eventToDebug] );
+ accepted[eventToDebug].print();
+// if( verbose ) print( accepted[0], sig.matrixElements(), verbose );
+ for( unsigned int i = 0 ; i != accepted.size(); ++i )
+ invertParity(accepted[i], accepted.eventType().size() );
+ accepted[eventToDebug].print();
sig.reset();
+ sig.setEvents(accepted);
sig.prepare();
- sig.debug( accepted[0] );
+ sig.debug( accepted[eventToDebug] );
}
int main( int argc, char** argv )
@@ -119,16 +71,20 @@ int main( int argc, char** argv )
int seed = NamedParameter<int>( "Seed", 156 );
TRandom3* rndm = new TRandom3( seed );
- EventType eventType( NamedParameter<std::string>( "EventType" ).getVector() );
+ EventType eventType( NamedParameter<std::string>( "EventType" , "", "EventType to generate, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector(),
+ NamedParameter<bool>( "GenerateTimeDependent", false , "Flag to include possible time dependence of the amplitude") );
bool verbose = NamedParameter<bool>("CoherentSum::Debug", 0 ) ||
NamedParameter<bool>("PolarisedSum::Debug", 0 );
INFO("Using verbose mode: " << verbose );
AmpGen::MinuitParameterSet MPS;
MPS.loadFromStream();
- if ( NamedParameter<bool>( "conj", false ) == true ) {
- eventType = eventType.conj( false );
- for ( auto& param : MPS ) invert_parameter( param, MPS );
+
+ if ( NamedParameter<bool>( "conj", false ) == true )
+ {
+ eventType = eventType.conj();
+ INFO( eventType );
+ AddCPConjugate(MPS);
}
INFO( "EventType = " << eventType );
@@ -136,13 +92,17 @@ int main( int argc, char** argv )
EventList accepted = infile == "" ? EventList( eventType ) : EventList( infile, eventType );
std::string input_units = NamedParameter<std::string>("Units","GeV");
- if( input_units == "MeV" && infile != "") accepted.transform([](auto& event){ for( int i = 0;i<16;++i) event[i]/=1000; } );
+ if( input_units == "MeV" && infile != "") accepted.transform([](auto& event){ for( unsigned i = 0;i< event.size();++i) event[i]/=1000; } );
if( infile == "" ){
- Event evt = PhaseSpace( eventType, rndm ).makeEvent();
- accepted.push_back(evt);
+ for( unsigned i = 0 ; i != 16; ++i ){
+ Event evt = PhaseSpace( eventType, rndm ).makeEvent();
+ evt.setIndex(i);
+ accepted.push_back(evt);
+ }
}
- accepted[0].print();
-
+ std::vector<double> event = NamedParameter<double>("Event",0).getVector();
+ if( event.size() != 1 ) accepted[0].set( event.data() );
+
std::string type = NamedParameter<std::string>("Type","CoherentSum");
if( type == "PolarisedSum")
@@ -158,7 +118,7 @@ int main( int argc, char** argv )
{
CoherentSum sig(eventType, MPS);
debug(sig, accepted, verbose, rndm, MPS);
- print(accepted[0], sig.matrixElements() , false);
+ // print(accepted[0], sig.matrixElements() , false);
INFO( "A(x) = " << sig.getValNoCache( accepted[0] ) );
}
else {
diff --git a/apps/Fitter.cpp b/apps/Fitter.cpp
index 406c20071ee..52ef74f1ad1 100644
--- a/apps/Fitter.cpp
+++ b/apps/Fitter.cpp
@@ -10,7 +10,6 @@
#include <vector>
#include "AmpGen/Chi2Estimator.h"
-#include "AmpGen/CoherenceFactor.h"
#include "AmpGen/ErrorPropagator.h"
#include "AmpGen/EventList.h"
#include "AmpGen/EventType.h"
@@ -29,13 +28,20 @@
#include "AmpGen/ThreeBodyCalculators.h"
#include "AmpGen/Utilities.h"
#include "AmpGen/Generator.h"
-#include "AmpGen/Plots.h"
#ifdef _OPENMP
#include <omp.h>
#include <thread>
#endif
+#if ENABLE_AVX2
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_type = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_type = AmpGen::EventList;
+#endif
+
#include "TFile.h"
#include "TRandom3.h"
@@ -52,25 +58,13 @@ std::vector<ThreeBodyCalculator> threeBodyCalculators( MinuitParameterSet& mps )
void randomizeStartingPoint( MinuitParameterSet& MPS, TRandom3& rand, bool SplineOnly = false )
{
double range = 5;
- for ( unsigned int i = 0; i < MPS.size(); ++i ) {
- auto param = MPS.getParPtr( i );
- if ( param->iFixInit() == 0 ) {
- if ( SplineOnly && param->name().find( "::Spline::" ) == std::string::npos ) continue;
- range = param->maxInit() - param->minInit();
- MPS.getParPtr( i )->setInit( range * rand.Rndm() + param->meanInit() );
- MPS.getParPtr( i )->print();
- std::cout << std::endl;
- }
- }
-}
-
-unsigned int count_amplitudes( const AmpGen::MinuitParameterSet& mps )
-{
- unsigned int counter = 0;
- for ( auto param = mps.cbegin(); param != mps.cend(); ++param ) {
- if ( ( *param )->name().find( "_Re" ) != std::string::npos ) counter++;
+ for (auto& param : MPS) {
+ if ( ! param->isFree() == 0 ) continue;
+ if ( SplineOnly && param->name().find( "::Spline::" ) == std::string::npos ) continue;
+ range = param->maxInit() - param->minInit();
+ param->setInit( range * rand.Rndm() + param->meanInit() );
+ std::cout << *param << std::endl;
}
- return counter;
}
template <typename SIGPDF>
@@ -93,11 +87,9 @@ void addExtendedTerms( Minimiser& mini, SIGPDF& pdf, MinuitParameterSet& mps )
template <typename PDF>
FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet& MPS )
{
- INFO( "Type = " << typeof<PDF>() );
-
+ INFO( "Type = " << type_string<PDF>() );
auto time_wall = std::chrono::high_resolution_clock::now();
auto time = std::clock();
-
pdf.setEvents( data );
Minimiser mini( pdf, &MPS );
@@ -112,11 +104,10 @@ FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet&
std::vector<MinuitParameter*> slowParamPtrs;
if ( nIterations != 0 ) {
for ( auto& param : SlowParams ) {
- auto mps_map = MPS.map();
- auto it = mps_map.find( param );
- if ( it != mps_map.end() ) {
- slowParamPtrs.push_back( it->second );
- it->second->fix();
+ auto it = MPS.find( param );
+ if ( it != nullptr ) {
+ slowParamPtrs.push_back( it );
+ it->fix();
} else {
WARNING( "Trying to release non-existent parameter: " << param );
}
@@ -138,13 +129,9 @@ FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet&
auto ep = fr->getErrorPropagator();
unsigned int counter = 1;
- for_each( pdf.m_pdfs, [&]( auto& f ) {
- std::function<double(const Event&)> FCN_sig =
- [&](const Event& evt){ return f.prob_unnormalised(evt) ; };
+ for_each( pdf.pdfs(), [&]( auto& f ) {
auto tStartIntegral2 = std::chrono::high_resolution_clock::now();
- auto mc_plot3 = mc.makeProjections( mc.eventType().defaultProjections(100), WeightFunction(f), Prefix("tMC_Category"+std::to_string(counter) ) );
-
- // auto mc_plot3 = bandPlot<100>( mc, "tMC_Category" + std::to_string( counter ) + "_", f, ep );
+ auto mc_plot3 = mc.makeProjections( mc.eventType().defaultProjections(100), WeightFunction(f), PlotOptions::Prefix("tMC_Category"+std::to_string(counter) ) );
auto tEndIntegral2 = std::chrono::high_resolution_clock::now();
double t2 = std::chrono::duration<double, std::milli>( tEndIntegral2 - tStartIntegral2 ).count();
INFO( "Time for plots = " << t2 );
@@ -156,7 +143,7 @@ FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet&
counter++;
} );
}
- Chi2Estimator chi2( data, mc, pdf, 15 );
+ Chi2Estimator chi2( data, mc, pdf, MinEvents(15) );
fr->addChi2( chi2.chi2(), chi2.nBins() );
auto twall_end = std::chrono::high_resolution_clock::now();
@@ -209,7 +196,7 @@ int main( int argc, char* argv[] )
if ( perturb ) {
for ( auto& param : MPS ) {
- if ( param->iFixInit() != 0 ) continue;
+ if ( !param->isFree() ) continue;
param->setCurrentFitVal( rndm.Gaus( param->mean(), param->err() ) );
}
}
@@ -230,14 +217,16 @@ int main( int argc, char* argv[] )
const std::string cut = NamedParameter<std::string>( "Cut", "1" );
const std::string simCut = NamedParameter<std::string>( "SimCut", "1" );
bool BAR = NamedParameter<bool>("Bar",false);
- size_t defaultCacheSize = count_amplitudes( MPS );
-
- EventList events( dataFile, !BAR ? evtType : evtType.conj() , CacheSize(defaultCacheSize), Filter(cut) );
- EventList eventsMC = mcFile == "" ? EventList( evtType) : EventList( mcFile, !BAR ? evtType : evtType.conj() , CacheSize(defaultCacheSize), Filter(simCut) ) ;
- auto scale_transform = [](auto& event){ for( size_t x = 0 ; x < event.size(); ++x ) event[x] /= 1000.; };
- INFO("Changing units from MeV -> GeV");
- events.transform( scale_transform );
- eventsMC.transform( scale_transform );
+
+ EventList events( dataFile, !BAR ? evtType : evtType.conj() , Filter(cut) );
+ EventList eventsMC = mcFile == "" ? EventList( evtType) : EventList( mcFile, !BAR ? evtType : evtType.conj(), Filter(simCut) ) ;
+
+ auto scale_transform = [](auto& event){ for( size_t x = 0 ; x < event.size(); ++x ) event[x] /= 1000.; };
+ if( NamedParameter<std::string>("Units", "GeV").getVal() == "MeV") {
+ INFO("Changing units from MeV -> GeV");
+ events.transform( scale_transform );
+ }
+ eventsMC.transform( scale_transform );
INFO( "Data events: " << events.size() );
INFO( "MC events : " << eventsMC.size() );
@@ -286,7 +275,7 @@ int main( int argc, char* argv[] )
fr->writeToFile( logFile );
output->cd();
- auto plots = events.makeDefaultProjections( Prefix( "Data_" ), Bins( NBins ) );
+ auto plots = events.makeDefaultProjections( PlotOptions::Prefix( "Data_" ), PlotOptions::Bins( NBins ) );
for ( auto& plot : plots ) plot->Write();
output->Write();
diff --git a/apps/Generator.cpp b/apps/Generator.cpp
deleted file mode 100644
index a80592dfa41..00000000000
--- a/apps/Generator.cpp
+++ /dev/null
@@ -1,149 +0,0 @@
-#include <Rtypes.h>
-#include <TH1.h>
-#include <dlfcn.h>
-#include <memory>
-#include <string>
-
-#include "TFile.h"
-#include "TRandom3.h"
-#include "TTree.h"
-
-#ifdef _OPENMP
-#include <omp.h>
-#include <thread>
-#endif
-
-#include "AmpGen/DynamicFCN.h"
-#include "AmpGen/EventList.h"
-#include "AmpGen/MsgService.h"
-#include "AmpGen/Particle.h"
-#include "AmpGen/RecursivePhaseSpace.h"
-#include "AmpGen/Utilities.h"
-#include "AmpGen/EventType.h"
-#include "AmpGen/CoherentSum.h"
-#include "AmpGen/Generator.h"
-#include "AmpGen/MinuitParameterSet.h"
-#include "AmpGen/NamedParameter.h"
-#include "AmpGen/PolarisedSum.h"
-#include "AmpGen/OptionsParser.h"
-
-using namespace AmpGen;
-
-struct FixedLibPDF {
- void* lib;
- AmpGen::DynamicFCN<double( const double*, int )> PDF;
-
- void prepare(){};
- void setEvents( AmpGen::EventList& evts ){};
- double prob_unnormalised( const AmpGen::Event& evt ) const { return PDF( evt, 1 ); }
- FixedLibPDF( const std::string& lib )
- {
- void* handle = dlopen( lib.c_str(), RTLD_NOW );
- if ( handle == nullptr ) ERROR( dlerror() );
- PDF = AmpGen::DynamicFCN<double( const double*, int )>( handle, "FCN" );
- }
- size_t size() { return 0; }
- void reset( const bool& flag = false ){};
-};
-
-template <class PDF_TYPE, class PRIOR_TYPE>
- void GenerateEvents( EventList& events
- , PDF_TYPE& pdf
- , PRIOR_TYPE& prior
- , const size_t& nEvents
- , const size_t& blockSize
- , TRandom* rndm )
-{
- Generator<PRIOR_TYPE> signalGenerator( prior );
- signalGenerator.setRandom( rndm);
- signalGenerator.setBlockSize( blockSize );
- signalGenerator.fillEventList( pdf, events, nEvents );
-}
-
-int main( int argc, char** argv )
-{
- OptionsParser::setArgs( argc, argv );
-
- size_t nEvents = NamedParameter<size_t> ("nEvents" , 1, "Total number of events to generate" );
- size_t blockSize = NamedParameter<size_t> ("BlockSize", 100000, "Number of events to generate per block" );
- int seed = NamedParameter<int> ("Seed" , 0, "Random seed used in event Generation" );
- std::string outfile = NamedParameter<std::string>("Output" , "Generate_Output.root" , "Name of output file" );
-
- std::string gen_type = NamedParameter<std::string>( "Type", "CoherentSum", optionalHelpString("Generator configuration to use:",
- { {"CoherentSum", "Full phase-space generator with (pseudo)scalar amplitude"}
- , {"PolarisedSum", "Full phase-space generator with particles carrying spin in the initial/final states"}
- , {"FixedLib", "Full phase-space generator with an amplitude from a precompiled library"}
- , {"RGenerator", "Recursive phase-space generator for intermediate (quasi)stable states such as the D-mesons"} } ) );
-
- std::string lib = NamedParameter<std::string>("Library","","Name of library to use for a fixed library generation");
- size_t nBins = NamedParameter<size_t> ("nBins" ,100, "Number of bins for monitoring plots." );
-
- #ifdef _OPENMP
- unsigned int concurentThreadsSupported = std::thread::hardware_concurrency();
- unsigned int nCores = NamedParameter<unsigned int>( "nCores", concurentThreadsSupported, "Number of cores to use (OpenMP only)" );
- omp_set_num_threads( nCores );
- omp_set_dynamic( 0 );
- #endif
-
- TRandom3 rand;
- rand.SetSeed( seed + 934534 );
-
- MinuitParameterSet MPS;
- MPS.loadFromStream();
-
- Particle p;
-
- EventType eventType( NamedParameter<std::string>( "EventType" , "", "EventType to generate, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector(),
- NamedParameter<bool>( "GenerateTimeDependent", false , "Flag to include possible time dependence of the amplitude") );
-
- EventList accepted( eventType );
-
- INFO("Generating events with type = " << eventType );
-
- if ( gen_type == "CoherentSum" ) {
- CoherentSum sig( eventType, MPS );
- PhaseSpace phsp(eventType,&rand);
- GenerateEvents( accepted, sig, phsp , nEvents, blockSize, &rand );
- }
- else if ( gen_type == "PolarisedSum" ){
- PolarisedSum sig( eventType, MPS );
- RecursivePhaseSpace phsp( sig.matrixElements()[0].decayTree.quasiStableTree() , eventType, &rand );
- GenerateEvents( accepted, sig, phsp, nEvents, blockSize, &rand );
- }
- else if ( gen_type == "RGenerator" ) {
- CoherentSum sig( eventType, MPS, "" );
- Generator<RecursivePhaseSpace> signalGenerator( sig[0].decayTree.quasiStableTree(), eventType );
- signalGenerator.setRandom( &rand );
- signalGenerator.fillEventList( sig, accepted, nEvents );
- }
- else if ( gen_type == "FixedLib" ) {
- Generator<> signalGenerator( eventType );
- signalGenerator.setRandom( &rand );
- signalGenerator.setBlockSize( blockSize );
- signalGenerator.setNormFlag( false );
- FixedLibPDF pdf( lib );
- signalGenerator.fillEventList( pdf, accepted, nEvents );
- }
- else {
- ERROR("Did not recognise configuration: " << gen_type );
- }
- if( accepted.size() == 0 ) return -1;
- TFile* f = TFile::Open( outfile.c_str(), "RECREATE" );
- accepted.tree( "DalitzEventList" )->Write();
- auto plots = accepted.makeDefaultProjections(Bins(nBins), LineColor(kBlack));
- for ( auto& plot : plots ) plot->Write();
- if( NamedParameter<bool>("plots_2d",true) == true ){
- auto proj = eventType.defaultProjections(nBins);
- INFO("Making 2D projections...");
- for( size_t i = 0 ; i < proj.size(); ++i ){
- for( size_t j = i+1 ; j < proj.size(); ++j ){
-
- accepted.makeProjection( Projection2D(proj[i],proj[j] ) )->Write();
- }
- }
- }
-
- INFO( "Writing output file " );
-
- f->Close();
-}
diff --git a/apps/LibDiff.cpp b/apps/LibDiff.cpp
new file mode 100644
index 00000000000..344f87b20ea
--- /dev/null
+++ b/apps/LibDiff.cpp
@@ -0,0 +1,121 @@
+#include "AmpGen/PhaseSpace.h"
+#include "AmpGen/DynamicFCN.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/OptionsParser.h"
+#include "AmpGen/NamedParameter.h"
+
+using namespace AmpGen;
+
+std::vector<std::string> cmd( const std::string& command ){
+ std::vector<std::string> output;
+ FILE* proc = popen(command.c_str(), "r");
+ char buf[4096];
+ while (!feof(proc) && fgets(buf, sizeof(buf), proc)) output.push_back(buf);
+ pclose(proc);
+ return output;
+}
+
+struct Counter {
+ int pass {0};
+ int total{0};
+ Counter() = default;
+ Counter( const bool& pass ) : pass(pass), total(1) {}
+ Counter( const double& a, const double& b, const std::string& name, const double& tolerance );
+ Counter( const complex_t& a, const complex_t& b, const std::string& name, const double& tolerance );
+ Counter(const std::vector<complex_t>& a, const std::vector<complex_t>& b, const std::string& name, const double& tolerance);
+ void operator+=( const Counter& other )
+ {
+ this->pass += other.pass;
+ this->total += other.total;
+ }
+
+};
+
+Counter::Counter(const double& a, const double& b, const std::string& name, const double& tolerance)
+{
+ double diff = std::abs(a-b);
+ total = 1;
+ if( diff > std::abs(tolerance) ){
+ ERROR( name << " (" << a << " " << b << ") = " << diff << " > " << tolerance);
+ pass = 0;
+ }
+ else pass =1;
+ DEBUG( name << " (" << a << " " << b << ") = " << diff << " > " << tolerance);
+}
+
+Counter::Counter(const complex_t& a, const complex_t& b, const std::string& name, const double& tolerance)
+{
+ double diff_re = std::abs(std::real(a)-std::real(b));
+ double diff_im = std::abs(std::imag(a)-std::imag(b));
+ total =1;
+ if( diff_re > std::abs(tolerance) || diff_im > std::abs(tolerance) ){
+ ERROR( name << " (" << a << " " << b << ") = " << diff_re << ", " << diff_im << " > " << tolerance);
+ pass =0;
+ }
+ else pass = 1;
+ DEBUG( name << " (" << a << " " << b << ") = " << diff_re << ", " << diff_im << " < " << tolerance);
+}
+
+Counter::Counter(const std::vector<complex_t>& a, const std::vector<complex_t>& b, const std::string& name, const double& tolerance)
+{
+ total = a.size();
+ for( size_t i = 0 ; i < a.size(); ++i ){
+ double diff_re = std::abs(std::real(a[i])-std::real(b[i]));
+ double diff_im = std::abs(std::imag(a[i])-std::imag(b[i]));
+ if( diff_re > std::abs(tolerance) || diff_im > std::abs(tolerance) ){
+ ERROR( name << " (" << a[i] << " " << b[i] << ") = " << diff_re << ", " << diff_im << " > " << tolerance);
+ }
+ else pass++;
+ DEBUG( name << " (" << a[i] << " " << b[i] << ") = " << diff_re << ", " << diff_im << " > " << tolerance);
+ }
+}
+
+int main( int argc, char** argv )
+{
+ std::string modelName = argv[1];
+ OptionsParser::getMe()->setQuiet();
+ OptionsParser::setArgs( argc, argv );
+ PhaseSpace phsp( EventType(NamedParameter<std::string>("EventType", "").getVector()) );
+ auto event = phsp.makeEvent();
+ auto event2 = phsp.makeEvent();
+ std::string lib = NamedParameter<std::string>("Lib","");
+ std::string refLib = NamedParameter<std::string>("RefLib","");
+ std::string type = NamedParameter<std::string>("Type","CoherentSum");
+ Counter total;
+
+ auto ftable = cmd("nm " + refLib + "| grep __wParams");
+ if( type == "CoherentSum"){
+ auto f1 = DynamicFCN<complex_t(const double*, const int&)>(lib, "AMP");
+ auto f2 = DynamicFCN<complex_t(const double*, const int&)>(refLib, "AMP");
+ total += Counter(f1(event,+1), f2(event,+1), modelName + " fcn(x)", 10e-6 );
+ total += Counter(f1(event,-1), f2(event,-1), modelName + " fcn(Px)", 10e-6);
+ for( auto& line : ftable )
+ {
+ auto i = trim( split(line,' ')[2] );
+ auto f = DynamicFCN<complex_t(const double*)>(lib, i );
+ auto g = DynamicFCN<complex_t(const double*)>(refLib, i );
+ if( !f.isLinked() || !g.isLinked() ) total += false ;
+ else total += Counter( f(event), g(event), i, 10e-6);
+ }
+ }
+ if( type == "PolarisedSum"){
+ auto f1 = DynamicFCN<double(const double*, const int&, const double&, const double&, const double&)>(lib , "FCN_extPol");
+ auto f2 = DynamicFCN<double(const double*, const int&, const double&, const double&, const double&)>(refLib, "FCN_extPol");
+ total += Counter(f1(event,+1,0,0,0), f2(event,+1,0,0,0), modelName + " fcn(x)" , 1e-6);
+ total += Counter(f1(event,-1,0,0,0), f2(event,-1,0,0,0), modelName + " fcn(Px)", 1e-6);
+ for( auto& line : ftable ){
+ auto i = trim( split(line,' ')[2] );
+ auto a1 = DynamicFCN<std::vector<complex_t>(const double*)>(lib , i );
+ auto a2 = DynamicFCN<std::vector<complex_t>(const double*)>(refLib, i );
+ if( ! a1.isLinked() || ! a2.isLinked() ) total += false;
+ else {
+ auto pass = Counter(a1(event), a2(event), i, 10e-6);
+ total += pass;
+ }
+ }
+ }
+ if(total.pass == total.total)
+ INFO("Library: " << modelName << " matches [passed = " << total.pass << " / " << total.total << "]" );
+ else
+ ERROR("Library: " << modelName << " does not match [passed = " << total.pass << " / " << total.total << "]" );
+}
diff --git a/doc/doxyfile b/doc/doxyfile
index 851d07e57da..f9b12378de2 100644
--- a/doc/doxyfile
+++ b/doc/doxyfile
@@ -33,14 +33,13 @@ DOXYFILE_ENCODING = UTF-8
# The default value is: My Project.
PROJECT_NAME = "AmpGen"
-PROJECT_NUMBER = 1.1
+PROJECT_NUMBER = 1.2
PROJECT_BRIEF =
PROJECT_LOGO = "figs/logo_small.png"
-OUTPUT_DIRECTORY = "../build/"
LAYOUT_FILE = "DoxygenLayout.xml"
HTML_EXTRA_STYLESHEET = "customdoxygen.css"
-INPUT = "../AmpGen" "../README.md"
-USE_MDFILE_AS_MAINPAGE = "../README.md"
+INPUT = "../AmpGen" "../README.tex.md"
+USE_MDFILE_AS_MAINPAGE = "../README.tex.md"
IMAGE_PATH = "figs/"
# If the CREATE_SUBDIRS tag is set to YES, then doxygen will create 4096 sub-
@@ -1248,7 +1247,7 @@ MAN_LINKS = NO
# captures the structure of the code including all documentation.
# The default value is: NO.
-GENERATE_XML = NO
+GENERATE_XML = YES
# The XML_OUTPUT tag is used to specify where the XML pages will be put. If a
# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
diff --git a/doc/figs/k3pi_s01.svg b/doc/figs/k3pi_s01.svg
new file mode 100644
index 00000000000..8aa81f430ac
--- /dev/null
+++ b/doc/figs/k3pi_s01.svg
@@ -0,0 +1,593 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="506pt" height="432pt" viewBox="0 0 506 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.515625 -1.203125 C 4.515625 -1.859375 3.953125 -2.375 3.34375 -2.375 C 2.625 -2.375 2.140625 -1.8125 2.140625 -1.203125 C 2.140625 -0.46875 2.75 0 3.3125 0 C 3.96875 0 4.515625 -0.515625 4.515625 -1.203125 Z M 4.515625 -1.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 8.859375 -15.96875 C 8.859375 -16.4375 8.859375 -16.5625 8.515625 -16.5625 C 8.3125 -16.5625 8.25 -16.5625 8.046875 -16.265625 L 0.65625 -4.8125 L 0.65625 -4.09375 L 7.109375 -4.09375 L 7.109375 -1.859375 C 7.109375 -0.953125 7.0625 -0.71875 5.28125 -0.71875 L 4.78125 -0.71875 L 4.78125 0 C 5.34375 -0.046875 7.28125 -0.046875 7.96875 -0.046875 C 8.65625 -0.046875 10.625 -0.046875 11.1875 0 L 11.1875 -0.71875 L 10.703125 -0.71875 C 8.921875 -0.71875 8.859375 -0.953125 8.859375 -1.859375 L 8.859375 -4.09375 L 11.328125 -4.09375 L 11.328125 -4.8125 L 8.859375 -4.8125 Z M 7.234375 -14.0625 L 7.234375 -4.8125 L 1.28125 -4.8125 Z M 7.234375 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-10">
+<path style="stroke:none;" d="M 3.015625 -8.53125 C 3.015625 -14.75 6.03125 -15.71875 7.359375 -15.71875 C 8.25 -15.71875 9.125 -15.453125 9.59375 -14.71875 C 9.296875 -14.71875 8.359375 -14.71875 8.359375 -13.71875 C 8.359375 -13.171875 8.734375 -12.703125 9.375 -12.703125 C 9.984375 -12.703125 10.40625 -13.078125 10.40625 -13.78125 C 10.40625 -15.0625 9.46875 -16.3125 7.328125 -16.3125 C 4.25 -16.3125 1 -13.15625 1 -7.75 C 1 -1 3.953125 0.515625 6.03125 0.515625 C 8.703125 0.515625 10.984375 -1.8125 10.984375 -5 C 10.984375 -8.265625 8.703125 -10.453125 6.25 -10.453125 C 4.078125 -10.453125 3.265625 -8.5625 3.015625 -7.875 Z M 6.03125 -0.140625 C 4.484375 -0.140625 3.75 -1.515625 3.53125 -2.03125 C 3.3125 -2.671875 3.0625 -3.875 3.0625 -5.59375 C 3.0625 -7.53125 3.953125 -9.953125 6.15625 -9.953125 C 7.5 -9.953125 8.21875 -9.046875 8.59375 -8.21875 C 8.984375 -7.3125 8.984375 -6.078125 8.984375 -5.03125 C 8.984375 -3.78125 8.984375 -2.671875 8.515625 -1.734375 C 7.90625 -0.5625 7.015625 -0.140625 6.03125 -0.140625 Z M 6.03125 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-11">
+<path style="stroke:none;" d="M 7.3125 -8.859375 C 8.53125 -9.515625 10.328125 -10.640625 10.328125 -12.703125 C 10.328125 -14.84375 8.265625 -16.3125 6.015625 -16.3125 C 3.578125 -16.3125 1.671875 -14.515625 1.671875 -12.296875 C 1.671875 -11.453125 1.90625 -10.625 2.59375 -9.78125 C 2.875 -9.46875 2.890625 -9.4375 4.609375 -8.25 C 2.234375 -7.140625 1 -5.5 1 -3.703125 C 1 -1.109375 3.484375 0.515625 5.984375 0.515625 C 8.703125 0.515625 10.984375 -1.5 10.984375 -4.078125 C 10.984375 -6.578125 9.21875 -7.671875 7.3125 -8.859375 Z M 3.96875 -11.0625 C 3.65625 -11.28125 2.671875 -11.921875 2.671875 -13.125 C 2.671875 -14.71875 4.34375 -15.71875 5.984375 -15.71875 C 7.75 -15.71875 9.328125 -14.453125 9.328125 -12.6875 C 9.328125 -11.1875 8.25 -9.984375 6.8125 -9.203125 Z M 5.125 -7.90625 L 8.09375 -5.96875 C 8.734375 -5.546875 9.859375 -4.78125 9.859375 -3.28125 C 9.859375 -1.421875 7.96875 -0.140625 6.015625 -0.140625 C 3.921875 -0.140625 2.140625 -1.671875 2.140625 -3.703125 C 2.140625 -5.625 3.53125 -7.15625 5.125 -7.90625 Z M 5.125 -7.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 8.78125 -6.5625 C 8.765625 -6.609375 8.671875 -6.765625 8.671875 -6.78125 C 8.671875 -6.8125 8.953125 -7.015625 9.125 -7.125 C 10.40625 -8.078125 12.171875 -9.34375 12.71875 -9.6875 C 13.546875 -10.21875 14.15625 -10.5625 14.890625 -10.625 C 15.015625 -10.640625 15.25 -10.65625 15.25 -10.953125 C 15.234375 -11.0625 15.140625 -11.15625 15.015625 -11.15625 C 15 -11.15625 14.546875 -11.109375 14.4375 -11.109375 L 13.78125 -11.109375 C 13.5 -11.109375 13.09375 -11.109375 12.9375 -11.125 C 12.828125 -11.125 12.1875 -11.15625 12.078125 -11.15625 C 11.96875 -11.15625 11.734375 -11.15625 11.734375 -10.859375 C 11.734375 -10.84375 11.75 -10.640625 12 -10.625 C 12.125 -10.609375 12.390625 -10.578125 12.390625 -10.375 C 12.390625 -10.109375 12.0625 -9.84375 12.03125 -9.828125 L 11.890625 -9.703125 C 11.84375 -9.65625 11.78125 -9.59375 11.703125 -9.546875 L 5.03125 -4.703125 L 6.328125 -9.890625 C 6.46875 -10.46875 6.5 -10.625 7.703125 -10.625 C 8.03125 -10.625 8.21875 -10.625 8.21875 -10.9375 C 8.21875 -10.953125 8.203125 -11.15625 7.9375 -11.15625 C 7.625 -11.15625 7.234375 -11.125 6.9375 -11.109375 L 5.90625 -11.109375 C 4.328125 -11.109375 3.90625 -11.15625 3.796875 -11.15625 C 3.703125 -11.15625 3.46875 -11.15625 3.46875 -10.859375 C 3.46875 -10.625 3.65625 -10.625 3.9375 -10.625 C 4.484375 -10.625 4.953125 -10.625 4.953125 -10.359375 C 4.953125 -10.296875 4.9375 -10.28125 4.890625 -10.0625 L 2.703125 -1.296875 C 2.546875 -0.671875 2.515625 -0.546875 1.3125 -0.546875 C 1 -0.546875 0.796875 -0.546875 0.796875 -0.234375 C 0.796875 -0.15625 0.84375 0 1.0625 0 C 1.375 0 1.765625 -0.03125 2.078125 -0.046875 L 4.1875 -0.046875 C 4.453125 -0.03125 4.984375 0 5.234375 0 C 5.3125 0 5.5625 0 5.5625 -0.296875 C 5.5625 -0.546875 5.359375 -0.546875 5.078125 -0.546875 C 4.96875 -0.546875 4.734375 -0.546875 4.46875 -0.578125 C 4.125 -0.609375 4.0625 -0.640625 4.0625 -0.796875 C 4.0625 -0.90625 4.1875 -1.3125 4.234375 -1.5625 L 4.859375 -4.03125 L 7.484375 -5.9375 L 9.453125 -1.890625 C 9.515625 -1.765625 9.6875 -1.40625 9.75 -1.265625 C 9.859375 -1.09375 9.859375 -1.0625 9.859375 -1 C 9.859375 -0.5625 9.25 -0.546875 9.078125 -0.546875 C 8.90625 -0.546875 8.671875 -0.546875 8.671875 -0.234375 C 8.671875 -0.21875 8.6875 0 8.953125 0 C 9.125 0 9.734375 -0.03125 9.890625 -0.046875 L 10.84375 -0.046875 C 12.34375 -0.046875 12.296875 0 12.5 0 C 12.5625 0 12.8125 0 12.8125 -0.3125 C 12.8125 -0.546875 12.578125 -0.546875 12.484375 -0.546875 C 11.84375 -0.5625 11.640625 -0.671875 11.375 -1.21875 Z M 8.78125 -6.5625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 4.640625 -5.96875 L 6.515625 -5.96875 C 6.171875 -4.484375 5.890625 -3.265625 5.890625 -2.0625 C 5.890625 -1.9375 5.890625 -1.234375 6.0625 -0.65625 C 6.28125 0.03125 6.4375 0.15625 6.734375 0.15625 C 7.09375 0.15625 7.46875 -0.140625 7.46875 -0.546875 C 7.46875 -0.65625 7.453125 -0.6875 7.390625 -0.828125 C 7.046875 -1.578125 6.796875 -2.375 6.796875 -3.703125 C 6.796875 -4.09375 6.796875 -4.765625 7.046875 -5.96875 L 9.015625 -5.96875 C 9.28125 -5.96875 9.46875 -5.96875 9.625 -6.09375 C 9.828125 -6.28125 9.875 -6.484375 9.875 -6.59375 C 9.875 -7.046875 9.46875 -7.046875 9.1875 -7.046875 L 3.28125 -7.046875 C 2.9375 -7.046875 2.328125 -7.046875 1.515625 -6.265625 C 0.9375 -5.671875 0.46875 -4.921875 0.46875 -4.8125 C 0.46875 -4.65625 0.59375 -4.609375 0.71875 -4.609375 C 0.875 -4.609375 0.921875 -4.65625 1.015625 -4.78125 C 1.8125 -5.96875 2.78125 -5.96875 3.15625 -5.96875 L 4.109375 -5.96875 C 3.625 -4.234375 2.765625 -2.25 2.15625 -1.0625 C 2.046875 -0.8125 1.875 -0.484375 1.875 -0.34375 C 1.875 0 2.15625 0.15625 2.421875 0.15625 C 3.046875 0.15625 3.203125 -0.453125 3.546875 -1.796875 Z M 4.640625 -5.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 6.046875 -2.75 L 10.015625 -2.75 C 10.1875 -2.75 10.484375 -2.75 10.484375 -3.0625 C 10.484375 -3.390625 10.1875 -3.390625 10.015625 -3.390625 L 6.046875 -3.390625 L 6.046875 -7.359375 C 6.046875 -7.53125 6.046875 -7.84375 5.734375 -7.84375 C 5.40625 -7.84375 5.40625 -7.53125 5.40625 -7.359375 L 5.40625 -3.390625 L 1.453125 -3.390625 C 1.28125 -3.390625 0.96875 -3.390625 0.96875 -3.0625 C 0.96875 -2.75 1.28125 -2.75 1.453125 -2.75 L 5.40625 -2.75 L 5.40625 1.234375 C 5.40625 1.390625 5.40625 1.703125 5.734375 1.703125 C 6.046875 1.703125 6.046875 1.390625 6.046875 1.234375 Z M 6.046875 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 9.765625 -2.75 C 9.953125 -2.75 10.265625 -2.75 10.265625 -3.0625 C 10.265625 -3.390625 9.953125 -3.390625 9.765625 -3.390625 L 2.03125 -3.390625 C 1.84375 -3.390625 1.53125 -3.390625 1.53125 -3.0625 C 1.53125 -2.75 1.84375 -2.75 2.03125 -2.75 Z M 9.765625 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-11">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-12">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-13">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph10-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 91.055656 80.408937 C 91.055656 81.069094 90.5205 81.60425 89.860344 81.60425 C 89.200187 81.60425 88.661125 81.069094 88.661125 80.408937 C 88.661125 79.748781 89.200187 79.213625 89.860344 79.213625 C 90.5205 79.213625 91.055656 79.748781 91.055656 80.408937 Z M 91.055656 80.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 95.186281 C 95.250969 95.846437 94.715812 96.381594 94.055656 96.381594 C 93.3955 96.381594 92.856437 95.846437 92.856437 95.186281 C 92.856437 94.526125 93.3955 93.987062 94.055656 93.987062 C 94.715812 93.987062 95.250969 94.526125 95.250969 95.186281 Z M 95.250969 95.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.446281 101.862062 C 99.446281 102.522219 98.911125 103.057375 98.250969 103.057375 C 97.590812 103.057375 97.05175 102.522219 97.05175 101.862062 C 97.05175 101.198 97.590812 100.662844 98.250969 100.662844 C 98.911125 100.662844 99.446281 101.198 99.446281 101.862062 Z M 99.446281 101.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 103.641594 108.194094 C 103.641594 108.85425 103.106437 109.389406 102.446281 109.389406 C 101.786125 109.389406 101.247062 108.85425 101.247062 108.194094 C 101.247062 107.533937 101.786125 106.994875 102.446281 106.994875 C 103.106437 106.994875 103.641594 107.533937 103.641594 108.194094 Z M 103.641594 108.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.836906 111.362062 C 107.836906 112.022219 107.30175 112.557375 106.641594 112.557375 C 105.981437 112.557375 105.442375 112.022219 105.442375 111.362062 C 105.442375 110.698 105.981437 110.162844 106.641594 110.162844 C 107.30175 110.162844 107.836906 110.698 107.836906 111.362062 Z M 107.836906 111.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 112.032219 112.975344 C 112.032219 113.6355 111.497062 114.170656 110.836906 114.170656 C 110.17675 114.170656 109.637687 113.6355 109.637687 112.975344 C 109.637687 112.311281 110.17675 111.776125 110.836906 111.776125 C 111.497062 111.776125 112.032219 112.311281 112.032219 112.975344 Z M 112.032219 112.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 116.576906 C 116.227531 117.237062 115.692375 117.772219 115.032219 117.772219 C 114.372062 117.772219 113.833 117.237062 113.833 116.576906 C 113.833 115.912844 114.372062 115.377687 115.032219 115.377687 C 115.692375 115.377687 116.227531 115.912844 116.227531 116.576906 Z M 116.227531 116.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.422844 116.576906 C 120.422844 117.237062 119.887687 117.772219 119.227531 117.772219 C 118.567375 117.772219 118.028312 117.237062 118.028312 116.576906 C 118.028312 115.912844 118.567375 115.377687 119.227531 115.377687 C 119.887687 115.377687 120.422844 115.912844 120.422844 116.576906 Z M 120.422844 116.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 124.618156 117.600344 C 124.618156 118.2605 124.083 118.795656 123.422844 118.795656 C 122.762687 118.795656 122.223625 118.2605 122.223625 117.600344 C 122.223625 116.940187 122.762687 116.401125 123.422844 116.401125 C 124.083 116.401125 124.618156 116.940187 124.618156 117.600344 Z M 124.618156 117.600344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 119.678469 C 128.813469 120.342531 128.278312 120.877687 127.618156 120.877687 C 126.958 120.877687 126.418937 120.342531 126.418937 119.678469 C 126.418937 119.018312 126.958 118.483156 127.618156 118.483156 C 128.278312 118.483156 128.813469 119.018312 128.813469 119.678469 Z M 128.813469 119.678469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 133.008781 122.846437 C 133.008781 123.506594 132.473625 124.04175 131.813469 124.04175 C 131.153312 124.04175 130.61425 123.506594 130.61425 122.846437 C 130.61425 122.186281 131.153312 121.651125 131.813469 121.651125 C 132.473625 121.651125 133.008781 122.186281 133.008781 122.846437 Z M 133.008781 122.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 137.204094 130.112062 C 137.204094 130.772219 136.668937 131.307375 136.008781 131.307375 C 135.348625 131.307375 134.809562 130.772219 134.809562 130.112062 C 134.809562 129.448 135.348625 128.912844 136.008781 128.912844 C 136.668937 128.912844 137.204094 129.448 137.204094 130.112062 Z M 137.204094 130.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.399406 135.201906 C 141.399406 135.862062 140.86425 136.397219 140.204094 136.397219 C 139.543937 136.397219 139.004875 135.862062 139.004875 135.201906 C 139.004875 134.54175 139.543937 134.006594 140.204094 134.006594 C 140.86425 134.006594 141.399406 134.54175 141.399406 135.201906 Z M 141.399406 135.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 149.451906 C 145.594719 150.112062 145.059562 150.647219 144.399406 150.647219 C 143.73925 150.647219 143.200187 150.112062 143.200187 149.451906 C 143.200187 148.79175 143.73925 148.252687 144.399406 148.252687 C 145.059562 148.252687 145.594719 148.79175 145.594719 149.451906 Z M 145.594719 149.451906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 149.790031 165.002687 C 149.790031 165.66675 149.254875 166.201906 148.594719 166.201906 C 147.934562 166.201906 147.3955 165.66675 147.3955 165.002687 C 147.3955 164.342531 147.934562 163.807375 148.594719 163.807375 C 149.254875 163.807375 149.790031 164.342531 149.790031 165.002687 Z M 149.790031 165.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 208.838625 C 153.985344 209.498781 153.450187 210.037844 152.790031 210.037844 C 152.129875 210.037844 151.590812 209.498781 151.590812 208.838625 C 151.590812 208.178469 152.129875 207.643312 152.790031 207.643312 C 153.450187 207.643312 153.985344 208.178469 153.985344 208.838625 Z M 153.985344 208.838625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 273.326906 L 156.985344 273.588625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 278.139406 L 156.985344 278.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 275.865969 C 158.180656 276.526125 157.6455 277.061281 156.985344 277.061281 C 156.325187 277.061281 155.786125 276.526125 155.786125 275.865969 C 155.786125 275.201906 156.325187 274.66675 156.985344 274.66675 C 157.6455 274.66675 158.180656 275.201906 158.180656 275.865969 Z M 158.180656 275.865969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 359.826906 L 161.180656 360.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 365.127687 L 161.180656 365.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 162.375969 362.850344 C 162.375969 363.5105 161.840812 364.045656 161.180656 364.045656 C 160.5205 364.045656 159.981437 363.5105 159.981437 362.850344 C 159.981437 362.190187 160.5205 361.655031 161.180656 361.655031 C 161.840812 361.655031 162.375969 362.190187 162.375969 362.850344 Z M 162.375969 362.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 380.213625 L 165.375969 381.065187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 385.615969 L 165.375969 386.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 166.571281 383.338625 C 166.571281 383.998781 166.036125 384.537844 165.375969 384.537844 C 164.715812 384.537844 164.17675 383.998781 164.17675 383.338625 C 164.17675 382.678469 164.715812 382.143312 165.375969 382.143312 C 166.036125 382.143312 166.571281 382.678469 166.571281 383.338625 Z M 166.571281 383.338625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 309.803469 L 169.571281 310.280031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 314.834719 L 169.571281 315.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 312.557375 C 170.766594 313.217531 170.231437 313.752687 169.571281 313.752687 C 168.911125 313.752687 168.372062 313.217531 168.372062 312.557375 C 168.372062 311.897219 168.911125 311.362062 169.571281 311.362062 C 170.231437 311.362062 170.766594 311.897219 170.766594 312.557375 Z M 170.766594 312.557375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 174.961906 235.475344 C 174.961906 236.1355 174.42675 236.670656 173.766594 236.670656 C 173.106437 236.670656 172.571281 236.1355 172.571281 235.475344 C 172.571281 234.815187 173.106437 234.280031 173.766594 234.280031 C 174.42675 234.280031 174.961906 234.815187 174.961906 235.475344 Z M 174.961906 235.475344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 179.157219 182.514406 C 179.157219 183.174562 178.622062 183.709719 177.961906 183.709719 C 177.30175 183.709719 176.762687 183.174562 176.762687 182.514406 C 176.762687 181.85425 177.30175 181.315187 177.961906 181.315187 C 178.622062 181.315187 179.157219 181.85425 179.157219 182.514406 Z M 179.157219 182.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 153.268312 C 183.352531 153.932375 182.817375 154.467531 182.157219 154.467531 C 181.497062 154.467531 180.958 153.932375 180.958 153.268312 C 180.958 152.608156 181.497062 152.073 182.157219 152.073 C 182.817375 152.073 183.352531 152.608156 183.352531 153.268312 Z M 183.352531 153.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 135.326906 C 187.547844 135.987062 187.012687 136.522219 186.352531 136.522219 C 185.692375 136.522219 185.157219 135.987062 185.157219 135.326906 C 185.157219 134.66675 185.692375 134.131594 186.352531 134.131594 C 187.012687 134.131594 187.547844 134.66675 187.547844 135.326906 Z M 187.547844 135.326906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 123.592531 C 191.743156 124.252687 191.208 124.787844 190.547844 124.787844 C 189.887687 124.787844 189.348625 124.252687 189.348625 123.592531 C 189.348625 122.932375 189.887687 122.393312 190.547844 122.393312 C 191.208 122.393312 191.743156 122.932375 191.743156 123.592531 Z M 191.743156 123.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 114.744875 C 195.938469 115.405031 195.403312 115.940187 194.743156 115.940187 C 194.083 115.940187 193.543937 115.405031 193.543937 114.744875 C 193.543937 114.084719 194.083 113.545656 194.743156 113.545656 C 195.403312 113.545656 195.938469 114.084719 195.938469 114.744875 Z M 195.938469 114.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 107.448 C 200.133781 108.108156 199.598625 108.643312 198.938469 108.643312 C 198.278312 108.643312 197.743156 108.108156 197.743156 107.448 C 197.743156 106.787844 198.278312 106.252687 198.938469 106.252687 C 199.598625 106.252687 200.133781 106.787844 200.133781 107.448 Z M 200.133781 107.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 103.940187 C 204.329094 104.600344 203.793937 105.1355 203.133781 105.1355 C 202.473625 105.1355 201.934562 104.600344 201.934562 103.940187 C 201.934562 103.280031 202.473625 102.744875 203.133781 102.744875 C 203.793937 102.744875 204.329094 103.280031 204.329094 103.940187 Z M 204.329094 103.940187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 99.842531 C 208.524406 100.502687 207.98925 101.037844 207.329094 101.037844 C 206.668937 101.037844 206.129875 100.502687 206.129875 99.842531 C 206.129875 99.182375 206.668937 98.647219 207.329094 98.647219 C 207.98925 98.647219 208.524406 99.182375 208.524406 99.842531 Z M 208.524406 99.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 96.240969 C 212.719719 96.901125 212.184562 97.436281 211.524406 97.436281 C 210.86425 97.436281 210.329094 96.901125 210.329094 96.240969 C 210.329094 95.580812 210.86425 95.045656 211.524406 95.045656 C 212.184562 95.045656 212.719719 95.580812 212.719719 96.240969 Z M 212.719719 96.240969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 94.998781 C 216.915031 95.658937 216.379875 96.198 215.719719 96.198 C 215.059562 96.198 214.524406 95.658937 214.524406 94.998781 C 214.524406 94.338625 215.059562 93.803469 215.719719 93.803469 C 216.379875 93.803469 216.915031 94.338625 216.915031 94.998781 Z M 216.915031 94.998781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 89.846437 C 221.110344 90.506594 220.575187 91.04175 219.915031 91.04175 C 219.254875 91.04175 218.715812 90.506594 218.715812 89.846437 C 218.715812 89.186281 219.254875 88.651125 219.915031 88.651125 C 220.575187 88.651125 221.110344 89.186281 221.110344 89.846437 Z M 221.110344 89.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 88.295656 C 225.305656 88.955812 224.7705 89.490969 224.110344 89.490969 C 223.450187 89.490969 222.915031 88.955812 222.915031 88.295656 C 222.915031 87.631594 223.450187 87.096437 224.110344 87.096437 C 224.7705 87.096437 225.305656 87.631594 225.305656 88.295656 Z M 225.305656 88.295656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 86.709719 C 229.500969 87.369875 228.965812 87.908937 228.305656 87.908937 C 227.6455 87.908937 227.110344 87.369875 227.110344 86.709719 C 227.110344 86.049562 227.6455 85.514406 228.305656 85.514406 C 228.965812 85.514406 229.500969 86.049562 229.500969 86.709719 Z M 229.500969 86.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 84.694094 C 233.696281 85.35425 233.161125 85.889406 232.500969 85.889406 C 231.840812 85.889406 231.30175 85.35425 231.30175 84.694094 C 231.30175 84.033937 231.840812 83.494875 232.500969 83.494875 C 233.161125 83.494875 233.696281 84.033937 233.696281 84.694094 Z M 233.696281 84.694094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 83.948 C 237.891594 84.608156 237.356437 85.143312 236.696281 85.143312 C 236.036125 85.143312 235.500969 84.608156 235.500969 83.948 C 235.500969 83.287844 236.036125 82.752687 236.696281 82.752687 C 237.356437 82.752687 237.891594 83.287844 237.891594 83.948 Z M 237.891594 83.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 82.022219 C 242.086906 82.682375 241.55175 83.221437 240.891594 83.221437 C 240.231437 83.221437 239.696281 82.682375 239.696281 82.022219 C 239.696281 81.362062 240.231437 80.826906 240.891594 80.826906 C 241.55175 80.826906 242.086906 81.362062 242.086906 82.022219 Z M 242.086906 82.022219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 81.651125 C 246.282219 82.311281 245.747062 82.846437 245.086906 82.846437 C 244.42675 82.846437 243.891594 82.311281 243.891594 81.651125 C 243.891594 80.990969 244.42675 80.455812 245.086906 80.455812 C 245.747062 80.455812 246.282219 80.990969 246.282219 81.651125 Z M 246.282219 81.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 80.967531 C 250.477531 81.627687 249.942375 82.162844 249.282219 82.162844 C 248.622062 82.162844 248.086906 81.627687 248.086906 80.967531 C 248.086906 80.307375 248.622062 79.772219 249.282219 79.772219 C 249.942375 79.772219 250.477531 80.307375 250.477531 80.967531 Z M 250.477531 80.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 79.073 C 254.672844 79.733156 254.137687 80.272219 253.477531 80.272219 C 252.817375 80.272219 252.282219 79.733156 252.282219 79.073 C 252.282219 78.412844 252.817375 77.877687 253.477531 77.877687 C 254.137687 77.877687 254.672844 78.412844 254.672844 79.073 Z M 254.672844 79.073 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 80.037844 C 258.868156 80.698 258.333 81.233156 257.672844 81.233156 C 257.012687 81.233156 256.477531 80.698 256.477531 80.037844 C 256.477531 79.373781 257.012687 78.838625 257.672844 78.838625 C 258.333 78.838625 258.868156 79.373781 258.868156 80.037844 Z M 258.868156 80.037844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 79.819094 C 263.063469 80.47925 262.528312 81.014406 261.868156 81.014406 C 261.208 81.014406 260.672844 80.47925 260.672844 79.819094 C 260.672844 79.158937 261.208 78.623781 261.868156 78.623781 C 262.528312 78.623781 263.063469 79.158937 263.063469 79.819094 Z M 263.063469 79.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 78.889406 C 267.258781 79.549562 266.723625 80.084719 266.063469 80.084719 C 265.403312 80.084719 264.868156 79.549562 264.868156 78.889406 C 264.868156 78.225344 265.403312 77.690187 266.063469 77.690187 C 266.723625 77.690187 267.258781 78.225344 267.258781 78.889406 Z M 267.258781 78.889406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 77.365969 C 271.454094 78.026125 270.918937 78.561281 270.258781 78.561281 C 269.598625 78.561281 269.063469 78.026125 269.063469 77.365969 C 269.063469 76.705812 269.598625 76.170656 270.258781 76.170656 C 270.918937 76.170656 271.454094 76.705812 271.454094 77.365969 Z M 271.454094 77.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 78.237062 C 275.649406 78.897219 275.11425 79.432375 274.454094 79.432375 C 273.793937 79.432375 273.258781 78.897219 273.258781 78.237062 C 273.258781 77.573 273.793937 77.037844 274.454094 77.037844 C 275.11425 77.037844 275.649406 77.573 275.649406 78.237062 Z M 275.649406 78.237062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 77.709719 C 279.844719 78.369875 279.309562 78.905031 278.649406 78.905031 C 277.98925 78.905031 277.454094 78.369875 277.454094 77.709719 C 277.454094 77.045656 277.98925 76.5105 278.649406 76.5105 C 279.309562 76.5105 279.844719 77.045656 279.844719 77.709719 Z M 279.844719 77.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 79.198 C 284.040031 79.858156 283.504875 80.393312 282.844719 80.393312 C 282.184562 80.393312 281.649406 79.858156 281.649406 79.198 C 281.649406 78.537844 282.184562 78.002687 282.844719 78.002687 C 283.504875 78.002687 284.040031 78.537844 284.040031 79.198 Z M 284.040031 79.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 77.678469 C 288.235344 78.338625 287.700187 78.873781 287.040031 78.873781 C 286.379875 78.873781 285.844719 78.338625 285.844719 77.678469 C 285.844719 77.014406 286.379875 76.47925 287.040031 76.47925 C 287.700187 76.47925 288.235344 77.014406 288.235344 77.678469 Z M 288.235344 77.678469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 78.420656 C 292.430656 79.084719 291.8955 79.619875 291.235344 79.619875 C 290.575187 79.619875 290.040031 79.084719 290.040031 78.420656 C 290.040031 77.7605 290.575187 77.225344 291.235344 77.225344 C 291.8955 77.225344 292.430656 77.7605 292.430656 78.420656 Z M 292.430656 78.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 77.955812 C 296.625969 78.615969 296.090812 79.151125 295.430656 79.151125 C 294.7705 79.151125 294.235344 78.615969 294.235344 77.955812 C 294.235344 77.295656 294.7705 76.7605 295.430656 76.7605 C 296.090812 76.7605 296.625969 77.295656 296.625969 77.955812 Z M 296.625969 77.955812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 78.889406 C 300.821281 79.549562 300.286125 80.084719 299.625969 80.084719 C 298.965812 80.084719 298.430656 79.549562 298.430656 78.889406 C 298.430656 78.225344 298.965812 77.690187 299.625969 77.690187 C 300.286125 77.690187 300.821281 78.225344 300.821281 78.889406 Z M 300.821281 78.889406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 77.647219 C 305.016594 78.307375 304.481437 78.842531 303.821281 78.842531 C 303.161125 78.842531 302.625969 78.307375 302.625969 77.647219 C 302.625969 76.983156 303.161125 76.448 303.821281 76.448 C 304.481437 76.448 305.016594 76.983156 305.016594 77.647219 Z M 305.016594 77.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 78.97925 C 309.211906 79.643312 308.67675 80.178469 308.016594 80.178469 C 307.356437 80.178469 306.821281 79.643312 306.821281 78.97925 C 306.821281 78.319094 307.356437 77.783937 308.016594 77.783937 C 308.67675 77.783937 309.211906 78.319094 309.211906 78.97925 Z M 309.211906 78.97925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 78.205812 C 313.407219 78.865969 312.872062 79.401125 312.211906 79.401125 C 311.55175 79.401125 311.016594 78.865969 311.016594 78.205812 C 311.016594 77.54175 311.55175 77.006594 312.211906 77.006594 C 312.872062 77.006594 313.407219 77.54175 313.407219 78.205812 Z M 313.407219 78.205812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 77.397219 C 317.602531 78.057375 317.067375 78.592531 316.407219 78.592531 C 315.747062 78.592531 315.211906 78.057375 315.211906 77.397219 C 315.211906 76.737062 315.747062 76.201906 316.407219 76.201906 C 317.067375 76.201906 317.602531 76.737062 317.602531 77.397219 Z M 317.602531 77.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 78.018312 C 321.797844 78.678469 321.262687 79.213625 320.602531 79.213625 C 319.942375 79.213625 319.407219 78.678469 319.407219 78.018312 C 319.407219 77.358156 319.942375 76.823 320.602531 76.823 C 321.262687 76.823 321.797844 77.358156 321.797844 78.018312 Z M 321.797844 78.018312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 78.858156 C 325.993156 79.518312 325.458 80.053469 324.797844 80.053469 C 324.137687 80.053469 323.602531 79.518312 323.602531 78.858156 C 323.602531 78.194094 324.137687 77.658937 324.797844 77.658937 C 325.458 77.658937 325.993156 78.194094 325.993156 78.858156 Z M 325.993156 78.858156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 78.451906 C 330.188469 79.112062 329.653312 79.651125 328.993156 79.651125 C 328.333 79.651125 327.797844 79.112062 327.797844 78.451906 C 327.797844 77.79175 328.333 77.256594 328.993156 77.256594 C 329.653312 77.256594 330.188469 77.79175 330.188469 78.451906 Z M 330.188469 78.451906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 78.205812 C 334.383781 78.865969 333.848625 79.401125 333.188469 79.401125 C 332.528312 79.401125 331.993156 78.865969 331.993156 78.205812 C 331.993156 77.54175 332.528312 77.006594 333.188469 77.006594 C 333.848625 77.006594 334.383781 77.54175 334.383781 78.205812 Z M 334.383781 78.205812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 78.420656 C 338.579094 79.084719 338.043937 79.619875 337.383781 79.619875 C 336.723625 79.619875 336.188469 79.084719 336.188469 78.420656 C 336.188469 77.7605 336.723625 77.225344 337.383781 77.225344 C 338.043937 77.225344 338.579094 77.7605 338.579094 78.420656 Z M 338.579094 78.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 78.733156 C 342.774406 79.393312 342.23925 79.928469 341.579094 79.928469 C 340.918937 79.928469 340.383781 79.393312 340.383781 78.733156 C 340.383781 78.073 340.918937 77.533937 341.579094 77.533937 C 342.23925 77.533937 342.774406 78.073 342.774406 78.733156 Z M 342.774406 78.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 77.334719 C 346.969719 77.994875 346.434562 78.533937 345.774406 78.533937 C 345.11425 78.533937 344.579094 77.994875 344.579094 77.334719 C 344.579094 76.674562 345.11425 76.139406 345.774406 76.139406 C 346.434562 76.139406 346.969719 76.674562 346.969719 77.334719 Z M 346.969719 77.334719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 76.311281 C 351.165031 76.971437 350.629875 77.506594 349.969719 77.506594 C 349.309562 77.506594 348.774406 76.971437 348.774406 76.311281 C 348.774406 75.651125 349.309562 75.115969 349.969719 75.115969 C 350.629875 75.115969 351.165031 75.651125 351.165031 76.311281 Z M 351.165031 76.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 76.994875 C 355.360344 77.655031 354.825187 78.190187 354.165031 78.190187 C 353.504875 78.190187 352.969719 77.655031 352.969719 76.994875 C 352.969719 76.334719 353.504875 75.795656 354.165031 75.795656 C 354.825187 75.795656 355.360344 76.334719 355.360344 76.994875 Z M 355.360344 76.994875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 76.776125 C 359.555656 77.436281 359.0205 77.971437 358.360344 77.971437 C 357.700187 77.971437 357.165031 77.436281 357.165031 76.776125 C 357.165031 76.115969 357.700187 75.580812 358.360344 75.580812 C 359.0205 75.580812 359.555656 76.115969 359.555656 76.776125 Z M 359.555656 76.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 76.776125 C 363.750969 77.436281 363.215812 77.971437 362.555656 77.971437 C 361.8955 77.971437 361.360344 77.436281 361.360344 76.776125 C 361.360344 76.115969 361.8955 75.580812 362.555656 75.580812 C 363.215812 75.580812 363.750969 76.115969 363.750969 76.776125 Z M 363.750969 76.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 367.946281 75.721437 C 367.946281 76.381594 367.411125 76.91675 366.750969 76.91675 C 366.090812 76.91675 365.555656 76.381594 365.555656 75.721437 C 365.555656 75.061281 366.090812 74.526125 366.750969 74.526125 C 367.411125 74.526125 367.946281 75.061281 367.946281 75.721437 Z M 367.946281 75.721437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 74.756594 C 372.141594 75.420656 371.606437 75.955812 370.946281 75.955812 C 370.286125 75.955812 369.750969 75.420656 369.750969 74.756594 C 369.750969 74.096437 370.286125 73.561281 370.946281 73.561281 C 371.606437 73.561281 372.141594 74.096437 372.141594 74.756594 Z M 372.141594 74.756594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 376.336906 74.54175 C 376.336906 75.201906 375.80175 75.737062 375.141594 75.737062 C 374.481437 75.737062 373.946281 75.201906 373.946281 74.54175 C 373.946281 73.881594 374.481437 73.346437 375.141594 73.346437 C 375.80175 73.346437 376.336906 73.881594 376.336906 74.54175 Z M 376.336906 74.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 73.268312 C 380.532219 73.928469 379.997062 74.463625 379.336906 74.463625 C 378.67675 74.463625 378.141594 73.928469 378.141594 73.268312 C 378.141594 72.608156 378.67675 72.073 379.336906 72.073 C 379.997062 72.073 380.532219 72.608156 380.532219 73.268312 Z M 380.532219 73.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 74.22925 C 384.727531 74.893312 384.192375 75.428469 383.532219 75.428469 C 382.872062 75.428469 382.336906 74.893312 382.336906 74.22925 C 382.336906 73.569094 382.872062 73.033937 383.532219 73.033937 C 384.192375 73.033937 384.727531 73.569094 384.727531 74.22925 Z M 384.727531 74.22925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 73.424562 C 388.922844 74.084719 388.387687 74.619875 387.727531 74.619875 C 387.067375 74.619875 386.532219 74.084719 386.532219 73.424562 C 386.532219 72.764406 387.067375 72.225344 387.727531 72.225344 C 388.387687 72.225344 388.922844 72.764406 388.922844 73.424562 Z M 388.922844 73.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 73.018312 C 393.118156 73.682375 392.583 74.217531 391.922844 74.217531 C 391.262687 74.217531 390.727531 73.682375 390.727531 73.018312 C 390.727531 72.358156 391.262687 71.823 391.922844 71.823 C 392.583 71.823 393.118156 72.358156 393.118156 73.018312 Z M 393.118156 73.018312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 72.834719 C 397.313469 73.494875 396.778312 74.030031 396.118156 74.030031 C 395.458 74.030031 394.922844 73.494875 394.922844 72.834719 C 394.922844 72.174562 395.458 71.639406 396.118156 71.639406 C 396.778312 71.639406 397.313469 72.174562 397.313469 72.834719 Z M 397.313469 72.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 401.508781 71.686281 C 401.508781 72.346437 400.973625 72.881594 400.313469 72.881594 C 399.653312 72.881594 399.118156 72.346437 399.118156 71.686281 C 399.118156 71.026125 399.653312 70.487062 400.313469 70.487062 C 400.973625 70.487062 401.508781 71.026125 401.508781 71.686281 Z M 401.508781 71.686281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 71.065187 C 405.704094 71.725344 405.168937 72.2605 404.508781 72.2605 C 403.848625 72.2605 403.313469 71.725344 403.313469 71.065187 C 403.313469 70.405031 403.848625 69.865969 404.508781 69.865969 C 405.168937 69.865969 405.704094 70.405031 405.704094 71.065187 Z M 405.704094 71.065187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 409.899406 71.096437 C 409.899406 71.756594 409.36425 72.29175 408.704094 72.29175 C 408.043937 72.29175 407.508781 71.756594 407.508781 71.096437 C 407.508781 70.436281 408.043937 69.897219 408.704094 69.897219 C 409.36425 69.897219 409.899406 70.436281 409.899406 71.096437 Z M 409.899406 71.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 414.094719 70.162844 C 414.094719 70.826906 413.559562 71.362062 412.899406 71.362062 C 412.23925 71.362062 411.704094 70.826906 411.704094 70.162844 C 411.704094 69.502687 412.23925 68.967531 412.899406 68.967531 C 413.559562 68.967531 414.094719 69.502687 414.094719 70.162844 Z M 414.094719 70.162844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 418.290031 70.350344 C 418.290031 71.0105 417.754875 71.545656 417.094719 71.545656 C 416.434562 71.545656 415.899406 71.0105 415.899406 70.350344 C 415.899406 69.690187 416.434562 69.155031 417.094719 69.155031 C 417.754875 69.155031 418.290031 69.690187 418.290031 70.350344 Z M 418.290031 70.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 69.823 C 422.485344 70.483156 421.950187 71.018312 421.290031 71.018312 C 420.629875 71.018312 420.094719 70.483156 420.094719 69.823 C 420.094719 69.162844 420.629875 68.627687 421.290031 68.627687 C 421.950187 68.627687 422.485344 69.162844 422.485344 69.823 Z M 422.485344 69.823 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.680656 69.85425 C 426.680656 70.514406 426.1455 71.049562 425.485344 71.049562 C 424.825187 71.049562 424.290031 70.514406 424.290031 69.85425 C 424.290031 69.194094 424.825187 68.655031 425.485344 68.655031 C 426.1455 68.655031 426.680656 69.194094 426.680656 69.85425 Z M 426.680656 69.85425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 69.60425 C 430.875969 70.264406 430.340812 70.803469 429.680656 70.803469 C 429.0205 70.803469 428.485344 70.264406 428.485344 69.60425 C 428.485344 68.944094 429.0205 68.408937 429.680656 68.408937 C 430.340812 68.408937 430.875969 68.944094 430.875969 69.60425 Z M 430.875969 69.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 69.201906 C 435.071281 69.862062 434.536125 70.397219 433.875969 70.397219 C 433.215812 70.397219 432.680656 69.862062 432.680656 69.201906 C 432.680656 68.54175 433.215812 68.006594 433.875969 68.006594 C 434.536125 68.006594 435.071281 68.54175 435.071281 69.201906 Z M 435.071281 69.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.266594 69.076906 C 439.266594 69.737062 438.731437 70.276125 438.071281 70.276125 C 437.411125 70.276125 436.875969 69.737062 436.875969 69.076906 C 436.875969 68.41675 437.411125 67.881594 438.071281 67.881594 C 438.731437 67.881594 439.266594 68.41675 439.266594 69.076906 Z M 439.266594 69.076906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 68.889406 C 443.461906 69.553469 442.92675 70.088625 442.266594 70.088625 C 441.606437 70.088625 441.071281 69.553469 441.071281 68.889406 C 441.071281 68.22925 441.606437 67.694094 442.266594 67.694094 C 442.92675 67.694094 443.461906 68.22925 443.461906 68.889406 Z M 443.461906 68.889406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 447.657219 68.799562 C 447.657219 69.459719 447.122062 69.994875 446.461906 69.994875 C 445.80175 69.994875 445.266594 69.459719 445.266594 68.799562 C 445.266594 68.1355 445.80175 67.600344 446.461906 67.600344 C 447.122062 67.600344 447.657219 68.1355 447.657219 68.799562 Z M 447.657219 68.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 68.799562 C 451.852531 69.459719 451.317375 69.994875 450.657219 69.994875 C 449.997062 69.994875 449.461906 69.459719 449.461906 68.799562 C 449.461906 68.1355 449.997062 67.600344 450.657219 67.600344 C 451.317375 67.600344 451.852531 68.1355 451.852531 68.799562 Z M 451.852531 68.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 68.549562 C 456.047844 69.209719 455.512687 69.744875 454.852531 69.744875 C 454.192375 69.744875 453.657219 69.209719 453.657219 68.549562 C 453.657219 67.889406 454.192375 67.35425 454.852531 67.35425 C 455.512687 67.35425 456.047844 67.889406 456.047844 68.549562 Z M 456.047844 68.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.243156 68.518312 C 460.243156 69.178469 459.708 69.713625 459.047844 69.713625 C 458.387687 69.713625 457.852531 69.178469 457.852531 68.518312 C 457.852531 67.858156 458.387687 67.323 459.047844 67.323 C 459.708 67.323 460.243156 67.858156 460.243156 68.518312 Z M 460.243156 68.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.438469 68.612062 C 464.438469 69.272219 463.903312 69.807375 463.243156 69.807375 C 462.583 69.807375 462.047844 69.272219 462.047844 68.612062 C 462.047844 67.951906 462.583 67.41675 463.243156 67.41675 C 463.903312 67.41675 464.438469 67.951906 464.438469 68.612062 Z M 464.438469 68.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.637687 68.549562 C 468.637687 69.209719 468.098625 69.744875 467.438469 69.744875 C 466.778312 69.744875 466.243156 69.209719 466.243156 68.549562 C 466.243156 67.889406 466.778312 67.35425 467.438469 67.35425 C 468.098625 67.35425 468.637687 67.889406 468.637687 68.549562 Z M 468.637687 68.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 77.990969 L 107.610344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 126.567375 73.240969 L 126.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.5205 73.240969 L 145.5205 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 164.473625 73.240969 L 164.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.42675 73.240969 L 183.42675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 202.379875 77.990969 L 202.379875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.336906 73.240969 L 221.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.290031 73.240969 L 240.290031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 259.243156 73.240969 L 259.243156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.196281 73.240969 L 278.196281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 297.149406 77.990969 L 297.149406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.102531 73.240969 L 316.102531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 335.059562 73.240969 L 335.059562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.012687 73.240969 L 354.012687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.965812 73.240969 L 372.965812 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.918937 77.990969 L 391.918937 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.872062 73.240969 L 410.872062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.829094 73.240969 L 429.829094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 448.782219 73.240969 L 448.782219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.735344 73.240969 L 467.735344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 77.990969 L 486.688469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 77.990969 L 107.610344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 88.657219 73.240969 L 88.657219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 77.990969 L 486.688469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="91.81" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="103.817975" y="389.053"/>
+ <use xlink:href="#glyph0-3" x="110.489072" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="195.917" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="281.346" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="293.353975" y="389.053"/>
+ <use xlink:href="#glyph0-3" x="300.025072" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="385.453" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="470.882" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="482.889975" y="389.053"/>
+ <use xlink:href="#glyph0-3" x="489.561072" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="311.866" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="323.177971" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="338.982727" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="351.474311" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="362.035433" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="379.9758" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-6" x="390.196373" y="417.528"/>
+ <use xlink:href="#glyph0-7" x="409.03977" y="417.528"/>
+ <use xlink:href="#glyph0-8" x="419.713526" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="438.047611" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.755308" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.763284" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-2" x="470.098195" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="479.807944" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 392.862062 L 107.610344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 126.567375 397.615969 L 126.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.5205 397.615969 L 145.5205 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 164.473625 397.615969 L 164.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.42675 397.615969 L 183.42675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 202.379875 392.862062 L 202.379875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.336906 397.615969 L 221.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.290031 397.615969 L 240.290031 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 259.243156 397.615969 L 259.243156 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.196281 397.615969 L 278.196281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 297.149406 392.862062 L 297.149406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.102531 397.615969 L 316.102531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 335.059562 397.615969 L 335.059562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.012687 397.615969 L 354.012687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.965812 397.615969 L 372.965812 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.918937 392.862062 L 391.918937 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.872062 397.615969 L 410.872062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.829094 397.615969 L 429.829094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 448.782219 397.615969 L 448.782219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.735344 397.615969 L 467.735344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 392.862062 L 486.688469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 392.862062 L 107.610344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 88.657219 397.615969 L 88.657219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 392.862062 L 486.688469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 84.0105 L 79.372062 84.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 99.533937 L 79.372062 99.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 115.053469 L 79.372062 115.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 130.576906 L 79.372062 130.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 146.100344 L 79.372062 146.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 161.619875 L 79.372062 161.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 177.143312 L 79.372062 177.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 192.66675 L 79.372062 192.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 208.186281 L 79.372062 208.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 223.709719 L 79.372062 223.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 239.233156 L 79.372062 239.233156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 254.752687 L 79.372062 254.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 270.276125 L 79.372062 270.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 285.799562 L 79.372062 285.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 301.323 L 79.372062 301.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 316.842531 L 79.372062 316.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 332.365969 L 79.372062 332.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 347.8855 L 79.372062 347.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 363.408937 L 79.372062 363.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 378.932375 L 79.372062 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 378.932375 L 79.372062 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 394.455812 L 79.372062 394.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="55.657" y="307.901"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-9" x="55.657" y="245.813"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-10" x="55.657" y="183.725"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-11" x="55.657" y="121.636"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="43.65" y="59.549"/>
+ <use xlink:href="#glyph0-1" x="55.657975" y="59.549"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-1" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph8-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph8-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph8-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph8-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph8-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-9" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph8-10" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph8-11" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph8-12" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph9-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-13" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 84.0105 L 498.903312 84.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 99.533937 L 498.903312 99.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 115.053469 L 498.903312 115.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 130.576906 L 498.903312 130.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 146.100344 L 498.903312 146.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 161.619875 L 498.903312 161.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 177.143312 L 498.903312 177.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 192.66675 L 498.903312 192.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 208.186281 L 498.903312 208.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 223.709719 L 498.903312 223.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 239.233156 L 498.903312 239.233156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 254.752687 L 498.903312 254.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 270.276125 L 498.903312 270.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 285.799562 L 498.903312 285.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 301.323 L 498.903312 301.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 316.842531 L 498.903312 316.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 332.365969 L 498.903312 332.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 347.8855 L 498.903312 347.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 363.408937 L 498.903312 363.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 378.932375 L 498.903312 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 378.932375 L 498.903312 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 394.455812 L 498.903312 394.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 77.990969 L 107.610344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 126.567375 73.240969 L 126.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.5205 73.240969 L 145.5205 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 164.473625 73.240969 L 164.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.42675 73.240969 L 183.42675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 202.379875 77.990969 L 202.379875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.336906 73.240969 L 221.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.290031 73.240969 L 240.290031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 259.243156 73.240969 L 259.243156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.196281 73.240969 L 278.196281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 297.149406 77.990969 L 297.149406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.102531 73.240969 L 316.102531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 335.059562 73.240969 L 335.059562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.012687 73.240969 L 354.012687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.965812 73.240969 L 372.965812 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.918937 77.990969 L 391.918937 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.872062 73.240969 L 410.872062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.829094 73.240969 L 429.829094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 448.782219 73.240969 L 448.782219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.735344 73.240969 L 467.735344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 77.990969 L 486.688469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 77.990969 L 107.610344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 88.657219 73.240969 L 88.657219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 77.990969 L 486.688469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 392.862062 L 107.610344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 126.567375 397.615969 L 126.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.5205 397.615969 L 145.5205 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 164.473625 397.615969 L 164.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.42675 397.615969 L 183.42675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 202.379875 392.862062 L 202.379875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.336906 397.615969 L 221.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.290031 397.615969 L 240.290031 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 259.243156 397.615969 L 259.243156 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.196281 397.615969 L 278.196281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 297.149406 392.862062 L 297.149406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.102531 397.615969 L 316.102531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 335.059562 397.615969 L 335.059562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.012687 397.615969 L 354.012687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.965812 397.615969 L 372.965812 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.918937 392.862062 L 391.918937 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.872062 397.615969 L 410.872062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.829094 397.615969 L 429.829094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 448.782219 397.615969 L 448.782219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.735344 397.615969 L 467.735344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 392.862062 L 486.688469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.610344 392.862062 L 107.610344 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 88.657219 397.615969 L 88.657219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 486.688469 392.862062 L 486.688469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 84.0105 L 79.372062 84.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 99.533937 L 79.372062 99.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 115.053469 L 79.372062 115.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 130.576906 L 79.372062 130.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 146.100344 L 79.372062 146.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 161.619875 L 79.372062 161.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 177.143312 L 79.372062 177.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 192.66675 L 79.372062 192.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 208.186281 L 79.372062 208.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 223.709719 L 79.372062 223.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 239.233156 L 79.372062 239.233156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 254.752687 L 79.372062 254.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 270.276125 L 79.372062 270.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 285.799562 L 79.372062 285.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 301.323 L 79.372062 301.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 316.842531 L 79.372062 316.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 332.365969 L 79.372062 332.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 347.8855 L 79.372062 347.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 363.408937 L 79.372062 363.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 378.932375 L 79.372062 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 378.932375 L 79.372062 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 394.455812 L 79.372062 394.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 84.0105 L 498.903312 84.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 99.533937 L 498.903312 99.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 115.053469 L 498.903312 115.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 130.576906 L 498.903312 130.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 146.100344 L 498.903312 146.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 161.619875 L 498.903312 161.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 177.143312 L 498.903312 177.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 192.66675 L 498.903312 192.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 208.186281 L 498.903312 208.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 223.709719 L 498.903312 223.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 239.233156 L 498.903312 239.233156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 254.752687 L 498.903312 254.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 270.276125 L 498.903312 270.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 285.799562 L 498.903312 285.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 301.323 L 498.903312 301.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 316.842531 L 498.903312 316.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 332.365969 L 498.903312 332.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 347.8855 L 498.903312 347.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 363.408937 L 498.903312 363.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 378.932375 L 498.903312 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 378.932375 L 498.903312 378.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 394.455812 L 498.903312 394.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/lb2jspiL_s01.svg b/doc/figs/lb2jspiL_s01.svg
new file mode 100644
index 00000000000..6e9f53f0acd
--- /dev/null
+++ b/doc/figs/lb2jspiL_s01.svg
@@ -0,0 +1,544 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="504pt" height="432pt" viewBox="0 0 504 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 4.515625 -1.203125 C 4.515625 -1.859375 3.953125 -2.375 3.34375 -2.375 C 2.625 -2.375 2.140625 -1.8125 2.140625 -1.203125 C 2.140625 -0.46875 2.75 0 3.3125 0 C 3.96875 0 4.515625 -0.515625 4.515625 -1.203125 Z M 4.515625 -1.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 8.859375 -15.96875 C 8.859375 -16.4375 8.859375 -16.5625 8.515625 -16.5625 C 8.3125 -16.5625 8.25 -16.5625 8.046875 -16.265625 L 0.65625 -4.8125 L 0.65625 -4.09375 L 7.109375 -4.09375 L 7.109375 -1.859375 C 7.109375 -0.953125 7.0625 -0.71875 5.28125 -0.71875 L 4.78125 -0.71875 L 4.78125 0 C 5.34375 -0.046875 7.28125 -0.046875 7.96875 -0.046875 C 8.65625 -0.046875 10.625 -0.046875 11.1875 0 L 11.1875 -0.71875 L 10.703125 -0.71875 C 8.921875 -0.71875 8.859375 -0.953125 8.859375 -1.859375 L 8.859375 -4.09375 L 11.328125 -4.09375 L 11.328125 -4.8125 L 8.859375 -4.8125 Z M 7.234375 -14.0625 L 7.234375 -4.8125 L 1.28125 -4.8125 Z M 7.234375 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-10">
+<path style="stroke:none;" d="M 3.015625 -8.53125 C 3.015625 -14.75 6.03125 -15.71875 7.359375 -15.71875 C 8.25 -15.71875 9.125 -15.453125 9.59375 -14.71875 C 9.296875 -14.71875 8.359375 -14.71875 8.359375 -13.71875 C 8.359375 -13.171875 8.734375 -12.703125 9.375 -12.703125 C 9.984375 -12.703125 10.40625 -13.078125 10.40625 -13.78125 C 10.40625 -15.0625 9.46875 -16.3125 7.328125 -16.3125 C 4.25 -16.3125 1 -13.15625 1 -7.75 C 1 -1 3.953125 0.515625 6.03125 0.515625 C 8.703125 0.515625 10.984375 -1.8125 10.984375 -5 C 10.984375 -8.265625 8.703125 -10.453125 6.25 -10.453125 C 4.078125 -10.453125 3.265625 -8.5625 3.015625 -7.875 Z M 6.03125 -0.140625 C 4.484375 -0.140625 3.75 -1.515625 3.53125 -2.03125 C 3.3125 -2.671875 3.0625 -3.875 3.0625 -5.59375 C 3.0625 -7.53125 3.953125 -9.953125 6.15625 -9.953125 C 7.5 -9.953125 8.21875 -9.046875 8.59375 -8.21875 C 8.984375 -7.3125 8.984375 -6.078125 8.984375 -5.03125 C 8.984375 -3.78125 8.984375 -2.671875 8.515625 -1.734375 C 7.90625 -0.5625 7.015625 -0.140625 6.03125 -0.140625 Z M 6.03125 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-11">
+<path style="stroke:none;" d="M 7.3125 -8.859375 C 8.53125 -9.515625 10.328125 -10.640625 10.328125 -12.703125 C 10.328125 -14.84375 8.265625 -16.3125 6.015625 -16.3125 C 3.578125 -16.3125 1.671875 -14.515625 1.671875 -12.296875 C 1.671875 -11.453125 1.90625 -10.625 2.59375 -9.78125 C 2.875 -9.46875 2.890625 -9.4375 4.609375 -8.25 C 2.234375 -7.140625 1 -5.5 1 -3.703125 C 1 -1.109375 3.484375 0.515625 5.984375 0.515625 C 8.703125 0.515625 10.984375 -1.5 10.984375 -4.078125 C 10.984375 -6.578125 9.21875 -7.671875 7.3125 -8.859375 Z M 3.96875 -11.0625 C 3.65625 -11.28125 2.671875 -11.921875 2.671875 -13.125 C 2.671875 -14.71875 4.34375 -15.71875 5.984375 -15.71875 C 7.75 -15.71875 9.328125 -14.453125 9.328125 -12.6875 C 9.328125 -11.1875 8.25 -9.984375 6.8125 -9.203125 Z M 5.125 -7.90625 L 8.09375 -5.96875 C 8.734375 -5.546875 9.859375 -4.78125 9.859375 -3.28125 C 9.859375 -1.421875 7.96875 -0.140625 6.015625 -0.140625 C 3.921875 -0.140625 2.140625 -1.671875 2.140625 -3.703125 C 2.140625 -5.625 3.53125 -7.15625 5.125 -7.90625 Z M 5.125 -7.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.953125 -5.765625 C 4.03125 -6.078125 4.171875 -6.625 4.171875 -6.703125 C 4.171875 -7.046875 3.90625 -7.203125 3.625 -7.203125 C 3.078125 -7.203125 2.9375 -6.671875 2.875 -6.4375 L 0.609375 2.625 C 0.546875 2.890625 0.546875 2.96875 0.546875 3 C 0.546875 3.421875 0.859375 3.515625 1.0625 3.515625 C 1.140625 3.515625 1.515625 3.5 1.734375 3.078125 C 1.78125 2.9375 2.25 1 2.578125 -0.3125 C 2.859375 -0.09375 3.421875 0.15625 4.25 0.15625 C 5.59375 0.15625 6.46875 -0.9375 6.515625 -1 C 6.8125 0.125 7.921875 0.15625 8.125 0.15625 C 8.875 0.15625 9.25 -0.453125 9.375 -0.734375 C 9.703125 -1.328125 9.9375 -2.265625 9.9375 -2.34375 C 9.9375 -2.4375 9.875 -2.546875 9.671875 -2.546875 C 9.484375 -2.546875 9.453125 -2.453125 9.34375 -2.046875 C 9.125 -1.140625 8.8125 -0.296875 8.171875 -0.296875 C 7.796875 -0.296875 7.65625 -0.609375 7.65625 -1.0625 C 7.65625 -1.34375 7.828125 -2.046875 7.9375 -2.515625 L 8.375 -4.1875 C 8.46875 -4.609375 8.546875 -4.953125 8.671875 -5.4375 C 8.765625 -5.796875 8.921875 -6.4375 8.921875 -6.53125 C 8.921875 -6.953125 8.59375 -7.046875 8.40625 -7.046875 C 7.828125 -7.046875 7.734375 -6.640625 7.546875 -5.90625 L 7.203125 -4.546875 L 6.703125 -2.5 L 6.53125 -1.84375 C 6.5 -1.75 6.0625 -1.125 5.6875 -0.8125 C 5.40625 -0.609375 4.9375 -0.296875 4.328125 -0.296875 C 3.5625 -0.296875 3.046875 -0.703125 3.046875 -1.71875 C 3.046875 -2.140625 3.171875 -2.625 3.265625 -3.03125 Z M 3.953125 -5.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 9.765625 -2.75 C 9.953125 -2.75 10.265625 -2.75 10.265625 -3.0625 C 10.265625 -3.390625 9.953125 -3.390625 9.765625 -3.390625 L 2.03125 -3.390625 C 1.84375 -3.390625 1.53125 -3.390625 1.53125 -3.0625 C 1.53125 -2.75 1.84375 -2.75 2.03125 -2.75 Z M 9.765625 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 6.046875 -2.75 L 10.015625 -2.75 C 10.1875 -2.75 10.484375 -2.75 10.484375 -3.0625 C 10.484375 -3.390625 10.1875 -3.390625 10.015625 -3.390625 L 6.046875 -3.390625 L 6.046875 -7.359375 C 6.046875 -7.53125 6.046875 -7.84375 5.734375 -7.84375 C 5.40625 -7.84375 5.40625 -7.53125 5.40625 -7.359375 L 5.40625 -3.390625 L 1.453125 -3.390625 C 1.28125 -3.390625 0.96875 -3.390625 0.96875 -3.0625 C 0.96875 -2.75 1.28125 -2.75 1.453125 -2.75 L 5.40625 -2.75 L 5.40625 1.234375 C 5.40625 1.390625 5.40625 1.703125 5.734375 1.703125 C 6.046875 1.703125 6.046875 1.390625 6.046875 1.234375 Z M 6.046875 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-3">
+<path style="stroke:none;" d="M 2.25 -5.40625 C 2.25 -6.765625 2.375 -7.953125 2.953125 -8.953125 C 3.453125 -9.78125 4.28125 -10.4375 5.3125 -10.4375 C 5.640625 -10.4375 6.390625 -10.390625 6.765625 -9.828125 C 6.03125 -9.796875 5.96875 -9.234375 5.96875 -9.046875 C 5.96875 -8.5625 6.34375 -8.28125 6.734375 -8.28125 C 7.03125 -8.28125 7.5 -8.46875 7.5 -9.09375 C 7.5 -10.0625 6.765625 -10.875 5.296875 -10.875 C 3.03125 -10.875 0.71875 -8.71875 0.71875 -5.1875 C 0.71875 -0.75 2.78125 0.34375 4.359375 0.34375 C 5.140625 0.34375 6 0.125 6.734375 -0.578125 C 7.390625 -1.203125 7.9375 -1.890625 7.9375 -3.3125 C 7.9375 -5.453125 6.328125 -6.96875 4.515625 -6.96875 C 3.328125 -6.96875 2.625 -6.203125 2.25 -5.40625 Z M 4.359375 -0.140625 C 3.5 -0.140625 2.953125 -0.75 2.71875 -1.203125 C 2.34375 -1.9375 2.296875 -3.0625 2.296875 -3.671875 C 2.296875 -5.296875 3.1875 -6.5 4.453125 -6.5 C 5.265625 -6.5 5.75 -6.078125 6.0625 -5.515625 C 6.40625 -4.90625 6.40625 -4.171875 6.40625 -3.328125 C 6.40625 -2.5 6.40625 -1.78125 6.078125 -1.1875 C 5.65625 -0.4375 5.078125 -0.140625 4.359375 -0.140625 Z M 4.359375 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-11">
+<path style="stroke:none;" d="M -15.71875 -7.0625 C -16.28125 -7.0625 -16.3125 -7.0625 -16.3125 -6.578125 C -15.65625 -5.984375 -14.75 -4.765625 -14.75 -2.234375 L -14.03125 -2.234375 C -14.03125 -2.796875 -14.03125 -4.015625 -14.671875 -5.375 L -1.890625 -5.375 C -1 -5.375 -0.71875 -5.296875 -0.71875 -3.140625 L -0.71875 -2.375 L 0 -2.375 C -0.046875 -3.046875 -0.046875 -5.421875 -0.046875 -6.234375 C -0.046875 -7.046875 -0.046875 -9.390625 0 -10.0625 L -0.71875 -10.0625 L -0.71875 -9.296875 C -0.71875 -7.140625 -1 -7.0625 -1.890625 -7.0625 Z M -15.71875 -7.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-12">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-13">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-14">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph10-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 68.487062 C 95.250969 69.147219 94.715812 69.686281 94.055656 69.686281 C 93.3955 69.686281 92.856437 69.147219 92.856437 68.487062 C 92.856437 67.826906 93.3955 67.29175 94.055656 67.29175 C 94.715812 67.29175 95.250969 67.826906 95.250969 68.487062 Z M 95.250969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 68.487062 C 116.227531 69.147219 115.692375 69.686281 115.032219 69.686281 C 114.372062 69.686281 113.833 69.147219 113.833 68.487062 C 113.833 67.826906 114.372062 67.29175 115.032219 67.29175 C 115.692375 67.29175 116.227531 67.826906 116.227531 68.487062 Z M 116.227531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 68.487062 C 128.813469 69.147219 128.278312 69.686281 127.618156 69.686281 C 126.958 69.686281 126.418937 69.147219 126.418937 68.487062 C 126.418937 67.826906 126.958 67.29175 127.618156 67.29175 C 128.278312 67.29175 128.813469 67.826906 128.813469 68.487062 Z M 128.813469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 68.487062 C 145.594719 69.147219 145.059562 69.686281 144.399406 69.686281 C 143.73925 69.686281 143.200187 69.147219 143.200187 68.487062 C 143.200187 67.826906 143.73925 67.29175 144.399406 67.29175 C 145.059562 67.29175 145.594719 67.826906 145.594719 68.487062 Z M 145.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 68.487062 C 153.985344 69.147219 153.450187 69.686281 152.790031 69.686281 C 152.129875 69.686281 151.590812 69.147219 151.590812 68.487062 C 151.590812 67.826906 152.129875 67.29175 152.790031 67.29175 C 153.450187 67.29175 153.985344 67.826906 153.985344 68.487062 Z M 153.985344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 68.487062 C 158.180656 69.147219 157.6455 69.686281 156.985344 69.686281 C 156.325187 69.686281 155.786125 69.147219 155.786125 68.487062 C 155.786125 67.826906 156.325187 67.29175 156.985344 67.29175 C 157.6455 67.29175 158.180656 67.826906 158.180656 68.487062 Z M 158.180656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 68.487062 C 170.766594 69.147219 170.231437 69.686281 169.571281 69.686281 C 168.911125 69.686281 168.372062 69.147219 168.372062 68.487062 C 168.372062 67.826906 168.911125 67.29175 169.571281 67.29175 C 170.231437 67.29175 170.766594 67.826906 170.766594 68.487062 Z M 170.766594 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 68.487062 C 183.352531 69.147219 182.817375 69.686281 182.157219 69.686281 C 181.497062 69.686281 180.958 69.147219 180.958 68.487062 C 180.958 67.826906 181.497062 67.29175 182.157219 67.29175 C 182.817375 67.29175 183.352531 67.826906 183.352531 68.487062 Z M 183.352531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 68.487062 C 187.547844 69.151125 187.012687 69.686281 186.352531 69.686281 C 185.692375 69.686281 185.157219 69.151125 185.157219 68.487062 C 185.157219 67.826906 185.692375 67.29175 186.352531 67.29175 C 187.012687 67.29175 187.547844 67.826906 187.547844 68.487062 Z M 187.547844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 68.487062 C 191.743156 69.147219 191.208 69.686281 190.547844 69.686281 C 189.887687 69.686281 189.348625 69.147219 189.348625 68.487062 C 189.348625 67.826906 189.887687 67.29175 190.547844 67.29175 C 191.208 67.29175 191.743156 67.826906 191.743156 68.487062 Z M 191.743156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 68.487062 C 195.938469 69.147219 195.403312 69.686281 194.743156 69.686281 C 194.083 69.686281 193.543937 69.147219 193.543937 68.487062 C 193.543937 67.826906 194.083 67.29175 194.743156 67.29175 C 195.403312 67.29175 195.938469 67.826906 195.938469 68.487062 Z M 195.938469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 68.487062 C 200.133781 69.151125 199.598625 69.686281 198.938469 69.686281 C 198.278312 69.686281 197.743156 69.151125 197.743156 68.487062 C 197.743156 67.826906 198.278312 67.29175 198.938469 67.29175 C 199.598625 67.29175 200.133781 67.826906 200.133781 68.487062 Z M 200.133781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 68.487062 C 204.329094 69.151125 203.793937 69.686281 203.133781 69.686281 C 202.473625 69.686281 201.934562 69.151125 201.934562 68.487062 C 201.934562 67.826906 202.473625 67.29175 203.133781 67.29175 C 203.793937 67.29175 204.329094 67.826906 204.329094 68.487062 Z M 204.329094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 68.487062 C 208.524406 69.147219 207.98925 69.686281 207.329094 69.686281 C 206.668937 69.686281 206.129875 69.147219 206.129875 68.487062 C 206.129875 67.826906 206.668937 67.29175 207.329094 67.29175 C 207.98925 67.29175 208.524406 67.826906 208.524406 68.487062 Z M 208.524406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 68.487062 C 212.719719 69.147219 212.184562 69.686281 211.524406 69.686281 C 210.86425 69.686281 210.329094 69.147219 210.329094 68.487062 C 210.329094 67.826906 210.86425 67.29175 211.524406 67.29175 C 212.184562 67.29175 212.719719 67.826906 212.719719 68.487062 Z M 212.719719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 68.487062 C 216.915031 69.151125 216.379875 69.686281 215.719719 69.686281 C 215.059562 69.686281 214.524406 69.151125 214.524406 68.487062 C 214.524406 67.826906 215.059562 67.29175 215.719719 67.29175 C 216.379875 67.29175 216.915031 67.826906 216.915031 68.487062 Z M 216.915031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 68.487062 C 221.110344 69.151125 220.575187 69.686281 219.915031 69.686281 C 219.254875 69.686281 218.715812 69.151125 218.715812 68.487062 C 218.715812 67.826906 219.254875 67.29175 219.915031 67.29175 C 220.575187 67.29175 221.110344 67.826906 221.110344 68.487062 Z M 221.110344 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 68.487062 C 225.305656 69.151125 224.7705 69.686281 224.110344 69.686281 C 223.450187 69.686281 222.915031 69.151125 222.915031 68.487062 C 222.915031 67.826906 223.450187 67.29175 224.110344 67.29175 C 224.7705 67.29175 225.305656 67.826906 225.305656 68.487062 Z M 225.305656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 68.487062 C 229.500969 69.151125 228.965812 69.686281 228.305656 69.686281 C 227.6455 69.686281 227.110344 69.151125 227.110344 68.487062 C 227.110344 67.826906 227.6455 67.29175 228.305656 67.29175 C 228.965812 67.29175 229.500969 67.826906 229.500969 68.487062 Z M 229.500969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 68.490969 C 233.696281 69.151125 233.161125 69.686281 232.500969 69.686281 C 231.840812 69.686281 231.30175 69.151125 231.30175 68.490969 C 231.30175 67.826906 231.840812 67.29175 232.500969 67.29175 C 233.161125 67.29175 233.696281 67.826906 233.696281 68.490969 Z M 233.696281 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 68.490969 C 237.891594 69.151125 237.356437 69.686281 236.696281 69.686281 C 236.036125 69.686281 235.500969 69.151125 235.500969 68.490969 C 235.500969 67.826906 236.036125 67.29175 236.696281 67.29175 C 237.356437 67.29175 237.891594 67.826906 237.891594 68.490969 Z M 237.891594 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 68.490969 C 242.086906 69.151125 241.55175 69.686281 240.891594 69.686281 C 240.231437 69.686281 239.696281 69.151125 239.696281 68.490969 C 239.696281 67.830812 240.231437 67.295656 240.891594 67.295656 C 241.55175 67.295656 242.086906 67.830812 242.086906 68.490969 Z M 242.086906 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 68.494875 C 246.282219 69.155031 245.747062 69.690187 245.086906 69.690187 C 244.42675 69.690187 243.891594 69.155031 243.891594 68.494875 C 243.891594 67.830812 244.42675 67.295656 245.086906 67.295656 C 245.747062 67.295656 246.282219 67.830812 246.282219 68.494875 Z M 246.282219 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 68.490969 C 250.477531 69.151125 249.942375 69.690187 249.282219 69.690187 C 248.622062 69.690187 248.086906 69.151125 248.086906 68.490969 C 248.086906 67.830812 248.622062 67.295656 249.282219 67.295656 C 249.942375 67.295656 250.477531 67.830812 250.477531 68.490969 Z M 250.477531 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 68.490969 C 254.672844 69.155031 254.137687 69.690187 253.477531 69.690187 C 252.817375 69.690187 252.282219 69.155031 252.282219 68.490969 C 252.282219 67.830812 252.817375 67.295656 253.477531 67.295656 C 254.137687 67.295656 254.672844 67.830812 254.672844 68.490969 Z M 254.672844 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 68.498781 C 258.868156 69.158937 258.333 69.694094 257.672844 69.694094 C 257.012687 69.694094 256.477531 69.158937 256.477531 68.498781 C 256.477531 67.834719 257.012687 67.299562 257.672844 67.299562 C 258.333 67.299562 258.868156 67.834719 258.868156 68.498781 Z M 258.868156 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 68.502687 C 263.063469 69.162844 262.528312 69.698 261.868156 69.698 C 261.208 69.698 260.672844 69.162844 260.672844 68.502687 C 260.672844 67.842531 261.208 67.307375 261.868156 67.307375 C 262.528312 67.307375 263.063469 67.842531 263.063469 68.502687 Z M 263.063469 68.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 68.533937 C 267.258781 69.194094 266.723625 69.72925 266.063469 69.72925 C 265.403312 69.72925 264.868156 69.194094 264.868156 68.533937 C 264.868156 67.873781 265.403312 67.338625 266.063469 67.338625 C 266.723625 67.338625 267.258781 67.873781 267.258781 68.533937 Z M 267.258781 68.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 68.756594 C 271.454094 69.41675 270.918937 69.951906 270.258781 69.951906 C 269.598625 69.951906 269.063469 69.41675 269.063469 68.756594 C 269.063469 68.096437 269.598625 67.561281 270.258781 67.561281 C 270.918937 67.561281 271.454094 68.096437 271.454094 68.756594 Z M 271.454094 68.756594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 386.147219 C 275.649406 386.811281 275.11425 387.346437 274.454094 387.346437 C 273.793937 387.346437 273.258781 386.811281 273.258781 386.147219 C 273.258781 385.487062 273.793937 384.951906 274.454094 384.951906 C 275.11425 384.951906 275.649406 385.487062 275.649406 386.147219 Z M 275.649406 386.147219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 68.639406 C 279.844719 69.299562 279.309562 69.834719 278.649406 69.834719 C 277.98925 69.834719 277.454094 69.299562 277.454094 68.639406 C 277.454094 67.97925 277.98925 67.444094 278.649406 67.444094 C 279.309562 67.444094 279.844719 67.97925 279.844719 68.639406 Z M 279.844719 68.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 68.518312 C 284.040031 69.182375 283.504875 69.717531 282.844719 69.717531 C 282.184562 69.717531 281.649406 69.182375 281.649406 68.518312 C 281.649406 67.858156 282.184562 67.323 282.844719 67.323 C 283.504875 67.323 284.040031 67.858156 284.040031 68.518312 Z M 284.040031 68.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 68.498781 C 288.235344 69.162844 287.700187 69.698 287.040031 69.698 C 286.379875 69.698 285.844719 69.162844 285.844719 68.498781 C 285.844719 67.838625 286.379875 67.303469 287.040031 67.303469 C 287.700187 67.303469 288.235344 67.838625 288.235344 68.498781 Z M 288.235344 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 68.494875 C 292.430656 69.155031 291.8955 69.690187 291.235344 69.690187 C 290.575187 69.690187 290.040031 69.155031 290.040031 68.494875 C 290.040031 67.834719 290.575187 67.295656 291.235344 67.295656 C 291.8955 67.295656 292.430656 67.834719 292.430656 68.494875 Z M 292.430656 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 68.494875 C 296.625969 69.155031 296.090812 69.690187 295.430656 69.690187 C 294.7705 69.690187 294.235344 69.155031 294.235344 68.494875 C 294.235344 67.830812 294.7705 67.295656 295.430656 67.295656 C 296.090812 67.295656 296.625969 67.830812 296.625969 68.494875 Z M 296.625969 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 68.490969 C 300.821281 69.151125 300.286125 69.686281 299.625969 69.686281 C 298.965812 69.686281 298.430656 69.151125 298.430656 68.490969 C 298.430656 67.830812 298.965812 67.295656 299.625969 67.295656 C 300.286125 67.295656 300.821281 67.830812 300.821281 68.490969 Z M 300.821281 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 68.490969 C 305.016594 69.151125 304.481437 69.686281 303.821281 69.686281 C 303.161125 69.686281 302.625969 69.151125 302.625969 68.490969 C 302.625969 67.830812 303.161125 67.29175 303.821281 67.29175 C 304.481437 67.29175 305.016594 67.830812 305.016594 68.490969 Z M 305.016594 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 68.487062 C 309.211906 69.151125 308.67675 69.686281 308.016594 69.686281 C 307.356437 69.686281 306.821281 69.151125 306.821281 68.487062 C 306.821281 67.826906 307.356437 67.29175 308.016594 67.29175 C 308.67675 67.29175 309.211906 67.826906 309.211906 68.487062 Z M 309.211906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 68.490969 C 313.407219 69.151125 312.872062 69.686281 312.211906 69.686281 C 311.55175 69.686281 311.016594 69.151125 311.016594 68.490969 C 311.016594 67.830812 311.55175 67.29175 312.211906 67.29175 C 312.872062 67.29175 313.407219 67.830812 313.407219 68.490969 Z M 313.407219 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 68.487062 C 317.602531 69.151125 317.067375 69.686281 316.407219 69.686281 C 315.747062 69.686281 315.211906 69.151125 315.211906 68.487062 C 315.211906 67.826906 315.747062 67.29175 316.407219 67.29175 C 317.067375 67.29175 317.602531 67.826906 317.602531 68.487062 Z M 317.602531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 68.487062 C 321.797844 69.151125 321.262687 69.686281 320.602531 69.686281 C 319.942375 69.686281 319.407219 69.151125 319.407219 68.487062 C 319.407219 67.826906 319.942375 67.29175 320.602531 67.29175 C 321.262687 67.29175 321.797844 67.826906 321.797844 68.487062 Z M 321.797844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 68.490969 C 325.993156 69.151125 325.458 69.686281 324.797844 69.686281 C 324.137687 69.686281 323.602531 69.151125 323.602531 68.490969 C 323.602531 67.826906 324.137687 67.29175 324.797844 67.29175 C 325.458 67.29175 325.993156 67.826906 325.993156 68.490969 Z M 325.993156 68.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 68.487062 C 330.188469 69.151125 329.653312 69.686281 328.993156 69.686281 C 328.333 69.686281 327.797844 69.151125 327.797844 68.487062 C 327.797844 67.826906 328.333 67.29175 328.993156 67.29175 C 329.653312 67.29175 330.188469 67.826906 330.188469 68.487062 Z M 330.188469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 68.487062 C 334.383781 69.147219 333.848625 69.686281 333.188469 69.686281 C 332.528312 69.686281 331.993156 69.147219 331.993156 68.487062 C 331.993156 67.826906 332.528312 67.29175 333.188469 67.29175 C 333.848625 67.29175 334.383781 67.826906 334.383781 68.487062 Z M 334.383781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 68.487062 C 338.579094 69.147219 338.043937 69.686281 337.383781 69.686281 C 336.723625 69.686281 336.188469 69.147219 336.188469 68.487062 C 336.188469 67.826906 336.723625 67.29175 337.383781 67.29175 C 338.043937 67.29175 338.579094 67.826906 338.579094 68.487062 Z M 338.579094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 68.487062 C 342.774406 69.147219 342.23925 69.686281 341.579094 69.686281 C 340.918937 69.686281 340.383781 69.147219 340.383781 68.487062 C 340.383781 67.826906 340.918937 67.29175 341.579094 67.29175 C 342.23925 67.29175 342.774406 67.826906 342.774406 68.487062 Z M 342.774406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 68.487062 C 346.969719 69.147219 346.434562 69.686281 345.774406 69.686281 C 345.11425 69.686281 344.579094 69.147219 344.579094 68.487062 C 344.579094 67.826906 345.11425 67.29175 345.774406 67.29175 C 346.434562 67.29175 346.969719 67.826906 346.969719 68.487062 Z M 346.969719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 68.487062 C 351.165031 69.151125 350.629875 69.686281 349.969719 69.686281 C 349.309562 69.686281 348.774406 69.151125 348.774406 68.487062 C 348.774406 67.826906 349.309562 67.29175 349.969719 67.29175 C 350.629875 67.29175 351.165031 67.826906 351.165031 68.487062 Z M 351.165031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 68.487062 C 359.555656 69.151125 359.0205 69.686281 358.360344 69.686281 C 357.700187 69.686281 357.165031 69.151125 357.165031 68.487062 C 357.165031 67.826906 357.700187 67.29175 358.360344 67.29175 C 359.0205 67.29175 359.555656 67.826906 359.555656 68.487062 Z M 359.555656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 68.487062 C 363.750969 69.147219 363.215812 69.686281 362.555656 69.686281 C 361.8955 69.686281 361.360344 69.147219 361.360344 68.487062 C 361.360344 67.826906 361.8955 67.29175 362.555656 67.29175 C 363.215812 67.29175 363.750969 67.826906 363.750969 68.487062 Z M 363.750969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 68.487062 C 372.141594 69.147219 371.606437 69.686281 370.946281 69.686281 C 370.286125 69.686281 369.750969 69.147219 369.750969 68.487062 C 369.750969 67.826906 370.286125 67.29175 370.946281 67.29175 C 371.606437 67.29175 372.141594 67.826906 372.141594 68.487062 Z M 372.141594 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 68.487062 C 393.118156 69.147219 392.583 69.686281 391.922844 69.686281 C 391.262687 69.686281 390.727531 69.147219 390.727531 68.487062 C 390.727531 67.826906 391.262687 67.29175 391.922844 67.29175 C 392.583 67.29175 393.118156 67.826906 393.118156 68.487062 Z M 393.118156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 68.487062 C 397.313469 69.147219 396.778312 69.686281 396.118156 69.686281 C 395.458 69.686281 394.922844 69.147219 394.922844 68.487062 C 394.922844 67.826906 395.458 67.29175 396.118156 67.29175 C 396.778312 67.29175 397.313469 67.826906 397.313469 68.487062 Z M 397.313469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 68.487062 C 435.071281 69.147219 434.536125 69.686281 433.875969 69.686281 C 433.215812 69.686281 432.680656 69.147219 432.680656 68.487062 C 432.680656 67.826906 433.215812 67.29175 433.875969 67.29175 C 434.536125 67.29175 435.071281 67.826906 435.071281 68.487062 Z M 435.071281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 77.990969 L 79.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.758781 73.240969 L 99.758781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.036125 73.240969 L 120.036125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.317375 73.240969 L 140.317375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.594719 73.240969 L 160.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 180.872062 77.990969 L 180.872062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 201.149406 73.240969 L 201.149406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.430656 73.240969 L 221.430656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 241.708 73.240969 L 241.708 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.98925 73.240969 L 261.98925 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.266594 77.990969 L 282.266594 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 302.543937 73.240969 L 302.543937 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.825187 73.240969 L 322.825187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 343.102531 73.240969 L 343.102531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.379875 73.240969 L 363.379875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.661125 77.990969 L 383.661125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 403.938469 73.240969 L 403.938469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 424.219719 73.240969 L 424.219719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 444.493156 73.240969 L 444.493156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.774406 73.240969 L 464.774406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 77.990969 L 485.055656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 77.990969 L 79.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 77.990969 L 485.055656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="73.016" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="174.408" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="269.797" y="389.053"/>
+ <use xlink:href="#glyph0-1" x="281.804975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="371.189" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="383.196975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="472.582" y="389.053"/>
+ <use xlink:href="#glyph0-1" x="484.589975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="317.332" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="328.643971" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="339.096364" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="351.926445" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="362.376786" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="379.976604" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="390.195126" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="409.038523" y="417.528"/>
+ <use xlink:href="#glyph0-7" x="419.712278" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="438.048415" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.756113" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.764088" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-2" x="470.098999" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="479.806697" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 392.862062 L 79.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.758781 397.615969 L 99.758781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.036125 397.615969 L 120.036125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.317375 397.615969 L 140.317375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.594719 397.615969 L 160.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 180.872062 392.862062 L 180.872062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 201.149406 397.615969 L 201.149406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.430656 397.615969 L 221.430656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 241.708 397.615969 L 241.708 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.98925 397.615969 L 261.98925 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.266594 392.862062 L 282.266594 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 302.543937 397.615969 L 302.543937 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.825187 397.615969 L 322.825187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 343.102531 397.615969 L 343.102531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.379875 397.615969 L 363.379875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.661125 392.862062 L 383.661125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 403.938469 397.615969 L 403.938469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 424.219719 397.615969 L 424.219719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 444.493156 397.615969 L 444.493156 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.774406 397.615969 L 464.774406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 392.862062 L 485.055656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 392.862062 L 79.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 392.862062 L 485.055656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 84.401125 L 79.372062 84.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 100.315187 L 79.372062 100.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 116.225344 L 79.372062 116.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 132.139406 L 79.372062 132.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 148.053469 L 79.372062 148.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 163.967531 L 79.372062 163.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 179.877687 L 79.372062 179.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 195.79175 L 79.372062 195.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 211.705812 L 79.372062 211.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 227.615969 L 79.372062 227.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 243.530031 L 79.372062 243.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 259.444094 L 79.372062 259.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.358156 L 79.372062 275.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 291.268312 L 79.372062 291.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 307.182375 L 79.372062 307.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 323.092531 L 79.372062 323.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 339.006594 L 79.372062 339.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 354.920656 L 79.372062 354.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 370.834719 L 79.372062 370.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 386.748781 L 79.372062 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 386.748781 L 79.372062 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="306.338"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="306.338"/>
+ <use xlink:href="#glyph0-4" x="55.658072" y="306.338"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="242.687"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="242.687"/>
+ <use xlink:href="#glyph0-9" x="55.658072" y="242.687"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="179.036"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="179.036"/>
+ <use xlink:href="#glyph0-10" x="55.658072" y="179.036"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="115.386"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="115.386"/>
+ <use xlink:href="#glyph0-11" x="55.658072" y="115.386"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.657" y="51.734"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-1" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph8-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph8-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph8-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph8-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph8-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph8-11" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph8-12" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph8-13" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph9-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-14" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 84.401125 L 498.903312 84.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 100.315187 L 498.903312 100.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 116.225344 L 498.903312 116.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 132.139406 L 498.903312 132.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 148.053469 L 498.903312 148.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 163.967531 L 498.903312 163.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 179.877687 L 498.903312 179.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 195.79175 L 498.903312 195.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 211.705812 L 498.903312 211.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 227.615969 L 498.903312 227.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 243.530031 L 498.903312 243.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 259.444094 L 498.903312 259.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.358156 L 498.903312 275.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 291.268312 L 498.903312 291.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 307.182375 L 498.903312 307.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 323.092531 L 498.903312 323.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 339.006594 L 498.903312 339.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 354.920656 L 498.903312 354.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 370.834719 L 498.903312 370.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 386.748781 L 498.903312 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 386.748781 L 498.903312 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 77.990969 L 79.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.758781 73.240969 L 99.758781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.036125 73.240969 L 120.036125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.317375 73.240969 L 140.317375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.594719 73.240969 L 160.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 180.872062 77.990969 L 180.872062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 201.149406 73.240969 L 201.149406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.430656 73.240969 L 221.430656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 241.708 73.240969 L 241.708 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.98925 73.240969 L 261.98925 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.266594 77.990969 L 282.266594 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 302.543937 73.240969 L 302.543937 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.825187 73.240969 L 322.825187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 343.102531 73.240969 L 343.102531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.379875 73.240969 L 363.379875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.661125 77.990969 L 383.661125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 403.938469 73.240969 L 403.938469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 424.219719 73.240969 L 424.219719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 444.493156 73.240969 L 444.493156 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.774406 73.240969 L 464.774406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 77.990969 L 485.055656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 77.990969 L 79.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 77.990969 L 485.055656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 392.862062 L 79.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.758781 397.615969 L 99.758781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.036125 397.615969 L 120.036125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.317375 397.615969 L 140.317375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.594719 397.615969 L 160.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 180.872062 392.862062 L 180.872062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 201.149406 397.615969 L 201.149406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.430656 397.615969 L 221.430656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 241.708 397.615969 L 241.708 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.98925 397.615969 L 261.98925 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.266594 392.862062 L 282.266594 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 302.543937 397.615969 L 302.543937 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.825187 397.615969 L 322.825187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 343.102531 397.615969 L 343.102531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.379875 397.615969 L 363.379875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.661125 392.862062 L 383.661125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 403.938469 397.615969 L 403.938469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 424.219719 397.615969 L 424.219719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 444.493156 397.615969 L 444.493156 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.774406 397.615969 L 464.774406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 392.862062 L 485.055656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.477531 392.862062 L 79.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.055656 392.862062 L 485.055656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 84.401125 L 79.372062 84.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 100.315187 L 79.372062 100.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 116.225344 L 79.372062 116.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 132.139406 L 79.372062 132.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 148.053469 L 79.372062 148.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 163.967531 L 79.372062 163.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 179.877687 L 79.372062 179.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 195.79175 L 79.372062 195.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 211.705812 L 79.372062 211.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 227.615969 L 79.372062 227.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 243.530031 L 79.372062 243.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 259.444094 L 79.372062 259.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.358156 L 79.372062 275.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 291.268312 L 79.372062 291.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 307.182375 L 79.372062 307.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 323.092531 L 79.372062 323.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 339.006594 L 79.372062 339.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 354.920656 L 79.372062 354.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 370.834719 L 79.372062 370.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 386.748781 L 79.372062 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 386.748781 L 79.372062 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 84.401125 L 498.903312 84.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 100.315187 L 498.903312 100.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 116.225344 L 498.903312 116.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 132.139406 L 498.903312 132.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 148.053469 L 498.903312 148.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 163.967531 L 498.903312 163.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 179.877687 L 498.903312 179.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 195.79175 L 498.903312 195.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 211.705812 L 498.903312 211.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 227.615969 L 498.903312 227.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 243.530031 L 498.903312 243.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 259.444094 L 498.903312 259.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.358156 L 498.903312 275.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 291.268312 L 498.903312 291.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 307.182375 L 498.903312 307.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 323.092531 L 498.903312 323.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 339.006594 L 498.903312 339.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 354.920656 L 498.903312 354.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 370.834719 L 498.903312 370.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 386.748781 L 498.903312 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 386.748781 L 498.903312 386.748781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/lb2jspiL_s012.svg b/doc/figs/lb2jspiL_s012.svg
new file mode 100644
index 00000000000..d0c6dcf3164
--- /dev/null
+++ b/doc/figs/lb2jspiL_s012.svg
@@ -0,0 +1,555 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="514pt" height="432pt" viewBox="0 0 514 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 4.515625 -8.8125 C 4.09375 -8.78125 4 -8.75 4 -8.53125 C 4 -8.296875 4.125 -8.296875 4.5625 -8.296875 L 5.6875 -8.296875 C 7.78125 -8.296875 8.703125 -6.578125 8.703125 -4.21875 C 8.703125 -1 7.046875 -0.140625 5.84375 -0.140625 C 4.65625 -0.140625 2.65625 -0.71875 1.9375 -2.328125 C 2.71875 -2.203125 3.4375 -2.65625 3.4375 -3.53125 C 3.4375 -4.25 2.921875 -4.734375 2.234375 -4.734375 C 1.640625 -4.734375 1 -4.390625 1 -3.453125 C 1 -1.28125 3.1875 0.515625 5.90625 0.515625 C 8.828125 0.515625 10.984375 -1.71875 10.984375 -4.1875 C 10.984375 -6.453125 9.171875 -8.21875 6.8125 -8.640625 C 8.953125 -9.25 10.328125 -11.046875 10.328125 -12.953125 C 10.328125 -14.890625 8.3125 -16.3125 5.9375 -16.3125 C 3.484375 -16.3125 1.671875 -14.8125 1.671875 -13.03125 C 1.671875 -12.046875 2.421875 -11.84375 2.796875 -11.84375 C 3.3125 -11.84375 3.90625 -12.21875 3.90625 -12.953125 C 3.90625 -13.734375 3.3125 -14.078125 2.765625 -14.078125 C 2.625 -14.078125 2.578125 -14.078125 2.5 -14.0625 C 3.4375 -15.71875 5.734375 -15.71875 5.859375 -15.71875 C 6.671875 -15.71875 8.265625 -15.359375 8.265625 -12.953125 C 8.265625 -12.484375 8.1875 -11.109375 7.484375 -10.0625 C 6.75 -8.984375 5.90625 -8.90625 5.25 -8.875 Z M 4.515625 -8.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.953125 -5.765625 C 4.03125 -6.078125 4.171875 -6.625 4.171875 -6.703125 C 4.171875 -7.046875 3.90625 -7.203125 3.625 -7.203125 C 3.078125 -7.203125 2.9375 -6.671875 2.875 -6.4375 L 0.609375 2.625 C 0.546875 2.890625 0.546875 2.96875 0.546875 3 C 0.546875 3.421875 0.859375 3.515625 1.0625 3.515625 C 1.140625 3.515625 1.515625 3.5 1.734375 3.078125 C 1.78125 2.9375 2.25 1 2.578125 -0.3125 C 2.859375 -0.09375 3.421875 0.15625 4.25 0.15625 C 5.59375 0.15625 6.46875 -0.9375 6.515625 -1 C 6.8125 0.125 7.921875 0.15625 8.125 0.15625 C 8.875 0.15625 9.25 -0.453125 9.375 -0.734375 C 9.703125 -1.328125 9.9375 -2.265625 9.9375 -2.34375 C 9.9375 -2.4375 9.875 -2.546875 9.671875 -2.546875 C 9.484375 -2.546875 9.453125 -2.453125 9.34375 -2.046875 C 9.125 -1.140625 8.8125 -0.296875 8.171875 -0.296875 C 7.796875 -0.296875 7.65625 -0.609375 7.65625 -1.0625 C 7.65625 -1.34375 7.828125 -2.046875 7.9375 -2.515625 L 8.375 -4.1875 C 8.46875 -4.609375 8.546875 -4.953125 8.671875 -5.4375 C 8.765625 -5.796875 8.921875 -6.4375 8.921875 -6.53125 C 8.921875 -6.953125 8.59375 -7.046875 8.40625 -7.046875 C 7.828125 -7.046875 7.734375 -6.640625 7.546875 -5.90625 L 7.203125 -4.546875 L 6.703125 -2.5 L 6.53125 -1.84375 C 6.5 -1.75 6.0625 -1.125 5.6875 -0.8125 C 5.40625 -0.609375 4.9375 -0.296875 4.328125 -0.296875 C 3.5625 -0.296875 3.046875 -0.703125 3.046875 -1.71875 C 3.046875 -2.140625 3.171875 -2.625 3.265625 -3.03125 Z M 3.953125 -5.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 0.84375 1.984375 C 0.71875 2.5 0.6875 2.625 0.03125 2.625 C -0.203125 2.625 -0.390625 2.625 -0.390625 2.9375 C -0.390625 3.09375 -0.25 3.171875 -0.15625 3.171875 C 0 3.171875 0.0625 3.125 1.28125 3.125 C 2.453125 3.125 2.796875 3.171875 2.90625 3.171875 C 2.96875 3.171875 3.21875 3.171875 3.21875 2.859375 C 3.21875 2.625 2.984375 2.625 2.796875 2.625 C 2.015625 2.625 2.015625 2.53125 2.015625 2.390625 C 2.015625 2.265625 2.296875 1.109375 2.796875 -0.796875 C 3 -0.421875 3.515625 0.15625 4.390625 0.15625 C 6.40625 0.15625 8.5 -2.15625 8.5 -4.53125 C 8.5 -6.140625 7.453125 -7.203125 6.140625 -7.203125 C 5.171875 -7.203125 4.375 -6.53125 3.90625 -6.046875 C 3.5625 -7.203125 2.46875 -7.203125 2.296875 -7.203125 C 1.71875 -7.203125 1.3125 -6.828125 1.046875 -6.328125 C 0.671875 -5.59375 0.484375 -4.75 0.484375 -4.703125 C 0.484375 -4.5625 0.609375 -4.5 0.734375 -4.5 C 0.953125 -4.5 0.96875 -4.5625 1.078125 -4.984375 C 1.296875 -5.8125 1.578125 -6.75 2.25 -6.75 C 2.65625 -6.75 2.78125 -6.375 2.78125 -5.984375 C 2.78125 -5.8125 2.71875 -5.421875 2.6875 -5.296875 Z M 3.859375 -5.03125 C 3.9375 -5.3125 3.9375 -5.34375 4.1875 -5.640625 C 4.8125 -6.375 5.515625 -6.75 6.09375 -6.75 C 6.90625 -6.75 7.21875 -5.953125 7.21875 -5.21875 C 7.21875 -4.609375 6.859375 -2.859375 6.375 -1.890625 C 5.953125 -1.015625 5.171875 -0.296875 4.390625 -0.296875 C 3.28125 -0.296875 3.03125 -1.5625 3.03125 -1.6875 C 3.03125 -1.71875 3.0625 -1.890625 3.078125 -1.9375 Z M 3.859375 -5.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 9.765625 -2.75 C 9.953125 -2.75 10.265625 -2.75 10.265625 -3.0625 C 10.265625 -3.390625 9.953125 -3.390625 9.765625 -3.390625 L 2.03125 -3.390625 C 1.84375 -3.390625 1.53125 -3.390625 1.53125 -3.0625 C 1.53125 -2.75 1.84375 -2.75 2.03125 -2.75 Z M 9.765625 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 6.046875 -2.75 L 10.015625 -2.75 C 10.1875 -2.75 10.484375 -2.75 10.484375 -3.0625 C 10.484375 -3.390625 10.1875 -3.390625 10.015625 -3.390625 L 6.046875 -3.390625 L 6.046875 -7.359375 C 6.046875 -7.53125 6.046875 -7.84375 5.734375 -7.84375 C 5.40625 -7.84375 5.40625 -7.53125 5.40625 -7.359375 L 5.40625 -3.390625 L 1.453125 -3.390625 C 1.28125 -3.390625 0.96875 -3.390625 0.96875 -3.0625 C 0.96875 -2.75 1.28125 -2.75 1.453125 -2.75 L 5.40625 -2.75 L 5.40625 1.234375 C 5.40625 1.390625 5.40625 1.703125 5.734375 1.703125 C 6.046875 1.703125 6.046875 1.390625 6.046875 1.234375 Z M 6.046875 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-11">
+<path style="stroke:none;" d="M -7.140625 -8.984375 C -1.34375 -8.984375 -0.140625 -6.40625 -0.140625 -4.9375 C -0.140625 -4.34375 -0.21875 -3.046875 -1.078125 -2.421875 L -1.078125 -2.578125 C -1.03125 -2.75 -1.171875 -3.625 -2.078125 -3.625 C -2.625 -3.625 -3.09375 -3.265625 -3.09375 -2.625 C -3.09375 -1.984375 -2.671875 -1.59375 -2.03125 -1.59375 C -0.515625 -1.59375 0.515625 -2.828125 0.515625 -4.953125 C 0.515625 -8.015625 -2.75 -10.984375 -8.078125 -10.984375 C -14.671875 -10.984375 -16.3125 -8.25 -16.3125 -6.078125 C -16.3125 -3.390625 -14.0625 -1 -10.8125 -1 C -7.578125 -1 -5.375 -3.28125 -5.375 -5.734375 C -5.375 -7.5625 -6.703125 -8.484375 -7.953125 -8.984375 Z M -5.859375 -5.84375 C -5.859375 -4.296875 -7.109375 -3.625 -7.578125 -3.40625 C -8.515625 -3.015625 -9.6875 -3.015625 -10.796875 -3.015625 C -12.171875 -3.015625 -13.34375 -3.015625 -14.34375 -3.65625 C -15.015625 -4.09375 -15.71875 -4.765625 -15.71875 -6.078125 C -15.71875 -7.484375 -14.5 -8.1875 -13.9375 -8.4375 C -12.734375 -8.921875 -10.640625 -8.921875 -10.28125 -8.921875 C -8.21875 -8.921875 -5.859375 -8 -5.859375 -5.84375 Z M -5.859375 -5.84375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-12">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-13">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-14">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph10-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 68.498781 C 275.649406 69.158937 275.11425 69.694094 274.454094 69.694094 C 273.793937 69.694094 273.258781 69.158937 273.258781 68.498781 C 273.258781 67.838625 273.793937 67.299562 274.454094 67.299562 C 275.11425 67.299562 275.649406 67.838625 275.649406 68.498781 Z M 275.649406 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 68.498781 C 288.235344 69.158937 287.700187 69.694094 287.040031 69.694094 C 286.379875 69.694094 285.844719 69.158937 285.844719 68.498781 C 285.844719 67.838625 286.379875 67.299562 287.040031 67.299562 C 287.700187 67.299562 288.235344 67.838625 288.235344 68.498781 Z M 288.235344 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 69.588625 C 300.821281 70.252687 300.286125 70.787844 299.625969 70.787844 C 298.965812 70.787844 298.430656 70.252687 298.430656 69.588625 C 298.430656 68.928469 298.965812 68.393312 299.625969 68.393312 C 300.286125 68.393312 300.821281 68.928469 300.821281 69.588625 Z M 300.821281 69.588625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 70.865969 C 305.016594 71.530031 304.481437 72.065187 303.821281 72.065187 C 303.161125 72.065187 302.625969 71.530031 302.625969 70.865969 C 302.625969 70.205812 303.161125 69.670656 303.821281 69.670656 C 304.481437 69.670656 305.016594 70.205812 305.016594 70.865969 Z M 305.016594 70.865969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 72.04175 C 309.211906 72.701906 308.67675 73.240969 308.016594 73.240969 C 307.356437 73.240969 306.821281 72.701906 306.821281 72.04175 C 306.821281 71.381594 307.356437 70.846437 308.016594 70.846437 C 308.67675 70.846437 309.211906 71.381594 309.211906 72.04175 Z M 309.211906 72.04175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 73.463625 C 313.407219 74.127687 312.872062 74.662844 312.211906 74.662844 C 311.55175 74.662844 311.016594 74.127687 311.016594 73.463625 C 311.016594 72.803469 311.55175 72.268312 312.211906 72.268312 C 312.872062 72.268312 313.407219 72.803469 313.407219 73.463625 Z M 313.407219 73.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 74.740969 C 317.602531 75.401125 317.067375 75.940187 316.407219 75.940187 C 315.747062 75.940187 315.211906 75.401125 315.211906 74.740969 C 315.211906 74.080812 315.747062 73.545656 316.407219 73.545656 C 317.067375 73.545656 317.602531 74.080812 317.602531 74.740969 Z M 317.602531 74.740969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 76.690187 C 321.797844 77.350344 321.262687 77.8855 320.602531 77.8855 C 319.942375 77.8855 319.407219 77.350344 319.407219 76.690187 C 319.407219 76.030031 319.942375 75.494875 320.602531 75.494875 C 321.262687 75.494875 321.797844 76.030031 321.797844 76.690187 Z M 321.797844 76.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 78.8855 C 325.993156 79.545656 325.458 80.080812 324.797844 80.080812 C 324.137687 80.080812 323.602531 79.545656 323.602531 78.8855 C 323.602531 78.225344 324.137687 77.686281 324.797844 77.686281 C 325.458 77.686281 325.993156 78.225344 325.993156 78.8855 Z M 325.993156 78.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 81.780031 C 330.188469 82.440187 329.653312 82.975344 328.993156 82.975344 C 328.333 82.975344 327.797844 82.440187 327.797844 81.780031 C 327.797844 81.119875 328.333 80.584719 328.993156 80.584719 C 329.653312 80.584719 330.188469 81.119875 330.188469 81.780031 Z M 330.188469 81.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 85.717531 C 334.383781 86.377687 333.848625 86.912844 333.188469 86.912844 C 332.528312 86.912844 331.993156 86.377687 331.993156 85.717531 C 331.993156 85.053469 332.528312 84.518312 333.188469 84.518312 C 333.848625 84.518312 334.383781 85.053469 334.383781 85.717531 Z M 334.383781 85.717531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 92.846437 C 338.579094 93.506594 338.043937 94.04175 337.383781 94.04175 C 336.723625 94.04175 336.188469 93.506594 336.188469 92.846437 C 336.188469 92.186281 336.723625 91.651125 337.383781 91.651125 C 338.043937 91.651125 338.579094 92.186281 338.579094 92.846437 Z M 338.579094 92.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 102.912844 C 342.774406 103.573 342.23925 104.112062 341.579094 104.112062 C 340.918937 104.112062 340.383781 103.573 340.383781 102.912844 C 340.383781 102.252687 340.918937 101.717531 341.579094 101.717531 C 342.23925 101.717531 342.774406 102.252687 342.774406 102.912844 Z M 342.774406 102.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 121.006594 C 346.969719 121.670656 346.434562 122.205812 345.774406 122.205812 C 345.11425 122.205812 344.579094 121.670656 344.579094 121.006594 C 344.579094 120.346437 345.11425 119.811281 345.774406 119.811281 C 346.434562 119.811281 346.969719 120.346437 346.969719 121.006594 Z M 346.969719 121.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 164.5105 C 351.165031 165.174562 350.629875 165.709719 349.969719 165.709719 C 349.309562 165.709719 348.774406 165.174562 348.774406 164.5105 C 348.774406 163.850344 349.309562 163.315187 349.969719 163.315187 C 350.629875 163.315187 351.165031 163.850344 351.165031 164.5105 Z M 351.165031 164.5105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 245.237062 C 355.360344 245.897219 354.825187 246.432375 354.165031 246.432375 C 353.504875 246.432375 352.969719 245.897219 352.969719 245.237062 C 352.969719 244.573 353.504875 244.037844 354.165031 244.037844 C 354.825187 244.037844 355.360344 244.573 355.360344 245.237062 Z M 355.360344 245.237062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 310.811281 C 359.555656 311.471437 359.0205 312.006594 358.360344 312.006594 C 357.700187 312.006594 357.165031 311.471437 357.165031 310.811281 C 357.165031 310.151125 357.700187 309.615969 358.360344 309.615969 C 359.0205 309.615969 359.555656 310.151125 359.555656 310.811281 Z M 359.555656 310.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 337.889406 C 363.750969 338.553469 363.215812 339.088625 362.555656 339.088625 C 361.8955 339.088625 361.360344 338.553469 361.360344 337.889406 C 361.360344 337.22925 361.8955 336.694094 362.555656 336.694094 C 363.215812 336.694094 363.750969 337.22925 363.750969 337.889406 Z M 363.750969 337.889406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 367.946281 351.987062 C 367.946281 352.647219 367.411125 353.186281 366.750969 353.186281 C 366.090812 353.186281 365.555656 352.647219 365.555656 351.987062 C 365.555656 351.326906 366.090812 350.79175 366.750969 350.79175 C 367.411125 350.79175 367.946281 351.326906 367.946281 351.987062 Z M 367.946281 351.987062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 361.405031 C 372.141594 362.065187 371.606437 362.600344 370.946281 362.600344 C 370.286125 362.600344 369.750969 362.065187 369.750969 361.405031 C 369.750969 360.744875 370.286125 360.209719 370.946281 360.209719 C 371.606437 360.209719 372.141594 360.744875 372.141594 361.405031 Z M 372.141594 361.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 376.336906 362.733156 C 376.336906 363.393312 375.80175 363.932375 375.141594 363.932375 C 374.481437 363.932375 373.946281 363.393312 373.946281 362.733156 C 373.946281 362.073 374.481437 361.537844 375.141594 361.537844 C 375.80175 361.537844 376.336906 362.073 376.336906 362.733156 Z M 376.336906 362.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 369.830812 C 380.532219 370.494875 379.997062 371.030031 379.336906 371.030031 C 378.67675 371.030031 378.141594 370.494875 378.141594 369.830812 C 378.141594 369.170656 378.67675 368.6355 379.336906 368.6355 C 379.997062 368.6355 380.532219 369.170656 380.532219 369.830812 Z M 380.532219 369.830812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 373.459719 C 384.727531 374.119875 384.192375 374.658937 383.532219 374.658937 C 382.872062 374.658937 382.336906 374.119875 382.336906 373.459719 C 382.336906 372.799562 382.872062 372.264406 383.532219 372.264406 C 384.192375 372.264406 384.727531 372.799562 384.727531 373.459719 Z M 384.727531 373.459719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 371.545656 C 388.922844 372.205812 388.387687 372.740969 387.727531 372.740969 C 387.067375 372.740969 386.532219 372.205812 386.532219 371.545656 C 386.532219 370.8855 387.067375 370.346437 387.727531 370.346437 C 388.387687 370.346437 388.922844 370.8855 388.922844 371.545656 Z M 388.922844 371.545656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 376.303469 C 393.118156 376.963625 392.583 377.498781 391.922844 377.498781 C 391.262687 377.498781 390.727531 376.963625 390.727531 376.303469 C 390.727531 375.643312 391.262687 375.108156 391.922844 375.108156 C 392.583 375.108156 393.118156 375.643312 393.118156 376.303469 Z M 393.118156 376.303469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 374.139406 C 397.313469 374.803469 396.778312 375.338625 396.118156 375.338625 C 395.458 375.338625 394.922844 374.803469 394.922844 374.139406 C 394.922844 373.47925 395.458 372.944094 396.118156 372.944094 C 396.778312 372.944094 397.313469 373.47925 397.313469 374.139406 Z M 397.313469 374.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 401.508781 378.408937 C 401.508781 379.069094 400.973625 379.60425 400.313469 379.60425 C 399.653312 379.60425 399.118156 379.069094 399.118156 378.408937 C 399.118156 377.744875 399.653312 377.209719 400.313469 377.209719 C 400.973625 377.209719 401.508781 377.744875 401.508781 378.408937 Z M 401.508781 378.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 376.994875 C 405.704094 377.655031 405.168937 378.190187 404.508781 378.190187 C 403.848625 378.190187 403.313469 377.655031 403.313469 376.994875 C 403.313469 376.334719 403.848625 375.799562 404.508781 375.799562 C 405.168937 375.799562 405.704094 376.334719 405.704094 376.994875 Z M 405.704094 376.994875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 409.899406 382.764406 C 409.899406 383.424562 409.36425 383.959719 408.704094 383.959719 C 408.043937 383.959719 407.508781 383.424562 407.508781 382.764406 C 407.508781 382.10425 408.043937 381.569094 408.704094 381.569094 C 409.36425 381.569094 409.899406 382.10425 409.899406 382.764406 Z M 409.899406 382.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 414.094719 379.264406 C 414.094719 379.924562 413.559562 380.459719 412.899406 380.459719 C 412.23925 380.459719 411.704094 379.924562 411.704094 379.264406 C 411.704094 378.600344 412.23925 378.065187 412.899406 378.065187 C 413.559562 378.065187 414.094719 378.600344 414.094719 379.264406 Z M 414.094719 379.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 418.290031 383.631594 C 418.290031 384.29175 417.754875 384.826906 417.094719 384.826906 C 416.434562 384.826906 415.899406 384.29175 415.899406 383.631594 C 415.899406 382.971437 416.434562 382.436281 417.094719 382.436281 C 417.754875 382.436281 418.290031 382.971437 418.290031 383.631594 Z M 418.290031 383.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 380.846437 C 422.485344 381.5105 421.950187 382.045656 421.290031 382.045656 C 420.629875 382.045656 420.094719 381.5105 420.094719 380.846437 C 420.094719 380.186281 420.629875 379.651125 421.290031 379.651125 C 421.950187 379.651125 422.485344 380.186281 422.485344 380.846437 Z M 422.485344 380.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.680656 381.053469 C 426.680656 381.717531 426.1455 382.252687 425.485344 382.252687 C 424.825187 382.252687 424.290031 381.717531 424.290031 381.053469 C 424.290031 380.393312 424.825187 379.858156 425.485344 379.858156 C 426.1455 379.858156 426.680656 380.393312 426.680656 381.053469 Z M 426.680656 381.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 381.733156 C 430.875969 382.397219 430.340812 382.932375 429.680656 382.932375 C 429.0205 382.932375 428.485344 382.397219 428.485344 381.733156 C 428.485344 381.073 429.0205 380.537844 429.680656 380.537844 C 430.340812 380.537844 430.875969 381.073 430.875969 381.733156 Z M 430.875969 381.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 384.658937 C 435.071281 385.323 434.536125 385.858156 433.875969 385.858156 C 433.215812 385.858156 432.680656 385.323 432.680656 384.658937 C 432.680656 383.998781 433.215812 383.463625 433.875969 383.463625 C 434.536125 383.463625 435.071281 383.998781 435.071281 384.658937 Z M 435.071281 384.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.266594 380.221437 C 439.266594 380.881594 438.731437 381.41675 438.071281 381.41675 C 437.411125 381.41675 436.875969 380.881594 436.875969 380.221437 C 436.875969 379.561281 437.411125 379.026125 438.071281 379.026125 C 438.731437 379.026125 439.266594 379.561281 439.266594 380.221437 Z M 439.266594 380.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 383.752687 C 443.461906 384.412844 442.92675 384.951906 442.266594 384.951906 C 441.606437 384.951906 441.071281 384.412844 441.071281 383.752687 C 441.071281 383.092531 441.606437 382.557375 442.266594 382.557375 C 442.92675 382.557375 443.461906 383.092531 443.461906 383.752687 Z M 443.461906 383.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 447.657219 383.518312 C 447.657219 384.178469 447.122062 384.713625 446.461906 384.713625 C 445.80175 384.713625 445.266594 384.178469 445.266594 383.518312 C 445.266594 382.858156 445.80175 382.323 446.461906 382.323 C 447.122062 382.323 447.657219 382.858156 447.657219 383.518312 Z M 447.657219 383.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 380.530031 C 451.852531 381.190187 451.317375 381.725344 450.657219 381.725344 C 449.997062 381.725344 449.461906 381.190187 449.461906 380.530031 C 449.461906 379.869875 449.997062 379.334719 450.657219 379.334719 C 451.317375 379.334719 451.852531 379.869875 451.852531 380.530031 Z M 451.852531 380.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 381.002687 C 456.047844 381.662844 455.512687 382.201906 454.852531 382.201906 C 454.192375 382.201906 453.657219 381.662844 453.657219 381.002687 C 453.657219 380.342531 454.192375 379.807375 454.852531 379.807375 C 455.512687 379.807375 456.047844 380.342531 456.047844 381.002687 Z M 456.047844 381.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.243156 382.342531 C 460.243156 383.002687 459.708 383.537844 459.047844 383.537844 C 458.387687 383.537844 457.852531 383.002687 457.852531 382.342531 C 457.852531 381.682375 458.387687 381.143312 459.047844 381.143312 C 459.708 381.143312 460.243156 381.682375 460.243156 382.342531 Z M 460.243156 382.342531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.438469 379.088625 C 464.438469 379.748781 463.903312 380.283937 463.243156 380.283937 C 462.583 380.283937 462.047844 379.748781 462.047844 379.088625 C 462.047844 378.428469 462.583 377.889406 463.243156 377.889406 C 463.903312 377.889406 464.438469 378.428469 464.438469 379.088625 Z M 464.438469 379.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.637687 381.362062 C 468.637687 382.026125 468.098625 382.561281 467.438469 382.561281 C 466.778312 382.561281 466.243156 382.026125 466.243156 381.362062 C 466.243156 380.701906 466.778312 380.16675 467.438469 380.16675 C 468.098625 380.16675 468.637687 380.701906 468.637687 381.362062 Z M 468.637687 381.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 472.829094 379.088625 C 472.829094 379.748781 472.293937 380.283937 471.633781 380.283937 C 470.973625 380.283937 470.438469 379.748781 470.438469 379.088625 C 470.438469 378.428469 470.973625 377.889406 471.633781 377.889406 C 472.293937 377.889406 472.829094 378.428469 472.829094 379.088625 Z M 472.829094 379.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 477.024406 375.338625 C 477.024406 375.998781 476.48925 376.533937 475.829094 376.533937 C 475.168937 376.533937 474.633781 375.998781 474.633781 375.338625 C 474.633781 374.674562 475.168937 374.139406 475.829094 374.139406 C 476.48925 374.139406 477.024406 374.674562 477.024406 375.338625 Z M 477.024406 375.338625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 481.223625 375.143312 C 481.223625 375.803469 480.684562 376.338625 480.024406 376.338625 C 479.36425 376.338625 478.829094 375.803469 478.829094 375.143312 C 478.829094 374.47925 479.36425 373.944094 480.024406 373.944094 C 480.684562 373.944094 481.223625 374.47925 481.223625 375.143312 Z M 481.223625 375.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.415031 369.6355 C 485.415031 370.295656 484.879875 370.834719 484.219719 370.834719 C 483.559562 370.834719 483.024406 370.295656 483.024406 369.6355 C 483.024406 368.975344 483.559562 368.440187 484.219719 368.440187 C 484.879875 368.440187 485.415031 368.975344 485.415031 369.6355 Z M 485.415031 369.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 489.610344 343.651125 C 489.610344 344.311281 489.075187 344.846437 488.415031 344.846437 C 487.754875 344.846437 487.219719 344.311281 487.219719 343.651125 C 487.219719 342.990969 487.754875 342.455812 488.415031 342.455812 C 489.075187 342.455812 489.610344 342.990969 489.610344 343.651125 Z M 489.610344 343.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.809562 186.080812 C 493.809562 186.740969 493.2705 187.276125 492.610344 187.276125 C 491.950187 187.276125 491.415031 186.740969 491.415031 186.080812 C 491.415031 185.41675 491.950187 184.881594 492.610344 184.881594 C 493.2705 184.881594 493.809562 185.41675 493.809562 186.080812 Z M 493.809562 186.080812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.004875 81.057375 C 498.004875 81.721437 497.465812 82.256594 496.805656 82.256594 C 496.1455 82.256594 495.610344 81.721437 495.610344 81.057375 C 495.610344 80.397219 496.1455 79.862062 496.805656 79.862062 C 497.465812 79.862062 498.004875 80.397219 498.004875 81.057375 Z M 498.004875 81.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 77.990969 L 206.450187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 235.567375 73.240969 L 235.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 264.684562 73.240969 L 264.684562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.80175 73.240969 L 293.80175 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.922844 73.240969 L 322.922844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 352.040031 77.990969 L 352.040031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 381.161125 73.240969 L 381.161125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.278312 73.240969 L 410.278312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.3955 73.240969 L 439.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.512687 73.240969 L 468.512687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 77.990969 L 497.633781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 77.990969 L 206.450187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.333 73.240969 L 177.333 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.211906 73.240969 L 148.211906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.094719 73.240969 L 119.094719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.977531 73.240969 L 89.977531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 77.990969 L 497.633781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="193.982" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="205.989975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="339.572" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="351.579975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="485.162" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="497.169975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="308.587" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="319.898971" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="330.349312" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="343.181444" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="353.631786" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="366.121318" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="379.977149" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="390.19567" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="409.039067" y="417.528"/>
+ <use xlink:href="#glyph0-7" x="419.712823" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="438.048959" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.756657" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.764632" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-2" x="470.099543" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="479.807241" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 392.862062 L 206.450187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 235.567375 397.615969 L 235.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 264.684562 397.615969 L 264.684562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.80175 397.615969 L 293.80175 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.922844 397.615969 L 322.922844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 352.040031 392.862062 L 352.040031 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 381.161125 397.615969 L 381.161125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.278312 397.615969 L 410.278312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.3955 397.615969 L 439.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.512687 397.615969 L 468.512687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 392.862062 L 497.633781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 392.862062 L 206.450187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.333 397.615969 L 177.333 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.211906 397.615969 L 148.211906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.094719 397.615969 L 119.094719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.977531 397.615969 L 89.977531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 392.862062 L 497.633781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 78.79175 L 79.372062 78.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 89.096437 L 79.372062 89.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 99.401125 L 79.372062 99.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 109.705812 L 79.372062 109.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 120.0105 L 79.372062 120.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 130.311281 L 79.372062 130.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 140.615969 L 79.372062 140.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 150.920656 L 79.372062 150.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 161.225344 L 79.372062 161.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 171.530031 L 79.372062 171.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 181.834719 L 79.372062 181.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 192.139406 L 79.372062 192.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 202.440187 L 79.372062 202.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 212.744875 L 79.372062 212.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 223.049562 L 79.372062 223.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 233.35425 L 79.372062 233.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 243.658937 L 79.372062 243.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.963625 L 79.372062 253.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.268312 L 79.372062 264.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 274.573 L 79.372062 274.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 284.877687 L 79.372062 284.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 295.182375 L 79.372062 295.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 305.487062 L 79.372062 305.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 315.787844 L 79.372062 315.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 326.092531 L 79.372062 326.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 336.397219 L 79.372062 336.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 346.701906 L 79.372062 346.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 357.006594 L 79.372062 357.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 367.311281 L 79.372062 367.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 377.612062 L 79.372062 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 377.612062 L 79.372062 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 387.91675 L 79.372062 387.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 398.221437 L 79.372062 398.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-8" x="55.657" y="318.468"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="43.65" y="266.948"/>
+ <use xlink:href="#glyph0-2" x="55.657975" y="266.948"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="43.65" y="215.428"/>
+ <use xlink:href="#glyph0-8" x="55.657975" y="215.428"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="43.65" y="163.908"/>
+ <use xlink:href="#glyph0-2" x="55.657975" y="163.908"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="43.65" y="112.387"/>
+ <use xlink:href="#glyph0-8" x="55.657975" y="112.387"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="43.65" y="60.867"/>
+ <use xlink:href="#glyph0-2" x="55.657975" y="60.867"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-2" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph8-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph8-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph8-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph8-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph8-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph8-11" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph8-12" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph8-13" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph9-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-14" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 78.79175 L 498.903312 78.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 89.096437 L 498.903312 89.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 99.401125 L 498.903312 99.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 109.705812 L 498.903312 109.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 120.0105 L 498.903312 120.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 130.311281 L 498.903312 130.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 140.615969 L 498.903312 140.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 150.920656 L 498.903312 150.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 161.225344 L 498.903312 161.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 171.530031 L 498.903312 171.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 181.834719 L 498.903312 181.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 192.139406 L 498.903312 192.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 202.440187 L 498.903312 202.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 212.744875 L 498.903312 212.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 223.049562 L 498.903312 223.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 233.35425 L 498.903312 233.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 243.658937 L 498.903312 243.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.963625 L 498.903312 253.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.268312 L 498.903312 264.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 274.573 L 498.903312 274.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 284.877687 L 498.903312 284.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 295.182375 L 498.903312 295.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 305.487062 L 498.903312 305.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 315.787844 L 498.903312 315.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 326.092531 L 498.903312 326.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 336.397219 L 498.903312 336.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 346.701906 L 498.903312 346.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 357.006594 L 498.903312 357.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 367.311281 L 498.903312 367.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 377.612062 L 498.903312 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 377.612062 L 498.903312 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 387.91675 L 498.903312 387.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 398.221437 L 498.903312 398.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 77.990969 L 206.450187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 235.567375 73.240969 L 235.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 264.684562 73.240969 L 264.684562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.80175 73.240969 L 293.80175 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.922844 73.240969 L 322.922844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 352.040031 77.990969 L 352.040031 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 381.161125 73.240969 L 381.161125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.278312 73.240969 L 410.278312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.3955 73.240969 L 439.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.512687 73.240969 L 468.512687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 77.990969 L 497.633781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 77.990969 L 206.450187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.333 73.240969 L 177.333 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.211906 73.240969 L 148.211906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.094719 73.240969 L 119.094719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.977531 73.240969 L 89.977531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 77.990969 L 497.633781 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 392.862062 L 206.450187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 235.567375 397.615969 L 235.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 264.684562 397.615969 L 264.684562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.80175 397.615969 L 293.80175 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 322.922844 397.615969 L 322.922844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 352.040031 392.862062 L 352.040031 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 381.161125 397.615969 L 381.161125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 410.278312 397.615969 L 410.278312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.3955 397.615969 L 439.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.512687 397.615969 L 468.512687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 392.862062 L 497.633781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 206.450187 392.862062 L 206.450187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.333 397.615969 L 177.333 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.211906 397.615969 L 148.211906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.094719 397.615969 L 119.094719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.977531 397.615969 L 89.977531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 497.633781 392.862062 L 497.633781 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 78.79175 L 79.372062 78.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 89.096437 L 79.372062 89.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 99.401125 L 79.372062 99.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 109.705812 L 79.372062 109.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 120.0105 L 79.372062 120.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 130.311281 L 79.372062 130.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 140.615969 L 79.372062 140.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 150.920656 L 79.372062 150.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 161.225344 L 79.372062 161.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 171.530031 L 79.372062 171.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 181.834719 L 79.372062 181.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 192.139406 L 79.372062 192.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 202.440187 L 79.372062 202.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 212.744875 L 79.372062 212.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 223.049562 L 79.372062 223.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 233.35425 L 79.372062 233.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 243.658937 L 79.372062 243.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.963625 L 79.372062 253.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.268312 L 79.372062 264.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 274.573 L 79.372062 274.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 284.877687 L 79.372062 284.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 295.182375 L 79.372062 295.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 305.487062 L 79.372062 305.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 315.787844 L 79.372062 315.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 326.092531 L 79.372062 326.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 336.397219 L 79.372062 336.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 346.701906 L 79.372062 346.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 357.006594 L 79.372062 357.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 367.311281 L 79.372062 367.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 377.612062 L 79.372062 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 377.612062 L 79.372062 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 387.91675 L 79.372062 387.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 398.221437 L 79.372062 398.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 78.79175 L 498.903312 78.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 89.096437 L 498.903312 89.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 99.401125 L 498.903312 99.401125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 109.705812 L 498.903312 109.705812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 120.0105 L 498.903312 120.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 130.311281 L 498.903312 130.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 140.615969 L 498.903312 140.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 150.920656 L 498.903312 150.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 161.225344 L 498.903312 161.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 171.530031 L 498.903312 171.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 181.834719 L 498.903312 181.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 192.139406 L 498.903312 192.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 202.440187 L 498.903312 202.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 212.744875 L 498.903312 212.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 223.049562 L 498.903312 223.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 233.35425 L 498.903312 233.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 243.658937 L 498.903312 243.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.963625 L 498.903312 253.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.268312 L 498.903312 264.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 274.573 L 498.903312 274.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 284.877687 L 498.903312 284.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 295.182375 L 498.903312 295.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 305.487062 L 498.903312 305.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 315.787844 L 498.903312 315.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 326.092531 L 498.903312 326.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 336.397219 L 498.903312 336.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 346.701906 L 498.903312 346.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 357.006594 L 498.903312 357.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 367.311281 L 498.903312 367.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 377.612062 L 498.903312 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 377.612062 L 498.903312 377.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 387.91675 L 498.903312 387.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 398.221437 L 498.903312 398.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/lb2pKpi_s01.svg b/doc/figs/lb2pKpi_s01.svg
new file mode 100644
index 00000000000..dfd139bd86e
--- /dev/null
+++ b/doc/figs/lb2pKpi_s01.svg
@@ -0,0 +1,594 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="504pt" height="432pt" viewBox="0 0 504 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 4.515625 -8.8125 C 4.09375 -8.78125 4 -8.75 4 -8.53125 C 4 -8.296875 4.125 -8.296875 4.5625 -8.296875 L 5.6875 -8.296875 C 7.78125 -8.296875 8.703125 -6.578125 8.703125 -4.21875 C 8.703125 -1 7.046875 -0.140625 5.84375 -0.140625 C 4.65625 -0.140625 2.65625 -0.71875 1.9375 -2.328125 C 2.71875 -2.203125 3.4375 -2.65625 3.4375 -3.53125 C 3.4375 -4.25 2.921875 -4.734375 2.234375 -4.734375 C 1.640625 -4.734375 1 -4.390625 1 -3.453125 C 1 -1.28125 3.1875 0.515625 5.90625 0.515625 C 8.828125 0.515625 10.984375 -1.71875 10.984375 -4.1875 C 10.984375 -6.453125 9.171875 -8.21875 6.8125 -8.640625 C 8.953125 -9.25 10.328125 -11.046875 10.328125 -12.953125 C 10.328125 -14.890625 8.3125 -16.3125 5.9375 -16.3125 C 3.484375 -16.3125 1.671875 -14.8125 1.671875 -13.03125 C 1.671875 -12.046875 2.421875 -11.84375 2.796875 -11.84375 C 3.3125 -11.84375 3.90625 -12.21875 3.90625 -12.953125 C 3.90625 -13.734375 3.3125 -14.078125 2.765625 -14.078125 C 2.625 -14.078125 2.578125 -14.078125 2.5 -14.0625 C 3.4375 -15.71875 5.734375 -15.71875 5.859375 -15.71875 C 6.671875 -15.71875 8.265625 -15.359375 8.265625 -12.953125 C 8.265625 -12.484375 8.1875 -11.109375 7.484375 -10.0625 C 6.75 -8.984375 5.90625 -8.90625 5.25 -8.875 Z M 4.515625 -8.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 8.859375 -15.96875 C 8.859375 -16.4375 8.859375 -16.5625 8.515625 -16.5625 C 8.3125 -16.5625 8.25 -16.5625 8.046875 -16.265625 L 0.65625 -4.8125 L 0.65625 -4.09375 L 7.109375 -4.09375 L 7.109375 -1.859375 C 7.109375 -0.953125 7.0625 -0.71875 5.28125 -0.71875 L 4.78125 -0.71875 L 4.78125 0 C 5.34375 -0.046875 7.28125 -0.046875 7.96875 -0.046875 C 8.65625 -0.046875 10.625 -0.046875 11.1875 0 L 11.1875 -0.71875 L 10.703125 -0.71875 C 8.921875 -0.71875 8.859375 -0.953125 8.859375 -1.859375 L 8.859375 -4.09375 L 11.328125 -4.09375 L 11.328125 -4.8125 L 8.859375 -4.8125 Z M 7.234375 -14.0625 L 7.234375 -4.8125 L 1.28125 -4.8125 Z M 7.234375 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 8.78125 -6.5625 C 8.765625 -6.609375 8.671875 -6.765625 8.671875 -6.78125 C 8.671875 -6.8125 8.953125 -7.015625 9.125 -7.125 C 10.40625 -8.078125 12.171875 -9.34375 12.71875 -9.6875 C 13.546875 -10.21875 14.15625 -10.5625 14.890625 -10.625 C 15.015625 -10.640625 15.25 -10.65625 15.25 -10.953125 C 15.234375 -11.0625 15.140625 -11.15625 15.015625 -11.15625 C 15 -11.15625 14.546875 -11.109375 14.4375 -11.109375 L 13.78125 -11.109375 C 13.5 -11.109375 13.09375 -11.109375 12.9375 -11.125 C 12.828125 -11.125 12.1875 -11.15625 12.078125 -11.15625 C 11.96875 -11.15625 11.734375 -11.15625 11.734375 -10.859375 C 11.734375 -10.84375 11.75 -10.640625 12 -10.625 C 12.125 -10.609375 12.390625 -10.578125 12.390625 -10.375 C 12.390625 -10.109375 12.0625 -9.84375 12.03125 -9.828125 L 11.890625 -9.703125 C 11.84375 -9.65625 11.78125 -9.59375 11.703125 -9.546875 L 5.03125 -4.703125 L 6.328125 -9.890625 C 6.46875 -10.46875 6.5 -10.625 7.703125 -10.625 C 8.03125 -10.625 8.21875 -10.625 8.21875 -10.9375 C 8.21875 -10.953125 8.203125 -11.15625 7.9375 -11.15625 C 7.625 -11.15625 7.234375 -11.125 6.9375 -11.109375 L 5.90625 -11.109375 C 4.328125 -11.109375 3.90625 -11.15625 3.796875 -11.15625 C 3.703125 -11.15625 3.46875 -11.15625 3.46875 -10.859375 C 3.46875 -10.625 3.65625 -10.625 3.9375 -10.625 C 4.484375 -10.625 4.953125 -10.625 4.953125 -10.359375 C 4.953125 -10.296875 4.9375 -10.28125 4.890625 -10.0625 L 2.703125 -1.296875 C 2.546875 -0.671875 2.515625 -0.546875 1.3125 -0.546875 C 1 -0.546875 0.796875 -0.546875 0.796875 -0.234375 C 0.796875 -0.15625 0.84375 0 1.0625 0 C 1.375 0 1.765625 -0.03125 2.078125 -0.046875 L 4.1875 -0.046875 C 4.453125 -0.03125 4.984375 0 5.234375 0 C 5.3125 0 5.5625 0 5.5625 -0.296875 C 5.5625 -0.546875 5.359375 -0.546875 5.078125 -0.546875 C 4.96875 -0.546875 4.734375 -0.546875 4.46875 -0.578125 C 4.125 -0.609375 4.0625 -0.640625 4.0625 -0.796875 C 4.0625 -0.90625 4.1875 -1.3125 4.234375 -1.5625 L 4.859375 -4.03125 L 7.484375 -5.9375 L 9.453125 -1.890625 C 9.515625 -1.765625 9.6875 -1.40625 9.75 -1.265625 C 9.859375 -1.09375 9.859375 -1.0625 9.859375 -1 C 9.859375 -0.5625 9.25 -0.546875 9.078125 -0.546875 C 8.90625 -0.546875 8.671875 -0.546875 8.671875 -0.234375 C 8.671875 -0.21875 8.6875 0 8.953125 0 C 9.125 0 9.734375 -0.03125 9.890625 -0.046875 L 10.84375 -0.046875 C 12.34375 -0.046875 12.296875 0 12.5 0 C 12.5625 0 12.8125 0 12.8125 -0.3125 C 12.8125 -0.546875 12.578125 -0.546875 12.484375 -0.546875 C 11.84375 -0.5625 11.640625 -0.671875 11.375 -1.21875 Z M 8.78125 -6.5625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 4.640625 -5.96875 L 6.515625 -5.96875 C 6.171875 -4.484375 5.890625 -3.265625 5.890625 -2.0625 C 5.890625 -1.9375 5.890625 -1.234375 6.0625 -0.65625 C 6.28125 0.03125 6.4375 0.15625 6.734375 0.15625 C 7.09375 0.15625 7.46875 -0.140625 7.46875 -0.546875 C 7.46875 -0.65625 7.453125 -0.6875 7.390625 -0.828125 C 7.046875 -1.578125 6.796875 -2.375 6.796875 -3.703125 C 6.796875 -4.09375 6.796875 -4.765625 7.046875 -5.96875 L 9.015625 -5.96875 C 9.28125 -5.96875 9.46875 -5.96875 9.625 -6.09375 C 9.828125 -6.28125 9.875 -6.484375 9.875 -6.59375 C 9.875 -7.046875 9.46875 -7.046875 9.1875 -7.046875 L 3.28125 -7.046875 C 2.9375 -7.046875 2.328125 -7.046875 1.515625 -6.265625 C 0.9375 -5.671875 0.46875 -4.921875 0.46875 -4.8125 C 0.46875 -4.65625 0.59375 -4.609375 0.71875 -4.609375 C 0.875 -4.609375 0.921875 -4.65625 1.015625 -4.78125 C 1.8125 -5.96875 2.78125 -5.96875 3.15625 -5.96875 L 4.109375 -5.96875 C 3.625 -4.234375 2.765625 -2.25 2.15625 -1.0625 C 2.046875 -0.8125 1.875 -0.484375 1.875 -0.34375 C 1.875 0 2.15625 0.15625 2.421875 0.15625 C 3.046875 0.15625 3.203125 -0.453125 3.546875 -1.796875 Z M 4.640625 -5.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 9.765625 -2.75 C 9.953125 -2.75 10.265625 -2.75 10.265625 -3.0625 C 10.265625 -3.390625 9.953125 -3.390625 9.765625 -3.390625 L 2.03125 -3.390625 C 1.84375 -3.390625 1.53125 -3.390625 1.53125 -3.0625 C 1.53125 -2.75 1.84375 -2.75 2.03125 -2.75 Z M 9.765625 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 6.75 -3.90625 C 6.75 -4.8125 6.75 -8.15625 3.734375 -8.15625 C 0.734375 -8.15625 0.734375 -4.8125 0.734375 -3.90625 C 0.734375 -3.03125 0.734375 0.25 3.734375 0.25 C 6.75 0.25 6.75 -3.03125 6.75 -3.90625 Z M 3.734375 -0.140625 C 3.21875 -0.140625 2.390625 -0.375 2.09375 -1.390625 C 1.90625 -2.109375 1.90625 -3.3125 1.90625 -4.078125 C 1.90625 -4.890625 1.90625 -5.84375 2.078125 -6.5 C 2.375 -7.609375 3.3125 -7.765625 3.734375 -7.765625 C 4.3125 -7.765625 5.109375 -7.5 5.390625 -6.5625 C 5.5625 -5.90625 5.578125 -5.015625 5.578125 -4.078125 C 5.578125 -3.28125 5.578125 -2.046875 5.375 -1.359375 C 5.03125 -0.296875 4.140625 -0.140625 3.734375 -0.140625 Z M 3.734375 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-11">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-12">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-13">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph10-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph10-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 82.665031 72.108156 C 82.665031 72.768312 82.129875 73.303469 81.469719 73.303469 C 80.805656 73.303469 80.2705 72.768312 80.2705 72.108156 C 80.2705 71.448 80.805656 70.912844 81.469719 70.912844 C 82.129875 70.912844 82.665031 71.448 82.665031 72.108156 Z M 82.665031 72.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.860344 245.897219 C 86.860344 246.557375 86.325187 247.092531 85.665031 247.092531 C 85.004875 247.092531 84.465812 246.557375 84.465812 245.897219 C 84.465812 245.237062 85.004875 244.698 85.665031 244.698 C 86.325187 244.698 86.860344 245.237062 86.860344 245.897219 Z M 86.860344 245.897219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 91.055656 385.1355 C 91.055656 385.795656 90.5205 386.334719 89.860344 386.334719 C 89.200187 386.334719 88.661125 385.795656 88.661125 385.1355 C 88.661125 384.475344 89.200187 383.940187 89.860344 383.940187 C 90.5205 383.940187 91.055656 384.475344 91.055656 385.1355 Z M 91.055656 385.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 97.182375 C 95.250969 97.842531 94.715812 98.377687 94.055656 98.377687 C 93.3955 98.377687 92.856437 97.842531 92.856437 97.182375 C 92.856437 96.522219 93.3955 95.983156 94.055656 95.983156 C 94.715812 95.983156 95.250969 96.522219 95.250969 97.182375 Z M 95.250969 97.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.446281 79.170656 C 99.446281 79.830812 98.911125 80.365969 98.250969 80.365969 C 97.590812 80.365969 97.05175 79.830812 97.05175 79.170656 C 97.05175 78.5105 97.590812 77.971437 98.250969 77.971437 C 98.911125 77.971437 99.446281 78.5105 99.446281 79.170656 Z M 99.446281 79.170656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 103.641594 74.053469 C 103.641594 74.713625 103.106437 75.248781 102.446281 75.248781 C 101.786125 75.248781 101.247062 74.713625 101.247062 74.053469 C 101.247062 73.389406 101.786125 72.85425 102.446281 72.85425 C 103.106437 72.85425 103.641594 73.389406 103.641594 74.053469 Z M 103.641594 74.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.836906 72.002687 C 107.836906 72.662844 107.30175 73.198 106.641594 73.198 C 105.981437 73.198 105.442375 72.662844 105.442375 72.002687 C 105.442375 71.342531 105.981437 70.803469 106.641594 70.803469 C 107.30175 70.803469 107.836906 71.342531 107.836906 72.002687 Z M 107.836906 72.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 112.032219 70.826906 C 112.032219 71.490969 111.497062 72.026125 110.836906 72.026125 C 110.17675 72.026125 109.637687 71.490969 109.637687 70.826906 C 109.637687 70.16675 110.17675 69.631594 110.836906 69.631594 C 111.497062 69.631594 112.032219 70.16675 112.032219 70.826906 Z M 112.032219 70.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 70.201906 C 116.227531 70.862062 115.692375 71.401125 115.032219 71.401125 C 114.372062 71.401125 113.833 70.862062 113.833 70.201906 C 113.833 69.54175 114.372062 69.006594 115.032219 69.006594 C 115.692375 69.006594 116.227531 69.54175 116.227531 70.201906 Z M 116.227531 70.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.422844 69.780031 C 120.422844 70.440187 119.887687 70.975344 119.227531 70.975344 C 118.567375 70.975344 118.028312 70.440187 118.028312 69.780031 C 118.028312 69.115969 118.567375 68.580812 119.227531 68.580812 C 119.887687 68.580812 120.422844 69.115969 120.422844 69.780031 Z M 120.422844 69.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 124.618156 69.537844 C 124.618156 70.198 124.083 70.733156 123.422844 70.733156 C 122.762687 70.733156 122.223625 70.198 122.223625 69.537844 C 122.223625 68.877687 122.762687 68.342531 123.422844 68.342531 C 124.083 68.342531 124.618156 68.877687 124.618156 69.537844 Z M 124.618156 69.537844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 69.248781 C 128.813469 69.908937 128.278312 70.444094 127.618156 70.444094 C 126.958 70.444094 126.418937 69.908937 126.418937 69.248781 C 126.418937 68.584719 126.958 68.049562 127.618156 68.049562 C 128.278312 68.049562 128.813469 68.584719 128.813469 69.248781 Z M 128.813469 69.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 133.008781 69.162844 C 133.008781 69.823 132.473625 70.362062 131.813469 70.362062 C 131.153312 70.362062 130.61425 69.823 130.61425 69.162844 C 130.61425 68.502687 131.153312 67.967531 131.813469 67.967531 C 132.473625 67.967531 133.008781 68.502687 133.008781 69.162844 Z M 133.008781 69.162844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 137.204094 68.963625 C 137.204094 69.623781 136.668937 70.158937 136.008781 70.158937 C 135.348625 70.158937 134.809562 69.623781 134.809562 68.963625 C 134.809562 68.303469 135.348625 67.764406 136.008781 67.764406 C 136.668937 67.764406 137.204094 68.303469 137.204094 68.963625 Z M 137.204094 68.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.399406 68.905031 C 141.399406 69.569094 140.86425 70.10425 140.204094 70.10425 C 139.543937 70.10425 139.004875 69.569094 139.004875 68.905031 C 139.004875 68.244875 139.543937 67.709719 140.204094 67.709719 C 140.86425 67.709719 141.399406 68.244875 141.399406 68.905031 Z M 141.399406 68.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 68.963625 C 145.594719 69.623781 145.059562 70.158937 144.399406 70.158937 C 143.73925 70.158937 143.200187 69.623781 143.200187 68.963625 C 143.200187 68.303469 143.73925 67.764406 144.399406 67.764406 C 145.059562 67.764406 145.594719 68.303469 145.594719 68.963625 Z M 145.594719 68.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 149.790031 68.834719 C 149.790031 69.494875 149.254875 70.030031 148.594719 70.030031 C 147.934562 70.030031 147.3955 69.494875 147.3955 68.834719 C 147.3955 68.174562 147.934562 67.6355 148.594719 67.6355 C 149.254875 67.6355 149.790031 68.174562 149.790031 68.834719 Z M 149.790031 68.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 68.7605 C 153.985344 69.420656 153.450187 69.959719 152.790031 69.959719 C 152.129875 69.959719 151.590812 69.420656 151.590812 68.7605 C 151.590812 68.100344 152.129875 67.565187 152.790031 67.565187 C 153.450187 67.565187 153.985344 68.100344 153.985344 68.7605 Z M 153.985344 68.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 68.7605 C 158.180656 69.420656 157.6455 69.959719 156.985344 69.959719 C 156.325187 69.959719 155.786125 69.420656 155.786125 68.7605 C 155.786125 68.100344 156.325187 67.565187 156.985344 67.565187 C 157.6455 67.565187 158.180656 68.100344 158.180656 68.7605 Z M 158.180656 68.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 162.375969 68.721437 C 162.375969 69.381594 161.840812 69.920656 161.180656 69.920656 C 160.5205 69.920656 159.981437 69.381594 159.981437 68.721437 C 159.981437 68.061281 160.5205 67.526125 161.180656 67.526125 C 161.840812 67.526125 162.375969 68.061281 162.375969 68.721437 Z M 162.375969 68.721437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 166.571281 68.643312 C 166.571281 69.303469 166.036125 69.842531 165.375969 69.842531 C 164.715812 69.842531 164.17675 69.303469 164.17675 68.643312 C 164.17675 67.983156 164.715812 67.448 165.375969 67.448 C 166.036125 67.448 166.571281 67.983156 166.571281 68.643312 Z M 166.571281 68.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 68.619875 C 170.766594 69.283937 170.231437 69.819094 169.571281 69.819094 C 168.911125 69.819094 168.372062 69.283937 168.372062 68.619875 C 168.372062 67.959719 168.911125 67.424562 169.571281 67.424562 C 170.231437 67.424562 170.766594 67.959719 170.766594 68.619875 Z M 170.766594 68.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 174.961906 68.639406 C 174.961906 69.299562 174.42675 69.834719 173.766594 69.834719 C 173.106437 69.834719 172.571281 69.299562 172.571281 68.639406 C 172.571281 67.97925 173.106437 67.440187 173.766594 67.440187 C 174.42675 67.440187 174.961906 67.97925 174.961906 68.639406 Z M 174.961906 68.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 179.157219 68.60425 C 179.157219 69.264406 178.622062 69.803469 177.961906 69.803469 C 177.30175 69.803469 176.762687 69.264406 176.762687 68.60425 C 176.762687 67.944094 177.30175 67.408937 177.961906 67.408937 C 178.622062 67.408937 179.157219 67.944094 179.157219 68.60425 Z M 179.157219 68.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 68.631594 C 183.352531 69.295656 182.817375 69.830812 182.157219 69.830812 C 181.497062 69.830812 180.958 69.295656 180.958 68.631594 C 180.958 67.971437 181.497062 67.436281 182.157219 67.436281 C 182.817375 67.436281 183.352531 67.971437 183.352531 68.631594 Z M 183.352531 68.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 68.565187 C 187.547844 69.225344 187.012687 69.764406 186.352531 69.764406 C 185.692375 69.764406 185.157219 69.225344 185.157219 68.565187 C 185.157219 67.905031 185.692375 67.369875 186.352531 67.369875 C 187.012687 67.369875 187.547844 67.905031 187.547844 68.565187 Z M 187.547844 68.565187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 68.627687 C 191.743156 69.287844 191.208 69.823 190.547844 69.823 C 189.887687 69.823 189.348625 69.287844 189.348625 68.627687 C 189.348625 67.967531 189.887687 67.432375 190.547844 67.432375 C 191.208 67.432375 191.743156 67.967531 191.743156 68.627687 Z M 191.743156 68.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 68.588625 C 195.938469 69.248781 195.403312 69.783937 194.743156 69.783937 C 194.083 69.783937 193.543937 69.248781 193.543937 68.588625 C 193.543937 67.928469 194.083 67.393312 194.743156 67.393312 C 195.403312 67.393312 195.938469 67.928469 195.938469 68.588625 Z M 195.938469 68.588625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 68.553469 C 200.133781 69.217531 199.598625 69.752687 198.938469 69.752687 C 198.278312 69.752687 197.743156 69.217531 197.743156 68.553469 C 197.743156 67.893312 198.278312 67.358156 198.938469 67.358156 C 199.598625 67.358156 200.133781 67.893312 200.133781 68.553469 Z M 200.133781 68.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 68.580812 C 204.329094 69.244875 203.793937 69.780031 203.133781 69.780031 C 202.473625 69.780031 201.934562 69.244875 201.934562 68.580812 C 201.934562 67.920656 202.473625 67.3855 203.133781 67.3855 C 203.793937 67.3855 204.329094 67.920656 204.329094 68.580812 Z M 204.329094 68.580812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 68.549562 C 208.524406 69.209719 207.98925 69.744875 207.329094 69.744875 C 206.668937 69.744875 206.129875 69.209719 206.129875 68.549562 C 206.129875 67.889406 206.668937 67.35425 207.329094 67.35425 C 207.98925 67.35425 208.524406 67.889406 208.524406 68.549562 Z M 208.524406 68.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 68.526125 C 212.719719 69.186281 212.184562 69.721437 211.524406 69.721437 C 210.86425 69.721437 210.329094 69.186281 210.329094 68.526125 C 210.329094 67.865969 210.86425 67.330812 211.524406 67.330812 C 212.184562 67.330812 212.719719 67.865969 212.719719 68.526125 Z M 212.719719 68.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 68.533937 C 216.915031 69.194094 216.379875 69.72925 215.719719 69.72925 C 215.059562 69.72925 214.524406 69.194094 214.524406 68.533937 C 214.524406 67.869875 215.059562 67.334719 215.719719 67.334719 C 216.379875 67.334719 216.915031 67.869875 216.915031 68.533937 Z M 216.915031 68.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 68.545656 C 221.110344 69.205812 220.575187 69.740969 219.915031 69.740969 C 219.254875 69.740969 218.715812 69.205812 218.715812 68.545656 C 218.715812 67.881594 219.254875 67.346437 219.915031 67.346437 C 220.575187 67.346437 221.110344 67.881594 221.110344 68.545656 Z M 221.110344 68.545656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 68.522219 C 225.305656 69.182375 224.7705 69.717531 224.110344 69.717531 C 223.450187 69.717531 222.915031 69.182375 222.915031 68.522219 C 222.915031 67.862062 223.450187 67.323 224.110344 67.323 C 224.7705 67.323 225.305656 67.862062 225.305656 68.522219 Z M 225.305656 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 68.522219 C 229.500969 69.182375 228.965812 69.717531 228.305656 69.717531 C 227.6455 69.717531 227.110344 69.182375 227.110344 68.522219 C 227.110344 67.862062 227.6455 67.323 228.305656 67.323 C 228.965812 67.323 229.500969 67.862062 229.500969 68.522219 Z M 229.500969 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 68.537844 C 233.696281 69.198 233.161125 69.733156 232.500969 69.733156 C 231.840812 69.733156 231.30175 69.198 231.30175 68.537844 C 231.30175 67.877687 231.840812 67.342531 232.500969 67.342531 C 233.161125 67.342531 233.696281 67.877687 233.696281 68.537844 Z M 233.696281 68.537844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 68.533937 C 237.891594 69.194094 237.356437 69.72925 236.696281 69.72925 C 236.036125 69.72925 235.500969 69.194094 235.500969 68.533937 C 235.500969 67.869875 236.036125 67.334719 236.696281 67.334719 C 237.356437 67.334719 237.891594 67.869875 237.891594 68.533937 Z M 237.891594 68.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 68.526125 C 242.086906 69.186281 241.55175 69.721437 240.891594 69.721437 C 240.231437 69.721437 239.696281 69.186281 239.696281 68.526125 C 239.696281 67.865969 240.231437 67.330812 240.891594 67.330812 C 241.55175 67.330812 242.086906 67.865969 242.086906 68.526125 Z M 242.086906 68.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 68.526125 C 246.282219 69.186281 245.747062 69.721437 245.086906 69.721437 C 244.42675 69.721437 243.891594 69.186281 243.891594 68.526125 C 243.891594 67.865969 244.42675 67.330812 245.086906 67.330812 C 245.747062 67.330812 246.282219 67.865969 246.282219 68.526125 Z M 246.282219 68.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 68.526125 C 250.477531 69.186281 249.942375 69.721437 249.282219 69.721437 C 248.622062 69.721437 248.086906 69.186281 248.086906 68.526125 C 248.086906 67.865969 248.622062 67.330812 249.282219 67.330812 C 249.942375 67.330812 250.477531 67.865969 250.477531 68.526125 Z M 250.477531 68.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 68.514406 C 254.672844 69.178469 254.137687 69.713625 253.477531 69.713625 C 252.817375 69.713625 252.282219 69.178469 252.282219 68.514406 C 252.282219 67.85425 252.817375 67.319094 253.477531 67.319094 C 254.137687 67.319094 254.672844 67.85425 254.672844 68.514406 Z M 254.672844 68.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 68.514406 C 258.868156 69.178469 258.333 69.713625 257.672844 69.713625 C 257.012687 69.713625 256.477531 69.178469 256.477531 68.514406 C 256.477531 67.85425 257.012687 67.319094 257.672844 67.319094 C 258.333 67.319094 258.868156 67.85425 258.868156 68.514406 Z M 258.868156 68.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 68.502687 C 263.063469 69.16675 262.528312 69.701906 261.868156 69.701906 C 261.208 69.701906 260.672844 69.16675 260.672844 68.502687 C 260.672844 67.842531 261.208 67.307375 261.868156 67.307375 C 262.528312 67.307375 263.063469 67.842531 263.063469 68.502687 Z M 263.063469 68.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 68.526125 C 267.258781 69.186281 266.723625 69.721437 266.063469 69.721437 C 265.403312 69.721437 264.868156 69.186281 264.868156 68.526125 C 264.868156 67.865969 265.403312 67.330812 266.063469 67.330812 C 266.723625 67.330812 267.258781 67.865969 267.258781 68.526125 Z M 267.258781 68.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 68.5105 C 271.454094 69.170656 270.918937 69.705812 270.258781 69.705812 C 269.598625 69.705812 269.063469 69.170656 269.063469 68.5105 C 269.063469 67.850344 269.598625 67.315187 270.258781 67.315187 C 270.918937 67.315187 271.454094 67.850344 271.454094 68.5105 Z M 271.454094 68.5105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 68.514406 C 275.649406 69.178469 275.11425 69.713625 274.454094 69.713625 C 273.793937 69.713625 273.258781 69.178469 273.258781 68.514406 C 273.258781 67.85425 273.793937 67.319094 274.454094 67.319094 C 275.11425 67.319094 275.649406 67.85425 275.649406 68.514406 Z M 275.649406 68.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 68.498781 C 279.844719 69.158937 279.309562 69.694094 278.649406 69.694094 C 277.98925 69.694094 277.454094 69.158937 277.454094 68.498781 C 277.454094 67.838625 277.98925 67.303469 278.649406 67.303469 C 279.309562 67.303469 279.844719 67.838625 279.844719 68.498781 Z M 279.844719 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 68.522219 C 284.040031 69.182375 283.504875 69.717531 282.844719 69.717531 C 282.184562 69.717531 281.649406 69.182375 281.649406 68.522219 C 281.649406 67.862062 282.184562 67.323 282.844719 67.323 C 283.504875 67.323 284.040031 67.862062 284.040031 68.522219 Z M 284.040031 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 68.522219 C 288.235344 69.182375 287.700187 69.717531 287.040031 69.717531 C 286.379875 69.717531 285.844719 69.182375 285.844719 68.522219 C 285.844719 67.862062 286.379875 67.323 287.040031 67.323 C 287.700187 67.323 288.235344 67.862062 288.235344 68.522219 Z M 288.235344 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 68.494875 C 292.430656 69.155031 291.8955 69.690187 291.235344 69.690187 C 290.575187 69.690187 290.040031 69.155031 290.040031 68.494875 C 290.040031 67.830812 290.575187 67.295656 291.235344 67.295656 C 291.8955 67.295656 292.430656 67.830812 292.430656 68.494875 Z M 292.430656 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 68.502687 C 296.625969 69.16675 296.090812 69.701906 295.430656 69.701906 C 294.7705 69.701906 294.235344 69.16675 294.235344 68.502687 C 294.235344 67.842531 294.7705 67.307375 295.430656 67.307375 C 296.090812 67.307375 296.625969 67.842531 296.625969 68.502687 Z M 296.625969 68.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 68.5105 C 300.821281 69.170656 300.286125 69.705812 299.625969 69.705812 C 298.965812 69.705812 298.430656 69.170656 298.430656 68.5105 C 298.430656 67.850344 298.965812 67.315187 299.625969 67.315187 C 300.286125 67.315187 300.821281 67.850344 300.821281 68.5105 Z M 300.821281 68.5105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 68.494875 C 305.016594 69.155031 304.481437 69.690187 303.821281 69.690187 C 303.161125 69.690187 302.625969 69.155031 302.625969 68.494875 C 302.625969 67.830812 303.161125 67.295656 303.821281 67.295656 C 304.481437 67.295656 305.016594 67.830812 305.016594 68.494875 Z M 305.016594 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 68.522219 C 309.211906 69.182375 308.67675 69.717531 308.016594 69.717531 C 307.356437 69.717531 306.821281 69.182375 306.821281 68.522219 C 306.821281 67.862062 307.356437 67.323 308.016594 67.323 C 308.67675 67.323 309.211906 67.862062 309.211906 68.522219 Z M 309.211906 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 68.522219 C 313.407219 69.182375 312.872062 69.717531 312.211906 69.717531 C 311.55175 69.717531 311.016594 69.182375 311.016594 68.522219 C 311.016594 67.862062 311.55175 67.323 312.211906 67.323 C 312.872062 67.323 313.407219 67.862062 313.407219 68.522219 Z M 313.407219 68.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 68.498781 C 317.602531 69.158937 317.067375 69.694094 316.407219 69.694094 C 315.747062 69.694094 315.211906 69.158937 315.211906 68.498781 C 315.211906 67.838625 315.747062 67.303469 316.407219 67.303469 C 317.067375 67.303469 317.602531 67.838625 317.602531 68.498781 Z M 317.602531 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 68.502687 C 321.797844 69.16675 321.262687 69.701906 320.602531 69.701906 C 319.942375 69.701906 319.407219 69.16675 319.407219 68.502687 C 319.407219 67.842531 319.942375 67.307375 320.602531 67.307375 C 321.262687 67.307375 321.797844 67.842531 321.797844 68.502687 Z M 321.797844 68.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 68.494875 C 325.993156 69.155031 325.458 69.690187 324.797844 69.690187 C 324.137687 69.690187 323.602531 69.155031 323.602531 68.494875 C 323.602531 67.830812 324.137687 67.295656 324.797844 67.295656 C 325.458 67.295656 325.993156 67.830812 325.993156 68.494875 Z M 325.993156 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 68.494875 C 330.188469 69.155031 329.653312 69.690187 328.993156 69.690187 C 328.333 69.690187 327.797844 69.155031 327.797844 68.494875 C 327.797844 67.830812 328.333 67.295656 328.993156 67.295656 C 329.653312 67.295656 330.188469 67.830812 330.188469 68.494875 Z M 330.188469 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 68.498781 C 338.579094 69.158937 338.043937 69.694094 337.383781 69.694094 C 336.723625 69.694094 336.188469 69.158937 336.188469 68.498781 C 336.188469 67.838625 336.723625 67.303469 337.383781 67.303469 C 338.043937 67.303469 338.579094 67.838625 338.579094 68.498781 Z M 338.579094 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 68.494875 C 342.774406 69.155031 342.23925 69.690187 341.579094 69.690187 C 340.918937 69.690187 340.383781 69.155031 340.383781 68.494875 C 340.383781 67.830812 340.918937 67.295656 341.579094 67.295656 C 342.23925 67.295656 342.774406 67.830812 342.774406 68.494875 Z M 342.774406 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 68.498781 C 346.969719 69.158937 346.434562 69.694094 345.774406 69.694094 C 345.11425 69.694094 344.579094 69.158937 344.579094 68.498781 C 344.579094 67.838625 345.11425 67.303469 345.774406 67.303469 C 346.434562 67.303469 346.969719 67.838625 346.969719 68.498781 Z M 346.969719 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 68.498781 C 355.360344 69.158937 354.825187 69.694094 354.165031 69.694094 C 353.504875 69.694094 352.969719 69.158937 352.969719 68.498781 C 352.969719 67.838625 353.504875 67.303469 354.165031 67.303469 C 354.825187 67.303469 355.360344 67.838625 355.360344 68.498781 Z M 355.360344 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 68.498781 C 359.555656 69.158937 359.0205 69.694094 358.360344 69.694094 C 357.700187 69.694094 357.165031 69.158937 357.165031 68.498781 C 357.165031 67.838625 357.700187 67.303469 358.360344 67.303469 C 359.0205 67.303469 359.555656 67.838625 359.555656 68.498781 Z M 359.555656 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 68.494875 C 363.750969 69.155031 363.215812 69.690187 362.555656 69.690187 C 361.8955 69.690187 361.360344 69.155031 361.360344 68.494875 C 361.360344 67.830812 361.8955 67.295656 362.555656 67.295656 C 363.215812 67.295656 363.750969 67.830812 363.750969 68.494875 Z M 363.750969 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 68.498781 C 380.532219 69.158937 379.997062 69.694094 379.336906 69.694094 C 378.67675 69.694094 378.141594 69.158937 378.141594 68.498781 C 378.141594 67.838625 378.67675 67.303469 379.336906 67.303469 C 379.997062 67.303469 380.532219 67.838625 380.532219 68.498781 Z M 380.532219 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 68.498781 C 384.727531 69.158937 384.192375 69.694094 383.532219 69.694094 C 382.872062 69.694094 382.336906 69.158937 382.336906 68.498781 C 382.336906 67.838625 382.872062 67.303469 383.532219 67.303469 C 384.192375 67.303469 384.727531 67.838625 384.727531 68.498781 Z M 384.727531 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 68.498781 C 388.922844 69.158937 388.387687 69.694094 387.727531 69.694094 C 387.067375 69.694094 386.532219 69.158937 386.532219 68.498781 C 386.532219 67.838625 387.067375 67.303469 387.727531 67.303469 C 388.387687 67.303469 388.922844 67.838625 388.922844 68.498781 Z M 388.922844 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 68.498781 C 393.118156 69.158937 392.583 69.694094 391.922844 69.694094 C 391.262687 69.694094 390.727531 69.158937 390.727531 68.498781 C 390.727531 67.838625 391.262687 67.303469 391.922844 67.303469 C 392.583 67.303469 393.118156 67.838625 393.118156 68.498781 Z M 393.118156 68.498781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 68.494875 C 397.313469 69.155031 396.778312 69.690187 396.118156 69.690187 C 395.458 69.690187 394.922844 69.155031 394.922844 68.494875 C 394.922844 67.830812 395.458 67.295656 396.118156 67.295656 C 396.778312 67.295656 397.313469 67.830812 397.313469 68.494875 Z M 397.313469 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 68.494875 C 405.704094 69.155031 405.168937 69.690187 404.508781 69.690187 C 403.848625 69.690187 403.313469 69.155031 403.313469 68.494875 C 403.313469 67.830812 403.848625 67.295656 404.508781 67.295656 C 405.168937 67.295656 405.704094 67.830812 405.704094 68.494875 Z M 405.704094 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 68.494875 C 422.485344 69.155031 421.950187 69.690187 421.290031 69.690187 C 420.629875 69.690187 420.094719 69.155031 420.094719 68.494875 C 420.094719 67.830812 420.629875 67.295656 421.290031 67.295656 C 421.950187 67.295656 422.485344 67.830812 422.485344 68.494875 Z M 422.485344 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 68.494875 C 430.875969 69.155031 430.340812 69.690187 429.680656 69.690187 C 429.0205 69.690187 428.485344 69.155031 428.485344 68.494875 C 428.485344 67.830812 429.0205 67.295656 429.680656 67.295656 C 430.340812 67.295656 430.875969 67.830812 430.875969 68.494875 Z M 430.875969 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 68.494875 C 435.071281 69.155031 434.536125 69.690187 433.875969 69.690187 C 433.215812 69.690187 432.680656 69.155031 432.680656 68.494875 C 432.680656 67.830812 433.215812 67.295656 433.875969 67.295656 C 434.536125 67.295656 435.071281 67.830812 435.071281 68.494875 Z M 435.071281 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 68.494875 C 443.461906 69.155031 442.92675 69.690187 442.266594 69.690187 C 441.606437 69.690187 441.071281 69.155031 441.071281 68.494875 C 441.071281 67.830812 441.606437 67.295656 442.266594 67.295656 C 442.92675 67.295656 443.461906 67.830812 443.461906 68.494875 Z M 443.461906 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 68.494875 C 451.852531 69.155031 451.317375 69.690187 450.657219 69.690187 C 449.997062 69.690187 449.461906 69.155031 449.461906 68.494875 C 449.461906 67.830812 449.997062 67.295656 450.657219 67.295656 C 451.317375 67.295656 451.852531 67.830812 451.852531 68.494875 Z M 451.852531 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 68.494875 C 456.047844 69.155031 455.512687 69.690187 454.852531 69.690187 C 454.192375 69.690187 453.657219 69.155031 453.657219 68.494875 C 453.657219 67.830812 454.192375 67.295656 454.852531 67.295656 C 455.512687 67.295656 456.047844 67.830812 456.047844 68.494875 Z M 456.047844 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 472.829094 68.494875 C 472.829094 69.155031 472.293937 69.690187 471.633781 69.690187 C 470.973625 69.690187 470.438469 69.155031 470.438469 68.494875 C 470.438469 67.830812 470.973625 67.295656 471.633781 67.295656 C 472.293937 67.295656 472.829094 67.830812 472.829094 68.494875 Z M 472.829094 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.415031 68.494875 C 485.415031 69.155031 484.879875 69.690187 484.219719 69.690187 C 483.559562 69.690187 483.024406 69.155031 483.024406 68.494875 C 483.024406 67.830812 483.559562 67.295656 484.219719 67.295656 C 484.879875 67.295656 485.415031 67.830812 485.415031 68.494875 Z M 485.415031 68.494875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 77.990969 L 169.672844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 189.075187 73.240969 L 189.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.473625 73.240969 L 208.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.875969 73.240969 L 227.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 247.274406 73.240969 L 247.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.67675 77.990969 L 266.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 286.075187 73.240969 L 286.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.477531 73.240969 L 305.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.875969 73.240969 L 324.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 344.274406 73.240969 L 344.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.67675 77.990969 L 363.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.075187 73.240969 L 383.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 402.477531 73.240969 L 402.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.875969 73.240969 L 421.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 441.278312 73.240969 L 441.278312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 77.990969 L 460.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 77.990969 L 169.672844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 150.274406 73.240969 L 150.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 130.875969 73.240969 L 130.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 111.473625 73.240969 L 111.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.075187 73.240969 L 92.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 77.990969 L 460.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.075187 73.240969 L 480.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="163.211" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="254.206" y="389.053"/>
+ <use xlink:href="#glyph0-3" x="266.213975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="351.205" y="389.053"/>
+ <use xlink:href="#glyph0-1" x="363.212975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="448.207" y="389.053"/>
+ <use xlink:href="#glyph0-3" x="460.214975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="315.84" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="327.151971" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="342.956727" y="416.984352"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="355.788859" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="366.352033" y="416.984352"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="379.976044" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="390.196617" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="409.040015" y="417.528"/>
+ <use xlink:href="#glyph0-7" x="419.71377" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="438.047855" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.755553" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.763528" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-2" x="470.098439" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="479.808189" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 392.862062 L 169.672844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 189.075187 397.615969 L 189.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.473625 397.615969 L 208.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.875969 397.615969 L 227.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 247.274406 397.615969 L 247.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.67675 392.862062 L 266.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 286.075187 397.615969 L 286.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.477531 397.615969 L 305.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.875969 397.615969 L 324.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 344.274406 397.615969 L 344.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.67675 392.862062 L 363.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.075187 397.615969 L 383.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 402.477531 397.615969 L 402.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.875969 397.615969 L 421.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 441.278312 397.615969 L 441.278312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 392.862062 L 460.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 392.862062 L 169.672844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 150.274406 397.615969 L 150.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 130.875969 397.615969 L 130.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 111.473625 397.615969 L 111.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.075187 397.615969 L 92.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 392.862062 L 460.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.075187 397.615969 L 480.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.662844 L 79.372062 79.662844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.834719 L 79.372062 90.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 102.006594 L 79.372062 102.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 113.182375 L 79.372062 113.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 124.35425 L 79.372062 124.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 135.530031 L 79.372062 135.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 146.701906 L 79.372062 146.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 157.877687 L 79.372062 157.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 169.049562 L 79.372062 169.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 180.225344 L 79.372062 180.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 191.397219 L 79.372062 191.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 202.569094 L 79.372062 202.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 213.744875 L 79.372062 213.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 224.91675 L 79.372062 224.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 236.092531 L 79.372062 236.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 247.264406 L 79.372062 247.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 258.440187 L 79.372062 258.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 269.612062 L 79.372062 269.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 280.787844 L 79.372062 280.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 291.959719 L 79.372062 291.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 303.131594 L 79.372062 303.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 314.307375 L 79.372062 314.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 325.47925 L 79.372062 325.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 336.655031 L 79.372062 336.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 347.826906 L 79.372062 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 347.826906 L 79.372062 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 359.002687 L 79.372062 359.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 370.174562 L 79.372062 370.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 381.350344 L 79.372062 381.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 392.522219 L 79.372062 392.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="43.65" y="314.122"/>
+ <use xlink:href="#glyph0-3" x="55.657975" y="314.122"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="43.65" y="258.255"/>
+ <use xlink:href="#glyph0-3" x="55.657975" y="258.255"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-8" x="43.65" y="202.387"/>
+ <use xlink:href="#glyph0-3" x="55.657975" y="202.387"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-9" x="43.65" y="146.519"/>
+ <use xlink:href="#glyph0-3" x="55.657975" y="146.519"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="43.65" y="90.654"/>
+ <use xlink:href="#glyph0-3" x="55.657975" y="90.654"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-3" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph8-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph8-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph8-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph8-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph8-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph8-10" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph8-11" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph8-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph8-12" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph9-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph10-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-13" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.662844 L 498.903312 79.662844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.834719 L 498.903312 90.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 102.006594 L 498.903312 102.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 113.182375 L 498.903312 113.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 124.35425 L 498.903312 124.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 135.530031 L 498.903312 135.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 146.701906 L 498.903312 146.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 157.877687 L 498.903312 157.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 169.049562 L 498.903312 169.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 180.225344 L 498.903312 180.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 191.397219 L 498.903312 191.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 202.569094 L 498.903312 202.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 213.744875 L 498.903312 213.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 224.91675 L 498.903312 224.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 236.092531 L 498.903312 236.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 247.264406 L 498.903312 247.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 258.440187 L 498.903312 258.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 269.612062 L 498.903312 269.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 280.787844 L 498.903312 280.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 291.959719 L 498.903312 291.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 303.131594 L 498.903312 303.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 314.307375 L 498.903312 314.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 325.47925 L 498.903312 325.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 336.655031 L 498.903312 336.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 347.826906 L 498.903312 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 347.826906 L 498.903312 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 359.002687 L 498.903312 359.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 370.174562 L 498.903312 370.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 381.350344 L 498.903312 381.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 392.522219 L 498.903312 392.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 77.990969 L 169.672844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 189.075187 73.240969 L 189.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.473625 73.240969 L 208.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.875969 73.240969 L 227.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 247.274406 73.240969 L 247.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.67675 77.990969 L 266.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 286.075187 73.240969 L 286.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.477531 73.240969 L 305.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.875969 73.240969 L 324.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 344.274406 73.240969 L 344.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.67675 77.990969 L 363.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.075187 73.240969 L 383.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 402.477531 73.240969 L 402.477531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.875969 73.240969 L 421.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 441.278312 73.240969 L 441.278312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 77.990969 L 460.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 77.990969 L 169.672844 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 150.274406 73.240969 L 150.274406 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 130.875969 73.240969 L 130.875969 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 111.473625 73.240969 L 111.473625 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.075187 73.240969 L 92.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 77.990969 L 460.67675 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.075187 73.240969 L 480.075187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 392.862062 L 169.672844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 189.075187 397.615969 L 189.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.473625 397.615969 L 208.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.875969 397.615969 L 227.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 247.274406 397.615969 L 247.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.67675 392.862062 L 266.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 286.075187 397.615969 L 286.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.477531 397.615969 L 305.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.875969 397.615969 L 324.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 344.274406 397.615969 L 344.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.67675 392.862062 L 363.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.075187 397.615969 L 383.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 402.477531 397.615969 L 402.477531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.875969 397.615969 L 421.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 441.278312 397.615969 L 441.278312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 392.862062 L 460.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.672844 392.862062 L 169.672844 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 150.274406 397.615969 L 150.274406 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 130.875969 397.615969 L 130.875969 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 111.473625 397.615969 L 111.473625 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.075187 397.615969 L 92.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.67675 392.862062 L 460.67675 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.075187 397.615969 L 480.075187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.662844 L 79.372062 79.662844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.834719 L 79.372062 90.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 102.006594 L 79.372062 102.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 113.182375 L 79.372062 113.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 124.35425 L 79.372062 124.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 135.530031 L 79.372062 135.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 146.701906 L 79.372062 146.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 157.877687 L 79.372062 157.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 169.049562 L 79.372062 169.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 180.225344 L 79.372062 180.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 191.397219 L 79.372062 191.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 202.569094 L 79.372062 202.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 213.744875 L 79.372062 213.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 224.91675 L 79.372062 224.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 236.092531 L 79.372062 236.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 247.264406 L 79.372062 247.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 258.440187 L 79.372062 258.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 269.612062 L 79.372062 269.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 280.787844 L 79.372062 280.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 291.959719 L 79.372062 291.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 303.131594 L 79.372062 303.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 314.307375 L 79.372062 314.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 325.47925 L 79.372062 325.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 336.655031 L 79.372062 336.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 347.826906 L 79.372062 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 347.826906 L 79.372062 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 359.002687 L 79.372062 359.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 370.174562 L 79.372062 370.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 381.350344 L 79.372062 381.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 392.522219 L 79.372062 392.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.662844 L 498.903312 79.662844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.834719 L 498.903312 90.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 102.006594 L 498.903312 102.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 113.182375 L 498.903312 113.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 124.35425 L 498.903312 124.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 135.530031 L 498.903312 135.530031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 146.701906 L 498.903312 146.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 157.877687 L 498.903312 157.877687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 169.049562 L 498.903312 169.049562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 180.225344 L 498.903312 180.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 191.397219 L 498.903312 191.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 202.569094 L 498.903312 202.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 213.744875 L 498.903312 213.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 224.91675 L 498.903312 224.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 236.092531 L 498.903312 236.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 247.264406 L 498.903312 247.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 258.440187 L 498.903312 258.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 269.612062 L 498.903312 269.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 280.787844 L 498.903312 280.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 291.959719 L 498.903312 291.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 303.131594 L 498.903312 303.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 314.307375 L 498.903312 314.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 325.47925 L 498.903312 325.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 336.655031 L 498.903312 336.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 347.826906 L 498.903312 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 347.826906 L 498.903312 347.826906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 359.002687 L 498.903312 359.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 370.174562 L 498.903312 370.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 381.350344 L 498.903312 381.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 392.522219 L 498.903312 392.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/lb2pKpi_s02.svg b/doc/figs/lb2pKpi_s02.svg
new file mode 100644
index 00000000000..d8c6194511e
--- /dev/null
+++ b/doc/figs/lb2pKpi_s02.svg
@@ -0,0 +1,713 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="513pt" height="432pt" viewBox="0 0 513 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 4.515625 -8.8125 C 4.09375 -8.78125 4 -8.75 4 -8.53125 C 4 -8.296875 4.125 -8.296875 4.5625 -8.296875 L 5.6875 -8.296875 C 7.78125 -8.296875 8.703125 -6.578125 8.703125 -4.21875 C 8.703125 -1 7.046875 -0.140625 5.84375 -0.140625 C 4.65625 -0.140625 2.65625 -0.71875 1.9375 -2.328125 C 2.71875 -2.203125 3.4375 -2.65625 3.4375 -3.53125 C 3.4375 -4.25 2.921875 -4.734375 2.234375 -4.734375 C 1.640625 -4.734375 1 -4.390625 1 -3.453125 C 1 -1.28125 3.1875 0.515625 5.90625 0.515625 C 8.828125 0.515625 10.984375 -1.71875 10.984375 -4.1875 C 10.984375 -6.453125 9.171875 -8.21875 6.8125 -8.640625 C 8.953125 -9.25 10.328125 -11.046875 10.328125 -12.953125 C 10.328125 -14.890625 8.3125 -16.3125 5.9375 -16.3125 C 3.484375 -16.3125 1.671875 -14.8125 1.671875 -13.03125 C 1.671875 -12.046875 2.421875 -11.84375 2.796875 -11.84375 C 3.3125 -11.84375 3.90625 -12.21875 3.90625 -12.953125 C 3.90625 -13.734375 3.3125 -14.078125 2.765625 -14.078125 C 2.625 -14.078125 2.578125 -14.078125 2.5 -14.0625 C 3.4375 -15.71875 5.734375 -15.71875 5.859375 -15.71875 C 6.671875 -15.71875 8.265625 -15.359375 8.265625 -12.953125 C 8.265625 -12.484375 8.1875 -11.109375 7.484375 -10.0625 C 6.75 -8.984375 5.90625 -8.90625 5.25 -8.875 Z M 4.515625 -8.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 4.515625 -1.203125 C 4.515625 -1.859375 3.953125 -2.375 3.34375 -2.375 C 2.625 -2.375 2.140625 -1.8125 2.140625 -1.203125 C 2.140625 -0.46875 2.75 0 3.3125 0 C 3.96875 0 4.515625 -0.515625 4.515625 -1.203125 Z M 4.515625 -1.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 8.78125 -6.5625 C 8.765625 -6.609375 8.671875 -6.765625 8.671875 -6.78125 C 8.671875 -6.8125 8.953125 -7.015625 9.125 -7.125 C 10.40625 -8.078125 12.171875 -9.34375 12.71875 -9.6875 C 13.546875 -10.21875 14.15625 -10.5625 14.890625 -10.625 C 15.015625 -10.640625 15.25 -10.65625 15.25 -10.953125 C 15.234375 -11.0625 15.140625 -11.15625 15.015625 -11.15625 C 15 -11.15625 14.546875 -11.109375 14.4375 -11.109375 L 13.78125 -11.109375 C 13.5 -11.109375 13.09375 -11.109375 12.9375 -11.125 C 12.828125 -11.125 12.1875 -11.15625 12.078125 -11.15625 C 11.96875 -11.15625 11.734375 -11.15625 11.734375 -10.859375 C 11.734375 -10.84375 11.75 -10.640625 12 -10.625 C 12.125 -10.609375 12.390625 -10.578125 12.390625 -10.375 C 12.390625 -10.109375 12.0625 -9.84375 12.03125 -9.828125 L 11.890625 -9.703125 C 11.84375 -9.65625 11.78125 -9.59375 11.703125 -9.546875 L 5.03125 -4.703125 L 6.328125 -9.890625 C 6.46875 -10.46875 6.5 -10.625 7.703125 -10.625 C 8.03125 -10.625 8.21875 -10.625 8.21875 -10.9375 C 8.21875 -10.953125 8.203125 -11.15625 7.9375 -11.15625 C 7.625 -11.15625 7.234375 -11.125 6.9375 -11.109375 L 5.90625 -11.109375 C 4.328125 -11.109375 3.90625 -11.15625 3.796875 -11.15625 C 3.703125 -11.15625 3.46875 -11.15625 3.46875 -10.859375 C 3.46875 -10.625 3.65625 -10.625 3.9375 -10.625 C 4.484375 -10.625 4.953125 -10.625 4.953125 -10.359375 C 4.953125 -10.296875 4.9375 -10.28125 4.890625 -10.0625 L 2.703125 -1.296875 C 2.546875 -0.671875 2.515625 -0.546875 1.3125 -0.546875 C 1 -0.546875 0.796875 -0.546875 0.796875 -0.234375 C 0.796875 -0.15625 0.84375 0 1.0625 0 C 1.375 0 1.765625 -0.03125 2.078125 -0.046875 L 4.1875 -0.046875 C 4.453125 -0.03125 4.984375 0 5.234375 0 C 5.3125 0 5.5625 0 5.5625 -0.296875 C 5.5625 -0.546875 5.359375 -0.546875 5.078125 -0.546875 C 4.96875 -0.546875 4.734375 -0.546875 4.46875 -0.578125 C 4.125 -0.609375 4.0625 -0.640625 4.0625 -0.796875 C 4.0625 -0.90625 4.1875 -1.3125 4.234375 -1.5625 L 4.859375 -4.03125 L 7.484375 -5.9375 L 9.453125 -1.890625 C 9.515625 -1.765625 9.6875 -1.40625 9.75 -1.265625 C 9.859375 -1.09375 9.859375 -1.0625 9.859375 -1 C 9.859375 -0.5625 9.25 -0.546875 9.078125 -0.546875 C 8.90625 -0.546875 8.671875 -0.546875 8.671875 -0.234375 C 8.671875 -0.21875 8.6875 0 8.953125 0 C 9.125 0 9.734375 -0.03125 9.890625 -0.046875 L 10.84375 -0.046875 C 12.34375 -0.046875 12.296875 0 12.5 0 C 12.5625 0 12.8125 0 12.8125 -0.3125 C 12.8125 -0.546875 12.578125 -0.546875 12.484375 -0.546875 C 11.84375 -0.5625 11.640625 -0.671875 11.375 -1.21875 Z M 8.78125 -6.5625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 0.84375 1.984375 C 0.71875 2.5 0.6875 2.625 0.03125 2.625 C -0.203125 2.625 -0.390625 2.625 -0.390625 2.9375 C -0.390625 3.09375 -0.25 3.171875 -0.15625 3.171875 C 0 3.171875 0.0625 3.125 1.28125 3.125 C 2.453125 3.125 2.796875 3.171875 2.90625 3.171875 C 2.96875 3.171875 3.21875 3.171875 3.21875 2.859375 C 3.21875 2.625 2.984375 2.625 2.796875 2.625 C 2.015625 2.625 2.015625 2.53125 2.015625 2.390625 C 2.015625 2.265625 2.296875 1.109375 2.796875 -0.796875 C 3 -0.421875 3.515625 0.15625 4.390625 0.15625 C 6.40625 0.15625 8.5 -2.15625 8.5 -4.53125 C 8.5 -6.140625 7.453125 -7.203125 6.140625 -7.203125 C 5.171875 -7.203125 4.375 -6.53125 3.90625 -6.046875 C 3.5625 -7.203125 2.46875 -7.203125 2.296875 -7.203125 C 1.71875 -7.203125 1.3125 -6.828125 1.046875 -6.328125 C 0.671875 -5.59375 0.484375 -4.75 0.484375 -4.703125 C 0.484375 -4.5625 0.609375 -4.5 0.734375 -4.5 C 0.953125 -4.5 0.96875 -4.5625 1.078125 -4.984375 C 1.296875 -5.8125 1.578125 -6.75 2.25 -6.75 C 2.65625 -6.75 2.78125 -6.375 2.78125 -5.984375 C 2.78125 -5.8125 2.71875 -5.421875 2.6875 -5.296875 Z M 3.859375 -5.03125 C 3.9375 -5.3125 3.9375 -5.34375 4.1875 -5.640625 C 4.8125 -6.375 5.515625 -6.75 6.09375 -6.75 C 6.90625 -6.75 7.21875 -5.953125 7.21875 -5.21875 C 7.21875 -4.609375 6.859375 -2.859375 6.375 -1.890625 C 5.953125 -1.015625 5.171875 -0.296875 4.390625 -0.296875 C 3.28125 -0.296875 3.03125 -1.5625 3.03125 -1.6875 C 3.03125 -1.71875 3.0625 -1.890625 3.078125 -1.9375 Z M 3.859375 -5.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 9.765625 -2.75 C 9.953125 -2.75 10.265625 -2.75 10.265625 -3.0625 C 10.265625 -3.390625 9.953125 -3.390625 9.765625 -3.390625 L 2.03125 -3.390625 C 1.84375 -3.390625 1.53125 -3.390625 1.53125 -3.0625 C 1.53125 -2.75 1.84375 -2.75 2.03125 -2.75 Z M 9.765625 -2.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-11">
+<path style="stroke:none;" d="M -8.859375 -7.3125 C -9.515625 -8.53125 -10.640625 -10.328125 -12.703125 -10.328125 C -14.84375 -10.328125 -16.3125 -8.265625 -16.3125 -6.015625 C -16.3125 -3.578125 -14.515625 -1.671875 -12.296875 -1.671875 C -11.453125 -1.671875 -10.625 -1.90625 -9.78125 -2.59375 C -9.46875 -2.875 -9.4375 -2.890625 -8.25 -4.609375 C -7.140625 -2.234375 -5.5 -1 -3.703125 -1 C -1.109375 -1 0.515625 -3.484375 0.515625 -5.984375 C 0.515625 -8.703125 -1.5 -10.984375 -4.078125 -10.984375 C -6.578125 -10.984375 -7.671875 -9.21875 -8.859375 -7.3125 Z M -11.0625 -3.96875 C -11.28125 -3.65625 -11.921875 -2.671875 -13.125 -2.671875 C -14.71875 -2.671875 -15.71875 -4.34375 -15.71875 -5.984375 C -15.71875 -7.75 -14.453125 -9.328125 -12.6875 -9.328125 C -11.1875 -9.328125 -9.984375 -8.25 -9.203125 -6.8125 Z M -7.90625 -5.125 L -5.96875 -8.09375 C -5.546875 -8.734375 -4.78125 -9.859375 -3.28125 -9.859375 C -1.421875 -9.859375 -0.140625 -7.96875 -0.140625 -6.015625 C -0.140625 -3.921875 -1.671875 -2.140625 -3.703125 -2.140625 C -5.625 -2.140625 -7.15625 -3.53125 -7.90625 -5.125 Z M -7.90625 -5.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-12">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-13">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-14">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 82.665031 68.584719 C 82.665031 69.244875 82.129875 69.783937 81.469719 69.783937 C 80.805656 69.783937 80.2705 69.244875 80.2705 68.584719 C 80.2705 67.924562 80.805656 67.389406 81.469719 67.389406 C 82.129875 67.389406 82.665031 67.924562 82.665031 68.584719 Z M 82.665031 68.584719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.860344 68.686281 C 86.860344 69.346437 86.325187 69.881594 85.665031 69.881594 C 85.004875 69.881594 84.465812 69.346437 84.465812 68.686281 C 84.465812 68.022219 85.004875 67.487062 85.665031 67.487062 C 86.325187 67.487062 86.860344 68.022219 86.860344 68.686281 Z M 86.860344 68.686281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 91.055656 69.66675 C 91.055656 70.326906 90.5205 70.865969 89.860344 70.865969 C 89.200187 70.865969 88.661125 70.326906 88.661125 69.66675 C 88.661125 69.006594 89.200187 68.471437 89.860344 68.471437 C 90.5205 68.471437 91.055656 69.006594 91.055656 69.66675 Z M 91.055656 69.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 69.174562 C 95.250969 69.838625 94.715812 70.373781 94.055656 70.373781 C 93.3955 70.373781 92.856437 69.838625 92.856437 69.174562 C 92.856437 68.514406 93.3955 67.97925 94.055656 67.97925 C 94.715812 67.97925 95.250969 68.514406 95.250969 69.174562 Z M 95.250969 69.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.446281 69.66675 C 99.446281 70.326906 98.911125 70.865969 98.250969 70.865969 C 97.590812 70.865969 97.05175 70.326906 97.05175 69.66675 C 97.05175 69.006594 97.590812 68.471437 98.250969 68.471437 C 98.911125 68.471437 99.446281 69.006594 99.446281 69.66675 Z M 99.446281 69.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 103.641594 69.862062 C 103.641594 70.526125 103.106437 71.061281 102.446281 71.061281 C 101.786125 71.061281 101.247062 70.526125 101.247062 69.862062 C 101.247062 69.201906 101.786125 68.66675 102.446281 68.66675 C 103.106437 68.66675 103.641594 69.201906 103.641594 69.862062 Z M 103.641594 69.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.836906 70.256594 C 107.836906 70.91675 107.30175 71.455812 106.641594 71.455812 C 105.981437 71.455812 105.442375 70.91675 105.442375 70.256594 C 105.442375 69.596437 105.981437 69.061281 106.641594 69.061281 C 107.30175 69.061281 107.836906 69.596437 107.836906 70.256594 Z M 107.836906 70.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 112.032219 71.733156 C 112.032219 72.393312 111.497062 72.928469 110.836906 72.928469 C 110.17675 72.928469 109.637687 72.393312 109.637687 71.733156 C 109.637687 71.073 110.17675 70.533937 110.836906 70.533937 C 111.497062 70.533937 112.032219 71.073 112.032219 71.733156 Z M 112.032219 71.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 71.733156 C 116.227531 72.393312 115.692375 72.928469 115.032219 72.928469 C 114.372062 72.928469 113.833 72.393312 113.833 71.733156 C 113.833 71.073 114.372062 70.533937 115.032219 70.533937 C 115.692375 70.533937 116.227531 71.073 116.227531 71.733156 Z M 116.227531 71.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.422844 72.815187 C 120.422844 73.475344 119.887687 74.0105 119.227531 74.0105 C 118.567375 74.0105 118.028312 73.475344 118.028312 72.815187 C 118.028312 72.151125 118.567375 71.615969 119.227531 71.615969 C 119.887687 71.615969 120.422844 72.151125 120.422844 72.815187 Z M 120.422844 72.815187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 124.618156 72.518312 C 124.618156 73.178469 124.083 73.713625 123.422844 73.713625 C 122.762687 73.713625 122.223625 73.178469 122.223625 72.518312 C 122.223625 71.858156 122.762687 71.323 123.422844 71.323 C 124.083 71.323 124.618156 71.858156 124.618156 72.518312 Z M 124.618156 72.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 73.994875 C 128.813469 74.655031 128.278312 75.190187 127.618156 75.190187 C 126.958 75.190187 126.418937 74.655031 126.418937 73.994875 C 126.418937 73.330812 126.958 72.795656 127.618156 72.795656 C 128.278312 72.795656 128.813469 73.330812 128.813469 73.994875 Z M 128.813469 73.994875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 133.008781 73.502687 C 133.008781 74.162844 132.473625 74.698 131.813469 74.698 C 131.153312 74.698 130.61425 74.162844 130.61425 73.502687 C 130.61425 72.842531 131.153312 72.303469 131.813469 72.303469 C 132.473625 72.303469 133.008781 72.842531 133.008781 73.502687 Z M 133.008781 73.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 137.204094 74.190187 C 137.204094 74.850344 136.668937 75.3855 136.008781 75.3855 C 135.348625 75.3855 134.809562 74.850344 134.809562 74.190187 C 134.809562 73.530031 135.348625 72.994875 136.008781 72.994875 C 136.668937 72.994875 137.204094 73.530031 137.204094 74.190187 Z M 137.204094 74.190187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.399406 73.994875 C 141.399406 74.655031 140.86425 75.190187 140.204094 75.190187 C 139.543937 75.190187 139.004875 74.655031 139.004875 73.994875 C 139.004875 73.330812 139.543937 72.795656 140.204094 72.795656 C 140.86425 72.795656 141.399406 73.330812 141.399406 73.994875 Z M 141.399406 73.994875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 76.842531 C 145.594719 77.506594 145.059562 78.04175 144.399406 78.04175 C 143.73925 78.04175 143.200187 77.506594 143.200187 76.842531 C 143.200187 76.182375 143.73925 75.647219 144.399406 75.647219 C 145.059562 75.647219 145.594719 76.182375 145.594719 76.842531 Z M 145.594719 76.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 149.790031 77.237062 C 149.790031 77.897219 149.254875 78.432375 148.594719 78.432375 C 147.934562 78.432375 147.3955 77.897219 147.3955 77.237062 C 147.3955 76.576906 147.934562 76.04175 148.594719 76.04175 C 149.254875 76.04175 149.790031 76.576906 149.790031 77.237062 Z M 149.790031 77.237062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 78.514406 C 153.985344 79.174562 153.450187 79.713625 152.790031 79.713625 C 152.129875 79.713625 151.590812 79.174562 151.590812 78.514406 C 151.590812 77.85425 152.129875 77.319094 152.790031 77.319094 C 153.450187 77.319094 153.985344 77.85425 153.985344 78.514406 Z M 153.985344 78.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 81.268312 C 158.180656 81.928469 157.6455 82.463625 156.985344 82.463625 C 156.325187 82.463625 155.786125 81.928469 155.786125 81.268312 C 155.786125 80.608156 156.325187 80.073 156.985344 80.073 C 157.6455 80.073 158.180656 80.608156 158.180656 81.268312 Z M 158.180656 81.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 162.375969 82.740969 C 162.375969 83.405031 161.840812 83.940187 161.180656 83.940187 C 160.5205 83.940187 159.981437 83.405031 159.981437 82.740969 C 159.981437 82.080812 160.5205 81.545656 161.180656 81.545656 C 161.840812 81.545656 162.375969 82.080812 162.375969 82.740969 Z M 162.375969 82.740969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 166.571281 83.725344 C 166.571281 84.3855 166.036125 84.924562 165.375969 84.924562 C 164.715812 84.924562 164.17675 84.3855 164.17675 83.725344 C 164.17675 83.065187 164.715812 82.530031 165.375969 82.530031 C 166.036125 82.530031 166.571281 83.065187 166.571281 83.725344 Z M 166.571281 83.725344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 86.873781 C 170.766594 87.533937 170.231437 88.069094 169.571281 88.069094 C 168.911125 88.069094 168.372062 87.533937 168.372062 86.873781 C 168.372062 86.209719 168.911125 85.674562 169.571281 85.674562 C 170.231437 85.674562 170.766594 86.209719 170.766594 86.873781 Z M 170.766594 86.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 174.961906 91.002687 C 174.961906 91.662844 174.42675 92.198 173.766594 92.198 C 173.106437 92.198 172.571281 91.662844 172.571281 91.002687 C 172.571281 90.338625 173.106437 89.803469 173.766594 89.803469 C 174.42675 89.803469 174.961906 90.338625 174.961906 91.002687 Z M 174.961906 91.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 179.157219 93.264406 C 179.157219 93.924562 178.622062 94.459719 177.961906 94.459719 C 177.30175 94.459719 176.762687 93.924562 176.762687 93.264406 C 176.762687 92.600344 177.30175 92.065187 177.961906 92.065187 C 178.622062 92.065187 179.157219 92.600344 179.157219 93.264406 Z M 179.157219 93.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 98.573 C 183.352531 99.233156 182.817375 99.768312 182.157219 99.768312 C 181.497062 99.768312 180.958 99.233156 180.958 98.573 C 180.958 97.908937 181.497062 97.373781 182.157219 97.373781 C 182.817375 97.373781 183.352531 97.908937 183.352531 98.573 Z M 183.352531 98.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 101.420656 C 187.547844 102.084719 187.012687 102.619875 186.352531 102.619875 C 185.692375 102.619875 185.157219 102.084719 185.157219 101.420656 C 185.157219 100.7605 185.692375 100.225344 186.352531 100.225344 C 187.012687 100.225344 187.547844 100.7605 187.547844 101.420656 Z M 187.547844 101.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 107.615969 C 191.743156 108.276125 191.208 108.811281 190.547844 108.811281 C 189.887687 108.811281 189.348625 108.276125 189.348625 107.615969 C 189.348625 106.955812 189.887687 106.420656 190.547844 106.420656 C 191.208 106.420656 191.743156 106.955812 191.743156 107.615969 Z M 191.743156 107.615969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 121.506594 L 194.743156 121.561281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 126.115969 L 194.743156 126.170656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 123.838625 C 195.938469 124.498781 195.403312 125.033937 194.743156 125.033937 C 194.083 125.033937 193.543937 124.498781 193.543937 123.838625 C 193.543937 123.178469 194.083 122.639406 194.743156 122.639406 C 195.403312 122.639406 195.938469 123.178469 195.938469 123.838625 Z M 195.938469 123.838625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 141.655031 L 198.938469 142.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 146.662844 L 198.938469 147.115969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 144.3855 C 200.133781 145.045656 199.598625 145.580812 198.938469 145.580812 C 198.278312 145.580812 197.743156 145.045656 197.743156 144.3855 C 197.743156 143.725344 198.278312 143.186281 198.938469 143.186281 C 199.598625 143.186281 200.133781 143.725344 200.133781 144.3855 Z M 200.133781 144.3855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 167.463625 L 203.133781 168.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 172.912844 L 203.133781 173.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 170.6355 C 204.329094 171.295656 203.793937 171.830812 203.133781 171.830812 C 202.473625 171.830812 201.934562 171.295656 201.934562 170.6355 C 201.934562 169.971437 202.473625 169.436281 203.133781 169.436281 C 203.793937 169.436281 204.329094 169.971437 204.329094 170.6355 Z M 204.329094 170.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 207.006594 L 207.329094 208.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 213.022219 L 207.329094 214.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 210.744875 C 208.524406 211.405031 207.98925 211.944094 207.329094 211.944094 C 206.668937 211.944094 206.129875 211.405031 206.129875 210.744875 C 206.129875 210.084719 206.668937 209.549562 207.329094 209.549562 C 207.98925 209.549562 208.524406 210.084719 208.524406 210.744875 Z M 208.524406 210.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 258.869875 L 211.524406 260.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 265.522219 L 211.524406 267.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 263.244875 C 212.719719 263.905031 212.184562 264.440187 211.524406 264.440187 C 210.86425 264.440187 210.329094 263.905031 210.329094 263.244875 C 210.329094 262.584719 210.86425 262.045656 211.524406 262.045656 C 212.184562 262.045656 212.719719 262.584719 212.719719 263.244875 Z M 212.719719 263.244875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 284.537844 L 215.719719 286.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 291.475344 L 215.719719 293.858156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 289.198 C 216.915031 289.862062 216.379875 290.397219 215.719719 290.397219 C 215.059562 290.397219 214.524406 289.862062 214.524406 289.198 C 214.524406 288.537844 215.059562 288.002687 215.719719 288.002687 C 216.379875 288.002687 216.915031 288.537844 216.915031 289.198 Z M 216.915031 289.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 296.60425 L 219.915031 299.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 303.66675 L 219.915031 306.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 301.389406 C 221.110344 302.049562 220.575187 302.584719 219.915031 302.584719 C 219.254875 302.584719 218.715812 302.049562 218.715812 301.389406 C 218.715812 300.72925 219.254875 300.194094 219.915031 300.194094 C 220.575187 300.194094 221.110344 300.72925 221.110344 301.389406 Z M 221.110344 301.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 286.678469 L 224.110344 289.084719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 293.639406 L 224.110344 296.04175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 291.362062 C 225.305656 292.022219 224.7705 292.561281 224.110344 292.561281 C 223.450187 292.561281 222.915031 292.022219 222.915031 291.362062 C 222.915031 290.701906 223.450187 290.16675 224.110344 290.16675 C 224.7705 290.16675 225.305656 290.701906 225.305656 291.362062 Z M 225.305656 291.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.305656 290.182375 L 228.305656 292.623781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.305656 297.174562 L 228.305656 299.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 294.901125 C 229.500969 295.561281 228.965812 296.096437 228.305656 296.096437 C 227.6455 296.096437 227.110344 295.561281 227.110344 294.901125 C 227.110344 294.240969 227.6455 293.701906 228.305656 293.701906 C 228.965812 293.701906 229.500969 294.240969 229.500969 294.901125 Z M 229.500969 294.901125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 232.500969 285.026125 L 232.500969 287.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 232.500969 291.967531 L 232.500969 294.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 289.690187 C 233.696281 290.350344 233.161125 290.8855 232.500969 290.8855 C 231.840812 290.8855 231.30175 290.350344 231.30175 289.690187 C 231.30175 289.030031 231.840812 288.494875 232.500969 288.494875 C 233.161125 288.494875 233.696281 289.030031 233.696281 289.690187 Z M 233.696281 289.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 236.696281 282.401125 L 236.696281 284.756594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 236.696281 289.315187 L 236.696281 291.670656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 287.037844 C 237.891594 287.698 237.356437 288.233156 236.696281 288.233156 C 236.036125 288.233156 235.500969 287.698 235.500969 287.037844 C 235.500969 286.377687 236.036125 285.838625 236.696281 285.838625 C 237.356437 285.838625 237.891594 286.377687 237.891594 287.037844 Z M 237.891594 287.037844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.891594 269.565187 L 240.891594 271.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.891594 276.334719 L 240.891594 278.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 274.057375 C 242.086906 274.721437 241.55175 275.256594 240.891594 275.256594 C 240.231437 275.256594 239.696281 274.721437 239.696281 274.057375 C 239.696281 273.397219 240.231437 272.862062 240.891594 272.862062 C 241.55175 272.862062 242.086906 273.397219 242.086906 274.057375 Z M 242.086906 274.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 245.086906 259.256594 L 245.086906 261.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 245.086906 265.912844 L 245.086906 268.018312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 263.639406 C 246.282219 264.299562 245.747062 264.834719 245.086906 264.834719 C 244.42675 264.834719 243.891594 264.299562 243.891594 263.639406 C 243.891594 262.975344 244.42675 262.440187 245.086906 262.440187 C 245.747062 262.440187 246.282219 262.975344 246.282219 263.639406 Z M 246.282219 263.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 249.282219 249.342531 L 249.282219 251.334719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 249.282219 255.8855 L 249.282219 257.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 253.608156 C 250.477531 254.272219 249.942375 254.807375 249.282219 254.807375 C 248.622062 254.807375 248.086906 254.272219 248.086906 253.608156 C 248.086906 252.948 248.622062 252.412844 249.282219 252.412844 C 249.942375 252.412844 250.477531 252.948 250.477531 253.608156 Z M 250.477531 253.608156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 253.477531 244.873781 L 253.477531 246.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 253.477531 251.365969 L 253.477531 253.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 249.088625 C 254.672844 249.748781 254.137687 250.283937 253.477531 250.283937 C 252.817375 250.283937 252.282219 249.748781 252.282219 249.088625 C 252.282219 248.424562 252.817375 247.889406 253.477531 247.889406 C 254.137687 247.889406 254.672844 248.424562 254.672844 249.088625 Z M 254.672844 249.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 257.672844 235.451906 L 257.672844 237.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 257.672844 241.826906 L 257.672844 243.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 239.549562 C 258.868156 240.213625 258.333 240.748781 257.672844 240.748781 C 257.012687 240.748781 256.477531 240.213625 256.477531 239.549562 C 256.477531 238.889406 257.012687 238.35425 257.672844 238.35425 C 258.333 238.35425 258.868156 238.889406 258.868156 239.549562 Z M 258.868156 239.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.868156 225.834719 L 261.868156 227.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 261.868156 232.096437 L 261.868156 233.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 229.819094 C 263.063469 230.47925 262.528312 231.014406 261.868156 231.014406 C 261.208 231.014406 260.672844 230.47925 260.672844 229.819094 C 260.672844 229.158937 261.208 228.619875 261.868156 228.619875 C 262.528312 228.619875 263.063469 229.158937 263.063469 229.819094 Z M 263.063469 229.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.063469 212.440187 L 266.063469 213.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 266.063469 218.526125 L 266.063469 220.061281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 216.252687 C 267.258781 216.912844 266.723625 217.448 266.063469 217.448 C 265.403312 217.448 264.868156 216.912844 264.868156 216.252687 C 264.868156 215.588625 265.403312 215.053469 266.063469 215.053469 C 266.723625 215.053469 267.258781 215.588625 267.258781 216.252687 Z M 267.258781 216.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 270.258781 201.670656 L 270.258781 203.061281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 270.258781 207.615969 L 270.258781 209.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 205.338625 C 271.454094 205.998781 270.918937 206.533937 270.258781 206.533937 C 269.598625 206.533937 269.063469 205.998781 269.063469 205.338625 C 269.063469 204.678469 269.598625 204.143312 270.258781 204.143312 C 270.918937 204.143312 271.454094 204.678469 271.454094 205.338625 Z M 271.454094 205.338625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 274.454094 200.119875 L 274.454094 201.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 274.454094 206.04175 L 274.454094 207.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 203.764406 C 275.649406 204.424562 275.11425 204.963625 274.454094 204.963625 C 273.793937 204.963625 273.258781 204.424562 273.258781 203.764406 C 273.258781 203.10425 273.793937 202.569094 274.454094 202.569094 C 275.11425 202.569094 275.649406 203.10425 275.649406 203.764406 Z M 275.649406 203.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 178.213625 L 278.649406 179.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 183.823 L 278.649406 184.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 181.545656 C 279.844719 182.209719 279.309562 182.744875 278.649406 182.744875 C 277.98925 182.744875 277.454094 182.209719 277.454094 181.545656 C 277.454094 180.8855 277.98925 180.350344 278.649406 180.350344 C 279.309562 180.350344 279.844719 180.8855 279.844719 181.545656 Z M 279.844719 181.545656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.844719 180.248781 L 282.844719 181.334719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 282.844719 185.889406 L 282.844719 186.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 183.612062 C 284.040031 184.272219 283.504875 184.807375 282.844719 184.807375 C 282.184562 184.807375 281.649406 184.272219 281.649406 183.612062 C 281.649406 182.951906 282.184562 182.412844 282.844719 182.412844 C 283.504875 182.412844 284.040031 182.951906 284.040031 183.612062 Z M 284.040031 183.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 167.369875 L 287.040031 168.2605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 172.811281 L 287.040031 173.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 170.533937 C 288.235344 171.198 287.700187 171.733156 287.040031 171.733156 C 286.379875 171.733156 285.844719 171.198 285.844719 170.533937 C 285.844719 169.873781 286.379875 169.338625 287.040031 169.338625 C 287.700187 169.338625 288.235344 169.873781 288.235344 170.533937 Z M 288.235344 170.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 164.561281 L 291.235344 165.408937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 169.963625 L 291.235344 170.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 167.686281 C 292.430656 168.346437 291.8955 168.881594 291.235344 168.881594 C 290.575187 168.881594 290.040031 168.346437 290.040031 167.686281 C 290.040031 167.022219 290.575187 166.487062 291.235344 166.487062 C 291.8955 166.487062 292.430656 167.022219 292.430656 167.686281 Z M 292.430656 167.686281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 152.280031 L 295.430656 152.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 157.475344 L 295.430656 158.119875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 155.198 C 296.625969 155.858156 296.090812 156.397219 295.430656 156.397219 C 294.7705 156.397219 294.235344 155.858156 294.235344 155.198 C 294.235344 154.537844 294.7705 154.002687 295.430656 154.002687 C 296.090812 154.002687 296.625969 154.537844 296.625969 155.198 Z M 296.625969 155.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 151.408937 L 299.625969 152.037844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 156.592531 L 299.625969 157.217531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 154.315187 C 300.821281 154.975344 300.286125 155.5105 299.625969 155.5105 C 298.965812 155.5105 298.430656 154.975344 298.430656 154.315187 C 298.430656 153.655031 298.965812 153.115969 299.625969 153.115969 C 300.286125 153.115969 300.821281 153.655031 300.821281 154.315187 Z M 300.821281 154.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 136.733156 L 303.821281 137.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 141.647219 L 303.821281 142.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 139.369875 C 305.016594 140.030031 304.481437 140.569094 303.821281 140.569094 C 303.161125 140.569094 302.625969 140.030031 302.625969 139.369875 C 302.625969 138.709719 303.161125 138.174562 303.821281 138.174562 C 304.481437 138.174562 305.016594 138.709719 305.016594 139.369875 Z M 305.016594 139.369875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 136.440187 L 308.016594 136.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 141.35425 L 308.016594 141.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 139.076906 C 309.211906 139.737062 308.67675 140.272219 308.016594 140.272219 C 307.356437 140.272219 306.821281 139.737062 306.821281 139.076906 C 306.821281 138.41675 307.356437 137.877687 308.016594 137.877687 C 308.67675 137.877687 309.211906 138.41675 309.211906 139.076906 Z M 309.211906 139.076906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 133.256594 L 312.211906 133.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 138.108156 L 312.211906 138.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 135.830812 C 313.407219 136.490969 312.872062 137.030031 312.211906 137.030031 C 311.55175 137.030031 311.016594 136.490969 311.016594 135.830812 C 311.016594 135.170656 311.55175 134.6355 312.211906 134.6355 C 312.872062 134.6355 313.407219 135.170656 313.407219 135.830812 Z M 313.407219 135.830812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 124.10425 L 316.407219 124.213625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 128.768312 L 316.407219 128.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 126.490969 C 317.602531 127.151125 317.067375 127.690187 316.407219 127.690187 C 315.747062 127.690187 315.211906 127.151125 315.211906 126.490969 C 315.211906 125.830812 315.747062 125.295656 316.407219 125.295656 C 317.067375 125.295656 317.602531 125.830812 317.602531 126.490969 Z M 317.602531 126.490969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 120.299562 C 321.797844 120.959719 321.262687 121.494875 320.602531 121.494875 C 319.942375 121.494875 319.407219 120.959719 319.407219 120.299562 C 319.407219 119.6355 319.942375 119.100344 320.602531 119.100344 C 321.262687 119.100344 321.797844 119.6355 321.797844 120.299562 Z M 321.797844 120.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 119.412844 C 325.993156 120.073 325.458 120.608156 324.797844 120.608156 C 324.137687 120.608156 323.602531 120.073 323.602531 119.412844 C 323.602531 118.752687 324.137687 118.217531 324.797844 118.217531 C 325.458 118.217531 325.993156 118.752687 325.993156 119.412844 Z M 325.993156 119.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 118.920656 C 330.188469 119.584719 329.653312 120.119875 328.993156 120.119875 C 328.333 120.119875 327.797844 119.584719 327.797844 118.920656 C 327.797844 118.2605 328.333 117.725344 328.993156 117.725344 C 329.653312 117.725344 330.188469 118.2605 330.188469 118.920656 Z M 330.188469 118.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 117.350344 C 334.383781 118.0105 333.848625 118.545656 333.188469 118.545656 C 332.528312 118.545656 331.993156 118.0105 331.993156 117.350344 C 331.993156 116.686281 332.528312 116.151125 333.188469 116.151125 C 333.848625 116.151125 334.383781 116.686281 334.383781 117.350344 Z M 334.383781 117.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 111.647219 C 338.579094 112.307375 338.043937 112.842531 337.383781 112.842531 C 336.723625 112.842531 336.188469 112.307375 336.188469 111.647219 C 336.188469 110.987062 336.723625 110.451906 337.383781 110.451906 C 338.043937 110.451906 338.579094 110.987062 338.579094 111.647219 Z M 338.579094 111.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 104.959719 C 342.774406 105.623781 342.23925 106.158937 341.579094 106.158937 C 340.918937 106.158937 340.383781 105.623781 340.383781 104.959719 C 340.383781 104.299562 340.918937 103.764406 341.579094 103.764406 C 342.23925 103.764406 342.774406 104.299562 342.774406 104.959719 Z M 342.774406 104.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 108.698 C 346.969719 109.358156 346.434562 109.893312 345.774406 109.893312 C 345.11425 109.893312 344.579094 109.358156 344.579094 108.698 C 344.579094 108.037844 345.11425 107.502687 345.774406 107.502687 C 346.434562 107.502687 346.969719 108.037844 346.969719 108.698 Z M 346.969719 108.698 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 111.744875 C 351.165031 112.405031 350.629875 112.940187 349.969719 112.940187 C 349.309562 112.940187 348.774406 112.405031 348.774406 111.744875 C 348.774406 111.084719 349.309562 110.549562 349.969719 110.549562 C 350.629875 110.549562 351.165031 111.084719 351.165031 111.744875 Z M 351.165031 111.744875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 108.600344 C 355.360344 109.2605 354.825187 109.795656 354.165031 109.795656 C 353.504875 109.795656 352.969719 109.2605 352.969719 108.600344 C 352.969719 107.936281 353.504875 107.401125 354.165031 107.401125 C 354.825187 107.401125 355.360344 107.936281 355.360344 108.600344 Z M 355.360344 108.600344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 104.076906 C 359.555656 104.737062 359.0205 105.272219 358.360344 105.272219 C 357.700187 105.272219 357.165031 104.737062 357.165031 104.076906 C 357.165031 103.41675 357.700187 102.881594 358.360344 102.881594 C 359.0205 102.881594 359.555656 103.41675 359.555656 104.076906 Z M 359.555656 104.076906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 110.467531 C 363.750969 111.127687 363.215812 111.662844 362.555656 111.662844 C 361.8955 111.662844 361.360344 111.127687 361.360344 110.467531 C 361.360344 109.807375 361.8955 109.268312 362.555656 109.268312 C 363.215812 109.268312 363.750969 109.807375 363.750969 110.467531 Z M 363.750969 110.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 367.946281 109.975344 C 367.946281 110.6355 367.411125 111.170656 366.750969 111.170656 C 366.090812 111.170656 365.555656 110.6355 365.555656 109.975344 C 365.555656 109.315187 366.090812 108.780031 366.750969 108.780031 C 367.411125 108.780031 367.946281 109.315187 367.946281 109.975344 Z M 367.946281 109.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 109.682375 C 372.141594 110.342531 371.606437 110.877687 370.946281 110.877687 C 370.286125 110.877687 369.750969 110.342531 369.750969 109.682375 C 369.750969 109.018312 370.286125 108.483156 370.946281 108.483156 C 371.606437 108.483156 372.141594 109.018312 372.141594 109.682375 Z M 372.141594 109.682375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 376.336906 111.252687 C 376.336906 111.912844 375.80175 112.451906 375.141594 112.451906 C 374.481437 112.451906 373.946281 111.912844 373.946281 111.252687 C 373.946281 110.592531 374.481437 110.057375 375.141594 110.057375 C 375.80175 110.057375 376.336906 110.592531 376.336906 111.252687 Z M 376.336906 111.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 119.315187 C 380.532219 119.975344 379.997062 120.5105 379.336906 120.5105 C 378.67675 120.5105 378.141594 119.975344 378.141594 119.315187 C 378.141594 118.655031 378.67675 118.119875 379.336906 118.119875 C 379.997062 118.119875 380.532219 118.655031 380.532219 119.315187 Z M 380.532219 119.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 122.467531 L 383.532219 122.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 127.096437 L 383.532219 127.174562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 124.819094 C 384.727531 125.483156 384.192375 126.018312 383.532219 126.018312 C 382.872062 126.018312 382.336906 125.483156 382.336906 124.819094 C 382.336906 124.158937 382.872062 123.623781 383.532219 123.623781 C 384.192375 123.623781 384.727531 124.158937 384.727531 124.819094 Z M 384.727531 124.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 122.178469 L 387.727531 122.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 126.803469 L 387.727531 126.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 124.526125 C 388.922844 125.186281 388.387687 125.721437 387.727531 125.721437 C 387.067375 125.721437 386.532219 125.186281 386.532219 124.526125 C 386.532219 123.865969 387.067375 123.330812 387.727531 123.330812 C 388.387687 123.330812 388.922844 123.865969 388.922844 124.526125 Z M 388.922844 124.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 129.209719 L 391.922844 129.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 133.97925 L 391.922844 134.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 131.701906 C 393.118156 132.362062 392.583 132.897219 391.922844 132.897219 C 391.262687 132.897219 390.727531 132.362062 390.727531 131.701906 C 390.727531 131.04175 391.262687 130.506594 391.922844 130.506594 C 392.583 130.506594 393.118156 131.04175 393.118156 131.701906 Z M 393.118156 131.701906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 132.006594 L 396.118156 132.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 136.830812 L 396.118156 137.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 134.553469 C 397.313469 135.213625 396.778312 135.748781 396.118156 135.748781 C 395.458 135.748781 394.922844 135.213625 394.922844 134.553469 C 394.922844 133.893312 395.458 133.358156 396.118156 133.358156 C 396.778312 133.358156 397.313469 133.893312 397.313469 134.553469 Z M 397.313469 134.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 138.276125 L 400.313469 138.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 143.221437 L 400.313469 143.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 401.508781 140.944094 C 401.508781 141.60425 400.973625 142.139406 400.313469 142.139406 C 399.653312 142.139406 399.118156 141.60425 399.118156 140.944094 C 399.118156 140.283937 399.653312 139.748781 400.313469 139.748781 C 400.973625 139.748781 401.508781 140.283937 401.508781 140.944094 Z M 401.508781 140.944094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 143.295656 L 404.508781 143.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 148.334719 L 404.508781 148.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 146.057375 C 405.704094 146.717531 405.168937 147.252687 404.508781 147.252687 C 403.848625 147.252687 403.313469 146.717531 403.313469 146.057375 C 403.313469 145.393312 403.848625 144.858156 404.508781 144.858156 C 405.168937 144.858156 405.704094 145.393312 405.704094 146.057375 Z M 405.704094 146.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 153.244875 L 408.704094 153.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 158.459719 L 408.704094 159.119875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 409.899406 156.182375 C 409.899406 156.842531 409.36425 157.377687 408.704094 157.377687 C 408.043937 157.377687 407.508781 156.842531 407.508781 156.182375 C 407.508781 155.522219 408.043937 154.987062 408.704094 154.987062 C 409.36425 154.987062 409.899406 155.522219 409.899406 156.182375 Z M 409.899406 156.182375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 159.823 L 412.899406 160.588625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 165.143312 L 412.899406 165.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 414.094719 162.865969 C 414.094719 163.530031 413.559562 164.065187 412.899406 164.065187 C 412.23925 164.065187 411.704094 163.530031 411.704094 162.865969 C 411.704094 162.205812 412.23925 161.670656 412.899406 161.670656 C 413.559562 161.670656 414.094719 162.205812 414.094719 162.865969 Z M 414.094719 162.865969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 168.240969 L 417.094719 169.143312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 173.698 L 417.094719 174.600344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 418.290031 171.420656 C 418.290031 172.080812 417.754875 172.615969 417.094719 172.615969 C 416.434562 172.615969 415.899406 172.080812 415.899406 171.420656 C 415.899406 170.7605 416.434562 170.225344 417.094719 170.225344 C 417.754875 170.225344 418.290031 170.7605 418.290031 171.420656 Z M 418.290031 171.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 176.276125 L 421.290031 177.303469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 181.858156 L 421.290031 182.8855 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 179.580812 C 422.485344 180.240969 421.950187 180.776125 421.290031 180.776125 C 420.629875 180.776125 420.094719 180.240969 420.094719 179.580812 C 420.094719 178.920656 420.629875 178.3855 421.290031 178.3855 C 421.950187 178.3855 422.485344 178.920656 422.485344 179.580812 Z M 422.485344 179.580812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 186.545656 L 425.485344 187.725344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 192.280031 L 425.485344 193.459719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.680656 190.002687 C 426.680656 190.662844 426.1455 191.198 425.485344 191.198 C 424.825187 191.198 424.290031 190.662844 424.290031 190.002687 C 424.290031 189.338625 424.825187 188.803469 425.485344 188.803469 C 426.1455 188.803469 426.680656 189.338625 426.680656 190.002687 Z M 426.680656 190.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 185.865969 L 429.680656 187.037844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 191.588625 L 429.680656 192.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 189.315187 C 430.875969 189.975344 430.340812 190.5105 429.680656 190.5105 C 429.0205 190.5105 428.485344 189.975344 428.485344 189.315187 C 428.485344 188.651125 429.0205 188.115969 429.680656 188.115969 C 430.340812 188.115969 430.875969 188.651125 430.875969 189.315187 Z M 430.875969 189.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 433.875969 204.3855 L 433.875969 205.815187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 433.875969 210.365969 L 433.875969 211.795656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 208.092531 C 435.071281 208.752687 434.536125 209.287844 433.875969 209.287844 C 433.215812 209.287844 432.680656 208.752687 432.680656 208.092531 C 432.680656 207.428469 433.215812 206.893312 433.875969 206.893312 C 434.536125 206.893312 435.071281 207.428469 435.071281 208.092531 Z M 435.071281 208.092531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 438.071281 212.244875 L 438.071281 213.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 438.071281 218.330812 L 438.071281 219.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.266594 216.053469 C 439.266594 216.713625 438.731437 217.252687 438.071281 217.252687 C 437.411125 217.252687 436.875969 216.713625 436.875969 216.053469 C 436.875969 215.393312 437.411125 214.858156 438.071281 214.858156 C 438.731437 214.858156 439.266594 215.393312 439.266594 216.053469 Z M 439.266594 216.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 442.266594 224.186281 L 442.266594 225.869875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 442.266594 230.424562 L 442.266594 232.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 228.147219 C 443.461906 228.807375 442.92675 229.342531 442.266594 229.342531 C 441.606437 229.342531 441.071281 228.807375 441.071281 228.147219 C 441.071281 227.487062 441.606437 226.951906 442.266594 226.951906 C 442.92675 226.951906 443.461906 227.487062 443.461906 228.147219 Z M 443.461906 228.147219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 446.461906 238.459719 L 446.461906 240.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 446.461906 244.877687 L 446.461906 246.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 447.657219 242.600344 C 447.657219 243.2605 447.122062 243.795656 446.461906 243.795656 C 445.80175 243.795656 445.266594 243.2605 445.266594 242.600344 C 445.266594 241.936281 445.80175 241.401125 446.461906 241.401125 C 447.122062 241.401125 447.657219 241.936281 447.657219 242.600344 Z M 447.657219 242.600344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 450.657219 243.514406 L 450.657219 245.432375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 450.657219 249.987062 L 450.657219 251.908937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 247.709719 C 451.852531 248.373781 451.317375 248.908937 450.657219 248.908937 C 449.997062 248.908937 449.461906 248.373781 449.461906 247.709719 C 449.461906 247.049562 449.997062 246.514406 450.657219 246.514406 C 451.317375 246.514406 451.852531 247.049562 451.852531 247.709719 Z M 451.852531 247.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 454.852531 258.47925 L 454.852531 260.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 454.852531 265.127687 L 454.852531 267.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 262.850344 C 456.047844 263.5105 455.512687 264.049562 454.852531 264.049562 C 454.192375 264.049562 453.657219 263.5105 453.657219 262.850344 C 453.657219 262.190187 454.192375 261.655031 454.852531 261.655031 C 455.512687 261.655031 456.047844 262.190187 456.047844 262.850344 Z M 456.047844 262.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 459.047844 275.0105 L 459.047844 277.287844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 459.047844 281.842531 L 459.047844 284.119875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.243156 279.565187 C 460.243156 280.225344 459.708 280.7605 459.047844 280.7605 C 458.387687 280.7605 457.852531 280.225344 457.852531 279.565187 C 457.852531 278.901125 458.387687 278.365969 459.047844 278.365969 C 459.708 278.365969 460.243156 278.901125 460.243156 279.565187 Z M 460.243156 279.565187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 463.243156 282.0105 L 463.243156 284.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 463.243156 288.920656 L 463.243156 291.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.438469 286.643312 C 464.438469 287.303469 463.903312 287.838625 463.243156 287.838625 C 462.583 287.838625 462.047844 287.303469 462.047844 286.643312 C 462.047844 285.983156 462.583 285.448 463.243156 285.448 C 463.903312 285.448 464.438469 285.983156 464.438469 286.643312 Z M 464.438469 286.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.438469 297.576906 L 467.438469 300.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.438469 304.647219 L 467.438469 307.170656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.637687 302.373781 C 468.637687 303.033937 468.098625 303.569094 467.438469 303.569094 C 466.778312 303.569094 466.243156 303.033937 466.243156 302.373781 C 466.243156 301.709719 466.778312 301.174562 467.438469 301.174562 C 468.098625 301.174562 468.637687 301.709719 468.637687 302.373781 Z M 468.637687 302.373781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 471.633781 315.096437 L 471.633781 317.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 471.633781 322.346437 L 471.633781 325.04175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 472.829094 320.069094 C 472.829094 320.72925 472.293937 321.264406 471.633781 321.264406 C 470.973625 321.264406 470.438469 320.72925 470.438469 320.069094 C 470.438469 319.408937 470.973625 318.873781 471.633781 318.873781 C 472.293937 318.873781 472.829094 319.408937 472.829094 320.069094 Z M 472.829094 320.069094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 475.829094 329.990969 L 475.829094 332.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 475.829094 337.3855 L 475.829094 340.22925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 477.024406 335.108156 C 477.024406 335.772219 476.48925 336.307375 475.829094 336.307375 C 475.168937 336.307375 474.633781 335.772219 474.633781 335.108156 C 474.633781 334.448 475.168937 333.912844 475.829094 333.912844 C 476.48925 333.912844 477.024406 334.448 477.024406 335.108156 Z M 477.024406 335.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.024406 350.342531 L 480.024406 353.377687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 480.024406 357.936281 L 480.024406 360.971437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 481.223625 355.658937 C 481.223625 356.319094 480.684562 356.85425 480.024406 356.85425 C 479.36425 356.85425 478.829094 356.319094 478.829094 355.658937 C 478.829094 354.998781 479.36425 354.463625 480.024406 354.463625 C 480.684562 354.463625 481.223625 354.998781 481.223625 355.658937 Z M 481.223625 355.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 484.219719 353.463625 L 484.219719 356.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 484.219719 361.080812 L 484.219719 364.147219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.415031 358.803469 C 485.415031 359.463625 484.879875 359.998781 484.219719 359.998781 C 483.559562 359.998781 483.024406 359.463625 483.024406 358.803469 C 483.024406 358.143312 483.559562 357.60425 484.219719 357.60425 C 484.879875 357.60425 485.415031 358.143312 485.415031 358.803469 Z M 485.415031 358.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 488.415031 375.381594 L 488.415031 378.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 488.415031 383.201906 L 488.415031 386.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 489.610344 380.924562 C 489.610344 381.584719 489.075187 382.119875 488.415031 382.119875 C 487.754875 382.119875 487.219719 381.584719 487.219719 380.924562 C 487.219719 380.264406 487.754875 379.72925 488.415031 379.72925 C 489.075187 379.72925 489.610344 380.264406 489.610344 380.924562 Z M 489.610344 380.924562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.610344 375.088625 L 492.610344 378.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.610344 382.905031 L 492.610344 386.16675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.809562 380.627687 C 493.809562 381.29175 493.2705 381.826906 492.610344 381.826906 C 491.950187 381.826906 491.415031 381.29175 491.415031 380.627687 C 491.415031 379.967531 491.950187 379.432375 492.610344 379.432375 C 493.2705 379.432375 493.809562 379.967531 493.809562 380.627687 Z M 493.809562 380.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.805656 247.498781 L 496.805656 249.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.805656 254.018312 L 496.805656 255.987062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.004875 251.740969 C 498.004875 252.401125 497.465812 252.940187 496.805656 252.940187 C 496.1455 252.940187 495.610344 252.401125 495.610344 251.740969 C 495.610344 251.080812 496.1455 250.545656 496.805656 250.545656 C 497.465812 250.545656 498.004875 251.080812 498.004875 251.740969 Z M 498.004875 251.740969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 77.990969 L 198.6455 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.465812 73.240969 L 228.465812 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.286125 73.240969 L 258.286125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.106437 73.240969 L 288.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.930656 73.240969 L 317.930656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 347.747062 77.990969 L 347.747062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 377.567375 73.240969 L 377.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 407.387687 73.240969 L 407.387687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 437.208 73.240969 L 437.208 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.032219 73.240969 L 467.032219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 77.990969 L 496.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 77.990969 L 198.6455 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 168.825187 73.240969 L 168.825187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 139.004875 73.240969 L 139.004875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 109.184562 73.240969 L 109.184562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 77.990969 L 496.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="186.178" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="198.185975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="335.277" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="347.284975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="484.38" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="496.387975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="326.173" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="337.484971" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="353.291778" y="416.914601"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="366.12186" y="421.571506"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="379.977691" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="390.196212" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="409.039609" y="417.528"/>
+ <use xlink:href="#glyph0-7" x="419.713365" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="438.04745" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.757199" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.765174" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="470.100085" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-2" x="479.807783" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 392.862062 L 198.6455 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.465812 397.615969 L 228.465812 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.286125 397.615969 L 258.286125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.106437 397.615969 L 288.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.930656 397.615969 L 317.930656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 347.747062 392.862062 L 347.747062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 377.567375 397.615969 L 377.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 407.387687 397.615969 L 407.387687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 437.208 397.615969 L 437.208 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.032219 397.615969 L 467.032219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 392.862062 L 496.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 392.862062 L 198.6455 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 168.825187 397.615969 L 168.825187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 139.004875 397.615969 L 139.004875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 109.184562 397.615969 L 109.184562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 392.862062 L 496.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 78.319094 L 79.372062 78.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 88.151125 L 79.372062 88.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 97.97925 L 79.372062 97.97925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 107.811281 L 79.372062 107.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 117.643312 L 79.372062 117.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 127.475344 L 79.372062 127.475344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 137.307375 L 79.372062 137.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 147.1355 L 79.372062 147.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 156.967531 L 79.372062 156.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 166.799562 L 79.372062 166.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 176.631594 L 79.372062 176.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 186.463625 L 79.372062 186.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 196.29175 L 79.372062 196.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 206.123781 L 79.372062 206.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 215.955812 L 79.372062 215.955812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 225.787844 L 79.372062 225.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 235.619875 L 79.372062 235.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 245.448 L 79.372062 245.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 255.280031 L 79.372062 255.280031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 265.112062 L 79.372062 265.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 274.944094 L 79.372062 274.944094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 284.776125 L 79.372062 284.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 294.60425 L 79.372062 294.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 304.436281 L 79.372062 304.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 314.268312 L 79.372062 314.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 324.100344 L 79.372062 324.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 333.932375 L 79.372062 333.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 343.7605 L 79.372062 343.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 353.592531 L 79.372062 353.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 363.424562 L 79.372062 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 363.424562 L 79.372062 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.256594 L 79.372062 373.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 383.088625 L 79.372062 383.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 392.91675 L 79.372062 392.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="36.979" y="320.834"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="320.834"/>
+ <use xlink:href="#glyph0-9" x="55.658072" y="320.834"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="55.657" y="271.678"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="222.522"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="222.522"/>
+ <use xlink:href="#glyph0-9" x="55.658072" y="222.522"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.657" y="173.367"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="36.979" y="124.21"/>
+ <use xlink:href="#glyph0-8" x="48.986975" y="124.21"/>
+ <use xlink:href="#glyph0-9" x="55.658072" y="124.21"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="55.657" y="75.055"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-2" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph7-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph7-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph7-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph7-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph7-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph7-11" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph7-12" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph7-13" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph8-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-14" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 78.319094 L 498.903312 78.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 88.151125 L 498.903312 88.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 97.97925 L 498.903312 97.97925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 107.811281 L 498.903312 107.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 117.643312 L 498.903312 117.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 127.475344 L 498.903312 127.475344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 137.307375 L 498.903312 137.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 147.1355 L 498.903312 147.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 156.967531 L 498.903312 156.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 166.799562 L 498.903312 166.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 176.631594 L 498.903312 176.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 186.463625 L 498.903312 186.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 196.29175 L 498.903312 196.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 206.123781 L 498.903312 206.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 215.955812 L 498.903312 215.955812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 225.787844 L 498.903312 225.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 235.619875 L 498.903312 235.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 245.448 L 498.903312 245.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 255.280031 L 498.903312 255.280031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 265.112062 L 498.903312 265.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 274.944094 L 498.903312 274.944094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 284.776125 L 498.903312 284.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 294.60425 L 498.903312 294.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 304.436281 L 498.903312 304.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 314.268312 L 498.903312 314.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 324.100344 L 498.903312 324.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 333.932375 L 498.903312 333.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 343.7605 L 498.903312 343.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 353.592531 L 498.903312 353.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 363.424562 L 498.903312 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 363.424562 L 498.903312 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.256594 L 498.903312 373.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 383.088625 L 498.903312 383.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 392.91675 L 498.903312 392.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 77.990969 L 198.6455 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.465812 73.240969 L 228.465812 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.286125 73.240969 L 258.286125 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.106437 73.240969 L 288.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.930656 73.240969 L 317.930656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 347.747062 77.990969 L 347.747062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 377.567375 73.240969 L 377.567375 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 407.387687 73.240969 L 407.387687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 437.208 73.240969 L 437.208 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.032219 73.240969 L 467.032219 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 77.990969 L 496.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 77.990969 L 198.6455 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 168.825187 73.240969 L 168.825187 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 139.004875 73.240969 L 139.004875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 109.184562 73.240969 L 109.184562 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 77.990969 L 496.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 392.862062 L 198.6455 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 228.465812 397.615969 L 228.465812 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.286125 397.615969 L 258.286125 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.106437 397.615969 L 288.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.930656 397.615969 L 317.930656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 347.747062 392.862062 L 347.747062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 377.567375 397.615969 L 377.567375 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 407.387687 397.615969 L 407.387687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 437.208 397.615969 L 437.208 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 467.032219 397.615969 L 467.032219 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 392.862062 L 496.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.6455 392.862062 L 198.6455 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 168.825187 397.615969 L 168.825187 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 139.004875 397.615969 L 139.004875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 109.184562 397.615969 L 109.184562 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 496.852531 392.862062 L 496.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 78.319094 L 79.372062 78.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 88.151125 L 79.372062 88.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 97.97925 L 79.372062 97.97925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 107.811281 L 79.372062 107.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 117.643312 L 79.372062 117.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 127.475344 L 79.372062 127.475344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 137.307375 L 79.372062 137.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 147.1355 L 79.372062 147.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 156.967531 L 79.372062 156.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 166.799562 L 79.372062 166.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 176.631594 L 79.372062 176.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 186.463625 L 79.372062 186.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 196.29175 L 79.372062 196.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 206.123781 L 79.372062 206.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 215.955812 L 79.372062 215.955812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 225.787844 L 79.372062 225.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 235.619875 L 79.372062 235.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 245.448 L 79.372062 245.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 255.280031 L 79.372062 255.280031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 265.112062 L 79.372062 265.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 274.944094 L 79.372062 274.944094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 284.776125 L 79.372062 284.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 294.60425 L 79.372062 294.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 304.436281 L 79.372062 304.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 314.268312 L 79.372062 314.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 324.100344 L 79.372062 324.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 333.932375 L 79.372062 333.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 343.7605 L 79.372062 343.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 353.592531 L 79.372062 353.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 363.424562 L 79.372062 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 363.424562 L 79.372062 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.256594 L 79.372062 373.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 383.088625 L 79.372062 383.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 392.91675 L 79.372062 392.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 78.319094 L 498.903312 78.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 88.151125 L 498.903312 88.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 97.97925 L 498.903312 97.97925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 107.811281 L 498.903312 107.811281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 117.643312 L 498.903312 117.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 127.475344 L 498.903312 127.475344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 137.307375 L 498.903312 137.307375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 147.1355 L 498.903312 147.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 156.967531 L 498.903312 156.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 166.799562 L 498.903312 166.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 176.631594 L 498.903312 176.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 186.463625 L 498.903312 186.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 196.29175 L 498.903312 196.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 206.123781 L 498.903312 206.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 215.955812 L 498.903312 215.955812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 225.787844 L 498.903312 225.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 235.619875 L 498.903312 235.619875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 245.448 L 498.903312 245.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 255.280031 L 498.903312 255.280031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 265.112062 L 498.903312 265.112062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 274.944094 L 498.903312 274.944094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 284.776125 L 498.903312 284.776125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 294.60425 L 498.903312 294.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 304.436281 L 498.903312 304.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 314.268312 L 498.903312 314.268312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 324.100344 L 498.903312 324.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 333.932375 L 498.903312 333.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 343.7605 L 498.903312 343.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 353.592531 L 498.903312 353.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 363.424562 L 498.903312 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 363.424562 L 498.903312 363.424562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.256594 L 498.903312 373.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 383.088625 L 498.903312 383.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 392.91675 L 498.903312 392.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/lb2pKpi_s12.svg b/doc/figs/lb2pKpi_s12.svg
new file mode 100644
index 00000000000..364f6647442
--- /dev/null
+++ b/doc/figs/lb2pKpi_s12.svg
@@ -0,0 +1,715 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="504pt" height="432pt" viewBox="0 0 504 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 4.515625 -1.203125 C 4.515625 -1.859375 3.953125 -2.375 3.34375 -2.375 C 2.625 -2.375 2.140625 -1.8125 2.140625 -1.203125 C 2.140625 -0.46875 2.75 0 3.3125 0 C 3.96875 0 4.515625 -0.515625 4.515625 -1.203125 Z M 4.515625 -1.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 4.515625 -8.8125 C 4.09375 -8.78125 4 -8.75 4 -8.53125 C 4 -8.296875 4.125 -8.296875 4.5625 -8.296875 L 5.6875 -8.296875 C 7.78125 -8.296875 8.703125 -6.578125 8.703125 -4.21875 C 8.703125 -1 7.046875 -0.140625 5.84375 -0.140625 C 4.65625 -0.140625 2.65625 -0.71875 1.9375 -2.328125 C 2.71875 -2.203125 3.4375 -2.65625 3.4375 -3.53125 C 3.4375 -4.25 2.921875 -4.734375 2.234375 -4.734375 C 1.640625 -4.734375 1 -4.390625 1 -3.453125 C 1 -1.28125 3.1875 0.515625 5.90625 0.515625 C 8.828125 0.515625 10.984375 -1.71875 10.984375 -4.1875 C 10.984375 -6.453125 9.171875 -8.21875 6.8125 -8.640625 C 8.953125 -9.25 10.328125 -11.046875 10.328125 -12.953125 C 10.328125 -14.890625 8.3125 -16.3125 5.9375 -16.3125 C 3.484375 -16.3125 1.671875 -14.8125 1.671875 -13.03125 C 1.671875 -12.046875 2.421875 -11.84375 2.796875 -11.84375 C 3.3125 -11.84375 3.90625 -12.21875 3.90625 -12.953125 C 3.90625 -13.734375 3.3125 -14.078125 2.765625 -14.078125 C 2.625 -14.078125 2.578125 -14.078125 2.5 -14.0625 C 3.4375 -15.71875 5.734375 -15.71875 5.859375 -15.71875 C 6.671875 -15.71875 8.265625 -15.359375 8.265625 -12.953125 C 8.265625 -12.484375 8.1875 -11.109375 7.484375 -10.0625 C 6.75 -8.984375 5.90625 -8.90625 5.25 -8.875 Z M 4.515625 -8.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 4.640625 -5.96875 L 6.515625 -5.96875 C 6.171875 -4.484375 5.890625 -3.265625 5.890625 -2.0625 C 5.890625 -1.9375 5.890625 -1.234375 6.0625 -0.65625 C 6.28125 0.03125 6.4375 0.15625 6.734375 0.15625 C 7.09375 0.15625 7.46875 -0.140625 7.46875 -0.546875 C 7.46875 -0.65625 7.453125 -0.6875 7.390625 -0.828125 C 7.046875 -1.578125 6.796875 -2.375 6.796875 -3.703125 C 6.796875 -4.09375 6.796875 -4.765625 7.046875 -5.96875 L 9.015625 -5.96875 C 9.28125 -5.96875 9.46875 -5.96875 9.625 -6.09375 C 9.828125 -6.28125 9.875 -6.484375 9.875 -6.59375 C 9.875 -7.046875 9.46875 -7.046875 9.1875 -7.046875 L 3.28125 -7.046875 C 2.9375 -7.046875 2.328125 -7.046875 1.515625 -6.265625 C 0.9375 -5.671875 0.46875 -4.921875 0.46875 -4.8125 C 0.46875 -4.65625 0.59375 -4.609375 0.71875 -4.609375 C 0.875 -4.609375 0.921875 -4.65625 1.015625 -4.78125 C 1.8125 -5.96875 2.78125 -5.96875 3.15625 -5.96875 L 4.109375 -5.96875 C 3.625 -4.234375 2.765625 -2.25 2.15625 -1.0625 C 2.046875 -0.8125 1.875 -0.484375 1.875 -0.34375 C 1.875 0 2.15625 0.15625 2.421875 0.15625 C 3.046875 0.15625 3.203125 -0.453125 3.546875 -1.796875 Z M 4.640625 -5.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 0.84375 1.984375 C 0.71875 2.5 0.6875 2.625 0.03125 2.625 C -0.203125 2.625 -0.390625 2.625 -0.390625 2.9375 C -0.390625 3.09375 -0.25 3.171875 -0.15625 3.171875 C 0 3.171875 0.0625 3.125 1.28125 3.125 C 2.453125 3.125 2.796875 3.171875 2.90625 3.171875 C 2.96875 3.171875 3.21875 3.171875 3.21875 2.859375 C 3.21875 2.625 2.984375 2.625 2.796875 2.625 C 2.015625 2.625 2.015625 2.53125 2.015625 2.390625 C 2.015625 2.265625 2.296875 1.109375 2.796875 -0.796875 C 3 -0.421875 3.515625 0.15625 4.390625 0.15625 C 6.40625 0.15625 8.5 -2.15625 8.5 -4.53125 C 8.5 -6.140625 7.453125 -7.203125 6.140625 -7.203125 C 5.171875 -7.203125 4.375 -6.53125 3.90625 -6.046875 C 3.5625 -7.203125 2.46875 -7.203125 2.296875 -7.203125 C 1.71875 -7.203125 1.3125 -6.828125 1.046875 -6.328125 C 0.671875 -5.59375 0.484375 -4.75 0.484375 -4.703125 C 0.484375 -4.5625 0.609375 -4.5 0.734375 -4.5 C 0.953125 -4.5 0.96875 -4.5625 1.078125 -4.984375 C 1.296875 -5.8125 1.578125 -6.75 2.25 -6.75 C 2.65625 -6.75 2.78125 -6.375 2.78125 -5.984375 C 2.78125 -5.8125 2.71875 -5.421875 2.6875 -5.296875 Z M 3.859375 -5.03125 C 3.9375 -5.3125 3.9375 -5.34375 4.1875 -5.640625 C 4.8125 -6.375 5.515625 -6.75 6.09375 -6.75 C 6.90625 -6.75 7.21875 -5.953125 7.21875 -5.21875 C 7.21875 -4.609375 6.859375 -2.859375 6.375 -1.890625 C 5.953125 -1.015625 5.171875 -0.296875 4.390625 -0.296875 C 3.28125 -0.296875 3.03125 -1.5625 3.03125 -1.6875 C 3.03125 -1.71875 3.0625 -1.890625 3.078125 -1.9375 Z M 3.859375 -5.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 6.75 -3.90625 C 6.75 -4.8125 6.75 -8.15625 3.734375 -8.15625 C 0.734375 -8.15625 0.734375 -4.8125 0.734375 -3.90625 C 0.734375 -3.03125 0.734375 0.25 3.734375 0.25 C 6.75 0.25 6.75 -3.03125 6.75 -3.90625 Z M 3.734375 -0.140625 C 3.21875 -0.140625 2.390625 -0.375 2.09375 -1.390625 C 1.90625 -2.109375 1.90625 -3.3125 1.90625 -4.078125 C 1.90625 -4.890625 1.90625 -5.84375 2.078125 -6.5 C 2.375 -7.609375 3.3125 -7.765625 3.734375 -7.765625 C 4.3125 -7.765625 5.109375 -7.5 5.390625 -6.5625 C 5.5625 -5.90625 5.578125 -5.015625 5.578125 -4.078125 C 5.578125 -3.28125 5.578125 -2.046875 5.375 -1.359375 C 5.03125 -0.296875 4.140625 -0.140625 3.734375 -0.140625 Z M 3.734375 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-11">
+<path style="stroke:none;" d="M -14.0625 -3.140625 C -13.71875 -4.1875 -13.6875 -5.046875 -13.6875 -5.328125 C -13.6875 -8.09375 -15.71875 -9.859375 -16.0625 -9.859375 C -16.171875 -9.859375 -16.28125 -9.8125 -16.28125 -9.671875 C -16.28125 -9.609375 -16.28125 -9.5625 -16.1875 -9.34375 C -15.609375 -7.96875 -15.53125 -6.796875 -15.53125 -6.15625 C -15.53125 -4.53125 -16.015625 -3.390625 -16.21875 -2.921875 C -16.28125 -2.75 -16.28125 -2.703125 -16.28125 -2.671875 C -16.28125 -2.484375 -16.140625 -2.484375 -15.75 -2.484375 L -8.46875 -2.484375 C -8.015625 -2.484375 -7.875 -2.484375 -7.875 -2.765625 C -7.875 -2.890625 -7.90625 -2.921875 -8.1875 -3.171875 C -9.203125 -3.84375 -9.78125 -5 -9.78125 -6.234375 C -9.78125 -7.53125 -8.59375 -8.171875 -8.171875 -8.359375 C -7.21875 -8.78125 -6.015625 -8.8125 -5.078125 -8.8125 C -4.140625 -8.8125 -2.75 -8.8125 -1.640625 -8.125 C -0.765625 -7.578125 -0.140625 -6.625 -0.140625 -5.546875 C -0.140625 -3.921875 -1.25 -2.328125 -3.046875 -1.890625 C -3 -2.015625 -2.96875 -2.15625 -2.96875 -2.28125 C -2.96875 -2.703125 -3.21875 -3.359375 -4.046875 -3.359375 C -4.734375 -3.359375 -5.125 -2.890625 -5.125 -2.28125 C -5.125 -1.84375 -4.90625 -1.203125 -3.953125 -1.203125 C -1.859375 -1.203125 0.515625 -2.875 0.515625 -5.59375 C 0.515625 -8.359375 -1.8125 -10.796875 -4.9375 -10.796875 C -7.84375 -10.796875 -10.28125 -8.828125 -10.28125 -6.25 C -10.28125 -4.859375 -9.671875 -3.78125 -8.984375 -3.140625 Z M -14.0625 -3.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-12">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-13">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-14">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 82.665031 71.54175 C 82.665031 72.201906 82.129875 72.737062 81.469719 72.737062 C 80.805656 72.737062 80.2705 72.201906 80.2705 71.54175 C 80.2705 70.877687 80.805656 70.342531 81.469719 70.342531 C 82.129875 70.342531 82.665031 70.877687 82.665031 71.54175 Z M 82.665031 71.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.860344 82.006594 C 86.860344 82.66675 86.325187 83.201906 85.665031 83.201906 C 85.004875 83.201906 84.465812 82.66675 84.465812 82.006594 C 84.465812 81.346437 85.004875 80.811281 85.665031 80.811281 C 86.325187 80.811281 86.860344 81.346437 86.860344 82.006594 Z M 86.860344 82.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.860344 118.326906 L 89.860344 118.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.860344 122.987062 L 89.860344 123.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 91.055656 120.713625 C 91.055656 121.373781 90.5205 121.908937 89.860344 121.908937 C 89.200187 121.908937 88.661125 121.373781 88.661125 120.713625 C 88.661125 120.049562 89.200187 119.514406 89.860344 119.514406 C 90.5205 119.514406 91.055656 120.049562 91.055656 120.713625 Z M 91.055656 120.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.055656 303.342531 L 94.055656 306.178469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.055656 310.733156 L 94.055656 313.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 308.455812 C 95.250969 309.115969 94.715812 309.651125 94.055656 309.651125 C 93.3955 309.651125 92.856437 309.115969 92.856437 308.455812 C 92.856437 307.795656 93.3955 307.2605 94.055656 307.2605 C 94.715812 307.2605 95.250969 307.795656 95.250969 308.455812 Z M 95.250969 308.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 98.250969 368.424562 L 98.250969 371.924562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 98.250969 376.475344 L 98.250969 379.971437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.446281 374.201906 C 99.446281 374.862062 98.911125 375.397219 98.250969 375.397219 C 97.590812 375.397219 97.05175 374.862062 97.05175 374.201906 C 97.05175 373.537844 97.590812 373.002687 98.250969 373.002687 C 98.911125 373.002687 99.446281 373.537844 99.446281 374.201906 Z M 99.446281 374.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 102.446281 374.799562 L 102.446281 378.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 102.446281 382.908937 L 102.446281 386.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 103.641594 380.631594 C 103.641594 381.29175 103.106437 381.830812 102.446281 381.830812 C 101.786125 381.830812 101.247062 381.29175 101.247062 380.631594 C 101.247062 379.971437 101.786125 379.436281 102.446281 379.436281 C 103.106437 379.436281 103.641594 379.971437 103.641594 380.631594 Z M 103.641594 380.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 106.641594 351.690187 L 106.641594 355.022219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 106.641594 359.576906 L 106.641594 362.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.836906 357.299562 C 107.836906 357.959719 107.30175 358.498781 106.641594 358.498781 C 105.981437 358.498781 105.442375 357.959719 105.442375 357.299562 C 105.442375 356.639406 105.981437 356.10425 106.641594 356.10425 C 107.30175 356.10425 107.836906 356.639406 107.836906 357.299562 Z M 107.836906 357.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 110.836906 347.803469 L 110.836906 351.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 110.836906 355.651125 L 110.836906 358.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 112.032219 353.377687 C 112.032219 354.037844 111.497062 354.573 110.836906 354.573 C 110.17675 354.573 109.637687 354.037844 109.637687 353.377687 C 109.637687 352.717531 110.17675 352.178469 110.836906 352.178469 C 111.497062 352.178469 112.032219 352.717531 112.032219 353.377687 Z M 112.032219 353.377687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 115.032219 332.365969 L 115.032219 335.506594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 115.032219 340.061281 L 115.032219 343.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 337.787844 C 116.227531 338.448 115.692375 338.983156 115.032219 338.983156 C 114.372062 338.983156 113.833 338.448 113.833 337.787844 C 113.833 337.123781 114.372062 336.588625 115.032219 336.588625 C 115.692375 336.588625 116.227531 337.123781 116.227531 337.787844 Z M 116.227531 337.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.227531 319.740969 L 119.227531 322.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.227531 327.307375 L 119.227531 330.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.422844 325.030031 C 120.422844 325.690187 119.887687 326.225344 119.227531 326.225344 C 118.567375 326.225344 118.028312 325.690187 118.028312 325.030031 C 118.028312 324.369875 118.567375 323.834719 119.227531 323.834719 C 119.887687 323.834719 120.422844 324.369875 120.422844 325.030031 Z M 120.422844 325.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 123.422844 314.346437 L 123.422844 317.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 123.422844 321.85425 L 123.422844 324.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 124.618156 319.576906 C 124.618156 320.237062 124.083 320.772219 123.422844 320.772219 C 122.762687 320.772219 122.223625 320.237062 122.223625 319.576906 C 122.223625 318.91675 122.762687 318.377687 123.422844 318.377687 C 124.083 318.377687 124.618156 318.91675 124.618156 319.576906 Z M 124.618156 319.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.618156 283.069094 L 127.618156 285.682375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.618156 290.237062 L 127.618156 292.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 287.959719 C 128.813469 288.619875 128.278312 289.155031 127.618156 289.155031 C 126.958 289.155031 126.418937 288.619875 126.418937 287.959719 C 126.418937 287.295656 126.958 286.7605 127.618156 286.7605 C 128.278312 286.7605 128.813469 287.295656 128.813469 287.959719 Z M 128.813469 287.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 131.813469 280.264406 L 131.813469 282.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 131.813469 287.401125 L 131.813469 289.987062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 133.008781 285.123781 C 133.008781 285.783937 132.473625 286.319094 131.813469 286.319094 C 131.153312 286.319094 130.61425 285.783937 130.61425 285.123781 C 130.61425 284.463625 131.153312 283.928469 131.813469 283.928469 C 132.473625 283.928469 133.008781 284.463625 133.008781 285.123781 Z M 133.008781 285.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 136.008781 266.252687 L 136.008781 268.674562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 136.008781 273.22925 L 136.008781 275.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 137.204094 270.951906 C 137.204094 271.612062 136.668937 272.147219 136.008781 272.147219 C 135.348625 272.147219 134.809562 271.612062 134.809562 270.951906 C 134.809562 270.29175 135.348625 269.752687 136.008781 269.752687 C 136.668937 269.752687 137.204094 270.29175 137.204094 270.951906 Z M 137.204094 270.951906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.204094 257.850344 L 140.204094 260.170656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.204094 264.725344 L 140.204094 267.045656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.399406 262.448 C 141.399406 263.108156 140.86425 263.643312 140.204094 263.643312 C 139.543937 263.643312 139.004875 263.108156 139.004875 262.448 C 139.004875 261.787844 139.543937 261.248781 140.204094 261.248781 C 140.86425 261.248781 141.399406 261.787844 141.399406 262.448 Z M 141.399406 262.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 144.399406 237.280031 L 144.399406 239.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 144.399406 243.901125 L 144.399406 245.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 241.623781 C 145.594719 242.283937 145.059562 242.819094 144.399406 242.819094 C 143.73925 242.819094 143.200187 242.283937 143.200187 241.623781 C 143.200187 240.963625 143.73925 240.424562 144.399406 240.424562 C 145.059562 240.424562 145.594719 240.963625 145.594719 241.623781 Z M 145.594719 241.623781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.594719 239.537844 L 148.594719 241.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.594719 246.190187 L 148.594719 248.283937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 149.790031 243.912844 C 149.790031 244.573 149.254875 245.108156 148.594719 245.108156 C 147.934562 245.108156 147.3955 244.573 147.3955 243.912844 C 147.3955 243.252687 147.934562 242.717531 148.594719 242.717531 C 149.254875 242.717531 149.790031 243.252687 149.790031 243.912844 Z M 149.790031 243.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 152.790031 227.268312 L 152.790031 229.205812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 152.790031 233.7605 L 152.790031 235.698 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 231.483156 C 153.985344 232.143312 153.450187 232.678469 152.790031 232.678469 C 152.129875 232.678469 151.590812 232.143312 151.590812 231.483156 C 151.590812 230.823 152.129875 230.287844 152.790031 230.287844 C 153.450187 230.287844 153.985344 230.823 153.985344 231.483156 Z M 153.985344 231.483156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 216.725344 L 156.985344 218.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 223.076906 L 156.985344 224.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 220.799562 C 158.180656 221.459719 157.6455 221.994875 156.985344 221.994875 C 156.325187 221.994875 155.786125 221.459719 155.786125 220.799562 C 155.786125 220.139406 156.325187 219.600344 156.985344 219.600344 C 157.6455 219.600344 158.180656 220.139406 158.180656 220.799562 Z M 158.180656 220.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 206.401125 L 161.180656 208.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 212.608156 L 161.180656 214.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 162.375969 210.330812 C 162.375969 210.990969 161.840812 211.530031 161.180656 211.530031 C 160.5205 211.530031 159.981437 210.990969 159.981437 210.330812 C 159.981437 209.670656 160.5205 209.1355 161.180656 209.1355 C 161.840812 209.1355 162.375969 209.670656 162.375969 210.330812 Z M 162.375969 210.330812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 197.694094 L 165.375969 199.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 203.776125 L 165.375969 205.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 166.571281 201.502687 C 166.571281 202.162844 166.036125 202.698 165.375969 202.698 C 164.715812 202.698 164.17675 202.162844 164.17675 201.502687 C 164.17675 200.838625 164.715812 200.303469 165.375969 200.303469 C 166.036125 200.303469 166.571281 200.838625 166.571281 201.502687 Z M 166.571281 201.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 185.658937 L 169.571281 187.014406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 191.565187 L 169.571281 192.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 189.29175 C 170.766594 189.951906 170.231437 190.487062 169.571281 190.487062 C 168.911125 190.487062 168.372062 189.951906 168.372062 189.29175 C 168.372062 188.627687 168.911125 188.092531 169.571281 188.092531 C 170.231437 188.092531 170.766594 188.627687 170.766594 189.29175 Z M 170.766594 189.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 173.766594 177.932375 L 173.766594 179.162844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 173.766594 183.717531 L 173.766594 184.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 174.961906 181.440187 C 174.961906 182.100344 174.42675 182.6355 173.766594 182.6355 C 173.106437 182.6355 172.571281 182.100344 172.571281 181.440187 C 172.571281 180.780031 173.106437 180.244875 173.766594 180.244875 C 174.42675 180.244875 174.961906 180.780031 174.961906 181.440187 Z M 174.961906 181.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.961906 171.061281 L 177.961906 172.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.961906 176.737062 L 177.961906 177.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 179.157219 174.463625 C 179.157219 175.123781 178.622062 175.658937 177.961906 175.658937 C 177.30175 175.658937 176.762687 175.123781 176.762687 174.463625 C 176.762687 173.799562 177.30175 173.264406 177.961906 173.264406 C 178.622062 173.264406 179.157219 173.799562 179.157219 174.463625 Z M 179.157219 174.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 182.157219 169.561281 L 182.157219 170.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 182.157219 175.213625 L 182.157219 176.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 172.936281 C 183.352531 173.596437 182.817375 174.131594 182.157219 174.131594 C 181.497062 174.131594 180.958 173.596437 180.958 172.936281 C 180.958 172.276125 181.497062 171.737062 182.157219 171.737062 C 182.817375 171.737062 183.352531 172.276125 183.352531 172.936281 Z M 183.352531 172.936281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 186.352531 159.053469 L 186.352531 159.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 186.352531 164.526125 L 186.352531 165.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 162.252687 C 187.547844 162.912844 187.012687 163.448 186.352531 163.448 C 185.692375 163.448 185.157219 162.912844 185.157219 162.252687 C 185.157219 161.588625 185.692375 161.053469 186.352531 161.053469 C 187.012687 161.053469 187.547844 161.588625 187.547844 162.252687 Z M 187.547844 162.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 190.547844 154.553469 L 190.547844 155.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 190.547844 159.948 L 190.547844 160.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 157.670656 C 191.743156 158.334719 191.208 158.869875 190.547844 158.869875 C 189.887687 158.869875 189.348625 158.334719 189.348625 157.670656 C 189.348625 157.0105 189.887687 156.475344 190.547844 156.475344 C 191.208 156.475344 191.743156 157.0105 191.743156 157.670656 Z M 191.743156 157.670656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 143.6355 L 194.743156 144.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 148.826906 L 194.743156 149.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 146.549562 C 195.938469 147.213625 195.403312 147.748781 194.743156 147.748781 C 194.083 147.748781 193.543937 147.213625 193.543937 146.549562 C 193.543937 145.889406 194.083 145.35425 194.743156 145.35425 C 195.403312 145.35425 195.938469 145.889406 195.938469 146.549562 Z M 195.938469 146.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 140.10425 L 198.938469 140.674562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 145.22925 L 198.938469 145.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 142.951906 C 200.133781 143.615969 199.598625 144.151125 198.938469 144.151125 C 198.278312 144.151125 197.743156 143.615969 197.743156 142.951906 C 197.743156 142.29175 198.278312 141.756594 198.938469 141.756594 C 199.598625 141.756594 200.133781 142.29175 200.133781 142.951906 Z M 200.133781 142.951906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 133.690187 L 203.133781 134.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 138.690187 L 203.133781 139.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 136.412844 C 204.329094 137.073 203.793937 137.608156 203.133781 137.608156 C 202.473625 137.608156 201.934562 137.073 201.934562 136.412844 C 201.934562 135.748781 202.473625 135.213625 203.133781 135.213625 C 203.793937 135.213625 204.329094 135.748781 204.329094 136.412844 Z M 204.329094 136.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 127.924562 L 207.329094 128.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 132.799562 L 207.329094 133.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 130.526125 C 208.524406 131.186281 207.98925 131.721437 207.329094 131.721437 C 206.668937 131.721437 206.129875 131.186281 206.129875 130.526125 C 206.129875 129.862062 206.668937 129.326906 207.329094 129.326906 C 207.98925 129.326906 208.524406 129.862062 208.524406 130.526125 Z M 208.524406 130.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 131.233156 L 211.524406 131.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 136.182375 L 211.524406 136.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 133.905031 C 212.719719 134.565187 212.184562 135.100344 211.524406 135.100344 C 210.86425 135.100344 210.329094 134.565187 210.329094 133.905031 C 210.329094 133.244875 210.86425 132.705812 211.524406 132.705812 C 212.184562 132.705812 212.719719 133.244875 212.719719 133.905031 Z M 212.719719 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 117.686281 L 215.719719 117.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 122.334719 L 215.719719 122.428469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 120.057375 C 216.915031 120.717531 216.379875 121.252687 215.719719 121.252687 C 215.059562 121.252687 214.524406 120.717531 214.524406 120.057375 C 214.524406 119.397219 215.059562 118.862062 215.719719 118.862062 C 216.379875 118.862062 216.915031 119.397219 216.915031 120.057375 Z M 216.915031 120.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 117.901125 L 219.915031 117.998781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 122.553469 L 219.915031 122.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 120.276125 C 221.110344 120.936281 220.575187 121.471437 219.915031 121.471437 C 219.254875 121.471437 218.715812 120.936281 218.715812 120.276125 C 218.715812 119.615969 219.254875 119.076906 219.915031 119.076906 C 220.575187 119.076906 221.110344 119.615969 221.110344 120.276125 Z M 221.110344 120.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 116.619875 L 224.110344 116.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 121.244875 L 224.110344 121.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 118.967531 C 225.305656 119.627687 224.7705 120.162844 224.110344 120.162844 C 223.450187 120.162844 222.915031 119.627687 222.915031 118.967531 C 222.915031 118.307375 223.450187 117.772219 224.110344 117.772219 C 224.7705 117.772219 225.305656 118.307375 225.305656 118.967531 Z M 225.305656 118.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 112.643312 C 229.500969 113.303469 228.965812 113.838625 228.305656 113.838625 C 227.6455 113.838625 227.110344 113.303469 227.110344 112.643312 C 227.110344 111.983156 227.6455 111.448 228.305656 111.448 C 228.965812 111.448 229.500969 111.983156 229.500969 112.643312 Z M 229.500969 112.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 109.91675 C 233.696281 110.580812 233.161125 111.115969 232.500969 111.115969 C 231.840812 111.115969 231.30175 110.580812 231.30175 109.91675 C 231.30175 109.256594 231.840812 108.721437 232.500969 108.721437 C 233.161125 108.721437 233.696281 109.256594 233.696281 109.91675 Z M 233.696281 109.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 109.91675 C 237.891594 110.580812 237.356437 111.115969 236.696281 111.115969 C 236.036125 111.115969 235.500969 110.580812 235.500969 109.91675 C 235.500969 109.256594 236.036125 108.721437 236.696281 108.721437 C 237.356437 108.721437 237.891594 109.256594 237.891594 109.91675 Z M 237.891594 109.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 110.79175 C 242.086906 111.451906 241.55175 111.987062 240.891594 111.987062 C 240.231437 111.987062 239.696281 111.451906 239.696281 110.79175 C 239.696281 110.127687 240.231437 109.592531 240.891594 109.592531 C 241.55175 109.592531 242.086906 110.127687 242.086906 110.79175 Z M 242.086906 110.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 105.119875 C 246.282219 105.780031 245.747062 106.319094 245.086906 106.319094 C 244.42675 106.319094 243.891594 105.780031 243.891594 105.119875 C 243.891594 104.459719 244.42675 103.924562 245.086906 103.924562 C 245.747062 103.924562 246.282219 104.459719 246.282219 105.119875 Z M 246.282219 105.119875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 102.287844 C 250.477531 102.948 249.942375 103.483156 249.282219 103.483156 C 248.622062 103.483156 248.086906 102.948 248.086906 102.287844 C 248.086906 101.623781 248.622062 101.088625 249.282219 101.088625 C 249.942375 101.088625 250.477531 101.623781 250.477531 102.287844 Z M 250.477531 102.287844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 109.045656 C 254.672844 109.705812 254.137687 110.240969 253.477531 110.240969 C 252.817375 110.240969 252.282219 109.705812 252.282219 109.045656 C 252.282219 108.3855 252.817375 107.850344 253.477531 107.850344 C 254.137687 107.850344 254.672844 108.3855 254.672844 109.045656 Z M 254.672844 109.045656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 110.79175 C 258.868156 111.451906 258.333 111.987062 257.672844 111.987062 C 257.012687 111.987062 256.477531 111.451906 256.477531 110.79175 C 256.477531 110.127687 257.012687 109.592531 257.672844 109.592531 C 258.333 109.592531 258.868156 110.127687 258.868156 110.79175 Z M 258.868156 110.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 107.194094 C 263.063469 107.85425 262.528312 108.389406 261.868156 108.389406 C 261.208 108.389406 260.672844 107.85425 260.672844 107.194094 C 260.672844 106.530031 261.208 105.994875 261.868156 105.994875 C 262.528312 105.994875 263.063469 106.530031 263.063469 107.194094 Z M 263.063469 107.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 106.647219 C 267.258781 107.307375 266.723625 107.842531 266.063469 107.842531 C 265.403312 107.842531 264.868156 107.307375 264.868156 106.647219 C 264.868156 105.987062 265.403312 105.451906 266.063469 105.451906 C 266.723625 105.451906 267.258781 105.987062 267.258781 106.647219 Z M 267.258781 106.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 108.393312 C 271.454094 109.053469 270.918937 109.588625 270.258781 109.588625 C 269.598625 109.588625 269.063469 109.053469 269.063469 108.393312 C 269.063469 107.72925 269.598625 107.194094 270.258781 107.194094 C 270.918937 107.194094 271.454094 107.72925 271.454094 108.393312 Z M 271.454094 108.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 115.04175 C 275.649406 115.701906 275.11425 116.240969 274.454094 116.240969 C 273.793937 116.240969 273.258781 115.701906 273.258781 115.04175 C 273.258781 114.381594 273.793937 113.846437 274.454094 113.846437 C 275.11425 113.846437 275.649406 114.381594 275.649406 115.04175 Z M 275.649406 115.04175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 115.237062 L 278.649406 115.272219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 119.826906 L 278.649406 119.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 117.549562 C 279.844719 118.209719 279.309562 118.744875 278.649406 118.744875 C 277.98925 118.744875 277.454094 118.209719 277.454094 117.549562 C 277.454094 116.889406 277.98925 116.35425 278.649406 116.35425 C 279.309562 116.35425 279.844719 116.889406 279.844719 117.549562 Z M 279.844719 117.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 112.971437 C 284.040031 113.631594 283.504875 114.16675 282.844719 114.16675 C 282.184562 114.16675 281.649406 113.631594 281.649406 112.971437 C 281.649406 112.311281 282.184562 111.772219 282.844719 111.772219 C 283.504875 111.772219 284.040031 112.311281 284.040031 112.971437 Z M 284.040031 112.971437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 119.498781 L 287.040031 119.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 124.186281 L 287.040031 124.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 121.912844 C 288.235344 122.573 287.700187 123.108156 287.040031 123.108156 C 286.379875 123.108156 285.844719 122.573 285.844719 121.912844 C 285.844719 121.248781 286.379875 120.713625 287.040031 120.713625 C 287.700187 120.713625 288.235344 121.248781 288.235344 121.912844 Z M 288.235344 121.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 121.201906 L 291.235344 121.377687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 125.932375 L 291.235344 126.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 123.655031 C 292.430656 124.315187 291.8955 124.85425 291.235344 124.85425 C 290.575187 124.85425 290.040031 124.315187 290.040031 123.655031 C 290.040031 122.994875 290.575187 122.459719 291.235344 122.459719 C 291.8955 122.459719 292.430656 122.994875 292.430656 123.655031 Z M 292.430656 123.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 124.5105 L 295.430656 124.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 129.311281 L 295.430656 129.561281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 127.033937 C 296.625969 127.698 296.090812 128.233156 295.430656 128.233156 C 294.7705 128.233156 294.235344 127.698 294.235344 127.033937 C 294.235344 126.373781 294.7705 125.838625 295.430656 125.838625 C 296.090812 125.838625 296.625969 126.373781 296.625969 127.033937 Z M 296.625969 127.033937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 130.698 L 299.625969 131.080812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 135.6355 L 299.625969 136.018312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 133.358156 C 300.821281 134.018312 300.286125 134.557375 299.625969 134.557375 C 298.965812 134.557375 298.430656 134.018312 298.430656 133.358156 C 298.430656 132.698 298.965812 132.162844 299.625969 132.162844 C 300.286125 132.162844 300.821281 132.698 300.821281 133.358156 Z M 300.821281 133.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 138.073 L 303.821281 138.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 143.158937 L 303.821281 143.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 140.881594 C 305.016594 141.54175 304.481437 142.076906 303.821281 142.076906 C 303.161125 142.076906 302.625969 141.54175 302.625969 140.881594 C 302.625969 140.221437 303.161125 139.686281 303.821281 139.686281 C 304.481437 139.686281 305.016594 140.221437 305.016594 140.881594 Z M 305.016594 140.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 136.576906 L 308.016594 137.076906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 141.631594 L 308.016594 142.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 139.35425 C 309.211906 140.018312 308.67675 140.553469 308.016594 140.553469 C 307.356437 140.553469 306.821281 140.018312 306.821281 139.35425 C 306.821281 138.694094 307.356437 138.158937 308.016594 138.158937 C 308.67675 138.158937 309.211906 138.694094 309.211906 139.35425 Z M 309.211906 139.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 146.737062 L 312.211906 147.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 151.990969 L 312.211906 152.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 149.713625 C 313.407219 150.373781 312.872062 150.908937 312.211906 150.908937 C 311.55175 150.908937 311.016594 150.373781 311.016594 149.713625 C 311.016594 149.053469 311.55175 148.514406 312.211906 148.514406 C 312.872062 148.514406 313.407219 149.053469 313.407219 149.713625 Z M 313.407219 149.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 153.268312 L 316.407219 154.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 158.639406 L 316.407219 159.459719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 156.362062 C 317.602531 157.026125 317.067375 157.561281 316.407219 157.561281 C 315.747062 157.561281 315.211906 157.026125 315.211906 156.362062 C 315.211906 155.701906 315.747062 155.16675 316.407219 155.16675 C 317.067375 155.16675 317.602531 155.701906 317.602531 156.362062 Z M 317.602531 156.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 320.602531 156.268312 L 320.602531 157.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 320.602531 161.694094 L 320.602531 162.565187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 159.41675 C 321.797844 160.076906 321.262687 160.612062 320.602531 160.612062 C 319.942375 160.612062 319.407219 160.076906 319.407219 159.41675 C 319.407219 158.756594 319.942375 158.221437 320.602531 158.221437 C 321.262687 158.221437 321.797844 158.756594 321.797844 159.41675 Z M 321.797844 159.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.797844 165.701906 L 324.797844 166.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.797844 171.287844 L 324.797844 172.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 169.0105 C 325.993156 169.670656 325.458 170.205812 324.797844 170.205812 C 324.137687 170.205812 323.602531 169.670656 323.602531 169.0105 C 323.602531 168.350344 324.137687 167.815187 324.797844 167.815187 C 325.458 167.815187 325.993156 168.350344 325.993156 169.0105 Z M 325.993156 169.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 328.993156 173.959719 L 328.993156 175.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 328.993156 179.682375 L 328.993156 180.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 177.405031 C 330.188469 178.065187 329.653312 178.60425 328.993156 178.60425 C 328.333 178.60425 327.797844 178.065187 327.797844 177.405031 C 327.797844 176.744875 328.333 176.209719 328.993156 176.209719 C 329.653312 176.209719 330.188469 176.744875 330.188469 177.405031 Z M 330.188469 177.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 333.188469 177.073 L 333.188469 178.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 333.188469 182.846437 L 333.188469 184.065187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 180.569094 C 334.383781 181.22925 333.848625 181.764406 333.188469 181.764406 C 332.528312 181.764406 331.993156 181.22925 331.993156 180.569094 C 331.993156 179.905031 332.528312 179.369875 333.188469 179.369875 C 333.848625 179.369875 334.383781 179.905031 334.383781 180.569094 Z M 334.383781 180.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 337.383781 181.795656 L 337.383781 183.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 337.383781 187.643312 L 337.383781 188.936281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 185.365969 C 338.579094 186.026125 338.043937 186.561281 337.383781 186.561281 C 336.723625 186.561281 336.188469 186.026125 336.188469 185.365969 C 336.188469 184.705812 336.723625 184.16675 337.383781 184.16675 C 338.043937 184.16675 338.579094 184.705812 338.579094 185.365969 Z M 338.579094 185.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 341.579094 197.584719 L 341.579094 199.115969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 341.579094 203.670656 L 341.579094 205.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 201.393312 C 342.774406 202.053469 342.23925 202.588625 341.579094 202.588625 C 340.918937 202.588625 340.383781 202.053469 340.383781 201.393312 C 340.383781 200.72925 340.918937 200.194094 341.579094 200.194094 C 342.23925 200.194094 342.774406 200.72925 342.774406 201.393312 Z M 342.774406 201.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 345.774406 203.928469 L 345.774406 205.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 345.774406 210.100344 L 345.774406 211.721437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 207.823 C 346.969719 208.487062 346.434562 209.022219 345.774406 209.022219 C 345.11425 209.022219 344.579094 208.487062 344.579094 207.823 C 344.579094 207.162844 345.11425 206.627687 345.774406 206.627687 C 346.434562 206.627687 346.969719 207.162844 346.969719 207.823 Z M 346.969719 207.823 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 349.969719 209.733156 L 349.969719 211.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 349.969719 215.987062 L 349.969719 217.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 213.713625 C 351.165031 214.373781 350.629875 214.908937 349.969719 214.908937 C 349.309562 214.908937 348.774406 214.373781 348.774406 213.713625 C 348.774406 213.049562 349.309562 212.514406 349.969719 212.514406 C 350.629875 212.514406 351.165031 213.049562 351.165031 213.713625 Z M 351.165031 213.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.165031 221.994875 L 354.165031 223.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.165031 228.41675 L 354.165031 230.287844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 226.139406 C 355.360344 226.803469 354.825187 227.338625 354.165031 227.338625 C 353.504875 227.338625 352.969719 226.803469 352.969719 226.139406 C 352.969719 225.47925 353.504875 224.944094 354.165031 224.944094 C 354.825187 224.944094 355.360344 225.47925 355.360344 226.139406 Z M 355.360344 226.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 358.360344 230.60425 L 358.360344 232.584719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 358.360344 237.139406 L 358.360344 239.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 234.862062 C 359.555656 235.526125 359.0205 236.061281 358.360344 236.061281 C 357.700187 236.061281 357.165031 235.526125 357.165031 234.862062 C 357.165031 234.201906 357.700187 233.66675 358.360344 233.66675 C 359.0205 233.66675 359.555656 234.201906 359.555656 234.862062 Z M 359.555656 234.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 362.555656 244.3855 L 362.555656 246.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 362.555656 251.096437 L 362.555656 253.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 248.819094 C 363.750969 249.47925 363.215812 250.014406 362.555656 250.014406 C 361.8955 250.014406 361.360344 249.47925 361.360344 248.819094 C 361.360344 248.158937 361.8955 247.623781 362.555656 247.623781 C 363.215812 247.623781 363.750969 248.158937 363.750969 248.819094 Z M 363.750969 248.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 366.750969 244.924562 L 366.750969 247.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 366.750969 251.639406 L 366.750969 253.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 367.946281 249.362062 C 367.946281 250.026125 367.411125 250.561281 366.750969 250.561281 C 366.090812 250.561281 365.555656 250.026125 365.555656 249.362062 C 365.555656 248.701906 366.090812 248.16675 366.750969 248.16675 C 367.411125 248.16675 367.946281 248.701906 367.946281 249.362062 Z M 367.946281 249.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 370.946281 253.862062 L 370.946281 256.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 370.946281 260.690187 L 370.946281 262.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 258.412844 C 372.141594 259.073 371.606437 259.608156 370.946281 259.608156 C 370.286125 259.608156 369.750969 259.073 369.750969 258.412844 C 369.750969 257.752687 370.286125 257.217531 370.946281 257.217531 C 371.606437 257.217531 372.141594 257.752687 372.141594 258.412844 Z M 372.141594 258.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 375.141594 263.881594 L 375.141594 266.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 375.141594 270.830812 L 375.141594 273.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 376.336906 268.553469 C 376.336906 269.213625 375.80175 269.748781 375.141594 269.748781 C 374.481437 269.748781 373.946281 269.213625 373.946281 268.553469 C 373.946281 267.893312 374.481437 267.35425 375.141594 267.35425 C 375.80175 267.35425 376.336906 267.893312 376.336906 268.553469 Z M 376.336906 268.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 379.336906 270.565187 L 379.336906 273.033937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 379.336906 277.588625 L 379.336906 280.061281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 275.311281 C 380.532219 275.975344 379.997062 276.5105 379.336906 276.5105 C 378.67675 276.5105 378.141594 275.975344 378.141594 275.311281 C 378.141594 274.651125 378.67675 274.115969 379.336906 274.115969 C 379.997062 274.115969 380.532219 274.651125 380.532219 275.311281 Z M 380.532219 275.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 285.549562 L 383.532219 288.190187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 292.744875 L 383.532219 295.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 290.467531 C 384.727531 291.127687 384.192375 291.662844 383.532219 291.662844 C 382.872062 291.662844 382.336906 291.127687 382.336906 290.467531 C 382.336906 289.807375 382.872062 289.268312 383.532219 289.268312 C 384.192375 289.268312 384.727531 289.807375 384.727531 290.467531 Z M 384.727531 290.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 288.889406 L 387.727531 291.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 296.123781 L 387.727531 298.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 293.846437 C 388.922844 294.506594 388.387687 295.04175 387.727531 295.04175 C 387.067375 295.04175 386.532219 294.506594 386.532219 293.846437 C 386.532219 293.186281 387.067375 292.651125 387.727531 292.651125 C 388.387687 292.651125 388.922844 293.186281 388.922844 293.846437 Z M 388.922844 293.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 283.069094 L 391.922844 285.682375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 290.237062 L 391.922844 292.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 287.959719 C 393.118156 288.619875 392.583 289.155031 391.922844 289.155031 C 391.262687 289.155031 390.727531 288.619875 390.727531 287.959719 C 390.727531 287.295656 391.262687 286.7605 391.922844 286.7605 C 392.583 286.7605 393.118156 287.295656 393.118156 287.959719 Z M 393.118156 287.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 293.530031 L 396.118156 296.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 300.811281 L 396.118156 303.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 298.533937 C 397.313469 299.194094 396.778312 299.72925 396.118156 299.72925 C 395.458 299.72925 394.922844 299.194094 394.922844 298.533937 C 394.922844 297.873781 395.458 297.338625 396.118156 297.338625 C 396.778312 297.338625 397.313469 297.873781 397.313469 298.533937 Z M 397.313469 298.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 294.60425 L 400.313469 297.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 301.901125 L 400.313469 304.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 401.508781 299.627687 C 401.508781 300.287844 400.973625 300.823 400.313469 300.823 C 399.653312 300.823 399.118156 300.287844 399.118156 299.627687 C 399.118156 298.963625 399.653312 298.428469 400.313469 298.428469 C 400.973625 298.428469 401.508781 298.963625 401.508781 299.627687 Z M 401.508781 299.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 297.733156 L 404.508781 300.5105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 305.061281 L 404.508781 307.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 302.787844 C 405.704094 303.448 405.168937 303.983156 404.508781 303.983156 C 403.848625 303.983156 403.313469 303.448 403.313469 302.787844 C 403.313469 302.123781 403.848625 301.588625 404.508781 301.588625 C 405.168937 301.588625 405.704094 302.123781 405.704094 302.787844 Z M 405.704094 302.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 281.66675 L 408.704094 284.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 288.819094 L 408.704094 291.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 409.899406 286.54175 C 409.899406 287.201906 409.36425 287.737062 408.704094 287.737062 C 408.043937 287.737062 407.508781 287.201906 407.508781 286.54175 C 407.508781 285.881594 408.043937 285.342531 408.704094 285.342531 C 409.36425 285.342531 409.899406 285.881594 409.899406 286.54175 Z M 409.899406 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 245.783937 L 412.899406 247.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 252.514406 L 412.899406 254.686281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 414.094719 250.237062 C 414.094719 250.897219 413.559562 251.432375 412.899406 251.432375 C 412.23925 251.432375 411.704094 250.897219 411.704094 250.237062 C 411.704094 249.576906 412.23925 249.037844 412.899406 249.037844 C 413.559562 249.037844 414.094719 249.576906 414.094719 250.237062 Z M 414.094719 250.237062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 202.6355 L 417.094719 204.240969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 208.79175 L 417.094719 210.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 418.290031 206.514406 C 418.290031 207.178469 417.754875 207.713625 417.094719 207.713625 C 416.434562 207.713625 415.899406 207.178469 415.899406 206.514406 C 415.899406 205.85425 416.434562 205.319094 417.094719 205.319094 C 417.754875 205.319094 418.290031 205.85425 418.290031 206.514406 Z M 418.290031 206.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 163.342531 L 421.290031 164.334719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 168.889406 L 421.290031 169.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 166.612062 C 422.485344 167.272219 421.950187 167.807375 421.290031 167.807375 C 420.629875 167.807375 420.094719 167.272219 420.094719 166.612062 C 420.094719 165.951906 420.629875 165.41675 421.290031 165.41675 C 421.950187 165.41675 422.485344 165.951906 422.485344 166.612062 Z M 422.485344 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 136.256594 L 425.485344 136.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 141.303469 L 425.485344 141.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.680656 139.030031 C 426.680656 139.690187 426.1455 140.225344 425.485344 140.225344 C 424.825187 140.225344 424.290031 139.690187 424.290031 139.030031 C 424.290031 138.365969 424.825187 137.830812 425.485344 137.830812 C 426.1455 137.830812 426.680656 138.365969 426.680656 139.030031 Z M 426.680656 139.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 116.834719 L 429.680656 116.908937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 121.463625 L 429.680656 121.537844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 119.186281 C 430.875969 119.846437 430.340812 120.381594 429.680656 120.381594 C 429.0205 120.381594 428.485344 119.846437 428.485344 119.186281 C 428.485344 118.526125 429.0205 117.987062 429.680656 117.987062 C 430.340812 117.987062 430.875969 118.526125 430.875969 119.186281 Z M 430.875969 119.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 113.405031 C 435.071281 114.069094 434.536125 114.60425 433.875969 114.60425 C 433.215812 114.60425 432.680656 114.069094 432.680656 113.405031 C 432.680656 112.744875 433.215812 112.209719 433.875969 112.209719 C 434.536125 112.209719 435.071281 112.744875 435.071281 113.405031 Z M 435.071281 113.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.266594 101.959719 C 439.266594 102.619875 438.731437 103.155031 438.071281 103.155031 C 437.411125 103.155031 436.875969 102.619875 436.875969 101.959719 C 436.875969 101.299562 437.411125 100.7605 438.071281 100.7605 C 438.731437 100.7605 439.266594 101.299562 439.266594 101.959719 Z M 439.266594 101.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 99.451906 C 443.461906 100.112062 442.92675 100.647219 442.266594 100.647219 C 441.606437 100.647219 441.071281 100.112062 441.071281 99.451906 C 441.071281 98.79175 441.606437 98.252687 442.266594 98.252687 C 442.92675 98.252687 443.461906 98.79175 443.461906 99.451906 Z M 443.461906 99.451906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 447.657219 95.198 C 447.657219 95.862062 447.122062 96.397219 446.461906 96.397219 C 445.80175 96.397219 445.266594 95.862062 445.266594 95.198 C 445.266594 94.537844 445.80175 94.002687 446.461906 94.002687 C 447.122062 94.002687 447.657219 94.537844 447.657219 95.198 Z M 447.657219 95.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 90.948 C 451.852531 91.608156 451.317375 92.143312 450.657219 92.143312 C 449.997062 92.143312 449.461906 91.608156 449.461906 90.948 C 449.461906 90.287844 449.997062 89.748781 450.657219 89.748781 C 451.317375 89.748781 451.852531 90.287844 451.852531 90.948 Z M 451.852531 90.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 87.350344 C 456.047844 88.0105 455.512687 88.545656 454.852531 88.545656 C 454.192375 88.545656 453.657219 88.0105 453.657219 87.350344 C 453.657219 86.690187 454.192375 86.151125 454.852531 86.151125 C 455.512687 86.151125 456.047844 86.690187 456.047844 87.350344 Z M 456.047844 87.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.243156 83.643312 C 460.243156 84.303469 459.708 84.838625 459.047844 84.838625 C 458.387687 84.838625 457.852531 84.303469 457.852531 83.643312 C 457.852531 82.983156 458.387687 82.444094 459.047844 82.444094 C 459.708 82.444094 460.243156 82.983156 460.243156 83.643312 Z M 460.243156 83.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.438469 80.47925 C 464.438469 81.143312 463.903312 81.678469 463.243156 81.678469 C 462.583 81.678469 462.047844 81.143312 462.047844 80.47925 C 462.047844 79.819094 462.583 79.283937 463.243156 79.283937 C 463.903312 79.283937 464.438469 79.819094 464.438469 80.47925 Z M 464.438469 80.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.637687 78.518312 C 468.637687 79.178469 468.098625 79.713625 467.438469 79.713625 C 466.778312 79.713625 466.243156 79.178469 466.243156 78.518312 C 466.243156 77.858156 466.778312 77.323 467.438469 77.323 C 468.098625 77.323 468.637687 77.858156 468.637687 78.518312 Z M 468.637687 78.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 472.829094 78.627687 C 472.829094 79.287844 472.293937 79.823 471.633781 79.823 C 470.973625 79.823 470.438469 79.287844 470.438469 78.627687 C 470.438469 77.967531 470.973625 77.432375 471.633781 77.432375 C 472.293937 77.432375 472.829094 77.967531 472.829094 78.627687 Z M 472.829094 78.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 477.024406 76.22925 C 477.024406 76.889406 476.48925 77.424562 475.829094 77.424562 C 475.168937 77.424562 474.633781 76.889406 474.633781 76.22925 C 474.633781 75.569094 475.168937 75.030031 475.829094 75.030031 C 476.48925 75.030031 477.024406 75.569094 477.024406 76.22925 Z M 477.024406 76.22925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 481.223625 74.592531 C 481.223625 75.252687 480.684562 75.79175 480.024406 75.79175 C 479.36425 75.79175 478.829094 75.252687 478.829094 74.592531 C 478.829094 73.932375 479.36425 73.397219 480.024406 73.397219 C 480.684562 73.397219 481.223625 73.932375 481.223625 74.592531 Z M 481.223625 74.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.415031 73.393312 C 485.415031 74.053469 484.879875 74.592531 484.219719 74.592531 C 483.559562 74.592531 483.024406 74.053469 483.024406 73.393312 C 483.024406 72.733156 483.559562 72.198 484.219719 72.198 C 484.879875 72.198 485.415031 72.733156 485.415031 73.393312 Z M 485.415031 73.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 489.610344 72.740969 C 489.610344 73.401125 489.075187 73.936281 488.415031 73.936281 C 487.754875 73.936281 487.219719 73.401125 487.219719 72.740969 C 487.219719 72.080812 487.754875 71.54175 488.415031 71.54175 C 489.075187 71.54175 489.610344 72.080812 489.610344 72.740969 Z M 489.610344 72.740969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.809562 72.412844 C 493.809562 73.073 493.2705 73.608156 492.610344 73.608156 C 491.950187 73.608156 491.415031 73.073 491.415031 72.412844 C 491.415031 71.752687 491.950187 71.217531 492.610344 71.217531 C 493.2705 71.217531 493.809562 71.752687 493.809562 72.412844 Z M 493.809562 72.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.004875 70.014406 C 498.004875 70.674562 497.465812 71.209719 496.805656 71.209719 C 496.1455 71.209719 495.610344 70.674562 495.610344 70.014406 C 495.610344 69.35425 496.1455 68.819094 496.805656 68.819094 C 497.465812 68.819094 498.004875 69.35425 498.004875 70.014406 Z M 498.004875 70.014406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 73.240969 L 260.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 73.240969 L 293.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 73.240969 L 327.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 73.240969 L 360.36425 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 73.240969 L 194.079094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 73.240969 L 160.821281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 73.240969 L 127.563469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 73.240969 L 94.305656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 73.240969 L 426.879875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 73.240969 L 460.137687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 73.240969 L 493.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="214.867" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="226.874975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="381.153" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="393.160975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="335.731" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="347.042971" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="357.606145" y="416.984352"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="366.121921" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="379.975701" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="390.196273" y="417.528"/>
+ <use xlink:href="#glyph0-5" x="409.039671" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="419.713426" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="438.047511" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.757261" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.765236" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="470.100147" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-2" x="479.807845" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 397.615969 L 260.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 397.615969 L 293.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 397.615969 L 327.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 397.615969 L 360.36425 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 397.615969 L 194.079094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 397.615969 L 160.821281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 397.615969 L 127.563469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 397.615969 L 94.305656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 397.615969 L 426.879875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 397.615969 L 460.137687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 397.615969 L 493.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.389406 L 79.372062 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.29175 L 79.372062 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 101.194094 L 79.372062 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 112.100344 L 79.372062 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 123.002687 L 79.372062 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 133.905031 L 79.372062 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 144.807375 L 79.372062 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 155.709719 L 79.372062 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 166.612062 L 79.372062 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 177.514406 L 79.372062 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 188.41675 L 79.372062 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 199.319094 L 79.372062 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 210.221437 L 79.372062 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 221.127687 L 79.372062 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 232.030031 L 79.372062 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 242.932375 L 79.372062 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.834719 L 79.372062 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.737062 L 79.372062 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.639406 L 79.372062 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 286.54175 L 79.372062 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 297.444094 L 79.372062 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 308.346437 L 79.372062 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 319.248781 L 79.372062 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 330.151125 L 79.372062 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 341.053469 L 79.372062 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 351.959719 L 79.372062 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 362.862062 L 79.372062 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.764406 L 79.372062 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 384.66675 L 79.372062 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="36.979" y="315.476"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="315.476"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="315.476"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="55.657" y="260.963"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="206.45"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="206.45"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="206.45"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.657" y="151.939"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="36.979" y="97.426"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="97.426"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="97.426"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-9" x="55.657" y="42.912"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-2" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph7-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph7-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph7-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph7-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph7-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph7-11" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph7-12" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph7-13" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph8-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-14" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.389406 L 498.903312 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.29175 L 498.903312 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 101.194094 L 498.903312 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 112.100344 L 498.903312 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 123.002687 L 498.903312 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 133.905031 L 498.903312 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 144.807375 L 498.903312 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 155.709719 L 498.903312 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 166.612062 L 498.903312 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 177.514406 L 498.903312 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 188.41675 L 498.903312 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 199.319094 L 498.903312 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 210.221437 L 498.903312 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 221.127687 L 498.903312 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 232.030031 L 498.903312 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 242.932375 L 498.903312 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.834719 L 498.903312 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.737062 L 498.903312 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.639406 L 498.903312 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 286.54175 L 498.903312 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 297.444094 L 498.903312 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 308.346437 L 498.903312 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 319.248781 L 498.903312 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 330.151125 L 498.903312 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 341.053469 L 498.903312 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 351.959719 L 498.903312 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 362.862062 L 498.903312 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.764406 L 498.903312 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 384.66675 L 498.903312 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 73.240969 L 260.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 73.240969 L 293.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 73.240969 L 327.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 73.240969 L 360.36425 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 73.240969 L 194.079094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 73.240969 L 160.821281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 73.240969 L 127.563469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 73.240969 L 94.305656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 73.240969 L 426.879875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 73.240969 L 460.137687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 73.240969 L 493.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 397.615969 L 260.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 397.615969 L 293.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 397.615969 L 327.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 397.615969 L 360.36425 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 397.615969 L 194.079094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 397.615969 L 160.821281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 397.615969 L 127.563469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 397.615969 L 94.305656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 397.615969 L 426.879875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 397.615969 L 460.137687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 397.615969 L 493.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.389406 L 79.372062 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.29175 L 79.372062 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 101.194094 L 79.372062 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 112.100344 L 79.372062 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 123.002687 L 79.372062 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 133.905031 L 79.372062 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 144.807375 L 79.372062 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 155.709719 L 79.372062 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 166.612062 L 79.372062 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 177.514406 L 79.372062 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 188.41675 L 79.372062 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 199.319094 L 79.372062 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 210.221437 L 79.372062 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 221.127687 L 79.372062 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 232.030031 L 79.372062 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 242.932375 L 79.372062 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.834719 L 79.372062 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.737062 L 79.372062 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.639406 L 79.372062 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 286.54175 L 79.372062 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 297.444094 L 79.372062 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 308.346437 L 79.372062 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 319.248781 L 79.372062 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 330.151125 L 79.372062 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 341.053469 L 79.372062 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 351.959719 L 79.372062 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 362.862062 L 79.372062 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.764406 L 79.372062 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 384.66675 L 79.372062 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.389406 L 498.903312 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.29175 L 498.903312 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 101.194094 L 498.903312 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 112.100344 L 498.903312 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 123.002687 L 498.903312 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 133.905031 L 498.903312 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 144.807375 L 498.903312 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 155.709719 L 498.903312 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 166.612062 L 498.903312 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 177.514406 L 498.903312 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 188.41675 L 498.903312 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 199.319094 L 498.903312 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 210.221437 L 498.903312 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 221.127687 L 498.903312 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 232.030031 L 498.903312 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 242.932375 L 498.903312 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.834719 L 498.903312 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.737062 L 498.903312 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.639406 L 498.903312 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 286.54175 L 498.903312 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 297.444094 L 498.903312 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 308.346437 L 498.903312 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 319.248781 L 498.903312 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 330.151125 L 498.903312 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 341.053469 L 498.903312 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 351.959719 L 498.903312 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 362.862062 L 498.903312 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.764406 L 498.903312 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 384.66675 L 498.903312 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/s12.svg b/doc/figs/s12.svg
new file mode 100644
index 00000000000..364f6647442
--- /dev/null
+++ b/doc/figs/s12.svg
@@ -0,0 +1,715 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="504pt" height="432pt" viewBox="0 0 504 432" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 7.0625 -15.71875 C 7.0625 -16.28125 7.0625 -16.3125 6.578125 -16.3125 C 5.984375 -15.65625 4.765625 -14.75 2.234375 -14.75 L 2.234375 -14.03125 C 2.796875 -14.03125 4.015625 -14.03125 5.375 -14.671875 L 5.375 -1.890625 C 5.375 -1 5.296875 -0.71875 3.140625 -0.71875 L 2.375 -0.71875 L 2.375 0 C 3.046875 -0.046875 5.421875 -0.046875 6.234375 -0.046875 C 7.046875 -0.046875 9.390625 -0.046875 10.0625 0 L 10.0625 -0.71875 L 9.296875 -0.71875 C 7.140625 -0.71875 7.0625 -1 7.0625 -1.890625 Z M 7.0625 -15.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 10.984375 -7.84375 C 10.984375 -9.890625 10.875 -11.875 9.984375 -13.734375 C 8.984375 -15.78125 7.21875 -16.3125 6.015625 -16.3125 C 4.59375 -16.3125 2.84375 -15.609375 1.9375 -13.5625 C 1.25 -12.015625 1 -10.5 1 -7.84375 C 1 -5.46875 1.171875 -3.6875 2.0625 -1.9375 C 3.015625 -0.078125 4.703125 0.515625 5.984375 0.515625 C 8.125 0.515625 9.34375 -0.765625 10.0625 -2.1875 C 10.9375 -4.015625 10.984375 -6.421875 10.984375 -7.84375 Z M 5.984375 0.03125 C 5.203125 0.03125 3.609375 -0.421875 3.140625 -3.09375 C 2.875 -4.5625 2.875 -6.421875 2.875 -8.140625 C 2.875 -10.15625 2.875 -11.96875 3.265625 -13.421875 C 3.6875 -15.0625 4.9375 -15.828125 5.984375 -15.828125 C 6.921875 -15.828125 8.34375 -15.265625 8.8125 -13.15625 C 9.125 -11.75 9.125 -9.8125 9.125 -8.140625 C 9.125 -6.5 9.125 -4.640625 8.859375 -3.140625 C 8.390625 -0.4375 6.84375 0.03125 5.984375 0.03125 Z M 5.984375 0.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 10.796875 -4.125 L 10.25 -4.125 C 10.1875 -3.703125 9.984375 -2.359375 9.734375 -1.96875 C 9.5625 -1.734375 8.171875 -1.734375 7.4375 -1.734375 L 2.890625 -1.734375 C 3.5625 -2.3125 5.046875 -3.875 5.6875 -4.46875 C 9.421875 -7.90625 10.796875 -9.171875 10.796875 -11.609375 C 10.796875 -14.421875 8.5625 -16.3125 5.71875 -16.3125 C 2.875 -16.3125 1.203125 -13.890625 1.203125 -11.78125 C 1.203125 -10.53125 2.28125 -10.53125 2.359375 -10.53125 C 2.875 -10.53125 3.515625 -10.890625 3.515625 -11.671875 C 3.515625 -12.359375 3.046875 -12.828125 2.359375 -12.828125 C 2.140625 -12.828125 2.078125 -12.828125 2.015625 -12.8125 C 2.484375 -14.46875 3.796875 -15.609375 5.390625 -15.609375 C 7.484375 -15.609375 8.75 -13.859375 8.75 -11.609375 C 8.75 -9.515625 7.5625 -7.703125 6.15625 -6.140625 L 1.203125 -0.59375 L 1.203125 0 L 10.15625 0 Z M 10.796875 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 15.96875 -4.859375 C 15.96875 -5.8125 16.0625 -5.9375 17.640625 -5.9375 L 17.640625 -6.640625 C 17 -6.59375 15.3125 -6.59375 14.578125 -6.59375 C 13.78125 -6.59375 11.65625 -6.59375 10.984375 -6.640625 L 10.984375 -5.9375 L 11.75 -5.9375 C 13.90625 -5.9375 13.984375 -5.640625 13.984375 -4.765625 L 13.984375 -3.1875 C 13.984375 -0.390625 10.765625 -0.203125 10.125 -0.203125 C 8.1875 -0.203125 3.609375 -1.375 3.609375 -8.390625 C 3.609375 -15.484375 8.25 -16.5625 9.953125 -16.5625 C 12.09375 -16.5625 14.640625 -15.015625 15.28125 -10.671875 C 15.328125 -10.40625 15.328125 -10.328125 15.625 -10.328125 C 15.96875 -10.328125 15.96875 -10.40625 15.96875 -10.890625 L 15.96875 -16.703125 C 15.96875 -17.140625 15.96875 -17.265625 15.71875 -17.265625 C 15.578125 -17.265625 15.546875 -17.21875 15.40625 -16.96875 L 14.203125 -15.03125 C 13.5 -15.921875 12 -17.265625 9.671875 -17.265625 C 5.21875 -17.265625 1.328125 -13.421875 1.328125 -8.390625 C 1.328125 -3.3125 5.21875 0.515625 9.6875 0.515625 C 11.4375 0.515625 13.421875 -0.046875 14.328125 -1.625 C 14.765625 -0.828125 15.578125 -0.03125 15.78125 -0.03125 C 15.96875 -0.03125 15.96875 -0.171875 15.96875 -0.5625 Z M 15.96875 -4.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 9.390625 -5.6875 C 9.9375 -5.6875 9.984375 -5.6875 9.984375 -6.15625 C 9.984375 -8.640625 8.65625 -10.9375 5.6875 -10.9375 C 2.890625 -10.9375 0.734375 -8.421875 0.734375 -5.375 C 0.734375 -2.140625 3.234375 0.25 5.96875 0.25 C 8.875 0.25 9.984375 -2.40625 9.984375 -2.921875 C 9.984375 -3.0625 9.859375 -3.171875 9.71875 -3.171875 C 9.515625 -3.171875 9.46875 -3.046875 9.421875 -2.921875 C 8.78125 -0.859375 7.140625 -0.296875 6.109375 -0.296875 C 5.078125 -0.296875 2.59375 -0.984375 2.59375 -5.21875 L 2.59375 -5.6875 Z M 2.625 -6.15625 C 2.828125 -10.015625 4.984375 -10.453125 5.671875 -10.453125 C 8.296875 -10.453125 8.4375 -6.984375 8.46875 -6.15625 Z M 2.625 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 14.984375 -14.328125 C 15.203125 -14.9375 15.625 -16.015625 17.546875 -16.046875 L 17.546875 -16.75 C 16.28125 -16.703125 16.234375 -16.703125 15.28125 -16.703125 C 14.625 -16.703125 13.390625 -16.703125 12.78125 -16.75 L 12.78125 -16.046875 C 14.03125 -16.015625 14.40625 -15.328125 14.40625 -14.84375 C 14.40625 -14.6875 14.40625 -14.640625 14.25 -14.296875 L 9.671875 -2.203125 L 4.828125 -14.96875 C 4.703125 -15.234375 4.703125 -15.28125 4.703125 -15.328125 C 4.703125 -16.046875 5.9375 -16.046875 6.546875 -16.046875 L 6.546875 -16.75 C 5.96875 -16.703125 4.09375 -16.703125 3.390625 -16.703125 C 2.703125 -16.703125 1.03125 -16.703125 0.4375 -16.75 L 0.4375 -16.046875 C 1.96875 -16.046875 2.359375 -16.046875 2.71875 -15.0625 L 8.46875 0.046875 C 8.59375 0.390625 8.640625 0.515625 8.984375 0.515625 C 9.328125 0.515625 9.34375 0.4375 9.515625 0.03125 Z M 14.984375 -14.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 4.515625 -1.203125 C 4.515625 -1.859375 3.953125 -2.375 3.34375 -2.375 C 2.625 -2.375 2.140625 -1.8125 2.140625 -1.203125 C 2.140625 -0.46875 2.75 0 3.3125 0 C 3.96875 0 4.515625 -0.515625 4.515625 -1.203125 Z M 4.515625 -1.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 3.140625 -14.0625 C 4.1875 -13.71875 5.046875 -13.6875 5.328125 -13.6875 C 8.09375 -13.6875 9.859375 -15.71875 9.859375 -16.0625 C 9.859375 -16.171875 9.8125 -16.28125 9.671875 -16.28125 C 9.609375 -16.28125 9.5625 -16.28125 9.34375 -16.1875 C 7.96875 -15.609375 6.796875 -15.53125 6.15625 -15.53125 C 4.53125 -15.53125 3.390625 -16.015625 2.921875 -16.21875 C 2.75 -16.28125 2.703125 -16.28125 2.671875 -16.28125 C 2.484375 -16.28125 2.484375 -16.140625 2.484375 -15.75 L 2.484375 -8.46875 C 2.484375 -8.015625 2.484375 -7.875 2.765625 -7.875 C 2.890625 -7.875 2.921875 -7.90625 3.171875 -8.1875 C 3.84375 -9.203125 5 -9.78125 6.234375 -9.78125 C 7.53125 -9.78125 8.171875 -8.59375 8.359375 -8.171875 C 8.78125 -7.21875 8.8125 -6.015625 8.8125 -5.078125 C 8.8125 -4.140625 8.8125 -2.75 8.125 -1.640625 C 7.578125 -0.765625 6.625 -0.140625 5.546875 -0.140625 C 3.921875 -0.140625 2.328125 -1.25 1.890625 -3.046875 C 2.015625 -3 2.15625 -2.96875 2.28125 -2.96875 C 2.703125 -2.96875 3.359375 -3.21875 3.359375 -4.046875 C 3.359375 -4.734375 2.890625 -5.125 2.28125 -5.125 C 1.84375 -5.125 1.203125 -4.90625 1.203125 -3.953125 C 1.203125 -1.859375 2.875 0.515625 5.59375 0.515625 C 8.359375 0.515625 10.796875 -1.8125 10.796875 -4.9375 C 10.796875 -7.84375 8.828125 -10.28125 6.25 -10.28125 C 4.859375 -10.28125 3.78125 -9.671875 3.140625 -8.984375 Z M 3.140625 -14.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 4.515625 -8.8125 C 4.09375 -8.78125 4 -8.75 4 -8.53125 C 4 -8.296875 4.125 -8.296875 4.5625 -8.296875 L 5.6875 -8.296875 C 7.78125 -8.296875 8.703125 -6.578125 8.703125 -4.21875 C 8.703125 -1 7.046875 -0.140625 5.84375 -0.140625 C 4.65625 -0.140625 2.65625 -0.71875 1.9375 -2.328125 C 2.71875 -2.203125 3.4375 -2.65625 3.4375 -3.53125 C 3.4375 -4.25 2.921875 -4.734375 2.234375 -4.734375 C 1.640625 -4.734375 1 -4.390625 1 -3.453125 C 1 -1.28125 3.1875 0.515625 5.90625 0.515625 C 8.828125 0.515625 10.984375 -1.71875 10.984375 -4.1875 C 10.984375 -6.453125 9.171875 -8.21875 6.8125 -8.640625 C 8.953125 -9.25 10.328125 -11.046875 10.328125 -12.953125 C 10.328125 -14.890625 8.3125 -16.3125 5.9375 -16.3125 C 3.484375 -16.3125 1.671875 -14.8125 1.671875 -13.03125 C 1.671875 -12.046875 2.421875 -11.84375 2.796875 -11.84375 C 3.3125 -11.84375 3.90625 -12.21875 3.90625 -12.953125 C 3.90625 -13.734375 3.3125 -14.078125 2.765625 -14.078125 C 2.625 -14.078125 2.578125 -14.078125 2.5 -14.0625 C 3.4375 -15.71875 5.734375 -15.71875 5.859375 -15.71875 C 6.671875 -15.71875 8.265625 -15.359375 8.265625 -12.953125 C 8.265625 -12.484375 8.1875 -11.109375 7.484375 -10.0625 C 6.75 -8.984375 5.90625 -8.90625 5.25 -8.875 Z M 4.515625 -8.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.59375 -4.90625 C 6.015625 -4.828125 6.671875 -4.6875 6.8125 -4.65625 C 7.140625 -4.5625 8.25 -4.171875 8.25 -3 C 8.25 -2.234375 7.5625 -0.25 4.703125 -0.25 C 4.1875 -0.25 2.359375 -0.3125 1.859375 -1.671875 C 2.84375 -1.546875 3.34375 -2.3125 3.34375 -2.84375 C 3.34375 -3.359375 3 -3.625 2.5 -3.625 C 1.96875 -3.625 1.25 -3.21875 1.25 -2.109375 C 1.25 -0.65625 2.71875 0.25 4.6875 0.25 C 8.421875 0.25 9.515625 -2.5 9.515625 -3.78125 C 9.515625 -4.140625 9.515625 -4.828125 8.734375 -5.625 C 8.125 -6.203125 7.53125 -6.328125 6.203125 -6.59375 C 5.546875 -6.75 4.484375 -6.96875 4.484375 -8.078125 C 4.484375 -8.5625 4.9375 -10.328125 7.265625 -10.328125 C 8.296875 -10.328125 9.296875 -9.9375 9.546875 -9.046875 C 8.46875 -9.046875 8.421875 -8.125 8.421875 -8.09375 C 8.421875 -7.578125 8.875 -7.4375 9.09375 -7.4375 C 9.4375 -7.4375 10.125 -7.703125 10.125 -8.734375 C 10.125 -9.765625 9.203125 -10.8125 7.28125 -10.8125 C 4.078125 -10.8125 3.21875 -8.296875 3.21875 -7.28125 C 3.21875 -5.421875 5.03125 -5.03125 5.59375 -4.90625 Z M 5.59375 -4.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 10.53125 -17.484375 C 10.53125 -17.515625 10.671875 -17.890625 10.671875 -17.9375 C 10.671875 -18.234375 10.421875 -18.40625 10.234375 -18.40625 C 10.109375 -18.40625 9.890625 -18.40625 9.6875 -17.859375 L 1.46875 5.21875 C 1.46875 5.25 1.328125 5.625 1.328125 5.671875 C 1.328125 5.96875 1.5625 6.140625 1.765625 6.140625 C 1.90625 6.140625 2.140625 6.109375 2.3125 5.59375 Z M 10.53125 -17.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 9.59375 -9.21875 C 9.125 -9.21875 8.90625 -9.21875 8.5625 -8.921875 C 8.421875 -8.8125 8.140625 -8.4375 8.140625 -8.046875 C 8.140625 -7.5625 8.515625 -7.265625 8.984375 -7.265625 C 9.5625 -7.265625 10.234375 -7.75 10.234375 -8.734375 C 10.234375 -9.90625 9.09375 -10.8125 7.40625 -10.8125 C 4.1875 -10.8125 0.984375 -7.3125 0.984375 -3.828125 C 0.984375 -1.6875 2.3125 0.25 4.8125 0.25 C 8.140625 0.25 10.25 -2.359375 10.25 -2.671875 C 10.25 -2.828125 10.109375 -2.9375 10.015625 -2.9375 C 9.9375 -2.9375 9.90625 -2.921875 9.6875 -2.703125 C 8.125 -0.609375 5.796875 -0.25 4.859375 -0.25 C 3.171875 -0.25 2.625 -1.71875 2.625 -2.9375 C 2.625 -3.796875 3.046875 -6.1875 3.921875 -7.84375 C 4.5625 -9 5.890625 -10.328125 7.4375 -10.328125 C 7.75 -10.328125 9.09375 -10.28125 9.59375 -9.21875 Z M 9.59375 -9.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 4.640625 -5.96875 L 6.515625 -5.96875 C 6.171875 -4.484375 5.890625 -3.265625 5.890625 -2.0625 C 5.890625 -1.9375 5.890625 -1.234375 6.0625 -0.65625 C 6.28125 0.03125 6.4375 0.15625 6.734375 0.15625 C 7.09375 0.15625 7.46875 -0.140625 7.46875 -0.546875 C 7.46875 -0.65625 7.453125 -0.6875 7.390625 -0.828125 C 7.046875 -1.578125 6.796875 -2.375 6.796875 -3.703125 C 6.796875 -4.09375 6.796875 -4.765625 7.046875 -5.96875 L 9.015625 -5.96875 C 9.28125 -5.96875 9.46875 -5.96875 9.625 -6.09375 C 9.828125 -6.28125 9.875 -6.484375 9.875 -6.59375 C 9.875 -7.046875 9.46875 -7.046875 9.1875 -7.046875 L 3.28125 -7.046875 C 2.9375 -7.046875 2.328125 -7.046875 1.515625 -6.265625 C 0.9375 -5.671875 0.46875 -4.921875 0.46875 -4.8125 C 0.46875 -4.65625 0.59375 -4.609375 0.71875 -4.609375 C 0.875 -4.609375 0.921875 -4.65625 1.015625 -4.78125 C 1.8125 -5.96875 2.78125 -5.96875 3.15625 -5.96875 L 4.109375 -5.96875 C 3.625 -4.234375 2.765625 -2.25 2.15625 -1.0625 C 2.046875 -0.8125 1.875 -0.484375 1.875 -0.34375 C 1.875 0 2.15625 0.15625 2.421875 0.15625 C 3.046875 0.15625 3.203125 -0.453125 3.546875 -1.796875 Z M 4.640625 -5.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 0.84375 1.984375 C 0.71875 2.5 0.6875 2.625 0.03125 2.625 C -0.203125 2.625 -0.390625 2.625 -0.390625 2.9375 C -0.390625 3.09375 -0.25 3.171875 -0.15625 3.171875 C 0 3.171875 0.0625 3.125 1.28125 3.125 C 2.453125 3.125 2.796875 3.171875 2.90625 3.171875 C 2.96875 3.171875 3.21875 3.171875 3.21875 2.859375 C 3.21875 2.625 2.984375 2.625 2.796875 2.625 C 2.015625 2.625 2.015625 2.53125 2.015625 2.390625 C 2.015625 2.265625 2.296875 1.109375 2.796875 -0.796875 C 3 -0.421875 3.515625 0.15625 4.390625 0.15625 C 6.40625 0.15625 8.5 -2.15625 8.5 -4.53125 C 8.5 -6.140625 7.453125 -7.203125 6.140625 -7.203125 C 5.171875 -7.203125 4.375 -6.53125 3.90625 -6.046875 C 3.5625 -7.203125 2.46875 -7.203125 2.296875 -7.203125 C 1.71875 -7.203125 1.3125 -6.828125 1.046875 -6.328125 C 0.671875 -5.59375 0.484375 -4.75 0.484375 -4.703125 C 0.484375 -4.5625 0.609375 -4.5 0.734375 -4.5 C 0.953125 -4.5 0.96875 -4.5625 1.078125 -4.984375 C 1.296875 -5.8125 1.578125 -6.75 2.25 -6.75 C 2.65625 -6.75 2.78125 -6.375 2.78125 -5.984375 C 2.78125 -5.8125 2.71875 -5.421875 2.6875 -5.296875 Z M 3.859375 -5.03125 C 3.9375 -5.3125 3.9375 -5.34375 4.1875 -5.640625 C 4.8125 -6.375 5.515625 -6.75 6.09375 -6.75 C 6.90625 -6.75 7.21875 -5.953125 7.21875 -5.21875 C 7.21875 -4.609375 6.859375 -2.859375 6.375 -1.890625 C 5.953125 -1.015625 5.171875 -0.296875 4.390625 -0.296875 C 3.28125 -0.296875 3.03125 -1.5625 3.03125 -1.6875 C 3.03125 -1.71875 3.0625 -1.890625 3.078125 -1.9375 Z M 3.859375 -5.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 6.75 -3.90625 C 6.75 -4.8125 6.75 -8.15625 3.734375 -8.15625 C 0.734375 -8.15625 0.734375 -4.8125 0.734375 -3.90625 C 0.734375 -3.03125 0.734375 0.25 3.734375 0.25 C 6.75 0.25 6.75 -3.03125 6.75 -3.90625 Z M 3.734375 -0.140625 C 3.21875 -0.140625 2.390625 -0.375 2.09375 -1.390625 C 1.90625 -2.109375 1.90625 -3.3125 1.90625 -4.078125 C 1.90625 -4.890625 1.90625 -5.84375 2.078125 -6.5 C 2.375 -7.609375 3.3125 -7.765625 3.734375 -7.765625 C 4.3125 -7.765625 5.109375 -7.5 5.390625 -6.5625 C 5.5625 -5.90625 5.578125 -5.015625 5.578125 -4.078125 C 5.578125 -3.28125 5.578125 -2.046875 5.375 -1.359375 C 5.03125 -0.296875 4.140625 -0.140625 3.734375 -0.140625 Z M 3.734375 -0.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 4.953125 28.4375 L 9.671875 28.4375 L 9.671875 27.453125 L 5.9375 27.453125 L 5.9375 0 L 9.671875 0 L 9.671875 -0.984375 L 4.953125 -0.984375 Z M 4.953125 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 5.25 28.4375 L 5.25 -0.984375 L 0.546875 -0.984375 L 0.546875 0 L 4.265625 0 L 4.265625 27.453125 L 0.546875 27.453125 L 0.546875 28.4375 Z M 5.25 28.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.609375 -3.328125 C 4.875 -3.578125 5.5625 -4.125 5.8125 -4.34375 C 6.828125 -5.28125 7.796875 -6.171875 7.796875 -7.671875 C 7.796875 -9.609375 6.15625 -10.875 4.125 -10.875 C 2.15625 -10.875 0.859375 -9.375 0.859375 -7.921875 C 0.859375 -7.125 1.5 -7.015625 1.734375 -7.015625 C 2.078125 -7.015625 2.578125 -7.25 2.578125 -7.875 C 2.578125 -8.734375 1.765625 -8.734375 1.5625 -8.734375 C 2.046875 -9.921875 3.140625 -10.328125 3.9375 -10.328125 C 5.453125 -10.328125 6.25 -9.03125 6.25 -7.671875 C 6.25 -5.96875 5.046875 -4.71875 3.125 -2.75 L 1.0625 -0.625 C 0.859375 -0.4375 0.859375 -0.40625 0.859375 0 L 7.328125 0 L 7.796875 -2.921875 L 7.296875 -2.921875 C 7.234375 -2.59375 7.109375 -1.78125 6.90625 -1.46875 C 6.8125 -1.34375 5.578125 -1.34375 5.3125 -1.34375 L 2.40625 -1.34375 Z M 4.609375 -3.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 6.4375 -10.578125 C 6.4375 -10.90625 6.4375 -11.03125 6.09375 -11.03125 C 5.890625 -11.03125 5.875 -11.015625 5.703125 -10.78125 L 0.484375 -3.21875 L 0.484375 -2.6875 L 5.09375 -2.6875 L 5.09375 -1.328125 C 5.09375 -0.71875 5.046875 -0.546875 3.796875 -0.546875 L 3.421875 -0.546875 L 3.421875 0 C 4.8125 -0.046875 4.84375 -0.046875 5.765625 -0.046875 C 6.703125 -0.046875 6.734375 -0.046875 8.125 0 L 8.125 -0.546875 L 7.75 -0.546875 C 6.484375 -0.546875 6.4375 -0.71875 6.4375 -1.328125 L 6.4375 -2.6875 L 8.171875 -2.6875 L 8.171875 -3.21875 L 6.4375 -3.21875 Z M 5.21875 -9.25 L 5.21875 -3.21875 L 1.0625 -3.21875 Z M 5.21875 -9.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-3">
+<path style="stroke:none;" d="M 4.140625 -5.453125 C 5.421875 -5.453125 6.25 -4.515625 6.25 -2.796875 C 6.25 -0.75 5.078125 -0.140625 4.21875 -0.140625 C 3.3125 -0.140625 2.09375 -0.46875 1.515625 -1.34375 C 2.109375 -1.34375 2.515625 -1.71875 2.515625 -2.25 C 2.515625 -2.78125 2.140625 -3.15625 1.625 -3.15625 C 1.171875 -3.15625 0.71875 -2.875 0.71875 -2.21875 C 0.71875 -0.671875 2.390625 0.34375 4.25 0.34375 C 6.421875 0.34375 7.9375 -1.15625 7.9375 -2.796875 C 7.9375 -4.15625 6.859375 -5.390625 5.203125 -5.75 C 6.484375 -6.203125 7.453125 -7.328125 7.453125 -8.625 C 7.453125 -9.9375 5.984375 -10.875 4.28125 -10.875 C 2.53125 -10.875 1.203125 -9.921875 1.203125 -8.671875 C 1.203125 -8.078125 1.625 -7.8125 2.046875 -7.8125 C 2.546875 -7.8125 2.875 -8.171875 2.875 -8.640625 C 2.875 -9.25 2.359375 -9.484375 2 -9.5 C 2.6875 -10.390625 3.9375 -10.4375 4.234375 -10.4375 C 4.65625 -10.4375 5.90625 -10.3125 5.90625 -8.625 C 5.90625 -7.484375 5.421875 -6.796875 5.203125 -6.53125 C 4.703125 -6.03125 4.328125 -6 3.328125 -5.9375 C 3.03125 -5.921875 2.890625 -5.90625 2.890625 -5.6875 C 2.890625 -5.453125 3.046875 -5.453125 3.3125 -5.453125 Z M 4.140625 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 9.546875 -6.8125 L 4.640625 -11.703125 C 4.34375 -12 4.296875 -12.046875 4.09375 -12.046875 C 3.84375 -12.046875 3.609375 -11.828125 3.609375 -11.546875 C 3.609375 -11.375 3.65625 -11.328125 3.921875 -11.0625 L 8.828125 -6.140625 L 3.921875 -1.203125 C 3.65625 -0.9375 3.609375 -0.890625 3.609375 -0.71875 C 3.609375 -0.4375 3.84375 -0.21875 4.09375 -0.21875 C 4.296875 -0.21875 4.34375 -0.265625 4.640625 -0.5625 L 9.515625 -5.453125 L 14.59375 -0.375 C 14.640625 -0.34375 14.8125 -0.21875 14.96875 -0.21875 C 15.265625 -0.21875 15.453125 -0.4375 15.453125 -0.71875 C 15.453125 -0.765625 15.453125 -0.859375 15.375 -0.984375 C 15.359375 -1.03125 11.453125 -4.875 10.234375 -6.140625 L 14.71875 -10.625 C 14.84375 -10.765625 15.203125 -11.09375 15.328125 -11.234375 C 15.359375 -11.28125 15.453125 -11.375 15.453125 -11.546875 C 15.453125 -11.828125 15.265625 -12.046875 14.96875 -12.046875 C 14.765625 -12.046875 14.671875 -11.953125 14.40625 -11.671875 Z M 9.546875 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph7-1">
+<path style="stroke:none;" d="M -6.28125 -15.65625 L -6.28125 -15.109375 C -2.453125 -14.515625 -0.71875 -13.9375 -0.71875 -9.78125 L -0.71875 -6.453125 C -0.71875 -5.375 -0.890625 -5.328125 -1.6875 -5.328125 L -8.3125 -5.328125 L -8.3125 -7.5625 C -8.3125 -9.90625 -7.5625 -10.1875 -5.453125 -10.1875 L -5.453125 -10.71875 L -11.890625 -10.71875 L -11.890625 -10.1875 C -9.78125 -10.1875 -9.03125 -9.90625 -9.03125 -7.5625 L -9.03125 -5.328125 L -15.015625 -5.328125 C -15.828125 -5.328125 -16 -5.375 -16 -6.453125 L -16 -9.71875 C -16 -13.328125 -14.765625 -14.078125 -11.234375 -14.453125 L -11.234375 -14.984375 L -16.703125 -14.34375 L -16.703125 -1 L -16 -1 L -16 -1.5 C -16 -3.265625 -15.75 -3.34375 -14.84375 -3.34375 L -1.859375 -3.34375 C -0.953125 -3.34375 -0.71875 -3.265625 -0.71875 -1.5 L -0.71875 -1 L 0 -1 L 0 -14.671875 Z M -6.28125 -15.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-2">
+<path style="stroke:none;" d="M -5.96875 -10.921875 C -8.25 -10.921875 -8.921875 -10.921875 -9.71875 -10.359375 C -10.671875 -9.640625 -10.8125 -8.484375 -10.8125 -7.65625 C -10.8125 -5.28125 -8.78125 -4.34375 -8.296875 -4.140625 L -8.296875 -4.125 L -10.8125 -4.125 L -10.546875 -0.78125 L -9.84375 -0.78125 C -9.84375 -2.453125 -9.671875 -2.65625 -8.46875 -2.65625 L -1.8125 -2.65625 C -0.71875 -2.65625 -0.71875 -2.375 -0.71875 -0.78125 L 0 -0.78125 C -0.046875 -1.421875 -0.046875 -2.75 -0.046875 -3.4375 C -0.046875 -4.140625 -0.046875 -5.46875 0 -6.109375 L -0.71875 -6.109375 C -0.71875 -4.53125 -0.71875 -4.25 -1.8125 -4.25 L -6.375 -4.25 C -8.953125 -4.25 -10.328125 -5.9375 -10.328125 -7.453125 C -10.328125 -8.984375 -9.078125 -9.328125 -7.578125 -9.328125 L -1.8125 -9.328125 C -0.71875 -9.328125 -0.71875 -9.046875 -0.71875 -7.453125 L 0 -7.453125 C -0.046875 -8.09375 -0.046875 -9.421875 -0.046875 -10.109375 C -0.046875 -10.8125 -0.046875 -12.140625 0 -12.78125 L -0.71875 -12.78125 C -0.71875 -11.546875 -0.71875 -10.9375 -1.453125 -10.921875 Z M -5.96875 -10.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-3">
+<path style="stroke:none;" d="M -9.859375 -4.125 L -9.859375 -7.578125 L -10.578125 -7.578125 L -10.578125 -4.125 L -15.09375 -4.125 L -15.09375 -3.578125 C -12.78125 -3.5625 -10.421875 -2.671875 -10.359375 -0.4375 L -9.859375 -0.4375 L -9.859375 -2.53125 L -3.046875 -2.53125 C -0.3125 -2.53125 0.25 -4.34375 0.25 -5.640625 C 0.25 -7.1875 -1.28125 -8 -3.046875 -8 L -4.4375 -8 L -4.4375 -7.453125 L -3.09375 -7.453125 C -1.328125 -7.453125 -0.296875 -6.75 -0.296875 -5.796875 C -0.296875 -4.125 -2.578125 -4.125 -3 -4.125 Z M -9.859375 -4.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-4">
+<path style="stroke:none;" d="M -5.71875 -4.09375 C -8.09375 -4.09375 -10.328125 -5.078125 -10.328125 -6.96875 C -10.328125 -7.15625 -10.328125 -7.21875 -10.296875 -7.3125 C -10.203125 -7.109375 -10.0625 -6.71875 -9.390625 -6.71875 C -8.6875 -6.71875 -8.421875 -7.28125 -8.421875 -7.671875 C -8.421875 -8.171875 -8.734375 -8.65625 -9.390625 -8.65625 C -10.125 -8.65625 -10.8125 -8 -10.8125 -6.9375 C -10.8125 -4.859375 -8.5625 -4.140625 -8.09375 -4 L -8.09375 -3.96875 L -10.8125 -3.96875 L -10.546875 -0.6875 L -9.84375 -0.6875 C -9.84375 -2.359375 -9.671875 -2.546875 -8.46875 -2.546875 L -1.8125 -2.546875 C -0.71875 -2.546875 -0.71875 -2.28125 -0.71875 -0.6875 L 0 -0.6875 C -0.046875 -1.375 -0.046875 -2.71875 -0.046875 -3.453125 C -0.046875 -4.125 -0.046875 -5.859375 0 -6.421875 L -0.71875 -6.421875 L -0.71875 -5.9375 C -0.71875 -4.140625 -0.984375 -4.09375 -1.859375 -4.09375 Z M -5.71875 -4.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-5">
+<path style="stroke:none;" d="M -15.109375 -4.265625 C -15.75 -4.265625 -16.3125 -3.75 -16.3125 -3.0625 C -16.3125 -2.421875 -15.796875 -1.890625 -15.140625 -1.890625 C -14.40625 -1.890625 -13.9375 -2.484375 -13.9375 -3.0625 C -13.9375 -3.828125 -14.578125 -4.265625 -15.109375 -4.265625 Z M -10.546875 -0.890625 L -9.84375 -0.890625 C -9.84375 -2.453125 -9.6875 -2.671875 -8.484375 -2.671875 L -1.8125 -2.671875 C -0.71875 -2.671875 -0.71875 -2.40625 -0.71875 -0.8125 L 0 -0.8125 C -0.046875 -1.5 -0.046875 -2.671875 -0.046875 -3.390625 C -0.046875 -3.65625 -0.046875 -5.078125 0 -5.90625 L -0.71875 -5.90625 C -0.71875 -4.3125 -0.828125 -4.21875 -1.796875 -4.21875 L -10.8125 -4.21875 Z M -10.546875 -0.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-6">
+<path style="stroke:none;" d="M -5.6875 -9.390625 C -5.6875 -9.9375 -5.6875 -9.984375 -6.15625 -9.984375 C -8.640625 -9.984375 -10.9375 -8.65625 -10.9375 -5.6875 C -10.9375 -2.890625 -8.421875 -0.734375 -5.375 -0.734375 C -2.140625 -0.734375 0.25 -3.234375 0.25 -5.96875 C 0.25 -8.875 -2.40625 -9.984375 -2.921875 -9.984375 C -3.0625 -9.984375 -3.171875 -9.859375 -3.171875 -9.71875 C -3.171875 -9.515625 -3.046875 -9.46875 -2.921875 -9.421875 C -0.859375 -8.78125 -0.296875 -7.140625 -0.296875 -6.109375 C -0.296875 -5.078125 -0.984375 -2.59375 -5.21875 -2.59375 L -5.6875 -2.59375 Z M -6.15625 -2.625 C -10.015625 -2.828125 -10.453125 -4.984375 -10.453125 -5.671875 C -10.453125 -8.296875 -6.984375 -8.4375 -6.15625 -8.46875 Z M -6.15625 -2.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-7">
+<path style="stroke:none;" d="M -10.375 -8.046875 C -10.8125 -8.046875 -10.9375 -8.046875 -10.9375 -7.796875 C -10.9375 -7.609375 -10.40625 -7.140625 -10.1875 -6.96875 C -10.796875 -6.203125 -10.9375 -5.453125 -10.9375 -4.65625 C -10.9375 -1.6875 -9.328125 -0.8125 -7.96875 -0.8125 C -7.703125 -0.8125 -6.84375 -0.8125 -5.984375 -1.734375 C -5.296875 -2.53125 -5.125 -3.359375 -4.90625 -4.484375 C -4.640625 -5.84375 -4.5625 -6.15625 -4.078125 -6.765625 C -3.703125 -7.21875 -3.171875 -7.53125 -2.484375 -7.53125 C -1.421875 -7.53125 -0.25 -6.921875 -0.25 -4.765625 C -0.25 -3.140625 -1.171875 -1.96875 -3.625 -1.421875 C -4.078125 -1.328125 -4.09375 -1.328125 -4.125 -1.296875 C -4.21875 -1.25 -4.21875 -1.15625 -4.21875 -1.078125 C -4.21875 -0.8125 -4.09375 -0.8125 -3.65625 -0.8125 L -0.3125 -0.8125 C 0.125 -0.8125 0.25 -0.8125 0.25 -1.0625 C 0.25 -1.171875 0.21875 -1.203125 -0.296875 -1.625 C -0.46875 -1.734375 -0.515625 -1.734375 -0.90625 -2.109375 C 0.25 -3.046875 0.25 -4.359375 0.25 -4.78125 C 0.25 -7.359375 -1.171875 -8.640625 -3.109375 -8.640625 C -4.4375 -8.640625 -5.21875 -7.828125 -5.453125 -7.609375 C -6.203125 -6.71875 -6.359375 -6.0625 -6.640625 -4.4375 C -6.796875 -3.703125 -7.140625 -1.90625 -8.609375 -1.90625 C -9.375 -1.90625 -10.5 -2.421875 -10.5 -4.640625 C -10.5 -7.3125 -8.21875 -7.453125 -7.453125 -7.5 C -7.265625 -7.53125 -7.265625 -7.703125 -7.265625 -7.78125 C -7.265625 -8.046875 -7.390625 -8.046875 -7.828125 -8.046875 Z M -10.375 -8.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-8">
+<path style="stroke:none;" d="M 5.96875 -7.96875 C 5.890625 -7.96875 5.84375 -7.96875 5.421875 -7.5625 C 2.9375 -5.109375 -1.109375 -3.734375 -6.109375 -3.734375 C -10.875 -3.734375 -14.96875 -4.875 -17.859375 -7.734375 C -18.078125 -7.96875 -18.125 -7.96875 -18.203125 -7.96875 C -18.34375 -7.96875 -18.40625 -7.84375 -18.40625 -7.75 C -18.40625 -7.4375 -16.625 -5.421875 -14.234375 -4.21875 C -11.75 -2.96875 -9.125 -2.40625 -6.109375 -2.40625 C -3.921875 -2.40625 -1 -2.75 1.625 -4.015625 C 4.5625 -5.46875 6.15625 -7.484375 6.15625 -7.75 C 6.15625 -7.84375 6.109375 -7.96875 5.96875 -7.96875 Z M 5.96875 -7.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-9">
+<path style="stroke:none;" d="M -7.84375 -10.984375 C -9.890625 -10.984375 -11.875 -10.875 -13.734375 -9.984375 C -15.78125 -8.984375 -16.3125 -7.21875 -16.3125 -6.015625 C -16.3125 -4.59375 -15.609375 -2.84375 -13.5625 -1.9375 C -12.015625 -1.25 -10.5 -1 -7.84375 -1 C -5.46875 -1 -3.6875 -1.171875 -1.9375 -2.0625 C -0.078125 -3.015625 0.515625 -4.703125 0.515625 -5.984375 C 0.515625 -8.125 -0.765625 -9.34375 -2.1875 -10.0625 C -4.015625 -10.9375 -6.421875 -10.984375 -7.84375 -10.984375 Z M 0.03125 -5.984375 C 0.03125 -5.203125 -0.421875 -3.609375 -3.09375 -3.140625 C -4.5625 -2.875 -6.421875 -2.875 -8.140625 -2.875 C -10.15625 -2.875 -11.96875 -2.875 -13.421875 -3.265625 C -15.0625 -3.6875 -15.828125 -4.9375 -15.828125 -5.984375 C -15.828125 -6.921875 -15.265625 -8.34375 -13.15625 -8.8125 C -11.75 -9.125 -9.8125 -9.125 -8.140625 -9.125 C -6.5 -9.125 -4.640625 -9.125 -3.140625 -8.859375 C -0.4375 -8.390625 0.03125 -6.84375 0.03125 -5.984375 Z M 0.03125 -5.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-10">
+<path style="stroke:none;" d="M -4.125 -10.796875 L -4.125 -10.25 C -3.703125 -10.1875 -2.359375 -9.984375 -1.96875 -9.734375 C -1.734375 -9.5625 -1.734375 -8.171875 -1.734375 -7.4375 L -1.734375 -2.890625 C -2.3125 -3.5625 -3.875 -5.046875 -4.46875 -5.6875 C -7.90625 -9.421875 -9.171875 -10.796875 -11.609375 -10.796875 C -14.421875 -10.796875 -16.3125 -8.5625 -16.3125 -5.71875 C -16.3125 -2.875 -13.890625 -1.203125 -11.78125 -1.203125 C -10.53125 -1.203125 -10.53125 -2.28125 -10.53125 -2.359375 C -10.53125 -2.875 -10.890625 -3.515625 -11.671875 -3.515625 C -12.359375 -3.515625 -12.828125 -3.046875 -12.828125 -2.359375 C -12.828125 -2.140625 -12.828125 -2.078125 -12.8125 -2.015625 C -14.46875 -2.484375 -15.609375 -3.796875 -15.609375 -5.390625 C -15.609375 -7.484375 -13.859375 -8.75 -11.609375 -8.75 C -9.515625 -8.75 -7.703125 -7.5625 -6.140625 -6.15625 L -0.59375 -1.203125 L 0 -1.203125 L 0 -10.15625 Z M -4.125 -10.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-11">
+<path style="stroke:none;" d="M -14.0625 -3.140625 C -13.71875 -4.1875 -13.6875 -5.046875 -13.6875 -5.328125 C -13.6875 -8.09375 -15.71875 -9.859375 -16.0625 -9.859375 C -16.171875 -9.859375 -16.28125 -9.8125 -16.28125 -9.671875 C -16.28125 -9.609375 -16.28125 -9.5625 -16.1875 -9.34375 C -15.609375 -7.96875 -15.53125 -6.796875 -15.53125 -6.15625 C -15.53125 -4.53125 -16.015625 -3.390625 -16.21875 -2.921875 C -16.28125 -2.75 -16.28125 -2.703125 -16.28125 -2.671875 C -16.28125 -2.484375 -16.140625 -2.484375 -15.75 -2.484375 L -8.46875 -2.484375 C -8.015625 -2.484375 -7.875 -2.484375 -7.875 -2.765625 C -7.875 -2.890625 -7.90625 -2.921875 -8.1875 -3.171875 C -9.203125 -3.84375 -9.78125 -5 -9.78125 -6.234375 C -9.78125 -7.53125 -8.59375 -8.171875 -8.171875 -8.359375 C -7.21875 -8.78125 -6.015625 -8.8125 -5.078125 -8.8125 C -4.140625 -8.8125 -2.75 -8.8125 -1.640625 -8.125 C -0.765625 -7.578125 -0.140625 -6.625 -0.140625 -5.546875 C -0.140625 -3.921875 -1.25 -2.328125 -3.046875 -1.890625 C -3 -2.015625 -2.96875 -2.15625 -2.96875 -2.28125 C -2.96875 -2.703125 -3.21875 -3.359375 -4.046875 -3.359375 C -4.734375 -3.359375 -5.125 -2.890625 -5.125 -2.28125 C -5.125 -1.84375 -4.90625 -1.203125 -3.953125 -1.203125 C -1.859375 -1.203125 0.515625 -2.875 0.515625 -5.59375 C 0.515625 -8.359375 -1.8125 -10.796875 -4.9375 -10.796875 C -7.84375 -10.796875 -10.28125 -8.828125 -10.28125 -6.25 C -10.28125 -4.859375 -9.671875 -3.78125 -8.984375 -3.140625 Z M -14.0625 -3.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-12">
+<path style="stroke:none;" d="M -4.859375 -15.96875 C -5.8125 -15.96875 -5.9375 -16.0625 -5.9375 -17.640625 L -6.640625 -17.640625 C -6.59375 -17 -6.59375 -15.3125 -6.59375 -14.578125 C -6.59375 -13.78125 -6.59375 -11.65625 -6.640625 -10.984375 L -5.9375 -10.984375 L -5.9375 -11.75 C -5.9375 -13.90625 -5.640625 -13.984375 -4.765625 -13.984375 L -3.1875 -13.984375 C -0.390625 -13.984375 -0.203125 -10.765625 -0.203125 -10.125 C -0.203125 -8.1875 -1.375 -3.609375 -8.390625 -3.609375 C -15.484375 -3.609375 -16.5625 -8.25 -16.5625 -9.953125 C -16.5625 -12.09375 -15.015625 -14.640625 -10.671875 -15.28125 C -10.40625 -15.328125 -10.328125 -15.328125 -10.328125 -15.625 C -10.328125 -15.96875 -10.40625 -15.96875 -10.890625 -15.96875 L -16.703125 -15.96875 C -17.140625 -15.96875 -17.265625 -15.96875 -17.265625 -15.71875 C -17.265625 -15.578125 -17.21875 -15.546875 -16.96875 -15.40625 L -15.03125 -14.203125 C -15.921875 -13.5 -17.265625 -12 -17.265625 -9.671875 C -17.265625 -5.21875 -13.421875 -1.328125 -8.390625 -1.328125 C -3.3125 -1.328125 0.515625 -5.21875 0.515625 -9.6875 C 0.515625 -11.4375 -0.046875 -13.421875 -1.625 -14.328125 C -0.828125 -14.765625 -0.03125 -15.578125 -0.03125 -15.78125 C -0.03125 -15.96875 -0.171875 -15.96875 -0.5625 -15.96875 Z M -4.859375 -15.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-13">
+<path style="stroke:none;" d="M -14.328125 -14.984375 C -14.9375 -15.203125 -16.015625 -15.625 -16.046875 -17.546875 L -16.75 -17.546875 C -16.703125 -16.28125 -16.703125 -16.234375 -16.703125 -15.28125 C -16.703125 -14.625 -16.703125 -13.390625 -16.75 -12.78125 L -16.046875 -12.78125 C -16.015625 -14.03125 -15.328125 -14.40625 -14.84375 -14.40625 C -14.6875 -14.40625 -14.640625 -14.40625 -14.296875 -14.25 L -2.203125 -9.671875 L -14.96875 -4.828125 C -15.234375 -4.703125 -15.28125 -4.703125 -15.328125 -4.703125 C -16.046875 -4.703125 -16.046875 -5.9375 -16.046875 -6.546875 L -16.75 -6.546875 C -16.703125 -5.96875 -16.703125 -4.09375 -16.703125 -3.390625 C -16.703125 -2.703125 -16.703125 -1.03125 -16.75 -0.4375 L -16.046875 -0.4375 C -16.046875 -1.96875 -16.046875 -2.359375 -15.0625 -2.71875 L 0.046875 -8.46875 C 0.390625 -8.59375 0.515625 -8.640625 0.515625 -8.984375 C 0.515625 -9.328125 0.4375 -9.34375 0.03125 -9.515625 Z M -14.328125 -14.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph7-14">
+<path style="stroke:none;" d="M -6.109375 -6.921875 C -7.96875 -6.921875 -11.015625 -6.671875 -13.859375 -5.296875 C -16.796875 -3.84375 -18.40625 -1.84375 -18.40625 -1.5625 C -18.40625 -1.46875 -18.34375 -1.34375 -18.203125 -1.34375 C -18.125 -1.34375 -18.078125 -1.34375 -17.65625 -1.765625 C -15.1875 -4.21875 -11.140625 -5.59375 -6.140625 -5.59375 C -1.375 -5.59375 2.71875 -4.4375 5.625 -1.59375 C 5.84375 -1.34375 5.890625 -1.34375 5.96875 -1.34375 C 6.109375 -1.34375 6.15625 -1.46875 6.15625 -1.5625 C 6.15625 -1.890625 4.390625 -3.90625 1.984375 -5.109375 C -0.515625 -6.359375 -3.171875 -6.921875 -6.109375 -6.921875 Z M -6.109375 -6.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph8-1">
+<path style="stroke:none;" d="M -17.484375 -10.53125 C -17.515625 -10.53125 -17.890625 -10.671875 -17.9375 -10.671875 C -18.234375 -10.671875 -18.40625 -10.421875 -18.40625 -10.234375 C -18.40625 -10.109375 -18.40625 -9.890625 -17.859375 -9.6875 L 5.21875 -1.46875 C 5.25 -1.46875 5.625 -1.328125 5.671875 -1.328125 C 5.96875 -1.328125 6.140625 -1.5625 6.140625 -1.765625 C 6.140625 -1.90625 6.109375 -2.140625 5.59375 -2.3125 Z M -17.484375 -10.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-2">
+<path style="stroke:none;" d="M -1.171875 -4.515625 C -1.890625 -4.515625 -2.375 -3.921875 -2.375 -3.34375 C -2.375 -2.625 -1.796875 -2.140625 -1.203125 -2.140625 C -0.484375 -2.140625 0 -2.71875 0 -3.3125 C 0 -4.015625 -0.59375 -4.515625 -1.171875 -4.515625 Z M -1.171875 -4.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph8-3">
+<path style="stroke:none;" d="M -9.21875 -9.59375 C -9.21875 -9.125 -9.21875 -8.90625 -8.921875 -8.5625 C -8.8125 -8.421875 -8.4375 -8.140625 -8.046875 -8.140625 C -7.5625 -8.140625 -7.265625 -8.515625 -7.265625 -8.984375 C -7.265625 -9.5625 -7.75 -10.234375 -8.734375 -10.234375 C -9.90625 -10.234375 -10.8125 -9.09375 -10.8125 -7.40625 C -10.8125 -4.1875 -7.3125 -0.984375 -3.828125 -0.984375 C -1.6875 -0.984375 0.25 -2.3125 0.25 -4.8125 C 0.25 -8.140625 -2.359375 -10.25 -2.671875 -10.25 C -2.828125 -10.25 -2.9375 -10.109375 -2.9375 -10.015625 C -2.9375 -9.9375 -2.921875 -9.90625 -2.703125 -9.6875 C -0.609375 -8.125 -0.25 -5.796875 -0.25 -4.859375 C -0.25 -3.171875 -1.71875 -2.625 -2.9375 -2.625 C -3.796875 -2.625 -6.1875 -3.046875 -7.84375 -3.921875 C -9 -4.5625 -10.328125 -5.890625 -10.328125 -7.4375 C -10.328125 -7.75 -10.28125 -9.09375 -9.21875 -9.59375 Z M -9.21875 -9.59375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph9-1">
+<path style="stroke:none;" d="M -3.328125 -4.609375 C -3.578125 -4.875 -4.125 -5.5625 -4.34375 -5.8125 C -5.28125 -6.828125 -6.171875 -7.796875 -7.671875 -7.796875 C -9.609375 -7.796875 -10.875 -6.15625 -10.875 -4.125 C -10.875 -2.15625 -9.375 -0.859375 -7.921875 -0.859375 C -7.125 -0.859375 -7.015625 -1.5 -7.015625 -1.734375 C -7.015625 -2.078125 -7.25 -2.578125 -7.875 -2.578125 C -8.734375 -2.578125 -8.734375 -1.765625 -8.734375 -1.5625 C -9.921875 -2.046875 -10.328125 -3.140625 -10.328125 -3.9375 C -10.328125 -5.453125 -9.03125 -6.25 -7.671875 -6.25 C -5.96875 -6.25 -4.71875 -5.046875 -2.75 -3.125 L -0.625 -1.0625 C -0.4375 -0.859375 -0.40625 -0.859375 0 -0.859375 L 0 -7.328125 L -2.921875 -7.796875 L -2.921875 -7.296875 C -2.59375 -7.234375 -1.78125 -7.109375 -1.46875 -6.90625 C -1.34375 -6.8125 -1.34375 -5.578125 -1.34375 -5.3125 L -1.34375 -2.40625 Z M -3.328125 -4.609375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph9-2">
+<path style="stroke:none;" d="M -10.578125 -6.4375 C -10.90625 -6.4375 -11.03125 -6.4375 -11.03125 -6.09375 C -11.03125 -5.890625 -11.015625 -5.875 -10.78125 -5.703125 L -3.21875 -0.484375 L -2.6875 -0.484375 L -2.6875 -5.09375 L -1.328125 -5.09375 C -0.71875 -5.09375 -0.546875 -5.046875 -0.546875 -3.796875 L -0.546875 -3.421875 L 0 -3.421875 C -0.046875 -4.8125 -0.046875 -4.84375 -0.046875 -5.765625 C -0.046875 -6.703125 -0.046875 -6.734375 0 -8.125 L -0.546875 -8.125 L -0.546875 -7.75 C -0.546875 -6.484375 -0.71875 -6.4375 -1.328125 -6.4375 L -2.6875 -6.4375 L -2.6875 -8.171875 L -3.21875 -8.171875 L -3.21875 -6.4375 Z M -9.25 -5.21875 L -3.21875 -5.21875 L -3.21875 -1.0625 Z M -9.25 -5.21875 "/>
+</symbol>
+</g>
+</defs>
+<g id="surface1">
+<path style="fill-rule:nonzero;fill:rgb(100%,100%,100%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,100%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00096875 -0.00121875 L 0.00096875 428.049562 L 566.934562 428.049562 L 566.934562 -0.00121875 Z M 0.00096875 -0.00121875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 L 498.903312 402.365969 L 498.903312 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 82.665031 71.54175 C 82.665031 72.201906 82.129875 72.737062 81.469719 72.737062 C 80.805656 72.737062 80.2705 72.201906 80.2705 71.54175 C 80.2705 70.877687 80.805656 70.342531 81.469719 70.342531 C 82.129875 70.342531 82.665031 70.877687 82.665031 71.54175 Z M 82.665031 71.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.860344 82.006594 C 86.860344 82.66675 86.325187 83.201906 85.665031 83.201906 C 85.004875 83.201906 84.465812 82.66675 84.465812 82.006594 C 84.465812 81.346437 85.004875 80.811281 85.665031 80.811281 C 86.325187 80.811281 86.860344 81.346437 86.860344 82.006594 Z M 86.860344 82.006594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.860344 118.326906 L 89.860344 118.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 89.860344 122.987062 L 89.860344 123.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 91.055656 120.713625 C 91.055656 121.373781 90.5205 121.908937 89.860344 121.908937 C 89.200187 121.908937 88.661125 121.373781 88.661125 120.713625 C 88.661125 120.049562 89.200187 119.514406 89.860344 119.514406 C 90.5205 119.514406 91.055656 120.049562 91.055656 120.713625 Z M 91.055656 120.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.055656 303.342531 L 94.055656 306.178469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.055656 310.733156 L 94.055656 313.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 95.250969 308.455812 C 95.250969 309.115969 94.715812 309.651125 94.055656 309.651125 C 93.3955 309.651125 92.856437 309.115969 92.856437 308.455812 C 92.856437 307.795656 93.3955 307.2605 94.055656 307.2605 C 94.715812 307.2605 95.250969 307.795656 95.250969 308.455812 Z M 95.250969 308.455812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 98.250969 368.424562 L 98.250969 371.924562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 98.250969 376.475344 L 98.250969 379.971437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 99.446281 374.201906 C 99.446281 374.862062 98.911125 375.397219 98.250969 375.397219 C 97.590812 375.397219 97.05175 374.862062 97.05175 374.201906 C 97.05175 373.537844 97.590812 373.002687 98.250969 373.002687 C 98.911125 373.002687 99.446281 373.537844 99.446281 374.201906 Z M 99.446281 374.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 102.446281 374.799562 L 102.446281 378.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 102.446281 382.908937 L 102.446281 386.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 103.641594 380.631594 C 103.641594 381.29175 103.106437 381.830812 102.446281 381.830812 C 101.786125 381.830812 101.247062 381.29175 101.247062 380.631594 C 101.247062 379.971437 101.786125 379.436281 102.446281 379.436281 C 103.106437 379.436281 103.641594 379.971437 103.641594 380.631594 Z M 103.641594 380.631594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 106.641594 351.690187 L 106.641594 355.022219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 106.641594 359.576906 L 106.641594 362.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 107.836906 357.299562 C 107.836906 357.959719 107.30175 358.498781 106.641594 358.498781 C 105.981437 358.498781 105.442375 357.959719 105.442375 357.299562 C 105.442375 356.639406 105.981437 356.10425 106.641594 356.10425 C 107.30175 356.10425 107.836906 356.639406 107.836906 357.299562 Z M 107.836906 357.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 110.836906 347.803469 L 110.836906 351.096437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 110.836906 355.651125 L 110.836906 358.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 112.032219 353.377687 C 112.032219 354.037844 111.497062 354.573 110.836906 354.573 C 110.17675 354.573 109.637687 354.037844 109.637687 353.377687 C 109.637687 352.717531 110.17675 352.178469 110.836906 352.178469 C 111.497062 352.178469 112.032219 352.717531 112.032219 353.377687 Z M 112.032219 353.377687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 115.032219 332.365969 L 115.032219 335.506594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 115.032219 340.061281 L 115.032219 343.201906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 116.227531 337.787844 C 116.227531 338.448 115.692375 338.983156 115.032219 338.983156 C 114.372062 338.983156 113.833 338.448 113.833 337.787844 C 113.833 337.123781 114.372062 336.588625 115.032219 336.588625 C 115.692375 336.588625 116.227531 337.123781 116.227531 337.787844 Z M 116.227531 337.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.227531 319.740969 L 119.227531 322.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 119.227531 327.307375 L 119.227531 330.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 120.422844 325.030031 C 120.422844 325.690187 119.887687 326.225344 119.227531 326.225344 C 118.567375 326.225344 118.028312 325.690187 118.028312 325.030031 C 118.028312 324.369875 118.567375 323.834719 119.227531 323.834719 C 119.887687 323.834719 120.422844 324.369875 120.422844 325.030031 Z M 120.422844 325.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 123.422844 314.346437 L 123.422844 317.299562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 123.422844 321.85425 L 123.422844 324.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 124.618156 319.576906 C 124.618156 320.237062 124.083 320.772219 123.422844 320.772219 C 122.762687 320.772219 122.223625 320.237062 122.223625 319.576906 C 122.223625 318.91675 122.762687 318.377687 123.422844 318.377687 C 124.083 318.377687 124.618156 318.91675 124.618156 319.576906 Z M 124.618156 319.576906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.618156 283.069094 L 127.618156 285.682375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.618156 290.237062 L 127.618156 292.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 128.813469 287.959719 C 128.813469 288.619875 128.278312 289.155031 127.618156 289.155031 C 126.958 289.155031 126.418937 288.619875 126.418937 287.959719 C 126.418937 287.295656 126.958 286.7605 127.618156 286.7605 C 128.278312 286.7605 128.813469 287.295656 128.813469 287.959719 Z M 128.813469 287.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 131.813469 280.264406 L 131.813469 282.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 131.813469 287.401125 L 131.813469 289.987062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 133.008781 285.123781 C 133.008781 285.783937 132.473625 286.319094 131.813469 286.319094 C 131.153312 286.319094 130.61425 285.783937 130.61425 285.123781 C 130.61425 284.463625 131.153312 283.928469 131.813469 283.928469 C 132.473625 283.928469 133.008781 284.463625 133.008781 285.123781 Z M 133.008781 285.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 136.008781 266.252687 L 136.008781 268.674562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 136.008781 273.22925 L 136.008781 275.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 137.204094 270.951906 C 137.204094 271.612062 136.668937 272.147219 136.008781 272.147219 C 135.348625 272.147219 134.809562 271.612062 134.809562 270.951906 C 134.809562 270.29175 135.348625 269.752687 136.008781 269.752687 C 136.668937 269.752687 137.204094 270.29175 137.204094 270.951906 Z M 137.204094 270.951906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.204094 257.850344 L 140.204094 260.170656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 140.204094 264.725344 L 140.204094 267.045656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.399406 262.448 C 141.399406 263.108156 140.86425 263.643312 140.204094 263.643312 C 139.543937 263.643312 139.004875 263.108156 139.004875 262.448 C 139.004875 261.787844 139.543937 261.248781 140.204094 261.248781 C 140.86425 261.248781 141.399406 261.787844 141.399406 262.448 Z M 141.399406 262.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 144.399406 237.280031 L 144.399406 239.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 144.399406 243.901125 L 144.399406 245.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 145.594719 241.623781 C 145.594719 242.283937 145.059562 242.819094 144.399406 242.819094 C 143.73925 242.819094 143.200187 242.283937 143.200187 241.623781 C 143.200187 240.963625 143.73925 240.424562 144.399406 240.424562 C 145.059562 240.424562 145.594719 240.963625 145.594719 241.623781 Z M 145.594719 241.623781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.594719 239.537844 L 148.594719 241.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 148.594719 246.190187 L 148.594719 248.283937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 149.790031 243.912844 C 149.790031 244.573 149.254875 245.108156 148.594719 245.108156 C 147.934562 245.108156 147.3955 244.573 147.3955 243.912844 C 147.3955 243.252687 147.934562 242.717531 148.594719 242.717531 C 149.254875 242.717531 149.790031 243.252687 149.790031 243.912844 Z M 149.790031 243.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 152.790031 227.268312 L 152.790031 229.205812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 152.790031 233.7605 L 152.790031 235.698 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 153.985344 231.483156 C 153.985344 232.143312 153.450187 232.678469 152.790031 232.678469 C 152.129875 232.678469 151.590812 232.143312 151.590812 231.483156 C 151.590812 230.823 152.129875 230.287844 152.790031 230.287844 C 153.450187 230.287844 153.985344 230.823 153.985344 231.483156 Z M 153.985344 231.483156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 216.725344 L 156.985344 218.522219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 156.985344 223.076906 L 156.985344 224.873781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 158.180656 220.799562 C 158.180656 221.459719 157.6455 221.994875 156.985344 221.994875 C 156.325187 221.994875 155.786125 221.459719 155.786125 220.799562 C 155.786125 220.139406 156.325187 219.600344 156.985344 219.600344 C 157.6455 219.600344 158.180656 220.139406 158.180656 220.799562 Z M 158.180656 220.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 206.401125 L 161.180656 208.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 161.180656 212.608156 L 161.180656 214.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 162.375969 210.330812 C 162.375969 210.990969 161.840812 211.530031 161.180656 211.530031 C 160.5205 211.530031 159.981437 210.990969 159.981437 210.330812 C 159.981437 209.670656 160.5205 209.1355 161.180656 209.1355 C 161.840812 209.1355 162.375969 209.670656 162.375969 210.330812 Z M 162.375969 210.330812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 197.694094 L 165.375969 199.225344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 165.375969 203.776125 L 165.375969 205.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 166.571281 201.502687 C 166.571281 202.162844 166.036125 202.698 165.375969 202.698 C 164.715812 202.698 164.17675 202.162844 164.17675 201.502687 C 164.17675 200.838625 164.715812 200.303469 165.375969 200.303469 C 166.036125 200.303469 166.571281 200.838625 166.571281 201.502687 Z M 166.571281 201.502687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 185.658937 L 169.571281 187.014406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 169.571281 191.565187 L 169.571281 192.920656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 170.766594 189.29175 C 170.766594 189.951906 170.231437 190.487062 169.571281 190.487062 C 168.911125 190.487062 168.372062 189.951906 168.372062 189.29175 C 168.372062 188.627687 168.911125 188.092531 169.571281 188.092531 C 170.231437 188.092531 170.766594 188.627687 170.766594 189.29175 Z M 170.766594 189.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 173.766594 177.932375 L 173.766594 179.162844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 173.766594 183.717531 L 173.766594 184.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 174.961906 181.440187 C 174.961906 182.100344 174.42675 182.6355 173.766594 182.6355 C 173.106437 182.6355 172.571281 182.100344 172.571281 181.440187 C 172.571281 180.780031 173.106437 180.244875 173.766594 180.244875 C 174.42675 180.244875 174.961906 180.780031 174.961906 181.440187 Z M 174.961906 181.440187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.961906 171.061281 L 177.961906 172.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 177.961906 176.737062 L 177.961906 177.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 179.157219 174.463625 C 179.157219 175.123781 178.622062 175.658937 177.961906 175.658937 C 177.30175 175.658937 176.762687 175.123781 176.762687 174.463625 C 176.762687 173.799562 177.30175 173.264406 177.961906 173.264406 C 178.622062 173.264406 179.157219 173.799562 179.157219 174.463625 Z M 179.157219 174.463625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 182.157219 169.561281 L 182.157219 170.658937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 182.157219 175.213625 L 182.157219 176.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 183.352531 172.936281 C 183.352531 173.596437 182.817375 174.131594 182.157219 174.131594 C 181.497062 174.131594 180.958 173.596437 180.958 172.936281 C 180.958 172.276125 181.497062 171.737062 182.157219 171.737062 C 182.817375 171.737062 183.352531 172.276125 183.352531 172.936281 Z M 183.352531 172.936281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 186.352531 159.053469 L 186.352531 159.975344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 186.352531 164.526125 L 186.352531 165.448 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 187.547844 162.252687 C 187.547844 162.912844 187.012687 163.448 186.352531 163.448 C 185.692375 163.448 185.157219 162.912844 185.157219 162.252687 C 185.157219 161.588625 185.692375 161.053469 186.352531 161.053469 C 187.012687 161.053469 187.547844 161.588625 187.547844 162.252687 Z M 187.547844 162.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 190.547844 154.553469 L 190.547844 155.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 190.547844 159.948 L 190.547844 160.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 191.743156 157.670656 C 191.743156 158.334719 191.208 158.869875 190.547844 158.869875 C 189.887687 158.869875 189.348625 158.334719 189.348625 157.670656 C 189.348625 157.0105 189.887687 156.475344 190.547844 156.475344 C 191.208 156.475344 191.743156 157.0105 191.743156 157.670656 Z M 191.743156 157.670656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 143.6355 L 194.743156 144.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.743156 148.826906 L 194.743156 149.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 195.938469 146.549562 C 195.938469 147.213625 195.403312 147.748781 194.743156 147.748781 C 194.083 147.748781 193.543937 147.213625 193.543937 146.549562 C 193.543937 145.889406 194.083 145.35425 194.743156 145.35425 C 195.403312 145.35425 195.938469 145.889406 195.938469 146.549562 Z M 195.938469 146.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 140.10425 L 198.938469 140.674562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.938469 145.22925 L 198.938469 145.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 200.133781 142.951906 C 200.133781 143.615969 199.598625 144.151125 198.938469 144.151125 C 198.278312 144.151125 197.743156 143.615969 197.743156 142.951906 C 197.743156 142.29175 198.278312 141.756594 198.938469 141.756594 C 199.598625 141.756594 200.133781 142.29175 200.133781 142.951906 Z M 200.133781 142.951906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 133.690187 L 203.133781 134.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 203.133781 138.690187 L 203.133781 139.131594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 204.329094 136.412844 C 204.329094 137.073 203.793937 137.608156 203.133781 137.608156 C 202.473625 137.608156 201.934562 137.073 201.934562 136.412844 C 201.934562 135.748781 202.473625 135.213625 203.133781 135.213625 C 203.793937 135.213625 204.329094 135.748781 204.329094 136.412844 Z M 204.329094 136.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 127.924562 L 207.329094 128.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 207.329094 132.799562 L 207.329094 133.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 208.524406 130.526125 C 208.524406 131.186281 207.98925 131.721437 207.329094 131.721437 C 206.668937 131.721437 206.129875 131.186281 206.129875 130.526125 C 206.129875 129.862062 206.668937 129.326906 207.329094 129.326906 C 207.98925 129.326906 208.524406 129.862062 208.524406 130.526125 Z M 208.524406 130.526125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 131.233156 L 211.524406 131.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 211.524406 136.182375 L 211.524406 136.573 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 212.719719 133.905031 C 212.719719 134.565187 212.184562 135.100344 211.524406 135.100344 C 210.86425 135.100344 210.329094 134.565187 210.329094 133.905031 C 210.329094 133.244875 210.86425 132.705812 211.524406 132.705812 C 212.184562 132.705812 212.719719 133.244875 212.719719 133.905031 Z M 212.719719 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 117.686281 L 215.719719 117.780031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 215.719719 122.334719 L 215.719719 122.428469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 216.915031 120.057375 C 216.915031 120.717531 216.379875 121.252687 215.719719 121.252687 C 215.059562 121.252687 214.524406 120.717531 214.524406 120.057375 C 214.524406 119.397219 215.059562 118.862062 215.719719 118.862062 C 216.379875 118.862062 216.915031 119.397219 216.915031 120.057375 Z M 216.915031 120.057375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 117.901125 L 219.915031 117.998781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 219.915031 122.553469 L 219.915031 122.651125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 221.110344 120.276125 C 221.110344 120.936281 220.575187 121.471437 219.915031 121.471437 C 219.254875 121.471437 218.715812 120.936281 218.715812 120.276125 C 218.715812 119.615969 219.254875 119.076906 219.915031 119.076906 C 220.575187 119.076906 221.110344 119.615969 221.110344 120.276125 Z M 221.110344 120.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 116.619875 L 224.110344 116.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 224.110344 121.244875 L 224.110344 121.315187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 225.305656 118.967531 C 225.305656 119.627687 224.7705 120.162844 224.110344 120.162844 C 223.450187 120.162844 222.915031 119.627687 222.915031 118.967531 C 222.915031 118.307375 223.450187 117.772219 224.110344 117.772219 C 224.7705 117.772219 225.305656 118.307375 225.305656 118.967531 Z M 225.305656 118.967531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 229.500969 112.643312 C 229.500969 113.303469 228.965812 113.838625 228.305656 113.838625 C 227.6455 113.838625 227.110344 113.303469 227.110344 112.643312 C 227.110344 111.983156 227.6455 111.448 228.305656 111.448 C 228.965812 111.448 229.500969 111.983156 229.500969 112.643312 Z M 229.500969 112.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 233.696281 109.91675 C 233.696281 110.580812 233.161125 111.115969 232.500969 111.115969 C 231.840812 111.115969 231.30175 110.580812 231.30175 109.91675 C 231.30175 109.256594 231.840812 108.721437 232.500969 108.721437 C 233.161125 108.721437 233.696281 109.256594 233.696281 109.91675 Z M 233.696281 109.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 237.891594 109.91675 C 237.891594 110.580812 237.356437 111.115969 236.696281 111.115969 C 236.036125 111.115969 235.500969 110.580812 235.500969 109.91675 C 235.500969 109.256594 236.036125 108.721437 236.696281 108.721437 C 237.356437 108.721437 237.891594 109.256594 237.891594 109.91675 Z M 237.891594 109.91675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 242.086906 110.79175 C 242.086906 111.451906 241.55175 111.987062 240.891594 111.987062 C 240.231437 111.987062 239.696281 111.451906 239.696281 110.79175 C 239.696281 110.127687 240.231437 109.592531 240.891594 109.592531 C 241.55175 109.592531 242.086906 110.127687 242.086906 110.79175 Z M 242.086906 110.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 246.282219 105.119875 C 246.282219 105.780031 245.747062 106.319094 245.086906 106.319094 C 244.42675 106.319094 243.891594 105.780031 243.891594 105.119875 C 243.891594 104.459719 244.42675 103.924562 245.086906 103.924562 C 245.747062 103.924562 246.282219 104.459719 246.282219 105.119875 Z M 246.282219 105.119875 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 250.477531 102.287844 C 250.477531 102.948 249.942375 103.483156 249.282219 103.483156 C 248.622062 103.483156 248.086906 102.948 248.086906 102.287844 C 248.086906 101.623781 248.622062 101.088625 249.282219 101.088625 C 249.942375 101.088625 250.477531 101.623781 250.477531 102.287844 Z M 250.477531 102.287844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 254.672844 109.045656 C 254.672844 109.705812 254.137687 110.240969 253.477531 110.240969 C 252.817375 110.240969 252.282219 109.705812 252.282219 109.045656 C 252.282219 108.3855 252.817375 107.850344 253.477531 107.850344 C 254.137687 107.850344 254.672844 108.3855 254.672844 109.045656 Z M 254.672844 109.045656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 258.868156 110.79175 C 258.868156 111.451906 258.333 111.987062 257.672844 111.987062 C 257.012687 111.987062 256.477531 111.451906 256.477531 110.79175 C 256.477531 110.127687 257.012687 109.592531 257.672844 109.592531 C 258.333 109.592531 258.868156 110.127687 258.868156 110.79175 Z M 258.868156 110.79175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 263.063469 107.194094 C 263.063469 107.85425 262.528312 108.389406 261.868156 108.389406 C 261.208 108.389406 260.672844 107.85425 260.672844 107.194094 C 260.672844 106.530031 261.208 105.994875 261.868156 105.994875 C 262.528312 105.994875 263.063469 106.530031 263.063469 107.194094 Z M 263.063469 107.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 267.258781 106.647219 C 267.258781 107.307375 266.723625 107.842531 266.063469 107.842531 C 265.403312 107.842531 264.868156 107.307375 264.868156 106.647219 C 264.868156 105.987062 265.403312 105.451906 266.063469 105.451906 C 266.723625 105.451906 267.258781 105.987062 267.258781 106.647219 Z M 267.258781 106.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 271.454094 108.393312 C 271.454094 109.053469 270.918937 109.588625 270.258781 109.588625 C 269.598625 109.588625 269.063469 109.053469 269.063469 108.393312 C 269.063469 107.72925 269.598625 107.194094 270.258781 107.194094 C 270.918937 107.194094 271.454094 107.72925 271.454094 108.393312 Z M 271.454094 108.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 275.649406 115.04175 C 275.649406 115.701906 275.11425 116.240969 274.454094 116.240969 C 273.793937 116.240969 273.258781 115.701906 273.258781 115.04175 C 273.258781 114.381594 273.793937 113.846437 274.454094 113.846437 C 275.11425 113.846437 275.649406 114.381594 275.649406 115.04175 Z M 275.649406 115.04175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 115.237062 L 278.649406 115.272219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 278.649406 119.826906 L 278.649406 119.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 279.844719 117.549562 C 279.844719 118.209719 279.309562 118.744875 278.649406 118.744875 C 277.98925 118.744875 277.454094 118.209719 277.454094 117.549562 C 277.454094 116.889406 277.98925 116.35425 278.649406 116.35425 C 279.309562 116.35425 279.844719 116.889406 279.844719 117.549562 Z M 279.844719 117.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 284.040031 112.971437 C 284.040031 113.631594 283.504875 114.16675 282.844719 114.16675 C 282.184562 114.16675 281.649406 113.631594 281.649406 112.971437 C 281.649406 112.311281 282.184562 111.772219 282.844719 111.772219 C 283.504875 111.772219 284.040031 112.311281 284.040031 112.971437 Z M 284.040031 112.971437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 119.498781 L 287.040031 119.6355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 287.040031 124.186281 L 287.040031 124.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 288.235344 121.912844 C 288.235344 122.573 287.700187 123.108156 287.040031 123.108156 C 286.379875 123.108156 285.844719 122.573 285.844719 121.912844 C 285.844719 121.248781 286.379875 120.713625 287.040031 120.713625 C 287.700187 120.713625 288.235344 121.248781 288.235344 121.912844 Z M 288.235344 121.912844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 121.201906 L 291.235344 121.377687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 291.235344 125.932375 L 291.235344 126.108156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 292.430656 123.655031 C 292.430656 124.315187 291.8955 124.85425 291.235344 124.85425 C 290.575187 124.85425 290.040031 124.315187 290.040031 123.655031 C 290.040031 122.994875 290.575187 122.459719 291.235344 122.459719 C 291.8955 122.459719 292.430656 122.994875 292.430656 123.655031 Z M 292.430656 123.655031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 124.5105 L 295.430656 124.7605 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 295.430656 129.311281 L 295.430656 129.561281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 296.625969 127.033937 C 296.625969 127.698 296.090812 128.233156 295.430656 128.233156 C 294.7705 128.233156 294.235344 127.698 294.235344 127.033937 C 294.235344 126.373781 294.7705 125.838625 295.430656 125.838625 C 296.090812 125.838625 296.625969 126.373781 296.625969 127.033937 Z M 296.625969 127.033937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 130.698 L 299.625969 131.080812 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 299.625969 135.6355 L 299.625969 136.018312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 300.821281 133.358156 C 300.821281 134.018312 300.286125 134.557375 299.625969 134.557375 C 298.965812 134.557375 298.430656 134.018312 298.430656 133.358156 C 298.430656 132.698 298.965812 132.162844 299.625969 132.162844 C 300.286125 132.162844 300.821281 132.698 300.821281 133.358156 Z M 300.821281 133.358156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 138.073 L 303.821281 138.60425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 303.821281 143.158937 L 303.821281 143.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 305.016594 140.881594 C 305.016594 141.54175 304.481437 142.076906 303.821281 142.076906 C 303.161125 142.076906 302.625969 141.54175 302.625969 140.881594 C 302.625969 140.221437 303.161125 139.686281 303.821281 139.686281 C 304.481437 139.686281 305.016594 140.221437 305.016594 140.881594 Z M 305.016594 140.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 136.576906 L 308.016594 137.076906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 308.016594 141.631594 L 308.016594 142.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 309.211906 139.35425 C 309.211906 140.018312 308.67675 140.553469 308.016594 140.553469 C 307.356437 140.553469 306.821281 140.018312 306.821281 139.35425 C 306.821281 138.694094 307.356437 138.158937 308.016594 138.158937 C 308.67675 138.158937 309.211906 138.694094 309.211906 139.35425 Z M 309.211906 139.35425 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 146.737062 L 312.211906 147.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 312.211906 151.990969 L 312.211906 152.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 313.407219 149.713625 C 313.407219 150.373781 312.872062 150.908937 312.211906 150.908937 C 311.55175 150.908937 311.016594 150.373781 311.016594 149.713625 C 311.016594 149.053469 311.55175 148.514406 312.211906 148.514406 C 312.872062 148.514406 313.407219 149.053469 313.407219 149.713625 Z M 313.407219 149.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 153.268312 L 316.407219 154.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 316.407219 158.639406 L 316.407219 159.459719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 317.602531 156.362062 C 317.602531 157.026125 317.067375 157.561281 316.407219 157.561281 C 315.747062 157.561281 315.211906 157.026125 315.211906 156.362062 C 315.211906 155.701906 315.747062 155.16675 316.407219 155.16675 C 317.067375 155.16675 317.602531 155.701906 317.602531 156.362062 Z M 317.602531 156.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 320.602531 156.268312 L 320.602531 157.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 320.602531 161.694094 L 320.602531 162.565187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 321.797844 159.41675 C 321.797844 160.076906 321.262687 160.612062 320.602531 160.612062 C 319.942375 160.612062 319.407219 160.076906 319.407219 159.41675 C 319.407219 158.756594 319.942375 158.221437 320.602531 158.221437 C 321.262687 158.221437 321.797844 158.756594 321.797844 159.41675 Z M 321.797844 159.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.797844 165.701906 L 324.797844 166.733156 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 324.797844 171.287844 L 324.797844 172.323 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 325.993156 169.0105 C 325.993156 169.670656 325.458 170.205812 324.797844 170.205812 C 324.137687 170.205812 323.602531 169.670656 323.602531 169.0105 C 323.602531 168.350344 324.137687 167.815187 324.797844 167.815187 C 325.458 167.815187 325.993156 168.350344 325.993156 169.0105 Z M 325.993156 169.0105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 328.993156 173.959719 L 328.993156 175.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 328.993156 179.682375 L 328.993156 180.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 330.188469 177.405031 C 330.188469 178.065187 329.653312 178.60425 328.993156 178.60425 C 328.333 178.60425 327.797844 178.065187 327.797844 177.405031 C 327.797844 176.744875 328.333 176.209719 328.993156 176.209719 C 329.653312 176.209719 330.188469 176.744875 330.188469 177.405031 Z M 330.188469 177.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 333.188469 177.073 L 333.188469 178.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 333.188469 182.846437 L 333.188469 184.065187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 334.383781 180.569094 C 334.383781 181.22925 333.848625 181.764406 333.188469 181.764406 C 332.528312 181.764406 331.993156 181.22925 331.993156 180.569094 C 331.993156 179.905031 332.528312 179.369875 333.188469 179.369875 C 333.848625 179.369875 334.383781 179.905031 334.383781 180.569094 Z M 334.383781 180.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 337.383781 181.795656 L 337.383781 183.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 337.383781 187.643312 L 337.383781 188.936281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 338.579094 185.365969 C 338.579094 186.026125 338.043937 186.561281 337.383781 186.561281 C 336.723625 186.561281 336.188469 186.026125 336.188469 185.365969 C 336.188469 184.705812 336.723625 184.16675 337.383781 184.16675 C 338.043937 184.16675 338.579094 184.705812 338.579094 185.365969 Z M 338.579094 185.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 341.579094 197.584719 L 341.579094 199.115969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 341.579094 203.670656 L 341.579094 205.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 342.774406 201.393312 C 342.774406 202.053469 342.23925 202.588625 341.579094 202.588625 C 340.918937 202.588625 340.383781 202.053469 340.383781 201.393312 C 340.383781 200.72925 340.918937 200.194094 341.579094 200.194094 C 342.23925 200.194094 342.774406 200.72925 342.774406 201.393312 Z M 342.774406 201.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 345.774406 203.928469 L 345.774406 205.549562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 345.774406 210.100344 L 345.774406 211.721437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 346.969719 207.823 C 346.969719 208.487062 346.434562 209.022219 345.774406 209.022219 C 345.11425 209.022219 344.579094 208.487062 344.579094 207.823 C 344.579094 207.162844 345.11425 206.627687 345.774406 206.627687 C 346.434562 206.627687 346.969719 207.162844 346.969719 207.823 Z M 346.969719 207.823 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 349.969719 209.733156 L 349.969719 211.436281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 349.969719 215.987062 L 349.969719 217.690187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 351.165031 213.713625 C 351.165031 214.373781 350.629875 214.908937 349.969719 214.908937 C 349.309562 214.908937 348.774406 214.373781 348.774406 213.713625 C 348.774406 213.049562 349.309562 212.514406 349.969719 212.514406 C 350.629875 212.514406 351.165031 213.049562 351.165031 213.713625 Z M 351.165031 213.713625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.165031 221.994875 L 354.165031 223.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 354.165031 228.41675 L 354.165031 230.287844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 355.360344 226.139406 C 355.360344 226.803469 354.825187 227.338625 354.165031 227.338625 C 353.504875 227.338625 352.969719 226.803469 352.969719 226.139406 C 352.969719 225.47925 353.504875 224.944094 354.165031 224.944094 C 354.825187 224.944094 355.360344 225.47925 355.360344 226.139406 Z M 355.360344 226.139406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 358.360344 230.60425 L 358.360344 232.584719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 358.360344 237.139406 L 358.360344 239.123781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 359.555656 234.862062 C 359.555656 235.526125 359.0205 236.061281 358.360344 236.061281 C 357.700187 236.061281 357.165031 235.526125 357.165031 234.862062 C 357.165031 234.201906 357.700187 233.66675 358.360344 233.66675 C 359.0205 233.66675 359.555656 234.201906 359.555656 234.862062 Z M 359.555656 234.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 362.555656 244.3855 L 362.555656 246.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 362.555656 251.096437 L 362.555656 253.252687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 363.750969 248.819094 C 363.750969 249.47925 363.215812 250.014406 362.555656 250.014406 C 361.8955 250.014406 361.360344 249.47925 361.360344 248.819094 C 361.360344 248.158937 361.8955 247.623781 362.555656 247.623781 C 363.215812 247.623781 363.750969 248.158937 363.750969 248.819094 Z M 363.750969 248.819094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 366.750969 244.924562 L 366.750969 247.088625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 366.750969 251.639406 L 366.750969 253.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 367.946281 249.362062 C 367.946281 250.026125 367.411125 250.561281 366.750969 250.561281 C 366.090812 250.561281 365.555656 250.026125 365.555656 249.362062 C 365.555656 248.701906 366.090812 248.16675 366.750969 248.16675 C 367.411125 248.16675 367.946281 248.701906 367.946281 249.362062 Z M 367.946281 249.362062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 370.946281 253.862062 L 370.946281 256.1355 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 370.946281 260.690187 L 370.946281 262.963625 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 372.141594 258.412844 C 372.141594 259.073 371.606437 259.608156 370.946281 259.608156 C 370.286125 259.608156 369.750969 259.073 369.750969 258.412844 C 369.750969 257.752687 370.286125 257.217531 370.946281 257.217531 C 371.606437 257.217531 372.141594 257.752687 372.141594 258.412844 Z M 372.141594 258.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 375.141594 263.881594 L 375.141594 266.276125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 375.141594 270.830812 L 375.141594 273.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 376.336906 268.553469 C 376.336906 269.213625 375.80175 269.748781 375.141594 269.748781 C 374.481437 269.748781 373.946281 269.213625 373.946281 268.553469 C 373.946281 267.893312 374.481437 267.35425 375.141594 267.35425 C 375.80175 267.35425 376.336906 267.893312 376.336906 268.553469 Z M 376.336906 268.553469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 379.336906 270.565187 L 379.336906 273.033937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 379.336906 277.588625 L 379.336906 280.061281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 380.532219 275.311281 C 380.532219 275.975344 379.997062 276.5105 379.336906 276.5105 C 378.67675 276.5105 378.141594 275.975344 378.141594 275.311281 C 378.141594 274.651125 378.67675 274.115969 379.336906 274.115969 C 379.997062 274.115969 380.532219 274.651125 380.532219 275.311281 Z M 380.532219 275.311281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 285.549562 L 383.532219 288.190187 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 383.532219 292.744875 L 383.532219 295.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 384.727531 290.467531 C 384.727531 291.127687 384.192375 291.662844 383.532219 291.662844 C 382.872062 291.662844 382.336906 291.127687 382.336906 290.467531 C 382.336906 289.807375 382.872062 289.268312 383.532219 289.268312 C 384.192375 289.268312 384.727531 289.807375 384.727531 290.467531 Z M 384.727531 290.467531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 288.889406 L 387.727531 291.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 387.727531 296.123781 L 387.727531 298.803469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 388.922844 293.846437 C 388.922844 294.506594 388.387687 295.04175 387.727531 295.04175 C 387.067375 295.04175 386.532219 294.506594 386.532219 293.846437 C 386.532219 293.186281 387.067375 292.651125 387.727531 292.651125 C 388.387687 292.651125 388.922844 293.186281 388.922844 293.846437 Z M 388.922844 293.846437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 283.069094 L 391.922844 285.682375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 391.922844 290.237062 L 391.922844 292.850344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.118156 287.959719 C 393.118156 288.619875 392.583 289.155031 391.922844 289.155031 C 391.262687 289.155031 390.727531 288.619875 390.727531 287.959719 C 390.727531 287.295656 391.262687 286.7605 391.922844 286.7605 C 392.583 286.7605 393.118156 287.295656 393.118156 287.959719 Z M 393.118156 287.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 293.530031 L 396.118156 296.256594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 396.118156 300.811281 L 396.118156 303.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 397.313469 298.533937 C 397.313469 299.194094 396.778312 299.72925 396.118156 299.72925 C 395.458 299.72925 394.922844 299.194094 394.922844 298.533937 C 394.922844 297.873781 395.458 297.338625 396.118156 297.338625 C 396.778312 297.338625 397.313469 297.873781 397.313469 298.533937 Z M 397.313469 298.533937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 294.60425 L 400.313469 297.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 400.313469 301.901125 L 400.313469 304.647219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 401.508781 299.627687 C 401.508781 300.287844 400.973625 300.823 400.313469 300.823 C 399.653312 300.823 399.118156 300.287844 399.118156 299.627687 C 399.118156 298.963625 399.653312 298.428469 400.313469 298.428469 C 400.973625 298.428469 401.508781 298.963625 401.508781 299.627687 Z M 401.508781 299.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 297.733156 L 404.508781 300.5105 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 404.508781 305.061281 L 404.508781 307.842531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 405.704094 302.787844 C 405.704094 303.448 405.168937 303.983156 404.508781 303.983156 C 403.848625 303.983156 403.313469 303.448 403.313469 302.787844 C 403.313469 302.123781 403.848625 301.588625 404.508781 301.588625 C 405.168937 301.588625 405.704094 302.123781 405.704094 302.787844 Z M 405.704094 302.787844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 281.66675 L 408.704094 284.264406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 408.704094 288.819094 L 408.704094 291.420656 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 409.899406 286.54175 C 409.899406 287.201906 409.36425 287.737062 408.704094 287.737062 C 408.043937 287.737062 407.508781 287.201906 407.508781 286.54175 C 407.508781 285.881594 408.043937 285.342531 408.704094 285.342531 C 409.36425 285.342531 409.899406 285.881594 409.899406 286.54175 Z M 409.899406 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 245.783937 L 412.899406 247.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 412.899406 252.514406 L 412.899406 254.686281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 414.094719 250.237062 C 414.094719 250.897219 413.559562 251.432375 412.899406 251.432375 C 412.23925 251.432375 411.704094 250.897219 411.704094 250.237062 C 411.704094 249.576906 412.23925 249.037844 412.899406 249.037844 C 413.559562 249.037844 414.094719 249.576906 414.094719 250.237062 Z M 414.094719 250.237062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 202.6355 L 417.094719 204.240969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 417.094719 208.79175 L 417.094719 210.397219 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 418.290031 206.514406 C 418.290031 207.178469 417.754875 207.713625 417.094719 207.713625 C 416.434562 207.713625 415.899406 207.178469 415.899406 206.514406 C 415.899406 205.85425 416.434562 205.319094 417.094719 205.319094 C 417.754875 205.319094 418.290031 205.85425 418.290031 206.514406 Z M 418.290031 206.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 163.342531 L 421.290031 164.334719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 421.290031 168.889406 L 421.290031 169.881594 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 422.485344 166.612062 C 422.485344 167.272219 421.950187 167.807375 421.290031 167.807375 C 420.629875 167.807375 420.094719 167.272219 420.094719 166.612062 C 420.094719 165.951906 420.629875 165.41675 421.290031 165.41675 C 421.950187 165.41675 422.485344 165.951906 422.485344 166.612062 Z M 422.485344 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 136.256594 L 425.485344 136.752687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 425.485344 141.303469 L 425.485344 141.799562 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.680656 139.030031 C 426.680656 139.690187 426.1455 140.225344 425.485344 140.225344 C 424.825187 140.225344 424.290031 139.690187 424.290031 139.030031 C 424.290031 138.365969 424.825187 137.830812 425.485344 137.830812 C 426.1455 137.830812 426.680656 138.365969 426.680656 139.030031 Z M 426.680656 139.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 116.834719 L 429.680656 116.908937 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 429.680656 121.463625 L 429.680656 121.537844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 430.875969 119.186281 C 430.875969 119.846437 430.340812 120.381594 429.680656 120.381594 C 429.0205 120.381594 428.485344 119.846437 428.485344 119.186281 C 428.485344 118.526125 429.0205 117.987062 429.680656 117.987062 C 430.340812 117.987062 430.875969 118.526125 430.875969 119.186281 Z M 430.875969 119.186281 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 435.071281 113.405031 C 435.071281 114.069094 434.536125 114.60425 433.875969 114.60425 C 433.215812 114.60425 432.680656 114.069094 432.680656 113.405031 C 432.680656 112.744875 433.215812 112.209719 433.875969 112.209719 C 434.536125 112.209719 435.071281 112.744875 435.071281 113.405031 Z M 435.071281 113.405031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 439.266594 101.959719 C 439.266594 102.619875 438.731437 103.155031 438.071281 103.155031 C 437.411125 103.155031 436.875969 102.619875 436.875969 101.959719 C 436.875969 101.299562 437.411125 100.7605 438.071281 100.7605 C 438.731437 100.7605 439.266594 101.299562 439.266594 101.959719 Z M 439.266594 101.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 443.461906 99.451906 C 443.461906 100.112062 442.92675 100.647219 442.266594 100.647219 C 441.606437 100.647219 441.071281 100.112062 441.071281 99.451906 C 441.071281 98.79175 441.606437 98.252687 442.266594 98.252687 C 442.92675 98.252687 443.461906 98.79175 443.461906 99.451906 Z M 443.461906 99.451906 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 447.657219 95.198 C 447.657219 95.862062 447.122062 96.397219 446.461906 96.397219 C 445.80175 96.397219 445.266594 95.862062 445.266594 95.198 C 445.266594 94.537844 445.80175 94.002687 446.461906 94.002687 C 447.122062 94.002687 447.657219 94.537844 447.657219 95.198 Z M 447.657219 95.198 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 451.852531 90.948 C 451.852531 91.608156 451.317375 92.143312 450.657219 92.143312 C 449.997062 92.143312 449.461906 91.608156 449.461906 90.948 C 449.461906 90.287844 449.997062 89.748781 450.657219 89.748781 C 451.317375 89.748781 451.852531 90.287844 451.852531 90.948 Z M 451.852531 90.948 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 456.047844 87.350344 C 456.047844 88.0105 455.512687 88.545656 454.852531 88.545656 C 454.192375 88.545656 453.657219 88.0105 453.657219 87.350344 C 453.657219 86.690187 454.192375 86.151125 454.852531 86.151125 C 455.512687 86.151125 456.047844 86.690187 456.047844 87.350344 Z M 456.047844 87.350344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.243156 83.643312 C 460.243156 84.303469 459.708 84.838625 459.047844 84.838625 C 458.387687 84.838625 457.852531 84.303469 457.852531 83.643312 C 457.852531 82.983156 458.387687 82.444094 459.047844 82.444094 C 459.708 82.444094 460.243156 82.983156 460.243156 83.643312 Z M 460.243156 83.643312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 464.438469 80.47925 C 464.438469 81.143312 463.903312 81.678469 463.243156 81.678469 C 462.583 81.678469 462.047844 81.143312 462.047844 80.47925 C 462.047844 79.819094 462.583 79.283937 463.243156 79.283937 C 463.903312 79.283937 464.438469 79.819094 464.438469 80.47925 Z M 464.438469 80.47925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 468.637687 78.518312 C 468.637687 79.178469 468.098625 79.713625 467.438469 79.713625 C 466.778312 79.713625 466.243156 79.178469 466.243156 78.518312 C 466.243156 77.858156 466.778312 77.323 467.438469 77.323 C 468.098625 77.323 468.637687 77.858156 468.637687 78.518312 Z M 468.637687 78.518312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 472.829094 78.627687 C 472.829094 79.287844 472.293937 79.823 471.633781 79.823 C 470.973625 79.823 470.438469 79.287844 470.438469 78.627687 C 470.438469 77.967531 470.973625 77.432375 471.633781 77.432375 C 472.293937 77.432375 472.829094 77.967531 472.829094 78.627687 Z M 472.829094 78.627687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 477.024406 76.22925 C 477.024406 76.889406 476.48925 77.424562 475.829094 77.424562 C 475.168937 77.424562 474.633781 76.889406 474.633781 76.22925 C 474.633781 75.569094 475.168937 75.030031 475.829094 75.030031 C 476.48925 75.030031 477.024406 75.569094 477.024406 76.22925 Z M 477.024406 76.22925 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 481.223625 74.592531 C 481.223625 75.252687 480.684562 75.79175 480.024406 75.79175 C 479.36425 75.79175 478.829094 75.252687 478.829094 74.592531 C 478.829094 73.932375 479.36425 73.397219 480.024406 73.397219 C 480.684562 73.397219 481.223625 73.932375 481.223625 74.592531 Z M 481.223625 74.592531 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.415031 73.393312 C 485.415031 74.053469 484.879875 74.592531 484.219719 74.592531 C 483.559562 74.592531 483.024406 74.053469 483.024406 73.393312 C 483.024406 72.733156 483.559562 72.198 484.219719 72.198 C 484.879875 72.198 485.415031 72.733156 485.415031 73.393312 Z M 485.415031 73.393312 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 489.610344 72.740969 C 489.610344 73.401125 489.075187 73.936281 488.415031 73.936281 C 487.754875 73.936281 487.219719 73.401125 487.219719 72.740969 C 487.219719 72.080812 487.754875 71.54175 488.415031 71.54175 C 489.075187 71.54175 489.610344 72.080812 489.610344 72.740969 Z M 489.610344 72.740969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.809562 72.412844 C 493.809562 73.073 493.2705 73.608156 492.610344 73.608156 C 491.950187 73.608156 491.415031 73.073 491.415031 72.412844 C 491.415031 71.752687 491.950187 71.217531 492.610344 71.217531 C 493.2705 71.217531 493.809562 71.752687 493.809562 72.412844 Z M 493.809562 72.412844 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.12;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.004875 70.014406 C 498.004875 70.674562 497.465812 71.209719 496.805656 71.209719 C 496.1455 71.209719 495.610344 70.674562 495.610344 70.014406 C 495.610344 69.35425 496.1455 68.819094 496.805656 68.819094 C 497.465812 68.819094 498.004875 69.35425 498.004875 70.014406 Z M 498.004875 70.014406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 73.240969 L 260.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 73.240969 L 293.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 73.240969 L 327.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 73.240969 L 360.36425 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 73.240969 L 194.079094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 73.240969 L 160.821281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 73.240969 L 127.563469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 73.240969 L 94.305656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 73.240969 L 426.879875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 73.240969 L 460.137687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 73.240969 L 493.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="214.867" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="226.874975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="381.153" y="389.053"/>
+ <use xlink:href="#glyph0-2" x="393.160975" y="389.053"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="335.731" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="347.042971" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="357.606145" y="416.984352"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="366.121921" y="421.639206"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="379.975701" y="397.661274"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-4" x="390.196273" y="417.528"/>
+ <use xlink:href="#glyph0-5" x="409.039671" y="417.528"/>
+ <use xlink:href="#glyph0-6" x="419.713426" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="438.047511" y="407.241779"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="447.757261" y="417.528"/>
+ <use xlink:href="#glyph1-3" x="459.765236" y="417.528"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="470.100147" y="408.628593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-2" x="479.807845" y="397.661274"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 397.615969 L 260.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 397.615969 L 293.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 397.615969 L 327.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 397.615969 L 360.36425 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 397.615969 L 194.079094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 397.615969 L 160.821281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 397.615969 L 127.563469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 397.615969 L 94.305656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 397.615969 L 426.879875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 397.615969 L 460.137687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 397.615969 L 493.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.389406 L 79.372062 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.29175 L 79.372062 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 101.194094 L 79.372062 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 112.100344 L 79.372062 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 123.002687 L 79.372062 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 133.905031 L 79.372062 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 144.807375 L 79.372062 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 155.709719 L 79.372062 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 166.612062 L 79.372062 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 177.514406 L 79.372062 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 188.41675 L 79.372062 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 199.319094 L 79.372062 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 210.221437 L 79.372062 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 221.127687 L 79.372062 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 232.030031 L 79.372062 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 242.932375 L 79.372062 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.834719 L 79.372062 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.737062 L 79.372062 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.639406 L 79.372062 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 286.54175 L 79.372062 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 297.444094 L 79.372062 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 308.346437 L 79.372062 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 319.248781 L 79.372062 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 330.151125 L 79.372062 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 341.053469 L 79.372062 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 351.959719 L 79.372062 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 362.862062 L 79.372062 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.764406 L 79.372062 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 384.66675 L 79.372062 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="55.657" y="369.989"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="36.979" y="315.476"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="315.476"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="315.476"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="55.657" y="260.963"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="36.979" y="206.45"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="206.45"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="206.45"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.657" y="151.939"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="36.979" y="97.426"/>
+ <use xlink:href="#glyph0-7" x="48.986975" y="97.426"/>
+ <use xlink:href="#glyph0-8" x="55.658072" y="97.426"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-9" x="55.657" y="42.912"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="87.325" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="106.399847" y="25.644"/>
+ <use xlink:href="#glyph0-2" x="118.407822" y="25.644"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-3" x="130.414706" y="16.744593"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-1" x="26.391" y="274.124"/>
+ <use xlink:href="#glyph7-2" x="26.391" y="257.784717"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-3" x="26.391" y="245.104727"/>
+ <use xlink:href="#glyph7-4" x="26.391" y="235.765191"/>
+ <use xlink:href="#glyph7-5" x="26.391" y="226.425655"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="219.754557"/>
+ <use xlink:href="#glyph7-7" x="26.391" y="209.080802"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="199.615571"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-8" x="26.391" y="187.608142"/>
+ <use xlink:href="#glyph7-9" x="26.391" y="178.268606"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-2" x="26.391" y="166.262284"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-10" x="26.391" y="159.590806"/>
+ <use xlink:href="#glyph7-11" x="26.391" y="147.582831"/>
+ <use xlink:href="#glyph7-12" x="26.391" y="135.574856"/>
+ <use xlink:href="#glyph7-6" x="26.391" y="116.731459"/>
+ <use xlink:href="#glyph7-13" x="26.391" y="106.057704"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-1" x="16.102728" y="87.72471"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph8-1" x="26.391" y="78.01496"/>
+ <use xlink:href="#glyph8-3" x="26.391" y="66.006985"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph9-2" x="17.489542" y="55.672074"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph7-14" x="26.391" y="45.964376"/>
+</g>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.389406 L 498.903312 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.29175 L 498.903312 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 101.194094 L 498.903312 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 112.100344 L 498.903312 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 123.002687 L 498.903312 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 133.905031 L 498.903312 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 144.807375 L 498.903312 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 155.709719 L 498.903312 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 166.612062 L 498.903312 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 177.514406 L 498.903312 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 188.41675 L 498.903312 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 199.319094 L 498.903312 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 210.221437 L 498.903312 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 221.127687 L 498.903312 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 232.030031 L 498.903312 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 242.932375 L 498.903312 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.834719 L 498.903312 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.737062 L 498.903312 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.639406 L 498.903312 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 286.54175 L 498.903312 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 297.444094 L 498.903312 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 308.346437 L 498.903312 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 319.248781 L 498.903312 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 330.151125 L 498.903312 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 341.053469 L 498.903312 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 351.959719 L 498.903312 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 362.862062 L 498.903312 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.764406 L 498.903312 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 384.66675 L 498.903312 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 73.240969 L 260.594719 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 73.240969 L 293.852531 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 73.240969 L 327.106437 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 73.240969 L 360.36425 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 77.990969 L 227.336906 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 73.240969 L 194.079094 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 73.240969 L 160.821281 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 73.240969 L 127.563469 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 73.240969 L 94.305656 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 77.990969 L 393.622062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 73.240969 L 426.879875 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 73.240969 L 460.137687 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 73.240969 L 493.3955 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 402.365969 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 260.594719 397.615969 L 260.594719 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 293.852531 397.615969 L 293.852531 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 327.106437 397.615969 L 327.106437 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 360.36425 397.615969 L 360.36425 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 227.336906 392.862062 L 227.336906 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 194.079094 397.615969 L 194.079094 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 160.821281 397.615969 L 160.821281 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 127.563469 397.615969 L 127.563469 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 94.305656 397.615969 L 94.305656 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 393.622062 392.862062 L 393.622062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 426.879875 397.615969 L 426.879875 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 460.137687 397.615969 L 460.137687 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 493.3955 397.615969 L 493.3955 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 79.372062 68.487062 L 79.372062 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 68.487062 L 79.372062 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 79.389406 L 79.372062 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 90.29175 L 79.372062 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 101.194094 L 79.372062 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 112.100344 L 79.372062 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 123.002687 L 79.372062 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 133.905031 L 79.372062 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 144.807375 L 79.372062 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 155.709719 L 79.372062 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 166.612062 L 79.372062 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 177.514406 L 79.372062 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 188.41675 L 79.372062 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 199.319094 L 79.372062 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 210.221437 L 79.372062 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 221.127687 L 79.372062 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 232.030031 L 79.372062 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 242.932375 L 79.372062 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 253.834719 L 79.372062 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 264.737062 L 79.372062 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 275.639406 L 79.372062 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 286.54175 L 79.372062 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 297.444094 L 79.372062 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 308.346437 L 79.372062 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 319.248781 L 79.372062 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 330.151125 L 79.372062 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 341.053469 L 79.372062 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 351.959719 L 79.372062 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 362.862062 L 79.372062 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 373.764406 L 79.372062 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 86.004875 384.66675 L 79.372062 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 92.637687 395.569094 L 79.372062 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 498.903312 68.487062 L 498.903312 402.365969 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 68.487062 L 498.903312 68.487062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 79.389406 L 498.903312 79.389406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 90.29175 L 498.903312 90.29175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 101.194094 L 498.903312 101.194094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 112.100344 L 498.903312 112.100344 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 123.002687 L 498.903312 123.002687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 133.905031 L 498.903312 133.905031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 144.807375 L 498.903312 144.807375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 155.709719 L 498.903312 155.709719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 166.612062 L 498.903312 166.612062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 177.514406 L 498.903312 177.514406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 188.41675 L 498.903312 188.41675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 199.319094 L 498.903312 199.319094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 210.221437 L 498.903312 210.221437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 221.127687 L 498.903312 221.127687 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 232.030031 L 498.903312 232.030031 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 242.932375 L 498.903312 242.932375 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 253.834719 L 498.903312 253.834719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 264.737062 L 498.903312 264.737062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 275.639406 L 498.903312 275.639406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 286.54175 L 498.903312 286.54175 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 297.444094 L 498.903312 297.444094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 308.346437 L 498.903312 308.346437 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 319.248781 L 498.903312 319.248781 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 330.151125 L 498.903312 330.151125 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 341.053469 L 498.903312 341.053469 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 351.959719 L 498.903312 351.959719 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 362.862062 L 498.903312 362.862062 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 373.764406 L 498.903312 373.764406 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 492.2705 384.66675 L 498.903312 384.66675 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 485.637687 395.569094 L 498.903312 395.569094 " transform="matrix(1,0,0,-1,-0.458,430.573)"/>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig0.svg b/doc/figs/tex/fig0.svg
new file mode 100644
index 00000000000..cd6a77bec58
--- /dev/null
+++ b/doc/figs/tex/fig0.svg
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.219pt" height="10.423pt" viewBox="0 0 47.219 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.0625 -1.5 L 5.078125 -1.5 C 5.171875 -1.5 5.328125 -1.5 5.328125 -1.65625 C 5.328125 -1.8125 5.171875 -1.8125 5.078125 -1.8125 L 3.0625 -1.8125 L 3.0625 -3.84375 C 3.0625 -3.9375 3.0625 -4.09375 2.90625 -4.09375 C 2.734375 -4.09375 2.734375 -3.9375 2.734375 -3.84375 L 2.734375 -1.8125 L 0.703125 -1.8125 C 0.625 -1.8125 0.46875 -1.8125 0.46875 -1.65625 C 0.46875 -1.5 0.609375 -1.5 0.703125 -1.5 L 2.734375 -1.5 L 2.734375 0.53125 C 2.734375 0.625 2.734375 0.78125 2.890625 0.78125 C 3.0625 0.78125 3.0625 0.625 3.0625 0.53125 Z M 3.0625 -1.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.868409" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.885591" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.121119" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.792342" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.51235" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.232358" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="30.952366" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.672374" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="39.343492" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig1.svg b/doc/figs/tex/fig1.svg
new file mode 100644
index 00000000000..6f3f59ddf13
--- /dev/null
+++ b/doc/figs/tex/fig1.svg
@@ -0,0 +1,71 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="48.101pt" height="10.6pt" viewBox="0 0 48.101 10.6" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 0.3125 1.65625 C 0.28125 1.78125 0.28125 1.796875 0.28125 1.8125 C 0.28125 1.953125 0.390625 2.078125 0.5625 2.078125 C 0.765625 2.078125 0.875 1.90625 0.890625 1.875 C 0.9375 1.78125 1.25 0.5 1.5 -0.53125 C 1.703125 -0.15625 2 0.109375 2.453125 0.109375 C 3.578125 0.109375 4.8125 -1.25 4.8125 -2.671875 C 4.8125 -3.6875 4.1875 -4.234375 3.484375 -4.234375 C 2.546875 -4.234375 1.546875 -3.28125 1.25 -2.109375 Z M 2.453125 -0.109375 C 1.78125 -0.109375 1.625 -0.875 1.625 -0.953125 C 1.625 -1 1.671875 -1.1875 1.703125 -1.3125 C 1.96875 -2.390625 2.0625 -2.734375 2.28125 -3.125 C 2.6875 -3.8125 3.171875 -4.03125 3.46875 -4.03125 C 3.8125 -4.03125 4.125 -3.75 4.125 -3.09375 C 4.125 -2.5625 3.84375 -1.484375 3.59375 -1.015625 C 3.265625 -0.40625 2.8125 -0.109375 2.453125 -0.109375 Z M 2.453125 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.890625 -3.875 C 4.875 -3.90625 4.828125 -3.984375 4.828125 -4.015625 C 4.828125 -4.015625 5.015625 -4.15625 5.109375 -4.234375 L 6.796875 -5.53125 C 7.6875 -6.1875 8.0625 -6.21875 8.359375 -6.25 C 8.4375 -6.265625 8.53125 -6.28125 8.53125 -6.453125 C 8.53125 -6.484375 8.5 -6.546875 8.421875 -6.546875 C 8.21875 -6.546875 7.96875 -6.53125 7.734375 -6.53125 C 7.390625 -6.53125 7.015625 -6.546875 6.671875 -6.546875 C 6.609375 -6.546875 6.5 -6.546875 6.5 -6.359375 C 6.5 -6.296875 6.546875 -6.265625 6.609375 -6.25 C 6.828125 -6.234375 6.90625 -6.1875 6.90625 -6.046875 C 6.90625 -5.875 6.625 -5.65625 6.5625 -5.609375 L 2.828125 -2.734375 L 3.59375 -5.8125 C 3.671875 -6.15625 3.6875 -6.25 4.390625 -6.25 C 4.640625 -6.25 4.71875 -6.25 4.71875 -6.453125 C 4.71875 -6.53125 4.640625 -6.546875 4.578125 -6.546875 C 4.3125 -6.546875 3.625 -6.53125 3.359375 -6.53125 C 3.078125 -6.53125 2.390625 -6.546875 2.125 -6.546875 C 2.046875 -6.546875 1.921875 -6.546875 1.921875 -6.375 C 1.921875 -6.25 2.015625 -6.25 2.203125 -6.25 C 2.328125 -6.25 2.5 -6.25 2.625 -6.234375 C 2.765625 -6.21875 2.828125 -6.1875 2.828125 -6.078125 C 2.828125 -6.046875 2.828125 -6.015625 2.796875 -5.90625 L 1.5 -0.75 C 1.40625 -0.375 1.390625 -0.296875 0.640625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.484375 0 0.515625 0 C 0.78125 0 1.453125 -0.03125 1.734375 -0.03125 C 1.921875 -0.03125 2.140625 -0.015625 2.34375 -0.015625 C 2.546875 -0.015625 2.765625 0 2.96875 0 C 3.03125 0 3.15625 0 3.15625 -0.1875 C 3.15625 -0.296875 3.0625 -0.296875 2.890625 -0.296875 C 2.53125 -0.296875 2.265625 -0.296875 2.265625 -0.46875 C 2.265625 -0.53125 2.328125 -0.75 2.34375 -0.890625 C 2.484375 -1.390625 2.609375 -1.90625 2.734375 -2.390625 L 4.15625 -3.515625 L 5.28125 -0.9375 C 5.390625 -0.671875 5.390625 -0.65625 5.390625 -0.59375 C 5.390625 -0.3125 4.984375 -0.296875 4.890625 -0.296875 C 4.78125 -0.296875 4.6875 -0.296875 4.6875 -0.109375 C 4.6875 0 4.796875 0 4.8125 0 C 5.203125 0 5.609375 -0.03125 5.984375 -0.03125 C 6.203125 -0.03125 6.71875 0 6.921875 0 C 6.96875 0 7.09375 0 7.09375 -0.1875 C 7.09375 -0.296875 7 -0.296875 6.90625 -0.296875 C 6.515625 -0.3125 6.390625 -0.390625 6.25 -0.734375 Z M 4.890625 -3.875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.171875 2.296875 C 3.171875 2.28125 3.171875 2.25 3.015625 2.09375 C 1.8125 0.875 1.5 -0.9375 1.5 -2.390625 C 1.5 -4.0625 1.875 -5.734375 3.046875 -6.9375 C 3.171875 -7.046875 3.171875 -7.078125 3.171875 -7.09375 C 3.171875 -7.171875 3.140625 -7.1875 3.078125 -7.1875 C 2.984375 -7.1875 2.125 -6.546875 1.546875 -5.328125 C 1.0625 -4.265625 0.953125 -3.203125 0.953125 -2.390625 C 0.953125 -1.65625 1.0625 -0.484375 1.578125 0.59375 C 2.15625 1.78125 2.984375 2.390625 3.078125 2.390625 C 3.140625 2.390625 3.171875 2.375 3.171875 2.296875 Z M 3.171875 2.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 4.5625 -5.84375 C 4.65625 -5.953125 4.65625 -5.984375 4.65625 -6.171875 L 2.328125 -6.171875 C 1.15625 -6.171875 1.125 -6.296875 1.09375 -6.484375 L 0.859375 -6.484375 L 0.53125 -4.515625 L 0.78125 -4.515625 C 0.8125 -4.65625 0.890625 -5.265625 1.015625 -5.375 C 1.078125 -5.4375 1.828125 -5.4375 1.953125 -5.4375 L 3.9375 -5.4375 C 3.84375 -5.28125 3.078125 -4.234375 2.875 -3.921875 C 2 -2.625 1.6875 -1.296875 1.6875 -0.3125 C 1.6875 -0.21875 1.6875 0.21875 2.125 0.21875 C 2.578125 0.21875 2.578125 -0.21875 2.578125 -0.3125 L 2.578125 -0.8125 C 2.578125 -1.328125 2.59375 -1.859375 2.671875 -2.375 C 2.71875 -2.59375 2.84375 -3.421875 3.265625 -4.015625 Z M 4.5625 -5.84375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 4.40625 -3.0625 C 4.40625 -3.84375 4.359375 -4.609375 4.03125 -5.3125 C 3.59375 -6.234375 2.796875 -6.390625 2.390625 -6.390625 C 1.828125 -6.390625 1.125 -6.140625 0.734375 -5.25 C 0.421875 -4.578125 0.375 -3.84375 0.375 -3.0625 C 0.375 -2.34375 0.40625 -1.484375 0.8125 -0.765625 C 1.21875 0.015625 1.921875 0.21875 2.390625 0.21875 C 2.90625 0.21875 3.640625 0.015625 4.0625 -0.90625 C 4.359375 -1.5625 4.40625 -2.3125 4.40625 -3.0625 Z M 2.390625 0 C 2.015625 0 1.453125 -0.234375 1.28125 -1.15625 C 1.171875 -1.734375 1.171875 -2.625 1.171875 -3.1875 C 1.171875 -3.796875 1.171875 -4.4375 1.25 -4.953125 C 1.421875 -6.09375 2.15625 -6.171875 2.390625 -6.171875 C 2.703125 -6.171875 3.34375 -6 3.515625 -5.0625 C 3.609375 -4.515625 3.609375 -3.796875 3.609375 -3.1875 C 3.609375 -2.46875 3.609375 -1.8125 3.515625 -1.203125 C 3.375 -0.28125 2.828125 0 2.390625 0 Z M 2.390625 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 2.765625 -2.390625 C 2.765625 -3.140625 2.671875 -4.3125 2.140625 -5.390625 C 1.5625 -6.578125 0.734375 -7.1875 0.640625 -7.1875 C 0.578125 -7.1875 0.546875 -7.15625 0.546875 -7.09375 C 0.546875 -7.078125 0.546875 -7.046875 0.734375 -6.875 C 1.671875 -5.921875 2.21875 -4.40625 2.21875 -2.390625 C 2.21875 -0.765625 1.859375 0.9375 0.671875 2.140625 C 0.546875 2.25 0.546875 2.28125 0.546875 2.296875 C 0.546875 2.359375 0.578125 2.390625 0.640625 2.390625 C 0.734375 2.390625 1.609375 1.75 2.171875 0.53125 C 2.65625 -0.53125 2.765625 -1.59375 2.765625 -2.390625 Z M 2.765625 -2.390625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.46875 -2.140625 C 3.46875 -2.875 3.375 -3.40625 3.078125 -3.890625 C 2.859375 -4.1875 2.453125 -4.46875 1.90625 -4.46875 C 0.34375 -4.46875 0.34375 -2.625 0.34375 -2.140625 C 0.34375 -1.65625 0.34375 0.140625 1.90625 0.140625 C 3.46875 0.140625 3.46875 -1.65625 3.46875 -2.140625 Z M 1.90625 -0.046875 C 1.59375 -0.046875 1.1875 -0.234375 1.0625 -0.78125 C 0.953125 -1.1875 0.953125 -1.734375 0.953125 -2.234375 C 0.953125 -2.71875 0.953125 -3.234375 1.0625 -3.59375 C 1.203125 -4.125 1.625 -4.265625 1.90625 -4.265625 C 2.265625 -4.265625 2.625 -4.046875 2.734375 -3.65625 C 2.84375 -3.296875 2.859375 -2.8125 2.859375 -2.234375 C 2.859375 -1.734375 2.859375 -1.234375 2.765625 -0.8125 C 2.640625 -0.203125 2.171875 -0.046875 1.90625 -0.046875 Z M 1.90625 -0.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 3.109375 -1.515625 L 5.171875 -1.515625 C 5.25 -1.515625 5.421875 -1.515625 5.421875 -1.671875 C 5.421875 -1.84375 5.265625 -1.84375 5.171875 -1.84375 L 3.109375 -1.84375 L 3.109375 -3.90625 C 3.109375 -4 3.109375 -4.15625 2.953125 -4.15625 C 2.78125 -4.15625 2.78125 -4 2.78125 -3.90625 L 2.78125 -1.84375 L 0.71875 -1.84375 C 0.625 -1.84375 0.46875 -1.84375 0.46875 -1.6875 C 0.46875 -1.515625 0.625 -1.515625 0.71875 -1.515625 L 2.78125 -1.515625 L 2.78125 0.546875 C 2.78125 0.625 2.78125 0.796875 2.9375 0.796875 C 3.109375 0.796875 3.109375 0.640625 3.109375 0.546875 Z M 3.109375 -1.515625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.441406 3 L 6 3 L 6 10 L 0.441406 10 Z M 0.441406 3 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 6 0 L 27 0 L 27 10.214844 L 6 10.214844 Z M 6 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.441409" y="7.814127"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="5.4051" y="7.814127"/>
+ <use xlink:href="#glyph1-2" x="9.138666" y="7.814127"/>
+ <use xlink:href="#glyph1-2" x="13.938828" y="7.814127"/>
+ <use xlink:href="#glyph1-3" x="18.738989" y="7.814127"/>
+ <use xlink:href="#glyph1-4" x="23.539151" y="7.814127"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="27.2729" y="4.330582"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="31.579391" y="7.814127"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="40.419791" y="4.330582"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig10.svg b/doc/figs/tex/fig10.svg
new file mode 100644
index 00000000000..b3c7c57fb17
--- /dev/null
+++ b/doc/figs/tex/fig10.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="5.151pt" height="8.856pt" viewBox="0 0 5.151 8.856" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.140625 -5.9375 L 0.984375 -4.765625 L 1.140625 -4.609375 L 2.140625 -5.484375 L 3.125 -4.609375 L 3.265625 -4.765625 Z M 2.140625 -5.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 0.28125 1.484375 C 0.25 1.578125 0.25 1.59375 0.25 1.609375 C 0.25 1.75 0.34375 1.84375 0.5 1.84375 C 0.671875 1.84375 0.78125 1.6875 0.796875 1.671875 C 0.84375 1.59375 1.109375 0.4375 1.34375 -0.484375 C 1.515625 -0.140625 1.78125 0.09375 2.1875 0.09375 C 3.1875 0.09375 4.296875 -1.109375 4.296875 -2.390625 C 4.296875 -3.296875 3.71875 -3.78125 3.109375 -3.78125 C 2.28125 -3.78125 1.375 -2.921875 1.125 -1.875 Z M 2.171875 -0.09375 C 1.578125 -0.09375 1.4375 -0.78125 1.4375 -0.859375 C 1.4375 -0.890625 1.484375 -1.0625 1.515625 -1.171875 C 1.75 -2.125 1.84375 -2.4375 2.03125 -2.78125 C 2.390625 -3.40625 2.828125 -3.59375 3.078125 -3.59375 C 3.40625 -3.59375 3.671875 -3.34375 3.671875 -2.75 C 3.671875 -2.28125 3.421875 -1.328125 3.203125 -0.90625 C 2.921875 -0.375 2.5 -0.09375 2.171875 -0.09375 Z M 2.171875 -0.09375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 0.566406 L 4.421875 0.566406 L 4.421875 2 L 1 2 Z M 1 0.566406 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 0 2 L 4.421875 2 L 4.421875 8.167969 L 0 8.167969 Z M 0 2 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.785527" y="6.504712"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="0" y="6.504712"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig11.svg b/doc/figs/tex/fig11.svg
new file mode 100644
index 00000000000..430714dc97d
--- /dev/null
+++ b/doc/figs/tex/fig11.svg
@@ -0,0 +1,35 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="6.362pt" height="11.852pt" viewBox="0 0 6.362 11.852" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.125 -4.03125 C 2.125 -4.203125 2.109375 -4.21875 1.9375 -4.21875 C 1.53125 -3.8125 0.953125 -3.8125 0.6875 -3.8125 L 0.6875 -3.578125 C 0.84375 -3.578125 1.265625 -3.578125 1.609375 -3.75 L 1.609375 -0.515625 C 1.609375 -0.3125 1.609375 -0.234375 0.984375 -0.234375 L 0.734375 -0.234375 L 0.734375 0 C 0.84375 0 1.625 -0.03125 1.859375 -0.03125 C 2.0625 -0.03125 2.859375 0 3 0 L 3 -0.234375 L 2.765625 -0.234375 C 2.125 -0.234375 2.125 -0.3125 2.125 -0.515625 Z M 2.125 -4.03125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 3.203125 -1.15625 L 2.984375 -1.15625 C 2.96875 -1.015625 2.90625 -0.640625 2.828125 -0.578125 C 2.765625 -0.546875 2.28125 -0.546875 2.1875 -0.546875 L 1.03125 -0.546875 C 1.6875 -1.125 1.921875 -1.3125 2.296875 -1.609375 C 2.765625 -1.984375 3.203125 -2.375 3.203125 -2.96875 C 3.203125 -3.75 2.53125 -4.21875 1.71875 -4.21875 C 0.9375 -4.21875 0.40625 -3.65625 0.40625 -3.078125 C 0.40625 -2.75 0.671875 -2.71875 0.734375 -2.71875 C 0.890625 -2.71875 1.078125 -2.828125 1.078125 -3.0625 C 1.078125 -3.171875 1.03125 -3.390625 0.703125 -3.390625 C 0.890625 -3.84375 1.328125 -3.984375 1.625 -3.984375 C 2.265625 -3.984375 2.59375 -3.484375 2.59375 -2.96875 C 2.59375 -2.421875 2.1875 -1.984375 1.984375 -1.75 L 0.46875 -0.25 C 0.40625 -0.1875 0.40625 -0.171875 0.40625 0 L 3.015625 0 Z M 3.203125 -1.15625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 0.472656 L 5 0.472656 L 5 5 L 1 5 Z M 1 0.472656 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 1 7 L 5 7 L 5 11.246094 L 1 11.246094 Z M 1 7 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="1.086993" y="4.557261"/>
+</g>
+</g>
+<path style="fill:none;stroke-width:0.398;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -0.00116151 -0.00069365 L 3.970172 -0.00069365 " transform="matrix(0.908857,0,0,-0.908857,1.086993,5.858745)"/>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="1.086993" y="11.244632"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig12.svg b/doc/figs/tex/fig12.svg
new file mode 100644
index 00000000000..9c2658ab34c
--- /dev/null
+++ b/doc/figs/tex/fig12.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="8.329pt" height="6.227pt" viewBox="0 0 8.329 6.227" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 0.40625 1.078125 C 0.328125 1.375 0.3125 1.4375 -0.078125 1.4375 C -0.1875 1.4375 -0.28125 1.4375 -0.28125 1.609375 C -0.28125 1.6875 -0.234375 1.71875 -0.171875 1.71875 C 0.078125 1.71875 0.328125 1.6875 0.578125 1.6875 C 0.875 1.6875 1.171875 1.71875 1.453125 1.71875 C 1.5 1.71875 1.609375 1.71875 1.609375 1.546875 C 1.609375 1.4375 1.53125 1.4375 1.40625 1.4375 C 0.953125 1.4375 0.953125 1.375 0.953125 1.296875 C 0.953125 1.203125 1.328125 -0.25 1.390625 -0.46875 C 1.5 -0.21875 1.75 0.09375 2.203125 0.09375 C 3.234375 0.09375 4.34375 -1.203125 4.34375 -2.5 C 4.34375 -3.328125 3.84375 -3.921875 3.15625 -3.921875 C 2.71875 -3.921875 2.296875 -3.59375 2 -3.25 C 1.90625 -3.734375 1.53125 -3.921875 1.203125 -3.921875 C 0.796875 -3.921875 0.625 -3.578125 0.546875 -3.40625 C 0.390625 -3.109375 0.28125 -2.578125 0.28125 -2.546875 C 0.28125 -2.46875 0.359375 -2.46875 0.375 -2.46875 C 0.46875 -2.46875 0.484375 -2.46875 0.53125 -2.671875 C 0.6875 -3.296875 0.859375 -3.71875 1.171875 -3.71875 C 1.328125 -3.71875 1.453125 -3.65625 1.453125 -3.3125 C 1.453125 -3.109375 1.421875 -3.015625 1.390625 -2.859375 Z M 1.953125 -2.765625 C 2.015625 -3 2.265625 -3.25 2.421875 -3.390625 C 2.734375 -3.65625 2.984375 -3.71875 3.140625 -3.71875 C 3.484375 -3.71875 3.703125 -3.40625 3.703125 -2.890625 C 3.703125 -2.359375 3.40625 -1.34375 3.25 -1.015625 C 2.953125 -0.390625 2.53125 -0.09375 2.203125 -0.09375 C 1.609375 -0.09375 1.5 -0.828125 1.5 -0.890625 C 1.5 -0.90625 1.5 -0.921875 1.53125 -1.03125 Z M 1.953125 -2.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.015625 -3.875 C 2.015625 -3.96875 1.9375 -4.109375 1.765625 -4.109375 C 1.59375 -4.109375 1.421875 -3.953125 1.421875 -3.765625 C 1.421875 -3.671875 1.5 -3.53125 1.65625 -3.53125 C 1.84375 -3.53125 2.015625 -3.703125 2.015625 -3.875 Z M 0.75 -0.71875 C 0.71875 -0.640625 0.6875 -0.578125 0.6875 -0.46875 C 0.6875 -0.171875 0.9375 0.0625 1.28125 0.0625 C 1.890625 0.0625 2.171875 -0.796875 2.171875 -0.890625 C 2.171875 -0.96875 2.09375 -0.96875 2.078125 -0.96875 C 1.984375 -0.96875 1.984375 -0.9375 1.953125 -0.859375 C 1.8125 -0.359375 1.53125 -0.109375 1.296875 -0.109375 C 1.171875 -0.109375 1.140625 -0.1875 1.140625 -0.328125 C 1.140625 -0.46875 1.1875 -0.59375 1.234375 -0.71875 C 1.296875 -0.890625 1.375 -1.0625 1.4375 -1.21875 C 1.5 -1.375 1.71875 -1.9375 1.75 -2.015625 C 1.765625 -2.078125 1.78125 -2.140625 1.78125 -2.203125 C 1.78125 -2.5 1.53125 -2.734375 1.1875 -2.734375 C 0.578125 -2.734375 0.296875 -1.890625 0.296875 -1.78125 C 0.296875 -1.703125 0.375 -1.703125 0.390625 -1.703125 C 0.484375 -1.703125 0.484375 -1.734375 0.515625 -1.8125 C 0.671875 -2.34375 0.9375 -2.5625 1.171875 -2.5625 C 1.265625 -2.5625 1.328125 -2.515625 1.328125 -2.34375 C 1.328125 -2.203125 1.296875 -2.109375 1.140625 -1.71875 Z M 0.75 -0.71875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.160156 0 L 5 0 L 5 5.539062 L 0.160156 5.539062 Z M 0.160156 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 4 1 L 7 1 L 7 5.539062 L 4 5.539062 Z M 4 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.161429" y="3.816261"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="4.619961" y="5.145281"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig13.svg b/doc/figs/tex/fig13.svg
new file mode 100644
index 00000000000..4772cdbc29a
--- /dev/null
+++ b/doc/figs/tex/fig13.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="9.01pt" height="5.784pt" viewBox="0 0 9.01 5.784" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.640625 -3.34375 C 4.765625 -3.34375 5.078125 -3.34375 5.078125 -3.65625 C 5.078125 -3.859375 4.890625 -3.859375 4.734375 -3.859375 L 2.6875 -3.859375 C 1.34375 -3.859375 0.34375 -2.390625 0.34375 -1.3125 C 0.34375 -0.53125 0.875 0.09375 1.6875 0.09375 C 2.75 0.09375 3.9375 -0.984375 3.9375 -2.375 C 3.9375 -2.515625 3.9375 -2.953125 3.65625 -3.34375 Z M 1.6875 -0.09375 C 1.25 -0.09375 0.890625 -0.421875 0.890625 -1.0625 C 0.890625 -1.34375 1 -2.078125 1.3125 -2.59375 C 1.6875 -3.21875 2.234375 -3.34375 2.53125 -3.34375 C 3.296875 -3.34375 3.359375 -2.75 3.359375 -2.46875 C 3.359375 -2.046875 3.1875 -1.3125 2.875 -0.859375 C 2.53125 -0.328125 2.046875 -0.09375 1.6875 -0.09375 Z M 1.6875 -0.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.03125 -3.921875 C 2.03125 -4.03125 1.953125 -4.171875 1.78125 -4.171875 C 1.609375 -4.171875 1.4375 -4 1.4375 -3.8125 C 1.4375 -3.71875 1.515625 -3.578125 1.6875 -3.578125 C 1.859375 -3.578125 2.03125 -3.75 2.03125 -3.921875 Z M 0.75 -0.734375 C 0.734375 -0.65625 0.703125 -0.578125 0.703125 -0.46875 C 0.703125 -0.171875 0.953125 0.0625 1.296875 0.0625 C 1.921875 0.0625 2.203125 -0.796875 2.203125 -0.890625 C 2.203125 -0.984375 2.109375 -0.984375 2.09375 -0.984375 C 2.015625 -0.984375 2 -0.9375 1.984375 -0.875 C 1.828125 -0.375 1.5625 -0.109375 1.3125 -0.109375 C 1.1875 -0.109375 1.15625 -0.1875 1.15625 -0.328125 C 1.15625 -0.484375 1.203125 -0.59375 1.25 -0.734375 C 1.3125 -0.90625 1.390625 -1.078125 1.453125 -1.234375 C 1.515625 -1.390625 1.734375 -1.953125 1.765625 -2.03125 C 1.78125 -2.09375 1.796875 -2.171875 1.796875 -2.234375 C 1.796875 -2.53125 1.546875 -2.765625 1.203125 -2.765625 C 0.578125 -2.765625 0.296875 -1.921875 0.296875 -1.8125 C 0.296875 -1.734375 0.390625 -1.734375 0.40625 -1.734375 C 0.484375 -1.734375 0.5 -1.765625 0.515625 -1.828125 C 0.671875 -2.375 0.953125 -2.59375 1.1875 -2.59375 C 1.28125 -2.59375 1.34375 -2.546875 1.34375 -2.375 C 1.34375 -2.234375 1.3125 -2.140625 1.15625 -1.75 Z M 0.75 -0.734375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.1875 L 6 0.1875 L 6 5 L 0 5 Z M 0 0.1875 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 5 1 L 8 1 L 8 5.398438 L 5 5.398438 Z M 5 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="4.05429"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="5.129393" y="5.400384"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig14.svg b/doc/figs/tex/fig14.svg
new file mode 100644
index 00000000000..53f2dc72ac6
--- /dev/null
+++ b/doc/figs/tex/fig14.svg
@@ -0,0 +1,99 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="53.111pt" height="8.856pt" viewBox="0 0 53.111 8.856" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.453125 -6.796875 L 1.140625 -5.46875 L 1.3125 -5.296875 L 2.453125 -6.296875 L 3.578125 -5.296875 L 3.75 -5.46875 Z M 2.453125 -6.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 6.734375 -3.203125 C 6.875 -3.203125 7.0625 -3.203125 7.0625 -3.40625 C 7.0625 -3.59375 6.875 -3.59375 6.734375 -3.59375 L 0.875 -3.59375 C 0.734375 -3.59375 0.546875 -3.59375 0.546875 -3.40625 C 0.546875 -3.203125 0.734375 -3.203125 0.875 -3.203125 Z M 6.734375 -1.296875 C 6.875 -1.296875 7.0625 -1.296875 7.0625 -1.5 C 7.0625 -1.6875 6.875 -1.6875 6.734375 -1.6875 L 0.875 -1.6875 C 0.734375 -1.6875 0.546875 -1.6875 0.546875 -1.5 C 0.546875 -1.296875 0.734375 -1.296875 0.875 -1.296875 Z M 6.734375 -1.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 4 -2.25 L 6.734375 -2.25 C 6.875 -2.25 7.0625 -2.25 7.0625 -2.453125 C 7.0625 -2.640625 6.875 -2.640625 6.734375 -2.640625 L 4 -2.640625 L 4 -5.390625 C 4 -5.53125 4 -5.71875 3.8125 -5.71875 C 3.609375 -5.71875 3.609375 -5.53125 3.609375 -5.390625 L 3.609375 -2.640625 L 0.875 -2.640625 C 0.734375 -2.640625 0.546875 -2.640625 0.546875 -2.453125 C 0.546875 -2.25 0.734375 -2.25 0.875 -2.25 L 3.609375 -2.25 L 3.609375 0.484375 C 3.609375 0.625 3.609375 0.8125 3.8125 0.8125 C 4 0.8125 4 0.625 4 0.484375 Z M 4 -2.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 0.328125 1.6875 C 0.296875 1.8125 0.296875 1.828125 0.296875 1.859375 C 0.296875 2 0.40625 2.109375 0.5625 2.109375 C 0.78125 2.109375 0.890625 1.9375 0.90625 1.90625 C 0.953125 1.828125 1.28125 0.515625 1.53125 -0.546875 C 1.734375 -0.15625 2.046875 0.109375 2.515625 0.109375 C 3.65625 0.109375 4.921875 -1.28125 4.921875 -2.734375 C 4.921875 -3.765625 4.265625 -4.328125 3.5625 -4.328125 C 2.609375 -4.328125 1.578125 -3.34375 1.28125 -2.15625 Z M 2.5 -0.109375 C 1.8125 -0.109375 1.65625 -0.890625 1.65625 -0.984375 C 1.65625 -1.015625 1.703125 -1.21875 1.734375 -1.34375 C 2.015625 -2.4375 2.109375 -2.796875 2.328125 -3.1875 C 2.75 -3.90625 3.234375 -4.109375 3.53125 -4.109375 C 3.90625 -4.109375 4.21875 -3.828125 4.21875 -3.15625 C 4.21875 -2.609375 3.921875 -1.515625 3.65625 -1.03125 C 3.34375 -0.421875 2.875 -0.109375 2.5 -0.109375 Z M 2.5 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.65625 -5.9375 C 3.75 -6.296875 3.78125 -6.390625 4.5625 -6.390625 C 4.796875 -6.390625 4.875 -6.390625 4.875 -6.578125 C 4.875 -6.6875 4.765625 -6.6875 4.71875 -6.6875 C 4.4375 -6.6875 3.71875 -6.65625 3.421875 -6.65625 C 3.140625 -6.65625 2.421875 -6.6875 2.125 -6.6875 C 2.0625 -6.6875 1.9375 -6.6875 1.9375 -6.5 C 1.9375 -6.390625 2.015625 -6.390625 2.203125 -6.390625 C 2.609375 -6.390625 2.875 -6.390625 2.875 -6.203125 C 2.875 -6.15625 2.875 -6.140625 2.859375 -6.046875 L 1.53125 -0.765625 C 1.453125 -0.40625 1.421875 -0.296875 0.640625 -0.296875 C 0.421875 -0.296875 0.328125 -0.296875 0.328125 -0.109375 C 0.328125 0 0.453125 0 0.484375 0 C 0.765625 0 1.484375 -0.03125 1.765625 -0.03125 C 2.0625 -0.03125 2.78125 0 3.078125 0 C 3.15625 0 3.265625 0 3.265625 -0.1875 C 3.265625 -0.296875 3.1875 -0.296875 2.984375 -0.296875 C 2.796875 -0.296875 2.75 -0.296875 2.5625 -0.328125 C 2.34375 -0.34375 2.3125 -0.375 2.3125 -0.484375 C 2.3125 -0.5625 2.328125 -0.640625 2.34375 -0.71875 Z M 3.65625 -5.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 5.078125 -3.65625 C 5.203125 -3.65625 5.5625 -3.65625 5.5625 -3.984375 C 5.5625 -4.21875 5.34375 -4.21875 5.171875 -4.21875 L 2.9375 -4.21875 C 1.453125 -4.21875 0.375 -2.609375 0.375 -1.4375 C 0.375 -0.578125 0.953125 0.109375 1.84375 0.109375 C 3 0.109375 4.296875 -1.078125 4.296875 -2.59375 C 4.296875 -2.75 4.296875 -3.21875 4 -3.65625 Z M 1.859375 -0.109375 C 1.375 -0.109375 0.984375 -0.453125 0.984375 -1.171875 C 0.984375 -1.453125 1.09375 -2.265625 1.4375 -2.84375 C 1.859375 -3.515625 2.4375 -3.65625 2.765625 -3.65625 C 3.59375 -3.65625 3.671875 -3 3.671875 -2.703125 C 3.671875 -2.25 3.484375 -1.4375 3.140625 -0.9375 C 2.765625 -0.359375 2.234375 -0.109375 1.859375 -0.109375 Z M 1.859375 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 0.4375 1.1875 C 0.359375 1.53125 0.34375 1.59375 -0.09375 1.59375 C -0.203125 1.59375 -0.3125 1.59375 -0.3125 1.78125 C -0.3125 1.859375 -0.265625 1.90625 -0.1875 1.90625 C 0.078125 1.90625 0.359375 1.875 0.640625 1.875 C 0.953125 1.875 1.296875 1.90625 1.609375 1.90625 C 1.65625 1.90625 1.78125 1.90625 1.78125 1.703125 C 1.78125 1.59375 1.6875 1.59375 1.546875 1.59375 C 1.0625 1.59375 1.0625 1.53125 1.0625 1.4375 C 1.0625 1.328125 1.46875 -0.28125 1.53125 -0.515625 C 1.671875 -0.234375 1.9375 0.109375 2.4375 0.109375 C 3.578125 0.109375 4.796875 -1.328125 4.796875 -2.765625 C 4.796875 -3.6875 4.234375 -4.328125 3.5 -4.328125 C 3 -4.328125 2.53125 -3.984375 2.21875 -3.59375 C 2.109375 -4.125 1.6875 -4.328125 1.328125 -4.328125 C 0.875 -4.328125 0.703125 -3.953125 0.609375 -3.765625 C 0.4375 -3.4375 0.296875 -2.84375 0.296875 -2.828125 C 0.296875 -2.71875 0.40625 -2.71875 0.421875 -2.71875 C 0.515625 -2.71875 0.53125 -2.734375 0.59375 -2.953125 C 0.75 -3.640625 0.953125 -4.109375 1.296875 -4.109375 C 1.46875 -4.109375 1.609375 -4.03125 1.609375 -3.65625 C 1.609375 -3.4375 1.578125 -3.328125 1.53125 -3.171875 Z M 2.171875 -3.0625 C 2.234375 -3.328125 2.5 -3.59375 2.671875 -3.75 C 3.015625 -4.046875 3.296875 -4.109375 3.46875 -4.109375 C 3.859375 -4.109375 4.09375 -3.765625 4.09375 -3.1875 C 4.09375 -2.609375 3.765625 -1.484375 3.59375 -1.109375 C 3.265625 -0.4375 2.796875 -0.109375 2.421875 -0.109375 C 1.78125 -0.109375 1.65625 -0.921875 1.65625 -0.984375 C 1.65625 -1 1.65625 -1.015625 1.6875 -1.140625 Z M 2.171875 -3.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 2.21875 -4.28125 C 2.21875 -4.390625 2.140625 -4.546875 1.953125 -4.546875 C 1.765625 -4.546875 1.5625 -4.375 1.5625 -4.171875 C 1.5625 -4.046875 1.65625 -3.90625 1.84375 -3.90625 C 2.03125 -3.90625 2.21875 -4.109375 2.21875 -4.28125 Z M 0.828125 -0.796875 C 0.796875 -0.71875 0.765625 -0.625 0.765625 -0.515625 C 0.765625 -0.1875 1.03125 0.0625 1.40625 0.0625 C 2.09375 0.0625 2.40625 -0.875 2.40625 -0.984375 C 2.40625 -1.0625 2.3125 -1.0625 2.296875 -1.0625 C 2.1875 -1.0625 2.1875 -1.03125 2.15625 -0.953125 C 2 -0.40625 1.703125 -0.125 1.4375 -0.125 C 1.296875 -0.125 1.265625 -0.21875 1.265625 -0.359375 C 1.265625 -0.515625 1.3125 -0.65625 1.375 -0.796875 C 1.4375 -0.984375 1.515625 -1.171875 1.59375 -1.34375 C 1.65625 -1.515625 1.90625 -2.140625 1.921875 -2.21875 C 1.953125 -2.296875 1.96875 -2.375 1.96875 -2.4375 C 1.96875 -2.765625 1.6875 -3.03125 1.3125 -3.03125 C 0.640625 -3.03125 0.328125 -2.09375 0.328125 -1.96875 C 0.328125 -1.890625 0.421875 -1.890625 0.4375 -1.890625 C 0.53125 -1.890625 0.546875 -1.921875 0.5625 -2 C 0.734375 -2.59375 1.046875 -2.828125 1.296875 -2.828125 C 1.40625 -2.828125 1.46875 -2.78125 1.46875 -2.59375 C 1.46875 -2.4375 1.421875 -2.328125 1.25 -1.90625 Z M 0.828125 -0.796875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 2 0.00390625 L 5 0.00390625 L 5 2 L 2 2 Z M 2 0.00390625 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 0 2 L 5 2 L 5 8.710938 L 0 8.710938 Z M 0 2 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 18 0.00390625 L 23 0.00390625 L 23 7 L 18 7 Z M 18 0.00390625 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 41 3 L 44 3 L 44 8.710938 L 41 8.710938 Z M 41 3 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 43 2 L 49 2 L 49 8.710938 L 43 8.710938 Z M 43 2 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 49 3 L 52 3 L 52 8.710938 L 49 8.710938 Z M 49 3 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.899936" y="6.807176"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="0" y="6.807176"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="7.787646" y="6.807176"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="18.130522" y="6.807176"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="25.384107" y="6.807176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="35.183087" y="6.807176"/>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="40.782363" y="8.27658"/>
+</g>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-4" x="44.044756" y="6.807176"/>
+</g>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="48.974243" y="8.27658"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig15.svg b/doc/figs/tex/fig15.svg
new file mode 100644
index 00000000000..d107ae8333f
--- /dev/null
+++ b/doc/figs/tex/fig15.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="10.713pt" height="8.413pt" viewBox="0 0 10.713 8.413" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.328125 -2.71875 C 3.703125 -1.734375 4.15625 -0.3125 4.296875 -0.109375 C 4.453125 0.109375 4.546875 0.109375 4.796875 0.109375 L 5 0.109375 C 5.09375 0.09375 5.109375 0.03125 5.109375 0.015625 C 5.109375 -0.015625 5.078125 -0.03125 5.0625 -0.078125 C 4.96875 -0.171875 4.90625 -0.3125 4.84375 -0.5 L 2.9375 -5.796875 C 2.75 -6.34375 2.25 -6.46875 1.8125 -6.46875 C 1.765625 -6.46875 1.640625 -6.46875 1.640625 -6.359375 C 1.640625 -6.28125 1.71875 -6.265625 1.71875 -6.265625 C 2.03125 -6.21875 2.09375 -6.15625 2.328125 -5.515625 L 3.234375 -2.984375 L 0.65625 -0.4375 C 0.546875 -0.328125 0.5 -0.265625 0.5 -0.15625 C 0.5 0.015625 0.625 0.125 0.765625 0.125 C 0.921875 0.125 1 0.015625 1.078125 -0.078125 Z M 3.328125 -2.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.046875 -4.328125 C 2.046875 -4.34375 2.0625 -4.421875 2.0625 -4.4375 C 2.0625 -4.46875 2.046875 -4.515625 1.96875 -4.515625 C 1.828125 -4.515625 1.296875 -4.46875 1.125 -4.453125 C 1.078125 -4.453125 0.984375 -4.4375 0.984375 -4.3125 C 0.984375 -4.21875 1.078125 -4.21875 1.15625 -4.21875 C 1.46875 -4.21875 1.46875 -4.171875 1.46875 -4.125 C 1.46875 -4.078125 1.453125 -4.03125 1.4375 -3.96875 L 0.515625 -0.28125 C 0.484375 -0.171875 0.484375 -0.15625 0.484375 -0.140625 C 0.484375 -0.046875 0.5625 0.0625 0.703125 0.0625 C 0.890625 0.0625 0.96875 -0.0625 1.015625 -0.203125 C 1.015625 -0.234375 1.296875 -1.375 1.328125 -1.46875 C 1.796875 -1.421875 2.15625 -1.28125 2.15625 -0.9375 C 2.15625 -0.90625 2.15625 -0.875 2.15625 -0.8125 C 2.125 -0.703125 2.125 -0.671875 2.125 -0.609375 C 2.125 -0.140625 2.5 0.0625 2.8125 0.0625 C 3.453125 0.0625 3.640625 -0.921875 3.640625 -0.9375 C 3.640625 -1.015625 3.5625 -1.015625 3.53125 -1.015625 C 3.453125 -1.015625 3.4375 -0.984375 3.40625 -0.859375 C 3.328125 -0.578125 3.15625 -0.125 2.828125 -0.125 C 2.65625 -0.125 2.609375 -0.28125 2.609375 -0.453125 C 2.609375 -0.5625 2.609375 -0.578125 2.640625 -0.75 C 2.65625 -0.765625 2.671875 -0.875 2.671875 -0.953125 C 2.671875 -1.53125 1.890625 -1.625 1.625 -1.640625 C 1.8125 -1.765625 2.046875 -1.96875 2.15625 -2.078125 C 2.5 -2.390625 2.828125 -2.6875 3.1875 -2.6875 C 3.265625 -2.6875 3.34375 -2.671875 3.40625 -2.609375 C 3.125 -2.5625 3.0625 -2.34375 3.0625 -2.234375 C 3.0625 -2.09375 3.171875 -2 3.328125 -2 C 3.5 -2 3.6875 -2.140625 3.6875 -2.421875 C 3.6875 -2.625 3.53125 -2.875 3.1875 -2.875 C 2.828125 -2.875 2.484375 -2.609375 2.15625 -2.296875 C 1.875 -2.046875 1.65625 -1.84375 1.390625 -1.734375 Z M 2.046875 -4.328125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.214844 0 L 6 0 L 6 7 L 0.214844 7 Z M 0.214844 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 6 3 L 10 3 L 10 7.863281 L 6 7.863281 Z M 6 3 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.215222" y="6.467727"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="5.648151" y="7.864285"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig16.svg b/doc/figs/tex/fig16.svg
new file mode 100644
index 00000000000..30e7319ca92
--- /dev/null
+++ b/doc/figs/tex/fig16.svg
@@ -0,0 +1,89 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="56.399pt" height="8.856pt" viewBox="0 0 56.399 8.856" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.453125 -6.796875 L 1.140625 -5.46875 L 1.3125 -5.296875 L 2.453125 -6.296875 L 3.578125 -5.296875 L 3.75 -5.46875 Z M 2.453125 -6.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 6.734375 -3.203125 C 6.875 -3.203125 7.0625 -3.203125 7.0625 -3.40625 C 7.0625 -3.59375 6.875 -3.59375 6.734375 -3.59375 L 0.875 -3.59375 C 0.734375 -3.59375 0.546875 -3.59375 0.546875 -3.40625 C 0.546875 -3.203125 0.734375 -3.203125 0.875 -3.203125 Z M 6.734375 -1.296875 C 6.875 -1.296875 7.0625 -1.296875 7.0625 -1.5 C 7.0625 -1.6875 6.875 -1.6875 6.734375 -1.6875 L 0.875 -1.6875 C 0.734375 -1.6875 0.546875 -1.6875 0.546875 -1.5 C 0.546875 -1.296875 0.734375 -1.296875 0.875 -1.296875 Z M 6.734375 -1.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 4 -2.25 L 6.734375 -2.25 C 6.875 -2.25 7.0625 -2.25 7.0625 -2.453125 C 7.0625 -2.640625 6.875 -2.640625 6.734375 -2.640625 L 4 -2.640625 L 4 -5.390625 C 4 -5.53125 4 -5.71875 3.8125 -5.71875 C 3.609375 -5.71875 3.609375 -5.53125 3.609375 -5.390625 L 3.609375 -2.640625 L 0.875 -2.640625 C 0.734375 -2.640625 0.546875 -2.640625 0.546875 -2.453125 C 0.546875 -2.25 0.734375 -2.25 0.875 -2.25 L 3.609375 -2.25 L 3.609375 0.484375 C 3.609375 0.625 3.609375 0.8125 3.8125 0.8125 C 4 0.8125 4 0.625 4 0.484375 Z M 4 -2.25 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 0.328125 1.6875 C 0.296875 1.8125 0.296875 1.828125 0.296875 1.859375 C 0.296875 2 0.40625 2.109375 0.5625 2.109375 C 0.78125 2.109375 0.890625 1.9375 0.90625 1.90625 C 0.953125 1.828125 1.28125 0.515625 1.53125 -0.546875 C 1.734375 -0.15625 2.046875 0.109375 2.515625 0.109375 C 3.65625 0.109375 4.921875 -1.28125 4.921875 -2.734375 C 4.921875 -3.765625 4.265625 -4.328125 3.5625 -4.328125 C 2.609375 -4.328125 1.578125 -3.34375 1.28125 -2.15625 Z M 2.5 -0.109375 C 1.8125 -0.109375 1.65625 -0.890625 1.65625 -0.984375 C 1.65625 -1.015625 1.703125 -1.21875 1.734375 -1.34375 C 2.015625 -2.4375 2.109375 -2.796875 2.328125 -3.1875 C 2.75 -3.90625 3.234375 -4.109375 3.53125 -4.109375 C 3.90625 -4.109375 4.21875 -3.828125 4.21875 -3.15625 C 4.21875 -2.609375 3.921875 -1.515625 3.65625 -1.03125 C 3.34375 -0.421875 2.875 -0.109375 2.5 -0.109375 Z M 2.5 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.65625 -5.9375 C 3.75 -6.296875 3.78125 -6.390625 4.5625 -6.390625 C 4.796875 -6.390625 4.875 -6.390625 4.875 -6.578125 C 4.875 -6.6875 4.765625 -6.6875 4.71875 -6.6875 C 4.4375 -6.6875 3.71875 -6.65625 3.421875 -6.65625 C 3.140625 -6.65625 2.421875 -6.6875 2.125 -6.6875 C 2.0625 -6.6875 1.9375 -6.6875 1.9375 -6.5 C 1.9375 -6.390625 2.015625 -6.390625 2.203125 -6.390625 C 2.609375 -6.390625 2.875 -6.390625 2.875 -6.203125 C 2.875 -6.15625 2.875 -6.140625 2.859375 -6.046875 L 1.53125 -0.765625 C 1.453125 -0.40625 1.421875 -0.296875 0.640625 -0.296875 C 0.421875 -0.296875 0.328125 -0.296875 0.328125 -0.109375 C 0.328125 0 0.453125 0 0.484375 0 C 0.765625 0 1.484375 -0.03125 1.765625 -0.03125 C 2.0625 -0.03125 2.78125 0 3.078125 0 C 3.15625 0 3.265625 0 3.265625 -0.1875 C 3.265625 -0.296875 3.1875 -0.296875 2.984375 -0.296875 C 2.796875 -0.296875 2.75 -0.296875 2.5625 -0.328125 C 2.34375 -0.34375 2.3125 -0.375 2.3125 -0.484375 C 2.3125 -0.5625 2.328125 -0.640625 2.34375 -0.71875 Z M 3.65625 -5.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 3.5 -2.859375 C 3.90625 -1.828125 4.375 -0.328125 4.53125 -0.109375 C 4.6875 0.109375 4.78125 0.109375 5.046875 0.109375 L 5.265625 0.109375 C 5.359375 0.09375 5.375 0.046875 5.375 0.015625 C 5.375 -0.015625 5.34375 -0.046875 5.3125 -0.078125 C 5.21875 -0.1875 5.15625 -0.328125 5.09375 -0.53125 L 3.09375 -6.109375 C 2.890625 -6.671875 2.359375 -6.796875 1.90625 -6.796875 C 1.859375 -6.796875 1.71875 -6.796875 1.71875 -6.6875 C 1.71875 -6.609375 1.796875 -6.59375 1.8125 -6.59375 C 2.140625 -6.53125 2.203125 -6.46875 2.453125 -5.8125 L 3.40625 -3.140625 L 0.703125 -0.453125 C 0.578125 -0.34375 0.515625 -0.28125 0.515625 -0.15625 C 0.515625 0.015625 0.65625 0.125 0.8125 0.125 C 0.96875 0.125 1.0625 0.015625 1.140625 -0.078125 Z M 3.5 -2.859375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 0.4375 1.1875 C 0.359375 1.53125 0.34375 1.59375 -0.09375 1.59375 C -0.203125 1.59375 -0.3125 1.59375 -0.3125 1.78125 C -0.3125 1.859375 -0.265625 1.90625 -0.1875 1.90625 C 0.078125 1.90625 0.359375 1.875 0.640625 1.875 C 0.953125 1.875 1.296875 1.90625 1.609375 1.90625 C 1.65625 1.90625 1.78125 1.90625 1.78125 1.703125 C 1.78125 1.59375 1.6875 1.59375 1.546875 1.59375 C 1.0625 1.59375 1.0625 1.53125 1.0625 1.4375 C 1.0625 1.328125 1.46875 -0.28125 1.53125 -0.515625 C 1.671875 -0.234375 1.9375 0.109375 2.4375 0.109375 C 3.578125 0.109375 4.796875 -1.328125 4.796875 -2.765625 C 4.796875 -3.6875 4.234375 -4.328125 3.5 -4.328125 C 3 -4.328125 2.53125 -3.984375 2.21875 -3.59375 C 2.109375 -4.125 1.6875 -4.328125 1.328125 -4.328125 C 0.875 -4.328125 0.703125 -3.953125 0.609375 -3.765625 C 0.4375 -3.4375 0.296875 -2.84375 0.296875 -2.828125 C 0.296875 -2.71875 0.40625 -2.71875 0.421875 -2.71875 C 0.515625 -2.71875 0.53125 -2.734375 0.59375 -2.953125 C 0.75 -3.640625 0.953125 -4.109375 1.296875 -4.109375 C 1.46875 -4.109375 1.609375 -4.03125 1.609375 -3.65625 C 1.609375 -3.4375 1.578125 -3.328125 1.53125 -3.171875 Z M 2.171875 -3.0625 C 2.234375 -3.328125 2.5 -3.59375 2.671875 -3.75 C 3.015625 -4.046875 3.296875 -4.109375 3.46875 -4.109375 C 3.859375 -4.109375 4.09375 -3.765625 4.09375 -3.1875 C 4.09375 -2.609375 3.765625 -1.484375 3.59375 -1.109375 C 3.265625 -0.4375 2.796875 -0.109375 2.421875 -0.109375 C 1.78125 -0.109375 1.65625 -0.921875 1.65625 -0.984375 C 1.65625 -1 1.65625 -1.015625 1.6875 -1.140625 Z M 2.171875 -3.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 2.140625 -4.546875 C 2.15625 -4.5625 2.171875 -4.65625 2.171875 -4.671875 C 2.171875 -4.703125 2.140625 -4.765625 2.0625 -4.765625 C 1.921875 -4.765625 1.359375 -4.703125 1.1875 -4.6875 C 1.125 -4.6875 1.03125 -4.671875 1.03125 -4.53125 C 1.03125 -4.4375 1.125 -4.4375 1.21875 -4.4375 C 1.546875 -4.4375 1.546875 -4.390625 1.546875 -4.328125 C 1.546875 -4.28125 1.53125 -4.25 1.515625 -4.1875 L 0.546875 -0.296875 C 0.515625 -0.171875 0.515625 -0.171875 0.515625 -0.15625 C 0.515625 -0.046875 0.59375 0.0625 0.75 0.0625 C 0.9375 0.0625 1.015625 -0.0625 1.0625 -0.21875 C 1.078125 -0.25 1.375 -1.453125 1.40625 -1.546875 C 1.890625 -1.5 2.28125 -1.34375 2.28125 -0.984375 C 2.28125 -0.953125 2.28125 -0.921875 2.265625 -0.84375 C 2.234375 -0.75 2.234375 -0.71875 2.234375 -0.640625 C 2.234375 -0.15625 2.640625 0.0625 2.96875 0.0625 C 3.625 0.0625 3.828125 -0.96875 3.828125 -0.984375 C 3.828125 -1.0625 3.75 -1.0625 3.71875 -1.0625 C 3.625 -1.0625 3.625 -1.03125 3.59375 -0.90625 C 3.5 -0.609375 3.3125 -0.125 2.984375 -0.125 C 2.796875 -0.125 2.75 -0.296875 2.75 -0.484375 C 2.75 -0.59375 2.75 -0.609375 2.78125 -0.78125 C 2.796875 -0.8125 2.8125 -0.921875 2.8125 -1 C 2.8125 -1.609375 2 -1.703125 1.703125 -1.734375 C 1.90625 -1.859375 2.15625 -2.078125 2.28125 -2.1875 C 2.625 -2.515625 2.96875 -2.828125 3.359375 -2.828125 C 3.4375 -2.828125 3.53125 -2.8125 3.578125 -2.75 C 3.28125 -2.703125 3.21875 -2.46875 3.21875 -2.359375 C 3.21875 -2.203125 3.34375 -2.109375 3.5 -2.109375 C 3.6875 -2.109375 3.890625 -2.25 3.890625 -2.546875 C 3.890625 -2.765625 3.71875 -3.03125 3.359375 -3.03125 C 2.96875 -3.03125 2.609375 -2.75 2.265625 -2.421875 C 1.96875 -2.140625 1.75 -1.9375 1.46875 -1.8125 Z M 2.140625 -4.546875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.15625 2 L 6 2 L 6 8.714844 L 0.15625 8.714844 Z M 0.15625 2 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 41 3 L 45 3 L 45 8.714844 L 41 8.714844 Z M 41 3 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 45 2 L 51 2 L 51 8.714844 L 45 8.714844 Z M 45 2 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 51 3 L 55 3 L 55 8.714844 L 51 8.714844 Z M 51 3 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="1.05586" y="6.808296"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="0.1555" y="6.808296"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="7.946812" y="6.808296"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="18.294556" y="6.808296"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="25.551556" y="6.808296"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="35.355148" y="6.808296"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="41.073172" y="8.278392"/>
+</g>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-4" x="45.89674" y="6.808296"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="50.829532" y="8.278392"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig17.svg b/doc/figs/tex/fig17.svg
new file mode 100644
index 00000000000..e06cb3fea26
--- /dev/null
+++ b/doc/figs/tex/fig17.svg
@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="9.914pt" height="6.227pt" viewBox="0 0 9.914 6.227" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 0.40625 1.078125 C 0.328125 1.375 0.3125 1.4375 -0.078125 1.4375 C -0.1875 1.4375 -0.28125 1.4375 -0.28125 1.609375 C -0.28125 1.6875 -0.234375 1.71875 -0.171875 1.71875 C 0.078125 1.71875 0.328125 1.6875 0.578125 1.6875 C 0.875 1.6875 1.171875 1.71875 1.453125 1.71875 C 1.5 1.71875 1.609375 1.71875 1.609375 1.546875 C 1.609375 1.4375 1.53125 1.4375 1.40625 1.4375 C 0.953125 1.4375 0.953125 1.375 0.953125 1.296875 C 0.953125 1.203125 1.328125 -0.25 1.390625 -0.46875 C 1.5 -0.21875 1.75 0.09375 2.203125 0.09375 C 3.234375 0.09375 4.34375 -1.203125 4.34375 -2.5 C 4.34375 -3.328125 3.84375 -3.921875 3.15625 -3.921875 C 2.71875 -3.921875 2.296875 -3.59375 2 -3.25 C 1.90625 -3.734375 1.53125 -3.921875 1.203125 -3.921875 C 0.796875 -3.921875 0.625 -3.578125 0.546875 -3.40625 C 0.390625 -3.109375 0.28125 -2.578125 0.28125 -2.546875 C 0.28125 -2.46875 0.359375 -2.46875 0.375 -2.46875 C 0.46875 -2.46875 0.484375 -2.46875 0.53125 -2.671875 C 0.6875 -3.296875 0.859375 -3.71875 1.171875 -3.71875 C 1.328125 -3.71875 1.453125 -3.65625 1.453125 -3.3125 C 1.453125 -3.109375 1.421875 -3.015625 1.390625 -2.859375 Z M 1.953125 -2.765625 C 2.015625 -3 2.265625 -3.25 2.421875 -3.390625 C 2.734375 -3.65625 2.984375 -3.71875 3.140625 -3.71875 C 3.484375 -3.71875 3.703125 -3.40625 3.703125 -2.890625 C 3.703125 -2.359375 3.40625 -1.34375 3.25 -1.015625 C 2.953125 -0.390625 2.53125 -0.09375 2.203125 -0.09375 C 1.609375 -0.09375 1.5 -0.828125 1.5 -0.890625 C 1.5 -0.90625 1.5 -0.921875 1.53125 -1.03125 Z M 1.953125 -2.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 1.9375 -4.125 C 1.953125 -4.125 1.96875 -4.21875 1.96875 -4.21875 C 1.96875 -4.25 1.9375 -4.3125 1.859375 -4.3125 C 1.75 -4.3125 1.234375 -4.25 1.078125 -4.25 C 1.03125 -4.234375 0.9375 -4.234375 0.9375 -4.09375 C 0.9375 -4.015625 1.03125 -4.015625 1.09375 -4.015625 C 1.390625 -4.015625 1.390625 -3.96875 1.390625 -3.921875 C 1.390625 -3.875 1.390625 -3.84375 1.375 -3.78125 L 0.5 -0.265625 C 0.46875 -0.15625 0.46875 -0.15625 0.46875 -0.140625 C 0.46875 -0.046875 0.546875 0.0625 0.671875 0.0625 C 0.84375 0.0625 0.921875 -0.0625 0.96875 -0.203125 C 0.96875 -0.21875 1.234375 -1.3125 1.265625 -1.40625 C 1.703125 -1.359375 2.0625 -1.21875 2.0625 -0.890625 C 2.0625 -0.859375 2.0625 -0.828125 2.046875 -0.765625 C 2.015625 -0.671875 2.015625 -0.640625 2.015625 -0.578125 C 2.015625 -0.140625 2.375 0.0625 2.6875 0.0625 C 3.28125 0.0625 3.46875 -0.875 3.46875 -0.890625 C 3.46875 -0.96875 3.390625 -0.96875 3.375 -0.96875 C 3.28125 -0.96875 3.28125 -0.9375 3.25 -0.8125 C 3.171875 -0.546875 3 -0.109375 2.703125 -0.109375 C 2.53125 -0.109375 2.484375 -0.265625 2.484375 -0.4375 C 2.484375 -0.546875 2.484375 -0.546875 2.515625 -0.71875 C 2.53125 -0.734375 2.546875 -0.84375 2.546875 -0.90625 C 2.546875 -1.453125 1.8125 -1.546875 1.546875 -1.5625 C 1.71875 -1.671875 1.953125 -1.875 2.0625 -1.96875 C 2.375 -2.265625 2.6875 -2.5625 3.03125 -2.5625 C 3.109375 -2.5625 3.1875 -2.546875 3.234375 -2.484375 C 2.96875 -2.4375 2.921875 -2.234375 2.921875 -2.140625 C 2.921875 -2 3.015625 -1.90625 3.15625 -1.90625 C 3.328125 -1.90625 3.515625 -2.046875 3.515625 -2.296875 C 3.515625 -2.5 3.375 -2.734375 3.046875 -2.734375 C 2.6875 -2.734375 2.359375 -2.484375 2.046875 -2.1875 C 1.78125 -1.9375 1.578125 -1.75 1.328125 -1.640625 Z M 1.9375 -4.125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.507812 0 L 5 0 L 5 5.539062 L 0.507812 5.539062 Z M 0.507812 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 5 0 L 9 0 L 9 5.539062 L 5 5.539062 Z M 5 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.509143" y="3.816261"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="4.967675" y="5.145281"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig18.svg b/doc/figs/tex/fig18.svg
new file mode 100644
index 00000000000..2c2621e562f
--- /dev/null
+++ b/doc/figs/tex/fig18.svg
@@ -0,0 +1,118 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="85.598pt" height="12.492pt" viewBox="0 0 85.598 12.492" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.328125 -6.546875 C 1.984375 -6.546875 0.953125 -5.890625 0.5625 -5.4375 C 0.234375 -5.0625 0.203125 -4.78125 0.203125 -4.765625 C 0.203125 -4.703125 0.234375 -4.6875 0.296875 -4.6875 C 0.453125 -4.6875 0.671875 -4.8125 0.75 -4.859375 C 0.953125 -5 0.984375 -5.0625 1.03125 -5.234375 C 1.171875 -5.625 1.4375 -5.953125 2.640625 -6.015625 C 2.46875 -3.859375 1.890625 -1.765625 1.09375 0.234375 C 1.03125 0.390625 1.03125 0.40625 1.03125 0.40625 C 1.03125 0.4375 1.0625 0.484375 1.125 0.484375 C 1.28125 0.484375 1.75 0.265625 1.84375 0.015625 C 2.34375 -1.15625 3.125 -3.359375 3.421875 -6.015625 L 3.921875 -6.015625 C 5.09375 -6.015625 6.203125 -5.5625 6.203125 -4.609375 C 6.203125 -3.890625 5.515625 -2.546875 3.65625 -2.484375 C 3.453125 -2.484375 3.359375 -2.484375 3.078125 -2.3125 C 2.90625 -2.1875 2.828125 -2.09375 2.828125 -2.03125 C 2.828125 -1.96875 2.890625 -1.96875 3.015625 -1.96875 C 4.765625 -1.96875 7.015625 -3.4375 7.015625 -5.015625 C 7.015625 -6.109375 5.734375 -6.546875 4.609375 -6.546875 Z M 3.328125 -6.546875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 1.515625 -6.84375 C 1.515625 -7.015625 1.515625 -7.1875 1.328125 -7.1875 C 1.140625 -7.1875 1.140625 -7.015625 1.140625 -6.84375 L 1.140625 2.046875 C 1.140625 2.21875 1.140625 2.390625 1.328125 2.390625 C 1.515625 2.390625 1.515625 2.21875 1.515625 2.046875 Z M 1.515625 -6.84375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.171875 2.296875 C 3.171875 2.265625 3.171875 2.25 3 2.09375 C 1.8125 0.875 1.5 -0.921875 1.5 -2.390625 C 1.5 -4.0625 1.875 -5.734375 3.046875 -6.921875 C 3.171875 -7.046875 3.171875 -7.0625 3.171875 -7.09375 C 3.171875 -7.15625 3.125 -7.1875 3.078125 -7.1875 C 2.984375 -7.1875 2.109375 -6.53125 1.546875 -5.3125 C 1.0625 -4.265625 0.953125 -3.203125 0.953125 -2.390625 C 0.953125 -1.640625 1.046875 -0.484375 1.578125 0.59375 C 2.15625 1.765625 2.984375 2.390625 3.078125 2.390625 C 3.125 2.390625 3.171875 2.359375 3.171875 2.296875 Z M 3.171875 2.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.765625 -2.390625 C 2.765625 -3.140625 2.65625 -4.296875 2.140625 -5.390625 C 1.5625 -6.5625 0.734375 -7.1875 0.640625 -7.1875 C 0.578125 -7.1875 0.546875 -7.140625 0.546875 -7.09375 C 0.546875 -7.0625 0.546875 -7.046875 0.734375 -6.875 C 1.671875 -5.921875 2.21875 -4.390625 2.21875 -2.390625 C 2.21875 -0.75 1.859375 0.921875 0.671875 2.140625 C 0.546875 2.25 0.546875 2.265625 0.546875 2.296875 C 0.546875 2.359375 0.578125 2.390625 0.640625 2.390625 C 0.734375 2.390625 1.59375 1.75 2.171875 0.53125 C 2.65625 -0.53125 2.765625 -1.59375 2.765625 -2.390625 Z M 2.765625 -2.390625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 6.578125 -3.125 C 6.71875 -3.125 6.90625 -3.125 6.90625 -3.328125 C 6.90625 -3.515625 6.71875 -3.515625 6.59375 -3.515625 L 0.859375 -3.515625 C 0.71875 -3.515625 0.53125 -3.515625 0.53125 -3.328125 C 0.53125 -3.125 0.71875 -3.125 0.859375 -3.125 Z M 6.59375 -1.28125 C 6.71875 -1.28125 6.90625 -1.28125 6.90625 -1.46875 C 6.90625 -1.65625 6.71875 -1.65625 6.578125 -1.65625 L 0.859375 -1.65625 C 0.71875 -1.65625 0.53125 -1.65625 0.53125 -1.46875 C 0.53125 -1.28125 0.71875 -1.28125 0.859375 -1.28125 Z M 6.59375 -1.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.3125 -2.359375 L 4.4375 -3.59375 C 4.5625 -3.734375 4.609375 -3.796875 5.40625 -3.796875 L 5.40625 -4.25 C 5.078125 -4.234375 4.578125 -4.21875 4.53125 -4.21875 C 4.296875 -4.21875 3.8125 -4.25 3.546875 -4.25 L 3.546875 -3.796875 C 3.671875 -3.796875 3.796875 -3.78125 3.90625 -3.71875 C 3.875 -3.65625 3.875 -3.640625 3.828125 -3.59375 L 3.03125 -2.703125 L 2.09375 -3.796875 L 2.46875 -3.796875 L 2.46875 -4.25 C 2.21875 -4.25 1.625 -4.21875 1.3125 -4.21875 C 1 -4.21875 0.578125 -4.25 0.265625 -4.25 L 0.265625 -3.796875 L 0.9375 -3.796875 L 2.4375 -2.046875 L 1.171875 -0.625 C 1.015625 -0.453125 0.671875 -0.453125 0.203125 -0.453125 L 0.203125 0 C 0.546875 -0.015625 1.046875 -0.03125 1.09375 -0.03125 C 1.328125 -0.03125 1.890625 -0.015625 2.078125 0 L 2.078125 -0.453125 C 1.90625 -0.453125 1.71875 -0.5 1.71875 -0.5625 C 1.71875 -0.5625 1.71875 -0.578125 1.796875 -0.65625 L 2.71875 -1.703125 L 3.78125 -0.453125 L 3.40625 -0.453125 L 3.40625 0 C 3.65625 -0.015625 4.234375 -0.03125 4.546875 -0.03125 C 4.859375 -0.03125 5.28125 -0.015625 5.609375 0 L 5.609375 -0.453125 L 4.921875 -0.453125 Z M 3.3125 -2.359375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.03125 5.109375 L 0.625 9.3125 C 0.5625 9.421875 0.546875 9.4375 0.546875 9.46875 C 0.546875 9.578125 0.625 9.578125 0.796875 9.578125 L 8.75 9.578125 L 9.5625 7.1875 L 9.328125 7.1875 C 9.09375 7.90625 8.453125 8.5 7.640625 8.78125 C 7.484375 8.828125 6.8125 9.046875 5.40625 9.046875 L 1.34375 9.046875 L 4.671875 4.9375 C 4.734375 4.859375 4.75 4.828125 4.75 4.796875 C 4.75 4.75 4.734375 4.734375 4.6875 4.65625 L 1.578125 0.390625 L 5.359375 0.390625 C 6.453125 0.390625 8.65625 0.453125 9.328125 2.234375 L 9.5625 2.234375 L 8.75 0 L 0.796875 0 C 0.546875 0 0.53125 0.015625 0.53125 0.3125 Z M 4.03125 5.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 2.09375 -4.453125 C 2.109375 -4.46875 2.125 -4.546875 2.125 -4.5625 C 2.125 -4.59375 2.09375 -4.65625 2.015625 -4.65625 C 1.890625 -4.65625 1.328125 -4.59375 1.15625 -4.578125 C 1.109375 -4.578125 1.015625 -4.578125 1.015625 -4.4375 C 1.015625 -4.34375 1.109375 -4.34375 1.1875 -4.34375 C 1.515625 -4.34375 1.515625 -4.296875 1.515625 -4.234375 C 1.515625 -4.1875 1.5 -4.15625 1.484375 -4.09375 L 0.53125 -0.296875 C 0.5 -0.171875 0.5 -0.15625 0.5 -0.140625 C 0.5 -0.046875 0.578125 0.0625 0.734375 0.0625 C 0.90625 0.0625 1 -0.0625 1.03125 -0.21875 C 1.046875 -0.234375 1.34375 -1.421875 1.375 -1.515625 C 1.84375 -1.46875 2.21875 -1.3125 2.21875 -0.96875 C 2.21875 -0.9375 2.21875 -0.890625 2.21875 -0.828125 C 2.1875 -0.734375 2.1875 -0.703125 2.1875 -0.625 C 2.1875 -0.140625 2.578125 0.0625 2.890625 0.0625 C 3.546875 0.0625 3.75 -0.953125 3.75 -0.953125 C 3.75 -1.046875 3.65625 -1.046875 3.640625 -1.046875 C 3.546875 -1.046875 3.546875 -1.015625 3.5 -0.890625 C 3.421875 -0.59375 3.25 -0.125 2.921875 -0.125 C 2.734375 -0.125 2.6875 -0.28125 2.6875 -0.46875 C 2.6875 -0.578125 2.6875 -0.59375 2.71875 -0.765625 C 2.734375 -0.796875 2.75 -0.90625 2.75 -0.984375 C 2.75 -1.578125 1.953125 -1.671875 1.671875 -1.6875 C 1.859375 -1.8125 2.109375 -2.03125 2.21875 -2.125 C 2.5625 -2.453125 2.90625 -2.765625 3.28125 -2.765625 C 3.359375 -2.765625 3.453125 -2.75 3.5 -2.6875 C 3.203125 -2.640625 3.15625 -2.40625 3.15625 -2.3125 C 3.15625 -2.15625 3.265625 -2.0625 3.421875 -2.0625 C 3.59375 -2.0625 3.796875 -2.203125 3.796875 -2.484375 C 3.796875 -2.703125 3.640625 -2.953125 3.28125 -2.953125 C 2.90625 -2.953125 2.546875 -2.6875 2.21875 -2.359375 C 1.9375 -2.09375 1.703125 -1.890625 1.4375 -1.78125 Z M 2.09375 -4.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.515625 -3.609375 C 4.515625 -3.671875 4.546875 -3.71875 4.546875 -3.78125 C 4.546875 -3.953125 4.421875 -4.046875 4.265625 -4.046875 C 4.171875 -4.046875 3.90625 -3.96875 3.875 -3.625 C 3.703125 -3.984375 3.359375 -4.234375 2.984375 -4.234375 C 1.890625 -4.234375 0.703125 -2.890625 0.703125 -1.515625 C 0.703125 -0.5625 1.28125 0 1.96875 0 C 2.53125 0 2.984375 -0.453125 3.078125 -0.5625 L 3.09375 -0.546875 C 2.890625 0.3125 2.78125 0.703125 2.78125 0.71875 C 2.734375 0.796875 2.40625 1.75 1.390625 1.75 C 1.21875 1.75 0.90625 1.75 0.625 1.65625 C 0.921875 1.578125 1.03125 1.328125 1.03125 1.15625 C 1.03125 1 0.921875 0.828125 0.65625 0.828125 C 0.453125 0.828125 0.140625 1 0.140625 1.375 C 0.140625 1.765625 0.5 1.96875 1.421875 1.96875 C 2.609375 1.96875 3.296875 1.21875 3.453125 0.640625 Z M 3.265625 -1.21875 C 3.203125 -0.984375 2.984375 -0.734375 2.78125 -0.5625 C 2.578125 -0.390625 2.28125 -0.203125 2 -0.203125 C 1.515625 -0.203125 1.375 -0.703125 1.375 -1.09375 C 1.375 -1.546875 1.65625 -2.6875 1.921875 -3.171875 C 2.171875 -3.640625 2.59375 -4.015625 2.984375 -4.015625 C 3.625 -4.015625 3.75 -3.25 3.75 -3.203125 C 3.75 -3.15625 3.734375 -3.09375 3.71875 -3.0625 Z M 3.265625 -1.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 1.71875 -1.09375 C 1.328125 -0.453125 0.953125 -0.328125 0.53125 -0.296875 C 0.421875 -0.28125 0.328125 -0.28125 0.328125 -0.109375 C 0.328125 -0.046875 0.390625 0 0.453125 0 C 0.71875 0 1.015625 -0.03125 1.28125 -0.03125 C 1.59375 -0.03125 1.9375 0 2.234375 0 C 2.296875 0 2.421875 0 2.421875 -0.1875 C 2.421875 -0.28125 2.34375 -0.296875 2.265625 -0.296875 C 2.046875 -0.3125 1.8125 -0.390625 1.8125 -0.625 C 1.8125 -0.75 1.875 -0.859375 1.953125 -0.984375 L 2.6875 -2.21875 L 5.09375 -2.21875 C 5.109375 -2.015625 5.234375 -0.703125 5.234375 -0.609375 C 5.234375 -0.328125 4.734375 -0.296875 4.546875 -0.296875 C 4.421875 -0.296875 4.3125 -0.296875 4.3125 -0.109375 C 4.3125 0 4.4375 0 4.453125 0 C 4.84375 0 5.265625 -0.03125 5.65625 -0.03125 C 5.890625 -0.03125 6.5 0 6.734375 0 C 6.796875 0 6.90625 0 6.90625 -0.1875 C 6.90625 -0.296875 6.8125 -0.296875 6.6875 -0.296875 C 6.09375 -0.296875 6.09375 -0.359375 6.0625 -0.640625 L 5.484375 -6.625 C 5.453125 -6.8125 5.453125 -6.859375 5.296875 -6.859375 C 5.140625 -6.859375 5.109375 -6.796875 5.046875 -6.6875 Z M 2.859375 -2.515625 L 4.75 -5.671875 L 5.0625 -2.515625 Z M 2.859375 -2.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 3.390625 -1.21875 L 3.15625 -1.21875 C 3.140625 -1.078125 3.0625 -0.671875 2.984375 -0.609375 C 2.921875 -0.5625 2.40625 -0.5625 2.3125 -0.5625 L 1.078125 -0.5625 C 1.796875 -1.1875 2.03125 -1.375 2.421875 -1.703125 C 2.921875 -2.09375 3.390625 -2.5 3.390625 -3.140625 C 3.390625 -3.953125 2.671875 -4.453125 1.8125 -4.453125 C 0.984375 -4.453125 0.421875 -3.875 0.421875 -3.25 C 0.421875 -2.90625 0.703125 -2.875 0.78125 -2.875 C 0.9375 -2.875 1.140625 -2.984375 1.140625 -3.234375 C 1.140625 -3.359375 1.078125 -3.59375 0.734375 -3.59375 C 0.9375 -4.0625 1.40625 -4.203125 1.71875 -4.203125 C 2.390625 -4.203125 2.734375 -3.6875 2.734375 -3.140625 C 2.734375 -2.5625 2.3125 -2.09375 2.109375 -1.859375 L 0.484375 -0.265625 C 0.421875 -0.203125 0.421875 -0.1875 0.421875 0 L 3.1875 0 Z M 3.390625 -1.21875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1.480469 2 L 9 2 L 9 10 L 1.480469 10 Z M 1.480469 2 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 45 7 L 49 7 L 49 12.003906 L 45 12.003906 Z M 45 7 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="1.479308" y="9.131652"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.925501" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="12.648117" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="18.458818" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="24.843247" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="34.946337" y="1.951635"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="45.051404" y="12.003851"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="51.356981" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="56.266337" y="5.657915"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="55.923287" y="11.843377"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="62.228865" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="64.887739" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="72.067756" y="10.568232"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="76.778201" y="9.131652"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="79.438036" y="4.318388"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig19.svg b/doc/figs/tex/fig19.svg
new file mode 100644
index 00000000000..c4756c76dc2
--- /dev/null
+++ b/doc/figs/tex/fig19.svg
@@ -0,0 +1,32 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="12.994pt" height="8.11pt" viewBox="0 0 12.994 8.11" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 1.421875 -0.703125 C 1.34375 -0.34375 1.328125 -0.28125 0.609375 -0.28125 C 0.453125 -0.28125 0.359375 -0.28125 0.359375 -0.109375 C 0.359375 0 0.4375 0 0.609375 0 L 3.578125 0 C 5.453125 0 7.21875 -1.890625 7.21875 -3.859375 C 7.21875 -5.125 6.453125 -6.140625 5.109375 -6.140625 L 2.09375 -6.140625 C 1.921875 -6.140625 1.828125 -6.140625 1.828125 -5.96875 C 1.828125 -5.859375 1.90625 -5.859375 2.078125 -5.859375 C 2.203125 -5.859375 2.359375 -5.84375 2.46875 -5.84375 C 2.609375 -5.828125 2.671875 -5.796875 2.671875 -5.703125 C 2.671875 -5.65625 2.65625 -5.640625 2.625 -5.53125 Z M 3.375 -5.515625 C 3.453125 -5.828125 3.46875 -5.859375 3.859375 -5.859375 L 4.8125 -5.859375 C 5.703125 -5.859375 6.4375 -5.375 6.4375 -4.203125 C 6.4375 -3.75 6.265625 -2.28125 5.5 -1.296875 C 5.234375 -0.96875 4.53125 -0.28125 3.421875 -0.28125 L 2.40625 -0.28125 C 2.28125 -0.28125 2.265625 -0.28125 2.203125 -0.28125 C 2.125 -0.296875 2.09375 -0.3125 2.09375 -0.375 C 2.09375 -0.40625 2.09375 -0.421875 2.140625 -0.578125 Z M 3.375 -5.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.234375 -2 C 3.234375 -2.6875 3.15625 -3.1875 2.875 -3.625 C 2.671875 -3.921875 2.28125 -4.171875 1.78125 -4.171875 C 0.328125 -4.171875 0.328125 -2.453125 0.328125 -2 C 0.328125 -1.546875 0.328125 0.125 1.78125 0.125 C 3.234375 0.125 3.234375 -1.546875 3.234375 -2 Z M 1.78125 -0.046875 C 1.5 -0.046875 1.109375 -0.21875 0.984375 -0.734375 C 0.890625 -1.109375 0.890625 -1.625 0.890625 -2.078125 C 0.890625 -2.546875 0.890625 -3.015625 1 -3.359375 C 1.125 -3.859375 1.53125 -4 1.78125 -4 C 2.125 -4 2.453125 -3.78125 2.5625 -3.421875 C 2.65625 -3.078125 2.671875 -2.625 2.671875 -2.078125 C 2.671875 -1.625 2.671875 -1.15625 2.59375 -0.765625 C 2.46875 -0.1875 2.03125 -0.046875 1.78125 -0.046875 Z M 1.78125 -0.046875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 1 L 8 1 L 8 7.308594 L 1 7.308594 Z M 1 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.639778" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.32175" y="4.050494"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig2.svg b/doc/figs/tex/fig2.svg
new file mode 100644
index 00000000000..1d0aad29aeb
--- /dev/null
+++ b/doc/figs/tex/fig2.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="6.047pt" height="4.705pt" viewBox="0 0 6.047 4.705" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.984375 -2.125 L 3.984375 -3.234375 C 4.09375 -3.359375 4.15625 -3.421875 4.859375 -3.421875 L 4.859375 -3.828125 C 4.5625 -3.8125 4.109375 -3.796875 4.078125 -3.796875 C 3.859375 -3.796875 3.421875 -3.8125 3.1875 -3.828125 L 3.1875 -3.421875 C 3.3125 -3.421875 3.40625 -3.40625 3.515625 -3.34375 C 3.484375 -3.28125 3.484375 -3.265625 3.4375 -3.234375 L 2.71875 -2.421875 L 1.875 -3.421875 L 2.21875 -3.421875 L 2.21875 -3.828125 C 2 -3.8125 1.453125 -3.796875 1.171875 -3.796875 C 0.90625 -3.796875 0.515625 -3.8125 0.234375 -3.828125 L 0.234375 -3.421875 L 0.84375 -3.421875 L 2.1875 -1.828125 L 1.0625 -0.5625 C 0.90625 -0.40625 0.609375 -0.40625 0.1875 -0.40625 L 0.1875 0 C 0.484375 -0.015625 0.9375 -0.03125 0.984375 -0.03125 C 1.203125 -0.03125 1.703125 -0.015625 1.875 0 L 1.875 -0.40625 C 1.71875 -0.40625 1.546875 -0.453125 1.546875 -0.5 C 1.546875 -0.515625 1.546875 -0.515625 1.609375 -0.578125 L 2.4375 -1.53125 L 3.390625 -0.40625 L 3.0625 -0.40625 L 3.0625 0 C 3.28125 -0.015625 3.8125 -0.03125 4.09375 -0.03125 C 4.359375 -0.03125 4.75 -0.015625 5.03125 0 L 5.03125 -0.40625 L 4.421875 -0.40625 Z M 2.984375 -2.125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.191406 L 5.222656 0.191406 L 5.222656 4.257812 L 0 4.257812 Z M 0 0.191406 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="4.018017"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig20.svg b/doc/figs/tex/fig20.svg
new file mode 100644
index 00000000000..1bc66dad39a
--- /dev/null
+++ b/doc/figs/tex/fig20.svg
@@ -0,0 +1,36 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="14.432pt" height="8.11pt" viewBox="0 0 14.432 8.11" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.640625 -5.75 C 2.640625 -5.96875 2.640625 -5.984375 2.4375 -5.984375 C 1.875 -5.40625 1.09375 -5.40625 0.796875 -5.40625 L 0.796875 -5.125 C 0.984375 -5.125 1.515625 -5.125 1.96875 -5.359375 L 1.96875 -0.703125 C 1.96875 -0.390625 1.953125 -0.28125 1.140625 -0.28125 L 0.859375 -0.28125 L 0.859375 0 C 1.171875 -0.03125 1.953125 -0.03125 2.3125 -0.03125 C 2.671875 -0.03125 3.453125 -0.03125 3.765625 0 L 3.765625 -0.28125 L 3.484375 -0.28125 C 2.671875 -0.28125 2.640625 -0.375 2.640625 -0.703125 Z M 2.640625 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.125 -2.875 C 4.125 -3.59375 4.09375 -4.3125 3.765625 -4.984375 C 3.359375 -5.84375 2.625 -5.984375 2.25 -5.984375 C 1.703125 -5.984375 1.046875 -5.75 0.6875 -4.921875 C 0.390625 -4.296875 0.34375 -3.59375 0.34375 -2.875 C 0.34375 -2.203125 0.390625 -1.390625 0.75 -0.703125 C 1.140625 0.015625 1.796875 0.203125 2.234375 0.203125 C 2.71875 0.203125 3.40625 0.015625 3.796875 -0.84375 C 4.09375 -1.46875 4.125 -2.171875 4.125 -2.875 Z M 2.234375 0 C 1.890625 0 1.359375 -0.21875 1.1875 -1.09375 C 1.09375 -1.625 1.09375 -2.453125 1.09375 -2.984375 C 1.09375 -3.5625 1.09375 -4.15625 1.171875 -4.640625 C 1.34375 -5.703125 2.015625 -5.78125 2.234375 -5.78125 C 2.53125 -5.78125 3.125 -5.625 3.296875 -4.734375 C 3.390625 -4.234375 3.390625 -3.546875 3.390625 -2.984375 C 3.390625 -2.3125 3.390625 -1.703125 3.28125 -1.125 C 3.15625 -0.265625 2.640625 0 2.234375 0 Z M 2.234375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 0.9375 -2.046875 C 0.9375 -2.5625 0.984375 -3.03125 1.21875 -3.421875 C 1.4375 -3.75 1.78125 -3.984375 2.171875 -3.984375 C 2.375 -3.984375 2.625 -3.9375 2.75 -3.765625 C 2.59375 -3.75 2.453125 -3.65625 2.453125 -3.46875 C 2.453125 -3.3125 2.5625 -3.171875 2.75 -3.171875 C 2.9375 -3.171875 3.046875 -3.296875 3.046875 -3.484375 C 3.046875 -3.84375 2.78125 -4.171875 2.171875 -4.171875 C 1.265625 -4.171875 0.34375 -3.34375 0.34375 -1.984375 C 0.34375 -0.359375 1.109375 0.125 1.796875 0.125 C 2.5625 0.125 3.234375 -0.453125 3.234375 -1.28125 C 3.234375 -2.078125 2.59375 -2.671875 1.859375 -2.671875 C 1.359375 -2.671875 1.078125 -2.34375 0.9375 -2.046875 Z M 1.796875 -0.078125 C 1.484375 -0.078125 1.234375 -0.25 1.109375 -0.53125 C 1.015625 -0.71875 0.96875 -1.03125 0.96875 -1.40625 C 0.96875 -2.015625 1.328125 -2.5 1.828125 -2.5 C 2.109375 -2.5 2.3125 -2.375 2.46875 -2.140625 C 2.625 -1.90625 2.625 -1.640625 2.625 -1.28125 C 2.625 -0.921875 2.625 -0.65625 2.453125 -0.421875 C 2.3125 -0.1875 2.109375 -0.078125 1.796875 -0.078125 Z M 1.796875 -0.078125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 1 L 10 1 L 10 7.308594 L 1 7.308594 Z M 1 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.457667" y="7.308011"/>
+ <use xlink:href="#glyph0-2" x="4.946371" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="9.435437" y="4.050494"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig21.svg b/doc/figs/tex/fig21.svg
new file mode 100644
index 00000000000..9d2d8902ad9
--- /dev/null
+++ b/doc/figs/tex/fig21.svg
@@ -0,0 +1,105 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="82.453pt" height="8.11pt" viewBox="0 0 82.453 8.11" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 1.421875 -0.703125 C 1.34375 -0.34375 1.328125 -0.28125 0.609375 -0.28125 C 0.453125 -0.28125 0.359375 -0.28125 0.359375 -0.109375 C 0.359375 0 0.4375 0 0.609375 0 L 3.578125 0 C 5.453125 0 7.21875 -1.890625 7.21875 -3.859375 C 7.21875 -5.125 6.453125 -6.140625 5.109375 -6.140625 L 2.09375 -6.140625 C 1.921875 -6.140625 1.828125 -6.140625 1.828125 -5.96875 C 1.828125 -5.859375 1.90625 -5.859375 2.078125 -5.859375 C 2.203125 -5.859375 2.359375 -5.84375 2.46875 -5.84375 C 2.609375 -5.828125 2.671875 -5.796875 2.671875 -5.703125 C 2.671875 -5.65625 2.65625 -5.640625 2.625 -5.53125 Z M 3.375 -5.515625 C 3.453125 -5.828125 3.46875 -5.859375 3.859375 -5.859375 L 4.8125 -5.859375 C 5.703125 -5.859375 6.4375 -5.375 6.4375 -4.203125 C 6.4375 -3.75 6.265625 -2.28125 5.5 -1.296875 C 5.234375 -0.96875 4.53125 -0.28125 3.421875 -0.28125 L 2.40625 -0.28125 C 2.28125 -0.28125 2.265625 -0.28125 2.203125 -0.28125 C 2.125 -0.296875 2.09375 -0.3125 2.09375 -0.375 C 2.09375 -0.40625 2.09375 -0.421875 2.140625 -0.578125 Z M 3.375 -5.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.578125 -3.625 C 4.5625 -3.65625 4.53125 -3.734375 4.53125 -3.75 C 4.53125 -3.765625 4.6875 -3.890625 4.78125 -3.96875 L 6.359375 -5.171875 C 7.203125 -5.796875 7.5625 -5.828125 7.828125 -5.859375 C 7.890625 -5.859375 7.984375 -5.875 7.984375 -6.03125 C 7.984375 -6.078125 7.953125 -6.140625 7.890625 -6.140625 C 7.6875 -6.140625 7.46875 -6.109375 7.25 -6.109375 C 6.921875 -6.109375 6.578125 -6.140625 6.25 -6.140625 C 6.1875 -6.140625 6.078125 -6.140625 6.078125 -5.953125 C 6.078125 -5.890625 6.125 -5.859375 6.1875 -5.859375 C 6.390625 -5.84375 6.46875 -5.796875 6.46875 -5.671875 C 6.46875 -5.5 6.203125 -5.296875 6.140625 -5.25 L 2.640625 -2.5625 L 3.359375 -5.4375 C 3.4375 -5.765625 3.453125 -5.859375 4.109375 -5.859375 C 4.34375 -5.859375 4.421875 -5.859375 4.421875 -6.03125 C 4.421875 -6.125 4.34375 -6.140625 4.296875 -6.140625 C 4.046875 -6.140625 3.390625 -6.109375 3.140625 -6.109375 C 2.890625 -6.109375 2.25 -6.140625 1.984375 -6.140625 C 1.921875 -6.140625 1.8125 -6.140625 1.8125 -5.96875 C 1.8125 -5.859375 1.890625 -5.859375 2.0625 -5.859375 C 2.1875 -5.859375 2.34375 -5.84375 2.453125 -5.84375 C 2.59375 -5.828125 2.65625 -5.796875 2.65625 -5.703125 C 2.65625 -5.65625 2.640625 -5.640625 2.609375 -5.53125 L 1.40625 -0.703125 C 1.328125 -0.34375 1.296875 -0.28125 0.59375 -0.28125 C 0.4375 -0.28125 0.34375 -0.28125 0.34375 -0.109375 C 0.34375 0 0.453125 0 0.46875 0 C 0.734375 0 1.359375 -0.03125 1.609375 -0.03125 C 1.8125 -0.03125 2 -0.015625 2.1875 -0.015625 C 2.390625 -0.015625 2.59375 0 2.78125 0 C 2.84375 0 2.953125 0 2.953125 -0.171875 C 2.953125 -0.28125 2.875 -0.28125 2.703125 -0.28125 C 2.375 -0.28125 2.125 -0.28125 2.125 -0.4375 C 2.125 -0.5 2.171875 -0.703125 2.203125 -0.828125 C 2.328125 -1.296875 2.4375 -1.78125 2.5625 -2.25 L 3.90625 -3.28125 L 4.9375 -0.875 C 5.046875 -0.625 5.046875 -0.609375 5.046875 -0.5625 C 5.046875 -0.28125 4.65625 -0.28125 4.578125 -0.28125 C 4.484375 -0.28125 4.390625 -0.28125 4.390625 -0.09375 C 4.390625 0 4.484375 0 4.515625 0 C 4.875 0 5.25 -0.03125 5.609375 -0.03125 C 5.796875 -0.03125 6.28125 0 6.484375 0 C 6.53125 0 6.640625 0 6.640625 -0.171875 C 6.640625 -0.28125 6.546875 -0.28125 6.46875 -0.28125 C 6.09375 -0.28125 5.984375 -0.375 5.84375 -0.6875 Z M 4.578125 -3.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 2.375 -3.34375 L 3.390625 -3.34375 C 3.09375 -2.015625 3.015625 -1.640625 3.015625 -1.03125 C 3.015625 -0.890625 3.015625 -0.65625 3.09375 -0.34375 C 3.1875 0.046875 3.28125 0.09375 3.40625 0.09375 C 3.59375 0.09375 3.78125 -0.0625 3.78125 -0.25 C 3.78125 -0.296875 3.78125 -0.3125 3.734375 -0.4375 C 3.46875 -1.09375 3.46875 -1.671875 3.46875 -1.921875 C 3.46875 -2.40625 3.53125 -2.890625 3.625 -3.34375 L 4.65625 -3.34375 C 4.765625 -3.34375 5.09375 -3.34375 5.09375 -3.65625 C 5.09375 -3.875 4.90625 -3.875 4.734375 -3.875 L 1.71875 -3.875 C 1.53125 -3.875 1.1875 -3.875 0.796875 -3.453125 C 0.46875 -3.09375 0.25 -2.6875 0.25 -2.640625 C 0.25 -2.625 0.25 -2.546875 0.34375 -2.546875 C 0.421875 -2.546875 0.4375 -2.59375 0.5 -2.65625 C 0.9375 -3.34375 1.453125 -3.34375 1.640625 -3.34375 L 2.140625 -3.34375 C 1.859375 -2.265625 1.375 -1.171875 1 -0.359375 C 0.921875 -0.21875 0.921875 -0.203125 0.921875 -0.140625 C 0.921875 0.03125 1.0625 0.09375 1.1875 0.09375 C 1.453125 0.09375 1.53125 -0.15625 1.640625 -0.484375 C 1.765625 -0.890625 1.765625 -0.921875 1.875 -1.359375 Z M 2.375 -3.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.234375 -2 C 3.234375 -2.6875 3.15625 -3.1875 2.875 -3.625 C 2.671875 -3.921875 2.28125 -4.171875 1.78125 -4.171875 C 0.328125 -4.171875 0.328125 -2.453125 0.328125 -2 C 0.328125 -1.546875 0.328125 0.125 1.78125 0.125 C 3.234375 0.125 3.234375 -1.546875 3.234375 -2 Z M 1.78125 -0.046875 C 1.5 -0.046875 1.109375 -0.21875 0.984375 -0.734375 C 0.890625 -1.109375 0.890625 -1.625 0.890625 -2.078125 C 0.890625 -2.546875 0.890625 -3.015625 1 -3.359375 C 1.125 -3.859375 1.53125 -4 1.78125 -4 C 2.125 -4 2.453125 -3.78125 2.5625 -3.421875 C 2.65625 -3.078125 2.671875 -2.625 2.671875 -2.078125 C 2.671875 -1.625 2.671875 -1.15625 2.59375 -0.765625 C 2.46875 -0.1875 2.03125 -0.046875 1.78125 -0.046875 Z M 1.78125 -0.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.90625 -1.421875 L 4.828125 -1.421875 C 4.90625 -1.421875 5.0625 -1.421875 5.0625 -1.5625 C 5.0625 -1.734375 4.921875 -1.734375 4.828125 -1.734375 L 2.90625 -1.734375 L 2.90625 -3.65625 C 2.90625 -3.734375 2.90625 -3.890625 2.75 -3.890625 C 2.59375 -3.890625 2.59375 -3.75 2.59375 -3.65625 L 2.59375 -1.734375 L 0.671875 -1.734375 C 0.59375 -1.734375 0.4375 -1.734375 0.4375 -1.578125 C 0.4375 -1.421875 0.578125 -1.421875 0.671875 -1.421875 L 2.59375 -1.421875 L 2.59375 0.515625 C 2.59375 0.59375 2.59375 0.734375 2.75 0.734375 C 2.90625 0.734375 2.90625 0.59375 2.90625 0.515625 Z M 2.90625 -1.421875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 7.5 -2.0625 C 7 -1.6875 6.75 -1.328125 6.6875 -1.203125 C 6.28125 -0.578125 6.203125 -0.015625 6.203125 -0.015625 C 6.203125 0.09375 6.3125 0.09375 6.390625 0.09375 C 6.546875 0.09375 6.546875 0.078125 6.578125 -0.078125 C 6.796875 -0.96875 7.328125 -1.71875 8.34375 -2.125 C 8.4375 -2.171875 8.46875 -2.1875 8.46875 -2.25 C 8.46875 -2.3125 8.421875 -2.328125 8.40625 -2.34375 C 8 -2.5 6.921875 -2.953125 6.578125 -4.453125 C 6.546875 -4.5625 6.546875 -4.59375 6.390625 -4.59375 C 6.3125 -4.59375 6.203125 -4.59375 6.203125 -4.484375 C 6.203125 -4.46875 6.28125 -3.90625 6.671875 -3.296875 C 6.84375 -3.03125 7.109375 -2.71875 7.5 -2.421875 L 0.8125 -2.421875 C 0.65625 -2.421875 0.5 -2.421875 0.5 -2.25 C 0.5 -2.0625 0.65625 -2.0625 0.8125 -2.0625 Z M 7.5 -2.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.671875 -1.421875 C 4.78125 -1.421875 4.921875 -1.421875 4.921875 -1.5625 C 4.921875 -1.734375 4.78125 -1.734375 4.671875 -1.734375 L 0.921875 -1.734375 C 0.828125 -1.734375 0.671875 -1.734375 0.671875 -1.578125 C 0.671875 -1.421875 0.828125 -1.421875 0.921875 -1.421875 Z M 4.671875 -1.421875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 4 1 L 12 1 L 12 7.308594 L 4 7.308594 Z M 4 1 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 18 2 L 27 2 L 27 7.308594 L 18 7.308594 Z M 18 2 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 29 1 L 38 1 L 38 7.308594 L 29 7.308594 Z M 29 1 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 44 3 L 49 3 L 49 7.308594 L 44 7.308594 Z M 44 3 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 55 3 L 61 3 L 61 7.308594 L 55 7.308594 Z M 55 3 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 66 3 L 72 3 L 72 7.308594 L 66 7.308594 Z M 66 3 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="3.830389" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="11.512361" y="4.050494"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="18.033702" y="7.308011"/>
+</g>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="29.504847" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="37.77164" y="4.050494"/>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="43.830711" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="49.270719" y="4.050494"/>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="55.230668" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="60.669774" y="4.050494"/>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="66.629723" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="72.069731" y="4.050494"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig22.svg b/doc/figs/tex/fig22.svg
new file mode 100644
index 00000000000..7d96049e8cc
--- /dev/null
+++ b/doc/figs/tex/fig22.svg
@@ -0,0 +1,63 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="40.394pt" height="8.302pt" viewBox="0 0 40.394 8.302" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.203125 -6.28125 C 1.90625 -6.28125 0.921875 -5.65625 0.546875 -5.21875 C 0.21875 -4.84375 0.1875 -4.578125 0.1875 -4.5625 C 0.1875 -4.515625 0.234375 -4.5 0.28125 -4.5 C 0.4375 -4.5 0.640625 -4.625 0.71875 -4.671875 C 0.90625 -4.796875 0.9375 -4.84375 1 -5.03125 C 1.125 -5.390625 1.375 -5.71875 2.53125 -5.765625 C 2.375 -3.703125 1.8125 -1.6875 1.046875 0.234375 C 1 0.375 1 0.390625 1 0.390625 C 1 0.421875 1.015625 0.453125 1.078125 0.453125 C 1.234375 0.453125 1.671875 0.25 1.765625 0.015625 C 2.25 -1.109375 3 -3.21875 3.28125 -5.765625 L 3.75 -5.765625 C 4.875 -5.765625 5.953125 -5.34375 5.953125 -4.421875 C 5.953125 -3.734375 5.296875 -2.4375 3.515625 -2.390625 C 3.3125 -2.375 3.21875 -2.375 2.953125 -2.21875 C 2.796875 -2.109375 2.71875 -2 2.71875 -1.953125 C 2.71875 -1.890625 2.78125 -1.890625 2.890625 -1.890625 C 4.5625 -1.890625 6.734375 -3.296875 6.734375 -4.8125 C 6.734375 -5.859375 5.5 -6.28125 4.421875 -6.28125 Z M 3.203125 -6.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.296875 -1.953125 C 5.296875 -2.515625 5.015625 -2.84375 4.328125 -2.84375 C 3.8125 -2.84375 3.46875 -2.5625 3.296875 -2.234375 C 3.171875 -2.703125 2.8125 -2.84375 2.34375 -2.84375 C 1.828125 -2.84375 1.484375 -2.546875 1.296875 -2.21875 L 1.296875 -2.84375 L 0.34375 -2.765625 L 0.34375 -2.53125 C 0.78125 -2.53125 0.828125 -2.484375 0.828125 -2.171875 L 0.828125 -0.515625 C 0.828125 -0.234375 0.765625 -0.234375 0.34375 -0.234375 L 0.34375 0 C 0.359375 0 0.8125 -0.03125 1.078125 -0.03125 C 1.3125 -0.03125 1.765625 0 1.828125 0 L 1.828125 -0.234375 C 1.40625 -0.234375 1.34375 -0.234375 1.34375 -0.515625 L 1.34375 -1.671875 C 1.34375 -2.34375 1.875 -2.65625 2.296875 -2.65625 C 2.75 -2.65625 2.8125 -2.296875 2.8125 -1.96875 L 2.8125 -0.515625 C 2.8125 -0.234375 2.75 -0.234375 2.328125 -0.234375 L 2.328125 0 C 2.34375 0 2.78125 -0.03125 3.0625 -0.03125 C 3.296875 -0.03125 3.734375 0 3.796875 0 L 3.796875 -0.234375 C 3.375 -0.234375 3.3125 -0.234375 3.3125 -0.515625 L 3.3125 -1.671875 C 3.3125 -2.34375 3.84375 -2.65625 4.28125 -2.65625 C 4.71875 -2.65625 4.78125 -2.296875 4.78125 -1.96875 L 4.78125 -0.515625 C 4.78125 -0.234375 4.71875 -0.234375 4.296875 -0.234375 L 4.296875 0 C 4.3125 0 4.765625 -0.03125 5.03125 -0.03125 C 5.265625 -0.03125 5.71875 0 5.78125 0 L 5.78125 -0.234375 C 5.359375 -0.234375 5.296875 -0.234375 5.296875 -0.515625 Z M 5.296875 -1.953125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.875 -1.71875 C 2.875 -2.0625 2.875 -2.3125 2.578125 -2.546875 C 2.3125 -2.765625 2 -2.875 1.625 -2.875 C 1.015625 -2.875 0.578125 -2.640625 0.578125 -2.25 C 0.578125 -2.046875 0.71875 -1.9375 0.890625 -1.9375 C 1.0625 -1.9375 1.1875 -2.0625 1.1875 -2.234375 C 1.1875 -2.34375 1.140625 -2.484375 0.96875 -2.53125 C 1.203125 -2.6875 1.578125 -2.6875 1.609375 -2.6875 C 1.96875 -2.6875 2.359375 -2.453125 2.359375 -1.90625 L 2.359375 -1.71875 C 2.015625 -1.703125 1.578125 -1.6875 1.109375 -1.5 C 0.53125 -1.296875 0.359375 -0.9375 0.359375 -0.65625 C 0.359375 -0.09375 1.03125 0.0625 1.484375 0.0625 C 2 0.0625 2.296875 -0.21875 2.4375 -0.46875 C 2.453125 -0.21875 2.640625 0.03125 2.921875 0.03125 C 2.9375 0.03125 3.5625 0.03125 3.5625 -0.578125 L 3.5625 -0.9375 L 3.34375 -0.9375 L 3.34375 -0.578125 C 3.34375 -0.515625 3.34375 -0.21875 3.109375 -0.21875 C 2.875 -0.21875 2.875 -0.515625 2.875 -0.59375 Z M 2.359375 -0.90625 C 2.359375 -0.296875 1.828125 -0.109375 1.53125 -0.109375 C 1.203125 -0.109375 0.890625 -0.328125 0.890625 -0.65625 C 0.890625 -1 1.203125 -1.5 2.359375 -1.546875 Z M 2.359375 -0.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 2.1875 -1.4375 C 2.171875 -1.453125 2.125 -1.5 2.125 -1.5 C 2.125 -1.53125 2.5625 -1.984375 2.609375 -2.046875 C 2.84375 -2.296875 3.0625 -2.53125 3.578125 -2.546875 L 3.578125 -2.78125 C 3.390625 -2.765625 3.203125 -2.75 3.03125 -2.75 C 2.84375 -2.75 2.59375 -2.75 2.390625 -2.78125 L 2.390625 -2.546875 C 2.5 -2.53125 2.53125 -2.453125 2.53125 -2.390625 C 2.53125 -2.375 2.53125 -2.28125 2.421875 -2.171875 L 1.96875 -1.671875 L 1.4375 -2.28125 C 1.375 -2.34375 1.375 -2.375 1.375 -2.40625 C 1.375 -2.5 1.46875 -2.546875 1.546875 -2.546875 L 1.546875 -2.78125 C 1.3125 -2.75 1.0625 -2.75 0.828125 -2.75 C 0.625 -2.75 0.390625 -2.75 0.203125 -2.78125 L 0.203125 -2.546875 C 0.5 -2.546875 0.65625 -2.546875 0.828125 -2.34375 L 1.640625 -1.421875 C 1.640625 -1.421875 1.6875 -1.359375 1.6875 -1.359375 C 1.6875 -1.34375 1.203125 -0.8125 1.140625 -0.734375 C 0.90625 -0.484375 0.6875 -0.25 0.171875 -0.234375 L 0.171875 0 C 0.359375 -0.015625 0.5 -0.03125 0.703125 -0.03125 C 0.890625 -0.03125 1.15625 -0.015625 1.34375 0 L 1.34375 -0.234375 C 1.265625 -0.25 1.21875 -0.296875 1.21875 -0.375 C 1.21875 -0.5 1.28125 -0.578125 1.390625 -0.6875 L 1.84375 -1.1875 L 2.40625 -0.546875 C 2.53125 -0.421875 2.53125 -0.40625 2.53125 -0.359375 C 2.53125 -0.234375 2.375 -0.234375 2.34375 -0.234375 L 2.34375 0 C 2.40625 0 2.875 -0.03125 3.078125 -0.03125 C 3.28125 -0.03125 3.484375 -0.015625 3.6875 0 L 3.6875 -0.234375 C 3.265625 -0.234375 3.21875 -0.265625 3.0625 -0.4375 Z M 2.1875 -1.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 6.203125 -4.578125 C 6.3125 -4.625 6.375 -4.671875 6.375 -4.78125 C 6.375 -4.875 6.296875 -4.96875 6.1875 -4.96875 C 6.171875 -4.96875 6.140625 -4.96875 6.03125 -4.890625 L 0.9375 -2.5 C 0.84375 -2.453125 0.765625 -2.40625 0.765625 -2.296875 C 0.765625 -2.1875 0.84375 -2.140625 0.9375 -2.09375 L 6.03125 0.296875 C 6.140625 0.375 6.171875 0.375 6.1875 0.375 C 6.296875 0.375 6.375 0.28125 6.375 0.1875 C 6.375 0.078125 6.3125 0.03125 6.203125 -0.015625 L 1.375 -2.296875 Z M 6.203125 -4.578125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 2.703125 -5.875 C 2.703125 -6.09375 2.703125 -6.125 2.484375 -6.125 C 1.921875 -5.53125 1.109375 -5.53125 0.8125 -5.53125 L 0.8125 -5.25 C 1 -5.25 1.546875 -5.25 2.015625 -5.484375 L 2.015625 -0.71875 C 2.015625 -0.390625 2 -0.28125 1.171875 -0.28125 L 0.875 -0.28125 L 0.875 0 C 1.1875 -0.03125 2 -0.03125 2.359375 -0.03125 C 2.734375 -0.03125 3.53125 -0.03125 3.84375 0 L 3.84375 -0.28125 L 3.5625 -0.28125 C 2.734375 -0.28125 2.703125 -0.390625 2.703125 -0.71875 Z M 2.703125 -5.875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1.285156 0 L 9 0 L 9 7 L 1.285156 7 Z M 1.285156 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 8 4 L 22 4 L 22 7.65625 L 8 7.65625 Z M 8 4 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="1.286889" y="6.280002"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.679429" y="7.658134"/>
+ <use xlink:href="#glyph1-2" x="13.716746" y="7.658134"/>
+ <use xlink:href="#glyph1-3" x="17.380307" y="7.658134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="24.252988" y="6.280002"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="33.953414" y="6.280002"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig23.svg b/doc/figs/tex/fig23.svg
new file mode 100644
index 00000000000..64b0735b240
--- /dev/null
+++ b/doc/figs/tex/fig23.svg
@@ -0,0 +1,77 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="51.411pt" height="9.87pt" viewBox="0 0 51.411 9.87" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.640625 -6.828125 C 3.578125 -7.015625 3.515625 -7.03125 3.40625 -7.03125 C 3.25 -7.03125 3.234375 -7 3.1875 -6.828125 L 1.296875 -0.984375 C 1.203125 -0.6875 1 -0.296875 0.3125 -0.296875 L 0.3125 0 C 0.640625 -0.015625 1.140625 -0.03125 1.234375 -0.03125 C 1.515625 -0.03125 2.03125 -0.015625 2.34375 0 L 2.34375 -0.296875 C 1.8125 -0.3125 1.578125 -0.578125 1.578125 -0.8125 C 1.578125 -0.859375 1.578125 -0.890625 1.625 -1.03125 L 3.109375 -5.609375 L 4.65625 -0.78125 C 4.703125 -0.640625 4.703125 -0.625 4.703125 -0.59375 C 4.703125 -0.296875 4.125 -0.296875 3.875 -0.296875 L 3.875 0 C 4.21875 -0.03125 4.90625 -0.03125 5.28125 -0.03125 C 5.671875 -0.03125 6.109375 -0.015625 6.5 0 L 6.5 -0.296875 C 5.75 -0.296875 5.71875 -0.359375 5.609375 -0.734375 Z M 3.640625 -6.828125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 1.8125 -4.578125 C 1.828125 -4.59375 1.84375 -4.671875 1.84375 -4.6875 C 1.84375 -4.71875 1.8125 -4.78125 1.734375 -4.78125 C 1.59375 -4.78125 1.03125 -4.734375 0.859375 -4.71875 C 0.796875 -4.703125 0.703125 -4.703125 0.703125 -4.546875 C 0.703125 -4.453125 0.796875 -4.453125 0.875 -4.453125 C 1.21875 -4.453125 1.21875 -4.40625 1.21875 -4.359375 C 1.21875 -4.3125 1.140625 -4.03125 1.109375 -3.875 L 0.9375 -3.234375 C 0.875 -3 0.5 -1.5 0.484375 -1.40625 C 0.453125 -1.234375 0.453125 -1.15625 0.453125 -1.0625 C 0.453125 -0.375 0.890625 0.0625 1.46875 0.0625 C 2.328125 0.0625 3.25 -0.875 3.25 -1.890625 C 3.25 -2.6875 2.6875 -3.03125 2.21875 -3.03125 C 1.859375 -3.03125 1.546875 -2.84375 1.34375 -2.65625 Z M 1.46875 -0.125 C 1.140625 -0.125 0.9375 -0.421875 0.9375 -0.828125 C 0.9375 -1.078125 1 -1.3125 1.203125 -2.09375 C 1.234375 -2.21875 1.234375 -2.234375 1.375 -2.390625 C 1.640625 -2.6875 1.9375 -2.84375 2.1875 -2.84375 C 2.453125 -2.84375 2.6875 -2.640625 2.6875 -2.171875 C 2.6875 -1.890625 2.546875 -1.1875 2.328125 -0.796875 C 2.171875 -0.453125 1.828125 -0.125 1.46875 -0.125 Z M 1.46875 -0.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 8.203125 -2.265625 C 7.65625 -1.84375 7.390625 -1.4375 7.3125 -1.3125 C 6.875 -0.640625 6.796875 -0.015625 6.796875 -0.015625 C 6.796875 0.109375 6.90625 0.109375 6.984375 0.109375 C 7.15625 0.109375 7.171875 0.09375 7.203125 -0.09375 C 7.4375 -1.046875 8.015625 -1.875 9.125 -2.328125 C 9.234375 -2.375 9.265625 -2.390625 9.265625 -2.453125 C 9.265625 -2.53125 9.203125 -2.5625 9.1875 -2.5625 C 8.75 -2.734375 7.5625 -3.21875 7.1875 -4.875 C 7.171875 -5 7.15625 -5.015625 6.984375 -5.015625 C 6.90625 -5.015625 6.796875 -5.015625 6.796875 -4.90625 C 6.796875 -4.890625 6.875 -4.265625 7.296875 -3.609375 C 7.484375 -3.3125 7.78125 -2.96875 8.203125 -2.65625 L 0.890625 -2.65625 C 0.71875 -2.65625 0.546875 -2.65625 0.546875 -2.453125 C 0.546875 -2.265625 0.71875 -2.265625 0.890625 -2.265625 Z M 8.203125 -2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 0.4375 1.203125 C 0.359375 1.53125 0.34375 1.609375 -0.09375 1.609375 C -0.203125 1.609375 -0.3125 1.609375 -0.3125 1.78125 C -0.3125 1.875 -0.265625 1.90625 -0.1875 1.90625 C 0.078125 1.90625 0.359375 1.875 0.640625 1.875 C 0.96875 1.875 1.296875 1.90625 1.609375 1.90625 C 1.65625 1.90625 1.78125 1.90625 1.78125 1.703125 C 1.78125 1.609375 1.6875 1.609375 1.546875 1.609375 C 1.0625 1.609375 1.0625 1.53125 1.0625 1.4375 C 1.0625 1.328125 1.46875 -0.28125 1.546875 -0.515625 C 1.671875 -0.234375 1.953125 0.109375 2.453125 0.109375 C 3.59375 0.109375 4.8125 -1.328125 4.8125 -2.765625 C 4.8125 -3.703125 4.25 -4.34375 3.515625 -4.34375 C 3.015625 -4.34375 2.546875 -3.984375 2.21875 -3.609375 C 2.125 -4.140625 1.703125 -4.34375 1.34375 -4.34375 C 0.890625 -4.34375 0.703125 -3.953125 0.609375 -3.78125 C 0.4375 -3.453125 0.296875 -2.859375 0.296875 -2.828125 C 0.296875 -2.734375 0.40625 -2.734375 0.421875 -2.734375 C 0.515625 -2.734375 0.53125 -2.734375 0.59375 -2.953125 C 0.75 -3.65625 0.953125 -4.125 1.3125 -4.125 C 1.46875 -4.125 1.609375 -4.046875 1.609375 -3.671875 C 1.609375 -3.453125 1.578125 -3.34375 1.546875 -3.171875 Z M 2.171875 -3.0625 C 2.234375 -3.328125 2.5 -3.609375 2.6875 -3.75 C 3.03125 -4.0625 3.3125 -4.125 3.484375 -4.125 C 3.875 -4.125 4.109375 -3.78125 4.109375 -3.203125 C 4.109375 -2.625 3.78125 -1.5 3.609375 -1.125 C 3.265625 -0.4375 2.796875 -0.109375 2.4375 -0.109375 C 1.78125 -0.109375 1.65625 -0.921875 1.65625 -0.984375 C 1.65625 -1 1.65625 -1.015625 1.6875 -1.140625 Z M 2.171875 -3.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-2">
+<path style="stroke:none;" d="M 5 -3.96875 C 5 -4 4.953125 -4.078125 4.953125 -4.109375 C 4.953125 -4.125 5.125 -4.25 5.234375 -4.328125 L 6.953125 -5.65625 C 7.875 -6.34375 8.265625 -6.375 8.5625 -6.40625 C 8.640625 -6.421875 8.734375 -6.421875 8.734375 -6.609375 C 8.734375 -6.640625 8.703125 -6.71875 8.625 -6.71875 C 8.40625 -6.71875 8.171875 -6.6875 7.9375 -6.6875 C 7.578125 -6.6875 7.1875 -6.71875 6.84375 -6.71875 C 6.765625 -6.71875 6.65625 -6.71875 6.65625 -6.515625 C 6.65625 -6.453125 6.703125 -6.421875 6.765625 -6.40625 C 6.984375 -6.390625 7.078125 -6.34375 7.078125 -6.203125 C 7.078125 -6.03125 6.78125 -5.796875 6.71875 -5.75 L 2.890625 -2.796875 L 3.671875 -5.953125 C 3.765625 -6.3125 3.78125 -6.40625 4.5 -6.40625 C 4.75 -6.40625 4.828125 -6.40625 4.828125 -6.609375 C 4.828125 -6.6875 4.75 -6.71875 4.703125 -6.71875 C 4.421875 -6.71875 3.71875 -6.6875 3.4375 -6.6875 C 3.15625 -6.6875 2.453125 -6.71875 2.171875 -6.71875 C 2.109375 -6.71875 1.96875 -6.71875 1.96875 -6.53125 C 1.96875 -6.40625 2.0625 -6.40625 2.265625 -6.40625 C 2.390625 -6.40625 2.5625 -6.390625 2.6875 -6.390625 C 2.84375 -6.375 2.90625 -6.34375 2.90625 -6.234375 C 2.90625 -6.1875 2.890625 -6.15625 2.859375 -6.046875 L 1.546875 -0.765625 C 1.4375 -0.390625 1.421875 -0.296875 0.65625 -0.296875 C 0.484375 -0.296875 0.375 -0.296875 0.375 -0.125 C 0.375 0 0.484375 0 0.515625 0 C 0.796875 0 1.5 -0.03125 1.765625 -0.03125 C 1.96875 -0.03125 2.1875 -0.015625 2.390625 -0.015625 C 2.609375 -0.015625 2.828125 0 3.03125 0 C 3.109375 0 3.234375 0 3.234375 -0.203125 C 3.234375 -0.296875 3.140625 -0.296875 2.953125 -0.296875 C 2.59375 -0.296875 2.3125 -0.296875 2.3125 -0.484375 C 2.3125 -0.546875 2.375 -0.765625 2.40625 -0.90625 C 2.546875 -1.421875 2.671875 -1.953125 2.796875 -2.453125 L 4.265625 -3.59375 L 5.40625 -0.953125 C 5.515625 -0.6875 5.515625 -0.671875 5.515625 -0.609375 C 5.515625 -0.3125 5.09375 -0.296875 5.015625 -0.296875 C 4.90625 -0.296875 4.796875 -0.296875 4.796875 -0.109375 C 4.796875 0 4.90625 0 4.9375 0 C 5.328125 0 5.734375 -0.03125 6.125 -0.03125 C 6.34375 -0.03125 6.875 0 7.09375 0 C 7.140625 0 7.265625 0 7.265625 -0.203125 C 7.265625 -0.296875 7.171875 -0.296875 7.078125 -0.296875 C 6.671875 -0.3125 6.546875 -0.40625 6.390625 -0.75 Z M 5 -3.96875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 2.21875 -1.71875 C 2.796875 -1.96875 3.046875 -2.0625 3.21875 -2.140625 C 3.34375 -2.203125 3.40625 -2.21875 3.40625 -2.359375 C 3.40625 -2.46875 3.328125 -2.578125 3.203125 -2.578125 C 3.15625 -2.578125 3.140625 -2.578125 3.046875 -2.515625 L 2.109375 -1.890625 L 2.21875 -2.90625 C 2.234375 -3.03125 2.21875 -3.203125 2.015625 -3.203125 C 1.921875 -3.203125 1.796875 -3.15625 1.796875 -3 C 1.796875 -2.9375 1.828125 -2.734375 1.828125 -2.65625 C 1.84375 -2.546875 1.890625 -2.046875 1.90625 -1.890625 L 0.984375 -2.515625 C 0.90625 -2.5625 0.890625 -2.578125 0.828125 -2.578125 C 0.703125 -2.578125 0.609375 -2.46875 0.609375 -2.359375 C 0.609375 -2.21875 0.703125 -2.1875 0.765625 -2.15625 L 1.796875 -1.71875 C 1.234375 -1.46875 0.984375 -1.375 0.8125 -1.296875 C 0.671875 -1.234375 0.609375 -1.21875 0.609375 -1.078125 C 0.609375 -0.96875 0.703125 -0.859375 0.828125 -0.859375 C 0.875 -0.859375 0.890625 -0.859375 0.96875 -0.921875 L 1.90625 -1.546875 L 1.796875 -0.4375 C 1.796875 -0.296875 1.921875 -0.234375 2.015625 -0.234375 C 2.09375 -0.234375 2.21875 -0.296875 2.21875 -0.4375 C 2.21875 -0.5 2.203125 -0.703125 2.1875 -0.78125 C 2.171875 -0.890625 2.125 -1.390625 2.109375 -1.546875 L 2.9375 -1 C 3.125 -0.859375 3.140625 -0.859375 3.203125 -0.859375 C 3.328125 -0.859375 3.40625 -0.96875 3.40625 -1.078125 C 3.40625 -1.21875 3.328125 -1.25 3.265625 -1.28125 Z M 2.21875 -1.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 5.125 -1.5625 C 5.234375 -1.5625 5.40625 -1.5625 5.40625 -1.71875 C 5.40625 -1.890625 5.25 -1.890625 5.125 -1.890625 L 1.015625 -1.890625 C 0.90625 -1.890625 0.75 -1.890625 0.75 -1.734375 C 0.75 -1.5625 0.90625 -1.5625 1.015625 -1.5625 Z M 5.125 -1.5625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.0429688 0 L 7 0 L 7 8 L 0.0429688 8 Z M 0.0429688 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 7 4 L 11 4 L 11 9.742188 L 7 9.742188 Z M 7 4 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 25 1 L 40 1 L 40 9.742188 L 25 9.742188 Z M 25 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.0435" y="7.829871"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="6.871566" y="9.304449"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.552569" y="7.829871"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="26.117079" y="7.829871"/>
+ <use xlink:href="#glyph3-2" x="31.064105" y="7.829871"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="40.119648" y="4.260879"/>
+ <use xlink:href="#glyph4-2" x="44.14835" y="4.260879"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig24.svg b/doc/figs/tex/fig24.svg
new file mode 100644
index 00000000000..203e006c887
--- /dev/null
+++ b/doc/figs/tex/fig24.svg
@@ -0,0 +1,57 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="21.544pt" height="9.963pt" viewBox="0 0 21.544 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.390625 -6.65625 C 2.015625 -6.65625 0.96875 -6 0.578125 -5.53125 C 0.234375 -5.140625 0.203125 -4.859375 0.203125 -4.84375 C 0.203125 -4.78125 0.25 -4.765625 0.296875 -4.765625 C 0.453125 -4.765625 0.6875 -4.90625 0.765625 -4.953125 C 0.96875 -5.09375 1 -5.140625 1.046875 -5.328125 C 1.1875 -5.71875 1.46875 -6.0625 2.6875 -6.125 C 2.515625 -3.921875 1.9375 -1.796875 1.109375 0.25 C 1.046875 0.390625 1.046875 0.40625 1.046875 0.421875 C 1.046875 0.453125 1.078125 0.484375 1.15625 0.484375 C 1.3125 0.484375 1.78125 0.265625 1.875 0.015625 C 2.390625 -1.171875 3.1875 -3.40625 3.484375 -6.125 L 3.984375 -6.125 C 5.171875 -6.125 6.3125 -5.671875 6.3125 -4.6875 C 6.3125 -3.953125 5.609375 -2.59375 3.71875 -2.53125 C 3.515625 -2.53125 3.40625 -2.53125 3.140625 -2.34375 C 2.96875 -2.234375 2.890625 -2.125 2.890625 -2.0625 C 2.890625 -2 2.9375 -2 3.078125 -2 C 4.84375 -2 7.140625 -3.5 7.140625 -5.109375 C 7.140625 -6.21875 5.828125 -6.65625 4.703125 -6.65625 Z M 3.390625 -6.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.234375 2.34375 C 3.234375 2.3125 3.234375 2.296875 3.0625 2.125 C 1.84375 0.890625 1.53125 -0.953125 1.53125 -2.4375 C 1.53125 -4.140625 1.90625 -5.828125 3.09375 -7.046875 C 3.234375 -7.171875 3.234375 -7.1875 3.234375 -7.21875 C 3.234375 -7.28125 3.1875 -7.3125 3.125 -7.3125 C 3.03125 -7.3125 2.15625 -6.65625 1.578125 -5.40625 C 1.078125 -4.34375 0.96875 -3.25 0.96875 -2.4375 C 0.96875 -1.671875 1.078125 -0.5 1.609375 0.609375 C 2.1875 1.796875 3.03125 2.4375 3.125 2.4375 C 3.1875 2.4375 3.234375 2.40625 3.234375 2.34375 Z M 3.234375 2.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.8125 -2.4375 C 2.8125 -3.203125 2.703125 -4.375 2.171875 -5.484375 C 1.59375 -6.671875 0.75 -7.3125 0.65625 -7.3125 C 0.59375 -7.3125 0.5625 -7.265625 0.5625 -7.21875 C 0.5625 -7.1875 0.5625 -7.171875 0.734375 -6.984375 C 1.703125 -6.03125 2.25 -4.46875 2.25 -2.4375 C 2.25 -0.765625 1.890625 0.953125 0.6875 2.171875 C 0.5625 2.296875 0.5625 2.3125 0.5625 2.34375 C 0.5625 2.40625 0.59375 2.4375 0.65625 2.4375 C 0.75 2.4375 1.625 1.78125 2.203125 0.53125 C 2.703125 -0.53125 2.8125 -1.625 2.8125 -2.4375 Z M 2.8125 -2.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.375 -2.40625 L 4.515625 -3.671875 C 4.640625 -3.796875 4.703125 -3.875 5.515625 -3.875 L 5.515625 -4.328125 C 5.171875 -4.3125 4.65625 -4.296875 4.609375 -4.296875 C 4.375 -4.296875 3.875 -4.3125 3.609375 -4.328125 L 3.609375 -3.875 C 3.75 -3.875 3.859375 -3.84375 3.984375 -3.78125 C 3.9375 -3.71875 3.9375 -3.703125 3.90625 -3.671875 L 3.078125 -2.75 L 2.125 -3.875 L 2.515625 -3.875 L 2.515625 -4.328125 C 2.265625 -4.3125 1.640625 -4.296875 1.328125 -4.296875 C 1.03125 -4.296875 0.578125 -4.3125 0.265625 -4.328125 L 0.265625 -3.875 L 0.953125 -3.875 L 2.46875 -2.078125 L 1.203125 -0.640625 C 1.03125 -0.453125 0.6875 -0.453125 0.21875 -0.453125 L 0.21875 0 C 0.5625 -0.015625 1.0625 -0.03125 1.109375 -0.03125 C 1.359375 -0.03125 1.921875 -0.015625 2.109375 0 L 2.109375 -0.453125 C 1.9375 -0.453125 1.75 -0.5 1.75 -0.5625 C 1.75 -0.578125 1.75 -0.578125 1.828125 -0.65625 L 2.765625 -1.71875 L 3.84375 -0.453125 L 3.46875 -0.453125 L 3.46875 0 C 3.71875 -0.015625 4.3125 -0.03125 4.625 -0.03125 C 4.9375 -0.03125 5.375 -0.015625 5.703125 0 L 5.703125 -0.453125 L 5.015625 -0.453125 Z M 3.375 -2.40625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.0859375 L 8 0.0859375 L 8 8 L 0 8 Z M 0 0.0859375 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 8 0.0859375 L 11 0.0859375 L 11 9.839844 L 8 9.839844 Z M 8 0.0859375 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 17 0.0859375 L 21 0.0859375 L 21 9.839844 L 17 9.839844 Z M 17 0.0859375 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="7.402262"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.588384" y="7.402262"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="11.382087" y="7.402262"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.303749" y="7.402262"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig25.svg b/doc/figs/tex/fig25.svg
new file mode 100644
index 00000000000..1d0aad29aeb
--- /dev/null
+++ b/doc/figs/tex/fig25.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="6.047pt" height="4.705pt" viewBox="0 0 6.047 4.705" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.984375 -2.125 L 3.984375 -3.234375 C 4.09375 -3.359375 4.15625 -3.421875 4.859375 -3.421875 L 4.859375 -3.828125 C 4.5625 -3.8125 4.109375 -3.796875 4.078125 -3.796875 C 3.859375 -3.796875 3.421875 -3.8125 3.1875 -3.828125 L 3.1875 -3.421875 C 3.3125 -3.421875 3.40625 -3.40625 3.515625 -3.34375 C 3.484375 -3.28125 3.484375 -3.265625 3.4375 -3.234375 L 2.71875 -2.421875 L 1.875 -3.421875 L 2.21875 -3.421875 L 2.21875 -3.828125 C 2 -3.8125 1.453125 -3.796875 1.171875 -3.796875 C 0.90625 -3.796875 0.515625 -3.8125 0.234375 -3.828125 L 0.234375 -3.421875 L 0.84375 -3.421875 L 2.1875 -1.828125 L 1.0625 -0.5625 C 0.90625 -0.40625 0.609375 -0.40625 0.1875 -0.40625 L 0.1875 0 C 0.484375 -0.015625 0.9375 -0.03125 0.984375 -0.03125 C 1.203125 -0.03125 1.703125 -0.015625 1.875 0 L 1.875 -0.40625 C 1.71875 -0.40625 1.546875 -0.453125 1.546875 -0.5 C 1.546875 -0.515625 1.546875 -0.515625 1.609375 -0.578125 L 2.4375 -1.53125 L 3.390625 -0.40625 L 3.0625 -0.40625 L 3.0625 0 C 3.28125 -0.015625 3.8125 -0.03125 4.09375 -0.03125 C 4.359375 -0.03125 4.75 -0.015625 5.03125 0 L 5.03125 -0.40625 L 4.421875 -0.40625 Z M 2.984375 -2.125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.191406 L 5.222656 0.191406 L 5.222656 4.257812 L 0 4.257812 Z M 0 0.191406 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="4.018017"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig26.svg b/doc/figs/tex/fig26.svg
new file mode 100644
index 00000000000..7d652ec63a2
--- /dev/null
+++ b/doc/figs/tex/fig26.svg
@@ -0,0 +1,165 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="127.885pt" height="9.963pt" viewBox="0 0 127.885 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.453125 -6.78125 C 2.046875 -6.78125 0.984375 -6.109375 0.578125 -5.640625 C 0.234375 -5.234375 0.203125 -4.953125 0.203125 -4.9375 C 0.203125 -4.875 0.25 -4.859375 0.3125 -4.859375 C 0.46875 -4.859375 0.6875 -4.984375 0.78125 -5.046875 C 0.984375 -5.171875 1.015625 -5.234375 1.078125 -5.421875 C 1.203125 -5.828125 1.484375 -6.171875 2.734375 -6.234375 C 2.5625 -4 1.96875 -1.828125 1.125 0.25 C 1.078125 0.390625 1.078125 0.421875 1.078125 0.421875 C 1.078125 0.453125 1.09375 0.5 1.171875 0.5 C 1.328125 0.5 1.8125 0.28125 1.921875 0.015625 C 2.4375 -1.1875 3.25 -3.46875 3.546875 -6.234375 L 4.0625 -6.234375 C 5.265625 -6.234375 6.421875 -5.765625 6.421875 -4.765625 C 6.421875 -4.03125 5.71875 -2.640625 3.796875 -2.578125 C 3.578125 -2.5625 3.46875 -2.5625 3.1875 -2.390625 C 3.015625 -2.265625 2.9375 -2.15625 2.9375 -2.109375 C 2.9375 -2.03125 3 -2.03125 3.125 -2.03125 C 4.9375 -2.03125 7.265625 -3.5625 7.265625 -5.203125 C 7.265625 -6.328125 5.9375 -6.78125 4.78125 -6.78125 Z M 3.453125 -6.78125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 3.859375 -2.765625 L 1.875 -4.734375 C 1.75 -4.859375 1.734375 -4.875 1.65625 -4.875 C 1.5625 -4.875 1.453125 -4.78125 1.453125 -4.671875 C 1.453125 -4.609375 1.484375 -4.578125 1.59375 -4.46875 L 3.578125 -2.484375 L 1.59375 -0.484375 C 1.484375 -0.375 1.453125 -0.359375 1.453125 -0.28125 C 1.453125 -0.171875 1.5625 -0.09375 1.65625 -0.09375 C 1.734375 -0.09375 1.75 -0.109375 1.875 -0.234375 L 3.84375 -2.203125 L 5.90625 -0.15625 C 5.921875 -0.140625 6 -0.09375 6.046875 -0.09375 C 6.171875 -0.09375 6.25 -0.171875 6.25 -0.28125 C 6.25 -0.3125 6.25 -0.34375 6.21875 -0.390625 C 6.21875 -0.421875 4.640625 -1.96875 4.140625 -2.484375 L 5.953125 -4.296875 C 6 -4.359375 6.15625 -4.484375 6.203125 -4.546875 C 6.21875 -4.5625 6.25 -4.609375 6.25 -4.671875 C 6.25 -4.78125 6.171875 -4.875 6.046875 -4.875 C 5.96875 -4.875 5.9375 -4.828125 5.828125 -4.71875 Z M 3.859375 -2.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.28125 2.375 C 3.28125 2.34375 3.28125 2.328125 3.109375 2.15625 C 1.875 0.90625 1.5625 -0.96875 1.5625 -2.484375 C 1.5625 -4.203125 1.9375 -5.9375 3.15625 -7.171875 C 3.28125 -7.296875 3.28125 -7.3125 3.28125 -7.34375 C 3.28125 -7.40625 3.25 -7.4375 3.1875 -7.4375 C 3.078125 -7.4375 2.1875 -6.765625 1.609375 -5.5 C 1.09375 -4.421875 0.984375 -3.3125 0.984375 -2.484375 C 0.984375 -1.703125 1.09375 -0.5 1.640625 0.609375 C 2.234375 1.828125 3.078125 2.484375 3.1875 2.484375 C 3.25 2.484375 3.28125 2.453125 3.28125 2.375 Z M 3.28125 2.375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.875 -2.484375 C 2.875 -3.25 2.765625 -4.453125 2.21875 -5.578125 C 1.625 -6.796875 0.765625 -7.4375 0.671875 -7.4375 C 0.609375 -7.4375 0.5625 -7.40625 0.5625 -7.34375 C 0.5625 -7.3125 0.5625 -7.296875 0.75 -7.109375 C 1.71875 -6.125 2.296875 -4.546875 2.296875 -2.484375 C 2.296875 -0.78125 1.921875 0.96875 0.6875 2.21875 C 0.5625 2.328125 0.5625 2.34375 0.5625 2.375 C 0.5625 2.4375 0.609375 2.484375 0.671875 2.484375 C 0.765625 2.484375 1.65625 1.8125 2.25 0.546875 C 2.75 -0.546875 2.875 -1.640625 2.875 -2.484375 Z M 2.875 -2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 4.5625 -3.171875 C 4.5625 -3.96875 4.515625 -4.765625 4.171875 -5.5 C 3.703125 -6.453125 2.890625 -6.609375 2.484375 -6.609375 C 1.890625 -6.609375 1.15625 -6.34375 0.75 -5.421875 C 0.4375 -4.75 0.390625 -3.96875 0.390625 -3.171875 C 0.390625 -2.4375 0.421875 -1.53125 0.828125 -0.78125 C 1.265625 0.015625 1.984375 0.21875 2.46875 0.21875 C 3 0.21875 3.765625 0.015625 4.203125 -0.9375 C 4.515625 -1.625 4.5625 -2.390625 4.5625 -3.171875 Z M 2.46875 0 C 2.078125 0 1.5 -0.25 1.3125 -1.203125 C 1.203125 -1.796875 1.203125 -2.703125 1.203125 -3.296875 C 1.203125 -3.921875 1.203125 -4.578125 1.296875 -5.125 C 1.484375 -6.296875 2.21875 -6.390625 2.46875 -6.390625 C 2.796875 -6.390625 3.453125 -6.21875 3.640625 -5.234375 C 3.734375 -4.671875 3.734375 -3.921875 3.734375 -3.296875 C 3.734375 -2.546875 3.734375 -1.875 3.625 -1.234375 C 3.484375 -0.296875 2.921875 0 2.46875 0 Z M 2.46875 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 2.921875 -6.34375 C 2.921875 -6.59375 2.921875 -6.609375 2.6875 -6.609375 C 2.078125 -5.96875 1.203125 -5.96875 0.890625 -5.96875 L 0.890625 -5.671875 C 1.078125 -5.671875 1.671875 -5.671875 2.1875 -5.921875 L 2.1875 -0.78125 C 2.1875 -0.421875 2.15625 -0.3125 1.265625 -0.3125 L 0.9375 -0.3125 L 0.9375 0 C 1.296875 -0.03125 2.15625 -0.03125 2.546875 -0.03125 C 2.953125 -0.03125 3.8125 -0.03125 4.15625 0 L 4.15625 -0.3125 L 3.84375 -0.3125 C 2.953125 -0.3125 2.921875 -0.421875 2.921875 -0.78125 Z M 2.921875 -6.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.4375 -2.4375 L 4.59375 -3.734375 C 4.71875 -3.875 4.78125 -3.9375 5.609375 -3.9375 L 5.609375 -4.40625 C 5.265625 -4.390625 4.75 -4.375 4.6875 -4.375 C 4.4375 -4.375 3.953125 -4.390625 3.671875 -4.40625 L 3.671875 -3.9375 C 3.8125 -3.9375 3.921875 -3.921875 4.046875 -3.84375 C 4.015625 -3.796875 4.015625 -3.765625 3.96875 -3.734375 L 3.140625 -2.796875 L 2.15625 -3.9375 L 2.5625 -3.9375 L 2.5625 -4.40625 C 2.296875 -4.390625 1.671875 -4.375 1.359375 -4.375 C 1.046875 -4.375 0.59375 -4.390625 0.265625 -4.40625 L 0.265625 -3.9375 L 0.96875 -3.9375 L 2.515625 -2.109375 L 1.21875 -0.65625 C 1.046875 -0.46875 0.6875 -0.46875 0.21875 -0.46875 L 0.21875 0 C 0.5625 -0.015625 1.078125 -0.03125 1.125 -0.03125 C 1.375 -0.03125 1.953125 -0.015625 2.15625 0 L 2.15625 -0.46875 C 1.96875 -0.46875 1.78125 -0.515625 1.78125 -0.578125 C 1.78125 -0.578125 1.78125 -0.59375 1.859375 -0.671875 L 2.8125 -1.75 L 3.90625 -0.46875 L 3.515625 -0.46875 L 3.515625 0 C 3.78125 -0.015625 4.390625 -0.03125 4.71875 -0.03125 C 5.03125 -0.03125 5.484375 -0.015625 5.796875 0 L 5.796875 -0.46875 L 5.09375 -0.46875 Z M 3.4375 -2.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 6.703125 -2.265625 C 6.8125 -2.3125 6.890625 -2.359375 6.890625 -2.484375 C 6.890625 -2.59375 6.8125 -2.65625 6.703125 -2.703125 L 1.203125 -5.28125 C 1.078125 -5.359375 1.046875 -5.359375 1.015625 -5.359375 C 0.90625 -5.359375 0.828125 -5.265625 0.828125 -5.15625 C 0.828125 -5.0625 0.875 -5.015625 1.015625 -4.9375 L 6.21875 -2.484375 L 1.015625 -0.015625 C 0.875 0.046875 0.828125 0.109375 0.828125 0.203125 C 0.828125 0.3125 0.90625 0.390625 1.015625 0.390625 C 1.046875 0.390625 1.078125 0.390625 1.203125 0.328125 Z M 6.703125 -2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-2">
+<path style="stroke:none;" d="M 2.015625 -0.015625 C 2.015625 -0.671875 1.765625 -1.046875 1.375 -1.046875 C 1.046875 -1.046875 0.859375 -0.796875 0.859375 -0.53125 C 0.859375 -0.265625 1.046875 0 1.375 0 C 1.5 0 1.625 -0.046875 1.71875 -0.125 C 1.75 -0.15625 1.765625 -0.15625 1.78125 -0.15625 C 1.78125 -0.15625 1.796875 -0.15625 1.796875 -0.015625 C 1.796875 0.71875 1.453125 1.3125 1.125 1.640625 C 1.015625 1.75 1.015625 1.78125 1.015625 1.8125 C 1.015625 1.875 1.0625 1.921875 1.109375 1.921875 C 1.21875 1.921875 2.015625 1.15625 2.015625 -0.015625 Z M 2.015625 -0.015625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 5.71875 -2.109375 C 5.71875 -2.71875 5.421875 -3.0625 4.671875 -3.0625 C 4.125 -3.0625 3.75 -2.765625 3.5625 -2.421875 C 3.421875 -2.90625 3.046875 -3.0625 2.53125 -3.0625 C 1.96875 -3.0625 1.59375 -2.75 1.40625 -2.390625 L 1.390625 -2.390625 L 1.390625 -3.0625 L 0.375 -2.984375 L 0.375 -2.734375 C 0.84375 -2.734375 0.890625 -2.6875 0.890625 -2.34375 L 0.890625 -0.546875 C 0.890625 -0.25 0.828125 -0.25 0.375 -0.25 L 0.375 0 C 0.390625 0 0.875 -0.03125 1.171875 -0.03125 C 1.421875 -0.03125 1.90625 0 1.96875 0 L 1.96875 -0.25 C 1.515625 -0.25 1.453125 -0.25 1.453125 -0.546875 L 1.453125 -1.796875 C 1.453125 -2.53125 2.015625 -2.875 2.484375 -2.875 C 2.96875 -2.875 3.03125 -2.484375 3.03125 -2.140625 L 3.03125 -0.546875 C 3.03125 -0.25 2.96875 -0.25 2.515625 -0.25 L 2.515625 0 C 2.53125 0 3.015625 -0.03125 3.296875 -0.03125 C 3.5625 -0.03125 4.046875 0 4.109375 0 L 4.109375 -0.25 C 3.65625 -0.25 3.578125 -0.25 3.578125 -0.546875 L 3.578125 -1.796875 C 3.578125 -2.53125 4.15625 -2.875 4.609375 -2.875 C 5.109375 -2.875 5.171875 -2.484375 5.171875 -2.140625 L 5.171875 -0.546875 C 5.171875 -0.25 5.09375 -0.25 4.640625 -0.25 L 4.640625 0 C 4.65625 0 5.140625 -0.03125 5.4375 -0.03125 C 5.6875 -0.03125 6.171875 0 6.234375 0 L 6.234375 -0.25 C 5.78125 -0.25 5.71875 -0.25 5.71875 -0.546875 Z M 5.71875 -2.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 3.09375 -1.859375 C 3.09375 -2.234375 3.09375 -2.5 2.78125 -2.75 C 2.5 -2.984375 2.15625 -3.09375 1.75 -3.09375 C 1.09375 -3.09375 0.625 -2.84375 0.625 -2.421875 C 0.625 -2.203125 0.78125 -2.09375 0.953125 -2.09375 C 1.140625 -2.09375 1.28125 -2.21875 1.28125 -2.40625 C 1.28125 -2.53125 1.234375 -2.671875 1.046875 -2.734375 C 1.296875 -2.90625 1.703125 -2.90625 1.734375 -2.90625 C 2.125 -2.90625 2.546875 -2.65625 2.546875 -2.0625 L 2.546875 -1.84375 C 2.171875 -1.828125 1.703125 -1.8125 1.203125 -1.625 C 0.578125 -1.390625 0.375 -1.015625 0.375 -0.703125 C 0.375 -0.109375 1.109375 0.0625 1.59375 0.0625 C 2.15625 0.0625 2.484375 -0.25 2.625 -0.515625 C 2.65625 -0.234375 2.84375 0.03125 3.15625 0.03125 C 3.171875 0.03125 3.859375 0.03125 3.859375 -0.625 L 3.859375 -1.015625 L 3.609375 -1.015625 L 3.609375 -0.625 C 3.609375 -0.5625 3.609375 -0.234375 3.359375 -0.234375 C 3.09375 -0.234375 3.09375 -0.5625 3.09375 -0.640625 Z M 2.546875 -0.984375 C 2.546875 -0.3125 1.96875 -0.125 1.65625 -0.125 C 1.296875 -0.125 0.96875 -0.359375 0.96875 -0.703125 C 0.96875 -1.078125 1.296875 -1.625 2.546875 -1.671875 Z M 2.546875 -0.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-3">
+<path style="stroke:none;" d="M 2.359375 -1.5625 C 2.34375 -1.5625 2.296875 -1.625 2.296875 -1.625 C 2.296875 -1.640625 2.765625 -2.140625 2.828125 -2.203125 C 3.0625 -2.46875 3.3125 -2.734375 3.859375 -2.75 L 3.859375 -3 C 3.671875 -2.984375 3.46875 -2.96875 3.28125 -2.96875 C 3.0625 -2.96875 2.796875 -2.96875 2.59375 -3 L 2.59375 -2.75 C 2.703125 -2.71875 2.71875 -2.65625 2.71875 -2.59375 C 2.71875 -2.578125 2.71875 -2.46875 2.625 -2.34375 L 2.140625 -1.796875 L 1.5625 -2.46875 C 1.484375 -2.53125 1.484375 -2.578125 1.484375 -2.59375 C 1.484375 -2.703125 1.578125 -2.75 1.671875 -2.75 L 1.671875 -3 C 1.40625 -2.96875 1.140625 -2.96875 0.890625 -2.96875 C 0.6875 -2.96875 0.421875 -2.96875 0.21875 -3 L 0.21875 -2.75 C 0.53125 -2.75 0.71875 -2.75 0.890625 -2.53125 L 1.765625 -1.53125 C 1.765625 -1.53125 1.828125 -1.46875 1.828125 -1.46875 C 1.828125 -1.453125 1.296875 -0.875 1.234375 -0.796875 C 0.96875 -0.515625 0.734375 -0.265625 0.1875 -0.25 L 0.1875 0 C 0.390625 -0.015625 0.546875 -0.03125 0.765625 -0.03125 C 0.96875 -0.03125 1.25 -0.015625 1.453125 0 L 1.453125 -0.25 C 1.375 -0.265625 1.3125 -0.3125 1.3125 -0.40625 C 1.3125 -0.546875 1.390625 -0.625 1.5 -0.75 L 1.984375 -1.28125 L 2.59375 -0.59375 C 2.71875 -0.453125 2.71875 -0.4375 2.71875 -0.390625 C 2.71875 -0.25 2.5625 -0.25 2.53125 -0.25 L 2.53125 0 C 2.59375 0 3.09375 -0.03125 3.328125 -0.03125 C 3.546875 -0.03125 3.765625 -0.015625 3.984375 0 L 3.984375 -0.25 C 3.53125 -0.25 3.46875 -0.296875 3.3125 -0.46875 Z M 2.359375 -1.5625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.453125 -5.453125 L 4.75 -5.453125 C 4.90625 -5.453125 5.15625 -5.453125 5.15625 -5.765625 C 5.15625 -6.0625 4.90625 -6.0625 4.75 -6.0625 L 3.46875 -6.0625 C 3.328125 -6.0625 3.0625 -6.0625 3.0625 -5.765625 C 3.0625 -5.453125 3.328125 -5.453125 3.46875 -5.453125 L 3.765625 -5.453125 L 3.765625 -2.078125 C 3.765625 -1.015625 3.109375 -0.5 2.59375 -0.5 C 2.078125 -0.5 1.421875 -1.015625 1.421875 -2.078125 L 1.421875 -5.453125 L 1.71875 -5.453125 C 1.875 -5.453125 2.140625 -5.453125 2.140625 -5.765625 C 2.140625 -6.0625 1.875 -6.0625 1.71875 -6.0625 L 0.453125 -6.0625 C 0.296875 -6.0625 0.046875 -6.0625 0.046875 -5.765625 C 0.046875 -5.453125 0.296875 -5.453125 0.453125 -5.453125 L 0.75 -5.453125 L 0.75 -2.03125 C 0.75 -0.796875 1.609375 0.109375 2.59375 0.109375 C 3.59375 0.109375 4.453125 -0.796875 4.453125 -2.03125 Z M 4.453125 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 1.640625 -3.8125 C 1.640625 -4.125 1.640625 -4.28125 1.25 -4.28125 L 0.53125 -4.28125 C 0.359375 -4.28125 0.125 -4.28125 0.125 -3.96875 C 0.125 -3.671875 0.375 -3.671875 0.515625 -3.671875 L 0.96875 -3.671875 L 0.96875 -0.609375 L 0.53125 -0.609375 C 0.359375 -0.609375 0.125 -0.609375 0.125 -0.296875 C 0.125 0 0.375 0 0.515625 0 L 2.09375 0 C 2.234375 0 2.484375 0 2.484375 -0.296875 C 2.484375 -0.609375 2.25 -0.609375 2.078125 -0.609375 L 1.640625 -0.609375 L 1.640625 -2.359375 C 1.640625 -3.359375 2.375 -3.734375 2.890625 -3.734375 C 3.40625 -3.734375 3.546875 -3.453125 3.546875 -2.859375 L 3.546875 -0.609375 L 3.171875 -0.609375 C 3 -0.609375 2.765625 -0.609375 2.765625 -0.296875 C 2.765625 0 3.03125 0 3.171875 0 L 4.6875 0 C 4.828125 0 5.078125 0 5.078125 -0.296875 C 5.078125 -0.609375 4.828125 -0.609375 4.671875 -0.609375 L 4.234375 -0.609375 L 4.234375 -2.90625 C 4.234375 -3.90625 3.734375 -4.328125 2.953125 -4.328125 C 2.28125 -4.328125 1.828125 -4 1.640625 -3.8125 Z M 1.640625 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-3">
+<path style="stroke:none;" d="M 3.0625 -3.875 C 3.0625 -4.171875 3 -4.28125 2.671875 -4.28125 L 1.265625 -4.28125 C 1.109375 -4.28125 0.859375 -4.28125 0.859375 -3.984375 C 0.859375 -3.671875 1.109375 -3.671875 1.265625 -3.671875 L 2.375 -3.671875 L 2.375 -0.609375 L 1.1875 -0.609375 C 1.015625 -0.609375 0.78125 -0.609375 0.78125 -0.296875 C 0.78125 0 1.03125 0 1.1875 0 L 4.109375 0 C 4.25 0 4.515625 0 4.515625 -0.296875 C 4.515625 -0.609375 4.25 -0.609375 4.109375 -0.609375 L 3.0625 -0.609375 Z M 3.0625 -5.578125 C 3.0625 -5.859375 2.84375 -6.078125 2.5625 -6.078125 C 2.296875 -6.078125 2.078125 -5.859375 2.078125 -5.578125 C 2.078125 -5.296875 2.296875 -5.078125 2.5625 -5.078125 C 2.84375 -5.078125 3.0625 -5.296875 3.0625 -5.578125 Z M 3.0625 -5.578125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-4">
+<path style="stroke:none;" d="M 2.515625 -3.671875 L 3.71875 -3.671875 C 3.875 -3.671875 4.125 -3.671875 4.125 -3.96875 C 4.125 -4.28125 3.875 -4.28125 3.71875 -4.28125 L 2.515625 -4.28125 L 2.515625 -4.75 C 2.515625 -5.515625 3.171875 -5.515625 3.46875 -5.515625 C 3.46875 -5.484375 3.5625 -5.09375 3.90625 -5.09375 C 4.109375 -5.09375 4.328125 -5.25 4.328125 -5.53125 C 4.328125 -6.125 3.546875 -6.125 3.390625 -6.125 C 2.59375 -6.125 1.828125 -5.671875 1.828125 -4.796875 L 1.828125 -4.28125 L 0.828125 -4.28125 C 0.671875 -4.28125 0.421875 -4.28125 0.421875 -3.96875 C 0.421875 -3.671875 0.671875 -3.671875 0.828125 -3.671875 L 1.828125 -3.671875 L 1.828125 -0.609375 L 0.828125 -0.609375 C 0.671875 -0.609375 0.421875 -0.609375 0.421875 -0.3125 C 0.421875 0 0.671875 0 0.828125 0 L 3.515625 0 C 3.65625 0 3.921875 0 3.921875 -0.296875 C 3.921875 -0.609375 3.65625 -0.609375 3.515625 -0.609375 L 2.515625 -0.609375 Z M 2.515625 -3.671875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-5">
+<path style="stroke:none;" d="M 4.640625 -2.140625 C 4.640625 -3.390625 3.703125 -4.359375 2.59375 -4.359375 C 1.484375 -4.359375 0.5625 -3.390625 0.5625 -2.140625 C 0.5625 -0.890625 1.515625 0.0625 2.59375 0.0625 C 3.6875 0.0625 4.640625 -0.890625 4.640625 -2.140625 Z M 2.59375 -0.546875 C 1.859375 -0.546875 1.25 -1.296875 1.25 -2.21875 C 1.25 -3.109375 1.890625 -3.765625 2.59375 -3.765625 C 3.3125 -3.765625 3.953125 -3.109375 3.953125 -2.21875 C 3.953125 -1.296875 3.328125 -0.546875 2.59375 -0.546875 Z M 2.59375 -0.546875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-6">
+<path style="stroke:none;" d="M 2.203125 -1.84375 C 2.203125 -2.78125 2.78125 -3.734375 3.984375 -3.734375 C 4 -3.5 4.171875 -3.296875 4.421875 -3.296875 C 4.640625 -3.296875 4.828125 -3.453125 4.828125 -3.71875 C 4.828125 -3.921875 4.71875 -4.328125 3.890625 -4.328125 C 3.390625 -4.328125 2.75 -4.15625 2.203125 -3.53125 L 2.203125 -3.875 C 2.203125 -4.171875 2.140625 -4.28125 1.8125 -4.28125 L 0.71875 -4.28125 C 0.5625 -4.28125 0.3125 -4.28125 0.3125 -3.984375 C 0.3125 -3.671875 0.5625 -3.671875 0.71875 -3.671875 L 1.515625 -3.671875 L 1.515625 -0.609375 L 0.71875 -0.609375 C 0.5625 -0.609375 0.3125 -0.609375 0.3125 -0.3125 C 0.3125 0 0.5625 0 0.71875 0 L 3.296875 0 C 3.453125 0 3.703125 0 3.703125 -0.296875 C 3.703125 -0.609375 3.453125 -0.609375 3.296875 -0.609375 L 2.203125 -0.609375 Z M 2.203125 -1.84375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-7">
+<path style="stroke:none;" d="M 1.078125 -3.984375 C 1.0625 -4.28125 0.859375 -4.28125 0.6875 -4.28125 L 0.359375 -4.28125 C 0.21875 -4.28125 -0.046875 -4.28125 -0.046875 -3.984375 C -0.046875 -3.671875 0.171875 -3.671875 0.53125 -3.671875 L 0.53125 -0.609375 C 0.171875 -0.609375 -0.046875 -0.609375 -0.046875 -0.296875 C -0.046875 0 0.234375 0 0.359375 0 L 1.234375 0 C 1.390625 0 1.640625 0 1.640625 -0.296875 C 1.640625 -0.609375 1.4375 -0.609375 1.078125 -0.609375 L 1.078125 -2.375 C 1.078125 -3.265625 1.484375 -3.734375 1.890625 -3.734375 C 2.125 -3.734375 2.265625 -3.5625 2.265625 -2.921875 L 2.265625 -0.609375 C 2.078125 -0.609375 1.828125 -0.609375 1.828125 -0.296875 C 1.828125 0 2.09375 0 2.234375 0 L 2.96875 0 C 3.125 0 3.390625 0 3.390625 -0.296875 C 3.390625 -0.609375 3.171875 -0.609375 2.8125 -0.609375 L 2.8125 -2.375 C 2.8125 -3.265625 3.21875 -3.734375 3.625 -3.734375 C 3.859375 -3.734375 4 -3.5625 4 -2.921875 L 4 -0.609375 C 3.8125 -0.609375 3.5625 -0.609375 3.5625 -0.296875 C 3.5625 0 3.828125 0 3.96875 0 L 4.71875 0 C 4.859375 0 5.125 0 5.125 -0.296875 C 5.125 -0.609375 4.90625 -0.609375 4.546875 -0.609375 L 4.546875 -3 C 4.546875 -3.203125 4.546875 -4.328125 3.671875 -4.328125 C 3.375 -4.328125 2.96875 -4.203125 2.6875 -3.8125 C 2.546875 -4.15625 2.265625 -4.328125 1.9375 -4.328125 C 1.625 -4.328125 1.3125 -4.203125 1.078125 -3.984375 Z M 1.078125 -3.984375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.179688 0 L 8 0 L 8 8 L 0.179688 8 Z M 0.179688 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 8 0 L 12 0 L 12 9.925781 L 8 9.925781 Z M 8 0 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 18 0 L 21 0 L 21 9.925781 L 18 9.925781 Z M 18 0 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 42 5 L 57 5 L 57 9.925781 L 42 9.925781 Z M 42 5 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 106 0 L 114 0 L 114 9.925781 L 106 9.925781 Z M 106 0 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 115 6 L 117 6 L 117 9.925781 L 115 9.925781 Z M 115 6 "/>
+</clipPath>
+<clipPath id="clip7">
+ <path d="M 119 0 L 127 0 L 127 9.925781 L 119 9.925781 Z M 119 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.1793" y="7.444354"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.899629" y="7.444354"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="11.759295" y="7.444354"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.783921" y="7.444354"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="24.401346" y="7.444354"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="34.878436" y="7.444354"/>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="41.781799" y="8.933822"/>
+ <use xlink:href="#glyph4-2" x="48.302494" y="8.933822"/>
+ <use xlink:href="#glyph4-3" x="52.259378" y="8.933822"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="59.131367" y="7.444354"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="69.057504" y="7.444354"/>
+ <use xlink:href="#glyph5-2" x="74.268517" y="7.444354"/>
+ <use xlink:href="#glyph5-3" x="79.479529" y="7.444354"/>
+ <use xlink:href="#glyph5-4" x="84.690542" y="7.444354"/>
+ <use xlink:href="#glyph5-5" x="89.901555" y="7.444354"/>
+ <use xlink:href="#glyph5-6" x="95.112567" y="7.444354"/>
+ <use xlink:href="#glyph5-7" x="100.32358" y="7.444354"/>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="105.53404" y="7.444354"/>
+ <use xlink:href="#glyph1-3" x="109.394159" y="7.444354"/>
+</g>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-2" x="114.357273" y="7.444354"/>
+</g>
+</g>
+<g clip-path="url(#clip7)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-4" x="118.768889" y="7.444354"/>
+ <use xlink:href="#glyph1-2" x="123.731758" y="7.444354"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig27.svg b/doc/figs/tex/fig27.svg
new file mode 100644
index 00000000000..219c86f4c1a
--- /dev/null
+++ b/doc/figs/tex/fig27.svg
@@ -0,0 +1,45 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="22.13pt" height="8.302pt" viewBox="0 0 22.13 8.302" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.203125 -6.28125 C 1.90625 -6.28125 0.921875 -5.65625 0.546875 -5.21875 C 0.21875 -4.84375 0.1875 -4.578125 0.1875 -4.5625 C 0.1875 -4.515625 0.234375 -4.5 0.28125 -4.5 C 0.4375 -4.5 0.640625 -4.625 0.71875 -4.671875 C 0.90625 -4.796875 0.9375 -4.84375 1 -5.03125 C 1.125 -5.390625 1.375 -5.71875 2.53125 -5.765625 C 2.375 -3.703125 1.8125 -1.6875 1.046875 0.234375 C 1 0.375 1 0.390625 1 0.390625 C 1 0.421875 1.015625 0.453125 1.078125 0.453125 C 1.234375 0.453125 1.671875 0.25 1.765625 0.015625 C 2.25 -1.109375 3 -3.21875 3.28125 -5.765625 L 3.75 -5.765625 C 4.875 -5.765625 5.953125 -5.34375 5.953125 -4.421875 C 5.953125 -3.734375 5.296875 -2.4375 3.515625 -2.390625 C 3.3125 -2.375 3.21875 -2.375 2.953125 -2.21875 C 2.796875 -2.109375 2.71875 -2 2.71875 -1.953125 C 2.71875 -1.890625 2.78125 -1.890625 2.890625 -1.890625 C 4.5625 -1.890625 6.734375 -3.296875 6.734375 -4.8125 C 6.734375 -5.859375 5.5 -6.28125 4.421875 -6.28125 Z M 3.203125 -6.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 5.296875 -1.953125 C 5.296875 -2.515625 5.015625 -2.84375 4.328125 -2.84375 C 3.8125 -2.84375 3.46875 -2.5625 3.296875 -2.234375 C 3.171875 -2.703125 2.8125 -2.84375 2.34375 -2.84375 C 1.828125 -2.84375 1.484375 -2.546875 1.296875 -2.21875 L 1.296875 -2.84375 L 0.34375 -2.765625 L 0.34375 -2.53125 C 0.78125 -2.53125 0.828125 -2.484375 0.828125 -2.171875 L 0.828125 -0.515625 C 0.828125 -0.234375 0.765625 -0.234375 0.34375 -0.234375 L 0.34375 0 C 0.359375 0 0.8125 -0.03125 1.078125 -0.03125 C 1.3125 -0.03125 1.765625 0 1.828125 0 L 1.828125 -0.234375 C 1.40625 -0.234375 1.34375 -0.234375 1.34375 -0.515625 L 1.34375 -1.671875 C 1.34375 -2.34375 1.875 -2.65625 2.296875 -2.65625 C 2.75 -2.65625 2.8125 -2.296875 2.8125 -1.96875 L 2.8125 -0.515625 C 2.8125 -0.234375 2.75 -0.234375 2.328125 -0.234375 L 2.328125 0 C 2.34375 0 2.78125 -0.03125 3.0625 -0.03125 C 3.296875 -0.03125 3.734375 0 3.796875 0 L 3.796875 -0.234375 C 3.375 -0.234375 3.3125 -0.234375 3.3125 -0.515625 L 3.3125 -1.671875 C 3.3125 -2.34375 3.84375 -2.65625 4.28125 -2.65625 C 4.71875 -2.65625 4.78125 -2.296875 4.78125 -1.96875 L 4.78125 -0.515625 C 4.78125 -0.234375 4.71875 -0.234375 4.296875 -0.234375 L 4.296875 0 C 4.3125 0 4.765625 -0.03125 5.03125 -0.03125 C 5.265625 -0.03125 5.71875 0 5.78125 0 L 5.78125 -0.234375 C 5.359375 -0.234375 5.296875 -0.234375 5.296875 -0.515625 Z M 5.296875 -1.953125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.875 -1.71875 C 2.875 -2.0625 2.875 -2.3125 2.578125 -2.546875 C 2.3125 -2.765625 2 -2.875 1.625 -2.875 C 1.015625 -2.875 0.578125 -2.640625 0.578125 -2.25 C 0.578125 -2.046875 0.71875 -1.9375 0.890625 -1.9375 C 1.0625 -1.9375 1.1875 -2.0625 1.1875 -2.234375 C 1.1875 -2.34375 1.140625 -2.484375 0.96875 -2.53125 C 1.203125 -2.6875 1.578125 -2.6875 1.609375 -2.6875 C 1.96875 -2.6875 2.359375 -2.453125 2.359375 -1.90625 L 2.359375 -1.71875 C 2.015625 -1.703125 1.578125 -1.6875 1.109375 -1.5 C 0.53125 -1.296875 0.359375 -0.9375 0.359375 -0.65625 C 0.359375 -0.09375 1.03125 0.0625 1.484375 0.0625 C 2 0.0625 2.296875 -0.21875 2.4375 -0.46875 C 2.453125 -0.21875 2.640625 0.03125 2.921875 0.03125 C 2.9375 0.03125 3.5625 0.03125 3.5625 -0.578125 L 3.5625 -0.9375 L 3.34375 -0.9375 L 3.34375 -0.578125 C 3.34375 -0.515625 3.34375 -0.21875 3.109375 -0.21875 C 2.875 -0.21875 2.875 -0.515625 2.875 -0.59375 Z M 2.359375 -0.90625 C 2.359375 -0.296875 1.828125 -0.109375 1.53125 -0.109375 C 1.203125 -0.109375 0.890625 -0.328125 0.890625 -0.65625 C 0.890625 -1 1.203125 -1.5 2.359375 -1.546875 Z M 2.359375 -0.90625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 2.1875 -1.4375 C 2.171875 -1.453125 2.125 -1.5 2.125 -1.5 C 2.125 -1.53125 2.5625 -1.984375 2.609375 -2.046875 C 2.84375 -2.296875 3.0625 -2.53125 3.578125 -2.546875 L 3.578125 -2.78125 C 3.390625 -2.765625 3.203125 -2.75 3.03125 -2.75 C 2.84375 -2.75 2.59375 -2.75 2.390625 -2.78125 L 2.390625 -2.546875 C 2.5 -2.53125 2.53125 -2.453125 2.53125 -2.390625 C 2.53125 -2.375 2.53125 -2.28125 2.421875 -2.171875 L 1.96875 -1.671875 L 1.4375 -2.28125 C 1.375 -2.34375 1.375 -2.375 1.375 -2.40625 C 1.375 -2.5 1.46875 -2.546875 1.546875 -2.546875 L 1.546875 -2.78125 C 1.3125 -2.75 1.0625 -2.75 0.828125 -2.75 C 0.625 -2.75 0.390625 -2.75 0.203125 -2.78125 L 0.203125 -2.546875 C 0.5 -2.546875 0.65625 -2.546875 0.828125 -2.34375 L 1.640625 -1.421875 C 1.640625 -1.421875 1.6875 -1.359375 1.6875 -1.359375 C 1.6875 -1.34375 1.203125 -0.8125 1.140625 -0.734375 C 0.90625 -0.484375 0.6875 -0.25 0.171875 -0.234375 L 0.171875 0 C 0.359375 -0.015625 0.5 -0.03125 0.703125 -0.03125 C 0.890625 -0.03125 1.15625 -0.015625 1.34375 0 L 1.34375 -0.234375 C 1.265625 -0.25 1.21875 -0.296875 1.21875 -0.375 C 1.21875 -0.5 1.28125 -0.578125 1.390625 -0.6875 L 1.84375 -1.1875 L 2.40625 -0.546875 C 2.53125 -0.421875 2.53125 -0.40625 2.53125 -0.359375 C 2.53125 -0.234375 2.375 -0.234375 2.34375 -0.234375 L 2.34375 0 C 2.40625 0 2.875 -0.03125 3.078125 -0.03125 C 3.28125 -0.03125 3.484375 -0.015625 3.6875 0 L 3.6875 -0.234375 C 3.265625 -0.234375 3.21875 -0.265625 3.0625 -0.4375 Z M 2.1875 -1.4375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.457031 0 L 8 0 L 8 7 L 0.457031 7 Z M 0.457031 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 7 4 L 20.871094 4 L 20.871094 7.65625 L 7 7.65625 Z M 7 4 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.456889" y="6.280002"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="6.849429" y="7.658134"/>
+ <use xlink:href="#glyph1-2" x="12.886746" y="7.658134"/>
+ <use xlink:href="#glyph1-3" x="16.550307" y="7.658134"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig28.svg b/doc/figs/tex/fig28.svg
new file mode 100644
index 00000000000..203e006c887
--- /dev/null
+++ b/doc/figs/tex/fig28.svg
@@ -0,0 +1,57 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="21.544pt" height="9.963pt" viewBox="0 0 21.544 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.390625 -6.65625 C 2.015625 -6.65625 0.96875 -6 0.578125 -5.53125 C 0.234375 -5.140625 0.203125 -4.859375 0.203125 -4.84375 C 0.203125 -4.78125 0.25 -4.765625 0.296875 -4.765625 C 0.453125 -4.765625 0.6875 -4.90625 0.765625 -4.953125 C 0.96875 -5.09375 1 -5.140625 1.046875 -5.328125 C 1.1875 -5.71875 1.46875 -6.0625 2.6875 -6.125 C 2.515625 -3.921875 1.9375 -1.796875 1.109375 0.25 C 1.046875 0.390625 1.046875 0.40625 1.046875 0.421875 C 1.046875 0.453125 1.078125 0.484375 1.15625 0.484375 C 1.3125 0.484375 1.78125 0.265625 1.875 0.015625 C 2.390625 -1.171875 3.1875 -3.40625 3.484375 -6.125 L 3.984375 -6.125 C 5.171875 -6.125 6.3125 -5.671875 6.3125 -4.6875 C 6.3125 -3.953125 5.609375 -2.59375 3.71875 -2.53125 C 3.515625 -2.53125 3.40625 -2.53125 3.140625 -2.34375 C 2.96875 -2.234375 2.890625 -2.125 2.890625 -2.0625 C 2.890625 -2 2.9375 -2 3.078125 -2 C 4.84375 -2 7.140625 -3.5 7.140625 -5.109375 C 7.140625 -6.21875 5.828125 -6.65625 4.703125 -6.65625 Z M 3.390625 -6.65625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.234375 2.34375 C 3.234375 2.3125 3.234375 2.296875 3.0625 2.125 C 1.84375 0.890625 1.53125 -0.953125 1.53125 -2.4375 C 1.53125 -4.140625 1.90625 -5.828125 3.09375 -7.046875 C 3.234375 -7.171875 3.234375 -7.1875 3.234375 -7.21875 C 3.234375 -7.28125 3.1875 -7.3125 3.125 -7.3125 C 3.03125 -7.3125 2.15625 -6.65625 1.578125 -5.40625 C 1.078125 -4.34375 0.96875 -3.25 0.96875 -2.4375 C 0.96875 -1.671875 1.078125 -0.5 1.609375 0.609375 C 2.1875 1.796875 3.03125 2.4375 3.125 2.4375 C 3.1875 2.4375 3.234375 2.40625 3.234375 2.34375 Z M 3.234375 2.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.8125 -2.4375 C 2.8125 -3.203125 2.703125 -4.375 2.171875 -5.484375 C 1.59375 -6.671875 0.75 -7.3125 0.65625 -7.3125 C 0.59375 -7.3125 0.5625 -7.265625 0.5625 -7.21875 C 0.5625 -7.1875 0.5625 -7.171875 0.734375 -6.984375 C 1.703125 -6.03125 2.25 -4.46875 2.25 -2.4375 C 2.25 -0.765625 1.890625 0.953125 0.6875 2.171875 C 0.5625 2.296875 0.5625 2.3125 0.5625 2.34375 C 0.5625 2.40625 0.59375 2.4375 0.65625 2.4375 C 0.75 2.4375 1.625 1.78125 2.203125 0.53125 C 2.703125 -0.53125 2.8125 -1.625 2.8125 -2.4375 Z M 2.8125 -2.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.375 -2.40625 L 4.515625 -3.671875 C 4.640625 -3.796875 4.703125 -3.875 5.515625 -3.875 L 5.515625 -4.328125 C 5.171875 -4.3125 4.65625 -4.296875 4.609375 -4.296875 C 4.375 -4.296875 3.875 -4.3125 3.609375 -4.328125 L 3.609375 -3.875 C 3.75 -3.875 3.859375 -3.84375 3.984375 -3.78125 C 3.9375 -3.71875 3.9375 -3.703125 3.90625 -3.671875 L 3.078125 -2.75 L 2.125 -3.875 L 2.515625 -3.875 L 2.515625 -4.328125 C 2.265625 -4.3125 1.640625 -4.296875 1.328125 -4.296875 C 1.03125 -4.296875 0.578125 -4.3125 0.265625 -4.328125 L 0.265625 -3.875 L 0.953125 -3.875 L 2.46875 -2.078125 L 1.203125 -0.640625 C 1.03125 -0.453125 0.6875 -0.453125 0.21875 -0.453125 L 0.21875 0 C 0.5625 -0.015625 1.0625 -0.03125 1.109375 -0.03125 C 1.359375 -0.03125 1.921875 -0.015625 2.109375 0 L 2.109375 -0.453125 C 1.9375 -0.453125 1.75 -0.5 1.75 -0.5625 C 1.75 -0.578125 1.75 -0.578125 1.828125 -0.65625 L 2.765625 -1.71875 L 3.84375 -0.453125 L 3.46875 -0.453125 L 3.46875 0 C 3.71875 -0.015625 4.3125 -0.03125 4.625 -0.03125 C 4.9375 -0.03125 5.375 -0.015625 5.703125 0 L 5.703125 -0.453125 L 5.015625 -0.453125 Z M 3.375 -2.40625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.0859375 L 8 0.0859375 L 8 8 L 0 8 Z M 0 0.0859375 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 8 0.0859375 L 11 0.0859375 L 11 9.839844 L 8 9.839844 Z M 8 0.0859375 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 17 0.0859375 L 21 0.0859375 L 21 9.839844 L 17 9.839844 Z M 17 0.0859375 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="7.402262"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.588384" y="7.402262"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="11.382087" y="7.402262"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.303749" y="7.402262"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig29.svg b/doc/figs/tex/fig29.svg
new file mode 100644
index 00000000000..c1b4811dcda
--- /dev/null
+++ b/doc/figs/tex/fig29.svg
@@ -0,0 +1,89 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="58.752pt" height="9.963pt" viewBox="0 0 58.752 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.453125 -5.453125 L 4.75 -5.453125 C 4.90625 -5.453125 5.15625 -5.453125 5.15625 -5.765625 C 5.15625 -6.0625 4.90625 -6.0625 4.75 -6.0625 L 3.46875 -6.0625 C 3.328125 -6.0625 3.0625 -6.0625 3.0625 -5.765625 C 3.0625 -5.453125 3.328125 -5.453125 3.46875 -5.453125 L 3.765625 -5.453125 L 3.765625 -2.078125 C 3.765625 -1.015625 3.109375 -0.5 2.59375 -0.5 C 2.078125 -0.5 1.421875 -1.015625 1.421875 -2.078125 L 1.421875 -5.453125 L 1.71875 -5.453125 C 1.875 -5.453125 2.140625 -5.453125 2.140625 -5.765625 C 2.140625 -6.0625 1.875 -6.0625 1.71875 -6.0625 L 0.453125 -6.0625 C 0.296875 -6.0625 0.046875 -6.0625 0.046875 -5.765625 C 0.046875 -5.453125 0.296875 -5.453125 0.453125 -5.453125 L 0.75 -5.453125 L 0.75 -2.03125 C 0.75 -0.796875 1.609375 0.109375 2.59375 0.109375 C 3.59375 0.109375 4.453125 -0.796875 4.453125 -2.03125 Z M 4.453125 -5.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 1.640625 -3.8125 C 1.640625 -4.125 1.640625 -4.28125 1.25 -4.28125 L 0.53125 -4.28125 C 0.359375 -4.28125 0.125 -4.28125 0.125 -3.96875 C 0.125 -3.671875 0.375 -3.671875 0.515625 -3.671875 L 0.96875 -3.671875 L 0.96875 -0.609375 L 0.53125 -0.609375 C 0.359375 -0.609375 0.125 -0.609375 0.125 -0.296875 C 0.125 0 0.375 0 0.515625 0 L 2.09375 0 C 2.234375 0 2.484375 0 2.484375 -0.296875 C 2.484375 -0.609375 2.25 -0.609375 2.078125 -0.609375 L 1.640625 -0.609375 L 1.640625 -2.359375 C 1.640625 -3.359375 2.375 -3.734375 2.890625 -3.734375 C 3.40625 -3.734375 3.546875 -3.453125 3.546875 -2.859375 L 3.546875 -0.609375 L 3.171875 -0.609375 C 3 -0.609375 2.765625 -0.609375 2.765625 -0.296875 C 2.765625 0 3.03125 0 3.171875 0 L 4.6875 0 C 4.828125 0 5.078125 0 5.078125 -0.296875 C 5.078125 -0.609375 4.828125 -0.609375 4.671875 -0.609375 L 4.234375 -0.609375 L 4.234375 -2.90625 C 4.234375 -3.90625 3.734375 -4.328125 2.953125 -4.328125 C 2.28125 -4.328125 1.828125 -4 1.640625 -3.8125 Z M 1.640625 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 3.0625 -3.875 C 3.0625 -4.171875 3 -4.28125 2.671875 -4.28125 L 1.265625 -4.28125 C 1.109375 -4.28125 0.859375 -4.28125 0.859375 -3.984375 C 0.859375 -3.671875 1.109375 -3.671875 1.265625 -3.671875 L 2.375 -3.671875 L 2.375 -0.609375 L 1.1875 -0.609375 C 1.015625 -0.609375 0.78125 -0.609375 0.78125 -0.296875 C 0.78125 0 1.03125 0 1.1875 0 L 4.109375 0 C 4.25 0 4.515625 0 4.515625 -0.296875 C 4.515625 -0.609375 4.25 -0.609375 4.109375 -0.609375 L 3.0625 -0.609375 Z M 3.0625 -5.578125 C 3.0625 -5.859375 2.84375 -6.078125 2.5625 -6.078125 C 2.296875 -6.078125 2.078125 -5.859375 2.078125 -5.578125 C 2.078125 -5.296875 2.296875 -5.078125 2.5625 -5.078125 C 2.84375 -5.078125 3.0625 -5.296875 3.0625 -5.578125 Z M 3.0625 -5.578125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 2.515625 -3.671875 L 3.71875 -3.671875 C 3.875 -3.671875 4.125 -3.671875 4.125 -3.96875 C 4.125 -4.28125 3.875 -4.28125 3.71875 -4.28125 L 2.515625 -4.28125 L 2.515625 -4.75 C 2.515625 -5.515625 3.171875 -5.515625 3.46875 -5.515625 C 3.46875 -5.484375 3.5625 -5.09375 3.90625 -5.09375 C 4.109375 -5.09375 4.328125 -5.25 4.328125 -5.53125 C 4.328125 -6.125 3.546875 -6.125 3.390625 -6.125 C 2.59375 -6.125 1.828125 -5.671875 1.828125 -4.796875 L 1.828125 -4.28125 L 0.828125 -4.28125 C 0.671875 -4.28125 0.421875 -4.28125 0.421875 -3.96875 C 0.421875 -3.671875 0.671875 -3.671875 0.828125 -3.671875 L 1.828125 -3.671875 L 1.828125 -0.609375 L 0.828125 -0.609375 C 0.671875 -0.609375 0.421875 -0.609375 0.421875 -0.3125 C 0.421875 0 0.671875 0 0.828125 0 L 3.515625 0 C 3.65625 0 3.921875 0 3.921875 -0.296875 C 3.921875 -0.609375 3.65625 -0.609375 3.515625 -0.609375 L 2.515625 -0.609375 Z M 2.515625 -3.671875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 4.640625 -2.140625 C 4.640625 -3.390625 3.703125 -4.359375 2.59375 -4.359375 C 1.484375 -4.359375 0.5625 -3.390625 0.5625 -2.140625 C 0.5625 -0.890625 1.515625 0.0625 2.59375 0.0625 C 3.6875 0.0625 4.640625 -0.890625 4.640625 -2.140625 Z M 2.59375 -0.546875 C 1.859375 -0.546875 1.25 -1.296875 1.25 -2.21875 C 1.25 -3.109375 1.890625 -3.765625 2.59375 -3.765625 C 3.3125 -3.765625 3.953125 -3.109375 3.953125 -2.21875 C 3.953125 -1.296875 3.328125 -0.546875 2.59375 -0.546875 Z M 2.59375 -0.546875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 2.203125 -1.84375 C 2.203125 -2.78125 2.78125 -3.734375 3.984375 -3.734375 C 4 -3.5 4.171875 -3.296875 4.421875 -3.296875 C 4.640625 -3.296875 4.828125 -3.453125 4.828125 -3.71875 C 4.828125 -3.921875 4.71875 -4.328125 3.890625 -4.328125 C 3.390625 -4.328125 2.75 -4.15625 2.203125 -3.53125 L 2.203125 -3.875 C 2.203125 -4.171875 2.140625 -4.28125 1.8125 -4.28125 L 0.71875 -4.28125 C 0.5625 -4.28125 0.3125 -4.28125 0.3125 -3.984375 C 0.3125 -3.671875 0.5625 -3.671875 0.71875 -3.671875 L 1.515625 -3.671875 L 1.515625 -0.609375 L 0.71875 -0.609375 C 0.5625 -0.609375 0.3125 -0.609375 0.3125 -0.3125 C 0.3125 0 0.5625 0 0.71875 0 L 3.296875 0 C 3.453125 0 3.703125 0 3.703125 -0.296875 C 3.703125 -0.609375 3.453125 -0.609375 3.296875 -0.609375 L 2.203125 -0.609375 Z M 2.203125 -1.84375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 1.078125 -3.984375 C 1.0625 -4.28125 0.859375 -4.28125 0.6875 -4.28125 L 0.359375 -4.28125 C 0.21875 -4.28125 -0.046875 -4.28125 -0.046875 -3.984375 C -0.046875 -3.671875 0.171875 -3.671875 0.53125 -3.671875 L 0.53125 -0.609375 C 0.171875 -0.609375 -0.046875 -0.609375 -0.046875 -0.296875 C -0.046875 0 0.234375 0 0.359375 0 L 1.234375 0 C 1.390625 0 1.640625 0 1.640625 -0.296875 C 1.640625 -0.609375 1.4375 -0.609375 1.078125 -0.609375 L 1.078125 -2.375 C 1.078125 -3.265625 1.484375 -3.734375 1.890625 -3.734375 C 2.125 -3.734375 2.265625 -3.5625 2.265625 -2.921875 L 2.265625 -0.609375 C 2.078125 -0.609375 1.828125 -0.609375 1.828125 -0.296875 C 1.828125 0 2.09375 0 2.234375 0 L 2.96875 0 C 3.125 0 3.390625 0 3.390625 -0.296875 C 3.390625 -0.609375 3.171875 -0.609375 2.8125 -0.609375 L 2.8125 -2.375 C 2.8125 -3.265625 3.21875 -3.734375 3.625 -3.734375 C 3.859375 -3.734375 4 -3.5625 4 -2.921875 L 4 -0.609375 C 3.8125 -0.609375 3.5625 -0.609375 3.5625 -0.296875 C 3.5625 0 3.828125 0 3.96875 0 L 4.71875 0 C 4.859375 0 5.125 0 5.125 -0.296875 C 5.125 -0.609375 4.90625 -0.609375 4.546875 -0.609375 L 4.546875 -3 C 4.546875 -3.203125 4.546875 -4.328125 3.671875 -4.328125 C 3.375 -4.328125 2.96875 -4.203125 2.6875 -3.8125 C 2.546875 -4.15625 2.265625 -4.328125 1.9375 -4.328125 C 1.625 -4.328125 1.3125 -4.203125 1.078125 -3.984375 Z M 1.078125 -3.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.28125 2.375 C 3.28125 2.34375 3.28125 2.328125 3.109375 2.15625 C 1.875 0.90625 1.5625 -0.96875 1.5625 -2.484375 C 1.5625 -4.203125 1.9375 -5.9375 3.15625 -7.171875 C 3.28125 -7.296875 3.28125 -7.3125 3.28125 -7.34375 C 3.28125 -7.40625 3.25 -7.4375 3.1875 -7.4375 C 3.078125 -7.4375 2.1875 -6.765625 1.609375 -5.5 C 1.09375 -4.421875 0.984375 -3.3125 0.984375 -2.484375 C 0.984375 -1.703125 1.09375 -0.5 1.640625 0.609375 C 2.234375 1.828125 3.078125 2.484375 3.1875 2.484375 C 3.25 2.484375 3.28125 2.453125 3.28125 2.375 Z M 3.28125 2.375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 4.5625 -3.171875 C 4.5625 -3.96875 4.515625 -4.765625 4.171875 -5.5 C 3.703125 -6.453125 2.890625 -6.609375 2.484375 -6.609375 C 1.890625 -6.609375 1.15625 -6.34375 0.75 -5.421875 C 0.4375 -4.75 0.390625 -3.96875 0.390625 -3.171875 C 0.390625 -2.4375 0.421875 -1.53125 0.828125 -0.78125 C 1.265625 0.015625 1.984375 0.21875 2.46875 0.21875 C 3 0.21875 3.765625 0.015625 4.203125 -0.9375 C 4.515625 -1.625 4.5625 -2.390625 4.5625 -3.171875 Z M 2.46875 0 C 2.078125 0 1.5 -0.25 1.3125 -1.203125 C 1.203125 -1.796875 1.203125 -2.703125 1.203125 -3.296875 C 1.203125 -3.921875 1.203125 -4.578125 1.296875 -5.125 C 1.484375 -6.296875 2.21875 -6.390625 2.46875 -6.390625 C 2.796875 -6.390625 3.453125 -6.21875 3.640625 -5.234375 C 3.734375 -4.671875 3.734375 -3.921875 3.734375 -3.296875 C 3.734375 -2.546875 3.734375 -1.875 3.625 -1.234375 C 3.484375 -0.296875 2.921875 0 2.46875 0 Z M 2.46875 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 2.921875 -6.34375 C 2.921875 -6.59375 2.921875 -6.609375 2.6875 -6.609375 C 2.078125 -5.96875 1.203125 -5.96875 0.890625 -5.96875 L 0.890625 -5.671875 C 1.078125 -5.671875 1.671875 -5.671875 2.1875 -5.921875 L 2.1875 -0.78125 C 2.1875 -0.421875 2.15625 -0.3125 1.265625 -0.3125 L 0.9375 -0.3125 L 0.9375 0 C 1.296875 -0.03125 2.15625 -0.03125 2.546875 -0.03125 C 2.953125 -0.03125 3.8125 -0.03125 4.15625 0 L 4.15625 -0.3125 L 3.84375 -0.3125 C 2.953125 -0.3125 2.921875 -0.421875 2.921875 -0.78125 Z M 2.921875 -6.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 2.875 -2.484375 C 2.875 -3.25 2.765625 -4.453125 2.21875 -5.578125 C 1.625 -6.796875 0.765625 -7.4375 0.671875 -7.4375 C 0.609375 -7.4375 0.5625 -7.40625 0.5625 -7.34375 C 0.5625 -7.3125 0.5625 -7.296875 0.75 -7.109375 C 1.71875 -6.125 2.296875 -4.546875 2.296875 -2.484375 C 2.296875 -0.78125 1.921875 0.96875 0.6875 2.21875 C 0.5625 2.328125 0.5625 2.34375 0.5625 2.375 C 0.5625 2.4375 0.609375 2.484375 0.671875 2.484375 C 0.765625 2.484375 1.65625 1.8125 2.25 0.546875 C 2.75 -0.546875 2.875 -1.640625 2.875 -2.484375 Z M 2.875 -2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 2.015625 -0.015625 C 2.015625 -0.671875 1.765625 -1.046875 1.375 -1.046875 C 1.046875 -1.046875 0.859375 -0.796875 0.859375 -0.53125 C 0.859375 -0.265625 1.046875 0 1.375 0 C 1.5 0 1.625 -0.046875 1.71875 -0.125 C 1.75 -0.15625 1.765625 -0.15625 1.78125 -0.15625 C 1.78125 -0.15625 1.796875 -0.15625 1.796875 -0.015625 C 1.796875 0.71875 1.453125 1.3125 1.125 1.640625 C 1.015625 1.75 1.015625 1.78125 1.015625 1.8125 C 1.015625 1.875 1.0625 1.921875 1.109375 1.921875 C 1.21875 1.921875 2.015625 1.15625 2.015625 -0.015625 Z M 2.015625 -0.015625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 37 0.00390625 L 45 0.00390625 L 45 9.921875 L 37 9.921875 Z M 37 0.00390625 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 46 6 L 48 6 L 48 9.921875 L 46 9.921875 Z M 46 6 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 50 0.00390625 L 58 0.00390625 L 58 9.921875 L 50 9.921875 Z M 50 0.00390625 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="7.443109"/>
+ <use xlink:href="#glyph0-2" x="5.20838" y="7.443109"/>
+ <use xlink:href="#glyph0-3" x="10.416759" y="7.443109"/>
+ <use xlink:href="#glyph0-4" x="15.625139" y="7.443109"/>
+ <use xlink:href="#glyph0-5" x="20.833519" y="7.443109"/>
+ <use xlink:href="#glyph0-6" x="26.041899" y="7.443109"/>
+ <use xlink:href="#glyph0-7" x="31.250278" y="7.443109"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="36.458105" y="7.443109"/>
+ <use xlink:href="#glyph1-2" x="40.316275" y="7.443109"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="45.27688" y="7.443109"/>
+</g>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="49.686268" y="7.443109"/>
+ <use xlink:href="#glyph1-4" x="54.646629" y="7.443109"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig3.svg b/doc/figs/tex/fig3.svg
new file mode 100644
index 00000000000..74395b91b9f
--- /dev/null
+++ b/doc/figs/tex/fig3.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="7.958pt" height="6.808pt" viewBox="0 0 7.958 6.808" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.703125 -6.015625 L 6.3125 -6.015625 C 7.59375 -6.015625 8.078125 -6.75 8.078125 -6.875 C 8.078125 -6.921875 8.046875 -6.953125 7.984375 -6.953125 C 7.890625 -6.953125 7.640625 -6.84375 7.390625 -6.671875 C 7.3125 -6.609375 7.296875 -6.609375 7.109375 -6.609375 L 2.875 -6.609375 C 1.671875 -6.609375 0.328125 -5.578125 0.328125 -4.78125 C 0.328125 -4.734375 0.328125 -4.671875 0.40625 -4.671875 C 0.640625 -4.671875 1.25 -4.984375 1.265625 -5.21875 C 1.28125 -5.390625 1.296875 -5.5625 1.484375 -5.828125 C 1.59375 -5.9375 1.671875 -6.015625 2.09375 -6.015625 L 4.015625 -6.015625 C 3.859375 -5.90625 3.8125 -5.765625 3.796875 -5.671875 L 2.6875 -1.28125 C 2.578125 -0.796875 2.375 -0.1875 2.09375 0.4375 C 2.03125 0.546875 2.03125 0.578125 2.03125 0.59375 C 2.03125 0.65625 2.078125 0.65625 2.125 0.65625 C 2.3125 0.65625 2.796875 0.390625 2.9375 0.1875 C 3 0.09375 3.421875 -0.890625 3.625 -1.6875 Z M 4.703125 -6.015625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.0898438 0 L 7.828125 0 L 7.828125 6.621094 L 0.0898438 6.621094 Z M 0.0898438 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.0887143" y="6.621266"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig30.svg b/doc/figs/tex/fig30.svg
new file mode 100644
index 00000000000..fae269e3c3d
--- /dev/null
+++ b/doc/figs/tex/fig30.svg
@@ -0,0 +1,38 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="17.758pt" height="9.963pt" viewBox="0 0 17.758 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 5.3125 -6 C 5.390625 -6.3125 5.421875 -6.40625 5.953125 -6.40625 C 6.109375 -6.40625 6.21875 -6.40625 6.21875 -6.59375 C 6.21875 -6.6875 6.15625 -6.71875 6.078125 -6.71875 C 5.84375 -6.71875 5.234375 -6.6875 5 -6.6875 C 4.671875 -6.6875 3.875 -6.71875 3.546875 -6.71875 C 3.453125 -6.71875 3.34375 -6.71875 3.34375 -6.515625 C 3.34375 -6.40625 3.421875 -6.40625 3.671875 -6.40625 C 3.90625 -6.40625 4 -6.40625 4.25 -6.390625 C 4.484375 -6.359375 4.546875 -6.328125 4.546875 -6.1875 C 4.546875 -6.125 4.53125 -6.0625 4.515625 -5.984375 L 3.375 -1.46875 C 3.140625 -0.515625 2.484375 0 1.96875 0 C 1.703125 0 1.1875 -0.09375 1.03125 -0.609375 C 1.0625 -0.59375 1.125 -0.59375 1.15625 -0.59375 C 1.53125 -0.59375 1.78125 -0.9375 1.78125 -1.234375 C 1.78125 -1.546875 1.515625 -1.640625 1.359375 -1.640625 C 1.171875 -1.640625 0.703125 -1.515625 0.703125 -0.859375 C 0.703125 -0.25 1.21875 0.21875 2 0.21875 C 2.90625 0.21875 3.921875 -0.4375 4.171875 -1.40625 Z M 5.3125 -6 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.3125 -7 C 4.359375 -7.125 4.359375 -7.171875 4.359375 -7.171875 C 4.359375 -7.28125 4.28125 -7.375 4.171875 -7.375 C 4.09375 -7.375 4.03125 -7.34375 4 -7.28125 L 0.59375 2.078125 C 0.546875 2.21875 0.546875 2.25 0.546875 2.265625 C 0.546875 2.375 0.625 2.453125 0.734375 2.453125 C 0.859375 2.453125 0.890625 2.390625 0.953125 2.21875 Z M 4.3125 -7 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 4.734375 -6.5625 C 4.75 -6.609375 4.765625 -6.65625 4.765625 -6.71875 C 4.765625 -6.8125 4.703125 -6.828125 4.65625 -6.828125 C 4.546875 -6.828125 4.546875 -6.796875 4.5 -6.625 L 2.875 -0.125 C 2.125 -0.21875 1.75 -0.578125 1.75 -1.234375 C 1.75 -1.421875 1.75 -1.6875 2.28125 -3.0625 C 2.3125 -3.171875 2.390625 -3.34375 2.390625 -3.53125 C 2.390625 -3.984375 2.078125 -4.34375 1.578125 -4.34375 C 0.65625 -4.34375 0.28125 -2.921875 0.28125 -2.828125 C 0.28125 -2.734375 0.390625 -2.734375 0.40625 -2.734375 C 0.5 -2.734375 0.515625 -2.75 0.5625 -2.90625 C 0.828125 -3.84375 1.21875 -4.125 1.546875 -4.125 C 1.625 -4.125 1.796875 -4.125 1.796875 -3.8125 C 1.796875 -3.5625 1.703125 -3.3125 1.578125 -2.96875 C 1.09375 -1.734375 1.09375 -1.46875 1.09375 -1.3125 C 1.09375 -0.375 1.875 0.03125 2.8125 0.09375 C 2.734375 0.4375 2.734375 0.46875 2.59375 0.984375 C 2.5625 1.09375 2.375 1.890625 2.375 1.921875 C 2.375 1.921875 2.375 2.015625 2.484375 2.015625 C 2.5 2.015625 2.5625 2.015625 2.578125 1.96875 C 2.609375 1.953125 2.65625 1.703125 2.6875 1.578125 L 3.0625 0.109375 C 3.4375 0.109375 4.296875 0.109375 5.21875 -0.9375 C 5.625 -1.390625 5.828125 -1.828125 5.9375 -2.125 C 6.03125 -2.375 6.234375 -3.21875 6.234375 -3.65625 C 6.234375 -4.203125 5.96875 -4.34375 5.8125 -4.34375 C 5.5625 -4.34375 5.3125 -4.09375 5.3125 -3.875 C 5.3125 -3.75 5.375 -3.6875 5.46875 -3.609375 C 5.578125 -3.5 5.8125 -3.25 5.8125 -2.765625 C 5.8125 -2.140625 5.3125 -1.34375 4.96875 -0.984375 C 4.09375 -0.109375 3.46875 -0.109375 3.109375 -0.109375 Z M 4.734375 -6.5625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.046875 L 7 0.046875 L 7 8 L 0 8 Z M 0 0.046875 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 6 0.046875 L 17.519531 0.046875 L 17.519531 9.878906 L 6 9.878906 Z M 6 0.046875 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="7.420265"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="5.852966" y="7.420265"/>
+ <use xlink:href="#glyph0-3" x="10.767295" y="7.420265"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig31.svg b/doc/figs/tex/fig31.svg
new file mode 100644
index 00000000000..1bc66dad39a
--- /dev/null
+++ b/doc/figs/tex/fig31.svg
@@ -0,0 +1,36 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="14.432pt" height="8.11pt" viewBox="0 0 14.432 8.11" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.640625 -5.75 C 2.640625 -5.96875 2.640625 -5.984375 2.4375 -5.984375 C 1.875 -5.40625 1.09375 -5.40625 0.796875 -5.40625 L 0.796875 -5.125 C 0.984375 -5.125 1.515625 -5.125 1.96875 -5.359375 L 1.96875 -0.703125 C 1.96875 -0.390625 1.953125 -0.28125 1.140625 -0.28125 L 0.859375 -0.28125 L 0.859375 0 C 1.171875 -0.03125 1.953125 -0.03125 2.3125 -0.03125 C 2.671875 -0.03125 3.453125 -0.03125 3.765625 0 L 3.765625 -0.28125 L 3.484375 -0.28125 C 2.671875 -0.28125 2.640625 -0.375 2.640625 -0.703125 Z M 2.640625 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.125 -2.875 C 4.125 -3.59375 4.09375 -4.3125 3.765625 -4.984375 C 3.359375 -5.84375 2.625 -5.984375 2.25 -5.984375 C 1.703125 -5.984375 1.046875 -5.75 0.6875 -4.921875 C 0.390625 -4.296875 0.34375 -3.59375 0.34375 -2.875 C 0.34375 -2.203125 0.390625 -1.390625 0.75 -0.703125 C 1.140625 0.015625 1.796875 0.203125 2.234375 0.203125 C 2.71875 0.203125 3.40625 0.015625 3.796875 -0.84375 C 4.09375 -1.46875 4.125 -2.171875 4.125 -2.875 Z M 2.234375 0 C 1.890625 0 1.359375 -0.21875 1.1875 -1.09375 C 1.09375 -1.625 1.09375 -2.453125 1.09375 -2.984375 C 1.09375 -3.5625 1.09375 -4.15625 1.171875 -4.640625 C 1.34375 -5.703125 2.015625 -5.78125 2.234375 -5.78125 C 2.53125 -5.78125 3.125 -5.625 3.296875 -4.734375 C 3.390625 -4.234375 3.390625 -3.546875 3.390625 -2.984375 C 3.390625 -2.3125 3.390625 -1.703125 3.28125 -1.125 C 3.15625 -0.265625 2.640625 0 2.234375 0 Z M 2.234375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 0.9375 -2.046875 C 0.9375 -2.5625 0.984375 -3.03125 1.21875 -3.421875 C 1.4375 -3.75 1.78125 -3.984375 2.171875 -3.984375 C 2.375 -3.984375 2.625 -3.9375 2.75 -3.765625 C 2.59375 -3.75 2.453125 -3.65625 2.453125 -3.46875 C 2.453125 -3.3125 2.5625 -3.171875 2.75 -3.171875 C 2.9375 -3.171875 3.046875 -3.296875 3.046875 -3.484375 C 3.046875 -3.84375 2.78125 -4.171875 2.171875 -4.171875 C 1.265625 -4.171875 0.34375 -3.34375 0.34375 -1.984375 C 0.34375 -0.359375 1.109375 0.125 1.796875 0.125 C 2.5625 0.125 3.234375 -0.453125 3.234375 -1.28125 C 3.234375 -2.078125 2.59375 -2.671875 1.859375 -2.671875 C 1.359375 -2.671875 1.078125 -2.34375 0.9375 -2.046875 Z M 1.796875 -0.078125 C 1.484375 -0.078125 1.234375 -0.25 1.109375 -0.53125 C 1.015625 -0.71875 0.96875 -1.03125 0.96875 -1.40625 C 0.96875 -2.015625 1.328125 -2.5 1.828125 -2.5 C 2.109375 -2.5 2.3125 -2.375 2.46875 -2.140625 C 2.625 -1.90625 2.625 -1.640625 2.625 -1.28125 C 2.625 -0.921875 2.625 -0.65625 2.453125 -0.421875 C 2.3125 -0.1875 2.109375 -0.078125 1.796875 -0.078125 Z M 1.796875 -0.078125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 1 L 10 1 L 10 7.308594 L 1 7.308594 Z M 1 1 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.457667" y="7.308011"/>
+ <use xlink:href="#glyph0-2" x="4.946371" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="9.435437" y="4.050494"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig32.svg b/doc/figs/tex/fig32.svg
new file mode 100644
index 00000000000..e7d8901dec9
--- /dev/null
+++ b/doc/figs/tex/fig32.svg
@@ -0,0 +1,204 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="149.488pt" height="10.931pt" viewBox="0 0 149.488 10.931" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.671875 -6.890625 C 3.609375 -7.078125 3.546875 -7.09375 3.4375 -7.09375 C 3.28125 -7.09375 3.265625 -7.046875 3.203125 -6.890625 L 1.3125 -0.984375 C 1.203125 -0.6875 1.015625 -0.3125 0.3125 -0.3125 L 0.3125 0 C 0.640625 -0.015625 1.15625 -0.03125 1.234375 -0.03125 C 1.53125 -0.03125 2.046875 -0.015625 2.359375 0 L 2.359375 -0.3125 C 1.828125 -0.3125 1.59375 -0.578125 1.59375 -0.828125 C 1.59375 -0.875 1.59375 -0.90625 1.640625 -1.046875 L 3.125 -5.65625 L 4.703125 -0.78125 C 4.75 -0.640625 4.75 -0.625 4.75 -0.609375 C 4.75 -0.3125 4.15625 -0.3125 3.90625 -0.3125 L 3.90625 0 C 4.25 -0.03125 4.953125 -0.03125 5.328125 -0.03125 C 5.71875 -0.03125 6.15625 -0.015625 6.546875 0 L 6.546875 -0.3125 C 5.796875 -0.3125 5.765625 -0.359375 5.640625 -0.734375 Z M 3.671875 -6.890625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 2.53125 2.484375 L 2.53125 2.078125 L 1.5625 2.078125 L 1.5625 -7.03125 L 2.53125 -7.03125 L 2.53125 -7.4375 L 1.171875 -7.4375 L 1.171875 2.484375 Z M 2.53125 2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 1.578125 -7.4375 L 0.21875 -7.4375 L 0.21875 -7.03125 L 1.171875 -7.03125 L 1.171875 2.078125 L 0.21875 2.078125 L 0.21875 2.484375 L 1.578125 2.484375 Z M 1.578125 -7.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 3.28125 2.375 C 3.28125 2.34375 3.28125 2.328125 3.109375 2.15625 C 1.875 0.90625 1.5625 -0.953125 1.5625 -2.484375 C 1.5625 -4.203125 1.9375 -5.921875 3.15625 -7.15625 C 3.28125 -7.28125 3.28125 -7.296875 3.28125 -7.328125 C 3.28125 -7.40625 3.234375 -7.4375 3.1875 -7.4375 C 3.078125 -7.4375 2.1875 -6.75 1.609375 -5.5 C 1.09375 -4.40625 0.984375 -3.3125 0.984375 -2.484375 C 0.984375 -1.703125 1.09375 -0.5 1.640625 0.609375 C 2.234375 1.828125 3.078125 2.484375 3.1875 2.484375 C 3.234375 2.484375 3.28125 2.453125 3.28125 2.375 Z M 3.28125 2.375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 2.90625 -6.34375 C 2.90625 -6.578125 2.90625 -6.59375 2.6875 -6.59375 C 2.078125 -5.96875 1.203125 -5.96875 0.875 -5.96875 L 0.875 -5.65625 C 1.078125 -5.65625 1.671875 -5.65625 2.171875 -5.90625 L 2.171875 -0.78125 C 2.171875 -0.421875 2.15625 -0.3125 1.265625 -0.3125 L 0.9375 -0.3125 L 0.9375 0 C 1.28125 -0.03125 2.15625 -0.03125 2.546875 -0.03125 C 2.9375 -0.03125 3.796875 -0.03125 4.15625 0 L 4.15625 -0.3125 L 3.828125 -0.3125 C 2.9375 -0.3125 2.90625 -0.421875 2.90625 -0.78125 Z M 2.90625 -6.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 2.90625 -1.640625 L 2.90625 -0.765625 C 2.90625 -0.421875 2.890625 -0.3125 2.15625 -0.3125 L 1.953125 -0.3125 L 1.953125 0 C 2.359375 -0.03125 2.875 -0.03125 3.28125 -0.03125 C 3.703125 -0.03125 4.234375 -0.03125 4.640625 0 L 4.640625 -0.3125 L 4.421875 -0.3125 C 3.6875 -0.3125 3.671875 -0.421875 3.671875 -0.765625 L 3.671875 -1.640625 L 4.671875 -1.640625 L 4.671875 -1.9375 L 3.671875 -1.9375 L 3.671875 -6.453125 C 3.671875 -6.640625 3.671875 -6.703125 3.515625 -6.703125 C 3.421875 -6.703125 3.390625 -6.703125 3.3125 -6.59375 L 0.28125 -1.9375 L 0.28125 -1.640625 Z M 2.96875 -1.9375 L 0.5625 -1.9375 L 2.96875 -5.640625 Z M 2.96875 -1.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 4.5625 -3.171875 C 4.5625 -3.96875 4.5 -4.75 4.15625 -5.484375 C 3.703125 -6.4375 2.890625 -6.59375 2.484375 -6.59375 C 1.875 -6.59375 1.15625 -6.34375 0.75 -5.421875 C 0.4375 -4.734375 0.390625 -3.96875 0.390625 -3.171875 C 0.390625 -2.421875 0.421875 -1.53125 0.828125 -0.78125 C 1.265625 0.015625 1.984375 0.21875 2.46875 0.21875 C 3 0.21875 3.75 0.015625 4.1875 -0.9375 C 4.5 -1.609375 4.5625 -2.390625 4.5625 -3.171875 Z M 2.46875 0 C 2.078125 0 1.5 -0.25 1.3125 -1.203125 C 1.203125 -1.796875 1.203125 -2.703125 1.203125 -3.28125 C 1.203125 -3.921875 1.203125 -4.578125 1.28125 -5.109375 C 1.46875 -6.296875 2.21875 -6.375 2.46875 -6.375 C 2.796875 -6.375 3.453125 -6.203125 3.640625 -5.21875 C 3.734375 -4.671875 3.734375 -3.90625 3.734375 -3.28125 C 3.734375 -2.546875 3.734375 -1.875 3.625 -1.234375 C 3.484375 -0.296875 2.90625 0 2.46875 0 Z M 2.46875 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-8">
+<path style="stroke:none;" d="M 4.453125 -1.984375 C 4.453125 -3.171875 3.640625 -4.15625 2.5625 -4.15625 C 2.09375 -4.15625 1.671875 -4 1.3125 -3.65625 L 1.3125 -5.59375 C 1.5 -5.53125 1.828125 -5.453125 2.15625 -5.453125 C 3.375 -5.453125 4.0625 -6.359375 4.0625 -6.484375 C 4.0625 -6.546875 4.03125 -6.59375 3.96875 -6.59375 C 3.953125 -6.59375 3.9375 -6.59375 3.890625 -6.5625 C 3.6875 -6.484375 3.203125 -6.28125 2.53125 -6.28125 C 2.140625 -6.28125 1.6875 -6.34375 1.21875 -6.5625 C 1.140625 -6.59375 1.125 -6.59375 1.09375 -6.59375 C 1 -6.59375 1 -6.515625 1 -6.34375 L 1 -3.421875 C 1 -3.234375 1 -3.15625 1.140625 -3.15625 C 1.203125 -3.15625 1.234375 -3.1875 1.265625 -3.25 C 1.375 -3.40625 1.75 -3.9375 2.546875 -3.9375 C 3.0625 -3.9375 3.3125 -3.484375 3.390625 -3.3125 C 3.546875 -2.9375 3.5625 -2.5625 3.5625 -2.0625 C 3.5625 -1.71875 3.5625 -1.125 3.328125 -0.703125 C 3.09375 -0.3125 2.71875 -0.0625 2.265625 -0.0625 C 1.546875 -0.0625 0.984375 -0.578125 0.8125 -1.171875 C 0.84375 -1.15625 0.875 -1.15625 0.984375 -1.15625 C 1.3125 -1.15625 1.46875 -1.390625 1.46875 -1.640625 C 1.46875 -1.875 1.3125 -2.125 0.984375 -2.125 C 0.84375 -2.125 0.5 -2.046875 0.5 -1.59375 C 0.5 -0.75 1.171875 0.21875 2.28125 0.21875 C 3.4375 0.21875 4.453125 -0.734375 4.453125 -1.984375 Z M 4.453125 -1.984375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-9">
+<path style="stroke:none;" d="M 2.859375 -2.484375 C 2.859375 -3.25 2.75 -4.453125 2.203125 -5.5625 C 1.609375 -6.78125 0.765625 -7.4375 0.65625 -7.4375 C 0.609375 -7.4375 0.5625 -7.390625 0.5625 -7.328125 C 0.5625 -7.296875 0.5625 -7.28125 0.75 -7.109375 C 1.71875 -6.125 2.28125 -4.546875 2.28125 -2.484375 C 2.28125 -0.78125 1.921875 0.953125 0.6875 2.203125 C 0.5625 2.328125 0.5625 2.34375 0.5625 2.375 C 0.5625 2.4375 0.609375 2.484375 0.65625 2.484375 C 0.765625 2.484375 1.65625 1.796875 2.234375 0.546875 C 2.75 -0.546875 2.859375 -1.640625 2.859375 -2.484375 Z M 2.859375 -2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.578125 -2.21875 C 3.578125 -2.96875 3.484375 -3.53125 3.171875 -4.015625 C 2.953125 -4.328125 2.53125 -4.609375 1.96875 -4.609375 C 0.359375 -4.609375 0.359375 -2.71875 0.359375 -2.21875 C 0.359375 -1.71875 0.359375 0.140625 1.96875 0.140625 C 3.578125 0.140625 3.578125 -1.71875 3.578125 -2.21875 Z M 1.96875 -0.0625 C 1.65625 -0.0625 1.234375 -0.25 1.09375 -0.8125 C 0.984375 -1.21875 0.984375 -1.796875 0.984375 -2.296875 C 0.984375 -2.8125 0.984375 -3.34375 1.09375 -3.71875 C 1.234375 -4.265625 1.6875 -4.40625 1.96875 -4.40625 C 2.34375 -4.40625 2.703125 -4.1875 2.828125 -3.78125 C 2.9375 -3.40625 2.953125 -2.90625 2.953125 -2.296875 C 2.953125 -1.796875 2.953125 -1.28125 2.859375 -0.84375 C 2.71875 -0.203125 2.25 -0.0625 1.96875 -0.0625 Z M 1.96875 -0.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.21875 -1.5625 L 5.328125 -1.5625 C 5.421875 -1.5625 5.59375 -1.5625 5.59375 -1.734375 C 5.59375 -1.90625 5.4375 -1.90625 5.328125 -1.90625 L 3.21875 -1.90625 L 3.21875 -4.03125 C 3.21875 -4.125 3.21875 -4.296875 3.046875 -4.296875 C 2.875 -4.296875 2.875 -4.140625 2.875 -4.03125 L 2.875 -1.90625 L 0.75 -1.90625 C 0.65625 -1.90625 0.484375 -1.90625 0.484375 -1.734375 C 0.484375 -1.5625 0.640625 -1.5625 0.75 -1.5625 L 2.875 -1.5625 L 2.875 0.5625 C 2.875 0.65625 2.875 0.8125 3.03125 0.8125 C 3.21875 0.8125 3.21875 0.65625 3.21875 0.5625 Z M 3.21875 -1.5625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 1.828125 -4.609375 C 1.84375 -4.625 1.859375 -4.703125 1.859375 -4.71875 C 1.859375 -4.75 1.828125 -4.8125 1.75 -4.8125 C 1.609375 -4.8125 1.03125 -4.765625 0.859375 -4.75 C 0.8125 -4.734375 0.703125 -4.734375 0.703125 -4.578125 C 0.703125 -4.484375 0.8125 -4.484375 0.890625 -4.484375 C 1.21875 -4.484375 1.21875 -4.4375 1.21875 -4.390625 C 1.21875 -4.34375 1.15625 -4.0625 1.109375 -3.90625 L 0.953125 -3.265625 C 0.890625 -3.03125 0.5 -1.5 0.5 -1.421875 C 0.453125 -1.25 0.453125 -1.15625 0.453125 -1.078125 C 0.453125 -0.375 0.90625 0.0625 1.484375 0.0625 C 2.34375 0.0625 3.265625 -0.875 3.265625 -1.90625 C 3.265625 -2.71875 2.703125 -3.0625 2.234375 -3.0625 C 1.859375 -3.0625 1.5625 -2.859375 1.359375 -2.671875 Z M 1.484375 -0.125 C 1.140625 -0.125 0.953125 -0.421875 0.953125 -0.828125 C 0.953125 -1.09375 1.015625 -1.328125 1.203125 -2.109375 C 1.25 -2.234375 1.25 -2.25 1.375 -2.40625 C 1.640625 -2.71875 1.953125 -2.859375 2.203125 -2.859375 C 2.484375 -2.859375 2.71875 -2.65625 2.71875 -2.1875 C 2.71875 -1.90625 2.5625 -1.203125 2.359375 -0.796875 C 2.1875 -0.453125 1.84375 -0.125 1.484375 -0.125 Z M 1.484375 -0.125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 8.265625 -2.28125 C 7.71875 -1.859375 7.453125 -1.453125 7.375 -1.328125 C 6.921875 -0.640625 6.84375 -0.015625 6.84375 -0.015625 C 6.84375 0.109375 6.96875 0.109375 7.046875 0.109375 C 7.21875 0.109375 7.21875 0.09375 7.265625 -0.09375 C 7.484375 -1.0625 8.078125 -1.890625 9.1875 -2.34375 C 9.3125 -2.390625 9.34375 -2.40625 9.34375 -2.484375 C 9.34375 -2.546875 9.28125 -2.578125 9.265625 -2.578125 C 8.828125 -2.75 7.625 -3.25 7.25 -4.90625 C 7.21875 -5.03125 7.21875 -5.0625 7.046875 -5.0625 C 6.96875 -5.0625 6.84375 -5.0625 6.84375 -4.9375 C 6.84375 -4.921875 6.9375 -4.296875 7.34375 -3.640625 C 7.546875 -3.34375 7.828125 -2.984375 8.265625 -2.671875 L 0.90625 -2.671875 C 0.71875 -2.671875 0.546875 -2.671875 0.546875 -2.484375 C 0.546875 -2.28125 0.71875 -2.28125 0.90625 -2.28125 Z M 8.265625 -2.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 5.359375 -6.046875 C 5.4375 -6.375 5.453125 -6.453125 6 -6.453125 C 6.15625 -6.453125 6.265625 -6.453125 6.265625 -6.640625 C 6.265625 -6.734375 6.21875 -6.765625 6.125 -6.765625 C 5.890625 -6.765625 5.28125 -6.734375 5.03125 -6.734375 C 4.703125 -6.734375 3.90625 -6.765625 3.578125 -6.765625 C 3.484375 -6.765625 3.375 -6.765625 3.375 -6.5625 C 3.375 -6.453125 3.453125 -6.453125 3.703125 -6.453125 C 3.9375 -6.453125 4.03125 -6.453125 4.28125 -6.4375 C 4.515625 -6.40625 4.59375 -6.375 4.59375 -6.234375 C 4.59375 -6.1875 4.5625 -6.109375 4.546875 -6.03125 L 3.40625 -1.484375 C 3.171875 -0.53125 2.5 0 1.984375 0 C 1.71875 0 1.203125 -0.09375 1.046875 -0.609375 C 1.0625 -0.609375 1.140625 -0.609375 1.15625 -0.609375 C 1.546875 -0.609375 1.796875 -0.9375 1.796875 -1.234375 C 1.796875 -1.5625 1.53125 -1.65625 1.359375 -1.65625 C 1.1875 -1.65625 0.703125 -1.53125 0.703125 -0.859375 C 0.703125 -0.25 1.234375 0.21875 2.015625 0.21875 C 2.921875 0.21875 3.953125 -0.4375 4.203125 -1.421875 Z M 5.359375 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 4.34375 -7.046875 C 4.390625 -7.1875 4.390625 -7.21875 4.390625 -7.234375 C 4.390625 -7.34375 4.3125 -7.4375 4.203125 -7.4375 C 4.125 -7.4375 4.0625 -7.40625 4.03125 -7.34375 L 0.59375 2.09375 C 0.546875 2.234375 0.546875 2.265625 0.546875 2.28125 C 0.546875 2.390625 0.640625 2.484375 0.75 2.484375 C 0.875 2.484375 0.90625 2.40625 0.953125 2.234375 Z M 4.34375 -7.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-3">
+<path style="stroke:none;" d="M 4.78125 -6.625 C 4.78125 -6.65625 4.796875 -6.71875 4.796875 -6.765625 C 4.796875 -6.859375 4.734375 -6.875 4.6875 -6.875 C 4.59375 -6.875 4.578125 -6.859375 4.53125 -6.671875 L 2.890625 -0.125 C 2.140625 -0.21875 1.765625 -0.578125 1.765625 -1.234375 C 1.765625 -1.4375 1.765625 -1.6875 2.296875 -3.078125 C 2.34375 -3.203125 2.40625 -3.375 2.40625 -3.5625 C 2.40625 -4.015625 2.09375 -4.375 1.59375 -4.375 C 0.65625 -4.375 0.28125 -2.9375 0.28125 -2.859375 C 0.28125 -2.75 0.390625 -2.75 0.40625 -2.75 C 0.5 -2.75 0.515625 -2.78125 0.5625 -2.9375 C 0.828125 -3.875 1.234375 -4.15625 1.5625 -4.15625 C 1.640625 -4.15625 1.8125 -4.15625 1.8125 -3.84375 C 1.8125 -3.59375 1.71875 -3.34375 1.578125 -2.984375 C 1.109375 -1.75 1.109375 -1.484375 1.109375 -1.3125 C 1.109375 -0.375 1.875 0.03125 2.828125 0.09375 C 2.75 0.453125 2.75 0.46875 2.609375 0.984375 C 2.578125 1.09375 2.390625 1.90625 2.390625 1.9375 C 2.390625 1.9375 2.390625 2.03125 2.5 2.03125 C 2.53125 2.03125 2.578125 2.03125 2.59375 1.984375 C 2.625 1.96875 2.6875 1.71875 2.71875 1.578125 L 3.09375 0.109375 C 3.453125 0.109375 4.328125 0.109375 5.265625 -0.953125 C 5.671875 -1.40625 5.875 -1.84375 5.984375 -2.140625 C 6.078125 -2.390625 6.296875 -3.25 6.296875 -3.6875 C 6.296875 -4.234375 6.015625 -4.375 5.859375 -4.375 C 5.609375 -4.375 5.359375 -4.125 5.359375 -3.90625 C 5.359375 -3.78125 5.421875 -3.71875 5.515625 -3.640625 C 5.609375 -3.53125 5.859375 -3.265625 5.859375 -2.796875 C 5.859375 -2.15625 5.34375 -1.34375 5 -0.984375 C 4.125 -0.109375 3.5 -0.109375 3.140625 -0.109375 Z M 4.78125 -6.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-4">
+<path style="stroke:none;" d="M 2.28125 -3.484375 C 2.34375 -3.6875 2.4375 -4.0625 2.4375 -4.109375 C 2.4375 -4.28125 2.3125 -4.375 2.15625 -4.375 C 2.125 -4.375 1.84375 -4.375 1.75 -4.015625 L 0.328125 1.71875 C 0.296875 1.828125 0.296875 1.859375 0.296875 1.875 C 0.296875 2.015625 0.40625 2.140625 0.578125 2.140625 C 0.78125 2.140625 0.90625 1.96875 0.921875 1.9375 C 0.953125 1.84375 1.09375 1.328125 1.46875 -0.203125 C 1.78125 0.0625 2.234375 0.109375 2.421875 0.109375 C 3.125 0.109375 3.5 -0.34375 3.75 -0.609375 C 3.828125 -0.171875 4.203125 0.109375 4.640625 0.109375 C 4.984375 0.109375 5.203125 -0.125 5.375 -0.4375 C 5.53125 -0.796875 5.671875 -1.390625 5.671875 -1.421875 C 5.671875 -1.515625 5.578125 -1.515625 5.546875 -1.515625 C 5.453125 -1.515625 5.4375 -1.46875 5.40625 -1.34375 C 5.234375 -0.6875 5.0625 -0.109375 4.65625 -0.109375 C 4.390625 -0.109375 4.359375 -0.359375 4.359375 -0.5625 C 4.359375 -0.78125 4.484375 -1.25 4.5625 -1.59375 L 4.828125 -2.671875 C 4.859375 -2.8125 4.96875 -3.1875 5 -3.34375 C 5.046875 -3.5625 5.15625 -3.9375 5.15625 -4 C 5.15625 -4.1875 5.015625 -4.265625 4.859375 -4.265625 C 4.8125 -4.265625 4.5625 -4.265625 4.484375 -3.921875 L 4.015625 -2.078125 C 3.890625 -1.578125 3.78125 -1.15625 3.75 -1.0625 C 3.75 -1.015625 3.265625 -0.109375 2.46875 -0.109375 C 1.96875 -0.109375 1.734375 -0.4375 1.734375 -0.96875 C 1.734375 -1.265625 1.796875 -1.53125 1.875 -1.8125 Z M 2.28125 -3.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-5">
+<path style="stroke:none;" d="M 0.453125 1.203125 C 0.359375 1.546875 0.34375 1.609375 -0.09375 1.609375 C -0.203125 1.609375 -0.3125 1.609375 -0.3125 1.796875 C -0.3125 1.875 -0.265625 1.921875 -0.1875 1.921875 C 0.078125 1.921875 0.359375 1.890625 0.640625 1.890625 C 0.96875 1.890625 1.3125 1.921875 1.625 1.921875 C 1.671875 1.921875 1.796875 1.921875 1.796875 1.71875 C 1.796875 1.609375 1.703125 1.609375 1.5625 1.609375 C 1.0625 1.609375 1.0625 1.546875 1.0625 1.453125 C 1.0625 1.34375 1.484375 -0.28125 1.5625 -0.53125 C 1.6875 -0.234375 1.96875 0.109375 2.46875 0.109375 C 3.609375 0.109375 4.859375 -1.34375 4.859375 -2.796875 C 4.859375 -3.71875 4.296875 -4.375 3.53125 -4.375 C 3.046875 -4.375 2.5625 -4.015625 2.234375 -3.640625 C 2.140625 -4.171875 1.71875 -4.375 1.34375 -4.375 C 0.890625 -4.375 0.703125 -4 0.609375 -3.8125 C 0.4375 -3.484375 0.3125 -2.875 0.3125 -2.859375 C 0.3125 -2.75 0.40625 -2.75 0.421875 -2.75 C 0.53125 -2.75 0.53125 -2.765625 0.59375 -2.984375 C 0.765625 -3.6875 0.953125 -4.15625 1.3125 -4.15625 C 1.484375 -4.15625 1.625 -4.078125 1.625 -3.703125 C 1.625 -3.484375 1.59375 -3.375 1.5625 -3.203125 Z M 2.1875 -3.09375 C 2.265625 -3.359375 2.53125 -3.640625 2.703125 -3.78125 C 3.046875 -4.09375 3.34375 -4.15625 3.5 -4.15625 C 3.90625 -4.15625 4.140625 -3.8125 4.140625 -3.234375 C 4.140625 -2.640625 3.8125 -1.5 3.640625 -1.125 C 3.296875 -0.4375 2.828125 -0.109375 2.453125 -0.109375 C 1.796875 -0.109375 1.671875 -0.9375 1.671875 -0.984375 C 1.671875 -1.015625 1.671875 -1.03125 1.703125 -1.15625 Z M 2.1875 -3.09375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-6">
+<path style="stroke:none;" d="M 2.625 -3.6875 L 3.75 -3.6875 C 3.421875 -2.234375 3.328125 -1.796875 3.328125 -1.140625 C 3.328125 -0.984375 3.328125 -0.71875 3.40625 -0.390625 C 3.5 0.046875 3.609375 0.109375 3.765625 0.109375 C 3.96875 0.109375 4.171875 -0.0625 4.171875 -0.265625 C 4.171875 -0.328125 4.171875 -0.34375 4.109375 -0.484375 C 3.828125 -1.203125 3.828125 -1.84375 3.828125 -2.125 C 3.828125 -2.640625 3.890625 -3.1875 4 -3.6875 L 5.125 -3.6875 C 5.265625 -3.6875 5.609375 -3.6875 5.609375 -4.03125 C 5.609375 -4.265625 5.40625 -4.265625 5.21875 -4.265625 L 1.90625 -4.265625 C 1.6875 -4.265625 1.3125 -4.265625 0.875 -3.796875 C 0.53125 -3.421875 0.265625 -2.96875 0.265625 -2.90625 C 0.265625 -2.90625 0.265625 -2.8125 0.390625 -2.8125 C 0.46875 -2.8125 0.484375 -2.859375 0.546875 -2.9375 C 1.03125 -3.6875 1.609375 -3.6875 1.796875 -3.6875 L 2.375 -3.6875 C 2.046875 -2.5 1.515625 -1.296875 1.09375 -0.390625 C 1.015625 -0.25 1.015625 -0.234375 1.015625 -0.15625 C 1.015625 0.03125 1.171875 0.109375 1.3125 0.109375 C 1.609375 0.109375 1.6875 -0.171875 1.796875 -0.53125 C 1.9375 -0.984375 1.9375 -1.015625 2.078125 -1.5 Z M 2.625 -3.6875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 5.15625 -1.5625 C 5.265625 -1.5625 5.4375 -1.5625 5.4375 -1.734375 C 5.4375 -1.90625 5.28125 -1.90625 5.15625 -1.90625 L 1.03125 -1.90625 C 0.921875 -1.90625 0.75 -1.90625 0.75 -1.734375 C 0.75 -1.5625 0.90625 -1.5625 1.03125 -1.5625 Z M 5.15625 -1.5625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.214844 0 L 7 0 L 7 9 L 0.214844 9 Z M 0.214844 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 7 6 L 11 6 L 11 10.863281 L 7 10.863281 Z M 7 6 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 33 0 L 45 0 L 45 10.863281 L 33 10.863281 Z M 33 0 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 47 0 L 49 0 L 49 10.863281 L 47 10.863281 Z M 47 0 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 49 3 L 55 3 L 55 10.863281 L 49 10.863281 Z M 49 3 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 61 3 L 68 3 L 68 10.863281 L 61 10.863281 Z M 61 3 "/>
+</clipPath>
+<clipPath id="clip7">
+ <path d="M 74 0 L 76 0 L 76 10.863281 L 74 10.863281 Z M 74 0 "/>
+</clipPath>
+<clipPath id="clip8">
+ <path d="M 78 0 L 112 0 L 112 10.863281 L 78 10.863281 Z M 78 0 "/>
+</clipPath>
+<clipPath id="clip9">
+ <path d="M 120 0 L 122 0 L 122 10.863281 L 120 10.863281 Z M 120 0 "/>
+</clipPath>
+<clipPath id="clip10">
+ <path d="M 146 0 L 148 0 L 148 10.863281 L 146 10.863281 Z M 146 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.214455" y="8.058134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.08906" y="4.46581"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="7.08906" y="10.862433"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="14.280664" y="8.058134"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="26.930812" y="8.058134"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-2" x="32.826326" y="8.058134"/>
+ <use xlink:href="#glyph4-3" x="37.77638" y="8.058134"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="46.227008" y="8.058134"/>
+</g>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-4" x="48.976652" y="8.058134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="54.941997" y="4.46581"/>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-4" x="61.515503" y="8.058134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="67.480847" y="4.46581"/>
+</g>
+<g clip-path="url(#clip7)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="74.16267" y="8.058134"/>
+</g>
+</g>
+<g clip-path="url(#clip8)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="78.566237" y="8.058134"/>
+ <use xlink:href="#glyph0-4" x="85.440872" y="8.058134"/>
+ <use xlink:href="#glyph0-5" x="89.291024" y="8.058134"/>
+ <use xlink:href="#glyph0-6" x="94.241077" y="8.058134"/>
+ <use xlink:href="#glyph0-7" x="99.191131" y="8.058134"/>
+ <use xlink:href="#glyph0-8" x="104.141185" y="8.058134"/>
+ <use xlink:href="#glyph0-9" x="109.091238" y="8.058134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="112.938901" y="4.46581"/>
+</g>
+<g clip-path="url(#clip9)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="119.029456" y="8.058134"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-5" x="121.780093" y="8.058134"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="126.760654" y="4.46581"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-6" x="133.333166" y="8.058134"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="139.332298" y="4.46581"/>
+</g>
+<g clip-path="url(#clip10)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="146.015114" y="8.058134"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig33.svg b/doc/figs/tex/fig33.svg
new file mode 100644
index 00000000000..237a622257f
--- /dev/null
+++ b/doc/figs/tex/fig33.svg
@@ -0,0 +1,61 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="39.062pt" height="10.6pt" viewBox="0 0 39.062 10.6" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.546875 -6.671875 C 3.484375 -6.84375 3.4375 -6.875 3.328125 -6.875 C 3.171875 -6.875 3.15625 -6.828125 3.109375 -6.671875 L 1.265625 -0.953125 C 1.171875 -0.671875 0.984375 -0.296875 0.3125 -0.296875 L 0.3125 0 C 0.625 -0.015625 1.109375 -0.03125 1.203125 -0.03125 C 1.484375 -0.03125 1.984375 -0.015625 2.28125 0 L 2.28125 -0.296875 C 1.765625 -0.3125 1.546875 -0.5625 1.546875 -0.796875 C 1.546875 -0.84375 1.546875 -0.875 1.59375 -1 L 3.03125 -5.484375 L 4.546875 -0.765625 C 4.59375 -0.625 4.59375 -0.609375 4.59375 -0.578125 C 4.59375 -0.296875 4.03125 -0.296875 3.78125 -0.296875 L 3.78125 0 C 4.109375 -0.03125 4.796875 -0.03125 5.15625 -0.03125 C 5.53125 -0.03125 5.96875 -0.015625 6.34375 0 L 6.34375 -0.296875 C 5.609375 -0.296875 5.578125 -0.359375 5.46875 -0.703125 Z M 3.546875 -6.671875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 3.171875 2.296875 C 3.171875 2.28125 3.171875 2.25 3.015625 2.09375 C 1.8125 0.875 1.5 -0.9375 1.5 -2.390625 C 1.5 -4.0625 1.875 -5.734375 3.046875 -6.9375 C 3.171875 -7.046875 3.171875 -7.078125 3.171875 -7.09375 C 3.171875 -7.171875 3.140625 -7.1875 3.078125 -7.1875 C 2.984375 -7.1875 2.125 -6.546875 1.546875 -5.328125 C 1.0625 -4.265625 0.953125 -3.203125 0.953125 -2.390625 C 0.953125 -1.65625 1.0625 -0.484375 1.578125 0.59375 C 2.15625 1.78125 2.984375 2.390625 3.078125 2.390625 C 3.140625 2.390625 3.171875 2.375 3.171875 2.296875 Z M 3.171875 2.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 2.828125 -6.140625 C 2.828125 -6.375 2.828125 -6.390625 2.59375 -6.390625 C 2 -5.78125 1.15625 -5.78125 0.859375 -5.78125 L 0.859375 -5.484375 C 1.046875 -5.484375 1.609375 -5.484375 2.109375 -5.734375 L 2.109375 -0.765625 C 2.109375 -0.40625 2.078125 -0.296875 1.21875 -0.296875 L 0.90625 -0.296875 L 0.90625 0 C 1.25 -0.03125 2.078125 -0.03125 2.46875 -0.03125 C 2.84375 -0.03125 3.6875 -0.03125 4.015625 0 L 4.015625 -0.296875 L 3.71875 -0.296875 C 2.84375 -0.296875 2.828125 -0.40625 2.828125 -0.765625 Z M 2.828125 -6.140625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 2.828125 -1.578125 L 2.828125 -0.75 C 2.828125 -0.40625 2.796875 -0.296875 2.09375 -0.296875 L 1.890625 -0.296875 L 1.890625 0 C 2.28125 -0.03125 2.78125 -0.03125 3.1875 -0.03125 C 3.59375 -0.03125 4.09375 -0.03125 4.484375 0 L 4.484375 -0.296875 L 4.28125 -0.296875 C 3.578125 -0.296875 3.5625 -0.40625 3.5625 -0.75 L 3.5625 -1.578125 L 4.515625 -1.578125 L 4.515625 -1.875 L 3.5625 -1.875 L 3.5625 -6.25 C 3.5625 -6.4375 3.5625 -6.5 3.40625 -6.5 C 3.3125 -6.5 3.296875 -6.5 3.21875 -6.375 L 0.265625 -1.875 L 0.265625 -1.578125 Z M 2.875 -1.875 L 0.53125 -1.875 L 2.875 -5.453125 Z M 2.875 -1.875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 4.40625 -3.0625 C 4.40625 -3.84375 4.359375 -4.609375 4.03125 -5.3125 C 3.59375 -6.234375 2.796875 -6.390625 2.390625 -6.390625 C 1.828125 -6.390625 1.125 -6.140625 0.734375 -5.25 C 0.421875 -4.578125 0.375 -3.84375 0.375 -3.0625 C 0.375 -2.34375 0.40625 -1.484375 0.8125 -0.765625 C 1.21875 0.015625 1.921875 0.21875 2.390625 0.21875 C 2.90625 0.21875 3.640625 0.015625 4.0625 -0.90625 C 4.359375 -1.5625 4.40625 -2.3125 4.40625 -3.0625 Z M 2.390625 0 C 2.015625 0 1.453125 -0.234375 1.28125 -1.15625 C 1.171875 -1.734375 1.171875 -2.625 1.171875 -3.1875 C 1.171875 -3.796875 1.171875 -4.4375 1.25 -4.953125 C 1.421875 -6.09375 2.15625 -6.171875 2.390625 -6.171875 C 2.703125 -6.171875 3.34375 -6 3.515625 -5.0625 C 3.609375 -4.515625 3.609375 -3.796875 3.609375 -3.1875 C 3.609375 -2.46875 3.609375 -1.8125 3.515625 -1.203125 C 3.375 -0.28125 2.828125 0 2.390625 0 Z M 2.390625 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 4.3125 -1.921875 C 4.3125 -3.0625 3.515625 -4.03125 2.484375 -4.03125 C 2.03125 -4.03125 1.609375 -3.875 1.265625 -3.546875 L 1.265625 -5.40625 C 1.453125 -5.359375 1.78125 -5.28125 2.078125 -5.28125 C 3.265625 -5.28125 3.9375 -6.15625 3.9375 -6.28125 C 3.9375 -6.34375 3.90625 -6.390625 3.84375 -6.390625 C 3.828125 -6.390625 3.8125 -6.390625 3.765625 -6.359375 C 3.5625 -6.28125 3.09375 -6.078125 2.453125 -6.078125 C 2.078125 -6.078125 1.625 -6.15625 1.1875 -6.34375 C 1.109375 -6.375 1.078125 -6.375 1.0625 -6.375 C 0.96875 -6.375 0.96875 -6.296875 0.96875 -6.15625 L 0.96875 -3.3125 C 0.96875 -3.140625 0.96875 -3.0625 1.109375 -3.0625 C 1.171875 -3.0625 1.1875 -3.09375 1.234375 -3.140625 C 1.328125 -3.296875 1.6875 -3.8125 2.46875 -3.8125 C 2.96875 -3.8125 3.203125 -3.375 3.28125 -3.203125 C 3.4375 -2.84375 3.453125 -2.46875 3.453125 -2 C 3.453125 -1.65625 3.453125 -1.078125 3.21875 -0.6875 C 3 -0.3125 2.640625 -0.0625 2.203125 -0.0625 C 1.5 -0.0625 0.953125 -0.5625 0.78125 -1.125 C 0.8125 -1.125 0.84375 -1.109375 0.953125 -1.109375 C 1.265625 -1.109375 1.421875 -1.359375 1.421875 -1.578125 C 1.421875 -1.8125 1.265625 -2.046875 0.953125 -2.046875 C 0.8125 -2.046875 0.484375 -1.984375 0.484375 -1.546875 C 0.484375 -0.71875 1.140625 0.21875 2.21875 0.21875 C 3.328125 0.21875 4.3125 -0.703125 4.3125 -1.921875 Z M 4.3125 -1.921875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 2.765625 -2.390625 C 2.765625 -3.140625 2.671875 -4.3125 2.140625 -5.390625 C 1.5625 -6.578125 0.734375 -7.1875 0.640625 -7.1875 C 0.578125 -7.1875 0.546875 -7.15625 0.546875 -7.09375 C 0.546875 -7.078125 0.546875 -7.046875 0.734375 -6.875 C 1.671875 -5.921875 2.21875 -4.40625 2.21875 -2.390625 C 2.21875 -0.765625 1.859375 0.9375 0.671875 2.140625 C 0.546875 2.25 0.546875 2.28125 0.546875 2.296875 C 0.546875 2.359375 0.578125 2.390625 0.640625 2.390625 C 0.734375 2.390625 1.609375 1.75 2.171875 0.53125 C 2.65625 -0.53125 2.765625 -1.59375 2.765625 -2.390625 Z M 2.765625 -2.390625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.46875 -2.140625 C 3.46875 -2.875 3.375 -3.40625 3.078125 -3.890625 C 2.859375 -4.1875 2.453125 -4.46875 1.90625 -4.46875 C 0.34375 -4.46875 0.34375 -2.625 0.34375 -2.140625 C 0.34375 -1.65625 0.34375 0.140625 1.90625 0.140625 C 3.46875 0.140625 3.46875 -1.65625 3.46875 -2.140625 Z M 1.90625 -0.046875 C 1.59375 -0.046875 1.1875 -0.234375 1.0625 -0.78125 C 0.953125 -1.1875 0.953125 -1.734375 0.953125 -2.234375 C 0.953125 -2.71875 0.953125 -3.234375 1.0625 -3.59375 C 1.203125 -4.125 1.625 -4.265625 1.90625 -4.265625 C 2.265625 -4.265625 2.625 -4.046875 2.734375 -3.65625 C 2.84375 -3.296875 2.859375 -2.8125 2.859375 -2.234375 C 2.859375 -1.734375 2.859375 -1.234375 2.765625 -0.8125 C 2.640625 -0.203125 2.171875 -0.046875 1.90625 -0.046875 Z M 1.90625 -0.046875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.257812 0 L 33 0 L 33 10.214844 L 0.257812 10.214844 Z M 0.257812 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 33 0 L 37.898438 0 L 37.898438 5 L 33 5 Z M 33 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.258273" y="7.814127"/>
+ <use xlink:href="#glyph0-2" x="6.924737" y="7.814127"/>
+ <use xlink:href="#glyph0-3" x="10.658303" y="7.814127"/>
+ <use xlink:href="#glyph0-4" x="15.458465" y="7.814127"/>
+ <use xlink:href="#glyph0-5" x="20.258627" y="7.814127"/>
+ <use xlink:href="#glyph0-6" x="25.058789" y="7.814127"/>
+ <use xlink:href="#glyph0-7" x="29.858951" y="7.814127"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="33.593345" y="4.330582"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig34.svg b/doc/figs/tex/fig34.svg
new file mode 100644
index 00000000000..cd6a77bec58
--- /dev/null
+++ b/doc/figs/tex/fig34.svg
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.219pt" height="10.423pt" viewBox="0 0 47.219 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.0625 -1.5 L 5.078125 -1.5 C 5.171875 -1.5 5.328125 -1.5 5.328125 -1.65625 C 5.328125 -1.8125 5.171875 -1.8125 5.078125 -1.8125 L 3.0625 -1.8125 L 3.0625 -3.84375 C 3.0625 -3.9375 3.0625 -4.09375 2.90625 -4.09375 C 2.734375 -4.09375 2.734375 -3.9375 2.734375 -3.84375 L 2.734375 -1.8125 L 0.703125 -1.8125 C 0.625 -1.8125 0.46875 -1.8125 0.46875 -1.65625 C 0.46875 -1.5 0.609375 -1.5 0.703125 -1.5 L 2.734375 -1.5 L 2.734375 0.53125 C 2.734375 0.625 2.734375 0.78125 2.890625 0.78125 C 3.0625 0.78125 3.0625 0.625 3.0625 0.53125 Z M 3.0625 -1.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.868409" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.885591" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.121119" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.792342" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.51235" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.232358" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="30.952366" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.672374" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="39.343492" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig35.svg b/doc/figs/tex/fig35.svg
new file mode 100644
index 00000000000..cd6a77bec58
--- /dev/null
+++ b/doc/figs/tex/fig35.svg
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.219pt" height="10.423pt" viewBox="0 0 47.219 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.0625 -1.5 L 5.078125 -1.5 C 5.171875 -1.5 5.328125 -1.5 5.328125 -1.65625 C 5.328125 -1.8125 5.171875 -1.8125 5.078125 -1.8125 L 3.0625 -1.8125 L 3.0625 -3.84375 C 3.0625 -3.9375 3.0625 -4.09375 2.90625 -4.09375 C 2.734375 -4.09375 2.734375 -3.9375 2.734375 -3.84375 L 2.734375 -1.8125 L 0.703125 -1.8125 C 0.625 -1.8125 0.46875 -1.8125 0.46875 -1.65625 C 0.46875 -1.5 0.609375 -1.5 0.703125 -1.5 L 2.734375 -1.5 L 2.734375 0.53125 C 2.734375 0.625 2.734375 0.78125 2.890625 0.78125 C 3.0625 0.78125 3.0625 0.625 3.0625 0.53125 Z M 3.0625 -1.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.868409" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.885591" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.121119" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.792342" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.51235" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.232358" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="30.952366" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.672374" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="39.343492" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig36.svg b/doc/figs/tex/fig36.svg
new file mode 100644
index 00000000000..b3116a75348
--- /dev/null
+++ b/doc/figs/tex/fig36.svg
@@ -0,0 +1,90 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="56.939pt" height="9.963pt" viewBox="0 0 56.939 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.53125 2.484375 L 2.53125 2.078125 L 1.5625 2.078125 L 1.5625 -7.046875 L 2.53125 -7.046875 L 2.53125 -7.4375 L 1.171875 -7.4375 L 1.171875 2.484375 Z M 2.53125 2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.5625 -3.171875 C 4.5625 -3.96875 4.515625 -4.765625 4.171875 -5.5 C 3.703125 -6.453125 2.890625 -6.609375 2.484375 -6.609375 C 1.890625 -6.609375 1.15625 -6.34375 0.75 -5.421875 C 0.4375 -4.75 0.390625 -3.96875 0.390625 -3.171875 C 0.390625 -2.4375 0.421875 -1.53125 0.828125 -0.78125 C 1.265625 0.015625 1.984375 0.21875 2.46875 0.21875 C 3 0.21875 3.765625 0.015625 4.203125 -0.9375 C 4.515625 -1.625 4.5625 -2.390625 4.5625 -3.171875 Z M 2.46875 0 C 2.078125 0 1.5 -0.25 1.3125 -1.203125 C 1.203125 -1.796875 1.203125 -2.703125 1.203125 -3.296875 C 1.203125 -3.921875 1.203125 -4.578125 1.296875 -5.125 C 1.484375 -6.296875 2.21875 -6.390625 2.46875 -6.390625 C 2.796875 -6.390625 3.453125 -6.21875 3.640625 -5.234375 C 3.734375 -4.671875 3.734375 -3.921875 3.734375 -3.296875 C 3.734375 -2.546875 3.734375 -1.875 3.625 -1.234375 C 3.484375 -0.296875 2.921875 0 2.46875 0 Z M 2.46875 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 1.265625 -0.765625 L 2.3125 -1.78125 C 3.859375 -3.15625 4.453125 -3.6875 4.453125 -4.6875 C 4.453125 -5.8125 3.5625 -6.609375 2.34375 -6.609375 C 1.234375 -6.609375 0.5 -5.6875 0.5 -4.8125 C 0.5 -4.25 0.984375 -4.25 1.015625 -4.25 C 1.1875 -4.25 1.53125 -4.375 1.53125 -4.78125 C 1.53125 -5.046875 1.359375 -5.296875 1.015625 -5.296875 C 0.9375 -5.296875 0.90625 -5.296875 0.890625 -5.28125 C 1.109375 -5.9375 1.640625 -6.296875 2.21875 -6.296875 C 3.125 -6.296875 3.546875 -5.5 3.546875 -4.6875 C 3.546875 -3.890625 3.0625 -3.109375 2.515625 -2.484375 L 0.609375 -0.359375 C 0.5 -0.265625 0.5 -0.234375 0.5 0 L 4.171875 0 L 4.453125 -1.71875 L 4.203125 -1.71875 C 4.15625 -1.421875 4.09375 -0.984375 3.984375 -0.84375 C 3.921875 -0.765625 3.265625 -0.765625 3.046875 -0.765625 Z M 1.265625 -0.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 1.578125 -7.4375 L 0.21875 -7.4375 L 0.21875 -7.046875 L 1.1875 -7.046875 L 1.1875 2.078125 L 0.21875 2.078125 L 0.21875 2.484375 L 1.578125 2.484375 Z M 1.578125 -7.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-5">
+<path style="stroke:none;" d="M 5.890625 -0.625 C 6.015625 -0.40625 6.40625 -0.015625 6.515625 -0.015625 C 6.609375 -0.015625 6.609375 -0.09375 6.609375 -0.234375 L 6.609375 -1.96875 C 6.609375 -2.34375 6.640625 -2.40625 7.296875 -2.40625 L 7.296875 -2.703125 C 6.921875 -2.703125 6.375 -2.671875 6.078125 -2.671875 C 5.6875 -2.671875 4.84375 -2.671875 4.484375 -2.703125 L 4.484375 -2.40625 L 4.796875 -2.40625 C 5.6875 -2.40625 5.71875 -2.296875 5.71875 -1.921875 L 5.71875 -1.296875 C 5.71875 -0.171875 4.46875 -0.09375 4.1875 -0.09375 C 3.546875 -0.09375 1.578125 -0.4375 1.578125 -3.390625 C 1.578125 -6.359375 3.53125 -6.6875 4.125 -6.6875 C 5.1875 -6.6875 6.09375 -5.796875 6.296875 -4.328125 C 6.3125 -4.203125 6.3125 -4.171875 6.453125 -4.171875 C 6.609375 -4.171875 6.609375 -4.203125 6.609375 -4.40625 L 6.609375 -6.75 C 6.609375 -6.921875 6.609375 -7 6.5 -7 C 6.453125 -7 6.421875 -7 6.34375 -6.875 L 5.84375 -6.140625 C 5.53125 -6.453125 4.984375 -7 4.015625 -7 C 2.15625 -7 0.5625 -5.421875 0.5625 -3.390625 C 0.5625 -1.359375 2.140625 0.21875 4.03125 0.21875 C 4.75 0.21875 5.546875 -0.046875 5.890625 -0.625 Z M 5.890625 -0.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-6">
+<path style="stroke:none;" d="M 1.109375 -2.5 C 1.171875 -3.984375 2 -4.234375 2.34375 -4.234375 C 3.359375 -4.234375 3.46875 -2.890625 3.46875 -2.5 Z M 1.09375 -2.296875 L 3.875 -2.296875 C 4.09375 -2.296875 4.125 -2.296875 4.125 -2.5 C 4.125 -3.484375 3.578125 -4.4375 2.34375 -4.4375 C 1.1875 -4.4375 0.28125 -3.421875 0.28125 -2.1875 C 0.28125 -0.859375 1.3125 0.109375 2.453125 0.109375 C 3.671875 0.109375 4.125 -0.984375 4.125 -1.1875 C 4.125 -1.28125 4.03125 -1.296875 3.984375 -1.296875 C 3.90625 -1.296875 3.875 -1.234375 3.859375 -1.15625 C 3.515625 -0.140625 2.625 -0.140625 2.515625 -0.140625 C 2.03125 -0.140625 1.625 -0.4375 1.40625 -0.796875 C 1.09375 -1.28125 1.09375 -1.9375 1.09375 -2.296875 Z M 1.09375 -2.296875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-7">
+<path style="stroke:none;" d="M 6.15625 -5.796875 C 6.296875 -6.171875 6.5625 -6.453125 7.25 -6.46875 L 7.25 -6.78125 C 6.9375 -6.75 6.53125 -6.75 6.28125 -6.75 C 5.984375 -6.75 5.40625 -6.765625 5.15625 -6.78125 L 5.15625 -6.46875 C 5.671875 -6.453125 5.875 -6.203125 5.875 -5.96875 C 5.875 -5.890625 5.84375 -5.828125 5.828125 -5.78125 L 4.015625 -0.984375 L 2.109375 -6 C 2.046875 -6.140625 2.046875 -6.15625 2.046875 -6.1875 C 2.046875 -6.46875 2.625 -6.46875 2.875 -6.46875 L 2.875 -6.78125 C 2.515625 -6.75 1.828125 -6.75 1.453125 -6.75 C 0.96875 -6.75 0.546875 -6.765625 0.1875 -6.78125 L 0.1875 -6.46875 C 0.828125 -6.46875 1.015625 -6.46875 1.15625 -6.09375 L 3.46875 0 C 3.53125 0.1875 3.578125 0.21875 3.703125 0.21875 C 3.875 0.21875 3.90625 0.171875 3.953125 0.03125 Z M 6.15625 -5.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 1.90625 -0.53125 C 1.90625 -0.8125 1.671875 -1.046875 1.375 -1.046875 C 1.09375 -1.046875 0.859375 -0.8125 0.859375 -0.53125 C 0.859375 -0.234375 1.09375 0 1.375 0 C 1.671875 0 1.90625 -0.234375 1.90625 -0.53125 Z M 1.90625 -0.53125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.015625 -0.015625 C 2.015625 -0.671875 1.765625 -1.046875 1.375 -1.046875 C 1.046875 -1.046875 0.859375 -0.796875 0.859375 -0.53125 C 0.859375 -0.265625 1.046875 0 1.375 0 C 1.5 0 1.625 -0.046875 1.71875 -0.125 C 1.75 -0.15625 1.765625 -0.15625 1.78125 -0.15625 C 1.78125 -0.15625 1.796875 -0.15625 1.796875 -0.015625 C 1.796875 0.71875 1.453125 1.3125 1.125 1.640625 C 1.015625 1.75 1.015625 1.78125 1.015625 1.8125 C 1.015625 1.875 1.0625 1.921875 1.109375 1.921875 C 1.21875 1.921875 2.015625 1.15625 2.015625 -0.015625 Z M 2.015625 -0.015625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 1 0 L 8 0 L 8 9.925781 L 1 9.925781 Z M 1 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 16 6 L 18 6 L 18 9.925781 L 16 9.925781 Z M 16 6 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 28 0 L 35 0 L 35 9.925781 L 28 9.925781 Z M 28 0 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 37 0 L 56.804688 0 L 56.804688 8 L 37 8 Z M 37 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.07495" y="7.444354"/>
+ <use xlink:href="#glyph0-2" x="2.83232" y="7.444354"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.795279" y="7.444354"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="10.552041" y="7.444354"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="15.514611" y="7.444354"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="19.926228" y="7.444354"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="24.889794" y="7.444354"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="27.646556" y="7.444354"/>
+ <use xlink:href="#glyph0-4" x="32.609425" y="7.444354"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-5" x="37.024394" y="7.444354"/>
+ <use xlink:href="#glyph0-6" x="44.813121" y="7.444354"/>
+ <use xlink:href="#glyph0-7" x="49.224119" y="7.444354"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig37.svg b/doc/figs/tex/fig37.svg
new file mode 100644
index 00000000000..cd6a77bec58
--- /dev/null
+++ b/doc/figs/tex/fig37.svg
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.219pt" height="10.423pt" viewBox="0 0 47.219 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.0625 -1.5 L 5.078125 -1.5 C 5.171875 -1.5 5.328125 -1.5 5.328125 -1.65625 C 5.328125 -1.8125 5.171875 -1.8125 5.078125 -1.8125 L 3.0625 -1.8125 L 3.0625 -3.84375 C 3.0625 -3.9375 3.0625 -4.09375 2.90625 -4.09375 C 2.734375 -4.09375 2.734375 -3.9375 2.734375 -3.84375 L 2.734375 -1.8125 L 0.703125 -1.8125 C 0.625 -1.8125 0.46875 -1.8125 0.46875 -1.65625 C 0.46875 -1.5 0.609375 -1.5 0.703125 -1.5 L 2.734375 -1.5 L 2.734375 0.53125 C 2.734375 0.625 2.734375 0.78125 2.890625 0.78125 C 3.0625 0.78125 3.0625 0.625 3.0625 0.53125 Z M 3.0625 -1.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.868409" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.885591" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.121119" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.792342" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.51235" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.232358" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="30.952366" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.672374" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="39.343492" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig38.svg b/doc/figs/tex/fig38.svg
new file mode 100644
index 00000000000..60c45e30ba3
--- /dev/null
+++ b/doc/figs/tex/fig38.svg
@@ -0,0 +1,70 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.33pt" height="10.423pt" viewBox="0 0 47.33 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.921875 -1.5 C 5.015625 -1.5 5.1875 -1.5 5.1875 -1.65625 C 5.1875 -1.8125 5.03125 -1.8125 4.921875 -1.8125 L 0.984375 -1.8125 C 0.875 -1.8125 0.71875 -1.8125 0.71875 -1.65625 C 0.71875 -1.5 0.859375 -1.5 0.984375 -1.5 Z M 4.921875 -1.5 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.923909" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.941091" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.176619" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.847842" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.56785" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.287858" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="31.007866" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.727874" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="39.398992" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig39.svg b/doc/figs/tex/fig39.svg
new file mode 100644
index 00000000000..2b237e03225
--- /dev/null
+++ b/doc/figs/tex/fig39.svg
@@ -0,0 +1,105 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="85.59pt" height="8.11pt" viewBox="0 0 85.59 8.11" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 1.421875 -0.703125 C 1.34375 -0.34375 1.328125 -0.28125 0.609375 -0.28125 C 0.453125 -0.28125 0.359375 -0.28125 0.359375 -0.109375 C 0.359375 0 0.4375 0 0.609375 0 L 3.578125 0 C 5.453125 0 7.21875 -1.890625 7.21875 -3.859375 C 7.21875 -5.125 6.453125 -6.140625 5.109375 -6.140625 L 2.09375 -6.140625 C 1.921875 -6.140625 1.828125 -6.140625 1.828125 -5.96875 C 1.828125 -5.859375 1.90625 -5.859375 2.078125 -5.859375 C 2.203125 -5.859375 2.359375 -5.84375 2.46875 -5.84375 C 2.609375 -5.828125 2.671875 -5.796875 2.671875 -5.703125 C 2.671875 -5.65625 2.65625 -5.640625 2.625 -5.53125 Z M 3.375 -5.515625 C 3.453125 -5.828125 3.46875 -5.859375 3.859375 -5.859375 L 4.8125 -5.859375 C 5.703125 -5.859375 6.4375 -5.375 6.4375 -4.203125 C 6.4375 -3.75 6.265625 -2.28125 5.5 -1.296875 C 5.234375 -0.96875 4.53125 -0.28125 3.421875 -0.28125 L 2.40625 -0.28125 C 2.28125 -0.28125 2.265625 -0.28125 2.203125 -0.28125 C 2.125 -0.296875 2.09375 -0.3125 2.09375 -0.375 C 2.09375 -0.40625 2.09375 -0.421875 2.140625 -0.578125 Z M 3.375 -5.515625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.578125 -3.625 C 4.5625 -3.65625 4.53125 -3.734375 4.53125 -3.75 C 4.53125 -3.765625 4.6875 -3.890625 4.78125 -3.96875 L 6.359375 -5.171875 C 7.203125 -5.796875 7.5625 -5.828125 7.828125 -5.859375 C 7.890625 -5.859375 7.984375 -5.875 7.984375 -6.03125 C 7.984375 -6.078125 7.953125 -6.140625 7.890625 -6.140625 C 7.6875 -6.140625 7.46875 -6.109375 7.25 -6.109375 C 6.921875 -6.109375 6.578125 -6.140625 6.25 -6.140625 C 6.1875 -6.140625 6.078125 -6.140625 6.078125 -5.953125 C 6.078125 -5.890625 6.125 -5.859375 6.1875 -5.859375 C 6.390625 -5.84375 6.46875 -5.796875 6.46875 -5.671875 C 6.46875 -5.5 6.203125 -5.296875 6.140625 -5.25 L 2.640625 -2.5625 L 3.359375 -5.4375 C 3.4375 -5.765625 3.453125 -5.859375 4.109375 -5.859375 C 4.34375 -5.859375 4.421875 -5.859375 4.421875 -6.03125 C 4.421875 -6.125 4.34375 -6.140625 4.296875 -6.140625 C 4.046875 -6.140625 3.390625 -6.109375 3.140625 -6.109375 C 2.890625 -6.109375 2.25 -6.140625 1.984375 -6.140625 C 1.921875 -6.140625 1.8125 -6.140625 1.8125 -5.96875 C 1.8125 -5.859375 1.890625 -5.859375 2.0625 -5.859375 C 2.1875 -5.859375 2.34375 -5.84375 2.453125 -5.84375 C 2.59375 -5.828125 2.65625 -5.796875 2.65625 -5.703125 C 2.65625 -5.65625 2.640625 -5.640625 2.609375 -5.53125 L 1.40625 -0.703125 C 1.328125 -0.34375 1.296875 -0.28125 0.59375 -0.28125 C 0.4375 -0.28125 0.34375 -0.28125 0.34375 -0.109375 C 0.34375 0 0.453125 0 0.46875 0 C 0.734375 0 1.359375 -0.03125 1.609375 -0.03125 C 1.8125 -0.03125 2 -0.015625 2.1875 -0.015625 C 2.390625 -0.015625 2.59375 0 2.78125 0 C 2.84375 0 2.953125 0 2.953125 -0.171875 C 2.953125 -0.28125 2.875 -0.28125 2.703125 -0.28125 C 2.375 -0.28125 2.125 -0.28125 2.125 -0.4375 C 2.125 -0.5 2.171875 -0.703125 2.203125 -0.828125 C 2.328125 -1.296875 2.4375 -1.78125 2.5625 -2.25 L 3.90625 -3.28125 L 4.9375 -0.875 C 5.046875 -0.625 5.046875 -0.609375 5.046875 -0.5625 C 5.046875 -0.28125 4.65625 -0.28125 4.578125 -0.28125 C 4.484375 -0.28125 4.390625 -0.28125 4.390625 -0.09375 C 4.390625 0 4.484375 0 4.515625 0 C 4.875 0 5.25 -0.03125 5.609375 -0.03125 C 5.796875 -0.03125 6.28125 0 6.484375 0 C 6.53125 0 6.640625 0 6.640625 -0.171875 C 6.640625 -0.28125 6.546875 -0.28125 6.46875 -0.28125 C 6.09375 -0.28125 5.984375 -0.375 5.84375 -0.6875 Z M 4.578125 -3.625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 2.375 -3.34375 L 3.390625 -3.34375 C 3.09375 -2.015625 3.015625 -1.640625 3.015625 -1.03125 C 3.015625 -0.890625 3.015625 -0.65625 3.09375 -0.34375 C 3.1875 0.046875 3.28125 0.09375 3.40625 0.09375 C 3.59375 0.09375 3.78125 -0.0625 3.78125 -0.25 C 3.78125 -0.296875 3.78125 -0.3125 3.734375 -0.4375 C 3.46875 -1.09375 3.46875 -1.671875 3.46875 -1.921875 C 3.46875 -2.40625 3.53125 -2.890625 3.625 -3.34375 L 4.65625 -3.34375 C 4.765625 -3.34375 5.09375 -3.34375 5.09375 -3.65625 C 5.09375 -3.875 4.90625 -3.875 4.734375 -3.875 L 1.71875 -3.875 C 1.53125 -3.875 1.1875 -3.875 0.796875 -3.453125 C 0.46875 -3.09375 0.25 -2.6875 0.25 -2.640625 C 0.25 -2.625 0.25 -2.546875 0.34375 -2.546875 C 0.421875 -2.546875 0.4375 -2.59375 0.5 -2.65625 C 0.9375 -3.34375 1.453125 -3.34375 1.640625 -3.34375 L 2.140625 -3.34375 C 1.859375 -2.265625 1.375 -1.171875 1 -0.359375 C 0.921875 -0.21875 0.921875 -0.203125 0.921875 -0.140625 C 0.921875 0.03125 1.0625 0.09375 1.1875 0.09375 C 1.453125 0.09375 1.53125 -0.15625 1.640625 -0.484375 C 1.765625 -0.890625 1.765625 -0.921875 1.875 -1.359375 Z M 2.375 -3.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.234375 -2 C 3.234375 -2.6875 3.15625 -3.1875 2.875 -3.625 C 2.671875 -3.921875 2.28125 -4.171875 1.78125 -4.171875 C 0.328125 -4.171875 0.328125 -2.453125 0.328125 -2 C 0.328125 -1.546875 0.328125 0.125 1.78125 0.125 C 3.234375 0.125 3.234375 -1.546875 3.234375 -2 Z M 1.78125 -0.046875 C 1.5 -0.046875 1.109375 -0.21875 0.984375 -0.734375 C 0.890625 -1.109375 0.890625 -1.625 0.890625 -2.078125 C 0.890625 -2.546875 0.890625 -3.015625 1 -3.359375 C 1.125 -3.859375 1.53125 -4 1.78125 -4 C 2.125 -4 2.453125 -3.78125 2.5625 -3.421875 C 2.65625 -3.078125 2.671875 -2.625 2.671875 -2.078125 C 2.671875 -1.625 2.671875 -1.15625 2.59375 -0.765625 C 2.46875 -0.1875 2.03125 -0.046875 1.78125 -0.046875 Z M 1.78125 -0.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.90625 -1.421875 L 4.828125 -1.421875 C 4.90625 -1.421875 5.0625 -1.421875 5.0625 -1.5625 C 5.0625 -1.734375 4.921875 -1.734375 4.828125 -1.734375 L 2.90625 -1.734375 L 2.90625 -3.65625 C 2.90625 -3.734375 2.90625 -3.890625 2.75 -3.890625 C 2.59375 -3.890625 2.59375 -3.75 2.59375 -3.65625 L 2.59375 -1.734375 L 0.671875 -1.734375 C 0.59375 -1.734375 0.4375 -1.734375 0.4375 -1.578125 C 0.4375 -1.421875 0.578125 -1.421875 0.671875 -1.421875 L 2.59375 -1.421875 L 2.59375 0.515625 C 2.59375 0.59375 2.59375 0.734375 2.75 0.734375 C 2.90625 0.734375 2.90625 0.59375 2.90625 0.515625 Z M 2.90625 -1.421875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 7.5 -2.0625 C 7 -1.6875 6.75 -1.328125 6.6875 -1.203125 C 6.28125 -0.578125 6.203125 -0.015625 6.203125 -0.015625 C 6.203125 0.09375 6.3125 0.09375 6.390625 0.09375 C 6.546875 0.09375 6.546875 0.078125 6.578125 -0.078125 C 6.796875 -0.96875 7.328125 -1.71875 8.34375 -2.125 C 8.4375 -2.171875 8.46875 -2.1875 8.46875 -2.25 C 8.46875 -2.3125 8.421875 -2.328125 8.40625 -2.34375 C 8 -2.5 6.921875 -2.953125 6.578125 -4.453125 C 6.546875 -4.5625 6.546875 -4.59375 6.390625 -4.59375 C 6.3125 -4.59375 6.203125 -4.59375 6.203125 -4.484375 C 6.203125 -4.46875 6.28125 -3.90625 6.671875 -3.296875 C 6.84375 -3.03125 7.109375 -2.71875 7.5 -2.421875 L 0.8125 -2.421875 C 0.65625 -2.421875 0.5 -2.421875 0.5 -2.25 C 0.5 -2.0625 0.65625 -2.0625 0.8125 -2.0625 Z M 7.5 -2.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.671875 -1.421875 C 4.78125 -1.421875 4.921875 -1.421875 4.921875 -1.5625 C 4.921875 -1.734375 4.78125 -1.734375 4.671875 -1.734375 L 0.921875 -1.734375 C 0.828125 -1.734375 0.671875 -1.734375 0.671875 -1.578125 C 0.671875 -1.421875 0.828125 -1.421875 0.921875 -1.421875 Z M 4.671875 -1.421875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 4.046875 1 L 12 1 L 12 7.308594 L 4.046875 7.308594 Z M 4.046875 1 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 18 2 L 27 2 L 27 7.308594 L 18 7.308594 Z M 18 2 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 30 1 L 38 1 L 38 7.308594 L 30 7.308594 Z M 30 1 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 44 1 L 53 1 L 53 7.308594 L 44 7.308594 Z M 44 1 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 58 3 L 64 3 L 64 7.308594 L 58 7.308594 Z M 58 3 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 70 3 L 75 3 L 75 7.308594 L 70 7.308594 Z M 70 3 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="4.047222" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="11.729194" y="4.050494"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="18.250536" y="7.308011"/>
+</g>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="29.72168" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="37.988473" y="4.050494"/>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="44.047544" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="52.314338" y="4.050494"/>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="58.274287" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="63.714294" y="4.050494"/>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="69.774267" y="7.308011"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="75.213373" y="4.050494"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig4.svg b/doc/figs/tex/fig4.svg
new file mode 100644
index 00000000000..50106b737b3
--- /dev/null
+++ b/doc/figs/tex/fig4.svg
@@ -0,0 +1,136 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="87.938pt" height="10.461pt" viewBox="0 0 87.938 10.461" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.609375 -5.875 L 6.171875 -5.875 C 7.421875 -5.875 7.890625 -6.59375 7.890625 -6.71875 C 7.890625 -6.765625 7.859375 -6.796875 7.8125 -6.796875 C 7.703125 -6.796875 7.46875 -6.6875 7.21875 -6.53125 C 7.15625 -6.46875 7.125 -6.46875 6.953125 -6.46875 L 2.8125 -6.46875 C 1.640625 -6.46875 0.328125 -5.453125 0.328125 -4.671875 C 0.328125 -4.625 0.328125 -4.5625 0.390625 -4.5625 C 0.625 -4.5625 1.21875 -4.875 1.234375 -5.109375 C 1.25 -5.265625 1.265625 -5.4375 1.453125 -5.6875 C 1.546875 -5.796875 1.625 -5.875 2.046875 -5.875 L 3.921875 -5.875 C 3.765625 -5.78125 3.734375 -5.640625 3.71875 -5.546875 L 2.625 -1.25 C 2.515625 -0.78125 2.3125 -0.1875 2.046875 0.421875 C 1.984375 0.546875 1.984375 0.5625 1.984375 0.578125 C 1.984375 0.640625 2.03125 0.640625 2.078125 0.640625 C 2.265625 0.640625 2.734375 0.390625 2.875 0.1875 C 2.921875 0.09375 3.34375 -0.875 3.546875 -1.65625 Z M 4.609375 -5.875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.140625 2.265625 C 3.140625 2.25 3.140625 2.21875 2.96875 2.0625 C 1.796875 0.875 1.484375 -0.921875 1.484375 -2.375 C 1.484375 -4.015625 1.84375 -5.65625 3.015625 -6.84375 C 3.140625 -6.953125 3.140625 -6.984375 3.140625 -7 C 3.140625 -7.078125 3.09375 -7.109375 3.046875 -7.109375 C 2.9375 -7.109375 2.09375 -6.453125 1.53125 -5.25 C 1.046875 -4.21875 0.9375 -3.15625 0.9375 -2.375 C 0.9375 -1.625 1.046875 -0.484375 1.5625 0.59375 C 2.125 1.75 2.9375 2.375 3.046875 2.375 C 3.09375 2.375 3.140625 2.34375 3.140625 2.265625 Z M 3.140625 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.734375 -2.375 C 2.734375 -3.109375 2.625 -4.25 2.109375 -5.328125 C 1.546875 -6.484375 0.734375 -7.109375 0.640625 -7.109375 C 0.578125 -7.109375 0.546875 -7.0625 0.546875 -7 C 0.546875 -6.984375 0.546875 -6.953125 0.71875 -6.796875 C 1.640625 -5.859375 2.1875 -4.34375 2.1875 -2.375 C 2.1875 -0.75 1.84375 0.921875 0.65625 2.109375 C 0.546875 2.21875 0.546875 2.25 0.546875 2.265625 C 0.546875 2.328125 0.578125 2.375 0.640625 2.375 C 0.734375 2.375 1.578125 1.71875 2.140625 0.515625 C 2.625 -0.515625 2.734375 -1.578125 2.734375 -2.375 Z M 2.734375 -2.375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 6.5 -3.09375 C 6.640625 -3.09375 6.828125 -3.09375 6.828125 -3.28125 C 6.828125 -3.46875 6.640625 -3.46875 6.515625 -3.46875 L 0.84375 -3.46875 C 0.703125 -3.46875 0.53125 -3.46875 0.53125 -3.28125 C 0.53125 -3.09375 0.703125 -3.09375 0.859375 -3.09375 Z M 6.515625 -1.265625 C 6.640625 -1.265625 6.828125 -1.265625 6.828125 -1.453125 C 6.828125 -1.640625 6.640625 -1.640625 6.5 -1.640625 L 0.859375 -1.640625 C 0.703125 -1.640625 0.53125 -1.640625 0.53125 -1.453125 C 0.53125 -1.265625 0.703125 -1.265625 0.84375 -1.265625 Z M 6.515625 -1.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.28125 -2.328125 L 4.390625 -3.5625 C 4.5 -3.6875 4.5625 -3.765625 5.34375 -3.765625 L 5.34375 -4.203125 C 5.015625 -4.1875 4.53125 -4.171875 4.484375 -4.171875 C 4.234375 -4.171875 3.765625 -4.1875 3.5 -4.203125 L 3.5 -3.765625 C 3.640625 -3.765625 3.75 -3.734375 3.859375 -3.671875 C 3.828125 -3.609375 3.828125 -3.59375 3.78125 -3.5625 L 2.984375 -2.671875 L 2.0625 -3.765625 L 2.4375 -3.765625 L 2.4375 -4.203125 C 2.203125 -4.1875 1.59375 -4.171875 1.296875 -4.171875 C 1 -4.171875 0.5625 -4.1875 0.25 -4.203125 L 0.25 -3.765625 L 0.921875 -3.765625 L 2.40625 -2.015625 L 1.171875 -0.625 C 1 -0.4375 0.65625 -0.4375 0.203125 -0.4375 L 0.203125 0 C 0.546875 -0.015625 1.03125 -0.03125 1.078125 -0.03125 C 1.3125 -0.03125 1.859375 -0.015625 2.0625 0 L 2.0625 -0.4375 C 1.890625 -0.4375 1.703125 -0.5 1.703125 -0.546875 C 1.703125 -0.5625 1.703125 -0.5625 1.765625 -0.640625 L 2.6875 -1.671875 L 3.734375 -0.4375 L 3.359375 -0.4375 L 3.359375 0 C 3.609375 -0.015625 4.1875 -0.03125 4.5 -0.03125 C 4.796875 -0.03125 5.234375 -0.015625 5.546875 0 L 5.546875 -0.4375 L 4.859375 -0.4375 Z M 3.28125 -2.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 3.984375 5.0625 L 0.625 9.21875 C 0.546875 9.3125 0.546875 9.328125 0.546875 9.359375 C 0.546875 9.46875 0.625 9.46875 0.796875 9.46875 L 8.640625 9.46875 L 9.453125 7.109375 L 9.21875 7.109375 C 8.984375 7.828125 8.34375 8.40625 7.546875 8.671875 C 7.390625 8.71875 6.734375 8.953125 5.34375 8.953125 L 1.328125 8.953125 L 4.609375 4.890625 C 4.671875 4.796875 4.703125 4.765625 4.703125 4.734375 C 4.703125 4.703125 4.6875 4.6875 4.625 4.609375 L 1.546875 0.375 L 5.296875 0.375 C 6.375 0.375 8.5625 0.4375 9.21875 2.21875 L 9.453125 2.21875 L 8.640625 0 L 0.796875 0 C 0.546875 0 0.53125 0.015625 0.53125 0.296875 Z M 3.984375 5.0625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 2.078125 -4.40625 C 2.078125 -4.40625 2.09375 -4.5 2.09375 -4.5 C 2.09375 -4.53125 2.078125 -4.59375 2 -4.59375 C 1.859375 -4.59375 1.3125 -4.546875 1.140625 -4.53125 C 1.09375 -4.53125 1 -4.515625 1 -4.375 C 1 -4.28125 1.09375 -4.28125 1.171875 -4.28125 C 1.484375 -4.28125 1.484375 -4.234375 1.484375 -4.1875 C 1.484375 -4.140625 1.484375 -4.09375 1.46875 -4.046875 L 0.53125 -0.296875 C 0.5 -0.171875 0.5 -0.15625 0.5 -0.140625 C 0.5 -0.046875 0.578125 0.0625 0.71875 0.0625 C 0.90625 0.0625 0.984375 -0.0625 1.03125 -0.21875 C 1.046875 -0.234375 1.328125 -1.40625 1.34375 -1.5 C 1.828125 -1.453125 2.203125 -1.296875 2.203125 -0.953125 C 2.203125 -0.921875 2.203125 -0.890625 2.1875 -0.828125 C 2.15625 -0.71875 2.15625 -0.6875 2.15625 -0.609375 C 2.15625 -0.140625 2.546875 0.0625 2.859375 0.0625 C 3.5 0.0625 3.703125 -0.9375 3.703125 -0.953125 C 3.703125 -1.03125 3.625 -1.03125 3.59375 -1.03125 C 3.5 -1.03125 3.5 -1 3.46875 -0.875 C 3.390625 -0.59375 3.203125 -0.125 2.875 -0.125 C 2.703125 -0.125 2.65625 -0.28125 2.65625 -0.46875 C 2.65625 -0.578125 2.65625 -0.59375 2.6875 -0.765625 C 2.703125 -0.78125 2.71875 -0.890625 2.71875 -0.96875 C 2.71875 -1.5625 1.921875 -1.65625 1.65625 -1.671875 C 1.84375 -1.78125 2.09375 -2 2.203125 -2.109375 C 2.53125 -2.421875 2.875 -2.734375 3.234375 -2.734375 C 3.3125 -2.734375 3.40625 -2.71875 3.453125 -2.65625 C 3.171875 -2.609375 3.109375 -2.375 3.109375 -2.28125 C 3.109375 -2.140625 3.21875 -2.03125 3.375 -2.03125 C 3.5625 -2.03125 3.75 -2.171875 3.75 -2.453125 C 3.75 -2.671875 3.59375 -2.921875 3.25 -2.921875 C 2.875 -2.921875 2.53125 -2.65625 2.1875 -2.34375 C 1.90625 -2.078125 1.6875 -1.875 1.421875 -1.75 Z M 2.078125 -4.40625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 4.453125 -3.5625 C 4.46875 -3.625 4.484375 -3.671875 4.484375 -3.734375 C 4.484375 -3.90625 4.375 -4 4.21875 -4 C 4.125 -4 3.859375 -3.921875 3.828125 -3.59375 C 3.65625 -3.9375 3.328125 -4.1875 2.9375 -4.1875 C 1.859375 -4.1875 0.6875 -2.859375 0.6875 -1.5 C 0.6875 -0.5625 1.265625 0 1.953125 0 C 2.515625 0 2.953125 -0.4375 3.046875 -0.546875 L 3.0625 -0.546875 C 2.859375 0.296875 2.75 0.6875 2.75 0.703125 C 2.703125 0.796875 2.390625 1.734375 1.375 1.734375 C 1.203125 1.734375 0.890625 1.71875 0.625 1.640625 C 0.90625 1.546875 1.015625 1.3125 1.015625 1.140625 C 1.015625 1 0.90625 0.8125 0.65625 0.8125 C 0.4375 0.8125 0.140625 0.984375 0.140625 1.359375 C 0.140625 1.75 0.5 1.9375 1.40625 1.9375 C 2.578125 1.9375 3.265625 1.203125 3.40625 0.640625 Z M 3.234375 -1.21875 C 3.171875 -0.96875 2.953125 -0.734375 2.75 -0.546875 C 2.546875 -0.375 2.25 -0.203125 1.984375 -0.203125 C 1.5 -0.203125 1.359375 -0.703125 1.359375 -1.078125 C 1.359375 -1.53125 1.640625 -2.65625 1.890625 -3.140625 C 2.15625 -3.59375 2.5625 -3.984375 2.953125 -3.984375 C 3.578125 -3.984375 3.71875 -3.203125 3.71875 -3.15625 C 3.71875 -3.109375 3.6875 -3.0625 3.6875 -3.015625 Z M 3.234375 -1.21875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 1.6875 -1.09375 C 1.3125 -0.453125 0.953125 -0.328125 0.53125 -0.296875 C 0.421875 -0.28125 0.328125 -0.28125 0.328125 -0.109375 C 0.328125 -0.046875 0.375 0 0.453125 0 C 0.703125 0 1 -0.03125 1.265625 -0.03125 C 1.578125 -0.03125 1.90625 0 2.21875 0 C 2.265625 0 2.390625 0 2.390625 -0.1875 C 2.390625 -0.28125 2.3125 -0.296875 2.25 -0.296875 C 2.03125 -0.3125 1.796875 -0.390625 1.796875 -0.625 C 1.796875 -0.734375 1.859375 -0.84375 1.9375 -0.96875 L 2.65625 -2.1875 L 5.03125 -2.1875 C 5.046875 -1.984375 5.171875 -0.703125 5.171875 -0.609375 C 5.171875 -0.328125 4.6875 -0.296875 4.5 -0.296875 C 4.359375 -0.296875 4.265625 -0.296875 4.265625 -0.109375 C 4.265625 0 4.390625 0 4.40625 0 C 4.796875 0 5.203125 -0.03125 5.59375 -0.03125 C 5.828125 -0.03125 6.421875 0 6.65625 0 C 6.71875 0 6.828125 0 6.828125 -0.1875 C 6.828125 -0.296875 6.734375 -0.296875 6.609375 -0.296875 C 6.015625 -0.296875 6.015625 -0.359375 6 -0.640625 L 5.421875 -6.546875 C 5.390625 -6.734375 5.390625 -6.78125 5.234375 -6.78125 C 5.078125 -6.78125 5.046875 -6.71875 4.984375 -6.625 Z M 2.828125 -2.484375 L 4.703125 -5.609375 L 5 -2.484375 Z M 2.828125 -2.484375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 2.125 0 L 11 0 L 11 8 L 2.125 8 Z M 2.125 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 10 0 L 13 0 L 13 9.949219 L 10 9.949219 Z M 10 0 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 19 0 L 22 0 L 22 9.949219 L 19 9.949219 Z M 19 0 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 35 0 L 45 0 L 45 9.949219 L 35 9.949219 Z M 35 0 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 45 5 L 50 5 L 50 9.949219 L 45 9.949219 Z M 45 5 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 51 2 L 57 2 L 57 9.949219 L 51 9.949219 Z M 51 2 "/>
+</clipPath>
+<clipPath id="clip7">
+ <path d="M 73 0 L 76 0 L 76 9.949219 L 73 9.949219 Z M 73 0 "/>
+</clipPath>
+<clipPath id="clip8">
+ <path d="M 82 0 L 85 0 L 85 9.949219 L 82 9.949219 Z M 82 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="2.125" y="7.105872"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="9.693058" y="7.105872"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.378183" y="7.105872"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="19.127929" y="7.105872"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="25.446428" y="7.105872"/>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="35.445187" y="0"/>
+</g>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="45.445903" y="9.948411"/>
+</g>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="51.686365" y="7.105872"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="56.205517" y="8.527617"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="60.867319" y="7.105872"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="67.973191" y="8.527617"/>
+</g>
+<g clip-path="url(#clip7)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="72.634993" y="7.105872"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="76.319167" y="7.105872"/>
+</g>
+<g clip-path="url(#clip8)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="82.069864" y="7.105872"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig40.svg b/doc/figs/tex/fig40.svg
new file mode 100644
index 00000000000..cd6a77bec58
--- /dev/null
+++ b/doc/figs/tex/fig40.svg
@@ -0,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="47.219pt" height="10.423pt" viewBox="0 0 47.219 10.423" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.796875 -3.8125 C 4.796875 -3.84375 4.75 -3.921875 4.75 -3.9375 C 4.75 -3.953125 4.921875 -4.09375 5.03125 -4.15625 L 6.6875 -5.4375 C 7.5625 -6.09375 7.9375 -6.125 8.21875 -6.15625 C 8.296875 -6.15625 8.390625 -6.171875 8.390625 -6.34375 C 8.390625 -6.375 8.359375 -6.453125 8.28125 -6.453125 C 8.078125 -6.453125 7.84375 -6.421875 7.609375 -6.421875 C 7.28125 -6.421875 6.90625 -6.453125 6.5625 -6.453125 C 6.5 -6.453125 6.390625 -6.453125 6.390625 -6.25 C 6.390625 -6.1875 6.4375 -6.15625 6.5 -6.15625 C 6.703125 -6.140625 6.796875 -6.09375 6.796875 -5.953125 C 6.796875 -5.78125 6.515625 -5.5625 6.453125 -5.515625 L 2.78125 -2.6875 L 3.53125 -5.71875 C 3.609375 -6.0625 3.640625 -6.15625 4.328125 -6.15625 C 4.5625 -6.15625 4.640625 -6.15625 4.640625 -6.34375 C 4.640625 -6.421875 4.5625 -6.453125 4.515625 -6.453125 C 4.25 -6.453125 3.5625 -6.421875 3.296875 -6.421875 C 3.03125 -6.421875 2.359375 -6.453125 2.078125 -6.453125 C 2.015625 -6.453125 1.890625 -6.453125 1.890625 -6.265625 C 1.890625 -6.15625 1.984375 -6.15625 2.171875 -6.15625 C 2.296875 -6.15625 2.46875 -6.140625 2.578125 -6.140625 C 2.734375 -6.109375 2.78125 -6.09375 2.78125 -5.984375 C 2.78125 -5.953125 2.78125 -5.921875 2.75 -5.796875 L 1.484375 -0.734375 C 1.390625 -0.375 1.375 -0.296875 0.625 -0.296875 C 0.46875 -0.296875 0.359375 -0.296875 0.359375 -0.109375 C 0.359375 0 0.46875 0 0.5 0 C 0.765625 0 1.4375 -0.03125 1.703125 -0.03125 C 1.890625 -0.03125 2.109375 -0.015625 2.296875 -0.015625 C 2.515625 -0.015625 2.71875 0 2.921875 0 C 2.984375 0 3.109375 0 3.109375 -0.1875 C 3.109375 -0.296875 3.015625 -0.296875 2.84375 -0.296875 C 2.484375 -0.296875 2.234375 -0.296875 2.234375 -0.46875 C 2.234375 -0.53125 2.28125 -0.734375 2.3125 -0.875 C 2.4375 -1.375 2.5625 -1.875 2.6875 -2.359375 L 4.09375 -3.453125 L 5.1875 -0.921875 C 5.296875 -0.65625 5.296875 -0.640625 5.296875 -0.578125 C 5.296875 -0.296875 4.890625 -0.296875 4.8125 -0.296875 C 4.703125 -0.296875 4.609375 -0.296875 4.609375 -0.109375 C 4.609375 0 4.71875 0 4.734375 0 C 5.109375 0 5.515625 -0.03125 5.890625 -0.03125 C 6.09375 -0.03125 6.609375 0 6.8125 0 C 6.859375 0 6.984375 0 6.984375 -0.1875 C 6.984375 -0.296875 6.875 -0.296875 6.796875 -0.296875 C 6.40625 -0.296875 6.28125 -0.390625 6.140625 -0.71875 Z M 4.796875 -3.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.21875 -4.203125 C 2.21875 -4.375 2.203125 -4.390625 2.015625 -4.390625 C 1.59375 -3.96875 0.984375 -3.96875 0.71875 -3.96875 L 0.71875 -3.734375 C 0.875 -3.734375 1.3125 -3.734375 1.671875 -3.90625 L 1.671875 -0.546875 C 1.671875 -0.328125 1.671875 -0.234375 1.015625 -0.234375 L 0.765625 -0.234375 L 0.765625 0 C 0.890625 0 1.703125 -0.03125 1.9375 -0.03125 C 2.140625 -0.03125 2.984375 0 3.125 0 L 3.125 -0.234375 L 2.875 -0.234375 C 2.21875 -0.234375 2.21875 -0.328125 2.21875 -0.546875 Z M 2.21875 -4.203125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 3.0625 -1.5 L 5.078125 -1.5 C 5.171875 -1.5 5.328125 -1.5 5.328125 -1.65625 C 5.328125 -1.8125 5.171875 -1.8125 5.078125 -1.8125 L 3.0625 -1.8125 L 3.0625 -3.84375 C 3.0625 -3.9375 3.0625 -4.09375 2.90625 -4.09375 C 2.734375 -4.09375 2.734375 -3.9375 2.734375 -3.84375 L 2.734375 -1.8125 L 0.703125 -1.8125 C 0.625 -1.8125 0.46875 -1.8125 0.46875 -1.65625 C 0.46875 -1.5 0.609375 -1.5 0.703125 -1.5 L 2.734375 -1.5 L 2.734375 0.53125 C 2.734375 0.625 2.734375 0.78125 2.890625 0.78125 C 3.0625 0.78125 3.0625 0.625 3.0625 0.53125 Z M 3.0625 -1.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.125 2.265625 C 3.125 2.234375 3.125 2.21875 2.96875 2.0625 C 1.78125 0.875 1.484375 -0.921875 1.484375 -2.359375 C 1.484375 -4 1.84375 -5.640625 3 -6.828125 C 3.125 -6.9375 3.125 -6.953125 3.125 -6.984375 C 3.125 -7.046875 3.09375 -7.078125 3.03125 -7.078125 C 2.9375 -7.078125 2.078125 -6.4375 1.53125 -5.234375 C 1.046875 -4.203125 0.9375 -3.15625 0.9375 -2.359375 C 0.9375 -1.625 1.03125 -0.484375 1.5625 0.578125 C 2.125 1.75 2.9375 2.359375 3.03125 2.359375 C 3.09375 2.359375 3.125 2.328125 3.125 2.265625 Z M 3.125 2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.78125 -6.046875 C 2.78125 -6.265625 2.78125 -6.28125 2.5625 -6.28125 C 1.96875 -5.6875 1.140625 -5.6875 0.84375 -5.6875 L 0.84375 -5.390625 C 1.03125 -5.390625 1.578125 -5.390625 2.078125 -5.640625 L 2.078125 -0.75 C 2.078125 -0.40625 2.046875 -0.296875 1.203125 -0.296875 L 0.890625 -0.296875 L 0.890625 0 C 1.234375 -0.03125 2.046875 -0.03125 2.421875 -0.03125 C 2.796875 -0.03125 3.625 -0.03125 3.953125 0 L 3.953125 -0.296875 L 3.65625 -0.296875 C 2.796875 -0.296875 2.78125 -0.390625 2.78125 -0.75 Z M 2.78125 -6.046875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 1.203125 -0.734375 L 2.203125 -1.703125 C 3.671875 -3 4.234375 -3.515625 4.234375 -4.453125 C 4.234375 -5.53125 3.390625 -6.28125 2.234375 -6.28125 C 1.171875 -6.28125 0.46875 -5.421875 0.46875 -4.578125 C 0.46875 -4.046875 0.9375 -4.046875 0.96875 -4.046875 C 1.125 -4.046875 1.46875 -4.15625 1.46875 -4.546875 C 1.46875 -4.796875 1.296875 -5.046875 0.96875 -5.046875 C 0.890625 -5.046875 0.875 -5.046875 0.84375 -5.03125 C 1.0625 -5.640625 1.5625 -6 2.109375 -6 C 2.96875 -6 3.375 -5.234375 3.375 -4.453125 C 3.375 -3.703125 2.90625 -2.953125 2.390625 -2.375 L 0.578125 -0.34375 C 0.46875 -0.25 0.46875 -0.21875 0.46875 0 L 3.96875 0 L 4.234375 -1.640625 L 4 -1.640625 C 3.953125 -1.359375 3.890625 -0.9375 3.796875 -0.796875 C 3.734375 -0.734375 3.109375 -0.734375 2.890625 -0.734375 Z M 1.203125 -0.734375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-4">
+<path style="stroke:none;" d="M 4.5 -5.75 C 4.578125 -5.859375 4.578125 -5.875 4.578125 -6.078125 L 2.28125 -6.078125 C 1.125 -6.078125 1.109375 -6.203125 1.078125 -6.375 L 0.84375 -6.375 L 0.53125 -4.4375 L 0.765625 -4.4375 C 0.796875 -4.59375 0.875 -5.1875 1 -5.296875 C 1.0625 -5.34375 1.796875 -5.34375 1.921875 -5.34375 L 3.875 -5.34375 C 3.78125 -5.203125 3.03125 -4.171875 2.828125 -3.859375 C 1.96875 -2.578125 1.65625 -1.28125 1.65625 -0.3125 C 1.65625 -0.21875 1.65625 0.203125 2.09375 0.203125 C 2.53125 0.203125 2.53125 -0.21875 2.53125 -0.3125 L 2.53125 -0.796875 C 2.53125 -1.3125 2.5625 -1.828125 2.640625 -2.34375 C 2.671875 -2.5625 2.796875 -3.375 3.21875 -3.953125 Z M 4.5 -5.75 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-5">
+<path style="stroke:none;" d="M 4.34375 -3.015625 C 4.34375 -3.78125 4.296875 -4.53125 3.96875 -5.234375 C 3.53125 -6.140625 2.75 -6.28125 2.359375 -6.28125 C 1.796875 -6.28125 1.109375 -6.046875 0.71875 -5.15625 C 0.421875 -4.515625 0.375 -3.78125 0.375 -3.015625 C 0.375 -2.3125 0.40625 -1.46875 0.796875 -0.75 C 1.203125 0.015625 1.890625 0.203125 2.34375 0.203125 C 2.859375 0.203125 3.578125 0.015625 3.984375 -0.890625 C 4.296875 -1.53125 4.34375 -2.28125 4.34375 -3.015625 Z M 2.34375 0 C 1.984375 0 1.421875 -0.234375 1.25 -1.140625 C 1.15625 -1.703125 1.15625 -2.578125 1.15625 -3.140625 C 1.15625 -3.734375 1.15625 -4.359375 1.234375 -4.875 C 1.40625 -6 2.109375 -6.078125 2.34375 -6.078125 C 2.65625 -6.078125 3.28125 -5.90625 3.46875 -4.96875 C 3.5625 -4.4375 3.5625 -3.734375 3.5625 -3.140625 C 3.5625 -2.421875 3.5625 -1.78125 3.453125 -1.1875 C 3.3125 -0.28125 2.78125 0 2.34375 0 Z M 2.34375 0 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-6">
+<path style="stroke:none;" d="M 2.734375 -2.359375 C 2.734375 -3.09375 2.625 -4.234375 2.109375 -5.296875 C 1.53125 -6.46875 0.734375 -7.078125 0.625 -7.078125 C 0.578125 -7.078125 0.53125 -7.046875 0.53125 -6.984375 C 0.53125 -6.953125 0.53125 -6.9375 0.71875 -6.765625 C 1.640625 -5.828125 2.1875 -4.328125 2.1875 -2.359375 C 2.1875 -0.75 1.828125 0.921875 0.65625 2.109375 C 0.53125 2.21875 0.53125 2.234375 0.53125 2.265625 C 0.53125 2.328125 0.578125 2.359375 0.625 2.359375 C 0.734375 2.359375 1.578125 1.71875 2.140625 0.515625 C 2.609375 -0.515625 2.734375 -1.5625 2.734375 -2.359375 Z M 2.734375 -2.359375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 14 0 L 39 0 L 39 9.875 L 14 9.875 Z M 14 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.868409" y="7.515931"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.885591" y="8.932511"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="13.121119" y="7.515931"/>
+ <use xlink:href="#glyph2-2" x="16.792342" y="7.515931"/>
+ <use xlink:href="#glyph2-3" x="21.51235" y="7.515931"/>
+ <use xlink:href="#glyph2-4" x="26.232358" y="7.515931"/>
+ <use xlink:href="#glyph2-5" x="30.952366" y="7.515931"/>
+ <use xlink:href="#glyph2-6" x="35.672374" y="7.515931"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="39.343492" y="4.090554"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig41.svg b/doc/figs/tex/fig41.svg
new file mode 100644
index 00000000000..f2a072cea11
--- /dev/null
+++ b/doc/figs/tex/fig41.svg
@@ -0,0 +1,87 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="46.492pt" height="9.963pt" viewBox="0 0 46.492 9.963" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.265625 2.359375 C 3.265625 2.34375 3.265625 2.3125 3.09375 2.15625 C 1.859375 0.90625 1.546875 -0.953125 1.546875 -2.46875 C 1.546875 -4.1875 1.921875 -5.890625 3.140625 -7.125 C 3.265625 -7.25 3.265625 -7.265625 3.265625 -7.296875 C 3.265625 -7.359375 3.21875 -7.390625 3.171875 -7.390625 C 3.0625 -7.390625 2.171875 -6.71875 1.59375 -5.46875 C 1.09375 -4.390625 0.96875 -3.296875 0.96875 -2.46875 C 0.96875 -1.703125 1.078125 -0.5 1.625 0.609375 C 2.21875 1.828125 3.0625 2.46875 3.171875 2.46875 C 3.21875 2.46875 3.265625 2.4375 3.265625 2.359375 Z M 3.265625 2.359375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 4.03125 -2.265625 L 6.78125 -2.265625 C 6.921875 -2.265625 7.109375 -2.265625 7.109375 -2.46875 C 7.109375 -2.65625 6.921875 -2.65625 6.78125 -2.65625 L 4.03125 -2.65625 L 4.03125 -5.421875 C 4.03125 -5.5625 4.03125 -5.75 3.828125 -5.75 C 3.640625 -5.75 3.640625 -5.5625 3.640625 -5.421875 L 3.640625 -2.65625 L 0.875 -2.65625 C 0.734375 -2.65625 0.546875 -2.65625 0.546875 -2.46875 C 0.546875 -2.265625 0.734375 -2.265625 0.875 -2.265625 L 3.640625 -2.265625 L 3.640625 0.5 C 3.640625 0.625 3.640625 0.8125 3.828125 0.8125 C 4.03125 0.8125 4.03125 0.625 4.03125 0.5 Z M 4.03125 -2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 2.84375 -2.46875 C 2.84375 -3.234375 2.734375 -4.421875 2.203125 -5.546875 C 1.609375 -6.75 0.765625 -7.390625 0.65625 -7.390625 C 0.59375 -7.390625 0.5625 -7.359375 0.5625 -7.296875 C 0.5625 -7.265625 0.5625 -7.25 0.75 -7.0625 C 1.71875 -6.09375 2.28125 -4.53125 2.28125 -2.46875 C 2.28125 -0.78125 1.90625 0.953125 0.6875 2.203125 C 0.5625 2.3125 0.5625 2.34375 0.5625 2.359375 C 0.5625 2.421875 0.59375 2.46875 0.65625 2.46875 C 0.765625 2.46875 1.640625 1.796875 2.234375 0.546875 C 2.734375 -0.546875 2.84375 -1.640625 2.84375 -2.46875 Z M 2.84375 -2.46875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2 -0.015625 C 2 -0.65625 1.75 -1.046875 1.375 -1.046875 C 1.046875 -1.046875 0.84375 -0.796875 0.84375 -0.515625 C 0.84375 -0.25 1.046875 0 1.375 0 C 1.484375 0 1.609375 -0.046875 1.71875 -0.125 C 1.75 -0.140625 1.75 -0.15625 1.765625 -0.15625 C 1.78125 -0.15625 1.78125 -0.140625 1.78125 -0.015625 C 1.78125 0.71875 1.4375 1.3125 1.109375 1.640625 C 1 1.75 1 1.765625 1 1.796875 C 1 1.859375 1.0625 1.90625 1.109375 1.90625 C 1.21875 1.90625 2 1.140625 2 -0.015625 Z M 2 -0.015625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 4.328125 -7.015625 C 4.375 -7.140625 4.375 -7.1875 4.375 -7.203125 C 4.375 -7.3125 4.28125 -7.390625 4.1875 -7.390625 C 4.109375 -7.390625 4.046875 -7.359375 4.015625 -7.3125 L 0.59375 2.09375 C 0.546875 2.21875 0.546875 2.25 0.546875 2.265625 C 0.546875 2.375 0.625 2.46875 0.734375 2.46875 C 0.875 2.46875 0.890625 2.390625 0.953125 2.234375 Z M 4.328125 -7.015625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 6.5 -2.265625 C 6.671875 -2.265625 6.84375 -2.265625 6.84375 -2.46875 C 6.84375 -2.65625 6.671875 -2.65625 6.5 -2.65625 L 1.15625 -2.65625 C 1 -2.65625 0.8125 -2.65625 0.8125 -2.46875 C 0.8125 -2.265625 1 -2.265625 1.15625 -2.265625 Z M 6.5 -2.265625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 2.71875 -4.203125 C 2.71875 -4.34375 2.71875 -4.578125 2.46875 -4.578125 C 2.3125 -4.578125 2.171875 -4.453125 2.203125 -4.328125 L 2.203125 -4.203125 L 2.34375 -2.671875 L 1.078125 -3.59375 C 1 -3.640625 0.96875 -3.65625 0.90625 -3.65625 C 0.765625 -3.65625 0.640625 -3.515625 0.640625 -3.375 C 0.640625 -3.21875 0.734375 -3.1875 0.84375 -3.140625 L 2.234375 -2.46875 L 0.875 -1.796875 C 0.71875 -1.71875 0.640625 -1.6875 0.640625 -1.53125 C 0.640625 -1.390625 0.765625 -1.265625 0.90625 -1.265625 C 0.96875 -1.265625 1 -1.265625 1.25 -1.453125 L 2.34375 -2.25 L 2.203125 -0.59375 C 2.203125 -0.390625 2.375 -0.328125 2.453125 -0.328125 C 2.578125 -0.328125 2.71875 -0.40625 2.71875 -0.59375 L 2.578125 -2.25 L 3.828125 -1.328125 C 3.921875 -1.28125 3.9375 -1.265625 4.015625 -1.265625 C 4.15625 -1.265625 4.28125 -1.40625 4.28125 -1.53125 C 4.28125 -1.6875 4.1875 -1.734375 4.078125 -1.796875 C 3.484375 -2.09375 3.453125 -2.09375 2.6875 -2.453125 L 4.046875 -3.109375 C 4.203125 -3.1875 4.28125 -3.234375 4.28125 -3.375 C 4.28125 -3.53125 4.15625 -3.65625 4.015625 -3.65625 C 3.9375 -3.65625 3.921875 -3.65625 3.671875 -3.46875 L 2.578125 -2.671875 Z M 2.71875 -4.203125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.0351562 L 11 0.0351562 L 11 9.890625 L 0 9.890625 Z M 0 0.0351562 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 12 6 L 14 6 L 14 9.890625 L 12 9.890625 Z M 12 6 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 24 6 L 26 6 L 26 9.890625 L 24 9.890625 Z M 24 6 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 28 0.0351562 L 35 0.0351562 L 35 9.890625 L 28 9.890625 Z M 28 0.0351562 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 42 0.0351562 L 45.988281 0.0351562 L 45.988281 9.890625 L 42 9.890625 Z M 42 0.0351562 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="7.426781"/>
+ <use xlink:href="#glyph0-2" x="3.832578" y="7.426781"/>
+</g>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="11.497373" y="7.426781"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="15.877513" y="7.426781"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="23.542757" y="7.426781"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="27.926225" y="7.426781"/>
+ <use xlink:href="#glyph1-1" x="32.853685" y="7.426781"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="37.2302" y="7.426781"/>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="42.157363" y="7.426781"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig42.svg b/doc/figs/tex/fig42.svg
new file mode 100644
index 00000000000..8be51763347
--- /dev/null
+++ b/doc/figs/tex/fig42.svg
@@ -0,0 +1,43 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="18.905pt" height="8.797pt" viewBox="0 0 18.905 8.797" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.953125 -3.9375 C 4.9375 -3.96875 4.90625 -4.046875 4.90625 -4.0625 C 4.90625 -4.078125 5.078125 -4.21875 5.1875 -4.296875 L 6.890625 -5.609375 C 7.8125 -6.28125 8.1875 -6.3125 8.484375 -6.34375 C 8.5625 -6.359375 8.65625 -6.359375 8.65625 -6.546875 C 8.65625 -6.578125 8.625 -6.65625 8.546875 -6.65625 C 8.328125 -6.65625 8.09375 -6.625 7.859375 -6.625 C 7.5 -6.625 7.125 -6.65625 6.78125 -6.65625 C 6.703125 -6.65625 6.59375 -6.65625 6.59375 -6.453125 C 6.59375 -6.390625 6.640625 -6.359375 6.703125 -6.34375 C 6.921875 -6.328125 7.015625 -6.28125 7.015625 -6.140625 C 7.015625 -5.96875 6.71875 -5.75 6.65625 -5.6875 L 2.859375 -2.78125 L 3.640625 -5.90625 C 3.734375 -6.25 3.75 -6.34375 4.453125 -6.34375 C 4.703125 -6.34375 4.796875 -6.34375 4.796875 -6.546875 C 4.796875 -6.625 4.71875 -6.65625 4.65625 -6.65625 C 4.375 -6.65625 3.671875 -6.625 3.40625 -6.625 C 3.125 -6.625 2.4375 -6.65625 2.15625 -6.65625 C 2.078125 -6.65625 1.953125 -6.65625 1.953125 -6.46875 C 1.953125 -6.34375 2.046875 -6.34375 2.234375 -6.34375 C 2.359375 -6.34375 2.546875 -6.34375 2.65625 -6.328125 C 2.8125 -6.3125 2.875 -6.28125 2.875 -6.171875 C 2.875 -6.125 2.859375 -6.109375 2.828125 -5.984375 L 1.53125 -0.765625 C 1.4375 -0.375 1.40625 -0.296875 0.640625 -0.296875 C 0.484375 -0.296875 0.375 -0.296875 0.375 -0.109375 C 0.375 0 0.484375 0 0.515625 0 C 0.78125 0 1.484375 -0.03125 1.75 -0.03125 C 1.953125 -0.03125 2.171875 -0.015625 2.375 -0.015625 C 2.59375 -0.015625 2.796875 0 3.015625 0 C 3.078125 0 3.203125 0 3.203125 -0.1875 C 3.203125 -0.296875 3.109375 -0.296875 2.9375 -0.296875 C 2.5625 -0.296875 2.296875 -0.296875 2.296875 -0.484375 C 2.296875 -0.546875 2.359375 -0.765625 2.390625 -0.90625 C 2.515625 -1.40625 2.640625 -1.921875 2.78125 -2.4375 L 4.21875 -3.5625 L 5.359375 -0.9375 C 5.46875 -0.6875 5.46875 -0.65625 5.46875 -0.609375 C 5.46875 -0.3125 5.046875 -0.296875 4.96875 -0.296875 C 4.859375 -0.296875 4.75 -0.296875 4.75 -0.109375 C 4.75 0 4.875 0 4.890625 0 C 5.28125 0 5.6875 -0.03125 6.078125 -0.03125 C 6.28125 -0.03125 6.8125 0 7.03125 0 C 7.078125 0 7.203125 0 7.203125 -0.1875 C 7.203125 -0.296875 7.09375 -0.296875 7.015625 -0.296875 C 6.609375 -0.3125 6.484375 -0.40625 6.34375 -0.734375 Z M 4.953125 -3.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 0.328125 1.6875 C 0.296875 1.796875 0.296875 1.828125 0.296875 1.84375 C 0.296875 1.984375 0.40625 2.109375 0.5625 2.109375 C 0.765625 2.109375 0.890625 1.921875 0.90625 1.890625 C 0.953125 1.8125 1.265625 0.5 1.53125 -0.546875 C 1.71875 -0.15625 2.03125 0.109375 2.484375 0.109375 C 3.625 0.109375 4.890625 -1.265625 4.890625 -2.71875 C 4.890625 -3.75 4.25 -4.296875 3.53125 -4.296875 C 2.59375 -4.296875 1.5625 -3.328125 1.28125 -2.140625 Z M 2.484375 -0.109375 C 1.796875 -0.109375 1.640625 -0.890625 1.640625 -0.96875 C 1.640625 -1.015625 1.6875 -1.203125 1.71875 -1.328125 C 2 -2.421875 2.09375 -2.78125 2.3125 -3.15625 C 2.71875 -3.875 3.21875 -4.09375 3.515625 -4.09375 C 3.875 -4.09375 4.1875 -3.8125 4.1875 -3.140625 C 4.1875 -2.59375 3.90625 -1.515625 3.640625 -1.03125 C 3.3125 -0.421875 2.859375 -0.109375 2.484375 -0.109375 Z M 2.484375 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.203125 -1.703125 C 2.765625 -1.9375 3.015625 -2.03125 3.1875 -2.125 C 3.3125 -2.171875 3.375 -2.203125 3.375 -2.328125 C 3.375 -2.453125 3.28125 -2.546875 3.15625 -2.546875 C 3.109375 -2.546875 3.09375 -2.546875 3.015625 -2.484375 L 2.09375 -1.859375 L 2.1875 -2.875 C 2.203125 -3 2.1875 -3.171875 1.984375 -3.171875 C 1.90625 -3.171875 1.78125 -3.109375 1.78125 -2.96875 C 1.78125 -2.90625 1.8125 -2.703125 1.8125 -2.625 C 1.828125 -2.515625 1.875 -2.015625 1.890625 -1.859375 L 0.96875 -2.484375 C 0.90625 -2.53125 0.875 -2.546875 0.8125 -2.546875 C 0.6875 -2.546875 0.609375 -2.453125 0.609375 -2.328125 C 0.609375 -2.1875 0.6875 -2.15625 0.75 -2.125 L 1.78125 -1.703125 C 1.21875 -1.453125 0.96875 -1.359375 0.796875 -1.28125 C 0.671875 -1.21875 0.609375 -1.203125 0.609375 -1.0625 C 0.609375 -0.953125 0.6875 -0.859375 0.8125 -0.859375 C 0.859375 -0.859375 0.875 -0.859375 0.953125 -0.90625 L 1.890625 -1.53125 L 1.78125 -0.4375 C 1.78125 -0.28125 1.90625 -0.234375 1.984375 -0.234375 C 2.078125 -0.234375 2.203125 -0.28125 2.203125 -0.4375 C 2.203125 -0.5 2.171875 -0.703125 2.171875 -0.765625 C 2.15625 -0.890625 2.109375 -1.375 2.09375 -1.53125 L 2.90625 -0.984375 C 3.09375 -0.859375 3.09375 -0.859375 3.15625 -0.859375 C 3.28125 -0.859375 3.375 -0.953125 3.375 -1.0625 C 3.375 -1.203125 3.296875 -1.234375 3.234375 -1.265625 Z M 2.203125 -1.703125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.167969 0 L 9 0 L 9 7 L 0.167969 7 Z M 0.167969 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 13 2 L 18.644531 2 L 18.644531 8.597656 L 13 8.597656 Z M 13 2 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.166778" y="6.705269"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="9.133853" y="3.17083"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="13.610549" y="6.705269"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig43.svg b/doc/figs/tex/fig43.svg
new file mode 100644
index 00000000000..f2c928f67e8
--- /dev/null
+++ b/doc/figs/tex/fig43.svg
@@ -0,0 +1,24 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="9.963pt" height="6.42pt" viewBox="0 0 9.963 6.42" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.203125 -2.921875 C 4.203125 -3.65625 4.15625 -4.390625 3.84375 -5.0625 C 3.421875 -5.9375 2.671875 -6.09375 2.28125 -6.09375 C 1.734375 -6.09375 1.0625 -5.84375 0.6875 -5 C 0.40625 -4.375 0.359375 -3.65625 0.359375 -2.921875 C 0.359375 -2.234375 0.390625 -1.421875 0.765625 -0.71875 C 1.15625 0.015625 1.828125 0.203125 2.28125 0.203125 C 2.765625 0.203125 3.46875 0.015625 3.859375 -0.859375 C 4.15625 -1.484375 4.203125 -2.203125 4.203125 -2.921875 Z M 2.28125 0 C 1.921875 0 1.375 -0.234375 1.21875 -1.109375 C 1.109375 -1.65625 1.109375 -2.5 1.109375 -3.03125 C 1.109375 -3.625 1.109375 -4.21875 1.1875 -4.71875 C 1.359375 -5.796875 2.046875 -5.890625 2.28125 -5.890625 C 2.578125 -5.890625 3.1875 -5.71875 3.359375 -4.8125 C 3.453125 -4.3125 3.453125 -3.609375 3.453125 -3.03125 C 3.453125 -2.34375 3.453125 -1.734375 3.34375 -1.140625 C 3.203125 -0.28125 2.6875 0 2.28125 0 Z M 2.28125 0 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.394531 0 L 9.535156 0 L 9.535156 5.886719 L 0.394531 5.886719 Z M 0.394531 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.395786" y="5.888057"/>
+ <use xlink:href="#glyph0-1" x="4.964349" y="5.888057"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig44.svg b/doc/figs/tex/fig44.svg
new file mode 100644
index 00000000000..c63d8cd345a
--- /dev/null
+++ b/doc/figs/tex/fig44.svg
@@ -0,0 +1,43 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="23.426pt" height="6.808pt" viewBox="0 0 23.426 6.808" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.625 -5.875 C 3.703125 -6.21875 3.734375 -6.3125 4.5 -6.3125 C 4.734375 -6.3125 4.8125 -6.3125 4.8125 -6.5 C 4.8125 -6.609375 4.703125 -6.609375 4.671875 -6.609375 C 4.390625 -6.609375 3.671875 -6.59375 3.390625 -6.59375 C 3.09375 -6.59375 2.390625 -6.609375 2.109375 -6.609375 C 2.03125 -6.609375 1.90625 -6.609375 1.90625 -6.421875 C 1.90625 -6.3125 2 -6.3125 2.171875 -6.3125 C 2.59375 -6.3125 2.84375 -6.3125 2.84375 -6.125 C 2.84375 -6.078125 2.84375 -6.0625 2.828125 -5.984375 L 1.515625 -0.75 C 1.4375 -0.390625 1.40625 -0.296875 0.640625 -0.296875 C 0.421875 -0.296875 0.328125 -0.296875 0.328125 -0.109375 C 0.328125 0 0.453125 0 0.46875 0 C 0.75 0 1.46875 -0.03125 1.75 -0.03125 C 2.03125 -0.03125 2.75 0 3.046875 0 C 3.125 0 3.234375 0 3.234375 -0.1875 C 3.234375 -0.296875 3.15625 -0.296875 2.9375 -0.296875 C 2.765625 -0.296875 2.71875 -0.296875 2.53125 -0.3125 C 2.328125 -0.34375 2.28125 -0.375 2.28125 -0.484375 C 2.28125 -0.5625 2.3125 -0.640625 2.328125 -0.703125 Z M 3.625 -5.875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 6.65625 -3.171875 C 6.796875 -3.171875 6.984375 -3.171875 6.984375 -3.359375 C 6.984375 -3.5625 6.796875 -3.5625 6.671875 -3.5625 L 0.859375 -3.5625 C 0.71875 -3.5625 0.546875 -3.5625 0.546875 -3.359375 C 0.546875 -3.171875 0.71875 -3.171875 0.875 -3.171875 Z M 6.671875 -1.28125 C 6.796875 -1.28125 6.984375 -1.28125 6.984375 -1.484375 C 6.984375 -1.671875 6.796875 -1.671875 6.65625 -1.671875 L 0.875 -1.671875 C 0.71875 -1.671875 0.546875 -1.671875 0.546875 -1.484375 C 0.546875 -1.28125 0.71875 -1.28125 0.859375 -1.28125 Z M 6.671875 -1.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 4.453125 -3.09375 C 4.453125 -3.875 4.40625 -4.65625 4.0625 -5.359375 C 3.625 -6.296875 2.828125 -6.453125 2.421875 -6.453125 C 1.84375 -6.453125 1.140625 -6.203125 0.734375 -5.296875 C 0.421875 -4.625 0.375 -3.875 0.375 -3.09375 C 0.375 -2.375 0.421875 -1.5 0.8125 -0.765625 C 1.234375 0.015625 1.9375 0.21875 2.40625 0.21875 C 2.9375 0.21875 3.671875 0.015625 4.09375 -0.90625 C 4.40625 -1.578125 4.453125 -2.328125 4.453125 -3.09375 Z M 2.40625 0 C 2.03125 0 1.46875 -0.234375 1.28125 -1.171875 C 1.1875 -1.75 1.1875 -2.640625 1.1875 -3.21875 C 1.1875 -3.84375 1.1875 -4.46875 1.265625 -5 C 1.4375 -6.15625 2.171875 -6.234375 2.40625 -6.234375 C 2.734375 -6.234375 3.375 -6.0625 3.5625 -5.109375 C 3.65625 -4.5625 3.65625 -3.828125 3.65625 -3.21875 C 3.65625 -2.484375 3.65625 -1.828125 3.546875 -1.203125 C 3.40625 -0.296875 2.84375 0 2.40625 0 Z M 2.40625 0 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.0429688 0 L 5 0 L 5 6.621094 L 0.0429688 6.621094 Z M 0.0429688 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 18 0 L 22.824219 0 L 22.824219 6.621094 L 18 6.621094 Z M 18 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.0421429" y="6.621266"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.753662" y="6.621266"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.983667" y="6.621266"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig45.svg b/doc/figs/tex/fig45.svg
new file mode 100644
index 00000000000..58c801d5579
--- /dev/null
+++ b/doc/figs/tex/fig45.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="6.683pt" height="6.808pt" viewBox="0 0 6.683 6.808" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 6.140625 -6.609375 C 6.140625 -6.640625 6.125 -6.703125 6.03125 -6.703125 C 5.984375 -6.703125 5.96875 -6.703125 5.859375 -6.5625 L 5.40625 -6.015625 C 5.15625 -6.46875 4.65625 -6.703125 4.046875 -6.703125 C 2.828125 -6.703125 1.6875 -5.609375 1.6875 -4.46875 C 1.6875 -3.6875 2.203125 -3.25 2.6875 -3.109375 L 3.703125 -2.84375 C 4.046875 -2.765625 4.578125 -2.609375 4.578125 -1.84375 C 4.578125 -0.984375 3.796875 -0.078125 2.859375 -0.078125 C 2.25 -0.078125 1.203125 -0.296875 1.203125 -1.46875 C 1.203125 -1.703125 1.25 -1.9375 1.25 -1.984375 C 1.265625 -2.03125 1.28125 -2.03125 1.28125 -2.0625 C 1.28125 -2.15625 1.203125 -2.15625 1.15625 -2.15625 C 1.109375 -2.15625 1.09375 -2.15625 1.0625 -2.125 C 1.03125 -2.078125 0.5 0.078125 0.5 0.109375 C 0.5 0.171875 0.546875 0.203125 0.59375 0.203125 C 0.640625 0.203125 0.65625 0.203125 0.765625 0.0625 L 1.234375 -0.46875 C 1.640625 0.078125 2.296875 0.203125 2.84375 0.203125 C 4.140625 0.203125 5.265625 -1.0625 5.265625 -2.234375 C 5.265625 -2.890625 4.9375 -3.21875 4.796875 -3.34375 C 4.578125 -3.5625 4.4375 -3.609375 3.59375 -3.828125 C 3.375 -3.875 3.03125 -3.984375 2.953125 -4 C 2.6875 -4.078125 2.375 -4.359375 2.375 -4.859375 C 2.375 -5.640625 3.125 -6.4375 4.03125 -6.4375 C 4.828125 -6.4375 5.40625 -6.03125 5.40625 -4.96875 C 5.40625 -4.65625 5.359375 -4.484375 5.359375 -4.4375 C 5.359375 -4.421875 5.359375 -4.34375 5.484375 -4.34375 C 5.578125 -4.34375 5.578125 -4.375 5.625 -4.53125 Z M 6.140625 -6.609375 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.0625 L 6.378906 0.0625 L 6.378906 6.5625 L 0 6.5625 Z M 0 0.0625 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="6.562195"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig5.svg b/doc/figs/tex/fig5.svg
new file mode 100644
index 00000000000..285012c74e7
--- /dev/null
+++ b/doc/figs/tex/fig5.svg
@@ -0,0 +1,114 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="66.586pt" height="11.994pt" viewBox="0 0 66.586 11.994" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.453125 -6.765625 C 2.046875 -6.765625 0.984375 -6.09375 0.578125 -5.625 C 0.234375 -5.234375 0.203125 -4.9375 0.203125 -4.921875 C 0.203125 -4.859375 0.25 -4.84375 0.3125 -4.84375 C 0.46875 -4.84375 0.6875 -4.984375 0.765625 -5.03125 C 0.984375 -5.171875 1.015625 -5.234375 1.0625 -5.421875 C 1.203125 -5.8125 1.484375 -6.15625 2.734375 -6.21875 C 2.5625 -4 1.96875 -1.828125 1.125 0.25 C 1.0625 0.390625 1.0625 0.421875 1.0625 0.421875 C 1.0625 0.453125 1.09375 0.5 1.171875 0.5 C 1.328125 0.5 1.796875 0.28125 1.90625 0.015625 C 2.421875 -1.1875 3.234375 -3.46875 3.53125 -6.21875 L 4.046875 -6.21875 C 5.265625 -6.21875 6.421875 -5.75 6.421875 -4.765625 C 6.421875 -4.015625 5.703125 -2.640625 3.78125 -2.578125 C 3.578125 -2.5625 3.46875 -2.5625 3.1875 -2.390625 C 3.015625 -2.265625 2.9375 -2.15625 2.9375 -2.09375 C 2.9375 -2.03125 2.984375 -2.03125 3.125 -2.03125 C 4.921875 -2.03125 7.265625 -3.5625 7.265625 -5.1875 C 7.265625 -6.3125 5.921875 -6.765625 4.78125 -6.765625 Z M 3.453125 -6.765625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-2">
+<path style="stroke:none;" d="M 7.15625 -0.3125 C 7.109375 -0.3125 6.953125 -0.296875 6.921875 -0.296875 C 6.140625 -0.296875 5.609375 -1.0625 5.28125 -1.578125 C 5.1875 -1.75 4.90625 -2.15625 4.796875 -2.328125 C 5.046875 -2.859375 5.703125 -4.09375 6.890625 -4.09375 C 6.953125 -4.09375 7.046875 -4.09375 7.15625 -4.0625 C 7.15625 -4.3125 7.140625 -4.328125 7.125 -4.34375 C 7.046875 -4.375 6.90625 -4.375 6.8125 -4.375 C 5.5625 -4.375 4.828125 -3.171875 4.59375 -2.671875 C 4.1875 -3.28125 4.046875 -3.5 3.6875 -3.796875 C 3.078125 -4.328125 2.53125 -4.375 2.28125 -4.375 C 1.1875 -4.375 0.5625 -3.265625 0.5625 -2.125 C 0.5625 -1.015625 1.171875 0.109375 2.265625 0.109375 C 3.515625 0.109375 4.25 -1.09375 4.484375 -1.59375 C 4.890625 -0.984375 5.015625 -0.765625 5.390625 -0.46875 C 6 0.0625 6.53125 0.109375 6.78125 0.109375 C 6.90625 0.109375 7.0625 0.09375 7.15625 0.0625 Z M 4.265625 -1.9375 C 4.03125 -1.40625 3.375 -0.171875 2.1875 -0.171875 C 1.234375 -0.171875 0.765625 -1.234375 0.765625 -2.125 C 0.765625 -3.109375 1.328125 -3.96875 2.15625 -3.96875 C 2.9375 -3.96875 3.453125 -3.203125 3.796875 -2.6875 C 3.890625 -2.515625 4.15625 -2.109375 4.265625 -1.9375 Z M 4.265625 -1.9375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-3">
+<path style="stroke:none;" d="M 1.578125 -7.078125 C 1.578125 -7.25 1.578125 -7.4375 1.375 -7.4375 C 1.171875 -7.4375 1.171875 -7.25 1.171875 -7.078125 L 1.171875 2.125 C 1.171875 2.296875 1.171875 2.484375 1.375 2.484375 C 1.578125 2.484375 1.578125 2.296875 1.578125 2.125 Z M 1.578125 -7.078125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph0-4">
+<path style="stroke:none;" d="M 4.8125 -6.15625 L 6.453125 -6.15625 C 7.765625 -6.15625 8.265625 -6.90625 8.265625 -7.03125 C 8.265625 -7.078125 8.21875 -7.109375 8.171875 -7.109375 C 8.0625 -7.109375 7.8125 -7 7.5625 -6.828125 C 7.484375 -6.765625 7.453125 -6.765625 7.265625 -6.765625 L 2.9375 -6.765625 C 1.71875 -6.765625 0.34375 -5.703125 0.34375 -4.890625 C 0.34375 -4.828125 0.34375 -4.78125 0.421875 -4.78125 C 0.65625 -4.78125 1.28125 -5.109375 1.296875 -5.34375 C 1.3125 -5.515625 1.328125 -5.703125 1.53125 -5.953125 C 1.625 -6.078125 1.703125 -6.15625 2.140625 -6.15625 L 4.109375 -6.15625 C 3.9375 -6.046875 3.90625 -5.890625 3.890625 -5.796875 L 2.75 -1.3125 C 2.640625 -0.828125 2.421875 -0.203125 2.140625 0.453125 C 2.078125 0.5625 2.078125 0.578125 2.078125 0.609375 C 2.078125 0.65625 2.125 0.671875 2.171875 0.671875 C 2.375 0.671875 2.859375 0.40625 3 0.203125 C 3.0625 0.09375 3.5 -0.90625 3.703125 -1.734375 Z M 4.8125 -6.15625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.28125 2.375 C 3.28125 2.34375 3.28125 2.328125 3.109375 2.15625 C 1.875 0.90625 1.5625 -0.953125 1.5625 -2.484375 C 1.5625 -4.203125 1.9375 -5.921875 3.15625 -7.15625 C 3.28125 -7.28125 3.28125 -7.296875 3.28125 -7.328125 C 3.28125 -7.40625 3.234375 -7.4375 3.1875 -7.4375 C 3.078125 -7.4375 2.1875 -6.75 1.609375 -5.5 C 1.09375 -4.40625 0.984375 -3.3125 0.984375 -2.484375 C 0.984375 -1.703125 1.09375 -0.5 1.640625 0.609375 C 2.234375 1.828125 3.078125 2.484375 3.1875 2.484375 C 3.234375 2.484375 3.28125 2.453125 3.28125 2.375 Z M 3.28125 2.375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.859375 -2.484375 C 2.859375 -3.25 2.75 -4.453125 2.203125 -5.5625 C 1.609375 -6.78125 0.765625 -7.4375 0.65625 -7.4375 C 0.609375 -7.4375 0.5625 -7.390625 0.5625 -7.328125 C 0.5625 -7.296875 0.5625 -7.28125 0.75 -7.109375 C 1.71875 -6.125 2.28125 -4.546875 2.28125 -2.484375 C 2.28125 -0.78125 1.921875 0.953125 0.6875 2.203125 C 0.5625 2.328125 0.5625 2.34375 0.5625 2.375 C 0.5625 2.4375 0.609375 2.484375 0.65625 2.484375 C 0.765625 2.484375 1.65625 1.796875 2.234375 0.546875 C 2.75 -0.546875 2.859375 -1.640625 2.859375 -2.484375 Z M 2.859375 -2.484375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.421875 -2.4375 L 4.59375 -3.71875 C 4.71875 -3.859375 4.78125 -3.9375 5.59375 -3.9375 L 5.59375 -4.390625 C 5.25 -4.375 4.734375 -4.375 4.6875 -4.375 C 4.4375 -4.375 3.9375 -4.390625 3.671875 -4.390625 L 3.671875 -3.9375 C 3.796875 -3.9375 3.921875 -3.90625 4.046875 -3.84375 C 4 -3.78125 4 -3.765625 3.96875 -3.71875 L 3.125 -2.796875 L 2.15625 -3.9375 L 2.5625 -3.9375 L 2.5625 -4.390625 C 2.296875 -4.390625 1.671875 -4.375 1.359375 -4.375 C 1.046875 -4.375 0.59375 -4.390625 0.265625 -4.390625 L 0.265625 -3.9375 L 0.96875 -3.9375 L 2.515625 -2.109375 L 1.21875 -0.65625 C 1.046875 -0.46875 0.6875 -0.46875 0.21875 -0.46875 L 0.21875 0 C 0.5625 -0.015625 1.078125 -0.03125 1.125 -0.03125 C 1.375 -0.03125 1.953125 -0.015625 2.15625 0 L 2.15625 -0.46875 C 1.96875 -0.46875 1.78125 -0.515625 1.78125 -0.578125 C 1.78125 -0.578125 1.78125 -0.59375 1.859375 -0.671875 L 2.8125 -1.75 L 3.90625 -0.46875 L 3.515625 -0.46875 L 3.515625 0 C 3.78125 -0.015625 4.375 -0.03125 4.703125 -0.03125 C 5.015625 -0.03125 5.46875 -0.015625 5.796875 0 L 5.796875 -0.46875 L 5.09375 -0.46875 Z M 3.421875 -2.4375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 3.5 -1.265625 L 3.265625 -1.265625 C 3.25 -1.109375 3.171875 -0.703125 3.09375 -0.625 C 3.03125 -0.59375 2.5 -0.59375 2.40625 -0.59375 L 1.125 -0.59375 C 1.859375 -1.234375 2.09375 -1.421875 2.515625 -1.75 C 3.03125 -2.171875 3.5 -2.59375 3.5 -3.25 C 3.5 -4.09375 2.765625 -4.609375 1.875 -4.609375 C 1.015625 -4.609375 0.4375 -4 0.4375 -3.359375 C 0.4375 -3.015625 0.734375 -2.96875 0.8125 -2.96875 C 0.96875 -2.96875 1.171875 -3.09375 1.171875 -3.34375 C 1.171875 -3.46875 1.125 -3.71875 0.765625 -3.71875 C 0.984375 -4.203125 1.453125 -4.359375 1.78125 -4.359375 C 2.46875 -4.359375 2.828125 -3.8125 2.828125 -3.25 C 2.828125 -2.65625 2.40625 -2.171875 2.171875 -1.921875 L 0.5 -0.265625 C 0.4375 -0.203125 0.4375 -0.1875 0.4375 0 L 3.296875 0 Z M 3.5 -1.265625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 8 2 L 11 2 L 11 11.953125 L 8 11.953125 Z M 8 2 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 18 2 L 21 2 L 21 11.953125 L 18 11.953125 Z M 18 2 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 35 2 L 46 2 L 46 11.953125 L 35 11.953125 Z M 35 2 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 46 2 L 49 2 L 49 11.953125 L 46 11.953125 Z M 46 2 "/>
+</clipPath>
+<clipPath id="clip5">
+ <path d="M 55 2 L 58 2 L 58 11.953125 L 55 11.953125 Z M 55 2 "/>
+</clipPath>
+<clipPath id="clip6">
+ <path d="M 60 2 L 61 2 L 61 11.953125 L 60 11.953125 Z M 60 2 "/>
+</clipPath>
+<clipPath id="clip7">
+ <path d="M 62 0.0351562 L 66 0.0351562 L 66 5 L 62 5 Z M 62 0.0351562 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="9.478355"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="7.701118" y="9.478355"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="11.55118" y="9.478355"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.560815" y="9.478355"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-2" x="24.161774" y="9.478355"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="34.615292" y="9.478355"/>
+ <use xlink:href="#glyph0-4" x="37.365801" y="9.478355"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="45.271523" y="9.478355"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="49.122579" y="9.478355"/>
+</g>
+<g clip-path="url(#clip5)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="55.13122" y="9.478355"/>
+</g>
+</g>
+<g clip-path="url(#clip6)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-3" x="58.982276" y="9.478355"/>
+</g>
+</g>
+<g clip-path="url(#clip7)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="61.732179" y="4.500306"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig6.svg b/doc/figs/tex/fig6.svg
new file mode 100644
index 00000000000..d996c971647
--- /dev/null
+++ b/doc/figs/tex/fig6.svg
@@ -0,0 +1,103 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="80.63pt" height="12.636pt" viewBox="0 0 80.63 12.636" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 4.703125 -6.015625 L 6.3125 -6.015625 C 7.59375 -6.015625 8.078125 -6.75 8.078125 -6.875 C 8.078125 -6.921875 8.046875 -6.953125 7.984375 -6.953125 C 7.890625 -6.953125 7.640625 -6.84375 7.390625 -6.671875 C 7.3125 -6.609375 7.296875 -6.609375 7.109375 -6.609375 L 2.875 -6.609375 C 1.671875 -6.609375 0.328125 -5.578125 0.328125 -4.78125 C 0.328125 -4.734375 0.328125 -4.671875 0.40625 -4.671875 C 0.640625 -4.671875 1.25 -4.984375 1.265625 -5.21875 C 1.28125 -5.390625 1.296875 -5.5625 1.484375 -5.828125 C 1.59375 -5.9375 1.671875 -6.015625 2.09375 -6.015625 L 4.015625 -6.015625 C 3.859375 -5.90625 3.8125 -5.765625 3.796875 -5.671875 L 2.6875 -1.28125 C 2.578125 -0.796875 2.375 -0.1875 2.09375 0.4375 C 2.03125 0.546875 2.03125 0.578125 2.03125 0.59375 C 2.03125 0.65625 2.078125 0.65625 2.125 0.65625 C 2.3125 0.65625 2.796875 0.390625 2.9375 0.1875 C 3 0.09375 3.421875 -0.890625 3.625 -1.6875 Z M 4.703125 -6.015625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 2.203125 -4.234375 C 2.203125 -4.34375 2.109375 -4.5 1.921875 -4.5 C 1.75 -4.5 1.546875 -4.3125 1.546875 -4.125 C 1.546875 -4 1.640625 -3.859375 1.8125 -3.859375 C 2.015625 -3.859375 2.203125 -4.0625 2.203125 -4.234375 Z M 0.8125 -0.796875 C 0.78125 -0.703125 0.75 -0.625 0.75 -0.515625 C 0.75 -0.1875 1.03125 0.0625 1.390625 0.0625 C 2.078125 0.0625 2.375 -0.875 2.375 -0.96875 C 2.375 -1.0625 2.28125 -1.0625 2.265625 -1.0625 C 2.171875 -1.0625 2.15625 -1.015625 2.140625 -0.9375 C 1.984375 -0.40625 1.6875 -0.125 1.421875 -0.125 C 1.28125 -0.125 1.25 -0.203125 1.25 -0.359375 C 1.25 -0.515625 1.296875 -0.640625 1.359375 -0.796875 C 1.421875 -0.96875 1.5 -1.15625 1.578125 -1.328125 C 1.640625 -1.5 1.875 -2.109375 1.90625 -2.203125 C 1.921875 -2.265625 1.953125 -2.34375 1.953125 -2.421875 C 1.953125 -2.734375 1.671875 -2.984375 1.296875 -2.984375 C 0.625 -2.984375 0.3125 -2.0625 0.3125 -1.953125 C 0.3125 -1.859375 0.40625 -1.859375 0.4375 -1.859375 C 0.53125 -1.859375 0.53125 -1.90625 0.5625 -1.96875 C 0.734375 -2.5625 1.03125 -2.796875 1.28125 -2.796875 C 1.390625 -2.796875 1.453125 -2.75 1.453125 -2.5625 C 1.453125 -2.40625 1.40625 -2.3125 1.234375 -1.890625 Z M 0.8125 -0.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.765625 -2.671875 L 3.421875 -2.671875 C 3.5625 -2.671875 3.640625 -2.671875 3.640625 -2.828125 C 3.640625 -2.921875 3.5625 -2.921875 3.4375 -2.921875 L 2.8125 -2.921875 C 2.96875 -3.78125 3.015625 -4.09375 3.078125 -4.296875 C 3.109375 -4.4375 3.25 -4.578125 3.421875 -4.578125 C 3.421875 -4.578125 3.609375 -4.578125 3.734375 -4.5 C 3.453125 -4.421875 3.4375 -4.171875 3.4375 -4.125 C 3.4375 -3.984375 3.546875 -3.875 3.703125 -3.875 C 3.890625 -3.875 4.09375 -4.03125 4.09375 -4.296875 C 4.09375 -4.609375 3.765625 -4.78125 3.421875 -4.78125 C 3.125 -4.78125 2.78125 -4.609375 2.609375 -4.265625 C 2.46875 -4.015625 2.421875 -3.703125 2.265625 -2.921875 L 1.734375 -2.921875 C 1.59375 -2.921875 1.515625 -2.921875 1.515625 -2.78125 C 1.515625 -2.671875 1.59375 -2.671875 1.71875 -2.671875 L 2.21875 -2.671875 C 2.21875 -2.640625 1.796875 -0.203125 1.625 0.53125 C 1.59375 0.671875 1.484375 1.1875 1.15625 1.1875 C 1.140625 1.1875 0.984375 1.1875 0.859375 1.109375 C 1.125 1.03125 1.15625 0.78125 1.15625 0.734375 C 1.15625 0.59375 1.03125 0.484375 0.875 0.484375 C 0.703125 0.484375 0.5 0.640625 0.5 0.90625 C 0.5 1.203125 0.8125 1.390625 1.15625 1.390625 C 1.59375 1.390625 1.890625 0.9375 1.96875 0.78125 C 2.203125 0.328125 2.359375 -0.5 2.375 -0.578125 Z M 2.765625 -2.671875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 2.125 -4.5 C 2.125 -4.515625 2.15625 -4.609375 2.15625 -4.609375 C 2.15625 -4.640625 2.125 -4.703125 2.046875 -4.703125 C 1.90625 -4.703125 1.34375 -4.65625 1.171875 -4.640625 C 1.125 -4.625 1.03125 -4.625 1.03125 -4.484375 C 1.03125 -4.390625 1.125 -4.390625 1.203125 -4.390625 C 1.53125 -4.390625 1.53125 -4.34375 1.53125 -4.28125 C 1.53125 -4.234375 1.515625 -4.203125 1.5 -4.140625 L 0.546875 -0.296875 C 0.515625 -0.171875 0.515625 -0.15625 0.515625 -0.15625 C 0.515625 -0.046875 0.59375 0.0625 0.734375 0.0625 C 0.921875 0.0625 1.015625 -0.0625 1.046875 -0.21875 C 1.0625 -0.25 1.359375 -1.4375 1.390625 -1.53125 C 1.859375 -1.484375 2.25 -1.328125 2.25 -0.96875 C 2.25 -0.9375 2.25 -0.90625 2.234375 -0.84375 C 2.203125 -0.734375 2.203125 -0.703125 2.203125 -0.625 C 2.203125 -0.15625 2.609375 0.0625 2.921875 0.0625 C 3.59375 0.0625 3.796875 -0.96875 3.796875 -0.96875 C 3.796875 -1.0625 3.703125 -1.0625 3.6875 -1.0625 C 3.59375 -1.0625 3.578125 -1.03125 3.546875 -0.890625 C 3.46875 -0.609375 3.28125 -0.125 2.953125 -0.125 C 2.765625 -0.125 2.71875 -0.296875 2.71875 -0.46875 C 2.71875 -0.59375 2.71875 -0.609375 2.75 -0.78125 C 2.765625 -0.796875 2.78125 -0.921875 2.78125 -0.984375 C 2.78125 -1.59375 1.96875 -1.6875 1.6875 -1.703125 C 1.890625 -1.828125 2.140625 -2.0625 2.25 -2.15625 C 2.59375 -2.484375 2.9375 -2.796875 3.3125 -2.796875 C 3.390625 -2.796875 3.484375 -2.78125 3.546875 -2.71875 C 3.25 -2.671875 3.1875 -2.4375 3.1875 -2.328125 C 3.1875 -2.1875 3.296875 -2.078125 3.453125 -2.078125 C 3.640625 -2.078125 3.84375 -2.234375 3.84375 -2.515625 C 3.84375 -2.734375 3.6875 -2.984375 3.328125 -2.984375 C 2.9375 -2.984375 2.578125 -2.71875 2.234375 -2.390625 C 1.953125 -2.125 1.734375 -1.90625 1.453125 -1.796875 Z M 2.125 -4.5 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 6.65625 -3.171875 C 6.796875 -3.171875 6.984375 -3.171875 6.984375 -3.359375 C 6.984375 -3.5625 6.796875 -3.5625 6.671875 -3.5625 L 0.859375 -3.5625 C 0.71875 -3.5625 0.546875 -3.5625 0.546875 -3.359375 C 0.546875 -3.171875 0.71875 -3.171875 0.875 -3.171875 Z M 6.671875 -1.28125 C 6.796875 -1.28125 6.984375 -1.28125 6.984375 -1.484375 C 6.984375 -1.671875 6.796875 -1.671875 6.65625 -1.671875 L 0.875 -1.671875 C 0.71875 -1.671875 0.546875 -1.671875 0.546875 -1.484375 C 0.546875 -1.28125 0.71875 -1.28125 0.859375 -1.28125 Z M 6.671875 -1.28125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-2">
+<path style="stroke:none;" d="M 3.203125 2.328125 C 3.203125 2.296875 3.203125 2.28125 3.046875 2.109375 C 1.828125 0.890625 1.515625 -0.9375 1.515625 -2.421875 C 1.515625 -4.109375 1.890625 -5.796875 3.078125 -7 C 3.203125 -7.125 3.203125 -7.140625 3.203125 -7.171875 C 3.203125 -7.234375 3.171875 -7.265625 3.109375 -7.265625 C 3.015625 -7.265625 2.140625 -6.609375 1.5625 -5.375 C 1.078125 -4.3125 0.953125 -3.234375 0.953125 -2.421875 C 0.953125 -1.671875 1.0625 -0.5 1.59375 0.59375 C 2.171875 1.796875 3.015625 2.421875 3.109375 2.421875 C 3.171875 2.421875 3.203125 2.390625 3.203125 2.328125 Z M 3.203125 2.328125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-3">
+<path style="stroke:none;" d="M 2.796875 -2.421875 C 2.796875 -3.171875 2.6875 -4.34375 2.15625 -5.4375 C 1.578125 -6.640625 0.75 -7.265625 0.65625 -7.265625 C 0.59375 -7.265625 0.546875 -7.234375 0.546875 -7.171875 C 0.546875 -7.140625 0.546875 -7.125 0.734375 -6.953125 C 1.6875 -5.984375 2.234375 -4.453125 2.234375 -2.421875 C 2.234375 -0.765625 1.875 0.9375 0.671875 2.15625 C 0.546875 2.28125 0.546875 2.296875 0.546875 2.328125 C 0.546875 2.390625 0.59375 2.421875 0.65625 2.421875 C 0.75 2.421875 1.625 1.765625 2.1875 0.53125 C 2.6875 -0.53125 2.796875 -1.609375 2.796875 -2.421875 Z M 2.796875 -2.421875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.078125 5.171875 L 0.640625 9.421875 C 0.5625 9.515625 0.546875 9.546875 0.546875 9.578125 C 0.546875 9.6875 0.640625 9.6875 0.8125 9.6875 L 8.84375 9.6875 L 9.671875 7.28125 L 9.4375 7.28125 C 9.1875 8 8.546875 8.59375 7.71875 8.875 C 7.5625 8.921875 6.890625 9.15625 5.46875 9.15625 L 1.359375 9.15625 L 4.71875 5 C 4.78125 4.90625 4.8125 4.875 4.8125 4.84375 C 4.8125 4.8125 4.796875 4.796875 4.734375 4.703125 L 1.59375 0.390625 L 5.421875 0.390625 C 6.53125 0.390625 8.75 0.453125 9.4375 2.265625 L 9.671875 2.265625 L 8.84375 0 L 0.8125 0 C 0.546875 0 0.546875 0.015625 0.546875 0.3125 Z M 4.078125 5.171875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 4.5625 -3.65625 C 4.578125 -3.703125 4.59375 -3.765625 4.59375 -3.828125 C 4.59375 -3.984375 4.46875 -4.09375 4.3125 -4.09375 C 4.21875 -4.09375 3.953125 -4.015625 3.90625 -3.671875 C 3.734375 -4.03125 3.40625 -4.28125 3.015625 -4.28125 C 1.90625 -4.28125 0.703125 -2.921875 0.703125 -1.53125 C 0.703125 -0.578125 1.296875 0 2 0 C 2.5625 0 3.015625 -0.453125 3.125 -0.5625 L 3.125 -0.546875 C 2.921875 0.3125 2.8125 0.703125 2.8125 0.71875 C 2.765625 0.8125 2.4375 1.765625 1.421875 1.765625 C 1.234375 1.765625 0.90625 1.765625 0.640625 1.671875 C 0.9375 1.59375 1.03125 1.34375 1.03125 1.171875 C 1.03125 1.015625 0.9375 0.828125 0.671875 0.828125 C 0.453125 0.828125 0.140625 1 0.140625 1.390625 C 0.140625 1.796875 0.5 1.984375 1.4375 1.984375 C 2.640625 1.984375 3.34375 1.234375 3.484375 0.65625 Z M 3.296875 -1.234375 C 3.25 -0.984375 3.015625 -0.75 2.8125 -0.5625 C 2.609375 -0.390625 2.3125 -0.21875 2.03125 -0.21875 C 1.546875 -0.21875 1.390625 -0.71875 1.390625 -1.109375 C 1.390625 -1.5625 1.671875 -2.71875 1.9375 -3.203125 C 2.203125 -3.6875 2.609375 -4.0625 3.015625 -4.0625 C 3.65625 -4.0625 3.796875 -3.28125 3.796875 -3.234375 C 3.796875 -3.1875 3.78125 -3.125 3.765625 -3.09375 Z M 3.296875 -1.234375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 3.359375 -2.390625 L 4.484375 -3.640625 C 4.609375 -3.78125 4.671875 -3.84375 5.46875 -3.84375 L 5.46875 -4.296875 C 5.140625 -4.28125 4.625 -4.265625 4.578125 -4.265625 C 4.34375 -4.265625 3.859375 -4.296875 3.578125 -4.296875 L 3.578125 -3.84375 C 3.71875 -3.84375 3.84375 -3.828125 3.953125 -3.765625 C 3.90625 -3.703125 3.90625 -3.6875 3.875 -3.640625 L 3.0625 -2.734375 L 2.109375 -3.84375 L 2.5 -3.84375 L 2.5 -4.296875 C 2.25 -4.296875 1.640625 -4.265625 1.328125 -4.265625 C 1.015625 -4.265625 0.578125 -4.296875 0.265625 -4.296875 L 0.265625 -3.84375 L 0.953125 -3.84375 L 2.453125 -2.0625 L 1.1875 -0.640625 C 1.03125 -0.453125 0.671875 -0.453125 0.21875 -0.453125 L 0.21875 0 C 0.546875 -0.015625 1.0625 -0.03125 1.109375 -0.03125 C 1.34375 -0.03125 1.90625 -0.015625 2.109375 0 L 2.109375 -0.453125 C 1.921875 -0.453125 1.75 -0.5 1.75 -0.5625 C 1.75 -0.578125 1.75 -0.578125 1.8125 -0.65625 L 2.75 -1.71875 L 3.8125 -0.453125 L 3.4375 -0.453125 L 3.4375 0 C 3.6875 -0.015625 4.28125 -0.03125 4.59375 -0.03125 C 4.90625 -0.03125 5.34375 -0.015625 5.671875 0 L 5.671875 -0.453125 L 4.984375 -0.453125 Z M 3.359375 -2.390625 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 58 6 L 65 6 L 65 12.28125 L 58 12.28125 Z M 58 6 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.949" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="6.223072" y="9.674316"/>
+ <use xlink:href="#glyph1-2" x="8.962955" y="9.674316"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="16.673044" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="26.894596" y="0.958392"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="37.116148" y="11.126484"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="43.494412" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="48.113356" y="9.674316"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="52.8781" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="60.613276" y="4.707396"/>
+</g>
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="58.152172" y="10.96416"/>
+ <use xlink:href="#glyph1-2" x="60.892055" y="10.96416"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-2" x="65.911648" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="69.678148" y="8.221176"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-3" x="75.555832" y="8.221176"/>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig7.svg b/doc/figs/tex/fig7.svg
new file mode 100644
index 00000000000..c5c6dacc2ec
--- /dev/null
+++ b/doc/figs/tex/fig7.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="3.432pt" height="6.571pt" viewBox="0 0 3.432 6.571" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 2.421875 -5.34375 C 2.421875 -5.515625 2.3125 -5.65625 2.109375 -5.65625 C 1.875 -5.65625 1.65625 -5.421875 1.65625 -5.203125 C 1.65625 -5.03125 1.765625 -4.890625 1.96875 -4.890625 C 2.171875 -4.890625 2.421875 -5.078125 2.421875 -5.34375 Z M 1.78125 -2.125 C 1.875 -2.375 1.875 -2.390625 1.96875 -2.625 C 2.03125 -2.796875 2.078125 -2.921875 2.078125 -3.078125 C 2.078125 -3.46875 1.796875 -3.78125 1.375 -3.78125 C 0.578125 -3.78125 0.25 -2.53125 0.25 -2.46875 C 0.25 -2.375 0.328125 -2.375 0.34375 -2.375 C 0.4375 -2.375 0.4375 -2.390625 0.484375 -2.53125 C 0.71875 -3.328125 1.0625 -3.59375 1.34375 -3.59375 C 1.421875 -3.59375 1.5625 -3.59375 1.5625 -3.3125 C 1.5625 -3.140625 1.5 -2.953125 1.46875 -2.875 C 1.40625 -2.65625 1.015625 -1.65625 0.875 -1.296875 C 0.796875 -1.0625 0.6875 -0.78125 0.6875 -0.609375 C 0.6875 -0.203125 0.96875 0.09375 1.390625 0.09375 C 2.1875 0.09375 2.5 -1.140625 2.5 -1.21875 C 2.5 -1.3125 2.421875 -1.3125 2.40625 -1.3125 C 2.3125 -1.3125 2.3125 -1.28125 2.28125 -1.15625 C 2.125 -0.609375 1.84375 -0.09375 1.40625 -0.09375 C 1.25 -0.09375 1.203125 -0.171875 1.203125 -0.375 C 1.203125 -0.59375 1.25 -0.703125 1.4375 -1.234375 Z M 1.78125 -2.125 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0 0.28125 L 2.945312 0.28125 L 2.945312 5.921875 L 0 5.921875 Z M 0 0.28125 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0" y="5.920418"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig8.svg b/doc/figs/tex/fig8.svg
new file mode 100644
index 00000000000..1f058383058
--- /dev/null
+++ b/doc/figs/tex/fig8.svg
@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="5.95pt" height="8.856pt" viewBox="0 0 5.95 8.856" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.59375 -3.921875 L 4.4375 -3.921875 C 4.640625 -3.921875 4.734375 -3.921875 4.734375 -4.109375 C 4.734375 -4.21875 4.640625 -4.21875 4.46875 -4.21875 L 3.65625 -4.21875 L 3.859375 -5.34375 C 3.90625 -5.546875 4.03125 -6.234375 4.09375 -6.359375 C 4.1875 -6.546875 4.34375 -6.6875 4.5625 -6.6875 C 4.59375 -6.6875 4.84375 -6.6875 5.03125 -6.515625 C 4.609375 -6.46875 4.5 -6.140625 4.5 -5.984375 C 4.5 -5.765625 4.6875 -5.640625 4.875 -5.640625 C 5.125 -5.640625 5.40625 -5.859375 5.40625 -6.234375 C 5.40625 -6.6875 4.953125 -6.90625 4.5625 -6.90625 C 4.21875 -6.90625 3.609375 -6.734375 3.3125 -5.765625 C 3.25 -5.5625 3.21875 -5.453125 2.984375 -4.21875 L 2.3125 -4.21875 C 2.125 -4.21875 2.015625 -4.21875 2.015625 -4.03125 C 2.015625 -3.921875 2.109375 -3.921875 2.296875 -3.921875 L 2.9375 -3.921875 L 2.203125 -0.046875 C 2.03125 0.90625 1.859375 1.796875 1.359375 1.796875 C 1.3125 1.796875 1.0625 1.796875 0.875 1.609375 C 1.328125 1.59375 1.421875 1.234375 1.421875 1.09375 C 1.421875 0.859375 1.25 0.75 1.0625 0.75 C 0.796875 0.75 0.515625 0.953125 0.515625 1.328125 C 0.515625 1.765625 0.953125 2.015625 1.359375 2.015625 C 1.890625 2.015625 2.28125 1.4375 2.453125 1.0625 C 2.765625 0.4375 3 -0.75 3 -0.8125 Z M 3.59375 -3.921875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.0234375 0 L 5.878906 0 L 5.878906 8.714844 L 0.0234375 8.714844 Z M 0.0234375 0 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.023" y="6.808296"/>
+</g>
+</g>
+</g>
+</svg>
diff --git a/doc/figs/tex/fig9.svg b/doc/figs/tex/fig9.svg
new file mode 100644
index 00000000000..1b49bbf978b
--- /dev/null
+++ b/doc/figs/tex/fig9.svg
@@ -0,0 +1,158 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="123.238pt" height="11.817pt" viewBox="0 0 123.238 11.817" version="1.2">
+<defs>
+<g>
+<symbol overflow="visible" id="glyph0-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph0-1">
+<path style="stroke:none;" d="M 3.421875 -6.703125 C 2.03125 -6.703125 0.984375 -6.03125 0.578125 -5.578125 C 0.234375 -5.1875 0.203125 -4.890625 0.203125 -4.875 C 0.203125 -4.8125 0.25 -4.796875 0.296875 -4.796875 C 0.46875 -4.796875 0.6875 -4.9375 0.765625 -4.984375 C 0.96875 -5.125 1 -5.1875 1.0625 -5.375 C 1.203125 -5.765625 1.46875 -6.109375 2.703125 -6.15625 C 2.53125 -3.953125 1.9375 -1.8125 1.125 0.25 C 1.0625 0.390625 1.0625 0.40625 1.0625 0.421875 C 1.0625 0.453125 1.09375 0.484375 1.15625 0.484375 C 1.3125 0.484375 1.78125 0.28125 1.890625 0.015625 C 2.40625 -1.171875 3.203125 -3.4375 3.5 -6.15625 L 4.015625 -6.15625 C 5.203125 -6.15625 6.359375 -5.703125 6.359375 -4.71875 C 6.359375 -3.984375 5.65625 -2.609375 3.75 -2.546875 C 3.546875 -2.546875 3.4375 -2.546875 3.15625 -2.359375 C 2.984375 -2.25 2.90625 -2.140625 2.90625 -2.078125 C 2.90625 -2.015625 2.96875 -2.015625 3.09375 -2.015625 C 4.875 -2.015625 7.1875 -3.515625 7.1875 -5.140625 C 7.1875 -6.265625 5.875 -6.703125 4.734375 -6.703125 Z M 3.421875 -6.703125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph1-1">
+<path style="stroke:none;" d="M 3.25 2.359375 C 3.25 2.328125 3.25 2.3125 3.078125 2.140625 C 1.859375 0.90625 1.546875 -0.953125 1.546875 -2.453125 C 1.546875 -4.15625 1.90625 -5.875 3.125 -7.09375 C 3.25 -7.21875 3.25 -7.234375 3.25 -7.265625 C 3.25 -7.328125 3.203125 -7.359375 3.15625 -7.359375 C 3.046875 -7.359375 2.171875 -6.6875 1.59375 -5.453125 C 1.09375 -4.359375 0.96875 -3.28125 0.96875 -2.453125 C 0.96875 -1.6875 1.078125 -0.5 1.625 0.609375 C 2.203125 1.8125 3.046875 2.453125 3.15625 2.453125 C 3.203125 2.453125 3.25 2.421875 3.25 2.359375 Z M 3.25 2.359375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-2">
+<path style="stroke:none;" d="M 2.828125 -2.453125 C 2.828125 -3.21875 2.734375 -4.40625 2.1875 -5.515625 C 1.59375 -6.71875 0.75 -7.359375 0.65625 -7.359375 C 0.59375 -7.359375 0.5625 -7.3125 0.5625 -7.265625 C 0.5625 -7.234375 0.5625 -7.21875 0.75 -7.03125 C 1.703125 -6.0625 2.265625 -4.5 2.265625 -2.453125 C 2.265625 -0.78125 1.90625 0.953125 0.6875 2.1875 C 0.5625 2.3125 0.5625 2.328125 0.5625 2.359375 C 0.5625 2.40625 0.59375 2.453125 0.65625 2.453125 C 0.75 2.453125 1.640625 1.78125 2.21875 0.546875 C 2.71875 -0.546875 2.828125 -1.625 2.828125 -2.453125 Z M 2.828125 -2.453125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-3">
+<path style="stroke:none;" d="M 6.734375 -3.203125 C 6.890625 -3.203125 7.078125 -3.203125 7.078125 -3.40625 C 7.078125 -3.59375 6.890625 -3.59375 6.75 -3.59375 L 0.875 -3.59375 C 0.734375 -3.59375 0.546875 -3.59375 0.546875 -3.40625 C 0.546875 -3.203125 0.734375 -3.203125 0.890625 -3.203125 Z M 6.75 -1.3125 C 6.890625 -1.3125 7.078125 -1.3125 7.078125 -1.5 C 7.078125 -1.703125 6.890625 -1.703125 6.734375 -1.703125 L 0.890625 -1.703125 C 0.734375 -1.703125 0.546875 -1.703125 0.546875 -1.5 C 0.546875 -1.3125 0.734375 -1.3125 0.875 -1.3125 Z M 6.75 -1.3125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph1-4">
+<path style="stroke:none;" d="M 2.453125 -6.8125 L 1.140625 -5.46875 L 1.3125 -5.296875 L 2.453125 -6.296875 L 3.578125 -5.296875 L 3.765625 -5.46875 Z M 2.453125 -6.8125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph2-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph2-1">
+<path style="stroke:none;" d="M 3.390625 -2.40625 L 4.546875 -3.6875 C 4.671875 -3.828125 4.734375 -3.890625 5.546875 -3.890625 L 5.546875 -4.359375 C 5.203125 -4.34375 4.6875 -4.328125 4.640625 -4.328125 C 4.390625 -4.328125 3.90625 -4.34375 3.625 -4.359375 L 3.625 -3.890625 C 3.765625 -3.890625 3.890625 -3.875 4 -3.8125 C 3.96875 -3.75 3.96875 -3.734375 3.921875 -3.6875 L 3.09375 -2.765625 L 2.140625 -3.890625 L 2.53125 -3.890625 L 2.53125 -4.359375 C 2.28125 -4.34375 1.65625 -4.328125 1.34375 -4.328125 C 1.03125 -4.328125 0.59375 -4.34375 0.265625 -4.359375 L 0.265625 -3.890625 L 0.96875 -3.890625 L 2.5 -2.09375 L 1.203125 -0.640625 C 1.046875 -0.46875 0.6875 -0.46875 0.21875 -0.46875 L 0.21875 0 C 0.5625 -0.015625 1.0625 -0.03125 1.125 -0.03125 C 1.359375 -0.03125 1.9375 -0.015625 2.125 0 L 2.125 -0.46875 C 1.953125 -0.46875 1.765625 -0.515625 1.765625 -0.5625 C 1.765625 -0.578125 1.765625 -0.59375 1.828125 -0.671875 L 2.78125 -1.734375 L 3.859375 -0.46875 L 3.484375 -0.46875 L 3.484375 0 C 3.734375 -0.015625 4.34375 -0.03125 4.65625 -0.03125 C 4.96875 -0.03125 5.421875 -0.015625 5.734375 0 L 5.734375 -0.46875 L 5.046875 -0.46875 Z M 3.390625 -2.40625 "/>
+</symbol>
+<symbol overflow="visible" id="glyph3-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph3-1">
+<path style="stroke:none;" d="M 4.125 5.234375 L 0.640625 9.546875 C 0.5625 9.640625 0.5625 9.671875 0.5625 9.703125 C 0.5625 9.8125 0.640625 9.8125 0.828125 9.8125 L 8.953125 9.8125 L 9.796875 7.375 L 9.5625 7.375 C 9.3125 8.109375 8.65625 8.703125 7.828125 8.984375 C 7.65625 9.03125 6.984375 9.265625 5.546875 9.265625 L 1.375 9.265625 L 4.78125 5.0625 C 4.84375 4.96875 4.859375 4.953125 4.859375 4.90625 C 4.859375 4.859375 4.859375 4.859375 4.796875 4.765625 L 1.609375 0.390625 L 5.5 0.390625 C 6.609375 0.390625 8.875 0.46875 9.5625 2.296875 L 9.796875 2.296875 L 8.953125 0 L 0.828125 0 C 0.5625 0 0.546875 0.015625 0.546875 0.3125 Z M 4.125 5.234375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph4-1">
+<path style="stroke:none;" d="M 2.234375 -4.296875 C 2.234375 -4.40625 2.140625 -4.5625 1.953125 -4.5625 C 1.765625 -4.5625 1.5625 -4.375 1.5625 -4.1875 C 1.5625 -4.0625 1.65625 -3.921875 1.84375 -3.921875 C 2.046875 -3.921875 2.234375 -4.109375 2.234375 -4.296875 Z M 0.828125 -0.796875 C 0.796875 -0.71875 0.765625 -0.625 0.765625 -0.515625 C 0.765625 -0.1875 1.03125 0.0625 1.421875 0.0625 C 2.109375 0.0625 2.40625 -0.875 2.40625 -0.984375 C 2.40625 -1.078125 2.3125 -1.078125 2.296875 -1.078125 C 2.203125 -1.078125 2.1875 -1.03125 2.171875 -0.953125 C 2 -0.40625 1.703125 -0.125 1.4375 -0.125 C 1.296875 -0.125 1.265625 -0.21875 1.265625 -0.359375 C 1.265625 -0.515625 1.3125 -0.65625 1.375 -0.796875 C 1.4375 -0.984375 1.515625 -1.171875 1.59375 -1.359375 C 1.65625 -1.515625 1.90625 -2.140625 1.9375 -2.234375 C 1.953125 -2.296875 1.96875 -2.375 1.96875 -2.453125 C 1.96875 -2.765625 1.703125 -3.03125 1.3125 -3.03125 C 0.640625 -3.03125 0.328125 -2.09375 0.328125 -1.984375 C 0.328125 -1.890625 0.421875 -1.890625 0.4375 -1.890625 C 0.53125 -1.890625 0.546875 -1.921875 0.5625 -2 C 0.75 -2.59375 1.046875 -2.84375 1.296875 -2.84375 C 1.40625 -2.84375 1.46875 -2.78125 1.46875 -2.59375 C 1.46875 -2.4375 1.4375 -2.34375 1.265625 -1.90625 Z M 0.828125 -0.796875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-2">
+<path style="stroke:none;" d="M 2.796875 -2.71875 L 3.46875 -2.71875 C 3.609375 -2.71875 3.703125 -2.71875 3.703125 -2.859375 C 3.703125 -2.96875 3.609375 -2.96875 3.484375 -2.96875 L 2.84375 -2.96875 C 3 -3.84375 3.0625 -4.15625 3.109375 -4.359375 C 3.15625 -4.5 3.296875 -4.640625 3.46875 -4.640625 C 3.46875 -4.640625 3.65625 -4.640625 3.78125 -4.5625 C 3.5 -4.46875 3.484375 -4.234375 3.484375 -4.1875 C 3.484375 -4.03125 3.609375 -3.9375 3.765625 -3.9375 C 3.953125 -3.9375 4.15625 -4.09375 4.15625 -4.359375 C 4.15625 -4.671875 3.8125 -4.84375 3.46875 -4.84375 C 3.15625 -4.84375 2.828125 -4.671875 2.640625 -4.328125 C 2.5 -4.0625 2.453125 -3.765625 2.296875 -2.96875 L 1.765625 -2.96875 C 1.625 -2.96875 1.53125 -2.96875 1.53125 -2.8125 C 1.53125 -2.71875 1.625 -2.71875 1.75 -2.71875 L 2.25 -2.71875 C 2.25 -2.671875 1.8125 -0.203125 1.65625 0.53125 C 1.609375 0.6875 1.5 1.203125 1.171875 1.203125 C 1.15625 1.203125 1 1.203125 0.859375 1.125 C 1.140625 1.03125 1.171875 0.796875 1.171875 0.75 C 1.171875 0.59375 1.046875 0.5 0.890625 0.5 C 0.703125 0.5 0.5 0.65625 0.5 0.921875 C 0.5 1.21875 0.828125 1.40625 1.171875 1.40625 C 1.609375 1.40625 1.90625 0.953125 2 0.796875 C 2.234375 0.34375 2.40625 -0.515625 2.40625 -0.59375 Z M 2.796875 -2.71875 "/>
+</symbol>
+<symbol overflow="visible" id="glyph4-3">
+<path style="stroke:none;" d="M 3.015625 -4.296875 C 3.015625 -4.40625 2.921875 -4.5625 2.75 -4.5625 C 2.546875 -4.5625 2.359375 -4.359375 2.359375 -4.1875 C 2.359375 -4.0625 2.4375 -3.921875 2.640625 -3.921875 C 2.8125 -3.921875 3.015625 -4.09375 3.015625 -4.296875 Z M 1.5625 0.34375 C 1.4375 0.8125 1.078125 1.203125 0.671875 1.203125 C 0.578125 1.203125 0.5 1.203125 0.421875 1.171875 C 0.609375 1.09375 0.65625 0.921875 0.65625 0.8125 C 0.65625 0.65625 0.53125 0.5625 0.390625 0.5625 C 0.171875 0.5625 0 0.75 0 0.96875 C 0 1.234375 0.265625 1.40625 0.6875 1.40625 C 1.09375 1.40625 1.890625 1.15625 2.109375 0.3125 L 2.734375 -2.140625 C 2.75 -2.21875 2.765625 -2.28125 2.765625 -2.390625 C 2.765625 -2.765625 2.4375 -3.03125 2.03125 -3.03125 C 1.265625 -3.03125 0.828125 -2.078125 0.828125 -1.984375 C 0.828125 -1.890625 0.921875 -1.890625 0.9375 -1.890625 C 1.03125 -1.890625 1.03125 -1.90625 1.078125 -2.015625 C 1.25 -2.40625 1.609375 -2.84375 2 -2.84375 C 2.171875 -2.84375 2.234375 -2.71875 2.234375 -2.5 C 2.234375 -2.421875 2.234375 -2.328125 2.21875 -2.296875 Z M 1.5625 0.34375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph5-1">
+<path style="stroke:none;" d="M 0.328125 1.703125 C 0.296875 1.8125 0.296875 1.828125 0.296875 1.859375 C 0.296875 2 0.40625 2.125 0.5625 2.125 C 0.78125 2.125 0.890625 1.9375 0.90625 1.90625 C 0.96875 1.828125 1.28125 0.515625 1.546875 -0.546875 C 1.734375 -0.15625 2.046875 0.109375 2.515625 0.109375 C 3.65625 0.109375 4.921875 -1.28125 4.921875 -2.734375 C 4.921875 -3.78125 4.28125 -4.34375 3.5625 -4.34375 C 2.609375 -4.34375 1.578125 -3.359375 1.28125 -2.15625 Z M 2.5 -0.109375 C 1.8125 -0.109375 1.65625 -0.890625 1.65625 -0.984375 C 1.65625 -1.015625 1.703125 -1.21875 1.734375 -1.34375 C 2.015625 -2.4375 2.109375 -2.796875 2.328125 -3.1875 C 2.75 -3.90625 3.234375 -4.125 3.546875 -4.125 C 3.90625 -4.125 4.21875 -3.84375 4.21875 -3.15625 C 4.21875 -2.625 3.9375 -1.515625 3.671875 -1.046875 C 3.34375 -0.421875 2.875 -0.109375 2.5 -0.109375 Z M 2.5 -0.109375 "/>
+</symbol>
+<symbol overflow="visible" id="glyph5-2">
+<path style="stroke:none;" d="M 4.1875 -5.953125 C 4.265625 -6.234375 4.296875 -6.296875 4.421875 -6.3125 C 4.5 -6.34375 4.828125 -6.34375 5.03125 -6.34375 C 6.03125 -6.34375 6.46875 -6.296875 6.46875 -5.53125 C 6.46875 -5.390625 6.421875 -5 6.390625 -4.75 C 6.375 -4.703125 6.359375 -4.59375 6.359375 -4.5625 C 6.359375 -4.5 6.390625 -4.4375 6.46875 -4.4375 C 6.578125 -4.4375 6.609375 -4.515625 6.625 -4.65625 L 6.890625 -6.375 C 6.890625 -6.40625 6.90625 -6.5 6.90625 -6.53125 C 6.90625 -6.640625 6.8125 -6.640625 6.640625 -6.640625 L 1.203125 -6.640625 C 0.96875 -6.640625 0.953125 -6.640625 0.890625 -6.453125 L 0.296875 -4.71875 C 0.28125 -4.703125 0.234375 -4.5625 0.234375 -4.546875 C 0.234375 -4.484375 0.28125 -4.4375 0.359375 -4.4375 C 0.453125 -4.4375 0.46875 -4.484375 0.515625 -4.640625 C 1.046875 -6.15625 1.3125 -6.34375 2.75 -6.34375 L 3.140625 -6.34375 C 3.421875 -6.34375 3.421875 -6.296875 3.421875 -6.21875 C 3.421875 -6.15625 3.390625 -6.046875 3.375 -6.015625 L 2.0625 -0.78125 C 1.96875 -0.40625 1.9375 -0.296875 0.890625 -0.296875 C 0.546875 -0.296875 0.484375 -0.296875 0.484375 -0.125 C 0.484375 0 0.59375 0 0.640625 0 C 0.90625 0 1.1875 -0.015625 1.453125 -0.015625 C 1.734375 -0.015625 2.015625 -0.03125 2.28125 -0.03125 C 2.5625 -0.03125 2.828125 -0.015625 3.09375 -0.015625 C 3.390625 -0.015625 3.6875 0 3.953125 0 C 4.046875 0 4.171875 0 4.171875 -0.203125 C 4.171875 -0.296875 4.09375 -0.296875 3.84375 -0.296875 C 3.59375 -0.296875 3.46875 -0.296875 3.203125 -0.328125 C 2.921875 -0.359375 2.84375 -0.375 2.84375 -0.546875 C 2.84375 -0.546875 2.84375 -0.59375 2.890625 -0.75 Z M 4.1875 -5.953125 "/>
+</symbol>
+<symbol overflow="visible" id="glyph6-0">
+<path style="stroke:none;" d=""/>
+</symbol>
+<symbol overflow="visible" id="glyph6-1">
+<path style="stroke:none;" d="M 2.21875 -1.71875 C 2.78125 -1.953125 3.03125 -2.0625 3.203125 -2.140625 C 3.34375 -2.1875 3.40625 -2.21875 3.40625 -2.34375 C 3.40625 -2.46875 3.3125 -2.578125 3.1875 -2.578125 C 3.140625 -2.578125 3.125 -2.578125 3.046875 -2.515625 L 2.109375 -1.890625 L 2.21875 -2.90625 C 2.234375 -3.03125 2.21875 -3.203125 2 -3.203125 C 1.921875 -3.203125 1.796875 -3.140625 1.796875 -2.984375 C 1.796875 -2.921875 1.828125 -2.71875 1.828125 -2.65625 C 1.84375 -2.53125 1.890625 -2.046875 1.90625 -1.890625 L 0.96875 -2.515625 C 0.90625 -2.546875 0.890625 -2.578125 0.828125 -2.578125 C 0.703125 -2.578125 0.609375 -2.46875 0.609375 -2.34375 C 0.609375 -2.21875 0.6875 -2.171875 0.75 -2.15625 L 1.796875 -1.71875 C 1.234375 -1.46875 0.96875 -1.375 0.796875 -1.296875 C 0.671875 -1.234375 0.609375 -1.203125 0.609375 -1.078125 C 0.609375 -0.96875 0.703125 -0.859375 0.828125 -0.859375 C 0.875 -0.859375 0.890625 -0.859375 0.96875 -0.921875 L 1.90625 -1.546875 L 1.796875 -0.4375 C 1.796875 -0.28125 1.921875 -0.234375 2 -0.234375 C 2.09375 -0.234375 2.21875 -0.28125 2.21875 -0.4375 C 2.21875 -0.5 2.1875 -0.703125 2.1875 -0.78125 C 2.171875 -0.890625 2.125 -1.390625 2.109375 -1.546875 L 2.9375 -1 C 3.109375 -0.859375 3.125 -0.859375 3.1875 -0.859375 C 3.3125 -0.859375 3.40625 -0.96875 3.40625 -1.078125 C 3.40625 -1.21875 3.328125 -1.25 3.265625 -1.28125 Z M 2.21875 -1.71875 "/>
+</symbol>
+</g>
+<clipPath id="clip1">
+ <path d="M 0.566406 0 L 8 0 L 8 8 L 0.566406 8 Z M 0.566406 0 "/>
+</clipPath>
+<clipPath id="clip2">
+ <path d="M 45 5 L 53 5 L 53 11.636719 L 45 11.636719 Z M 45 5 "/>
+</clipPath>
+<clipPath id="clip3">
+ <path d="M 99 5 L 103 5 L 103 11.636719 L 99 11.636719 Z M 99 5 "/>
+</clipPath>
+<clipPath id="clip4">
+ <path d="M 103 5 L 108 5 L 108 11.636719 L 103 11.636719 Z M 103 5 "/>
+</clipPath>
+</defs>
+<g id="surface1">
+<g clip-path="url(#clip1)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph0-1" x="0.5645" y="7.358052"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="8.195328" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="12.010249" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="17.965032" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-3" x="24.507769" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph3-1" x="34.861373" y="0"/>
+</g>
+<g clip-path="url(#clip2)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="45.217004" y="10.30147"/>
+ <use xlink:href="#glyph4-2" x="47.992827" y="10.30147"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-4" x="55.614979" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-1" x="54.713933" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="59.78638" y="8.830253"/>
+ <use xlink:href="#glyph4-3" x="62.562203" y="8.830253"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="66.695386" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-1" x="72.428601" y="8.830253"/>
+ <use xlink:href="#glyph4-2" x="75.204424" y="8.830253"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="80.28986" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="84.105766" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="90.06055" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph5-2" x="93.875471" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph6-1" x="100.97158" y="3.798181"/>
+</g>
+<g clip-path="url(#clip3)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-3" x="99.608686" y="10.137017"/>
+</g>
+</g>
+<g clip-path="url(#clip4)" clip-rule="nonzero">
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph4-2" x="103.253241" y="10.137017"/>
+</g>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-1" x="108.33751" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph2-1" x="112.153416" y="7.358052"/>
+</g>
+<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
+ <use xlink:href="#glyph1-2" x="118.107214" y="7.358052"/>
+</g>
+</g>
+</svg>
diff --git a/doc/release.notes b/doc/release.notes
index 08a6f9a3dd8..cd850f12407 100644
--- a/doc/release.notes
+++ b/doc/release.notes
@@ -1,8 +1,24 @@
-!-----------------------------------------------------------------------------
-! Package : Gen/AmpGen
-! Responsible : Tim Evans
-! Purpose :
-!-----------------------------------------------------------------------------
+!=================== AmpGen v2r1 2020-28-10 ==================
+ - Improved cmake configuration to allow installation
+ - Consolidation of Generator and ConvertToSourceCode to single executable 'AmpGen'
+!=================== AmpGen v2r0 2020-25-04 ==================
+ - Refactored caching logic away from being computations being stored with event data.
+ - Support for AVX2 for amplitude evaluation / integration single/double precision.
+ - Updated plotting for making component amplitude plots.
+ - Better thread safety of integration should improve fit stability.
+ - Add GenericKmatrix lineshape for handling ... Generic K-matrices (L=0 only)
+!=================== AmpGen v1r2 2019-11-12 ==================
+ - New phase space Generator TreePhaseSpace for producing narrow resonances.
+ - Improved handling of CP conjugated amplitudes.
+ - Add vertices f_fS_S{L,R} f_Vf_S{L,R} for couplings with well-defined chirality.
+ - Add initial states with ill-defined flavour to PolarisedSum
+!=================== AmpGen v1r2 2019-08-13 ==================
+ - Tagged to match results in Gauss/LbAmpGen v49r14+
+ - Improved thread support for CoherentSum
+ - Add examples/QcGenerator for Ψ(3770) decays
+! 2019-05-29 - Tim Evans
+ - Updated ExpressionParser with improved stability.
+ - Removed unused / untested lineshapes AxialKaon and ObelixRho
!=================== AmpGen v1r1 2019-03-22 ==================
! 2019-03-22 - Tim Evans
- Added support for fitting more general final states, i.e. with multiple fermions, photons etc.
@@ -19,8 +35,6 @@
!=============================================================
! 2016-09-06 - Tim Evans
- First import of source, apps, headers
-
-
! 2016-09-02 - Tim Evans
- Empty structure for the package
!=============================================================
diff --git a/examples/BaryonFitter.cpp b/examples/BaryonFitter.cpp
new file mode 100644
index 00000000000..4e9c9a327ad
--- /dev/null
+++ b/examples/BaryonFitter.cpp
@@ -0,0 +1,237 @@
+#include <chrono>
+#include <ctime>
+#include <iostream>
+#include <map>
+#include <ratio>
+#include <string>
+#include <tuple>
+#include <utility>
+#include <vector>
+#include <THStack.h>
+#include <TCanvas.h>
+#include <TFile.h>
+
+#include "AmpGen/Chi2Estimator.h"
+#include "AmpGen/ErrorPropagator.h"
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_type = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_type = AmpGen::EventList;
+#endif
+#include "AmpGen/EventType.h"
+#include "AmpGen/Factory.h"
+#include "AmpGen/RecursivePhaseSpace.h"
+#include "AmpGen/FitResult.h"
+#include "AmpGen/IExtendLikelihood.h"
+#include "AmpGen/Minimiser.h"
+#include "AmpGen/MinuitParameter.h"
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/SumPDF.h"
+#include "AmpGen/ThreeBodyCalculators.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/Generator.h"
+#include "AmpGen/PolarisedSum.h"
+#include "AmpGen/Kinematics.h"
+
+#ifdef _OPENMP
+ #include <omp.h>
+ #include <thread>
+#endif
+
+using namespace AmpGen;
+
+void randomizeStartingPoint( MinuitParameterSet& mps, TRandom3& rand)
+{
+ for (auto& param : mps) {
+ if ( ! param->isFree() || param->name() == "Px" || param->name() == "Py" || param->name() == "Pz" ) continue;
+ double min = param->minInit();
+ double max = param->maxInit();
+ double new_value = rand.Uniform(param->mean()-param->stepInit(),param->mean()+param->stepInit());
+ if( min != 0 && max != 0 )
+ new_value = rand.Uniform(min,max);
+ param->setInit( new_value );
+ param->setCurrentFitVal( new_value );
+ INFO( param->name() << " = " << param->mean() << " " << param->stepInit() );
+ }
+}
+
+template <typename PDF>
+FitResult* doFit( PDF&& pdf, EventList_type& data, EventList_type& mc, MinuitParameterSet& MPS )
+{
+ auto time_wall = std::chrono::high_resolution_clock::now();
+ auto time = std::clock();
+
+ pdf.setEvents( data );
+
+ /* Minimiser is a general interface to Minuit1/Minuit2,
+ that is constructed from an object that defines an operator() that returns a double
+ (i.e. the likielihood, and a set of MinuitParameters. */
+ Minimiser mini( pdf, &MPS );
+ mini.doFit();
+ FitResult* fr = new FitResult(mini);
+
+ /* Estimate the chi2 using an adaptive / decision tree based binning,
+ down to a minimum bin population of 15, and add it to the output.*/
+ //if(data.eventType().size() < 5){
+ // Chi2Estimator chi2( data, mc, pdf, 15 );
+ // //chi2.writeBinningToFile("chi2_binning.txt");
+ // fr->addChi2( chi2.chi2(), chi2.nBins() );
+ //}
+
+ auto twall_end = std::chrono::high_resolution_clock::now();
+ double time_cpu = ( std::clock() - time ) / (double)CLOCKS_PER_SEC;
+ double tWall = std::chrono::duration<double, std::milli>( twall_end - time_wall ).count();
+ INFO( "Wall time = " << tWall / 1000. );
+ INFO( "CPU time = " << time_cpu );
+ fr->print();
+
+ /* Save weighted data and norm MC for the different components in the PDF, i.e. the signal and backgrounds.
+ The structure assumed the PDF is some SumPDF<T1,T2,...>. */
+ unsigned int counter = 1;
+ for_each(pdf.pdfs(), [&]( auto& f ){
+ mc.transform([&f](auto& mcevt){mcevt.setWeight(f.getValNoCache(mcevt)*mcevt.weight()/mcevt.genPdf());}).tree(counter>1?"MCt"+std::to_string(counter):"MCt")->Write();
+ data.tree(counter>1?"t"+std::to_string(counter):"t")->Write();
+ counter++;
+ } );
+
+ return fr;
+}
+
+void invertParity( Event& event, const size_t& nParticles=0)
+{
+ for( size_t i = 0 ; i < nParticles; ++i )
+ {
+ event[4*i + 0] = -event[4*i+0];
+ event[4*i + 1] = -event[4*i+1];
+ event[4*i + 2] = -event[4*i+2];
+ }
+}
+
+int main( int argc, char* argv[] )
+{
+ gErrorIgnoreLevel = 1001;
+
+ OptionsParser::setArgs( argc, argv );
+
+ const std::vector<std::string> dataFile = NamedParameter<std::string>("DataSample","").getVector();
+ const std::string simFile = NamedParameter<std::string>("SimFile", "" , "Name of file containing simulated sample for using in MC integration");
+ const std::string logFile = NamedParameter<std::string>("LogFile","Fitter.log");
+ const std::string plotFile = NamedParameter<std::string>("Plots","plots.root");
+ const std::string prefix = NamedParameter<std::string>("PlotPrefix","");
+ const std::string idbranch = NamedParameter<std::string>("IDBranch","");
+ const std::string mcidbranch = NamedParameter<std::string>("MCIDBranch","");
+ const std::string weight_branch = NamedParameter<std::string>("WeightBranch","","Name of branch containing event weights.");
+ const std::string mc_weight_branch = NamedParameter<std::string>("MCWeightBranch","","Name of branch containing event weights.");
+
+ const auto nev_MC = NamedParameter<int>("NEventsMC", 8e6, "Number of MC events for normalization.");
+ auto bNames = NamedParameter<std::string>("Branches", std::vector<std::string>(),
+ "List of branch names, assumed to be \033[3m daughter1_px ... daughter1_E, daughter2_px ... \033[0m" ).getVector();
+ auto MCbNames = NamedParameter<std::string>("MCBranches", std::vector<std::string>(),
+ "List of branch names, assumed to be \033[3m daughter1_px ... daughter1_E, daughter2_px ... \033[0m" ).getVector();
+ auto pNames = NamedParameter<std::string>("EventType" , ""
+ , "EventType to fit, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector();
+
+#if ENABLE_AVX
+ if(!idbranch.empty() || !weight_branch.empty() || !mcidbranch.empty() || !mc_weight_branch.empty()){
+ ERROR("Vectorized version currently not supported when adding extra branches");
+ return 1;
+ }
+#endif
+
+#ifdef _OPENMP
+ unsigned int concurentThreadsSupported = std::thread::hardware_concurrency();
+ unsigned int nThreads = NamedParameter<unsigned int>( "nCores", concurentThreadsSupported );
+ omp_set_num_threads( nThreads );
+ INFO( "Setting " << nThreads << " fixed threads for OpenMP" );
+ omp_set_dynamic( 0 );
+#endif
+
+
+ /* A MinuitParameterSet is (unsurprisingly) a set of fit parameters, and can be loaded from
+ the parsed options. For historical reasons, this is referred to as loading it from a "Stream" */
+ MinuitParameterSet MPS;
+ MPS.loadFromStream();
+ TRandom3 rndm = TRandom3( NamedParameter<unsigned int>("Seed", 1 ) ) ;
+ if( NamedParameter<bool>("RandomizeStartingPoint",false) ) randomizeStartingPoint(MPS,rndm );
+
+ /* An EventType specifies the initial and final state particles as a vector that will be described by the fit.
+ It is typically loaded from the interface parameter EventType. */
+ EventType evtType(pNames);
+
+ /* A CoherentSum is the typical amplitude to be used, that is some sum over quasi two-body contributions
+ weighted by an appropriate complex amplitude. The CoherentSum is generated from the couplings described
+ by a set of parameters (in a MinuitParameterSet), and an EventType, which matches these parameters
+ to a given final state and a set of data. A common set of rules can be matched to multiple final states,
+ i.e. to facilitate the analysis of coupled channels. */
+ PolarisedSum sig(evtType, MPS);
+
+ /* Events are read in from ROOT files. If only the filename and the event type are specified,
+ the file is assumed to be in the specific format that is defined by the event type,
+ unless the branches to load are specified in the user options */
+ EventList_type events(dataFile, evtType, Branches(bNames), GetGenPdf(false), WeightBranch(weight_branch), ExtraBranches(std::vector<std::string>{idbranch}) );
+
+ /* Generate events to normalise the PDF with. This can also be loaded from a file,
+ which will be the case when efficiency variations are included. */
+ EventList_type eventsMC = simFile == ""
+ ? EventList_type(Generator<RecursivePhaseSpace, EventList>(sig.matrixElements()[0].decayTree.quasiStableTree(), events.eventType(), &rndm).generate(nev_MC))
+ : EventList_type(simFile, evtType, Branches(MCbNames), WeightBranch(mc_weight_branch), ExtraBranches(std::vector<std::string>{mcidbranch}));
+
+ /* Transform data if we have an ID brach. That branch indicates that we operate on a sample with particles+antiparticles mixed.
+ The transformation also includes boosting to the restframe of the head of the decay chain.
+ TODO: There might be situations where you want to separate both transformations */
+ auto const n_final_state_particles = evtType.size();
+ std::vector<unsigned> daughters_as_ints(n_final_state_particles);
+ std::iota (daughters_as_ints.begin(), daughters_as_ints.end(), 0u);
+ auto frame_transform = [&daughters_as_ints, &n_final_state_particles](auto& event){
+ TVector3 pBeam(0,0,1);
+ if( event[event.size()-1] < 0 ){
+ invertParity( event, n_final_state_particles);
+ pBeam = -pBeam;
+ }
+ TLorentzVector pP = pFromEvent(event,daughters_as_ints);
+ //if( pP.P() < 10e-5) return;
+ TVector3 pZ = pP.Vect();
+ rotateBasis( event, (pBeam.Cross(pZ) ).Cross(pZ), pBeam.Cross(pZ), pZ );
+ boost( event, {0, 0, -1}, pP.P()/pP.E() );
+ };
+
+
+ for( auto& event : events )
+ if( event[event.size()-1] < 0 ){
+ event.print();
+ break;
+ }
+ events.transform( frame_transform );
+ for( auto& event : events )
+ if( event[event.size()-1] < 0 ){//E if there's no ID branch
+ event.print();
+ break;
+ }
+ for( auto& event : eventsMC )
+ if( event[event.size()-1] < 0 ){
+ event.print();
+ break;
+ }
+ eventsMC.transform( frame_transform );
+ for( auto& event : eventsMC )
+ if( event[event.size()-1] < 0 ){//E if there's no ID branch
+ event.print();
+ break;
+ }
+ sig.setMC(eventsMC);
+ sig.setEvents(events);
+
+ TFile* output = TFile::Open( plotFile.c_str(), "RECREATE" );
+ output->cd();
+ auto fr = doFit(make_pdf<EventList_type>(sig), events, eventsMC, MPS);
+
+ auto ff = sig.fitFractions( fr->getErrorPropagator() );
+ fr->addFractions(ff);
+ fr->writeToFile( logFile );
+ output->Close();
+ return 0;
+}
diff --git a/examples/FitHyperonParameters.cpp b/examples/FitHyperonParameters.cpp
new file mode 100644
index 00000000000..ccb856cfe76
--- /dev/null
+++ b/examples/FitHyperonParameters.cpp
@@ -0,0 +1,22 @@
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/Minimiser.h"
+#include "AmpGen/NamedParameter.h"
+
+using namespace AmpGen;
+
+int main( int argc, char* argv[] ){
+ OptionsParser::setArgs( argc, argv );
+ MinuitParameterSet mps;
+ mps.add("gRe",AmpGen::Flag::Free,0,0.1,-10,10);
+ mps.add("gIm",AmpGen::Flag::Free,0,0.1,-10,10);
+ const auto alpha_measured = NamedParameter<double>("alpha", 0.75);
+ const auto phi_measured = NamedParameter<double>("phi", -6.5);
+ const auto alpha_error = NamedParameter<double>("alpha_error", 0.012);
+ const auto phi_error = NamedParameter<double>("phi_error", 3.5);
+ std::function<double()> f = [&mps, &alpha_measured, &alpha_error, &phi_measured, &phi_error]() -> double {
+ auto alpha_pred = 2.*mps[0]->mean()/(1.+mps[0]->mean()*mps[0]->mean()+mps[1]->mean()*mps[1]->mean());
+ auto phi_pred = 180.*atan(2.*mps[1]->mean()/(1.-(mps[0]->mean()*mps[0]->mean()+mps[1]->mean()*mps[1]->mean())))/M_PI;
+ return pow((alpha_measured-alpha_pred)/alpha_error,2.)+pow((phi_measured-phi_pred)/phi_error,2.);
+ };
+ Minimiser(f, &mps).doFit();
+}
diff --git a/examples/FitterWithPolarisation.cpp b/examples/FitterWithPolarisation.cpp
index 25aad8ae32a..bc36c2ac700 100644
--- a/examples/FitterWithPolarisation.cpp
+++ b/examples/FitterWithPolarisation.cpp
@@ -9,6 +9,7 @@
#include <vector>
#include "AmpGen/Chi2Estimator.h"
+#include "AmpGen/RecursivePhaseSpace.h"
#include "AmpGen/EventList.h"
#include "AmpGen/EventType.h"
#include "AmpGen/CoherentSum.h"
@@ -32,10 +33,23 @@
#include <TFile.h>
#include <TRandom3.h>
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_type = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_type = AmpGen::EventList;
+#endif
+
using namespace AmpGen;
+template <typename pdf_t> Particle getTopology(const pdf_t& pdf)
+{
+ return pdf.matrixElements()[0].decayTree.quasiStableTree();
+}
+
template <typename PDF>
-FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet& MPS );
+FitResult* doFit( PDF&& pdf, EventList_type& data, EventList_type& mc, MinuitParameterSet& MPS );
int main( int argc, char* argv[] )
{
@@ -50,7 +64,7 @@ int main( int argc, char* argv[] )
std::string dataFile = NamedParameter<std::string>("DataSample", "" , "Name of file containing data sample to fit." );
std::string logFile = NamedParameter<std::string>("LogFile" , "Fitter.log", "Name of the output log file");
std::string plotFile = NamedParameter<std::string>("Plots" , "plots.root", "Name of the output plot file");
-
+ std::string simFile = NamedParameter<std::string>("SgIntegratorFname", "" , "Name of file containing simulated sample for using in MC integration");
auto bNames = NamedParameter<std::string>("Branches", std::vector<std::string>()
,"List of branch names, assumed to be \033[3m daughter1_px ... daughter1_E, daughter2_px ... \033[0m" ).getVector();
@@ -60,9 +74,7 @@ int main( int argc, char* argv[] )
if( dataFile == "" ) FATAL("Must specify input with option " << italic_on << "DataSample" << italic_off );
if( pNames.size() == 0 ) FATAL("Must specify event type with option " << italic_on << " EventType" << italic_off);
- [[maybe_unused]]
- size_t nThreads = NamedParameter<size_t> ("nCores" , 8 , "Number of threads to use" );
- size_t seed = NamedParameter<size_t> ("Seed" , 0 , "Random seed used" );
+ size_t seed = NamedParameter<size_t> ("Seed" , 1 , "Random seed used" );
TRandom3 rndm;
rndm.SetSeed( seed );
@@ -71,6 +83,7 @@ int main( int argc, char* argv[] )
INFO("LogFile: " << logFile << "; Plots: " << plotFile );
#ifdef _OPENMP
+ size_t nThreads = NamedParameter<size_t> ("nCores" , 8 , "Number of threads to use" );
omp_set_num_threads( nThreads );
INFO( "Setting " << nThreads << " fixed threads for OpenMP" );
omp_set_dynamic( 0 );
@@ -80,6 +93,7 @@ int main( int argc, char* argv[] )
the parsed options. For historical reasons, this is referred to as loading it from a "Stream" */
MinuitParameterSet MPS;
MPS.loadFromStream();
+ // for( auto& p : MPS ) if( p->flag() == Flag::Free ) p->setResult( gRandom->Gaus( p->mean(), p->err() ), p->err(), 0,0 );
/* An EventType specifies the initial and final state particles as a vector that will be described by the fit.
It is typically loaded from the interface parameter EventType. */
@@ -95,12 +109,14 @@ int main( int argc, char* argv[] )
/* Events are read in from ROOT files. If only the filename and the event type are specified,
the file is assumed to be in the specific format that is defined by the event type,
unless the branches to load are specified in the user options */
- EventList events(dataFile, evtType, Branches(bNames), GetGenPdf(false) );
+ EventList_type events(dataFile, evtType, Branches(bNames), GetGenPdf(false) );
/* Generate events to normalise the PDF with. This can also be loaded from a file,
which will be the case when efficiency variations are included. Default number of normalisation events
- is 5 million. */
- EventList eventsMC = Generator<>(evtType, &rndm).generate(5e6);
+ is 2 million. */
+ Generator<RecursivePhaseSpace, EventList> signalGenerator( getTopology(sig), events.eventType(), &rndm );
+ auto events_l = signalGenerator.generate(1e6);
+ EventList_type eventsMC = simFile == "" ? EventList_type(events_l) : EventList_type(simFile, evtType);
sig.setMC( eventsMC );
@@ -108,27 +124,21 @@ int main( int argc, char* argv[] )
/* Do the fit and return the fit results, which can be written to the log and contains the
covariance matrix, fit parameters, and other observables such as fit fractions */
- FitResult* fr = doFit(make_pdf(sig), events, eventsMC, MPS );
+ FitResult* fr = doFit(make_pdf<EventList_type>(sig), events, eventsMC, MPS );
/* Calculate the `fit fractions` using the signal model and the error propagator (i.e.
fit results + covariance matrix) of the fit result, and write them to a file.
*/
auto fitFractions = sig.fitFractions( fr->getErrorPropagator() );
-
+
+ INFO("Adding fraction to file...");
fr->addFractions( fitFractions );
- fr->writeToFile( logFile );
- output->cd();
-
- /* Write out the data plots. This also shows the first example of the named arguments
- to functions, emulating python's behaviour in this area */
-
- auto plots = events.makeDefaultProjections(Prefix("Data"), Bins(100));
- for ( auto& plot : plots ) plot->Write();
-
+ INFO("Writing file ... ");
+ fr->writeToFile( logFile );
output->Close();
}
template <typename PDF>
-FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet& MPS )
+FitResult* doFit( PDF&& pdf, EventList_type& data, EventList_type& mc, MinuitParameterSet& MPS )
{
auto time_wall = std::chrono::high_resolution_clock::now();
auto time = std::clock();
@@ -144,28 +154,29 @@ FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet&
/* Make the plots for the different components in the PDF, i.e. the signal and backgrounds.
The structure assumed the PDF is some SumPDF<T1,T2,...>. */
- unsigned int counter = 1;
- for_each(pdf.m_pdfs, [&]( auto& f ){
-// std::function<double(const Event&)> FCN_sig = [&](const Event& evt){ return f.prob_unnormalised(evt) ; };
- auto mc_plot3 = mc.makeDefaultProjections(WeightFunction(f), Prefix("Model_cat"+std::to_string(counter)));
- for( auto& plot : mc_plot3 )
- {
- plot->Scale( ( data.integral() * f.getWeight() ) / plot->Integral() );
- plot->Write();
- }
- counter++;
- } );
/* Estimate the chi2 using an adaptive / decision tree based binning,
down to a minimum bin population of 15, and add it to the output. */
- Chi2Estimator chi2( data, mc, pdf, 15 );
- chi2.writeBinningToFile("chi2_binning.txt");
- fr->addChi2( chi2.chi2(), chi2.nBins() );
+ // Chi2Estimator chi2( data, mc, pdf, 15 );
+ // chi2.writeBinningToFile("chi2_binning.txt");
+ // fr->addChi2( chi2.chi2(), chi2.nBins() );
auto twall_end = std::chrono::high_resolution_clock::now();
double time_cpu = ( std::clock() - time ) / (double)CLOCKS_PER_SEC;
double tWall = std::chrono::duration<double, std::milli>( twall_end - time_wall ).count();
INFO( "Wall time = " << tWall / 1000. );
INFO( "CPU time = " << time_cpu );
+ auto evaluator = pdf.componentEvaluator(&mc);
+ auto projections = data.eventType().defaultProjections(100);
+
+ /* Write out the data plots. This also shows the first example of the named arguments
+ to functions, emulating python's behaviour in this area */
+ auto evaluator_per_component = std::get<0>( pdf.pdfs() ).componentEvaluator();
+ for( const auto& proj : projections )
+ {
+ proj(mc, evaluator, PlotOptions::Norm(data.size()), PlotOptions::AutoWrite() );
+ proj(mc, evaluator_per_component, PlotOptions::Prefix("amp"), PlotOptions::Norm(data.size()), PlotOptions::AutoWrite() );
+ proj(data, PlotOptions::Prefix("Data") )->Write();
+ }
fr->print();
return fr;
}
diff --git a/examples/QcGenerator.cpp b/examples/QcGenerator.cpp
new file mode 100644
index 00000000000..7a410e5ab45
--- /dev/null
+++ b/examples/QcGenerator.cpp
@@ -0,0 +1,447 @@
+#include "AmpGen/CoherentSum.h"
+#include "AmpGen/Generator.h"
+#include "AmpGen/EventType.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/Kinematics.h"
+#include "AmpGen/OptionsParser.h"
+#include "AmpGen/ProfileClock.h"
+#include "AmpGen/ParticlePropertiesList.h"
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/AddCPConjugate.h"
+#include <TFile.h>
+#include <TRandom3.h>
+#include <TRandom.h>
+#ifdef _OPENMP
+#include <omp.h>
+#include <thread>
+#endif
+
+using namespace AmpGen;
+using namespace std::complex_literals;
+
+class FixedLibPdf
+{
+ public:
+ FixedLibPdf() = default;
+ FixedLibPdf(const EventType& type, MinuitParameterSet& mps) :
+ FixedLibPdf(NamedParameter<std::string>(type.decayDescriptor()+"::lib").getVal())
+ {
+ INFO("Constructing: " << type << " flib = " <<type.decayDescriptor()+"::lib" );
+ }
+ FixedLibPdf(const std::string& lib)
+ {
+ void* handle = dlopen( lib.c_str(), RTLD_NOW );
+ if ( handle == nullptr ) ERROR( dlerror() );
+ INFO("Constructing from " << lib );
+ amp = AmpGen::DynamicFCN<complex_t( const double*, const int& )>( handle, "AMP" );
+ }
+ void prepare(){};
+ void setEvents( AmpGen::EventList& evts ){};
+ double prob_unnormalised( const AmpGen::Event& evt ) const { return std::norm(getValNoCache(evt)); }
+ complex_t getValNoCache( const AmpGen::Event& evt ) const { return amp(evt,+1); }
+ size_t size() { return 0; }
+ void reset( const bool& flag = false ){};
+ private:
+ AmpGen::DynamicFCN<complex_t( const double*, const int& )> amp;
+};
+
+struct DTEvent
+{
+ AmpGen::Event signal;
+ AmpGen::Event tag;
+ double prob;
+ DTEvent() : signal(0,0), tag(0,0) {};
+ DTEvent( const AmpGen::Event& signal, const AmpGen::Event& tag ) : signal(signal), tag(tag) {};
+ void set( const AmpGen::Event& s1, const AmpGen::Event& s2 ) { signal.set(s1); tag.set(s2); };
+ void invertParity(){
+ for( size_t i = 0 ; i < signal.size(); ++i ) if( i % 4 != 3 ) signal[i] *= -1;
+ for( size_t i = 0 ; i < tag.size(); ++i ) if( i % 4 != 3 ) tag[i] *= -1;
+ }
+};
+
+struct DTEventList : public std::vector<DTEvent>
+{
+ AmpGen::EventType m_sigType;
+ AmpGen::EventType m_tagType;
+ DTEventList( const AmpGen::EventType& signal, const AmpGen::EventType& tag ) : m_sigType(signal), m_tagType(tag) {}
+ std::string particleName(const AmpGen::EventType& type, const size_t& j);
+ TTree* tree(const std::string& name);
+};
+
+class DTYieldCalculator {
+ public:
+ DTYieldCalculator(const double& productionCrossSection = 3260) :
+ productionCrossSection(productionCrossSection){}
+
+ double operator()(const double& lumi,
+ const AmpGen::EventType& t_signal,
+ const AmpGen::EventType& t_tag,
+ const bool& print = false);
+ double bf( const AmpGen::EventType& type ) const;
+ private:
+ double productionCrossSection;
+ std::map<std::string, double> getKeyed( const std::string& name );
+ std::map<std::string, double> branchingRatios = {getKeyed("BranchingRatios")};
+ std::map<std::string, double> efficiencies = {getKeyed("Efficiencies")};
+};
+
+template <class PDF> struct normalised_pdf {
+ PDF pdf;
+ complex_t norm;
+ normalised_pdf() = default;
+ normalised_pdf(const EventType& type, MinuitParameterSet& mps, const DTYieldCalculator& yc) : pdf(type, mps)
+ {
+ ProfileClock pc;
+ auto normEvents = Generator<PhaseSpace>(type).generate(1e6);
+ double n =0;
+ pdf.prepare();
+ #pragma omp parallel for reduction(+:n)
+ for(size_t i =0; i<normEvents.size(); ++i)
+ n += std::norm(pdf.getValNoCache(normEvents[i]));
+ auto it = mps.find( type.decayDescriptor() + "::strongPhase");
+ norm = sqrt(yc.bf(type)/n);
+ if( it != nullptr ) norm *= exp( 1i * it->mean() * M_PI/180. );
+ pc.stop();
+ INFO(type << " Time to construct: " << pc << "[ms], norm = " << norm << " " << type_string<PDF>() );
+ }
+ complex_t operator()(const Event& event){ return norm * pdf.getValNoCache(event); }
+};
+
+struct ModelStore {
+ MinuitParameterSet* mps;
+ DTYieldCalculator yieldCalculator;
+ std::map<std::string, normalised_pdf<CoherentSum>> genericModels;
+ std::map<std::string, normalised_pdf<FixedLibPdf>> flibModels;
+ ModelStore(MinuitParameterSet* mps, const DTYieldCalculator& yc) : mps(mps), yieldCalculator(yc) {}
+ template <class T> normalised_pdf<T>& get(const EventType& type, std::map<std::string, normalised_pdf<T>>& container)
+ {
+ auto key = type.decayDescriptor();
+ if( container.count(key) == 0 )
+ container[key] = normalised_pdf<T>(type, *mps, yieldCalculator);
+ return container[key];
+ }
+ template <class T> normalised_pdf<T>& find(const EventType& type);
+};
+
+template <class T1, class T2> class Psi3770 {
+ private:
+ EventType m_signalType;
+ EventType m_tagType;
+ normalised_pdf<T1>& m_signal;
+ normalised_pdf<T1>& m_signalBar;
+ normalised_pdf<T2>& m_tag;
+ normalised_pdf<T2>& m_tagBar;
+ PhaseSpace m_signalPhsp;
+ PhaseSpace m_tagPhsp;
+ PhaseSpace m_headPhsp;
+ bool m_printed = {false};
+ bool m_ignoreQc = {NamedParameter<bool>("IgnoreQC",false)};
+ size_t m_blockSize = {1000000};
+ public:
+ template <class T> std::tuple<double,double,double>
+ z(T& t1, T& t2, const EventType& type) const
+ {
+ double n1(0), n2(0), zR(0), zI(0);
+ auto normEvents = Generator<PhaseSpace>(type).generate(m_blockSize);
+ #pragma omp parallel for reduction(+:zR,zI,n1,n2)
+ for(size_t i = 0; i < m_blockSize; ++i){
+ auto p1 = t1(normEvents[i]);
+ auto p2 = t2(normEvents[i]);
+ auto f = p2 * std::conj(p1);
+ zR += std::real(f);
+ zI += std::imag(f);
+ n1 += std::norm(p1);
+ n2 += std::norm(p2);
+ }
+ complex_t z2(zR,zI);
+ auto arg = std::arg(z2);
+ return std::make_tuple( std::abs(z2/sqrt(n1*n2)), 180 * ( arg > 0 ? arg : 2*M_PI+arg) /M_PI, sqrt(n1/n2) );
+ }
+ Psi3770(ModelStore& models,
+ const EventType& signalType,
+ const EventType& tagType) :
+ m_signalType(signalType) ,
+ m_tagType (tagType) ,
+ m_signal (models.find<T1>(m_signalType)),
+ m_signalBar (models.find<T1>(m_signalType.conj(true))),
+ m_tag (models.find<T2>(m_tagType)) ,
+ m_tagBar (models.find<T2>(m_tagType.conj(true))) ,
+ m_signalPhsp(m_signalType ) ,
+ m_tagPhsp (m_tagType ) ,
+ m_headPhsp (EventType({"psi(3770)0","D0","Dbar0"}))
+ {
+ INFO("Type = " << m_signalType << " x " << m_tagType.conj(true) << "] - [" << m_signalType.conj(true) << " x " << m_tagType << "]");
+ auto z1 = z(m_signal, m_signalBar, m_signalType);
+ auto z2 = z(m_tag , m_tagBar , m_tagType);
+ INFO( "Signal: R = " << round(std::get<0>(z1),5) << "; δ = " << round(std::get<1>(z1),3) << "° ; r = " << round(std::get<2>(z1),5) );
+ INFO( "Tag : R = " << round(std::get<0>(z2),5) << "; δ = " << round(std::get<1>(z2),3) << "° ; r = " << round(std::get<2>(z2),5) );
+ }
+ complex_t operator()(const DTEvent& event ) const { return operator()( event.signal, event.tag ); }
+ complex_t operator()(const Event& signal, const Event& tag) const { return m_signal(signal)*m_tagBar(tag) - m_signalBar(signal) * m_tag(tag); }
+ double P(const DTEvent& event) const { return m_ignoreQc ? prob_noQC(event) : std::norm(operator()(event)); }
+ double prob_noQC (const DTEvent& event) const { return std::norm(m_signal(event.signal)*m_tagBar(event.tag)) + std::norm(m_signalBar(event.signal)*m_tag(event.tag)); }
+ DTEvent generatePhaseSpace() { return DTEvent( m_signalPhsp.makeEvent(), m_tagPhsp.makeEvent() ); }
+ DTEventList generate( const size_t& N )
+ {
+ DTEventList output( m_signalType, m_tagType );
+ ProgressBar pb(60, detail::trimmedString(__PRETTY_FUNCTION__));
+ auto tStartTotal = std::chrono::high_resolution_clock::now();
+ int currentSize = 0;
+ double norm = -1;
+ while( output.size() < N ){
+ auto events = generatePHSP(m_blockSize);
+ if(norm == -1 ){
+ for(auto& event : events) if(event.prob > norm ) norm = event.prob;
+ norm *= 1.5;
+ INFO("Calculated normalisation of PDF = " << norm );
+ }
+ for( auto& event : events ){
+ if( event.prob > norm * gRandom->Uniform() ) output.push_back( event );
+ if( output.size() >= N ) break ;
+ }
+ double efficiency = 100 * double(output.size() - currentSize )/double(m_blockSize);
+ double time = std::chrono::duration<double, std::milli>( std::chrono::high_resolution_clock::now() - tStartTotal ).count();
+ pb.print( double(output.size()) / double(N), " ε[gen] = " + mysprintf("%.2f",efficiency) + "% , " + std::to_string(int(time/1000.)) + " seconds" );
+ currentSize = output.size();
+ }
+ auto psi_q = PhaseSpace(m_headPhsp);
+ auto beta = [](const Event& event, const size_t&j){ return sqrt( event[4*j+0]*event[4*j+0] + event[4*j+1]*event[4*j+1] + event[4*j+2]*event[4*j+2] )/event[4*j+3] ; };
+ auto p = [](const Event& event, const size_t&j){ return std::make_tuple(event[4*j+0], event[4*j+1], event[4*j+2]); };
+ for( auto& event : output ){
+ auto psi_event = psi_q.makeEvent();
+ boost( event.signal, p(psi_event,0), beta(psi_event,0));
+ boost( event.tag , p(psi_event,1), beta(psi_event,1));
+ }
+ double time = std::chrono::duration<double, std::milli>( std::chrono::high_resolution_clock::now() - tStartTotal ).count();
+ pb.finish();
+ INFO("Requested: " << N << " events t=" << time/1000 << "[ms]");
+ return output;
+ }
+ DTEventList generatePHSP(const size_t& N, const bool& eval=true){
+ DTEventList output( m_signalType, m_tagType );
+ for(size_t x = 0 ; x < m_blockSize; ++x) output.emplace_back( generatePhaseSpace() );
+#pragma omp parallel for
+ for(size_t i = 0 ; i < m_blockSize; ++i ) output[i].prob = P(output[i]);
+ return output;
+ }
+ double rho() {
+ if( m_ignoreQc ) return 1;
+ double withQC=0;
+ double withoutQC =0;
+ DTEventList evts = generatePHSP(m_blockSize, false);
+#pragma omp parallel for reduction(+:withQC,withoutQC)
+ for( size_t x = 0; x<m_blockSize; ++x ){
+ auto event = evts[x];
+ withQC += P(event);
+ withoutQC += prob_noQC(event);
+ }
+ return withQC / withoutQC ;
+ }
+};
+
+int main( int argc, char** argv )
+{
+ OptionsParser::setArgs( argc, argv, "Toy simulation for Quantum Correlated Ψ(3770) decays");
+ auto time_wall = std::chrono::high_resolution_clock::now();
+ auto time = std::clock();
+ size_t hwt = std::thread::hardware_concurrency();
+ size_t nThreads = NamedParameter<size_t>("nCores" , hwt , "Number of threads to use");
+ double luminosity = NamedParameter<double>("Luminosity" , 818.3 , "Luminosity to generate. Defaults to CLEO-c integrated luminosity.");
+ size_t nEvents = NamedParameter<size_t>("nEvents" , 0 , "Can also generate a fixed number of events per tag, if unspecified use the CLEO-c integrated luminosity.");
+ size_t seed = NamedParameter<size_t>("Seed" , 0 , "Random seed to use.");
+ bool poissonYield = NamedParameter<bool >("PoissonYield", true , "Flag to include Poisson fluctuations in expected yields (only if nEvents is not specified)");
+ double crossSection = NamedParameter<double>("CrossSection", 3.26 * 1000 , "Cross section for e⁺e⁻ → Ψ(3770) → DD'");
+ std::string output = NamedParameter<std::string>("Output" , "ToyMC.root", "File containing output events");
+ auto pNames = NamedParameter<std::string>("EventType" , ""
+ , "EventType to generate, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector();
+ auto tags = NamedParameter<std::string>("TagTypes" , std::string(), "Vector of opposite side tags to generate, in the format \033[3m outputTreeName decayDescriptor \033[0m.").getVector();
+
+ gRandom = new TRandom3(seed);
+#ifdef _OPENMP
+ omp_set_num_threads( nThreads );
+ INFO("Setting " << nThreads << " fixed threads for OpenMP");
+ omp_set_dynamic(0);
+#endif
+ MinuitParameterSet MPS;
+ MPS.loadFromStream();
+ AddCPConjugate(MPS);
+ EventType signalType( pNames );
+ TFile* f = TFile::Open( output.c_str() ,"RECREATE");
+ auto yc = DTYieldCalculator(crossSection);
+ if( nEvents == 0 )
+ INFO("Generating events using PDG/efficiencies with luminosity = " << luminosity << " pb⁻¹; σ = " << crossSection << " pb" );
+ else INFO("Generating " << nEvents << " per sample");
+ ModelStore models(&MPS, yc);
+ for( auto& tag : tags ){
+ auto tokens = split(tag, ' ');
+ auto tagParticle = Particle(tokens[1], {}, false);
+ EventType type = tagParticle.eventType();
+ double yield_noQC = yc(luminosity,signalType,type,true);
+ std::string flib = NamedParameter<std::string>( type.decayDescriptor() +"::lib", "");
+ if( flib == "" ){
+ auto generator = Psi3770<CoherentSum,CoherentSum>(models, signalType, type);
+ double rho = generator.rho();
+ double yield = nEvents;
+ if( nEvents == 0 && poissonYield ) yield = gRandom->Poisson(yield_noQC*rho);
+ if( nEvents == 0 && !poissonYield ) yield = yield_noQC*rho;
+ INFO( "Tag = " << type << " Expected Yield [incoherent] = " << yield_noQC << " rho = " << rho << " requested = " << yield );
+ generator.generate(yield).tree(tokens[0])->Write();
+ }
+ else {
+ auto generator = Psi3770<CoherentSum,FixedLibPdf>(models, signalType, type);
+ double rho = generator.rho();
+ double yield = nEvents;
+ if( nEvents == 0 && poissonYield ) yield = gRandom->Poisson(yield_noQC*rho);
+ if( nEvents == 0 && !poissonYield ) yield = yield_noQC*rho;
+ INFO( "Tag = " << type << " Expected Yield [incoherent] = " << yield_noQC << " rho = " << rho << " requested = " << yield );
+ generator.generate(yield).tree(tokens[0])->Write();
+ }
+ }
+ f->Close();
+ auto twall_end = std::chrono::high_resolution_clock::now();
+ double time_cpu = ( std::clock() - time ) / (double)CLOCKS_PER_SEC;
+ double tWall = std::chrono::duration<double, std::milli>( twall_end - time_wall ).count();
+ INFO( "Wall time = " << tWall / 1000. );
+ INFO( "CPU time = " << time_cpu );
+}
+
+void add_CP_conjugate( MinuitParameterSet& mps )
+{
+ std::vector<MinuitParameter*> tmp;
+ for( auto& param : mps ){
+ const std::string name = param->name();
+ size_t pos=0;
+ std::string new_name = name;
+ int sgn=1;
+ if( name.find("::") != std::string::npos ){
+ pos = name.find("::");
+ auto props = AmpGen::ParticlePropertiesList::get( name.substr(0,pos), true );
+ if( props != 0 ) new_name = props->anti().name() + name.substr(pos);
+ }
+ else {
+ auto tokens=split(name,'_');
+ std::string reOrIm = *tokens.rbegin();
+ std::string pname = tokens[0];
+ if ( reOrIm == "Re" || reOrIm == "Im" ){
+ auto p = Particle( pname ).conj();
+ sgn = reOrIm == "Re" ? p.CP() : 1;
+ new_name = p.uniqueString() +"_"+reOrIm;
+ }
+ else if( tokens.size() == 2 ) {
+ auto props = AmpGen::ParticlePropertiesList::get( name );
+ if( props != 0 ) new_name = props->anti().name() + "_" + tokens[1];
+ }
+ }
+ if( mps.find( new_name ) == nullptr ){
+ tmp.push_back( new MinuitParameter(new_name, Flag::Free, sgn * param->mean(), param->err(), 0, 0));
+ }
+ }
+ for( auto& p : tmp ) mps.add( p );
+}
+
+std::map<std::string, double> DTYieldCalculator::getKeyed(const std::string& name)
+{
+ std::vector<std::string> things = AmpGen::NamedParameter<std::string>(name).getVector();
+ std::map< std::string , double > branchingRatios;
+ for( auto& thing : things ){
+ auto tokens = AmpGen::split( thing, ' ' );
+ AmpGen::Particle p(tokens[0]);
+ branchingRatios[p.uniqueString()] = stod(tokens[1]);
+ branchingRatios[p.conj().uniqueString()] = stod(tokens[1]);
+ }
+ return branchingRatios;
+}
+
+double DTYieldCalculator::operator()(const double& lumi,
+ const AmpGen::EventType& t_signal,
+ const AmpGen::EventType& t_tag,
+ const bool& print){
+ auto statisticalFactor = 2;
+ if( t_signal == t_tag || t_signal == t_tag.conj(false,true) ) statisticalFactor = 1;
+ auto signal = AmpGen::Particle(t_signal.decayDescriptor()).uniqueString();
+ auto tag = AmpGen::Particle(t_tag.decayDescriptor()).uniqueString();
+ auto signalBar = AmpGen::replaceAll( signal, "D0", "Dbar0");
+ auto tagBar = AmpGen::replaceAll( tag, "D0", "Dbar0");
+ auto eff = [this](const std::string& tag) -> double { auto it = efficiencies.find(tag);
+ if( it == efficiencies.end() ){
+ WARNING("Efficiency for final state: " << tag << " not found");
+ return 1;
+ }
+ return it->second;
+ };
+ double efficiency = eff(signal) * eff(tag);
+ double br = branchingRatios[signal] * branchingRatios[tagBar] + branchingRatios[signalBar] * branchingRatios[tag];
+ double totalDDbar = lumi * productionCrossSection;
+ if( print ){
+ INFO("Expected yield for final state: " << t_signal << " vs " << t_tag );
+ INFO("Total DDbar = " << totalDDbar );
+ INFO("Efficiency = " << efficiency );
+ INFO("BR = " << branchingRatios[signal] <<" x " << branchingRatios[tagBar]
+ << " + " << branchingRatios[signalBar] << " x " << branchingRatios[tag]
+ << " = " << br );
+ INFO("Total = " << statisticalFactor * totalDDbar * efficiency * br );
+ }
+ return statisticalFactor * totalDDbar * efficiency * br;
+}
+
+double DTYieldCalculator::bf( const AmpGen::EventType& type ) const {
+ auto p = AmpGen::Particle( type.decayDescriptor() );
+ auto it = branchingRatios.find(p.decayDescriptor());
+ if( it != branchingRatios.end() ) return it->second;
+ else {
+ ERROR("Tag: " << p.decayDescriptor() << " not found in branching ratios");
+ return 0;
+ }
+}
+std::string DTEventList::particleName(const AmpGen::EventType& type, const size_t& j)
+{
+ auto count = type.count(j);
+ if( count.second == 1 ) return programatic_name(type[j]);
+ return programatic_name(type[j])+std::to_string(count.first);
+}
+
+TTree* DTEventList::tree(const std::string& name)
+{
+ DTEvent tmp(at(0).signal, at(0).tag);
+ std::vector<int> id_sig(m_sigType.size()),
+ ids_sig(m_sigType.size()),
+ id_tag(m_tagType.size()),
+ ids_tag(m_tagType.size());
+
+ TTree* outputTree = new TTree(name.c_str(),name.c_str());
+ for(size_t i = 0 ; i < m_sigType.size(); ++i )
+ {
+ outputTree->Branch((particleName(m_sigType, i)+"_PX").c_str(), &tmp.signal[4*i+0]);
+ outputTree->Branch((particleName(m_sigType, i)+"_PY").c_str(), &tmp.signal[4*i+1]);
+ outputTree->Branch((particleName(m_sigType, i)+"_PZ").c_str(), &tmp.signal[4*i+2]);
+ outputTree->Branch((particleName(m_sigType, i)+"_E").c_str(), &tmp.signal[4*i+3]);
+ outputTree->Branch((particleName(m_sigType, i)+"_ID").c_str(), &id_sig[i]);
+ ids_sig[i] = ParticlePropertiesList::get( m_sigType[i] )->pdgID();
+ }
+ for(size_t i = 0 ; i < m_tagType.size(); ++i )
+ {
+ outputTree->Branch(("Tag_"+particleName(m_tagType, i)+"_PX").c_str(), &tmp.tag[4*i+0]);
+ outputTree->Branch(("Tag_"+particleName(m_tagType, i)+"_PY").c_str(), &tmp.tag[4*i+1]);
+ outputTree->Branch(("Tag_"+particleName(m_tagType, i)+"_PZ").c_str(), &tmp.tag[4*i+2]);
+ outputTree->Branch(("Tag_"+particleName(m_tagType, i)+"_E").c_str(), &tmp.tag[4*i+3]);
+ outputTree->Branch(("Tag_"+particleName(m_tagType, i)+"_ID").c_str(), &id_tag[i]);
+ ids_tag[i] = ParticlePropertiesList::get( m_tagType[i] )->pdgID();
+ }
+ bool sym = NamedParameter<bool>("symmetrise",true);
+ for( auto& evt: *this ){
+ bool swap = sym && ( gRandom->Uniform() > 0.5 );
+ tmp.set(evt.signal, evt.tag);
+ if( swap ) tmp.invertParity();
+ for(size_t i=0; i != m_sigType.size(); ++i)
+ id_sig[i] = swap ? -ids_sig[i] : ids_sig[i];
+ for(size_t i=0; i != m_tagType.size(); ++i)
+ id_tag[i] = swap ? -ids_tag[i] : ids_tag[i];
+ outputTree->Fill();
+ }
+
+ return outputTree;
+}
+
+template <> normalised_pdf<CoherentSum>& ModelStore::find(const EventType& type){ return get<CoherentSum>(type, genericModels); }
+template <> normalised_pdf<FixedLibPdf>& ModelStore::find(const EventType& type){ return get<FixedLibPdf>(type, flibModels); }
+
diff --git a/examples/SignalOnlyFitter.cpp b/examples/SignalOnlyFitter.cpp
index b7b1cafcbf7..611ae7dd6da 100644
--- a/examples/SignalOnlyFitter.cpp
+++ b/examples/SignalOnlyFitter.cpp
@@ -9,7 +9,6 @@
#include <vector>
#include "AmpGen/Chi2Estimator.h"
-#include "AmpGen/EventList.h"
#include "AmpGen/EventType.h"
#include "AmpGen/CoherentSum.h"
#include "AmpGen/IncoherentSum.h"
@@ -27,14 +26,21 @@
#include <thread>
#endif
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_type = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_type = AmpGen::EventList;
+#endif
+
#include <TH1.h>
#include <TFile.h>
#include <TRandom3.h>
using namespace AmpGen;
-template <typename PDF>
-FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet& MPS );
+template <typename PDF> FitResult* doFit( PDF&& pdf, EventList_type& data, EventList_type& mc, MinuitParameterSet& MPS );
int main( int argc, char* argv[] )
{
@@ -47,6 +53,7 @@ int main( int argc, char* argv[] )
then the default value, and then the help string that will be printed if --h is specified
as an option. */
std::string dataFile = NamedParameter<std::string>("DataSample", "" , "Name of file containing data sample to fit." );
+ std::string intFile = NamedParameter<std::string>("IntegrationSample","" , "Name of file containing events to use for MC integration.");
std::string logFile = NamedParameter<std::string>("LogFile" , "Fitter.log", "Name of the output log file");
std::string plotFile = NamedParameter<std::string>("Plots" , "plots.root", "Name of the output plot file");
@@ -56,13 +63,13 @@ int main( int argc, char* argv[] )
auto pNames = NamedParameter<std::string>("EventType" , ""
, "EventType to fit, in the format: \033[3m parent daughter1 daughter2 ... \033[0m" ).getVector();
- if( dataFile == "" ) FATAL("Must specify input with option " << italic_on << "DataSample" << italic_off );
- if( pNames.size() == 0 ) FATAL("Must specify event type with option " << italic_on << " EventType" << italic_off);
-
[[maybe_unused]]
size_t nThreads = NamedParameter<size_t> ("nCores" , 8 , "Number of threads to use" );
size_t seed = NamedParameter<size_t> ("Seed" , 0 , "Random seed used" );
-
+
+ if( dataFile == "" ) FATAL("Must specify input with option " << italic_on << "DataSample" << italic_off );
+ if( pNames.size() == 0 ) FATAL("Must specify event type with option " << italic_on << " EventType" << italic_off);
+
TRandom3 rndm;
rndm.SetSeed( seed );
gRandom = &rndm;
@@ -83,23 +90,26 @@ int main( int argc, char* argv[] )
/* An EventType specifies the initial and final state particles as a vector that will be described by the fit.
It is typically loaded from the interface parameter EventType. */
EventType evtType(pNames);
-
/* A CoherentSum is the typical amplitude to be used, that is some sum over quasi two-body contributions
weighted by an appropriate complex amplitude. The CoherentSum is generated from the couplings described
by a set of parameters (in a MinuitParameterSet), and an EventType, which matches these parameters
to a given final state and a set of data. A common set of rules can be matched to multiple final states,
- i.e. to facilitate the analysis of coupled channels. */
+ i.e. to facilitate the analysis of coupled channels.
+ The CoherentSum is only appropriate for decays involving only (pseudo)scalars in the inital / final state,
+ otherwise the sum must also be over initial / final spin states. In this case, as PolarisedSum should be used.
+ See FitterWithPolarisation for an example of this use case.
+ */
CoherentSum sig(evtType, MPS);
/* Events are read in from ROOT files. If only the filename and the event type are specified,
the file is assumed to be in the specific format that is defined by the event type,
unless the branches to load are specified in the user options */
- EventList events(dataFile, evtType, Branches(bNames), GetGenPdf(false) );
+ EventList_type events(dataFile, evtType, Branches(bNames), GetGenPdf(false) );
/* Generate events to normalise the PDF with. This can also be loaded from a file,
which will be the case when efficiency variations are included. Default number of normalisation events
is 5 million. */
- EventList eventsMC = Generator<>(evtType, &rndm).generate(5e6);
+ EventList_type eventsMC = intFile == "" ? Generator<>(evtType, &rndm).generate(2.5e6) : EventList_type(intFile, evtType, GetGenPdf(true));
sig.setMC( eventsMC );
@@ -107,7 +117,7 @@ int main( int argc, char* argv[] )
/* Do the fit and return the fit results, which can be written to the log and contains the
covariance matrix, fit parameters, and other observables such as fit fractions */
- FitResult* fr = doFit(make_pdf(sig), events, eventsMC, MPS );
+ FitResult* fr = doFit(make_likelihood(events, sig), events, eventsMC, MPS );
/* Calculate the `fit fractions` using the signal model and the error propagator (i.e.
fit results + covariance matrix) of the fit result, and write them to a file.
*/
@@ -115,57 +125,46 @@ int main( int argc, char* argv[] )
fr->addFractions( fitFractions );
fr->writeToFile( logFile );
- output->cd();
- /* Write out the data plots. This also shows the first example of the named arguments
- to functions, emulating python's behaviour in this area */
-
- auto plots = events.makeDefaultProjections(Prefix("Data"), Bins(100));
- for ( auto& plot : plots ) plot->Write();
-
output->Close();
}
-template <typename PDF>
-FitResult* doFit( PDF&& pdf, EventList& data, EventList& mc, MinuitParameterSet& MPS )
+template <typename likelihoodType>
+FitResult* doFit( likelihoodType&& likelihood, EventList_type& data, EventList_type& mc, MinuitParameterSet& MPS )
{
auto time_wall = std::chrono::high_resolution_clock::now();
auto time = std::clock();
-
- pdf.setEvents( data );
-
/* Minimiser is a general interface to Minuit1/Minuit2,
that is constructed from an object that defines an operator() that returns a double
(i.e. the likielihood, and a set of MinuitParameters. */
- Minimiser mini( pdf, &MPS );
+ Minimiser mini( likelihood, &MPS );
mini.doFit();
FitResult* fr = new FitResult(mini);
-
- /* Make the plots for the different components in the PDF, i.e. the signal and backgrounds.
- The structure assumed the PDF is some SumPDF<T1,T2,...>. */
- unsigned int counter = 1;
- for_each(pdf.m_pdfs, [&]( auto& f ){
- std::function<double(const Event&)> FCN_sig = [&](const Event& evt){ return f.prob_unnormalised(evt) ; };
- auto mc_plot3 = mc.makeDefaultProjections(WeightFunction(f), Prefix("Model_cat"+std::to_string(counter)));
- for( auto& plot : mc_plot3 )
- {
- plot->Scale( ( data.integral() * f.getWeight() ) / plot->Integral() );
- plot->Write();
- }
- counter++;
- } );
-
- /* Estimate the chi2 using an adaptive / decision tree based binning,
- down to a minimum bin population of 15, and add it to the output. */
- Chi2Estimator chi2( data, mc, pdf, 15 );
- chi2.writeBinningToFile("chi2_binning.txt");
- fr->addChi2( chi2.chi2(), chi2.nBins() );
auto twall_end = std::chrono::high_resolution_clock::now();
double time_cpu = ( std::clock() - time ) / (double)CLOCKS_PER_SEC;
double tWall = std::chrono::duration<double, std::milli>( twall_end - time_wall ).count();
INFO( "Wall time = " << tWall / 1000. );
INFO( "CPU time = " << time_cpu );
+
+ /* Estimate the chi2 using an adaptive / decision tree based binning,
+ down to a minimum bin population of 15, and add it to the output. */
+
+ Chi2Estimator chi2( data, mc, likelihood.evaluator(&mc), MinEvents(15), Dim(data.eventType().dof()) );
+ chi2.writeBinningToFile("chi2_binning.txt");
+ fr->addChi2( chi2.chi2(), chi2.nBins() );
fr->print();
+
+ /* Make the plots for the different components in the PDF, i.e. the signal and backgrounds.
+ The structure assumed the PDF is some SumPDF<eventListType, pdfType1, pdfType2,... >. */
+ auto evaluator = likelihood.componentEvaluator(&mc);
+ auto evaluator_per_component = std::get<0>( likelihood.pdfs() ).componentEvaluator(&mc);
+ auto projections = data.eventType().defaultProjections(100);
+ for( const auto& proj : projections )
+ {
+ proj(mc, evaluator, PlotOptions::Norm(data.size()), PlotOptions::AutoWrite() );
+ proj(mc, evaluator_per_component, PlotOptions::Prefix("amp"), PlotOptions::Norm(data.size()), PlotOptions::AutoWrite() );
+ proj(data, PlotOptions::Prefix("Data") )->Write();
+ }
return fr;
}
diff --git a/examples/SimFit.cpp b/examples/SimFit.cpp
new file mode 100644
index 00000000000..95345cd2797
--- /dev/null
+++ b/examples/SimFit.cpp
@@ -0,0 +1,98 @@
+#include "AmpGen/Particle.h"
+#include "AmpGen/CoherentSum.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/SumPDF.h"
+#include "AmpGen/FitResult.h"
+#include "AmpGen/IExtendLikelihood.h"
+#include "AmpGen/Minimiser.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/SimPDF.h"
+#include "AmpGen/Kinematics.h"
+#include "AmpGen/Generator.h"
+#include "AmpGen/PolarisedSum.h"
+#include "AmpGen/AddCPConjugate.h"
+#ifdef _OPENMP
+ #include <omp.h>
+#endif
+#if ENABLE_AVX
+ #include "AmpGen/EventListSIMD.h"
+ using EventList_type = AmpGen::EventListSIMD;
+#else
+ #include "AmpGen/EventList.h"
+ using EventList_type = AmpGen::EventList;
+#endif
+
+#include "TRandom3.h"
+#include "TFile.h"
+#include "TTree.h"
+
+using namespace AmpGen;
+
+int main(int argc , char* argv[] ){
+ OptionsParser::setArgs( argc, argv );
+
+ const auto datasets = NamedParameter<std::string>("Datasets","",
+ "List of data/simulated samples to fit, in the format \
+ \033[3m data[0] sim[0] data[1] sim[1] ... \033[0m. \nIf a simulated sample is specified FLAT, uniformly generated phase-space events are used for integrals ").getVector();
+
+ const std::string logFile = NamedParameter<std::string>("LogFile" , "Fitter.log",
+ "Name of the output log file");
+
+ const std::string plotFile = NamedParameter<std::string>("Plots" , "plots.root",
+ "Name of the output plot file");
+
+ const bool add_conj = NamedParameter<bool>("AddConj", false );
+
+ std::vector<EventList_type> data;
+ std::vector<EventList_type> mcs;
+
+ #ifdef _OPENMP
+ size_t hwThreads = std::thread::hardware_concurrency();
+ size_t usThreads = NamedParameter<size_t>( "nCores", hwThreads, "Number of cores to use (OpenMP only)" );
+ INFO("Using: " << usThreads << " / " << hwThreads << " threads" );
+ omp_set_num_threads(usThreads);
+ omp_set_dynamic(0);
+ #endif
+
+ INFO("Output : " << logFile << " plots = " << plotFile );
+
+ for(size_t i=0;i < datasets.size() ; i+=2 ){
+ data.emplace_back( datasets[i] );
+ if( datasets[i+1] == "FLAT" ) mcs.emplace_back(Generator<>(data.rbegin()->eventType() ).generate(1e6));
+ else mcs.emplace_back( datasets[i+1], data.rbegin()->eventType(), GetGenPdf(true) );
+ }
+
+ std::vector<PolarisedSum> fcs(data.size());
+ std::vector<SumPDF<EventList_type, PolarisedSum&>> pdfs;
+
+ pdfs.reserve(data.size());
+
+ SimFit totalLL;
+ MinuitParameterSet mps;
+ mps.loadFromStream();
+ if( add_conj ) AddCPConjugate(mps);
+ for(size_t i = 0; i < data.size(); ++i){
+ fcs[i] = PolarisedSum(data[i].eventType(), mps);
+ pdfs.emplace_back( make_pdf<EventList_type>(fcs[i]) );
+ pdfs[i].setEvents(data[i]);
+ auto& mc = mcs[i];
+ for_each( pdfs[i].pdfs(), [&mc](auto& pdf){pdf.setMC(mc);});
+ totalLL.add( pdfs[i] );
+ }
+ Minimiser mini( totalLL, &mps );
+ mini.doFit();
+ FitResult(mini).writeToFile("Fitter.log");
+ TFile* output_plots = TFile::Open( plotFile.c_str(), "RECREATE");
+ for( size_t i = 0 ; i < data.size(); ++i )
+ {
+ INFO("Making figures for sample: " << i << " ...");
+ for( auto proj : data[i].eventType().defaultProjections() )
+ {
+ proj(data[i], PlotOptions::Prefix("Data"+std::to_string(i)), PlotOptions::AutoWrite() );
+ proj(mcs[i] , pdfs[i].componentEvaluator(&mcs[i]), PlotOptions::Prefix("pdf"+std::to_string(i)), PlotOptions::Norm(data.size()), PlotOptions::AutoWrite() );
+ }
+ }
+ output_plots->Close();
+}
diff --git a/examples/qc_options_example.opt b/examples/qc_options_example.opt
new file mode 100644
index 00000000000..c2c8578d973
--- /dev/null
+++ b/examples/qc_options_example.opt
@@ -0,0 +1,47 @@
+
+EventType D0 K+ pi- pi- pi+
+
+TagTypes { "KK D0{K+,K-}"
+ "KPi D0{K-,pi+}"
+ "KsPi0 D0{K0S0,pi0}"
+ "PiK D0{K+,pi-}"
+ "PiKPiPi D0{K+,pi-,pi-,pi+}"
+ "KPiPiPi D0{K-,pi+,pi+,pi-}"
+ }
+
+Efficiencies {
+ "D0{K+,K-} 0.57"
+ "D0{K0S0,pi0} 0.31"
+ "D0{pi+,pi-} 0.71"
+ "D0{K-,pi+,pi+,pi-} 0.46"
+ "D0{K+,pi-,pi-,pi+} 0.46"
+ "D0{K-,pi+} 0.60"
+ "D0{K+,pi-} 0.60"
+}
+
+BranchingRatios {
+ "D0{K+,K-} 0.003970"
+ "D0{K0S0,pi0} 0.011900"
+ "D0{pi+,pi-} 0.001407"
+ "D0{K-,pi+,pi+,pi-} 0.0811"
+ "D0{K+,pi-,pi-,pi+} 0.000245"
+ "D0{K-,pi+} 0.0389"
+ "D0{K+,pi-} 0.0001366"
+}
+
+Import $AMPGENROOT/options/D02piKpipi.opt
+
+D0{K+,K-} 2 1 0 2 0 0
+Dbar0{K+,K-} 2 1 0 2 0 0
+
+D0{pi+,pi-} 2 1 0 2 0 0
+Dbar0{pi+,pi-} 2 1 0 2 0 0
+
+D0{K0S0,pi0} 2 1 0 2 0 0
+Dbar0{K0S0,pi0} 2 1 0 2 180 0
+
+D0{K-,pi+} 2 1 0 2 0.0 0
+Dbar0{K-,pi+} 2 1 0 2 -191.8 0
+
+D0{K+,pi-,pi-,pi+}::strongPhase 2 -130.0 0 #overall phase shift to add to the D0->K+,pi-,pi-,pi+
+Dbar0{K-,pi+,pi+,pi-}::strongPhase = D0{K+,pi-,pi-,pi+}::strongPhase
diff --git a/options/D02Kpipipi.opt b/options/D02Kpipipi.opt
index 5fe22c2017d..b4c83e6ab98 100644
--- a/options/D02Kpipipi.opt
+++ b/options/D02Kpipipi.opt
@@ -1,4 +1,5 @@
# Description of CF amplitude D0 -> K-,pi+,pi+,pi-
+EventType D0 K- pi+ pi+ pi-
Import $AMPGENROOT/options/kMatrix.opt
a(1)(1260)-::Spline 40 0.18412 1.9
diff --git a/options/D02piKpipi.opt b/options/D02piKpipi.opt
index b81c4db0536..189951d7289 100644
--- a/options/D02piKpipi.opt
+++ b/options/D02piKpipi.opt
@@ -1,21 +1,24 @@
# Description of DCS amplitude D0 -> K+,pi-,pi-,pi+
-
Import $AMPGENROOT/options/Dbar02piKpipi.opt #necessary for K1 couplings / shape parameters
-D0_radius 2 3.7559 0
-D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 0 0.205 0.019 0 -8.5 4.7
-D0[P]{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 0 0.390 0.002 0 -91.4 0.4
-D0[D]{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 1.000 0.000 2 0.0 0.0
-D0{rho(1450)0{pi+,pi-},K*(892)0{K+,pi-}} 0 0.541 0.042 0 -21.8 6.5
+CouplingConstant::Coordinates polar
+CouplingConstant::AngularUnits deg
+CoherentSum::Verbosity 0
+
+D0_radius 2 3.7559 0
+D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 0.205 0.019 2 -8.5 4.7
+D0[P]{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 0.390 0.002 2 -91.4 0.4
+D0[D]{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}} 2 1.000 0.000 2 0.0 0.0
+D0{rho(1450)0{pi+,pi-},K*(892)0{K+,pi-}} 2 0.541 0.042 2 -21.8 6.5
# There is an additional relative phase of 180 degrees here w.r.t
# what is written in the paper, due to a slightly different convention
# in how the K(1) couplings have been defined.
-D0{K(1)(1270)+,pi-} 0 0.653 0.040 0 69.3 5.1
-D0{K(1)(1400)+{K*(892)0{K+,pi-},pi+},pi-} 0 0.560 0.037 0 29.8 4.2
-D0{KPi40,PiPi40} 2 1.000 0.000 2 0.0 0.0
-KPi40[FOCUS.Kpi]{K+,pi-} 2 1.000 0.000 2 0.0 0.0
-KPi40[FOCUS.I32]{K+,pi-} 0 0.686 0.010 0 -149.4 4.3
-PiPi40[kMatrix.pole.1]{pi+,pi-} 0 0.438 0.009 0 -132.4 6.5
-PiPi40[kMatrix.prod.0]{pi+,pi-} 0 0.050 0.001 0 74.8 7.5
+D0{K(1)(1270)+,pi-} 2 0.653 0.040 2 69.3 5.1
+D0{K(1)(1400)+{K*(892)0{K+,pi-},pi+},pi-} 2 0.560 0.037 2 29.8 4.2
+D0{KPi40,PiPi40} 2 1.000 0.000 2 0.0 0.0
+KPi40[FOCUS.Kpi]{K+,pi-} 2 1.000 0.000 2 0.0 0.0
+KPi40[FOCUS.I32]{K+,pi-} 2 0.686 0.010 2 -149.4 4.3
+PiPi40[kMatrix.pole.1]{pi+,pi-} 2 0.438 0.009 2 -132.4 6.5
+PiPi40[kMatrix.prod.0]{pi+,pi-} 2 0.050 0.001 2 74.8 7.5
diff --git a/options/Dbar02piKpipi.opt b/options/Dbar02piKpipi.opt
index 6e254ae3811..b3ee7777480 100644
--- a/options/Dbar02piKpipi.opt
+++ b/options/Dbar02piKpipi.opt
@@ -46,8 +46,8 @@ PiPi20[kMatrix.pole.1]{pi+,pi-}
PiPi20[kMatrix.pole.0]{pi+,pi-} 2 0.291 0.007 2 165.8 1.3
PiPi20[kMatrix.prod.0]{pi+,pi-} 2 0.117 0.002 2 170.5 1.2
a(1)(1260)-[D;GSpline.EFF]{rho(770)0{pi+,pi-},pi-} 2 0.582 0.011 2 -152.8 1.2
-a(1)(1260)-_mass 2 1.19505 0.00105 2
-a(1)(1260)-_radius 2 1.70000 0.00000 2
+a(1)(1260)-_mass 2 1.19505 0.00105
+a(1)(1260)-_radius 2 1.70000 0.00000
a(1)(1260)-_width 2 0.42201 0.00210
K(1)(1270)+[GSpline.EFF]{rho(770)0{pi+,pi-},K+} 2 1.000 0.000 2 0.0 0.0
K(1)(1270)+[GSpline.EFF]{rho(1450)0{pi+,pi-},K+} 2 2.016 0.026 2 -119.5 0.9
diff --git a/options/FitterExample.opt b/options/FitterExample.opt
index feeb9f67ece..7446b538bf3 100644
--- a/options/FitterExample.opt
+++ b/options/FitterExample.opt
@@ -106,58 +106,3 @@ a(1)(1260)+::Spline::Gamma::30 2 1.17885 0
a(1)(1260)+::Spline::Gamma::31 2 1.21615 0
a(1)(1260)+::Spline::Gamma::32 2 1.25246 0
a(1)(1260)+::Spline::Gamma::33 2 1.28789 0
-
-#K(1)(1270)bar-_mass 0 1270 1 1000 1500
-#K(1)(1270)bar-_width 0 90 1 50 200
-#
-#gLASS::F 0 1.0 1.34906e-01
-#gLASS::R 2 1.00000e+00 0
-#gLASS::a 2 0.224 3.46447e-03
-#gLASS::phiF 0 0.0 2.45733e-01
-#gLASS::phiR 0 0.0 3.14745e-02
-#gLASS::r 2 -15.01 1.49288e-01
-#
-#K(1)(1270)bar-::Spline::Min 0.613246
-#K(1)(1270)bar-::Spline::Max 2.95978
-#K(1)(1270)bar-::Spline::N 40
-#K(1)(1270)bar-::Spline::Gamma::0 2 0.000162404 0
-#K(1)(1270)bar-::Spline::Gamma::1 2 0.00386694 0
-#K(1)(1270)bar-::Spline::Gamma::2 2 0.0128833 0
-#K(1)(1270)bar-::Spline::Gamma::3 2 0.0276225 0
-#K(1)(1270)bar-::Spline::Gamma::4 2 0.048283 0
-#K(1)(1270)bar-::Spline::Gamma::5 2 0.0748626 0
-#K(1)(1270)bar-::Spline::Gamma::6 2 0.107234 0
-#K(1)(1270)bar-::Spline::Gamma::7 2 0.145263 0
-#K(1)(1270)bar-::Spline::Gamma::8 2 0.188929 0
-#K(1)(1270)bar-::Spline::Gamma::9 2 0.238422 0
-#K(1)(1270)bar-::Spline::Gamma::10 2 0.294211 0
-#K(1)(1270)bar-::Spline::Gamma::11 2 0.357122 0
-#K(1)(1270)bar-::Spline::Gamma::12 2 0.428445 0
-#K(1)(1270)bar-::Spline::Gamma::13 2 0.510093 0
-#K(1)(1270)bar-::Spline::Gamma::14 2 0.604757 0
-#K(1)(1270)bar-::Spline::Gamma::15 2 0.715757 0
-#K(1)(1270)bar-::Spline::Gamma::16 2 0.845719 0
-#K(1)(1270)bar-::Spline::Gamma::17 2 0.993541 0
-#K(1)(1270)bar-::Spline::Gamma::18 2 1.15281 0
-#K(1)(1270)bar-::Spline::Gamma::19 2 1.31566 0
-#K(1)(1270)bar-::Spline::Gamma::20 2 1.47718 0
-#K(1)(1270)bar-::Spline::Gamma::21 2 1.63572 0
-#K(1)(1270)bar-::Spline::Gamma::22 2 1.79135 0
-#K(1)(1270)bar-::Spline::Gamma::23 2 1.94481 0
-#K(1)(1270)bar-::Spline::Gamma::24 2 2.09696 0
-#K(1)(1270)bar-::Spline::Gamma::25 2 2.24862 0
-#K(1)(1270)bar-::Spline::Gamma::26 2 2.40051 0
-#K(1)(1270)bar-::Spline::Gamma::27 2 2.55328 0
-#K(1)(1270)bar-::Spline::Gamma::28 2 2.70744 0
-#K(1)(1270)bar-::Spline::Gamma::29 2 2.86345 0
-#K(1)(1270)bar-::Spline::Gamma::30 2 3.02171 0
-#K(1)(1270)bar-::Spline::Gamma::31 2 3.18254 0
-#K(1)(1270)bar-::Spline::Gamma::32 2 3.34625 0
-#K(1)(1270)bar-::Spline::Gamma::33 2 3.51307 0
-#K(1)(1270)bar-::Spline::Gamma::34 2 3.68324 0
-#K(1)(1270)bar-::Spline::Gamma::35 2 3.85695 0
-#K(1)(1270)bar-::Spline::Gamma::36 2 4.03437 0
-#K(1)(1270)bar-::Spline::Gamma::37 2 4.21566 0
-#K(1)(1270)bar-::Spline::Gamma::38 2 4.40095 0
-#K(1)(1270)bar-::Spline::Gamma::39 2 4.59036 0
-#
diff --git a/options/MintDalitzSpecialParticles.csv b/options/MintDalitzSpecialParticles.csv
index 5d07dfbf05b..6565871935b 100644
--- a/options/MintDalitzSpecialParticles.csv
+++ b/options/MintDalitzSpecialParticles.csv
@@ -14,35 +14,41 @@
9.990E+03 ,1.0E+00,1.0E+00,9.9E+09 ,1.0E+00,1.0E+00,0 , ,1/2 ,+, ,F, 9988, 0,4,R,NonRes1p ,??
9.990E+03 ,1.0E+00,1.0E+00,9.9E+09 ,1.0E+00,1.0E+00,0 , ,3/2 ,-, ,F, 9989, 0,4,R,NonRes3m ,??
9.990E+03 ,1.0E+00,1.0E+00,9.9E+09 ,1.0E+00,1.0E+00,0 , ,3/2 ,+, ,F, 9910, 0,4,R,NonRes3p ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998100, 0, ,R,PiPi0 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998101, 0, ,R,PiPi1 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998102, 0, ,R,PiPi2 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998103, 0, ,R,PiPi3 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998104, 0, ,R,PiPi4 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998105, 0, ,R,PiPi5 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998106, 0, ,R,PiPi6 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998110, 0, ,R,KPi0 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998111, 0, ,R,KPi1 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998112, 0, ,R,KPi2 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998113, 0, ,R,KPi3 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998114, 0, ,R,KPi4 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998115, 0, ,R,KPi5 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998116, 0, ,R,KPi6 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+,F, 998117, 0, ,R,KPi7 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998120, 0, ,R,KK0 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998121, 0, ,R,KK1 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998122, 0, ,R,KK2 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998123, 0, ,R,KK3 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998124, 0, ,R,KK4 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998125, 0, ,R,KK5 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, , 998126, 0, ,R,KK6 ,x(uU+dD)+y(sS)
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998130, 0, ,R,rhoOmega0 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998131, 0, ,R,rhoOmega1 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998132, 0, ,R,rhoOmega2 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998133, 0, ,R,rhoOmega3 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998134, 0, ,R,rhoOmega4 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998135, 0, ,R,rhoOmega5 ,??
-9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,1 ,-,-, , 998136, 0, ,R,rhoOmega6 ,??
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998100, 0, ,R,PiPi0 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998101, 0, ,R,PiPi1 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998102, 0, ,R,PiPi2 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998103, 0, ,R,PiPi3 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998104, 0, ,R,PiPi4 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998105, 0, ,R,PiPi5 ,x(uU+dD)+y(sS)
+9.970E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998106, 0, ,R,PiPi6 ,x(uU+dD)+y(sS)
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998110, 0, ,R,KPi0 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998111, 0, ,R,KPi1 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998112, 0, ,R,KPi2 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998113, 0, ,R,KPi3 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998114, 0, ,R,KPi4 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998115, 0, ,R,KPi5 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998116, 0, ,R,KPi6 ,??
+9.980E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2,+,0 ,+,+,F, 998117, 0, ,R,KPi7 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998120, 0, ,R,KK0 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998121, 0, ,R,KK1 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998122, 0, ,R,KK2 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998123, 0, ,R,KK3 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998124, 0, ,R,KK4 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998125, 0, ,R,KK5 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,0 ,+,0 ,+, , , 998126, 0, ,R,KK6 ,x(uU+dD)+y(sS)
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998130, 0, ,R,rhoOmega0 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998131, 0, ,R,rhoOmega1 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998132, 0, ,R,rhoOmega2 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998133, 0, ,R,rhoOmega3 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998134, 0, ,R,rhoOmega4 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998135, 0, ,R,rhoOmega5 ,??
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 ,+,1 ,-,-, , 998136, 0, ,R,rhoOmega6 ,??
1.272E+03 ,7.0E+00,7.0E+00,9.0E+01 ,2.0E+01,2.0E+01,1/2, ,1 ,+, ,F, 998200, +, ,R,Ka ,uS
1.272E+03 ,7.0E+00,7.0E+00,9.0E+01 ,2.0E+01,2.0E+01,1/2, ,1 ,+, ,F, 998201, +, ,R,Kb ,uS
+1.86484E+03 ,1.7E-01,1.7E-01,1.605E-09 ,6.0E-12,6.0E-12,1/2, ,0 ,-, ,F, 998421, 0, ,R,D~ ,cU
+3.8948E+03 ,1.1E-02,1.1E-02,2.96E+00 ,2.1E-03,2.1E-03,1 ,+,1 ,+,-, , 999443, 0, ,R,Z(c)(3900) ,cCuU
+3.8948E+03 ,1.1E-02,1.1E-02,2.96E+00 ,2.1E-03,2.1E-03,1 ,+,1 ,+,-, , 999444, +, ,R,Z(c)(3900) ,cCuD
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1 , ,1/2 ,-, ,F, , 0,3,R,LambdaEta ,uds
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2, ,1/2 ,-, ,F, , -,3,R,XiPi ,dss
+9.990E+03 ,1.0E+01,1.0E+01,9.9E+09 ,3.0E+01,3.0E+01,1/2, ,1/2 ,-, ,F, , 0,3,R,XiPi ,uss
***
diff --git a/options/example_glass.opt b/options/example_glass.opt
new file mode 100644
index 00000000000..69babd9d999
--- /dev/null
+++ b/options/example_glass.opt
@@ -0,0 +1,24 @@
+EventType D0 K0S0 pi+ pi-
+
+D0{K(0)*(1430)+[GLASS]{K0S0,pi+},pi-} 2 1 0 2 0 0
+
+K(0)*(1430)+::GLASS::a 0 0.113 0.006
+K(0)*(1430)+::GLASS::r 0 -33.800 1.800
+K(0)*(1430)+::GLASS::R 2 1.000 0.000
+K(0)*(1430)+::GLASS::F 0 0.960 0.007
+K(0)*(1430)+::GLASS::phiR 0 -109.700 2.600
+K(0)*(1430)+::GLASS::phiF 0 0.100 0.300
+
+# K(0)*(1430)+::GLASS::a 0 2.070 0.006
+# K(0)*(1430)+::GLASS::r 0 3.320 1.800
+# K(0)*(1430)+::GLASS::R 2 1.000 0.000
+# K(0)*(1430)+::GLASS::F 0 1.000 0.007
+# K(0)*(1430)+::GLASS::phiR 0 0.000 2.600
+# K(0)*(1430)+::GLASS::phiF 0 0.000 0.300
+
+K(0)*(1430)bar-::GLASS::a = K(0)*(1430)+::GLASS::a
+K(0)*(1430)bar-::GLASS::r = K(0)*(1430)+::GLASS::r
+K(0)*(1430)bar-::GLASS::R = K(0)*(1430)+::GLASS::R
+K(0)*(1430)bar-::GLASS::F = K(0)*(1430)+::GLASS::F
+K(0)*(1430)bar-::GLASS::phiR = K(0)*(1430)+::GLASS::phiR
+K(0)*(1430)bar-::GLASS::phiF = K(0)*(1430)+::GLASS::phiF
diff --git a/options/mass_width.csv b/options/mass_width.csv
index 6f6050db895..6863674fe22 100644
--- a/options/mass_width.csv
+++ b/options/mass_width.csv
@@ -16,7 +16,7 @@
* A1. read table into any spreadsheet or database program that accepts a comma-separated format
* A2. For example, in EXCEL, open a blank workbook and import this file as external data,
* comma-delimited, starting the import at row 100, which contains column header names.
-* B1. In a FORTRAN program, ignore documentation lines that begin with "*" and process data lines using
+* B1. In a FORTRAN program, ignore documentation lines that begin with '*' and process data lines using
* FORMAT (BN, E14.0, 1X, 2(E7.0, 1X), E12.0, 1X, 2(E7.0, 1X), A3, 1X, A1, 1X, A4, 1X, 3(A1, 1X), A7, 1X, A4, 1X, 2(A1, 1X), A17, 1X, A)
* B2. WARNING. MINUS VALUE OF ERROR means its absence!
* B3. columns contents Fortran I/O
@@ -51,7 +51,7 @@
* with ascii name formed by concatenation of the name shown below with charge
* ( e- <--> e+, pi+ <--> pi-, K+ <--> K-, W+ <--> W- ).
* A = F - particle that has anti-particle partner different from particle
-* with ascii name formed by concatenation of the name shown below with string "bar" and charge
+* with ascii name formed by concatenation of the name shown below with string 'bar' and charge
* by the rule (nu(e) <--> nubar(e), p <--> pbar, Delta++ <--> Deltabar--)
* A = blank - particle that coincide with its antiparticle (gamma, pi0, eta).
* 85 comma (1X)
@@ -59,7 +59,7 @@
* The number used in the PDG Monte Carlo numbering scheme (see RPP).
* Only particles are shown in this table and they are given positive ID numbers.
* For antiparticles, change the ID to negative. Thus pi- has code -211.
-* The ID has up to 7 digits. See RPP "Monte Carlo particle numbering scheme"
+* The ID has up to 7 digits. See RPP 'Monte Carlo particle numbering scheme'
* for details.
* 94 comma (1X)
* 95 - 99 charge (A4)
@@ -81,7 +81,7 @@
* space even though they are well established.
* S - The particle is omitted from the particle properties Summary Tables
* because it is not well established.
-* F - Special case: "Further mesons", see RPP , these states are in the RPP
+* F - Special case: 'Further mesons', see RPP , these states are in the RPP
* database but are poorly established or observed by a single group and thus
* need confirmation. If used, these should be referred to the original publication.
* For these states we list a single line without charge and with C-parity, if known,
@@ -91,10 +91,10 @@
* 105 -122 particle name (A17)
* 123 comma (1X)
* 124 -139 Quark contents (A)
-* Note: capital letters represents anti-quarks, "qQ" stands for light quark, light
+* Note: capital letters represents anti-quarks, 'qQ' stands for light quark, light
* anti-quark pair with unknown wave functions.
* x, y - wave function coefficients, see RPP 'Quark Model' Review
-* p, q - CP violation parameters, See. RPP "CP violation in KL Decays" review.
+* p, q - CP violation parameters, See. RPP 'CP violation in KL Decays' review.
*
*
*MASS(MeV) ,Err+ ,Err- ,WIDTH(MeV) ,Err+ ,Err- ,I ,G,J ,P,C,A,PDG-MC ,Chrg,R,S,Name ,Quarks
@@ -104,9 +104,9 @@
5.10998910E-01,1.3E-08,1.3E-08,0.0E+00 ,0.0E+00,0.0E+00, , ,1/2 ,+, ,B, 11, -, ,R,e ,
1.05658367E+02,4.0E-06,4.0E-06,3.015937E-16,2.9E-21,2.9E-21, , ,1/2 ,+, ,B, 13, -, ,R,mu ,
1.77684E+03 ,1.7E-01,1.7E-01,2.280E-09 ,8.0E-12,8.0E-12, , ,1/2 ,+, ,B, 15, -, ,R,tau ,
-0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 12, 0, ,R,nu_e ,
-0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 14, 0, ,R,nu_mu ,
-0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 16, 0, ,R,nu_tau ,
+0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 12, 0, ,R,nue ,
+0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 14, 0, ,R,numu ,
+0.0E+00 ,0.0E+00,0.0E+00,0.0E+00 ,0.0E+00,0.0E+00,<2 , ,1/2 ,+, ,F, 16, 0, ,R,nutau ,
2.4E+00 ,9.0E-01,9.0E-01,-1 ,-1 ,-1 ,1/2, ,1/2 ,+, ,F, 2,+2/3, ,R,u ,u
4.8E+00 ,1.2E+00,1.2E+00,-1 ,-1 ,-1 ,1/2, ,1/2 ,+, ,F, 1,-1/3, ,R,d ,d
1.04E+02 ,2.6E+01,3.4E+01,-1 ,-1 ,-1 ,0 , ,1/2 ,+, ,F, 3,-1/3, ,R,s ,s
@@ -118,12 +118,12 @@
5.47853E+02 ,2.4E-02,2.4E-02,1.30E-03 ,7.0E-05,7.0E-05,0 ,+,0 ,-,+, , 221, 0, ,R,eta ,x(uU+dD)+y(sS)
8.0E+02 ,4.0E+02,4.0E+02,8.0E+02 ,2.0E+02,2.0E+02,0 ,+,0 ,+,+, ,9000221, 0, ,R,f(0)(600) ,Maybe non-qQ
7.7549E+02 ,3.4E-01,3.4E-01,1.4940E+02 ,1.0E+00,1.0E+00,1 ,+,1 ,-, ,B, 213, +, ,R,rho(770) ,uD
-7.7549E+02 ,3.4E-01,3.4E-01,1.4940E+02 ,1.0E+00,1.0E+00,1 ,+,1 ,-,-,B, 113, 0, ,R,rho(770) ,(uU-dD)/sqrt(2)
+7.7549E+02 ,3.4E-01,3.4E-01,1.4940E+02 ,1.0E+00,1.0E+00,1 ,+,1 ,-,-, , 113, 0, ,R,rho(770) ,(uU-dD)/sqrt(2)
7.8265E+02 ,1.2E-01,1.2E-01,8.49E+00 ,8.0E-02,8.0E-02,0 ,-,1 ,-,-, , 223, 0, ,R,omega(782) ,x(uU+dD)+y(sS)
9.5766E+02 ,2.4E-01,2.4E-01,2.05E-01 ,1.5E-02,1.5E-02,0 ,+,0 ,-,+, , 331, 0, ,R,eta'(958) ,x(uU+dD)+y(sS)
9.800E+02 ,1.0E+01,1.0E+01,7.0E+01 ,3.0E+01,3.0E+01,0 ,+,0 ,+,+, ,9010221, 0, ,R,f(0)(980) ,Maybe non-qQ
9.847E+02 ,1.2E+00,1.2E+00,7.5E+01 ,2.5E+01,2.5E+01,1 ,-,0 ,+, ,B,9000211, +, ,R,a(0)(980) ,Maybe non-qQ
-9.847E+02 ,1.2E+00,1.2E+00,7.5E+01 ,2.5E+01,2.5E+01,1 ,-,0 ,+,+,B,9000111, 0, ,R,a(0)(980) ,Maybe non-qQ
+9.847E+02 ,1.2E+00,1.2E+00,7.5E+01 ,2.5E+01,2.5E+01,1 ,-,0 ,+,+, ,9000111, 0, ,R,a(0)(980) ,Maybe non-qQ
1.019455E+03 ,2.0E-02,2.0E-02,4.26E+00 ,4.0E-02,4.0E-02,0 ,-,1 ,-,-, , 333, 0, ,R,phi(1020) ,x(uU+dD)+y(sS)
1.170E+03 ,2.0E+01,2.0E+01,3.6E+02 ,4.0E+01,4.0E+01,0 ,-,1 ,+,-, , 10223, 0, ,R,h(1)(1170) ,x(uU+dD)+y(sS)
1.2295E+03 ,3.2E+00,3.2E+00,1.42E+02 ,9.0E+00,9.0E+00,1 ,+,1 ,+, ,B, 10213, +, ,R,b(1)(1235) ,uD
@@ -134,9 +134,9 @@
1.2818E+03 ,6.0E-01,6.0E-01,2.43E+01 ,1.1E+00,1.1E+00,0 ,+,1 ,+,+, , 20223, 0, ,R,f(1)(1285) ,x(uU+dD)+y(sS)
1.294E+03 ,4.0E+00,4.0E+00,5.5E+01 ,5.0E+00,5.0E+00,0 ,+,0 ,-,+, , 100221, 0, ,R,eta(1295) ,x(uU+dD)+y(sS)
1.300E+03 ,1.0E+02,1.0E+02,4.0E+02 ,2.0E+02,2.0E+02,1 ,-,0 ,-, ,B, 100211, +, ,R,pi(1300) ,uD
-1.300E+03 ,1.0E+02,1.0E+02,4.0E+02 ,2.0E+02,2.0E+02,1 ,-,0 ,-,+,B, 100111, 0, ,R,pi(1300) ,(uU-dD)/sqrt(2)
+1.300E+03 ,1.0E+02,1.0E+02,4.0E+02 ,2.0E+02,2.0E+02,1 ,-,0 ,-,+, , 100111, 0, ,R,pi(1300) ,(uU-dD)/sqrt(2)
1.3183E+03 ,6.0E-01,6.0E-01,1.07E+02 ,5.0E+00,5.0E+00,1 ,-,2 ,+, ,B, 215, +, ,R,a(2)(1320) ,uD
-1.3183E+03 ,6.0E-01,6.0E-01,1.07E+02 ,5.0E+00,5.0E+00,1 ,-,2 ,+,+,B, 115, 0, ,R,a(2)(1320) ,(uU-dD)/sqrt(2)
+1.3183E+03 ,6.0E-01,6.0E-01,1.07E+02 ,5.0E+00,5.0E+00,1 ,-,2 ,+,+, , 115, 0, ,R,a(2)(1320) ,(uU-dD)/sqrt(2)
1.35E+03 ,1.5E+02,1.5E+02,3.5E+02 ,1.5E+02,1.5E+02,0 ,+,0 ,+,+, , 30221, 0, ,R,f(0)(1370) ,x(uU+dD)+y(sS)
1.386E+03 ,1.9E+01,1.9E+01,9.1E+01 ,3.0E+01,3.0E+01,? ,-,1 ,+,-, , 10333, 0, ,S,h(1)(1380) ,x(uU+dD)+y(sS)
1.351E+03 ,3.0E+01,3.0E+01,3.1E+02 ,4.0E+01,4.0E+01,1 ,-,1 ,-, , ,9000213, +, ,R,pi(1)(1400) ,Maybe non-qQ
@@ -146,9 +146,9 @@
1.425E+03 ,2.5E+01,2.5E+01,2.15E+02 ,3.5E+01,3.5E+01,0 ,-,1 ,-,-, , 100223, 0, ,R,omega(1420) ,x(uU+dD)+y(sS)
1.453E+03 ,4.0E+00,4.0E+00,1.3E+01 ,5.0E+00,5.0E+00,0 ,+,2 ,+,+, ,9000225, 0, ,S,f(2)(1430) ,x(uU+dD)+y(sS)
1.474E+03 ,1.9E+01,1.9E+01,2.65E+02 ,1.3E+01,1.3E+01,1 ,-,0 ,+, ,B, 10211, +, ,R,a(0)(1450) ,uD
-1.474E+03 ,1.9E+01,1.9E+01,2.65E+02 ,1.3E+01,1.3E+01,1 ,-,0 ,+,+,B, 10111, 0, ,R,a(0)(1450) ,(uU-dD)/sqrt(2)
+1.474E+03 ,1.9E+01,1.9E+01,2.65E+02 ,1.3E+01,1.3E+01,1 ,-,0 ,+,+, , 10111, 0, ,R,a(0)(1450) ,(uU-dD)/sqrt(2)
1.465E+03 ,2.5E+01,2.5E+01,4.0E+02 ,6.0E+01,6.0E+01,1 ,+,1 ,-, ,B, 100213, +, ,R,rho(1450) ,uD
-1.465E+03 ,2.5E+01,2.5E+01,4.0E+02 ,6.0E+01,6.0E+01,1 ,+,1 ,-,-,B, 100113, 0, ,R,rho(1450) ,(uU-dD)/sqrt(2)
+1.465E+03 ,2.5E+01,2.5E+01,4.0E+02 ,6.0E+01,6.0E+01,1 ,+,1 ,-,-, , 100113, 0, ,R,rho(1450) ,(uU-dD)/sqrt(2)
1.476E+03 ,4.0E+00,4.0E+00,8.5E+01 ,9.0E+00,9.0E+00,0 ,+,0 ,-,+, , 100331, 0, ,R,eta(1475) ,x(uU+dD)+y(sS)
1.505E+03 ,6.0E+00,6.0E+00,1.09E+02 ,7.0E+00,7.0E+00,0 ,+,0 ,+,+, ,9030221, 0, ,R,f(0)(1500) ,Maybe non-qQ
1.518E+03 ,5.0E+00,5.0E+00,7.3E+01 ,2.5E+01,2.5E+01,0 ,+,1 ,+,+, ,9000223, 0, ,S,f(1)(1510) ,x(uU+dD)+y(sS)
@@ -159,61 +159,61 @@
1.662E+03 ,1.5E+01,1.1E+01,2.3E+02 ,5.0E+01,5.0E+01,1 ,-,1 ,-, , ,9010213, +, ,R,pi(1)(1600) ,Maybe non-qQ
1.662E+03 ,1.5E+01,1.1E+01,2.3E+02 ,5.0E+01,5.0E+01,1 ,-,1 ,-,+, ,9010113, 0, ,R,pi(1)(1600) ,Maybe non-qQ
1.647E+03 ,2.2E+01,2.2E+01,2.54E+02 ,2.7E+01,2.7E+01,1 ,-,1 ,+, ,B,9020213, +, ,S,a(1)(1640) ,uD
-1.647E+03 ,2.2E+01,2.2E+01,2.54E+02 ,2.7E+01,2.7E+01,1 ,-,1 ,+,+,B,9020113, 0, ,S,a(1)(1640) ,(uU-dD)/sqrt(2)
+1.647E+03 ,2.2E+01,2.2E+01,2.54E+02 ,2.7E+01,2.7E+01,1 ,-,1 ,+,+, ,9020113, 0, ,S,a(1)(1640) ,(uU-dD)/sqrt(2)
1.639E+03 ,6.0E+00,6.0E+00,9.9E+01 ,6.0E+01,4.0E+01,0 ,+,2 ,+,+, ,9020225, 0, ,S,f(2)(1640) ,x(uU+dD)+y(sS)
1.617E+03 ,5.0E+00,5.0E+00,1.81E+02 ,1.1E+01,1.1E+01,0 ,+,2 ,-,+, , 10225, 0, ,R,eta(2)(1645) ,x(uU+dD)+y(sS)
1.670E+03 ,3.0E+01,3.0E+01,3.15E+02 ,3.5E+01,3.5E+01,0 ,-,1 ,-,-, , 30223, 0, ,R,omega(1650) ,x(uU+dD)+y(sS)
1.667E+03 ,4.0E+00,4.0E+00,1.680E+02 ,1.0E+01,1.0E+01,0 ,-,3 ,-,-, , 227, 0, ,R,omega(3)(1670) ,x(uU+dD)+y(sS)
1.6724E+03 ,3.2E+00,3.2E+00,2.59E+02 ,9.0E+00,9.0E+00,1 ,-,2 ,-, ,B, 10215, +, ,R,pi(2)(1670) ,uD
-1.6724E+03 ,3.2E+00,3.2E+00,2.59E+02 ,9.0E+00,9.0E+00,1 ,-,2 ,-,+,B, 10115, 0, ,R,pi(2)(1670) ,(uU-dD)/sqrt(2)
+1.6724E+03 ,3.2E+00,3.2E+00,2.59E+02 ,9.0E+00,9.0E+00,1 ,-,2 ,-,+, , 10115, 0, ,R,pi(2)(1670) ,(uU-dD)/sqrt(2)
1.680E+03 ,2.0E+01,2.0E+01,1.5E+02 ,5.0E+01,5.0E+01,0 ,-,1 ,-,-, , 100333, 0, ,R,phi(1680) ,x(uU+dD)+y(sS)
1.6888E+03 ,2.1E+00,2.1E+00,1.610E+02 ,1.0E+01,1.0E+01,1 ,+,3 ,-, ,B, 217, +, ,R,rho(3)(1690) ,uD
-1.6888E+03 ,2.1E+00,2.1E+00,1.610E+02 ,1.0E+01,1.0E+01,1 ,+,3 ,-,-,B, 117, 0, ,R,rho(3)(1690) ,(uU-dD)/sqrt(2)
+1.6888E+03 ,2.1E+00,2.1E+00,1.610E+02 ,1.0E+01,1.0E+01,1 ,+,3 ,-,-, , 117, 0, ,R,rho(3)(1690) ,(uU-dD)/sqrt(2)
1.720E+03 ,2.0E+01,2.0E+01,2.50E+02 ,1.0E+02,1.0E+02,1 ,+,1 ,-, ,B, 30213, +, ,R,rho(1700) ,uD
-1.720E+03 ,2.0E+01,2.0E+01,2.50E+02 ,1.0E+02,1.0E+02,1 ,+,1 ,-,-,B, 30113, 0, ,R,rho(1700) ,(uU-dD)/sqrt(2)
+1.720E+03 ,2.0E+01,2.0E+01,2.50E+02 ,1.0E+02,1.0E+02,1 ,+,1 ,-,-, , 30113, 0, ,R,rho(1700) ,(uU-dD)/sqrt(2)
1.732E+03 ,1.6E+01,1.6E+01,1.9E+02 ,4.0E+01,4.0E+01,1 ,-,2 ,+, ,B, 100215, +, ,S,a(2)(1700) ,uD
-1.732E+03 ,1.6E+01,1.6E+01,1.9E+02 ,4.0E+01,4.0E+01,1 ,-,2 ,+,+,B, 100115, 0, ,S,a(2)(1700) ,(uU-dD)/sqrt(2)
+1.732E+03 ,1.6E+01,1.6E+01,1.9E+02 ,4.0E+01,4.0E+01,1 ,-,2 ,+,+, , 100115, 0, ,S,a(2)(1700) ,(uU-dD)/sqrt(2)
1.724E+03 ,7.0E+00,7.0E+00,1.37E+02 ,8.0E+00,8.0E+00,0 ,+,0 ,+,+, , 10331, 0, ,R,f(0)(1710) ,x(uU+dD)+y(sS)
1.756E+03 ,9.0E+00,9.0E+00,9.6E+01 ,7.0E+01,7.0E+01,0 ,+,0 ,-,+, ,9040221, 0, ,S,eta(1760) ,x(uU+dD)+y(sS)
1.816E+03 ,1.4E+01,1.4E+01,2.08E+02 ,1.2E+01,1.2E+01,1 ,-,0 ,-, ,B,9010211, +, ,R,pi(1800) ,uD
-1.816E+03 ,1.4E+01,1.4E+01,2.08E+02 ,1.2E+01,1.2E+01,1 ,-,0 ,-,+,B,9010111, 0, ,R,pi(1800) ,(uU-dD)/sqrt(2)
+1.816E+03 ,1.4E+01,1.4E+01,2.08E+02 ,1.2E+01,1.2E+01,1 ,-,0 ,-,+, ,9010111, 0, ,R,pi(1800) ,(uU-dD)/sqrt(2)
1.815E+03 ,1.2E+01,1.2E+01,1.97E+02 ,2.2E+01,2.2E+01,0 ,+,2 ,+,+, ,9030225, 0, ,S,f(2)(1810) ,x(uU+dD)+y(sS)
1.834E+03 ,7.0E+00,7.0E+00,6.8E+01 ,2.2E+01,2.2E+01,? ,?,? ,-,+, , , 0, ,S,X(1835) ,x(uU+dD)+y(sS)
1.854E+03 ,7.0E+00,7.0E+00,8.7E+01 ,2.8E+01,2.3E+01,0 ,-,3 ,-,-, , 337, 0, ,R,phi(3)(1850) ,x(uU+dD)+y(sS)
1.842E+03 ,8.0E+00,8.0E+00,2.25E+02 ,1.4E+01,1.4E+01,0 ,+,2 ,-,+, , 10335, 0, ,S,eta(2)(1870) ,x(uU+dD)+y(sS)
1.895E+03 ,1.6E+01,1.6E+01,2.35E+02 ,3.4E+01,3.4E+01,1 ,-,2 ,-,+, , , 0, ,R,pi(2)(1880) ,x(uU+dD)+y(sS)
1.909E+03 ,3.0E+01,3.0E+01,4.8E+01 ,1.7E+01,1.7E+01,1 ,+,1 ,-, ,B,9030213, +, ,S,rho(1900) ,uD
-1.909E+03 ,3.0E+01,3.0E+01,4.8E+01 ,1.7E+01,1.7E+01,1 ,+,1 ,-,-,B,9030113, 0, ,S,rho(1900) ,(uU-dD)/sqrt(2)
+1.909E+03 ,3.0E+01,3.0E+01,4.8E+01 ,1.7E+01,1.7E+01,1 ,+,1 ,-,-, ,9030113, 0, ,S,rho(1900) ,(uU-dD)/sqrt(2)
1.903E+03 ,9.0E+00,9.0E+00,1.96E+02 ,3.1E+01,3.1E+01,0 ,+,2 ,+,+, ,9040225, 0, ,S,f(2)(1910) ,x(uU+dD)+y(sS)
1.944E+03 ,1.2E+01,1.2E+01,4.72E+02 ,1.8E+01,1.8E+01,0 ,+,2 ,+,+, ,9050225, 0, ,R,f(2)(1950) ,x(uU+dD)+y(sS)
1.982E+03 ,1.4E+01,1.4E+01,1.88E+02 ,2.4E+01,2.4E+01,1 ,+,3 ,-, ,B,9000217, +, ,S,rho(3)(1990) ,uD
-1.982E+03 ,1.4E+01,1.4E+01,1.88E+02 ,2.4E+01,2.4E+01,1 ,+,3 ,-,-,B,9000117, 0, ,S,rho(3)(1990) ,(uU-dD)/sqrt(2)
+1.982E+03 ,1.4E+01,1.4E+01,1.88E+02 ,2.4E+01,2.4E+01,1 ,+,3 ,-,-, ,9000117, 0, ,S,rho(3)(1990) ,(uU-dD)/sqrt(2)
2.01E+03 ,6.0E+01,8.0E+01,2.0E+02 ,6.0E+01,6.0E+01,0 ,+,2 ,+,+, ,9060225, 0, ,R,f(2)(2010) ,x(uU+dD)+y(sS)
1.992E+03 ,1.6E+01,1.6E+01,4.4E+02 ,6.0E+01,6.0E+01,0 ,+,0 ,+,+, ,9050221, 0, ,S,f(0)(2020) ,x(uU+dD)+y(sS)
2.0010E+03 ,1.0E+01,1.0E+01,3.13E+02 ,3.1E+01,3.1E+01,1 ,-,4 ,+, ,B, 219, +, ,R,a(4)(2040) ,uD
-2.0010E+03 ,1.0E+01,1.0E+01,3.13E+02 ,3.1E+01,3.1E+01,1 ,-,4 ,+,+,B, 119, 0, ,R,a(4)(2040) ,(uU-dD)/sqrt(2)
+2.0010E+03 ,1.0E+01,1.0E+01,3.13E+02 ,3.1E+01,3.1E+01,1 ,-,4 ,+,+, , 119, 0, ,R,a(4)(2040) ,(uU-dD)/sqrt(2)
2.018E+03 ,1.1E+01,1.1E+01,2.37E+02 ,1.8E+01,1.8E+01,0 ,+,4 ,+,+, , 229, 0, ,R,f(4)(2050) ,x(uU+dD)+y(sS)
2.090E+03 ,2.9E+01,2.9E+01,6.2E+02 ,5.0E+01,5.0E+01,1 ,-,2 ,-, ,B,9000215, +, ,S,pi(2)(2100) ,uD
-2.090E+03 ,2.9E+01,2.9E+01,6.2E+02 ,5.0E+01,5.0E+01,1 ,-,2 ,-,+,B,9000115, 0, ,S,pi(2)(2100) ,(uU-dD)/sqrt(2)
+2.090E+03 ,2.9E+01,2.9E+01,6.2E+02 ,5.0E+01,5.0E+01,1 ,-,2 ,-,+, ,9000115, 0, ,S,pi(2)(2100) ,(uU-dD)/sqrt(2)
2.103E+03 ,8.0E+00,8.0E+00,2.09E+02 ,1.9E+01,1.9E+01,0 ,+,0 ,+,+, ,9060221, 0, ,S,f(0)(2100) ,x(uU+dD)+y(sS)
2.156E+03 ,1.1E+01,1.1E+01,1.67E+02 ,3.0E+01,3.0E+01,0 ,+,2 ,+,+, ,9070225, 0, ,S,f(2)(2150) ,x(uU+dD)+y(sS)
2.149E+03 ,1.7E+01,1.7E+01,3.6E+02 ,4.0E+01,4.0E+01,1 ,+,1 ,-, ,B,9040213, +, ,S,rho(2150) ,uD
-2.149E+03 ,1.7E+01,1.7E+01,3.6E+02 ,4.0E+01,4.0E+01,1 ,+,1 ,-,-,B,9040113, 0, ,S,rho(2150) ,(uU-dD)/sqrt(2)
+2.149E+03 ,1.7E+01,1.7E+01,3.6E+02 ,4.0E+01,4.0E+01,1 ,+,1 ,-,-, ,9040113, 0, ,S,rho(2150) ,(uU-dD)/sqrt(2)
2.175E+03 ,1.5E+01,1.5E+01,6.1E+01 ,1.8E+01,1.8E+01,0 ,-,1 ,-, ,B, , +, ,S,phi(2170) ,uD
-2.175E+03 ,1.5E+01,1.5E+01,6.1E+01 ,1.8E+01,1.8E+01,0 ,-,1 ,-,-,B, , 0, ,S,phi(2170) ,(uU-dD)/sqrt(2)
+2.175E+03 ,1.5E+01,1.5E+01,6.1E+01 ,1.8E+01,1.8E+01,0 ,-,1 ,-,-, , , 0, ,S,phi(2170) ,(uU-dD)/sqrt(2)
2.189E+03 ,1.3E+01,1.3E+01,2.4E+02 ,5.0E+01,5.0E+01,0 ,+,0 ,+,+, ,9070221, 0, ,S,f(0)(2200) ,x(uU+dD)+y(sS)
2.2311E+03 ,3.5E+00,3.5E+00,2.3E+01 ,8.0E+00,7.0E+00,0 ,+,2 ,+,+, ,9000229, 0, ,S,f(J)(2220) ,x(uU+dD)+y(sS)
2.220E+03 ,1.8E+01,1.8E+01,1.5E+02 ,3.1E+02,8.0E+01,0 ,+,0 ,-,+, ,9080221, 0, ,S,eta(2225) ,x(uU+dD)+y(sS)
2.260E+03 ,2.0E+01,2.0E+01,1.60E+02 ,2.5E+01,2.5E+01,1 ,+,3 ,-, ,B,9010217, +, ,S,rho(3)(2250) ,uD
-2.260E+03 ,2.0E+01,2.0E+01,1.60E+02 ,2.5E+01,2.5E+01,1 ,+,3 ,-,-,B,9010117, 0, ,S,rho(3)(2250) ,(uU-dD)/sqrt(2)
+2.260E+03 ,2.0E+01,2.0E+01,1.60E+02 ,2.5E+01,2.5E+01,1 ,+,3 ,-,-, ,9010117, 0, ,S,rho(3)(2250) ,(uU-dD)/sqrt(2)
2.297E+03 ,2.8E+01,2.8E+01,1.5E+02 ,4.0E+01,4.0E+01,0 ,+,2 ,+,+, ,9080225, 0, ,R,f(2)(2300) ,x(uU+dD)+y(sS)
2.32E+03 ,6.0E+01,6.0E+01,2.5E+02 ,8.0E+01,8.0E+01,0 ,+,4 ,+,+, ,9010229, 0, ,S,f(4)(2300) ,x(uU+dD)+y(sS)
2.314E+03 ,2.5E+01,2.5E+01,1.44E+02 ,2.0E+01,2.0E+01,0 ,+,0 ,+,+, ,9090221, 0, ,S,f(0)(2330) ,x(uU+dD)+y(sS)
2.34E+03 ,6.0E+01,6.0E+01,3.2E+02 ,8.0E+01,7.0E+01,0 ,+,2 ,+,+, ,9090225, 0, ,R,f(2)(2340) ,x(uU+dD)+y(sS)
2.330E+03 ,3.5E+01,3.5E+01,4.00E+02 ,1.0E+02,1.0E+02,1 ,+,5 ,-, ,B, , +, ,S,rho(5)(2350) ,uD
-2.330E+03 ,3.5E+01,3.5E+01,4.00E+02 ,1.0E+02,1.0E+02,1 ,+,5 ,-,-,B, , 0, ,S,rho(5)(2350) ,(uU+dD)/sqrt(2)
+2.330E+03 ,3.5E+01,3.5E+01,4.00E+02 ,1.0E+02,1.0E+02,1 ,+,5 ,-,-, , , 0, ,S,rho(5)(2350) ,(uU+dD)/sqrt(2)
2.45E+03 ,1.3E+02,1.3E+02,4.0E+02 ,2.5E+02,2.5E+02,1 ,-,6 ,+, ,B, , +, ,S,a(6)(2450) ,uD
-2.45E+03 ,1.3E+02,1.3E+02,4.0E+02 ,2.5E+02,2.5E+02,1 ,-,6 ,+,+,B, , 0, ,S,a(6)(2450) ,(uU+dD)/sqrt(2)
+2.45E+03 ,1.3E+02,1.3E+02,4.0E+02 ,2.5E+02,2.5E+02,1 ,-,6 ,+,+, , , 0, ,S,a(6)(2450) ,(uU+dD)/sqrt(2)
2.46E+03 ,5.0E+01,5.0E+01,2.6E+02 ,4.0E+01,4.0E+01,0 ,+,6 ,+,+, , , 0, ,S,f(6)(2510) ,x(uU+dD)+y(sS)
1.0724E+03 ,8.0E-01,8.0E-01,3.50E+00 ,1.5E+00,1.0E+00,? ,?,0 ,+,+, , , 0, ,F,X(1070) ,??
1.107E+03 ,4.0E+00,4.0E+00,1.11E+02 ,1.7E+01,1.7E+01,0 ,+,? ,+,+, , , 0, ,F,X(1110) ,??
@@ -316,8 +316,8 @@
3.350E+03 ,2.2E+01,2.8E+01,7.0E+01 ,6.0E+01,5.0E+01,? ,?,? ,?,?, , , 0, ,F,X(3350) ,??
4.93677E+02 ,1.6E-02,1.6E-02,5.352E-14 ,9.0E-17,9.0E-17,1/2, ,0 ,-, ,B, 321, +, ,R,K ,uS
4.97614E+02 ,2.4E-02,2.4E-02,-1 ,-1 ,-1 ,1/2, ,0 ,-, ,F, 311, 0, ,R,K ,dS
-4.97614E+02 ,2.4E-02,2.4E-02,7.397E-12 ,4.0E-15,4.0E-15,1/2, ,0 ,-, , , 310, 0, ,R,K0S ,p(dS)+q(Ds)
-4.97614E+02 ,2.4E-02,2.4E-02,1.295E-14 ,5.0E-17,5.0E-17,1/2, ,0 ,-, , , 130, 0, ,R,K0L ,p(dS)-q(Ds)
+4.97614E+02 ,2.4E-02,2.4E-02,7.397E-12 ,4.0E-15,4.0E-15,1/2, ,0 ,-,-, , 310, 0, ,R,K0S ,p(dS)+q(Ds)
+4.97614E+02 ,2.4E-02,2.4E-02,1.295E-14 ,5.0E-17,5.0E-17,1/2, ,0 ,-,+, , 130, 0, ,R,K0L ,p(dS)-q(Ds)
6.7E+02 ,4.0E+01,4.0E+01,5.50E+02 ,3.4E+01,3.4E+01,1/2, ,0 ,+, ,F,9000321, +, ,S,K(0)*(800) ,uS
6.7E+02 ,4.0E+01,4.0E+01,5.50E+02 ,3.4E+01,3.4E+01,1/2, ,0 ,+, ,F,9000311, 0, ,S,K(0)*(800) ,dS
8.9166E+02 ,2.6E-01,2.6E-01,5.08E+01 ,9.0E-01,9.0E-01,1/2, ,1 ,-, ,F, 323, +, ,R,K*(892) ,uS
@@ -367,22 +367,22 @@
3.054E+03 ,1.1E+01,1.1E+01,4.2E+01 ,1.6E+01,1.6E+01,? ,?,? ,?,?, , , 0, ,S,K(3100) ,Maybe non-qQ
1.86962E+03 ,2.0E-01,2.0E-01,6.329E-10 ,4.0E-12,4.0E-12,1/2, ,0 ,-, ,B, 411, +, ,R,D ,cD
1.86484E+03 ,1.7E-01,1.7E-01,1.605E-09 ,6.0E-12,6.0E-12,1/2, ,0 ,-, ,F, 421, 0, ,R,D ,cU
-2.00697E+03 ,1.9E-01,1.9E-01,2.1 ,-1 ,-1 ,1/2, ,1 ,-, ,F, 423, 0, ,R,D*(2007) ,cU
+2.00697E+03 ,1.9E-01,1.9E-01,9.6E-02 ,-1 ,-1 ,1/2, ,1 ,-, ,F, 423, 0, ,R,D*(2007) ,cU
2.01027E+03 ,1.7E-01,1.7E-01,9.6E-02 ,2.2E-02,2.2E-02,1/2, ,1 ,-, ,B, 413, +, ,R,D*(2010) ,cD
-2.35E+03 ,5.0E+01,5.0E+01,2.6E+02 ,5.0E+01,5.0E+01,1/2, ,0 ,+, ,F, 10421, 0, ,S,D(0)*(2400) ,cU
-2.40E+03 ,4.0E+01,4.0E+01,2.8E+02 ,4.0E+01,4.0E+01,1/2, ,0 ,+, ,F, 10411, +, ,S,D(0)*(2400) ,cD
+2.30E+03 ,1.9E+01,1.9E+01,2.74E+02 ,4.0E+01,4.0E+01,1/2, ,0 ,+, ,F, 10421, 0, ,S,D(0)*(2300) ,cU
+2.349E+03 ,7.0E+00,7.0E+00,2.21E+02 ,1.8E+01,1.8E+01,1/2, ,0 ,+, ,F, 10411, +, ,S,D(0)*(2300) ,cD
2.4223E+03 ,1.3E+00,1.3E+00,2.04E+01 ,1.7E+00,1.7E+00,1/2, ,1 ,+, ,F, 10423, 0, ,R,D(1)(2420) ,cU
2.4234E+03 ,3.1E+00,3.1E+00,2.5E+01 ,6.0E+00,6.0E+00,1/2, ,? ,?, ,B, 10413, +, ,S,D(1)(2420) ,cD
2.43E+03 ,4.0E+01,4.0E+01,3.8E+02 ,1.3E+02,1.1E+02,1/2, ,1 ,+, ,F, 20423, 0, ,S,D(1)(2430) ,cU
-2.4611E+03 ,1.6E+00,1.6E+00,4.3E+01 ,4.0E+00,4.0E+00,1/2, ,2 ,+, ,F, 425, 0, ,R,D(2)*(2460) ,cU
-2.4601E+03 ,2.6E+00,3.5E+00,3.7E+01 ,6.0E+00,6.0E+00,1/2, ,2 ,+, ,B, 415, +, ,R,D(2)*(2460) ,cD
+2.4607E+03 ,0.4E+00,0.4E+00,4.75E+01 ,1.1E+00,1.1E+00,1/2, ,2 ,+, ,F, 425, 0, ,R,D(2)*(2460) ,cU
+2.4654E+03 ,1.3E+00,1.3E+00,4.67E+01 ,1.2E+00,1.2E+00,1/2, ,2 ,+, ,B, 415, +, ,R,D(2)*(2460) ,cD
2.637E+03 ,6.0E+00,6.0E+00,15 ,-1 ,-1 ,1/2, ,? ,?, ,F, , +, ,S,D*(2640) ,cD
1.96849E+03 ,3.4E-01,3.4E-01,1.325E-09 ,1.9E-11,1.9E-11,0 , ,0 ,-, ,B, 431, +, ,R,D(s) ,cS
-2.1123E+03 ,5.0E-01,5.0E-01,-1 ,-1 ,-1 ,0 , ,? ,?, ,B, 433, +, ,R,D(s)* ,cS
+2.1123E+03 ,5.0E-01,5.0E-01,1.0E-01 ,-1 ,-1 ,0 , ,1 ,-, ,B, 433, +, ,R,D(s)* ,cS
2.3178E+03 ,6.0E-01,6.0E-01,10 ,-1 ,-1 ,0 , ,0 ,+, ,B, 10431, +, ,R,D(s0)*(2317) ,cS
2.4596E+03 ,6.0E-01,6.0E-01,6.3 ,-1 ,-1 ,0 , ,1 ,+, ,B, 20433, +, ,R,D(s1)(2460) ,cS
2.5354E+03 ,6.0E-01,6.0E-01,2.5 ,-1 ,-1 ,0 , ,1 ,+, ,B, 10433, +, ,R,D(s1)(2536) ,cS
-2.5726E+03 ,9.0E-01,9.0E-01,2.0E+01 ,5.0E+00,5.0E+00,0 , ,? ,?, ,B, 435, +, ,R,D(s2)(2573) ,cS
+2.5726E+03 ,9.0E-01,9.0E-01,2.0E+01 ,5.0E+00,5.0E+00,0 , ,2 ,+, ,B, 435, +, ,R,D(s2)(2573) ,cS
2.690E+03 ,7.0E+00,7.0E+00,1.10E+02 ,2.7E+01,2.7E+01,0 , ,1 ,-, ,B, , +, ,S,D(s1)(2700) ,cS
5.27915E+03 ,3.1E-01,3.1E-01,4.045E-10 ,2.7E-12,2.7E-12,1/2, ,0 ,-, ,B, 521, +, ,R,B ,uB
5.27953E+03 ,3.3E-01,3.3E-01,4.331E-10 ,2.5E-12,2.5E-12,1/2, ,0 ,-, ,F, 511, 0, ,R,B ,dB
@@ -409,7 +409,7 @@
3.637E+03 ,4.0E+00,4.0E+00,1.4E+01 ,7.0E+00,7.0E+00,0 ,+,0 ,-,+, , 100441, 0, ,R,eta(c)(2S) ,cC
3.68609E+03 ,4.0E-02,4.0E-02,3.17E-01 ,9.0E-03,9.0E-03,0 ,-,1 ,-,-, , 100443, 0, ,R,psi(2S) ,cC
3.77292E+03 ,3.5E-01,3.5E-01,2.730E+01 ,1.0E+00,1.0E+00,0 ,-,1 ,-,-, , 30443, 0, ,R,psi(3770) ,cC
-3.8722E+03 ,8.0E-01,8.0E-01,3.0E+00 ,2.1E+00,1.7E+00,0 ,?,1 ,?,+, ,9930443, 0, ,R,X(3872) ,cC
+3.8722E+03 ,8.0E-01,8.0E-01,3.0E+00 ,2.1E+00,1.7E+00,0 ,+,1 ,+,+, ,9930443, 0, ,R,X(3872) ,cC
3.929E+03 ,5.0E+00,5.0E+00,2.90E+01 ,1.0E+01,1.0E+01,0 ,+,2 ,+,+, , 100445, 0, ,S,chi(c2)(2P) ,cC
3.943E+03 ,8.0E+00,8.0E+00,52 ,-1 ,-1 ,? ,?,? ,?,?, , , 0, ,S,X(3940) ,cC
3.943E+03 ,1.7E+01,1.7E+01,8.7E+01 ,3.4E+01,3.4E+01,? ,?,? ,?,?, , , 0, ,S,X(3945) ,cC
@@ -578,15 +578,15 @@
2.342E+03 ,3.0E+01,3.0E+01,1.6E+02 ,4.0E+01,4.0E+01,0 , ,3/2 ,-, ,F, , 0,1,S,Lambda(2325) ,uds
2.3500E+03 ,2.0E+01,1.0E+01,1.5E+02 ,1.0E+02,5.0E+01,0 , ,9/2 ,+, ,F, , 0,3,D,Lambda(2350) ,uds
2.530E+03 ,2.5E+01,2.5E+01,150 ,-1 ,-1 ,0 , ,? ,?, ,F, , 0,2,S,Lambda(2585) ,uds
-1.18937E+03 ,7.0E-02,7.0E-02,8.264E-12 ,2.7E-14,2.7E-14,1 , ,1/2 ,+, ,F, 3222, +,4,R,Sigma(P11) ,uus
-1.192642E+03 ,2.4E-02,2.4E-02,9.0E-03 ,8.0E-04,8.0E-04,1 , ,1/2 ,+, ,F, 3212, 0,4,R,Sigma(P11) ,uds
-1.197449E+03 ,3.0E-02,3.0E-02,4.480E-12 ,3.3E-14,3.3E-14,1 , ,1/2 ,+, ,F, 3112, -,4,R,Sigma(P11) ,dds
+1.18937E+03 ,7.0E-02,7.0E-02,8.264E-12 ,2.7E-14,2.7E-14,1 , ,1/2 ,+, ,F, 3222, +,4,R,Sigma ,uus
+1.192642E+03 ,2.4E-02,2.4E-02,9.0E-03 ,8.0E-04,8.0E-04,1 , ,1/2 ,+, ,F, 3212, 0,4,R,Sigma ,uds
+1.197449E+03 ,3.0E-02,3.0E-02,4.480E-12 ,3.3E-14,3.3E-14,1 , ,1/2 ,+, ,F, 3112, -,4,R,Sigma ,dds
1.3828E+03 ,4.0E-01,4.0E-01,3.58E+01 ,8.0E-01,8.0E-01,1 , ,3/2 ,+, ,F, 3224, +,4,R,Sigma(1385) ,uus
1.38370E+03 ,1.0E+00,1.0E+00,3.6E+01 ,5.0E+00,5.0E+00,1 , ,3/2 ,+, ,F, 3214, 0,4,R,Sigma(1385) ,uds
1.3872E+03 ,5.0E-01,5.0E-01,3.94E+01 ,2.1E+00,2.1E+00,1 , ,3/2 ,+, ,F, 3114, -,4,R,Sigma(1385) ,dds
-1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,? ,?, ,F, , +,1,S,Sigma(1480) ,uus
-1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,? ,?, ,F, , 0,1,S,Sigma(1480) ,uds
-1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,? ,?, ,F, , -,1,S,Sigma(1480) ,dds
+1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,1/2 ,+, ,F, , +,1,S,Sigma(1480) ,uus
+1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,1/2 ,+, ,F, , 0,1,S,Sigma(1480) ,uds
+1.480E+03 ,1.5E+01,1.5E+01,6.0E+01 ,1.5E+01,1.5E+01,1 , ,1/2 ,+, ,F, , -,1,S,Sigma(1480) ,dds
1.572E+03 ,4.0E+00,4.0E+00,7.9E+01 ,3.0E+01,3.0E+01,1 , ,? ,?, ,F, , +,2,S,Sigma(1560) ,uus
1.572E+03 ,4.0E+00,4.0E+00,7.9E+01 ,3.0E+01,3.0E+01,1 , ,? ,?, ,F, , 0,2,S,Sigma(1560) ,uds
1.572E+03 ,4.0E+00,4.0E+00,7.9E+01 ,3.0E+01,3.0E+01,1 , ,? ,?, ,F, , -,2,S,Sigma(1560) ,dds
@@ -666,16 +666,16 @@
1.32171E+03 ,7.0E-02,7.0E-02,4.04E-12 ,4.0E-14,4.0E-14,1/2, ,1/2 ,+, ,F, 3312, -,4,R,Xi ,dss
1.53180E+03 ,3.2E-01,3.2E-01,9.1E+00 ,5.0E-01,5.0E-01,1/2, ,3/2 ,+, ,F, 3324, 0,4,R,Xi(1530) ,uss
1.5350E+03 ,6.0E-01,6.0E-01,9.9E+00 ,1.7E+00,1.9E+00,1/2, ,3/2 ,+, ,F, 3314, -,4,R,Xi(1530) ,dss
-1.6240E+03 ,3.0E+00,3.0E+00,22.5 ,-1 ,-1 ,1/2, ,? ,?, ,F, , 0,1,S,Xi(1620) ,uss
-1.6240E+03 ,3.0E+00,3.0E+00,22.5 ,-1 ,-1 ,1/2, ,? ,?, ,F, , -,1,S,Xi(1620) ,dss
-1.6900E+03 ,1.0E+01,1.0E+01,-1 ,-1 ,-1 ,1/2, ,? ,?, ,F, , 0,3,D,Xi(1690) ,uss
-1.6900E+03 ,1.0E+01,1.0E+01,-1 ,-1 ,-1 ,1/2, ,? ,?, ,F, , -,3,D,Xi(1690) ,dss
+1.6240E+03 ,3.0E+00,3.0E+00,22.5 ,-1 ,-1 ,1/2, ,1/2 ,-, ,F, , 0,1,S,Xi(1620) ,uss
+1.6240E+03 ,3.0E+00,3.0E+00,22.5 ,-1 ,-1 ,1/2, ,1/2 ,-, ,F, , -,1,S,Xi(1620) ,dss
+1.6900E+03 ,1.0E+01,1.0E+01,-1 ,-1 ,-1 ,1/2, ,1/2 ,-, ,F, , 0,3,D,Xi(1690) ,uss
+1.6900E+03 ,1.0E+01,1.0E+01,-1 ,-1 ,-1 ,1/2, ,1/2 ,-, ,F, , -,3,D,Xi(1690) ,dss
1.823E+03 ,5.0E+00,5.0E+00,2.40E+01 ,1.5E+01,1.0E+01,1/2, ,3/2 ,-, ,F, 13324, 0,3,D,Xi(1820) ,uss
1.823E+03 ,5.0E+00,5.0E+00,2.40E+01 ,1.5E+01,1.0E+01,1/2, ,3/2 ,-, ,F, 13314, -,3,D,Xi(1820) ,dss
-1.950E+03 ,1.5E+01,1.5E+01,6.0E+01 ,2.0E+01,2.0E+01,1/2, ,? ,?, ,F, , 0,3,D,Xi(1950) ,uss
-1.950E+03 ,1.5E+01,1.5E+01,6.0E+01 ,2.0E+01,2.0E+01,1/2, ,? ,?, ,F, , -,3,D,Xi(1950) ,dss
-2.025E+03 ,5.0E+00,5.0E+00,2.0E+01 ,1.5E+01,5.0E+00,1/2, ,>3/2,?, ,F, , 0,3,D,Xi(2030) ,uss
-2.025E+03 ,5.0E+00,5.0E+00,2.0E+01 ,1.5E+01,5.0E+00,1/2, ,>3/2,?, ,F, , -,3,D,Xi(2030) ,dss
+1.950E+03 ,1.5E+01,1.5E+01,6.0E+01 ,2.0E+01,2.0E+01,1/2, ,5/2 ,-, ,F, , 0,3,D,Xi(1950) ,uss
+1.950E+03 ,1.5E+01,1.5E+01,6.0E+01 ,2.0E+01,2.0E+01,1/2, ,5/2 ,-, ,F, , -,3,D,Xi(1950) ,dss
+2.025E+03 ,5.0E+00,5.0E+00,2.0E+01 ,1.5E+01,5.0E+00,1/2, ,3/2 ,+, ,F, , 0,3,D,Xi(2030) ,uss
+2.025E+03 ,5.0E+00,5.0E+00,2.0E+01 ,1.5E+01,5.0E+00,1/2, ,3/2 ,+, ,F, , -,3,D,Xi(2030) ,dss
2.137E+03 ,4.0E+00,4.0E+00,20 ,-1 ,-1 ,1/2, ,? ,?, ,F, , 0,1,S,Xi(2120) ,uss
2.137E+03 ,4.0E+00,4.0E+00,20 ,-1 ,-1 ,1/2, ,? ,?, ,F, , -,1,S,Xi(2120) ,dss
2.189E+03 ,7.0E+00,7.0E+00,4.6E+01 ,2.7E+01,2.7E+01,1/2, ,? ,?, ,F, , 0,2,S,Xi(2250) ,uss
@@ -721,8 +721,9 @@
3.1229E+03 ,1.3E+00,1.3E+00,4.0E+00 ,4.0E+00,4.0E+00,? , ,? ,?, ,F, , +,1,S,Xi(c)(3123) ,usc
2.6975E+03 ,2.6E+00,2.6E+00,9.6E-09 ,1.7E-09,1.7E-09,0 , ,1/2 ,+, ,F, 4332, 0,3,R,Omega(c) ,ssc
2.7683E+03 ,3.0E+00,3.0E+00,-1 ,-1 ,-1 ,0 , ,3/2 ,+, ,F, 4334, 0,3,R,Omega(c)(2770) ,ssc
-3.5189E+03 ,9.0E-01,9.0E-01,2.0079E-08 ,-1 ,-1 ,? , ,? ,?, ,F, 4422, ++,1,S,Xi(cc) ,ucc
-3.5189E+03 ,9.0E-01,9.0E-01,2.0079E-08 ,-1 ,-1 ,? , ,? ,?, ,F, 4412, +,1,S,Xi(cc) ,dcc
+3.0004E+03 ,0.2E+00,0.2E+00,4.5E+00 ,0.7E+00,0.7E+00,0 , ,1/2 ,+, ,F, , 0,3,R,Omega(c)(3000) ,ssc
+3.5189E+03 ,9.0E-01,9.0E-01,2.0079E-08 ,-1 ,-1 ,? , ,1/2 ,+, ,F, 4422, ++,1,S,Xi(cc) ,ucc
+3.5189E+03 ,9.0E-01,9.0E-01,2.0079E-08 ,-1 ,-1 ,? , ,1/2 ,+, ,F, 4412, +,1,S,Xi(cc) ,dcc
5.6202E+03 ,1.6E+00,1.6E+00,4.79E-10 ,1.7E-11,1.7E-11,0 , ,1/2 ,+, ,F, 5122, 0,3,R,Lambda(b) ,udb
5.8078E+03 ,2.7E+00,2.7E+00,-1 ,-1 ,-1 ,1 , ,1/2 ,+, ,F, 5222, +,3,R,Sigma(b) ,uub
5.8078E+03 ,2.7E+00,2.7E+00,-1 ,-1 ,-1 ,1 , ,1/2 ,+, ,F, 5212, 0,3,R,Sigma(b) ,udb
@@ -732,4 +733,4 @@
5.8364E+03 ,2.8E+00,2.8E+00,-1 ,-1 ,-1 ,1 , ,3/2 ,+, ,F, 5114, -,3,R,Sigma(b)* ,ddb
5.7924E+03 ,3.0E+00,3.0E+00,1.42E-12 ,2.8E-13,2.4E-13,1/2, ,1/2 ,+, ,F, 5232, -,3,R,Xi(b) ,dsb
5.7924E+03 ,3.0E+00,3.0E+00,4.7E-10 ,9.0E-11,8.0E-11,1/2, ,1/2 ,+, ,F, 5132, 0,3,R,Xi(b) ,usb
-
+6.0461E+03 ,1.7E+00,1.7E+00,4.7E-10 ,9.0E-11,8.0E-11,1/2, ,1/2 ,+, ,F, 5334, -,3,R,Omega(b) ,ssb
diff --git a/options/pdgID_to_latex.dat b/options/pdgID_to_latex.dat
index 6c72b3250ee..86724739cc1 100644
--- a/options/pdgID_to_latex.dat
+++ b/options/pdgID_to_latex.dat
@@ -296,6 +296,7 @@
3334 \Omega^{-} \Omega^{+}
4332 \Omega_{c}^{0} \Omega_{c}^{0}
4334 \Omega_{c}^{*0} \Omega_{c}^{*0}
+5334 \Omega_{b}^{-} \Omega_{b}^{+}
9981 0^{+} 0^{+}
9983 1^{+} 1^{+}
9985 2^{+} 2^{+}
diff --git a/options/run_lbAmpGen_tests.sh b/options/run_lbAmpGen_tests.sh
new file mode 100755
index 00000000000..0e1ea585131
--- /dev/null
+++ b/options/run_lbAmpGen_tests.sh
@@ -0,0 +1,22 @@
+branch=mstahl_AmpGen
+
+tmp_dir=$(mktemp -d -t ci-XXXXXXXXXX)
+echo "TMPDIR=$tmp_dir"
+cd $tmp_dir
+
+wget https://gitlab.cern.ch/lhcb/Gauss/-/archive/$branch/Gauss-${branch}.zip?path=Gen/LbAmpGen -O LbAmpGen.zip >> /dev/null
+unzip LbAmpGen.zip >> /dev/null
+top=Gauss-$branch-Gen-LbAmpGen
+
+for model in $top/Gen/LbAmpGen/models/*.opt ; do
+ filename=$(basename $model)
+ without_ext=${filename%.*}
+ if [ $without_ext == "DtoKpipipi_v1" ] ||
+ [ $without_ext == "DtopiKpipi_v1" ] ||
+ [ $without_ext == "DtoKKpipi_v1" ] ; then continue ; fi # these are old models that kept for backwards compatability, dont expect to be able reproduce exactly
+ mkdir -p build/$without_ext
+ $AMPGENROOT/build/bin/ConvertToSourceCode $model --Output build/$without_ext/new.cpp >> /dev/null
+ g++ -Ofast -shared -rdynamic --std=c++11 -fPIC build/$without_ext/new.cpp -o build/$without_ext/new.so
+ g++ -Ofast -shared -rdynamic --std=c++11 -fPIC $top/Gen/LbAmpGen/src/${without_ext}.cpp -o build/$without_ext/gaussUpdate.so
+ $AMPGENROOT/build/bin/lib_diff $model --Lib=build/$without_ext/new.so --RefLib=build/$without_ext/gaussUpdate.so
+done
diff --git a/src/ASTResolver.cpp b/src/ASTResolver.cpp
index 0275b1b0bf2..b1366d6ba5e 100644
--- a/src/ASTResolver.cpp
+++ b/src/ASTResolver.cpp
@@ -12,100 +12,94 @@
using namespace AmpGen;
-ASTResolver::ASTResolver(const std::map<std::string, size_t>& evtMap,
+ASTResolver::ASTResolver(const std::map<std::string, unsigned>& evtMap,
const MinuitParameterSet* mps ) :
- evtMap(evtMap),
- mps(mps),
- nParameters(0)
+ m_evtMap(evtMap),
+ m_mps(mps),
+ m_nParameters(0)
{
- enable_cuda = NamedParameter<bool>("UseCUDA",false);
- enable_compileTimeConstants = NamedParameter<bool>("ASTResolver::CompileTimeConstants",false);
+ m_enable_cuda = NamedParameter<bool>("UseCUDA",false);
+ m_enable_compileTimeConstants = NamedParameter<bool>("ASTResolver::CompileTimeConstants", false);
+ m_check_hashes = NamedParameter<bool>("ASTResolver::CheckHashes", false );
}
-bool ASTResolver::hasSubExpressions() const
-{
- return subTrees.size() != 0;
-}
-
-void ASTResolver::reduceSubTrees()
-{
- subTrees.clear();
- for( auto& t : tempTrees ){
- auto expr = t.first->m_expression;
- uint64_t key = t.first->key();
- if( subTrees.count( key ) == 0 ){
- subTrees[ key ] = t.first->m_expression ;
- }
- }
- tempTrees.clear();
-}
-
-void ASTResolver::getOrderedSubExpressions(
- Expression& expression,
- std::vector< std::pair< uint64_t,Expression>>& dependentSubexpressions )
+std::vector<std::pair<uint64_t,Expression>> ASTResolver::getOrderedSubExpressions( const Expression& expression )
{
+ std::vector<std::pair<uint64_t, Expression>> subexpressions;
expression.resolve( *this );
- std::map< uint64_t , size_t> used_functions;
- for( size_t i = 0 ; i < dependentSubexpressions.size(); ++i )
- used_functions[ dependentSubexpressions[i].first ] = i;
+ std::map<uint64_t, size_t> used_functions;
+ std::map<uint64_t, Expression> subTrees;
do {
- reduceSubTrees();
- for( auto& expression : subTrees ) {
- expression.second.resolve( *this );
- auto stack_pos = used_functions.find( expression.first );
+ subTrees.clear();
+ for( auto& [t, s] : m_tempTrees )
+ {
+ uint64_t key = s->key();
+ if( subTrees.count( key ) == 0 ) subTrees[ key ] = s->expression();
+ // else if( m_check_hashes && t.first->m_expression.to_string() != subTrees[key].to_string() )
+ // {
+ // WARNING("Hash collision between in key = " << key << " other key = " << FNV1a_hash( subTrees[key].to_string() ) );
+ // }
+ }
+ m_tempTrees.clear();
+ for( auto& [key,expression] : subTrees ){
+ expression.resolve( *this );
+ auto stack_pos = used_functions.find(key);
if ( stack_pos == used_functions.end() ) {
- dependentSubexpressions.emplace_back( expression.first , expression.second );
- used_functions[expression.first] = dependentSubexpressions.size() - 1;
+ subexpressions.emplace_back(key , expression );
+ used_functions[key] = subexpressions.size() - 1;
continue;
}
- unsigned int oldPos = stack_pos->second;
- auto it = dependentSubexpressions.begin() + oldPos;
- if ( it == dependentSubexpressions.end() - 1 ) continue;
-
- std::rotate( it, it + 1, dependentSubexpressions.end() );
-
+ auto oldPos = stack_pos->second;
+ auto it = subexpressions.begin() + oldPos;
+ if ( it == subexpressions.end() - 1 ) continue;
+ std::rotate( it, it + 1, subexpressions.end() );
for ( auto uf = used_functions.begin(); uf != used_functions.end(); ++uf ) {
if ( uf->second >= oldPos ) uf->second = uf->second - 1;
}
- used_functions[expression.first] = dependentSubexpressions.size() - 1;
+ used_functions[key] = subexpressions.size() - 1;
}
- } while ( hasSubExpressions() );
- std::reverse( dependentSubexpressions.begin(), dependentSubexpressions.end() );
+ } while ( subTrees.size() !=0 );
+ std::reverse( subexpressions.begin(), subexpressions.end() );
+ return subexpressions;
}
template <> void ASTResolver::resolve<SubTree>( const SubTree& subTree )
{
- if( tempTrees.count( &subTree ) != 0 ) return;
- tempTrees[&subTree] = 1;
+ auto ptr = subTree.expression().get();
+ if( m_tempTrees.count(ptr) != 0 ) return;
+ else {
+ ptr->resolve( *this );
+ m_tempTrees[ptr] = &subTree;
+ }
}
template <> void ASTResolver::resolve<Spline>( const Spline& spline )
{
if( m_resolvedParameters.count( &spline) != 0 ) return ;
- auto address = addCacheFunction<SplineTransfer>(spline.m_name,spline.m_nKnots,spline.m_min,spline.m_max);
+ auto address = addCacheFunction<SplineTransfer>(spline.m_name, spline.m_nKnots, spline.m_min, spline.m_max);
addResolvedParameter( &spline, address );
addResolvedParameter( spline.m_points.top().get(), address );
auto splineTransfer = dynamic_cast<SplineTransfer*>( m_cacheFunctions[spline.m_name].get() );
- if( mps == nullptr ) ERROR("Fix me!");
+ if( m_mps == nullptr ) ERROR("Fix me: Spline parameters must come from a ParameterSet");
for( unsigned int i = 0 ; i < spline.m_nKnots; ++i )
- splineTransfer->set(i, mps->find(spline.m_name+"::"+std::to_string(i)) );
+ splineTransfer->set(i, m_mps->find(spline.m_name+"::"+std::to_string(i)) );
}
template <> void ASTResolver::resolve<Parameter>( const Parameter& parameter )
{
if( m_resolvedParameters.count(¶meter) != 0 || parameter.isResolved() ) return;
- auto res = evtMap.find(parameter.name());
- if( res != evtMap.end() ){
- if( enable_cuda ) {
+ auto res = m_evtMap.find(parameter.name());
+ if( res != m_evtMap.end() ){
+ if( m_enable_cuda ) {
size_t t = res->second;
std::string it = "";
- if( t % 3 == 0 ) it = "x";
- if( t % 3 == 1 ) it = "y";
- if( t % 3 == 2 ) it = "z";
+ if( t % 3 == 0 ) it = ".x";
+ if( t % 3 == 1 ) it = ".y";
+ if( t % 3 == 2 ) it = ".z";
int stg = t/3;
std::string nTimesStg = "+"+std::to_string(stg) +"*N";
if( stg == 0 ) nTimesStg = "";
- if( stg == 1 ) nTimesStg = "N";
+ if( stg == 1 ) nTimesStg = "+N";
addResolvedParameter( ¶meter, "x1[i"+nTimesStg+"]" +it );
}
else {
@@ -113,18 +107,17 @@ template <> void ASTResolver::resolve<Parameter>( const Parameter& parameter )
}
return;
}
- else if( mps != nullptr ){
- auto it = mps->find(parameter.name());
+ else if( m_mps != nullptr ){
+ auto it = m_mps->find(parameter.name());
if( it != nullptr ){
- if( enable_compileTimeConstants &&
- it->iFixInit() == MinuitParameter::Flag::CompileTimeConstant ){
- addResolvedParameter( ¶meter, std::to_string(it->mean()) );
+ if( m_enable_compileTimeConstants && it->flag() == Flag::CompileTimeConstant ){
+ addResolvedParameter( ¶meter, "("+std::to_string(it->mean()) +")" );
}
else addResolvedParameter( ¶meter, addCacheFunction<ParameterTransfer>( parameter.name(), it ) );
return;
}
}
- else if( enable_compileTimeConstants ){
+ else if( m_enable_compileTimeConstants ){
addResolvedParameter( ¶meter, std::to_string( parameter.defaultValue() ) );
return;
}
@@ -135,10 +128,16 @@ template <> void ASTResolver::resolve<Parameter>( const Parameter& parameter )
template <> void ASTResolver::resolve<MinuitParameterLink>(const MinuitParameterLink& parameter)
{
if( m_resolvedParameters.count(¶meter) != 0 ) return;
- if( mps == nullptr ) return;
- auto it = mps->find(parameter.name());
+ if( m_mps == nullptr ) return;
+ auto it = m_mps->find(parameter.name());
if( it == nullptr ) return;
- addResolvedParameter(¶meter, addCacheFunction<ParameterTransfer>( parameter.name(),it));
+ addResolvedParameter(¶meter, addCacheFunction<ParameterTransfer>(parameter.name(), it));
+}
+
+template <> void ASTResolver::resolve<LambdaExpression>( const LambdaExpression& obj)
+{
+ if( m_resolvedParameters.count(&obj) != 0 ) return;
+ addResolvedParameter(&obj, addCacheFunction<LambdaTransfer>( "lxpr_" + std::to_string(m_nParameters), &obj));
}
std::map<std::string, std::shared_ptr<CacheTransfer>> ASTResolver::cacheFunctions() const
@@ -161,8 +160,16 @@ std::string ASTResolver::resolvedParameter( const IExpression* param ) const
auto it = m_resolvedParameters.find(param);
if( it != m_resolvedParameters.end() ) return it->second;
else {
- ERROR( "Parameter cannot be resolved" << param );
+ ERROR( "Parameter cannot be resolved: [" << this << "]" << param );
return "";
}
}
+void ASTResolver::clear()
+{
+ m_resolvedParameters.clear();
+ m_cacheFunctions.clear();
+ m_parameterMapping.clear();
+ m_tempTrees.clear();
+ m_nParameters = 0;
+}
diff --git a/src/AddCPConjugate.cpp b/src/AddCPConjugate.cpp
new file mode 100644
index 00000000000..fea88b44661
--- /dev/null
+++ b/src/AddCPConjugate.cpp
@@ -0,0 +1,49 @@
+#include <string>
+#include <vector>
+
+#include "AmpGen/AddCPConjugate.h"
+#include "AmpGen/MinuitParameterSet.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/ExpressionParser.h"
+#include "AmpGen/MinuitExpression.h"
+#include "AmpGen/Particle.h"
+#include "AmpGen/ParticlePropertiesList.h"
+
+using namespace AmpGen;
+
+void AmpGen::AddCPConjugate( MinuitParameterSet& mps )
+{
+ std::vector<MinuitParameter*> tmp;
+ std::string cartOrPolar = NamedParameter<std::string>("CouplingConstant::Coordinates" ,"cartesian");
+ for( auto& param : mps ){
+ const std::string name = param->name();
+ size_t pos=0;
+ std::string new_name = name;
+ int sgn=1;
+ if( name.find("::") != std::string::npos ){
+ pos = name.find("::");
+ auto props = AmpGen::ParticlePropertiesList::get( name.substr(0,pos), true );
+ if( props != 0 ) new_name = props->anti().name() + name.substr(pos);
+ }
+ else {
+ auto tokens=split(name,'_');
+ std::string reOrIm = *tokens.rbegin();
+ std::string name = tokens[0];
+ if ( reOrIm == "Re" || reOrIm == "Im" ){
+ Particle test = Particle(name).conj();
+ if( cartOrPolar == "polar" ) sgn = reOrIm == "Re" ? test.CP() : 1;
+ if( cartOrPolar == "cartesian" ) sgn = test.CP();
+ new_name = test.uniqueString() +"_"+reOrIm;
+ }
+ else if( tokens.size() == 2 ) {
+ auto props = AmpGen::ParticlePropertiesList::get(name, true);
+ if( props != 0 ) new_name = props->anti().name() + "_" + tokens[1];
+ }
+ }
+ if( mps.find( new_name ) == nullptr )
+ {
+ tmp.push_back( new MinuitExpression(new_name, sgn * MinuitParameterLink(param) )) ;
+ }
+ }
+ for( auto& p : tmp ) mps.add( p );
+}
diff --git a/src/AmplitudeRules.cpp b/src/AmplitudeRules.cpp
index 11be23a6451..b3d56e136a4 100644
--- a/src/AmplitudeRules.cpp
+++ b/src/AmplitudeRules.cpp
@@ -5,8 +5,10 @@
#include <cmath>
#include <memory>
#include <ostream>
+#include <numeric>
#include "AmpGen/MinuitParameter.h"
+#include "AmpGen/MinuitExpression.h"
#include "AmpGen/MinuitParameterSet.h"
#include "AmpGen/MsgService.h"
#include "AmpGen/Particle.h"
@@ -14,67 +16,77 @@
#include "AmpGen/NamedParameter.h"
using namespace AmpGen;
+using namespace std::complex_literals;
-AmplitudeRule::AmplitudeRule( const std::string& reName,
- const std::map<std::string, MinuitParameter*>& mapping )
+Coupling::Coupling(MinuitParameter* re, MinuitParameter* im) :
+ m_re(re),
+ m_im(im)
{
- auto tokens = split( reName, '_' );
+ auto tokens = split( re->name(), '_' );
if ( tokens.size() == 3 ) {
m_prefix = tokens[0];
m_name = tokens[1];
- auto ire = mapping.find( reName );
- auto iim = mapping.find( tokens[0] + "_" + tokens[1] + "_Im" );
- if ( iim == mapping.end() ) {
- ERROR( "Well-formed coupling not identified for:" << reName );
- return;
- }
- m_re = ire->second;
- m_im = iim->second;
- m_isGood = true;
-
} else if ( tokens.size() == 2 ) {
- m_prefix = "";
m_name = tokens[0];
- auto ire = mapping.find( reName );
- auto iim = mapping.find( tokens[0] + "_Im" );
- if ( iim == mapping.end() ) {
- ERROR( "Well-formed coupling not identified for:" << reName );
- return;
- }
- m_re = ire->second;
- m_im = iim->second;
- m_isGood = true;
- } else {
- ERROR( "Too many tokens! " );
- m_isGood = false;
}
- if ( m_isGood ) {
- size_t pos = find_next_of( m_name, {"[", "{"} );
- if ( pos == std::string::npos )
- {
- ERROR( "Does not seem to be well formed decay descriptor [" << reName << "]" );
- m_isGood = false;
- }
+ else {
+ ERROR("Ill-formed decay descriptor: " << m_name );
}
m_particle = Particle(m_name);
+ coordinateType coord = NamedParameter<coordinateType>("CouplingConstant::Coordinates", coordinateType::cartesian);
+ angType degOrRad = NamedParameter<angType>("CouplingConstant::AngularUnits" , angType::rad);
+ m_isCartesian = true;
+
+ if( coord == coordinateType::polar ) m_isCartesian = false;
+
+ if ( coord == coordinateType::Invalid){
+ FATAL("Coordinates for coupling constants must be either cartesian or polar");
+ }
+ if ( degOrRad == angType::deg) m_sf = M_PI / 180;
+
+ if ( degOrRad == angType::Invalid ){
+ FATAL("TotalCoupling::AngularUnits must be either rad or deg");
+ }
}
+Coupling::Coupling(MinuitExpression* expression) :
+ m_name(expression->name()),
+ m_expr(expression),
+ m_particle(m_name){}
+
AmplitudeRules::AmplitudeRules( const MinuitParameterSet& mps )
{
- for ( auto& o : mps.const_map() ) {
- if ( o.first.find( "_Re" ) == std::string::npos ) continue;
- AmplitudeRule pAmp( o.first, mps.const_map() );
- if ( pAmp.m_isGood ) m_rules[pAmp.m_particle.name()].push_back( pAmp );
+ for ( auto& it_re : mps ) {
+ auto& name = it_re->name();
+ DEBUG("Attempting to parse: " << it_re->name() );
+ if ( name.find("_Re") != std::string::npos ){
+ auto it_im = mps.find(replaceAll( name, "_Re","_Im") );
+ if( it_im == nullptr ){
+ ERROR("Cannot find matching imaginary part / phase for: " << it_re->name() );
+ continue;
+ }
+ if( ! Particle::isValidDecayDescriptor( name.substr(0, name.find("_Re") ) ) ) continue;
+ Coupling p(it_re, it_im);
+ m_rules[p.head()].emplace_back(p);
+ }
+ else if( name.find("_Im") == std::string::npos ){
+ bool isCoupling = Particle::isValidDecayDescriptor( it_re->name() );
+ if( isCoupling ){
+ MinuitExpression* expression = dynamic_cast<MinuitExpression*>( it_re );
+ DEBUG("Constructing: " << expression << " " << it_re->name() );
+ if( expression != nullptr ){
+ Coupling p(expression);
+ m_rules[p.head()].emplace_back(p);
+ }
+ }
+ }
}
}
-CouplingConstant::CouplingConstant( const CouplingConstant& other,
- const AmplitudeRule& pA) :
- couplings(other.couplings ),
- isCartesian(other.isCartesian),
- sf(other.sf)
+TotalCoupling::TotalCoupling(const TotalCoupling& other, const Coupling& pA) :
+ couplings(other.couplings)
{
- couplings.emplace_back( pA.m_re, pA.m_im );
+ couplings.emplace_back(pA);
}
@@ -83,106 +95,78 @@ bool AmplitudeRules::hasDecay(const std::string& head)
return m_rules.find(head) != m_rules.end();
}
-std::vector<AmplitudeRule> AmplitudeRules::rulesForDecay(const std::string& head, const std::string& prefix)
+std::vector<Coupling> AmplitudeRules::rulesForDecay(const std::string& head, const std::string& prefix)
{
- if(!hasDecay(head)) return std::vector<AmplitudeRule>();
+ if(!hasDecay(head)) return std::vector<Coupling>();
if( prefix == "" )return m_rules[head];
- std::vector<AmplitudeRule> rt = m_rules[head];
- rt.erase( std::remove_if( std::begin(rt), std::end(rt), [&prefix](auto& p){ return p.prefix() != prefix; } ) );
+ std::vector<Coupling> rt = m_rules[head];
+ rt.erase( std::remove_if( std::begin(rt), std::end(rt), [&prefix](auto& p){ return p.prefix() != prefix; } ), rt.end() );
return rt;
}
-std::map<std::string, std::vector<AmplitudeRule>> AmplitudeRules::rules()
+const std::map<std::string, std::vector<Coupling>>& AmplitudeRules::rules() const
{
return m_rules;
}
-EventType AmplitudeRule::eventType() const
+EventType Coupling::eventType() const
{
Particle particle( m_name );
- std::vector<std::string> particleNames;
- particleNames.push_back( particle.name() );
+ std::vector<std::string> particleNames = { particle.name() };
std::vector<std::shared_ptr<Particle>> fs = particle.getFinalStateParticles();
std::stable_sort( fs.begin(), fs.end(), []( auto& A, auto& B ) { return *A < *B; } );
- for( auto& f : fs ) particleNames.push_back( f->name() );
+ std::transform( fs.begin(), fs.end(), std::back_inserter(particleNames), [](auto& p ) -> std::string { return p->name() ; } );
return EventType( particleNames );
}
-CouplingConstant::CouplingConstant(const AmplitudeRule& pA)
+TotalCoupling::TotalCoupling(const Coupling& pA)
{
- couplings.emplace_back( std::make_pair(pA.m_re,pA.m_im) );
- std::string cartOrPolar = NamedParameter<std::string>("CouplingConstant::Coordinates" ,"cartesian");
- std::string degOrRad = NamedParameter<std::string>("CouplingConstant::AngularUnits","rad");
- if( cartOrPolar == "polar" ){
- isCartesian = false;
- }
- else if ( cartOrPolar != "cartesian" ){
- FATAL("Coordinates for coupling constants must be either cartesian or polar");
- }
- if ( degOrRad == "deg") sf = M_PI / 180;
- else if ( degOrRad != "rad"){
- FATAL("CouplingConstant::AngularUnits must be either rad or deg");
- }
+ couplings.emplace_back(pA);
}
-std::complex<double> CouplingConstant::operator()() const
+std::complex<double> Coupling::operator()() const
{
- std::complex<double> F( 1, 0 );
- if ( isCartesian )
- for( auto& p : couplings ) F *= complex_t( p.first->mean() , p.second->mean() );
- else
- for( auto& p : couplings ) F *= p.first->mean() * complex_t( cos( sf * p.second->mean() ), sin( sf * p.second->mean() ) );
- return F;
+ return m_expr != nullptr ? m_expr->getVal() : ( m_isCartesian ? complex_t( m_re->mean(), m_im->mean() ) : m_re->mean() * exp( 1i* m_sf * m_im->mean() ) );
}
-Expression CouplingConstant::to_expression() const
+Expression Coupling::to_expression() const
{
- Expression J = Constant(0,1);
- if ( isCartesian ) {
- Expression total = 1;
- for ( auto& p : couplings ) {
- total = total * ( Parameter( p.first->name() ) + J * Parameter( p.second->name() ) );
- }
- return total;
- } else {
- Expression angle = 0;
- Expression amp = 1;
- for ( auto& p : couplings ) {
- angle = angle + Parameter( p.second->name() );
- amp = amp * Parameter( p.first->name() );
- }
- return amp * ( Cos( sf * angle ) + J * Sin( sf * angle ) );
- }
+ return m_expr != nullptr ? m_expr->expression() : ( m_isCartesian ? ComplexParameter(Parameter(m_re->name()), Parameter(m_im->name())) : Parameter( m_re->name() ) * fcn::exp( 1i * m_sf * Parameter(m_im->name()) ) );
}
-void CouplingConstant::print() const
+std::complex<double> TotalCoupling::operator()() const
{
- INFO( couplings[0].first->name() << " (" << isCartesian << ") = " << ( *this )() );
- if ( isCartesian )
- for ( auto& coupling : couplings ) INFO( coupling.first->name() + " i " + coupling.second->name() );
- else
- for ( auto& coupling : couplings ) INFO( coupling.first->name() << " x exp(i" << coupling.second->name() );
+ return std::accumulate( couplings.begin(), couplings.end(), complex_t(1,0), [](auto& prod, auto& coupling ){ return prod * coupling() ; } );
}
-std::vector< std::pair<Particle, CouplingConstant > > AmplitudeRules::getMatchingRules(
- const EventType& type, const std::string& prefix ){
+Expression TotalCoupling::to_expression() const
+{
+ return std::accumulate( couplings.begin(), couplings.end(), Expression(1), [](auto& prod, auto& coupling ){ return prod * coupling.to_expression(); } );
+}
- auto rules = rulesForDecay( type.mother() );
- std::vector<std::pair<Particle, CouplingConstant>> rt;
+void TotalCoupling::print() const
+{
+ INFO( this->operator()() << " -> " );
+ for( const auto& coupling :*this ) INFO( coupling.to_expression() << " = " << coupling() );
+}
+std::vector<std::pair<Particle, TotalCoupling>> AmplitudeRules::getMatchingRules(const EventType& type, const std::string& prefix )
+{
+ auto rules = rulesForDecay( type.mother() );
+ std::vector<std::pair<Particle, TotalCoupling>> rt;
for ( auto& rule : rules ) {
if ( rule.prefix() != prefix ) continue;
- std::vector<std::pair<Particle, CouplingConstant>> tmpParticles;
+ std::vector<std::pair<Particle, TotalCoupling>> tmpParticles;
auto fs = type.finalStates();
- tmpParticles.emplace_back( Particle( rule.name(), fs ), CouplingConstant(rule) );
+ tmpParticles.emplace_back( Particle( rule.name(), fs ), TotalCoupling(rule) );
do {
- std::vector<std::pair<Particle, CouplingConstant>> newTmpParticles;
- for ( auto& particleWithCouplingConstant : tmpParticles ) {
- auto protoParticle = particleWithCouplingConstant.first;
- auto coupling = particleWithCouplingConstant.second;
+ std::vector<std::pair<Particle, TotalCoupling>> newTmpParticles;
+ for ( auto& particleWithTotalCoupling : tmpParticles ) {
+ auto protoParticle = particleWithTotalCoupling.first;
+ auto coupling = particleWithTotalCoupling.second;
auto protoFinalStates = protoParticle.getFinalStateParticles();
if ( protoFinalStates.size() == type.size() ) {
- rt.emplace_back( particleWithCouplingConstant );
+ rt.emplace_back( particleWithTotalCoupling );
continue;
}
std::string nameToExpand = protoParticle.uniqueString();
@@ -192,7 +176,7 @@ std::vector< std::pair<Particle, CouplingConstant > > AmplitudeRules::getMatchin
for ( auto& subTree : expandedRules ) {
auto expanded_amplitude = replaceAll( nameToExpand, ifs->name(), subTree.name() );
auto fs2 = type.finalStates();
- newTmpParticles.emplace_back( Particle( expanded_amplitude, fs2 ), CouplingConstant( coupling, subTree) );
+ newTmpParticles.emplace_back( Particle( expanded_amplitude, fs2 ), TotalCoupling( coupling, subTree) );
}
break; // we should only break if there are rules to be expanded ...
}
@@ -200,26 +184,23 @@ std::vector< std::pair<Particle, CouplingConstant > > AmplitudeRules::getMatchin
tmpParticles = newTmpParticles;
} while ( tmpParticles.size() != 0 );
}
+ rt.erase( std::remove_if( std::begin(rt), std::end(rt), [](auto& p){ return !p.first.isStateGood(); } ), rt.end() );
+ auto end = std::end(rt);
+ for (auto it = rt.begin(); it != end; ++it) {
+ auto dd = it->first.decayDescriptor();
+ end = std::remove_if(it + 1, end, [dd](auto p){ return p.first.decayDescriptor() == dd;} );
+ }
+ rt.erase(end, rt.end());
return rt;
}
-bool CouplingConstant::isFixed() const
-{
- for( auto& c : couplings )
- if( c.first->iFixInit() == 0 or c.second->iFixInit() == 0 ) return false;
- return true;
-}
-
-bool CouplingConstant::contains( const std::string& label ) const
+bool TotalCoupling::isFixed() const
{
- for ( auto& reAndIm : couplings )
- if ( reAndIm.first->name().find( label ) != std::string::npos ) return true;
- return false;
+ return std::all_of(begin(), end(), [](auto& c){ return c.x()->isFixed() && c.y()->isFixed() ; } );
}
-void CouplingConstant::changeSign()
+bool TotalCoupling::contains( const std::string& label ) const
{
- auto& top_coupling = *couplings.begin();
- if( isCartesian ) top_coupling.first->setCurrentFitVal( top_coupling.first->mean() * -1. );
+ return std::any_of(begin(), end(), [&label](auto& c){ return c.name().find(label) != std::string::npos ; } );
}
diff --git a/src/Array.cpp b/src/Array.cpp
index c24cc378388..faaedacbf52 100644
--- a/src/Array.cpp
+++ b/src/Array.cpp
@@ -19,19 +19,13 @@ Array::Array( const Expression& top,
std::string Array::to_string(const ASTResolver* resolver) const {
auto head = m_top.to_string(resolver);
- if( is<Constant>(m_address) )
- return head+"["+ std::to_string(int(std::real(m_address()))) +"]";
- auto offset = m_address.to_string(resolver);
- auto pos = head.find_last_of("]");
- if( pos != std::string::npos ){
- auto st1 = head.substr(0,pos);
- auto st2 = head.substr(pos,head.size() - pos );
- return st1 + "+int("+offset+")" + st2;
- }
- else return head +"[ int("+offset+")]";
+ auto offset = Ternary( m_address >= 0 && m_address < m_size, m_address, 0.).to_string(resolver);
+ if( resolver != nullptr && resolver->enableAVX() ) return " gather( &(" + head + "), " + offset + ")";
+ if( head.find("[") == std::string::npos ) return head + "[int("+offset+")]";
+ else return " * ( & (" + head + ") + int("+offset+") )";
}
-void Array::resolve( ASTResolver& resolver )
+void Array::resolve( ASTResolver& resolver ) const
{
m_top.resolve( resolver );
m_address.resolve( resolver );
diff --git a/src/BinDT.cpp b/src/BinDT.cpp
index b1b13adf8a3..24a62280198 100644
--- a/src/BinDT.cpp
+++ b/src/BinDT.cpp
@@ -15,7 +15,7 @@
using namespace AmpGen;
-double nearestNeighbourVariance(std::vector<double*> evts, const size_t& index)
+double nearestNeighbourVariance( std::vector<double*> evts, const size_t& index)
{
auto dist = [&index](const double* x, const double* y){ return fabs( *(x+index) -*(y+index)) ;};
auto dist2 = [&index](const double* x, const double* y){ return ( *(x+index) -*(y+index))*( *(x+index) - *(y+index) ) ;};
@@ -69,25 +69,6 @@ unsigned int BinDT::getBinNumber( const double* evt ) const { return ( *m_top )(
unsigned int BinDT::size() const { return m_endNodes.size(); }
-namespace AmpGen
-{
- struct PackedDecision {
- uint8_t header; // = 2 bytes
- uint8_t index; // = 8 bytes
- uint32_t address; // = 2 + 4 bytes
- uint32_t left; // = 18
- uint32_t right; // = 24 bytes
- double cutVal; // = 14 bytes
- };
- struct PackedNode {
- uint8_t header;
- uint8_t packingBit[1];
- uint32_t address;
- uint32_t binNumber;
- uint32_t voxNumber;
- uint16_t packingBits[3];
- };
-} // namespace AmpGen
std::function<std::vector<double>( const Event& )> BinDT::makeDefaultFunctors()
{
if ( m_dim == 5 ) {
@@ -99,7 +80,7 @@ std::function<std::vector<double>( const Event& )> BinDT::makeDefaultFunctors()
DEBUG( "Problem has 2 d.o.f.s -> using Dalitz coordinates" );
return []( const Event& evt ) -> std::vector<double> { return {evt.s( 0, 1 ), evt.s( 1, 2 )}; };
}
- DEBUG( "No functors found for dim = " << m_dim );
+ ERROR( "No default functors found for dim = " << m_dim );
return nullptr;
}
@@ -109,19 +90,18 @@ BinDT::BinDT( const ArgumentPack& args )
m_maxDepth = args.getArg<MaxDepth>( 999 );
m_dim = args.getArg<Dim>( 5 );
m_functors = args.getArg<Functor>( makeDefaultFunctors() ).val;
- std::ifstream* stream = args.getArg<Stream>().val;
- auto fname = args.getArg<File>();
- if ( stream != nullptr && stream->is_open() ) {
- readFromBinary( *stream );
- } else if ( fname.name != "" ) {
- std::ifstream stream( fname.name, fname.mode | std::ios::in );
- if ( fname.mode & std::ios::binary )
- readFromBinary( stream );
- else
- readFromStream( stream );
+ auto fname = args.getArg<File>("").val;
+ if ( fname != "" ) {
+ auto stream = std::ifstream(fname);
+ readFromStream(stream);
}
}
+BinDT::BinDT( const EventList& events, const ArgumentPack& args ) : BinDT(args)
+{
+ makeNodes( events.begin(), events.end() );
+}
+
void BinDT::readFromStream( std::istream& stream )
{
std::map<std::string, std::pair<std::string, std::shared_ptr<INode>>> nodes;
@@ -159,79 +139,6 @@ void BinDT::readFromStream( std::istream& stream )
}
}
-void BinDT::readFromBinary( std::ifstream& stream )
-{
- std::map<uint32_t, std::shared_ptr<INode>> nodes;
- std::map<uint32_t, std::pair<uint32_t, uint32_t>> fti;
- char buffer[PACKET_SIZE]; // 24 byte word for the nodes //
- size_t edc = 0;
- while ( stream.read( buffer, PACKET_SIZE ) ) {
- if ( ( uint8_t( buffer[0] ) ) == 0xAA ) {
- PackedDecision pd;
- memcpy( &pd, buffer, PACKET_SIZE );
- nodes.emplace( pd.address, std::make_shared<Decision>( pd.index, pd.cutVal ) );
- DEBUG( "header = " << std::hex << (uint8_t)pd.header << std::dec << " index = " << pd.index
- << " cut-val = " << pd.cutVal << " left-node = " << pd.left << " right-node=" << std::hex
- << pd.right << " " << std::dec << sizeof( PackedDecision ) << " " << PACKET_SIZE );
- fti[pd.address] = std::make_pair( pd.left, pd.right );
- } else if ( uint8_t( buffer[0] ) == 0xBB ) {
- edc++;
- PackedNode pd;
- memcpy( &pd, buffer, PACKET_SIZE );
- nodes.emplace( pd.address, std::make_shared<EndNode>( pd.voxNumber, pd.binNumber ) );
- } else {
- ERROR( "Packet header: " << std::hex << uint8_t( buffer[0] ) << " not recognised" );
- }
- if ( nodes.size() == 1 ) m_top = nodes.begin()->second;
- }
- INFO( "Read: " << nodes.size() << " nodes from binary file, now re-establishing tree structure; EndNodes=" << edc );
-
- for ( auto& node : nodes ) {
- Decision* node_ptr = dynamic_cast<Decision*>( node.second.get() );
- if ( node_ptr == nullptr ) continue;
- auto child_nodes = fti.find( node.first );
- if ( child_nodes == fti.end() ) {
- ERROR( "Child nodes not found!" );
- }
- auto pL = nodes.find( child_nodes->second.first );
- auto pR = nodes.find( child_nodes->second.second );
- if ( pL == nodes.end() || pR == nodes.end() ) {
- ERROR( "Nodes for " << node_ptr << " not found! success counter "
- << " " << child_nodes->second.first << " " << child_nodes->second.second );
- } else {
- node_ptr->setChildren( pL->second, pR->second );
- }
- }
-}
-
-void BinDT::writeToBinary( std::ofstream& stream )
-{
- AddressCompressor counter;
- m_top->visit( [&stream, &counter]( const INode* node ) {
- std::array<char, PACKET_SIZE> word;
- const BinDT::Decision* decision = dynamic_cast<const BinDT::Decision*>( node );
- if ( decision != nullptr ) {
- PackedDecision pd;
- pd.header = 0xAA;
- pd.address = counter[decision]; // uint32_t ( 0xFFFFFFFF & (uint64_t)this );
- pd.index = decision->m_index;
- pd.cutVal = decision->m_value;
- pd.left = counter[decision->m_left.get()]; // (uint32_t)m_left.get();
- pd.right = counter[decision->m_right.get()]; // (uint32_t)m_right.get();
- memcpy( word.data(), &pd, PACKET_SIZE );
- } else if ( dynamic_cast<const BinDT::EndNode*>( node ) != nullptr ) {
- const BinDT::EndNode* endNode = dynamic_cast<const BinDT::EndNode*>( node );
- PackedNode pd;
- pd.header = 0xBB;
- pd.address = counter[endNode];
- pd.binNumber = endNode->m_binNumber;
- pd.voxNumber = endNode->m_voxNumber;
- memcpy( word.data(), &pd, PACKET_SIZE );
- }
- stream.write( (char*)( &word ), sizeof( word ) );
- } );
-}
-
void BinDT::serialize( std::ofstream& output )
{
output << std::setprecision( 17 );
@@ -247,7 +154,7 @@ void BinDT::serialize( const std::string& filename )
output.close();
}
-std::shared_ptr<BinDT::INode> BinDT::makeNodes( std::vector<double*> evts )
+std::shared_ptr<BinDT::INode> BinDT::makeNodes( const std::vector<double*>& evts )
{
INFO( "Making nodes" );
std::queue<unsigned int> iq;
@@ -260,8 +167,7 @@ std::shared_ptr<BinDT::INode> BinDT::makeNodes( std::vector<double*> evts )
return node;
}
-std::shared_ptr<BinDT::INode> BinDT::makeNodes( std::vector<double*> evts, std::queue<unsigned int> indexQueue,
- const unsigned int& depth )
+std::shared_ptr<BinDT::INode> BinDT::makeNodes( const std::vector<double*>& evts, std::queue<unsigned> indexQueue, const unsigned& depth )
{
unsigned int index = indexQueue.front();
DEBUG( "Depth = " << depth << " nodes = " << m_endNodes.size() << " maxDepth = " << m_maxDepth
@@ -282,7 +188,7 @@ std::shared_ptr<BinDT::INode> BinDT::makeNodes( std::vector<double*> evts, std::
return node;
}
-std::shared_ptr<BinDT::INode> BinDT::makeNodes( std::vector<double*> source, std::vector<double*> target )
+std::shared_ptr<BinDT::INode> BinDT::makeNodes( const std::vector<double*>& source, const std::vector<double*>& target )
{
std::queue<unsigned int> iq;
refreshQueue( source, iq, 0 );
@@ -440,17 +346,6 @@ void BinDT::Decision::setChildren( std::shared_ptr<INode> l, std::shared_ptr<INo
m_right->m_parent = this;
}
-uint32_t BinDT::AddressCompressor::operator[]( const void* ptr )
-{
- auto it = elements.find( ptr );
- if ( it != elements.end() )
- return it->second;
- else {
- elements[ptr] = counter++;
- return elements[ptr];
- }
-}
-
BinDT::EndNode::EndNode( const unsigned int& no, const unsigned int& binNumber ) :
m_voxNumber( no ),
m_binNumber( binNumber ) {}
@@ -464,7 +359,6 @@ void BinDT::EndNode::serialize( std::ostream& stream ) const
const BinDT::EndNode* BinDT::Decision::operator()( const double* evt ) const
{
-// INFO( m_index << " " << m_value << " " << *(evt+m_index));
return *( evt + m_index ) < m_value ? ( *m_right )( evt ) : ( *m_left )( evt );
}
@@ -474,3 +368,4 @@ void BinDT::Decision::visit( const std::function<void(BinDT::INode*)>& visit_fun
m_left->visit( visit_function );
m_right->visit( visit_function );
}
+
diff --git a/src/BinaryExpression.cpp b/src/BinaryExpression.cpp
index eeb1c5e2d3a..9416412a7ab 100644
--- a/src/BinaryExpression.cpp
+++ b/src/BinaryExpression.cpp
@@ -18,6 +18,9 @@ DEFINE_BINARY_OPERATOR( Equal )
DEFINE_BINARY_OPERATOR( Pow )
DEFINE_BINARY_OPERATOR( Fmod )
DEFINE_BINARY_OPERATOR( ATan2 )
+DEFINE_BINARY_OPERATOR( GreaterThanEqualTo )
+DEFINE_BINARY_OPERATOR( LessThanEqualTo )
+DEFINE_BINARY_OPERATOR( Or )
template < class condition >
std::string bracketed( const Expression& expression, condition&& use_brackets, const ASTResolver* resolver=nullptr ){
@@ -31,15 +34,21 @@ complex_t Divide::operator()() const { return lval() / rval(); }
complex_t And::operator()() const { return complex_t(std::real(lval()) && std::real(rval()),0); }
complex_t GreaterThan::operator()() const { return complex_t(std::real(lval()) > std::real(rval()) ,0); }
complex_t LessThan::operator()() const { return complex_t(std::real(lval()) < std::real(rval()) ,0); }
+complex_t GreaterThanEqualTo::operator()() const { return complex_t(std::real(lval()) >= std::real(rval()) ,0); }
+complex_t LessThanEqualTo::operator()() const { return complex_t(std::real(lval()) <= std::real(rval()) ,0); }
complex_t Pow::operator()() const { return pow( lval(), rval() ); }
complex_t Fmod::operator()() const { return 0; }
complex_t Equal::operator()() const { return lval() == rval() ; }
+complex_t Or::operator()() const { return std::real(lval()) || std::real(rval()) ; }
complex_t ATan2::operator()() const { return atan2( std::real(lval() ), std::real(rval() ) ); }
-std::string Sum::to_string(const ASTResolver* resolver) const {
+std::string Sum::to_string(const ASTResolver* resolver) const
+{
return lval.to_string(resolver) + " + " + rval.to_string(resolver) ;
}
-std::string Sub::to_string(const ASTResolver* resolver) const {
+
+std::string Sub::to_string(const ASTResolver* resolver) const
+{
return lval.to_string(resolver) + "-" + bracketed( rval, [](auto& expression){ return is<Sum>(expression) || is<Sub>(expression) ; } , resolver ) ;
}
std::string Equal::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + " == "+ rval.to_string(resolver) +")"; }
@@ -60,11 +69,14 @@ std::string Divide::to_string(const ASTResolver* resolver) const {
std::string LessThan::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + "<" + rval.to_string(resolver) +")"; }
std::string GreaterThan::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + ">" + rval.to_string(resolver) +")"; }
std::string And::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + "&&" + rval.to_string(resolver) +")"; }
+std::string LessThanEqualTo::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + "<=" + rval.to_string(resolver) +")"; }
+std::string GreaterThanEqualTo::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + ">=" + rval.to_string(resolver) +")"; }
+std::string Or::to_string(const ASTResolver* resolver) const { return "(" + lval.to_string(resolver) + "||" + rval.to_string(resolver) +")"; }
std::string Pow::to_string(const ASTResolver* resolver) const { return "pow(" + lval.to_string(resolver) + ", " + rval.to_string(resolver) +")"; }
std::string Fmod::to_string(const ASTResolver* resolver) const { return "fmod(" + lval.to_string(resolver) + "," + rval.to_string(resolver) +")"; }
std::string ATan2::to_string( const ASTResolver* resolver) const { return "atan2("+ lval.to_string(resolver) + "," + rval.to_string(resolver) +")"; }
-void IBinaryExpression::resolve( ASTResolver& resolver )
+void IBinaryExpression::resolve( ASTResolver& resolver ) const
{
lval.resolve( resolver );
rval.resolve( resolver );
diff --git a/src/CacheTransfer.cpp b/src/CacheTransfer.cpp
index 04f9edae16b..625ccc8ca1c 100644
--- a/src/CacheTransfer.cpp
+++ b/src/CacheTransfer.cpp
@@ -9,25 +9,56 @@
using namespace AmpGen;
-CacheTransfer::CacheTransfer( const unsigned int& address, const double& value, const size_t& size ) :
- m_address(address), m_value(value), m_size(size) {}
+CacheTransfer::CacheTransfer() = default;
+
+CacheTransfer::CacheTransfer( const size_t& address, const std::string& name, const double& value, const size_t& size ) :
+ m_address(address),
+ m_size(size),
+ m_value(value),
+ m_name(name)
+{
+}
void CacheTransfer::transfer( CompiledExpressionBase* destination )
{
destination->setExternal(m_value, m_address);
}
-void CacheTransfer::print() const { INFO( m_address << " " << m_value ) ; }
+
+void CacheTransfer::print() const
+{
+ INFO( m_address << " " << m_value << " " << m_name ) ;
+}
void ParameterTransfer::transfer( CompiledExpressionBase* destination )
{
destination->setExternal( m_source->mean(), m_address );
}
-CacheTransfer::CacheTransfer() : m_address( 0 ), m_value( 0 ) {}
+ParameterTransfer::ParameterTransfer(const size_t& address, const std::string& name, MinuitParameter* source )
+ : CacheTransfer(address, name, source->mean(), 1),
+ m_source( source )
+{
+}
+
+void ParameterTransfer::print() const
+{
+ INFO( "Source: " << m_source->name() << " address = " << m_address << " value = " << m_source->mean() );
+}
+
+
+LambdaTransfer::LambdaTransfer(const size_t& address, const std::string& name, const LambdaExpression* source )
+ : CacheTransfer(address, name, source->m_function(), 1),
+ m_function(source->m_function)
+{
+}
+
+void LambdaTransfer::transfer( CompiledExpressionBase* destination )
+{
+ destination->setExternal( m_function(), m_address );
+}
-ParameterTransfer::ParameterTransfer( const unsigned int& address, MinuitParameter* source )
- : m_address( address ), m_source( source )
+void LambdaTransfer::print() const
{
+ INFO( m_name << " = " << m_function() << " address = " << m_address );
}
-void ParameterTransfer::print() const { std::cout << this << " " << m_source->name() << " " << m_address << std::endl; INFO( "Source: " << m_source->name() << " address = " << m_address ); }
diff --git a/src/Chi2Estimator.cpp b/src/Chi2Estimator.cpp
index 58047ad5c4c..f879116277c 100644
--- a/src/Chi2Estimator.cpp
+++ b/src/Chi2Estimator.cpp
@@ -6,9 +6,9 @@
#include "AmpGen/ArgumentPack.h"
#include "AmpGen/EventType.h"
#include "AmpGen/MsgService.h"
-#include "AmpGen/EventList.h"
#include "AmpGen/Event.h"
+
using namespace AmpGen;
struct Moment {
@@ -33,26 +33,11 @@ struct Moment {
double var() { return N == 0 ? 0 : xx; }
};
-Chi2Estimator::Chi2Estimator( const EventList& dataEvents, const EventList& mcEvents,
- const std::function<double( const Event& )>& fcn, const unsigned int& minEvents ) :
- m_binning( dataEvents, MinEvents( minEvents ), Dim( dataEvents.eventType().dof() ) )
-{
- doChi2( dataEvents, mcEvents, fcn );
-}
-
-Chi2Estimator::Chi2Estimator( const EventList& dataEvents, const EventList& mcEvents,
- const std::function<double( const Event& )>& fcn, const std::string& filename ) :
- m_binning( File( filename ) )
-{
- doChi2( dataEvents, mcEvents, fcn );
-}
-
-
double Chi2Estimator::chi2() const { return m_chi2; }
double Chi2Estimator::nBins() const { return m_nBins; }
void Chi2Estimator::writeBinningToFile( const std::string& filename ) { m_binning.serialize( filename ); }
-void Chi2Estimator::doChi2( const EventList& dataEvents, const EventList& mcEvents,
+void Chi2Estimator::doChi2( const EventList_type& dataEvents, const EventList_type& mcEvents,
const std::function<double( const Event& )>& fcn )
{
std::vector<Moment> data( m_binning.size() );
@@ -63,7 +48,7 @@ void Chi2Estimator::doChi2( const EventList& dataEvents, const EventList& mcEv
unsigned int j = 0;
double total_data_weight = 0;
double total_int_weight = 0;
- for ( auto& d : dataEvents ) {
+ for ( const auto& d : dataEvents ) {
if ( j % 1000000 == 0 && j != 0 ) INFO( "Binned " << j << " data events" );
double w = d.weight();
data[m_binning.getBinNumber( d )].add( d.weight() );
@@ -71,10 +56,11 @@ void Chi2Estimator::doChi2( const EventList& dataEvents, const EventList& mcEv
j++;
}
j = 0;
- for ( auto& evt : mcEvents ) {
+ for ( auto& evt : mcEvents )
+ {
if ( j % 1000000 == 0 && j != 0 ) INFO( "Binned " << j << " sim. events" );
double w = fcn( evt ) * evt.weight() / evt.genPdf();
- mc[m_binning.getBinNumber( evt )].add( w );
+ mc[m_binning.getBinNumber(evt)].add( w );
total_int_weight += w;
j++;
}
@@ -83,10 +69,12 @@ void Chi2Estimator::doChi2( const EventList& dataEvents, const EventList& mcEv
for ( unsigned int i = 0; i < m_binning.size(); ++i ) {
mc[i].rescale( total_data_weight / total_int_weight );
double delta = data[i].val() - mc[i].val();
- double tChi2 = delta * delta / ( data[i].val() + mc[i].var() );
+ double tChi2 = delta * delta / ( data[i].var() + mc[i].var() );
chi2 += tChi2;
}
m_chi2 = chi2;
m_nBins = m_binning.size();
}
+
+
diff --git a/src/CoherenceFactor.cpp b/src/CoherenceFactor.cpp
deleted file mode 100644
index 1da28335737..00000000000
--- a/src/CoherenceFactor.cpp
+++ /dev/null
@@ -1,551 +0,0 @@
-#include "AmpGen/CoherenceFactor.h"
-
-#include <TRandom3.h>
-#include <memory.h>
-#include <algorithm>
-#include <cmath>
-#include <memory>
-#include <numeric>
-#include <ostream>
-#include <utility>
-
-#include "AmpGen/ArgumentPack.h"
-#include "AmpGen/DynamicContainer.h"
-#include "AmpGen/Generator.h"
-#include "AmpGen/Integrator.h"
-#include "AmpGen/MsgService.h"
-#include "AmpGen/PhaseSpace.h"
-#include "AmpGen/NamedParameter.h"
-#include "AmpGen/CompiledExpression.h"
-#include "AmpGen/Event.h"
-#include "AmpGen/Utilities.h"
-#include "TH1.h"
-
-using namespace AmpGen;
-
-void HadronicParameters::scale_p1( const real_t& sf )
-{
- n1 /= sf;
- coherence /= sqrt( sf );
-}
-void HadronicParameters::scale_p2( const real_t& sf )
-{
- n2 /= sf;
- coherence /= sqrt( sf );
-}
-
-void HadronicParameters::rotate( const real_t& angle )
-{
- coherence *= complex_t( cos( angle ), sin( angle ) );
-}
-
-void HadronicParameters::clear()
-{
- n1 = 0;
- n2 = 0;
- nFills = 0;
- id = 0;
- wt = 0;
- coherence = complex_t( 0, 0 );
-}
-
-void HadronicParameters::add( const complex_t& f1,
- const complex_t& f2,
- const real_t& weight )
-{
- n1 += weight * std::norm( f1 );
- n2 += weight * std::norm( f2 );
- wt += weight;
- coherence += weight * std::conj(f1) * f2 ;
- nFills++;
-}
-
-HadronicParameters::HadronicParameters( const real_t& _R, const real_t& _d, const real_t& k1 ) :
- n1(k1*k1),
- n2(1),
- wt(1),
- coherence(k1*_R*cos( M_PI*_d/180.), k1*_R*sin(M_PI*_d/180.)) {}
-
-HadronicParameters::HadronicParameters( const real_t& _R, const real_t& _d, const real_t& k1, const real_t& k2 )
- : n1( k1 ),
- n2( k2 ),
- wt(1),
- coherence( sqrt( k1 * k2 ) * _R * cos( _d ), sqrt( k1 * k2 ) * _R * sin( _d ) ) {}
-
-HadronicParameters HadronicParameters::operator+=( const HadronicParameters& other )
-{
- n1 += other.n1;
- n2 += other.n2;
- coherence += other.coherence;
- nFills += other.nFills;
- wt += other.wt;
- return *this;
-}
-
-HadronicParameters HadronicParameters::operator-=( const HadronicParameters& other )
-{
- n1 -= other.n1;
- n2 -= other.n2;
- coherence -= other.coherence;
- nFills -= other.nFills;
- wt -= other.wt;
- return *this;
-}
-HadronicParameters AmpGen::operator+( const HadronicParameters& a, const HadronicParameters& b )
-{
- HadronicParameters hp;
- hp.wt = a.wt + b.wt;
- hp.n1 = a.n1 + b.n1 ;
- hp.n2 = a.n2 + b.n2 ;
- hp.coherence = a.coherence + b.coherence ;
- hp.nFills = a.nFills + b.nFills;
- return hp;
-}
-
-std::string HadronicParameters::to_string() const
-{
- auto c = getCoherence();
- std::string total = "R = " + round( R() , 3 ) + " δ = " + round( 180 * d() / M_PI, 2 ) +
- " r = " + round( r(), 4 ) + " K = " + round( I1() , 6 ) + " K' = " + round( I2(), 6 ) + " N = " +
- std::to_string( wt ) + " ci = " + std::to_string( std::real( c ) ) + " si = " +
- std::to_string( std::imag( c ) ) ;
- return total;
-}
-
-void CoherenceFactor::makeCoherentMapping( const unsigned int& nBins,
- const std::function<std::vector<real_t>( const Event& )>& functors,
- const size_t& maxDepth,
- const size_t& minPop,
- const std::function<uint64_t( const Event& )>& flagFunctor,
- const bool& refreshEvents )
-{
- m_nBins = nBins;
-
- if ( m_data != nullptr ) {
- m_voxels = BinDT( *m_data, Functor( functors ), MinEvents( minPop ) );
- return;
- }
- if( !refreshEvents ){
- groupByStrongPhase({},false);
- return;
- }
-
- size_t population = pow( 2, maxDepth ) * 1.2 * minPop; /// 20 % safety factor ///
- Generator<> phsp( m_type );
- phsp.setRandom( new TRandom3() );
- size_t counter = 0;
- int otherCounter = 0;
- size_t blockSize = 1 * pow( 10, 5 );
- auto makeEvents = [&]( EventList& eventList ) {
- bool useFlatEvents = NamedParameter<bool> ("CoherenceFactor::FlatEvents",true);
- if( useFlatEvents ) phsp.fillEventListPhaseSpace( eventList, blockSize, 0);
- else phsp.fillEventList( *m_pdf2, eventList, blockSize );
-
- eventList.resetCache();
-
- m_pdf1->reset( true );
- m_pdf2->reset( true );
- m_pdf1->setEvents( eventList );
- m_pdf2->setEvents( eventList );
- m_pdf1->prepare();
- m_pdf2->prepare();
- counter += blockSize;
- INFO( "Generated: " << counter << " DT events (out of " << population
- << " requested); [evt counter=" << otherCounter << "]" );
- };
- DynamicContainer<Event, EventList> dlist( population, makeEvents );
- std::vector<CoherenceEvent> DTevents( population );
- std::vector<real_t*> addresses;
- std::vector<real_t*> addresses_veto;
- for ( auto evt : dlist ) {
- auto& te = DTevents[otherCounter++];
- te.weight = 1./evt.genPdf();
- te.amp1 = m_pdf1->getVal( evt );
- te.amp2 = m_pdf2->getVal( evt );
- auto coords = functors( evt );
- for ( unsigned int i = 0; i < 5; ++i )
- te.values[i] = coords[i];
- if ( flagFunctor != nullptr && flagFunctor( evt ) ) {
- te.flag = true;
- addresses_veto.push_back( te.values.data() );
- } else {
- addresses.push_back( te.values.data() );
- }
- }
- m_voxels = BinDT( addresses, Functor( functors ), MaxDepth( maxDepth ), MinEvents( minPop ) );
-
- INFO( "Generated " << dlist.size()
- << " events; entries per node = " << real_t( dlist.size() ) / real_t( m_voxels.nodes().size() ) );
- groupByStrongPhase( DTevents , true );
-}
-
-void CoherenceFactor::makeCoherentMapping( const unsigned int& nBins, const BinDT& binDT )
-{
- m_voxels = binDT;
- m_nBins = nBins;
- groupByStrongPhase();
-}
-
-void CoherenceFactor::calculateCoherenceFactorsPerVoxel()
-{
- m_paramsPerVoxel.clear();
- m_paramsPerVoxel.resize( m_voxels.size() + 1 );
- for ( unsigned int i = 0; i < m_paramsPerVoxel.size(); ++i ) m_paramsPerVoxel[i].id = i;
- auto pdf1CacheMap = m_pdf1->cacheAddresses( *m_data );
- auto pdf2CacheMap = m_pdf2->cacheAddresses( *m_data );
-
- TH1D* deltaPhaseWeightPdf1 = new TH1D( "deltaPhi1","",100,-180,180);
- TH1D* deltaPhaseWeightPdf2 = new TH1D( "deltaPhi2","",100,-180,180);
- TH1D* deltaPhaseNoWeight = new TH1D( "deltaPhase0","",100,-180,180);
- for ( auto& evt : *m_data ) {
- int binNumber = m_voxels.getBinNumber( evt );
- real_t w = evt.weight() / evt.genPdf();
- complex_t p1 = m_pdf1->getVal( evt, pdf1CacheMap );
- complex_t p2 = m_pdf2->getVal( evt, pdf2CacheMap );
- real_t arg = std::arg( p1* std::conj(p2 ) );
- deltaPhaseWeightPdf1->Fill( arg * 180 / M_PI, std::abs(p1) );
- deltaPhaseWeightPdf2->Fill( arg * 180 / M_PI, std::abs(p2) );
- deltaPhaseNoWeight->Fill( arg * 180 / M_PI, 1 );
- m_paramsPerVoxel[binNumber].add( p1, p2, w );
- }
- deltaPhaseWeightPdf1->Write();
- deltaPhaseWeightPdf2->Write();
- deltaPhaseNoWeight->Write();
-}
-
-void CoherenceFactor::calculateCoherenceFactorsPerVoxel( const std::vector<CoherenceEvent>& dtEvents )
-{
- m_paramsPerVoxel.clear();
- m_paramsPerVoxel.resize( m_voxels.size() + 1 );
- INFO( "h-Voxels = " << m_voxels.size() << " associating with ids" );
- for ( unsigned int i = 0; i < m_paramsPerVoxel.size(); ++i ) m_paramsPerVoxel[i].id = i;
-
- TH1D* deltaPhaseNoWeight = new TH1D( "deltaPhi0","",100,-180,180);
- TH1D* deltaPhaseWeightVN = new TH1D( "deltaVPhiN","",100,-180,180);
- TH1D* weight = new TH1D("weight","",100,0,100);
-
- HadronicParameters hG;
- for ( auto& evt : dtEvents ) {
- unsigned int binNumber = evt.flag ? m_voxels.size() : m_voxels.getBinNumber( evt.values.data() );
- DEBUG( "BinNumber: " << binNumber << " pos = {" << evt.values[0] << "," << evt.values[1] << "," << evt.values[2]
- << "," << evt.values[3] << "," << evt.values[4] << "}" );
- real_t arg = std::arg( std::conj(evt.amp1) * evt.amp2 );
- deltaPhaseNoWeight->Fill( arg * 180 / M_PI, 1 );
- weight->Fill( evt.weight );
- m_paramsPerVoxel[binNumber].add( evt.amp1, evt.amp2, evt.weight );
- hG.add( evt.amp1, evt.amp2, evt.weight );
- }
- INFO( hG.to_string() );
- for( auto& v : m_paramsPerVoxel ) deltaPhaseWeightVN->Fill( v.d()*180/M_PI, 1 );
- deltaPhaseNoWeight->Write();
- deltaPhaseWeightVN->Write();
- weight->Write();
-}
-
-void CoherenceFactor::groupByStrongPhase( const std::vector<CoherenceEvent>& coherenceEvent, const bool& recalculateVoxels )
-{
- if( recalculateVoxels ){
- if ( m_data != nullptr )
- calculateCoherenceFactorsPerVoxel();
- else
- calculateCoherenceFactorsPerVoxel( coherenceEvent );
- }
- INFO( "Got " << m_voxels.size() << " voxels" );
- HadronicParameters global_hp;
- for ( auto& h : m_paramsPerVoxel ) global_hp += h;
-
- INFO( "Global parameters = " << global_hp.to_string() );
- real_t phiTransform = m_globalPhase - global_hp.d();
- real_t rTransform = m_globalR * m_globalR * global_hp.n2 / global_hp.n1;
-
- INFO( "Global rotation = " << phiTransform * 180 / M_PI );
- for ( auto& h : m_paramsPerVoxel ) {
- h.scale_p1( 1. / rTransform );
- h.rotate( phiTransform );
- }
- INFO( "Transform = " << sqrt( rTransform ) << " ; phi = " << phiTransform );
-
- HadronicParameters global_hp_new = std::accumulate( m_paramsPerVoxel.begin(), m_paramsPerVoxel.end() - 1, HadronicParameters() );
- INFO( global_hp_new.to_string() );
- std::sort( m_paramsPerVoxel.begin(), m_paramsPerVoxel.end() - 1, []( auto& b1, auto& b2 ) { return b1.d() < b2.d(); } );
-
- real_t norm_target = global_hp_new.wt / real_t( m_nBins );
- unsigned int currentBin = 0;
- std::vector<std::pair<real_t, real_t>> binLimits;
- binLimits.emplace_back( -M_PI, 0 );
- INFO( "Normalisation-per-bin = " << norm_target << " i1 = " << global_hp_new.I1() );
- auto currentBinLimits = binLimits.rbegin();
- HadronicParameters hp_accumulator, glob_vox_test;
-
- for( auto ihp = m_paramsPerVoxel.begin(); ihp != m_paramsPerVoxel.end() - 1; ++ihp ) {
- ihp->binID = currentBin;
- m_nodeID2Bin[ihp->id] = currentBin;
- hp_accumulator += *ihp;
- if ( hp_accumulator.wt > norm_target ) {
- currentBinLimits->second = ihp->d();
- currentBin++;
- binLimits.emplace_back( ihp->d(), 0 );
- currentBinLimits = binLimits.rbegin();
- glob_vox_test += hp_accumulator;
- hp_accumulator.clear();
- }
- }
- INFO("Generated: " << currentBin << " bins");
- glob_vox_test += hp_accumulator;
- m_paramsPerVoxel.rbegin()->binID = m_nBins; // allocate veto bin ///
- // for( auto& bin : m_para
- // INFO( "[ " << currentBin + 1 << " ] " << hp_test.to_string() );
- INFO( "[ VETO ] " << m_paramsPerVoxel.rbegin()->to_string() );
- INFO( "[ NO VETO ] " << glob_vox_test.to_string() );
-
- glob_vox_test += *m_paramsPerVoxel.rbegin();
- INFO( "[SUM VOXELS] " << global_hp_new.to_string() );
- INFO( "[SUM BINS ] " << glob_vox_test.to_string() );
- if( recalculateVoxels && m_data == nullptr ) MakeEventDeltaPlots( coherenceEvent );
- // for ( auto& limits : binLimits ) {
- // INFO( "Bin Limits [" << limits.first << ", " << limits.second << "]" );
- // }
-}
-
-void CoherenceFactor::MakeEventDeltaPlots( const std::vector<CoherenceEvent>& events ) {
-
- std::vector<TH1D*> plots;
- for(size_t i = 0 ; i < m_nBins ; ++i )
- plots.push_back( new TH1D( ("Bin_"+std::to_string(i)+"_deltaPhi").c_str(),0,100,-180,180) );
- for( auto& event : events ){
- unsigned int voxNumber = event.flag ? m_voxels.size() : m_voxels.getBinNumber( event.values.data() );
- real_t arg = std::arg( std::conj(event.amp1) * event.amp2 );
- auto binNumber = m_nodeID2Bin[ voxNumber ];
- if( ! event.flag ) plots[binNumber]->Fill( arg*180/M_PI );
- }
- for( auto& plot : plots ) plot->Write();
-}
-
-
-
-void CoherenceFactor::testCoherenceFactor() const
-{
-
- BinnedIntegrator<8> bid( m_data );
- bid.setView( [this]( auto& evt ) { return this->getBinNumber( evt ); } );
- std::vector<CoherenceCalculator> calcs( 8, CoherenceCalculator( m_pdf1, m_pdf2 ) );
-
- size_t PDF1_size = m_pdf1->size();
- size_t PDF2_size = m_pdf2->size();
- for ( unsigned int i = 0; i < PDF1_size; ++i ) {
- for ( unsigned int j = 0; j < PDF2_size; ++j ) {
- bid.addIntegral( ( *m_pdf1 )[i].pdf, ( *m_pdf2 )[j].pdf, [i, j, &calcs]( const auto& val ) {
- for ( unsigned int bin = 0; bin < 8; ++bin ) calcs[bin].R.set( i, j, val[bin] );
- } );
- }
- }
- for ( unsigned int i = 0; i < PDF1_size; ++i ) {
- for ( unsigned int j = i; j < PDF1_size; ++j ) {
- bid.addIntegral( ( *m_pdf1 )[i].pdf, ( *m_pdf1 )[j].pdf, [i, j, &calcs]( const auto& val ) {
- for ( unsigned int bin = 0; bin < 8; ++bin ) {
- calcs[bin].N1.set( i, j, val[bin] );
- if ( i != j ) calcs[bin].N1.set( j, i, std::conj( val[bin] ) );
- }
- } );
- }
- }
- for ( unsigned int i = 0; i < PDF2_size; ++i ) {
- for ( unsigned int j = i; j < PDF2_size; ++j ) {
- bid.addIntegral( ( *m_pdf2 )[i].pdf, ( *m_pdf2 )[j].pdf, [i, j, &calcs]( const auto& val ) {
- for ( unsigned int bin = 0; bin < 8; ++bin ) {
- calcs[bin].N2.set( i, j, val[bin] );
- if ( i != j ) calcs[bin].N2.set( j, i, std::conj( val[bin] ) );
- }
- } );
- }
- }
- bid.flush();
-
- for ( unsigned int i = 0; i < 8; ++i ) {
- complex_t VALUE = calcs[i].getVal();
- INFO( "Bin [" << i + 1 << "] R=" << std::abs( VALUE ) << " d= " << 180 * std::arg( VALUE ) / M_PI
- << " N1= " << calcs[i].getN1() << " N2= " << calcs[i].getN2() );
- }
-}
-
-std::vector<HadronicParameters> CoherenceFactor::getCoherenceFactors() const
-{
- std::vector<HadronicParameters> R( m_nBins + 1 );
- HadronicParameters RG;
- auto pdf1CacheMap = m_pdf1->cacheAddresses( *m_data );
- auto pdf2CacheMap = m_pdf2->cacheAddresses( *m_data );
- for ( auto& evt : *m_data ) {
- unsigned int binNumber = getBinNumber( evt );
- real_t w = evt.weight() / evt.genPdf();
- complex_t p1 = m_pdf1->getVal( evt, pdf1CacheMap );
- complex_t p2 = m_pdf2->getVal( evt, pdf2CacheMap );
- R[binNumber].add( p1, p2, w );
- RG.add( p1, p2, w );
- }
- real_t phiTransform = m_globalPhase - std::arg( RG.coherence );
- real_t rTransform = m_globalR * m_globalR * RG.n2 / RG.n1;
- for ( auto& h : R ) {
- h.scale_p1( 1. / rTransform );
- h.rotate( phiTransform );
- }
- INFO( RG.to_string() );
- return R;
-}
-
-std::vector<HadronicParameters> CoherenceFactor::getCoherenceFactorsFast() const
-{
-
- std::vector<HadronicParameters> coherence_factors( m_nBins + 1 );
- for ( auto hp = m_paramsPerVoxel.begin(); hp != m_paramsPerVoxel.end() - 1; ++hp ) {
- coherence_factors[hp->binID] += *hp;
- }
- coherence_factors[m_nBins] = *m_paramsPerVoxel.rbegin();
- return coherence_factors;
-}
-
-std::vector<size_t> CoherenceFactor::getNumberOfEventsInEachBin( const EventList& events ) const
-{
-
- std::vector<size_t> counter( m_nBins + 1, 0 );
- for ( auto& event : events ) {
- counter[getBinNumber( event )]++;
- }
- return counter;
-}
-
-CoherenceFactor::CoherenceFactor( const std::string& filename ) { readBinsFromFile( filename ); }
-
-void CoherenceFactor::readBinsFromFile( const std::string& binName )
-{
- INFO( "Reading file = " << binName );
- m_voxels = BinDT( File( binName ) );
- m_nBins = 0;
- for ( auto& node : m_voxels.nodes() ) {
- m_nodeID2Bin[node->voxNumber()] = node->binNumber();
- if ( node->binNumber() != 999 && node->binNumber() >= m_nBins ) m_nBins = node->binNumber() + 1;
- }
- INFO( "Got " << m_nBins << " coherent bins and " << m_voxels.size() << " voxels" );
-}
-
-real_t CoherenceFactor::phase() { return std::arg( m_global.getCoherence() ); }
-real_t CoherenceFactor::getR() { return std::abs( m_global.getCoherence() ); }
-
-HadronicParameters CoherenceFactor::calculateGlobalCoherence( EventList* _data )
-{
- m_global.clear();
- bool freshData = false;
- if ( _data == nullptr ) {
- _data = new EventList( m_type );
- PhaseSpace phsp( m_type );
- phsp.setRandom( new TRandom3() );
- for ( unsigned int i = 0; i < 1e6; ++i ) _data->push_back( phsp.makeEvent( m_pdf1->size() + m_pdf2->size() ) );
- freshData = true;
- }
- m_pdf1->setMC( *_data );
- m_pdf2->setMC( *_data );
- m_pdf1->prepare();
- m_pdf2->prepare();
- auto pdf1CacheMap = m_pdf1->cacheAddresses( *_data );
- auto pdf2CacheMap = m_pdf2->cacheAddresses( *_data );
- for ( unsigned int i = 0; i < _data->size(); ++i ) {
- const Event& evt = ( *_data )[i];
- real_t w = evt.weight() / evt.genPdf();
- complex_t pdf1 = m_pdf1->getVal( evt, pdf1CacheMap );
- complex_t pdf2 = m_pdf2->getVal( evt, pdf2CacheMap );
- m_global.add( pdf1, pdf2, w );
- }
-
- if ( freshData ) delete _data;
- return m_global;
-}
-
-void CoherenceFactor::writeToFile( const std::string& filename )
-{
- auto endNodes = m_voxels.nodes();
- for ( auto& node : endNodes ) {
- node->setBinNumber( m_nodeID2Bin[node->voxNumber()] );
- }
- m_voxels.serialize( filename );
-}
-
-HadronicParameters CoherenceFactor::getVal() const { return m_global; }
-CoherenceFactor::CoherenceFactor() = default;
-
-CoherenceFactor::CoherenceFactor( CoherentSum* pdf1, CoherentSum* pdf2, EventList* data )
- : m_pdf1( pdf1 ), m_pdf2( pdf2 ), m_calc( pdf1, pdf2 ), m_data( data )
-{
- if ( m_data != nullptr ) {
- calculateGlobalCoherence( m_data );
- calculateNorms();
- m_type = m_data->eventType();
- }
-}
-
-CoherenceFactor::CoherenceFactor( CoherentSum* pdf1, CoherentSum* pdf2, const EventType& type )
- : m_pdf1( pdf1 ), m_pdf2( pdf2 ), m_calc( pdf1, pdf2 ), m_data( nullptr ), m_type( type )
-{
-}
-
-void CoherenceFactor::calculateNorms()
-{
- Integrator<10> id( m_data );
- for ( unsigned int i = 0; i < m_pdf1->size(); ++i ) {
- for ( unsigned int j = 0; j < m_pdf2->size(); ++j ) {
- id.addIntegral( ( *m_pdf1 )[i].pdf, ( *m_pdf2 )[j].pdf,
- [i, j, this]( const complex_t& val ) { this->m_calc.R.set( i, j, val ); } );
- }
- }
-
- for ( unsigned int i = 0; i < m_pdf1->size(); ++i ) {
- for ( unsigned int j = i; j < m_pdf1->size(); ++j ) {
- id.addIntegral( ( *m_pdf1 )[i].pdf, ( *m_pdf1 )[j].pdf, [i, j, this]( const complex_t& val ) {
- this->m_calc.N1.set( i, j, val );
- if ( i != j ) this->m_calc.N1.set( j, i, std::conj( val ) );
- } );
- }
- }
-
- for ( unsigned int i = 0; i < m_pdf2->size(); ++i ) {
- for ( unsigned int j = i; j < m_pdf2->size(); ++j ) {
- id.addIntegral( ( *m_pdf2 )[i].pdf, ( *m_pdf2 )[j].pdf, [i, j, this]( const complex_t& val ) {
- this->m_calc.N2.set( i, j, val );
- if ( i != j ) this->m_calc.N2.set( j, i, std::conj( val ) );
- } );
- }
- }
-
- id.flush();
-}
-
-std::vector<unsigned int> CoherentSum::cacheAddresses( const EventList& evts ) const
-{
- std::vector<unsigned int> addresses;
- for ( auto& mE : m_matrixElements ) {
- addresses.push_back( evts.getCacheIndex( mE.pdf ) );
- }
- return addresses;
-}
-
-complex_t CoherentSum::getVal( const Event& evt ) const
-{
- complex_t value( 0., 0. );
- for ( auto& mE : m_matrixElements ) {
- value += mE.coefficient * evt.getCache( mE.addressData );
- }
- return value;
-}
-
-complex_t CoherentSum::getVal( const Event& evt, const std::vector<unsigned int>& cacheAddresses ) const
-{
- complex_t value( 0., 0. );
- for ( unsigned int i = 0; i < m_matrixElements.size(); ++i )
- value += m_matrixElements[i].coefficient * evt.getCache( cacheAddresses[i] );
- return value;
-}
-
-unsigned int CoherenceFactor::getBinNumber( const Event& event ) const
-{
- int voxelID = m_voxels.getBinNumber( event );
- return voxelID == -1 ? m_nBins : m_nodeID2Bin.find( voxelID )->second;
-}
-real_t CoherenceFactor::operator()() { return std::abs( m_calc.getVal() ); }
diff --git a/src/CoherentSum.cpp b/src/CoherentSum.cpp
index 6acaf88989b..0465febdbf2 100644
--- a/src/CoherentSum.cpp
+++ b/src/CoherentSum.cpp
@@ -8,6 +8,7 @@
#include <iostream>
#include <numeric>
#include <ratio>
+#include <thread>
#include "AmpGen/CompiledExpression.h"
#include "AmpGen/ErrorPropagator.h"
@@ -24,128 +25,113 @@
#include "AmpGen/CompilerWrapper.h"
#include "AmpGen/ThreadPool.h"
#include "AmpGen/ProfileClock.h"
+#include "AmpGen/simd/utils.h"
-#ifdef __USE_OPENMP__
+#ifdef _OPENMP
#include <omp.h>
#endif
using namespace AmpGen;
+CoherentSum::CoherentSum() = default;
CoherentSum::CoherentSum( const EventType& type, const MinuitParameterSet& mps, const std::string& prefix )
- : m_protoAmplitudes( mps )
- , m_evtType( type )
- , m_printFreq(NamedParameter<size_t>( "CoherentSum::PrintFrequency", 100) )
- , m_dbThis (NamedParameter<bool>( "CoherentSum::Debug" , false))
- , m_verbosity(NamedParameter<bool>( "CoherentSum::Verbosity" , 0) )
- , m_objCache (NamedParameter<std::string>("CoherentSum::ObjectCache" ,"") )
- , m_prefix( prefix )
+ : m_rules (mps)
+ , m_evtType (type)
+ , m_printFreq(NamedParameter<size_t>( "CoherentSum::PrintFrequency", 100) )
+ , m_dbThis (NamedParameter<bool>( "CoherentSum::Debug" , false))
+ , m_verbosity(NamedParameter<bool>( "CoherentSum::Verbosity" , 0) )
+ , m_objCache (NamedParameter<std::string>("CoherentSum::ObjectCache" ,"") )
+ , m_prefix (prefix)
+ , m_mps(&mps)
{
- auto amplitudes = m_protoAmplitudes.getMatchingRules( m_evtType, prefix);
- for( auto& amp : amplitudes ) addMatrixElement( amp, mps );
- m_isConstant = isFixedPDF(mps);
- m_normalisations.resize( m_matrixElements.size(), m_matrixElements.size() );
- ThreadPool tp(8);
- for( auto& mE: m_matrixElements )
- tp.enqueue( [&]{ CompilerWrapper().compile( mE.pdf, this->m_objCache); } );
-}
-
-void CoherentSum::addMatrixElement( std::pair<Particle, CouplingConstant>& particleWithCouplingConstant, const MinuitParameterSet& mps )
-{
- auto& protoParticle = particleWithCouplingConstant.first;
- auto& coupling = particleWithCouplingConstant.second;
- if ( !protoParticle.isStateGood() ) return;
- const std::string name = protoParticle.uniqueString();
- DebugSymbols dbExpressions;
- INFO( name );
- for ( auto& mE : m_matrixElements ) {
- if ( name == mE.decayTree.uniqueString() ) return;
+ auto amplitudes = m_rules.getMatchingRules( m_evtType, prefix);
+ if( amplitudes.size() == 0 ){
+ WARNING("The defined amplitudes don't seem to be able to be able to generate eventType: " << type);
+ }
+ for( auto& amp : amplitudes ) INFO( amp.first.decayDescriptor() );
+ m_matrixElements.resize( amplitudes.size() );
+ m_normalisations.resize( m_matrixElements.size(), m_matrixElements.size() );
+ size_t nThreads = NamedParameter<size_t> ("nCores" , std::thread::hardware_concurrency(), "Number of threads to use" );
+ ThreadPool tp(nThreads);
+ for(size_t i = 0; i < m_matrixElements.size(); ++i){
+ tp.enqueue( [i,this,&mps,&litudes]{
+ auto& [p, c] = amplitudes[i];
+ DebugSymbols db;
+ m_matrixElements[i] =
+ TransitionMatrix<complex_v>(p, c,
+ CompiledExpression<complex_v(const real_t*, const float_v*)>( p.getExpression(m_dbThis ? &db : nullptr), p.decayDescriptor(),
+ this->m_evtType.getEventFormat(), db, &mps ) );
+ CompilerWrapper().compile( m_matrixElements[i], this->m_objCache);
+ } );
}
- m_matrixElements.emplace_back(protoParticle, coupling, mps, m_evtType.getEventFormat(), m_dbThis);
}
void CoherentSum::prepare()
{
- if ( m_weightParam != nullptr ) m_weight = m_weightParam->mean();
- if ( m_isConstant && m_prepareCalls != 0 ) return;
transferParameters();
-
- std::vector<unsigned int> changedPdfIndices;
ProfileClock clockEval;
- bool printed = false;
-
- for ( unsigned int i = 0; i < m_matrixElements.size(); ++i ) {
- auto& pdf = m_matrixElements[i].pdf;
- pdf.prepare();
- if ( m_prepareCalls != 0 && !pdf.hasExternalsChanged() ) continue;
- ProfileClock clockThisElement;
- if ( m_events != nullptr ) {
- if ( m_matrixElements[i].addressData == 999 )
- m_matrixElements[i].addressData = m_events->registerExpression( pdf );
- m_events->updateCache( pdf, m_matrixElements[i].addressData );
- }
- else if ( i == 0 && m_verbosity ) WARNING( "No data events specified for " << this );
- clockThisElement.stop();
- if ( m_verbosity && ( m_prepareCalls > m_lastPrint + m_printFreq || m_prepareCalls == 0 ) ) {
- INFO( pdf.name() << " (t = " << clockThisElement << " ms, nCalls = " << m_prepareCalls << ", events = " << m_events->size() << ")" );
- printed = true;
- }
- changedPdfIndices.push_back(i);
- pdf.resetExternals();
+ for (auto& t : m_matrixElements ) {
+ t.prepare();
+ if ( m_prepareCalls != 0 && !t.hasExternalsChanged() ) continue;
+ if ( m_events != nullptr ) m_cache.update(m_events->store(), t );
+ m_integrator.updateCache(t);
+ t.resetExternals();
+ t.workToDo = true;
}
clockEval.stop();
ProfileClock clockIntegral;
- if ( m_integrator.isReady()) updateNorms( changedPdfIndices );
+ if (m_integrator.isReady()) updateNorms();
else if ( m_verbosity ) WARNING( "No simulated sample specified for " << this );
-
- m_norm = norm();
- if ( m_verbosity && printed ) {
- clockIntegral.stop();
+ clockIntegral.stop();
+ if ( m_verbosity && m_prepareCalls % 100 == 0 ) {
INFO( "Time Performance: "
<< "Eval = " << clockEval << " ms"
<< ", Integral = " << clockIntegral << " ms"
<< ", Total = " << clockEval + clockIntegral << " ms; normalisation = " << m_norm );
m_lastPrint = m_prepareCalls;
}
+ for( auto& t : m_matrixElements ) t.workToDo = false;
m_prepareCalls++;
}
-void CoherentSum::updateNorms( const std::vector<unsigned int>& changedPdfIndices )
+void CoherentSum::updateNorms()
{
- for ( auto& i : changedPdfIndices ) m_integrator.prepareExpression( m_matrixElements[i].pdf );
- std::vector<size_t> cacheIndex;
- for( auto& m : m_matrixElements )
- cacheIndex.push_back( m_integrator.events().getCacheIndex( m.pdf ) );
- for ( auto& i : changedPdfIndices )
- for ( size_t j = 0; j < size(); ++j )
- m_integrator.queueIntegral( cacheIndex[i], cacheIndex[j] ,i, j, &m_normalisations );
+ if(std::any_of(m_matrixElements.begin(),m_matrixElements.end(), [](auto& me){ return me.workToDo; } ))
+ {
+ for ( unsigned i = 0; i != m_matrixElements.size(); ++i )
+ for ( size_t j = i; j < size(); ++j ){
+ if( m_matrixElements[i].workToDo || m_matrixElements[j].workToDo )
+ m_normalisations.get(i, j, &m_integrator, i, j);
+ }
+ }
m_integrator.flush();
m_normalisations.resetCalculateFlags();
+ m_norm = norm();
}
void CoherentSum::debug( const Event& evt, const std::string& nameMustContain )
{
prepare();
- for ( auto& pdf : m_matrixElements ) pdf.pdf.resetExternals();
- if ( nameMustContain == "" )
- for ( auto& pdf : m_matrixElements ) {
- auto A = pdf(evt);
- INFO( std::setw(70) << pdf.decayTree.uniqueString() << " A = [ "
- << std::real(A) << " " << std::imag(A) << " ] g = [ "
- << std::real(pdf.coupling()) << " " << std::imag(pdf.coupling()) << " ]" );
- if( m_dbThis ) pdf.pdf.debug( evt );
- }
- else
- for ( auto& pdf : m_matrixElements )
- if ( pdf.pdf.name().find( nameMustContain ) != std::string::npos ) pdf.pdf.debug( evt );
+ INFO("Weight = " << evt.weight() << " genPDF = " << evt.genPdf() );
- INFO( "Pdf = " << prob_unnormalised( evt ) );
+ for ( auto& me : m_matrixElements ) {
+ auto A = me(evt);
+ INFO( std::setw(70) << me.decayTree.uniqueString()
+ << " A = [ " << utils::get<0>(A.real()) << " " << utils::get<0>(A.imag())
+ << " ] g = [ "<< me.coupling().real() << " " << me.coupling().imag() << " ] "
+ << m_cache( evt.index(), std::distance(&m_matrixElements[0], &me ) )
+ << me.decayTree.CP() );
+ }
+ if( m_dbThis ) for ( auto& me : m_matrixElements ) me.debug( evt) ;
+ INFO( "A(x) = " << getVal(evt) << " without cache: " << getValNoCache(evt) );
}
std::vector<FitFraction> CoherentSum::fitFractions(const LinearErrorPropagator& linProp)
{
+ prepare();
bool recomputeIntegrals = NamedParameter<bool>("CoherentSum::RecomputeIntegrals", false );
std::vector<FitFraction> outputFractions;
- for(auto& rule : m_protoAmplitudes.rules())
+ for(auto& rule : m_rules.rules())
{
FitFractionCalculator<CoherentSum> pCalc(this, findIndices(m_matrixElements, rule.first), recomputeIntegrals);
for(auto& process : rule.second)
@@ -157,17 +143,17 @@ std::vector<FitFraction> CoherentSum::fitFractions(const LinearErrorPropagator&
}
if( pCalc.calculators.size() == 0 ) continue;
auto fractions = pCalc(rule.first, linProp);
- for( auto& f : fractions ) outputFractions.emplace_back(f);
+ std::transform( fractions.begin(), fractions.end(), std::back_inserter(outputFractions),[](auto& p){ return p;} );
};
- auto ffForHead = m_protoAmplitudes.rulesForDecay(m_evtType.mother(), m_prefix);
+ auto ffForHead = m_rules.rulesForDecay(m_evtType.mother(), m_prefix);
FitFractionCalculator<CoherentSum> iCalc(this, findIndices(m_matrixElements, m_evtType.mother()), recomputeIntegrals);
for ( size_t i = 0; i < ffForHead.size(); ++i )
{
for ( size_t j = i + 1; j < ffForHead.size(); ++j )
{
iCalc.emplace_back(ffForHead[i].name() + "x" + ffForHead[j].name(),
- processIndex(m_matrixElements, ffForHead[i].name()),
- processIndex(m_matrixElements, ffForHead[j].name()) );
+ processIndex(m_matrixElements, ffForHead[i].name()),
+ processIndex(m_matrixElements, ffForHead[j].name()) );
}
}
std::vector<FitFraction> interferenceFractions = iCalc(m_evtType.mother()+"_interference",linProp);
@@ -176,7 +162,7 @@ std::vector<FitFraction> CoherentSum::fitFractions(const LinearErrorPropagator&
return outputFractions;
}
-void CoherentSum::generateSourceCode( const std::string& fname, const double& normalisation, bool add_mt )
+void CoherentSum::generateSourceCode(const std::string& fname, const double& normalisation, bool add_mt)
{
std::ofstream stream( fname );
transferParameters();
@@ -186,32 +172,34 @@ void CoherentSum::generateSourceCode( const std::string& fname, const double& no
stream << "#include <math.h>\n";
if ( add_mt ) stream << "#include <thread>\n";
bool includePythonBindings = NamedParameter<bool>("CoherentSum::IncludePythonBindings",false);
- bool enableCuda = NamedParameter<bool>("CoherentSum::EnableCuda",false);
for ( auto& p : m_matrixElements ){
- stream << p.pdf << std::endl;
- if( ! enableCuda ) p.pdf.compileWithParameters( stream );
- if( includePythonBindings ) p.pdf.compileDetails( stream );
+ auto expr = CompiledExpression<complex_t(const real_t*, const real_t*)>(
+ p.expression(),
+ p.decayDescriptor(),
+ m_evtType.getEventFormat(), DebugSymbols(), disableBatch(), m_mps );
+ expr.prepare();
+ stream << expr << std::endl;
+ expr.compileWithParameters( stream );
+ if( includePythonBindings ) p.compileDetails( stream );
}
- Expression event = Parameter("x0",0,true,0);
- Expression pa = Parameter("double(x1)",0,true,0);
+ Expression event = Parameter("x0",0,true);
+ Expression pa = Parameter("double(x1)",0,true);
Expression amplitude;
for( unsigned int i = 0 ; i < size(); ++i ){
auto& p = m_matrixElements[i];
- Expression this_amplitude = p.coupling() * Function( programatic_name( p.pdf.name() ) + "_wParams", {event} );
+ Expression this_amplitude = p.coupling() * Function( programatic_name( p.name() ) + "_wParams", {event} );
amplitude = amplitude + ( p.decayTree.finalStateParity() == 1 ? 1 : pa ) * this_amplitude;
}
- if( !enableCuda ){
- stream << CompiledExpression< std::complex<double>, const double*, int>( amplitude , "AMP" ) << std::endl;
- stream << CompiledExpression< double, const double*, int>(fcn::norm(amplitude) / normalisation, "FCN" ) << std::endl;
- }
+ stream << CompiledExpression<std::complex<double>(const double*, const int&)>( amplitude , "AMP", disableBatch() ) << std::endl;
+ stream << CompiledExpression<double(const double*, const int&)>(fcn::norm(amplitude) / normalisation, "FCN", disableBatch() ) << std::endl;
if( includePythonBindings ){
- stream << CompiledExpression< unsigned int >( m_matrixElements.size(), "matrix_elements_n" ) << std::endl;
- stream << CompiledExpression< double > ( normalisation, "normalization") << std::endl;
+ stream << CompiledExpression<unsigned int(void)>( m_matrixElements.size(), "matrix_elements_n" ) << std::endl;
+ stream << CompiledExpression<double (void)>( normalisation, "normalization") << std::endl;
stream << "extern \"C\" const char* matrix_elements(int n) {\n";
for ( size_t i = 0; i < m_matrixElements.size(); i++ ) {
- stream << " if(n ==" << i << ") return \"" << m_matrixElements.at(i).pdf.progName() << "\" ;\n";
+ stream << " if(n ==" << i << ") return \"" << m_matrixElements.at(i).progName() << "\" ;\n";
}
stream << " return 0;\n}\n";
stream << "extern \"C\" void FCN_all(double* out, double* events, unsigned int size, int parity, double* amps){\n";
@@ -233,25 +221,10 @@ void CoherentSum::generateSourceCode( const std::string& fname, const double& no
int parity = p.decayTree.finalStateParity();
if ( parity == -1 ) stream << "double(parity) * ";
stream << "std::complex<double>(amps[" << i * 2 << "],amps[" << i * 2 + 1 << "]) * ";
- stream << programatic_name( p.pdf.name() )<< "_wParams( E )";
+ stream << programatic_name( p.name() )<< "_wParams( E )";
stream << ( i == size() - 1 ? ";" : " +" ) << "\n";
}
stream << " out[i] = std::norm(amplitude) / " << normalisation << ";\n }\n}\n";
- stream << "extern \"C\" void FCN_mt(double* out, double* events, unsigned int size, int parity, double* amps){\n";
- stream << " unsigned int n = std::thread::hardware_concurrency();\n";
- stream << " unsigned int batch_size = size / n;\n";
- stream << " std::vector<std::thread> threads;\n";
- stream << " for(size_t i=0; i<n; i++) {\n";
- stream << " size_t start = batch_size*i;\n";
- stream << " size_t len = i+1!=n ? batch_size : size-start;\n";
- stream << " threads.emplace_back(FCN_all, out+start"
- << ", events+start*"
- << ( *this->m_events )[0].size()
- << ", len, parity, amps);\n";
- stream << " }\n";
- stream << " for(auto &thread : threads)\n";
- stream << " thread.join();\n";
- stream << "}\n\n";
stream << "extern \"C\" double coefficients( int n, int which, int parity){\n";
for ( size_t i = 0; i < size(); i++ ) {
@@ -267,49 +240,40 @@ void CoherentSum::generateSourceCode( const std::string& fname, const double& no
stream.close();
}
-bool CoherentSum::isFixedPDF(const MinuitParameterSet& mps) const
-{
- for ( auto& matrixElement : m_matrixElements ) {
- if( ! matrixElement.coupling.isFixed() ) return false;
- }
- return true;
-}
-
-void CoherentSum::PConjugate()
-{
- for ( auto& matrixElement : m_matrixElements ) {
- if ( matrixElement.decayTree.finalStateParity() == -1 ) matrixElement.coupling.changeSign();
- }
-}
-
complex_t CoherentSum::getValNoCache( const Event& evt ) const
{
- return std::accumulate( m_matrixElements.begin(),
- m_matrixElements.end(),
- complex_t(0,0),
- [&evt]( auto& a, auto& b ){ return a + b.coefficient * b(evt);} );
+ return utils::get<0>( complex_v(std::accumulate( m_matrixElements.begin(),
+ m_matrixElements.end(),
+ complex_v(0,0),
+ [&evt]( const auto& a, const auto& b ){ return a + b.coefficient * b(evt);} )) );
}
void CoherentSum::reset( bool resetEvents )
{
m_prepareCalls = 0;
m_lastPrint = 0;
- for ( auto& mE : m_matrixElements ) mE.addressData = 999;
- if ( resetEvents ) m_events = nullptr;
+ if ( resetEvents ){
+ m_events = nullptr;
+ m_integrator = Integrator();
+ }
}
-void CoherentSum::setEvents( EventList& list )
+void CoherentSum::setEvents( const EventList_type& list )
{
- if ( m_verbosity ) INFO( "Setting events to size = " << list.size() << " for " << this );
+ DEBUG( "Setting event list with:" << list.size() << " events for " << this );
reset();
+ for( auto& me : m_matrixElements ){ DEBUG("Registering: " << me.name() ) ; }
+ if( m_ownEvents && m_events != nullptr ) delete m_events;
m_events = &list;
+ m_cache . allocate( m_events->size(), m_matrixElements );
}
-void CoherentSum::setMC( EventList& sim )
+
+void CoherentSum::setMC( const EventList_type& sim )
{
- if ( m_verbosity ) INFO( "Setting MC = " << &sim << " for " << this );
+ if ( m_verbosity ) INFO( "Setting norm. event list with:" << sim.size() << " events for " << this );
reset();
- m_integrator = Integrator<10>(&sim);
+ m_integrator = Integrator( &sim, m_matrixElements );
}
real_t CoherentSum::norm() const
@@ -322,16 +286,15 @@ real_t CoherentSum::norm(const Bilinears& norms) const
complex_t acc(0, 0);
for ( size_t i = 0; i < size(); ++i ) {
for ( size_t j = 0; j < size(); ++j ) {
- auto val = norms.get(i, j)
- * m_matrixElements[i].coefficient
- * std::conj(m_matrixElements[j].coefficient);
- acc += val;
+ acc += m_matrixElements[i].coefficient
+ * std::conj(m_matrixElements[j].coefficient)
+ * ( i > j ? std::conj(norm(j,i)) : norm(i,j) );
}
}
return acc.real();
}
-complex_t CoherentSum::norm(const unsigned int& x, const unsigned int& y) const
+complex_t CoherentSum::norm(const size_t& x, const size_t& y) const
{
return m_normalisations.get(x, y);
}
@@ -339,18 +302,101 @@ complex_t CoherentSum::norm(const unsigned int& x, const unsigned int& y) const
void CoherentSum::transferParameters()
{
for ( auto& mE : m_matrixElements ) mE.coefficient = mE.coupling();
+ m_weight.update();
}
void CoherentSum::printVal(const Event& evt)
{
for ( auto& mE : m_matrixElements ) {
- unsigned int address = mE.addressData;
- std::cout << mE.decayTree.decayDescriptor() << " = " << mE.coefficient << " x " << evt.getCache( address )
+ unsigned int address = std::distance( &mE , &m_matrixElements[0] );
+ std::cout << mE.decayTree.decayDescriptor() << " = " << mE.coefficient << " x " << m_cache( evt.index() / utils::size<float_v>::value, address )
<< " address = " << address << " " << mE( evt ) << std::endl;
- if( mE.coupling.couplings.size() != 1 ){
+ if( mE.coupling.size() != 1 ){
std::cout << "CouplingConstants: " << std::endl;
mE.coupling.print();
std::cout << "================================" << std::endl;
}
}
}
+
+complex_t CoherentSum::getVal( const Event& evt ) const
+{
+ complex_v value( 0., 0. );
+ for (unsigned int i = 0 ; i != m_matrixElements.size(); ++i ) {
+ value = value + m_matrixElements[i].coefficient * m_cache(evt.index() / utils::size<float_v>::value, i );
+ }
+#if ENABLE_AVX
+ return value.at(evt.index() % utils::size<float_v>::value );
+#else
+ return value;
+#endif
+}
+
+float_v CoherentSum::operator()( const float_v* /*evt*/, const unsigned block ) const
+{
+ complex_v value( 0., 0. );
+ for ( const auto& mE : m_matrixElements )
+ {
+ unsigned address = &mE - &m_matrixElements[0];
+ value = value + mE.coefficient * m_cache(block, address);
+ }
+ return (m_weight/m_norm ) * utils::norm(value);
+}
+
+#if ENABLE_AVX
+double CoherentSum::operator()( const double* /*evt*/, const unsigned block ) const
+{
+ return operator()((const float_v*)nullptr, block / utils::size<float_v>::value ).at( block % utils::size<float_v>::value );
+}
+#endif
+
+std::function<real_t(const Event&)> CoherentSum::evaluator(const EventList_type* ievents) const
+{
+ auto events = ievents == nullptr ? m_integrator.events<EventList_type>() : ievents;
+ Store<complex_v, Alignment::AoS> store( events->size(), m_matrixElements);
+ for( auto& me : m_matrixElements ) store.update(events->store(), me );
+
+ std::vector<double> values( events->aligned_size() );
+ #ifdef _OPENMP
+ #pragma omp parallel for
+ #endif
+ for( unsigned int block = 0 ; block < events->nBlocks(); ++block )
+ {
+ complex_v amp(0.,0.);
+ for( unsigned j = 0 ; j != m_matrixElements.size(); ++j )
+ amp = amp + m_matrixElements[j].coefficient * store(block, j);
+ utils::store( values.data() + block * utils::size<float_v>::value, (m_weight/m_norm) * utils::norm(amp) );
+ }
+ return arrayToFunctor<double, typename EventList_type::value_type>(values);
+}
+
+KeyedFunctors<double(Event)> CoherentSum::componentEvaluator(const EventList_type* ievents) const
+{
+ using store_t = Store<complex_v, Alignment::SoA>;
+ auto events = ievents == nullptr ? m_integrator.events<EventList_type>() : ievents;
+ KeyedFunctors<double(Event)> rt;
+ std::shared_ptr<const store_t> cache;
+ if( events != m_integrator.events<EventList_type>() )
+ {
+ cache = std::make_shared<const store_t>(events->size(), m_matrixElements);
+ for( auto& me : m_matrixElements ) const_cast<store_t*>(cache.get())->update(events->store(), me);
+ }
+ else cache = std::shared_ptr<const store_t>( & m_integrator.cache(), [](const store_t* t){} );
+ /// this little slice of weirdness allows either a new cache to be instantiated, or one to just get a pointer to the one used for the integration.
+
+ for( unsigned i = 0 ; i != m_matrixElements.size(); ++i )
+ {
+ for( unsigned j = i ; j != m_matrixElements.size(); ++j )
+ {
+ auto mi = m_matrixElements[i];
+ auto mj = m_matrixElements[j];
+ auto ci = this->m_matrixElements[i].coefficient;
+ auto cj = this->m_matrixElements[j].coefficient;
+ double s = (i==j) ? 1 : 2 ;
+ auto name = programatic_name(mi.decayTree.decayDescriptor()) + "_" + programatic_name( mj.decayTree.decayDescriptor() );
+ auto functor = [ci,cj,i,j,s, cache](const Event& event){ return s * std::real( ci * cache->get<complex_t>( event.index(), i ) * std::conj( cj * cache->get<complex_t>( event.index(), j ) ) ) ;};
+ rt.add(functor, name, "");
+ }
+ }
+ return rt;
+}
diff --git a/src/CompiledExpressionBase.cpp b/src/CompiledExpressionBase.cpp
index c4e70d99b86..acd4eb0d50c 100644
--- a/src/CompiledExpressionBase.cpp
+++ b/src/CompiledExpressionBase.cpp
@@ -11,9 +11,29 @@
#include "AmpGen/ThreadPool.h"
#include "AmpGen/CompilerWrapper.h"
#include "AmpGen/ASTResolver.h"
-
+#include "AmpGen/ProfileClock.h"
+#include "AmpGen/Tensor.h"
+#include "AmpGen/simd/utils.h"
using namespace AmpGen;
+CompiledExpressionBase::CompiledExpressionBase() = default;
+
+CompiledExpressionBase::CompiledExpressionBase( const std::string& name ) :
+ m_name( name ),
+ m_progName( programatic_name(name) ) {}
+
+CompiledExpressionBase::CompiledExpressionBase( const Expression& expression,
+ const std::string& name,
+ const DebugSymbols& db,
+ const std::map<std::string, unsigned>& evtMapping ) :
+ m_obj( expression ),
+ m_name( name ),
+ m_progName( programatic_name(name) ),
+ m_db(db),
+ m_evtMap(evtMapping) {}
+
+CompiledExpressionBase::~CompiledExpressionBase() {}
+
std::string AmpGen::programatic_name( std::string s )
{
std::replace( s.begin(), s.end(), '-', 'm' );
@@ -28,12 +48,17 @@ std::string AmpGen::programatic_name( std::string s )
void CompiledExpressionBase::resolve(const MinuitParameterSet* mps)
{
- if( m_resolver != nullptr ) delete m_resolver ;
- m_resolver = new ASTResolver( m_evtMap, mps );
- m_resolver->getOrderedSubExpressions( m_obj, m_dependentSubexpressions );
- for ( auto& sym : m_db ){
- sym.second.resolve( *m_resolver );
- m_resolver->getOrderedSubExpressions( sym.second, m_debugSubexpressions );
+ if( m_resolver == nullptr ) m_resolver = std::make_shared<ASTResolver>( m_evtMap, mps );
+ if( fcnSignature().find("AVX") != std::string::npos ) {
+ m_resolver->setEnableAVX();
+ }
+ m_dependentSubexpressions = m_resolver->getOrderedSubExpressions( m_obj );
+ for ( auto& sym : m_db ){
+ auto expressions_for_this = m_resolver->getOrderedSubExpressions( sym.second);
+ for( auto& it : expressions_for_this ){
+ auto is_same = [&it](const auto& jt){ return it.first == jt.first ; };
+ if( !std::any_of( m_debugSubexpressions.begin(), m_debugSubexpressions.end(), is_same) ) m_debugSubexpressions.push_back( it );
+ }
}
m_cacheTransfers.clear();
for( auto& expression : m_resolver->cacheFunctions() )
@@ -42,22 +67,6 @@ void CompiledExpressionBase::resolve(const MinuitParameterSet* mps)
prepare();
}
-CompiledExpressionBase::CompiledExpressionBase( const Expression& expression,
- const std::string& name,
- const DebugSymbols& db,
- const std::map<std::string, size_t>& evtMapping )
- : m_obj( expression ),
- m_name( name ),
- m_progName( programatic_name(name) ),
- m_db(db),
- m_evtMap(evtMapping),
- m_readyFlag(nullptr) {}
-
-CompiledExpressionBase::CompiledExpressionBase( const std::string& name )
- : m_name( name ),
- m_progName( programatic_name(name) ),
- m_readyFlag(nullptr) {}
-
std::string CompiledExpressionBase::name() const { return m_name; }
std::string CompiledExpressionBase::progName() const { return m_progName; }
unsigned int CompiledExpressionBase::hash() const { return FNV1a_hash(m_name); }
@@ -70,7 +79,7 @@ void CompiledExpressionBase::prepare()
void CompiledExpressionBase::addDependentExpressions( std::ostream& stream, size_t& sizeOfStream ) const
{
for ( auto& dep : m_dependentSubexpressions ) {
- std::string rt = "auto v" + std::to_string(dep.first) + " = " + dep.second.to_string(m_resolver) +";";
+ std::string rt = " auto v" + std::to_string(dep.first) + " = " + dep.second.to_string(m_resolver.get()) +";";
stream << rt << "\n";
sizeOfStream += sizeof(char) * rt.size(); /// bytes ///
}
@@ -80,35 +89,40 @@ void CompiledExpressionBase::to_stream( std::ostream& stream ) const
{
if( m_db.size() !=0 ) stream << "#include<iostream>\n";
stream << "extern \"C\" const char* " << progName() << "_name() { return \"" << m_name << "\"; } \n";
- bool enable_cuda = NamedParameter<bool>("EnableCUDA",false);
-
- size_t sizeOfStream = 0;
- if( !enable_cuda ){
- // Avoid a warning about std::complex not being C compatible (it is)
- stream << "#pragma clang diagnostic push\n"
- << "#pragma clang diagnostic ignored \"-Wreturn-type-c-linkage\"\n";
-
+ bool enable_cuda = NamedParameter<bool>("UseCUDA",false);
+ size_t sizeOfStream = 0;
+ if( use_rto() )
+ {
+
+ stream << "extern \"C\" " << returnTypename() << " " << progName() << "(" << fcnSignature() << "){\n";
+ addDependentExpressions( stream , sizeOfStream );\
+ std::string return_type = arg_type(0);
+ return_type = return_type.substr(0,return_type.size()-1);
+ if( is<TensorExpression>(m_obj) == false ){
+ stream << "*r = " << return_type << "(" << m_obj.to_string(m_resolver.get()) << ");\n";
+ stream << "}\n";
+ }
+ else {
+ auto as_tensor = cast<TensorExpression>(m_obj).tensor();
+
+ for(unsigned j=0; j != as_tensor.size(); ++j )
+ stream << "r[s * "<< j<<"] = " << return_type << "(" << as_tensor[j].to_string(m_resolver.get()) << ");\n";
+ stream << "}\n";
+ }
+ }
+ else if( !enable_cuda ){
stream << "extern \"C\" " << returnTypename() << " " << progName() << "(" << fcnSignature() << "){\n";
addDependentExpressions( stream , sizeOfStream );
- std::string objString = m_obj.to_string(m_resolver);
- stream << "return " << objString << ";\n}\n";
+ stream << "return " << m_obj.to_string(m_resolver.get()) << ";\n}\n";
}
else {
- std::string rt_cpp = returnTypename();
- std::string rt_cuda = "";
- if( rt_cpp == "double" || rt_cpp == "float" || rt_cpp == "real_t" )
- rt_cuda = "float* r, const int N";
- if( rt_cpp == "std::complex<double>" || rt_cpp == "std::complex<float>" || rt_cpp == "complex_t" )
- rt_cuda = "ampgen_cuda::complex_t* r, const int N";
- stream << "__global__ void " << progName() << "( " << rt_cuda << ", const float_t* x0, const float3* x1){\n";
+ stream << "__global__ void " << progName() << "( " << returnTypename() + "* r, const int N, " << fcnSignature() << "){\n";
stream << " int i = blockIdx.x * blockDim.x + threadIdx.x;\n";
addDependentExpressions( stream, sizeOfStream);
- std::string objString = m_obj.to_string(m_resolver);
- stream << " r[i] = " << objString << ";\n}\n";
+ stream << " r[i] = " << m_obj.to_string(m_resolver.get()) << ";\n}\n";
}
- if( NamedParameter<bool>("IncludePythonBindings", false) == true ){
- stream << "#pragma clang diagnostic pop\n\n";
+ if( NamedParameter<bool>("IncludePythonBindings", false) == true && returnTypename().find("complex") != std::string::npos ){
stream << "extern \"C\" void " << progName() << "_c" << "(double *real, double *imag, " << fcnSignature() << "){\n";
stream << " auto val = " << progName() << "(" << args() << ") ;\n";
stream << " *real = val.real();\n";
@@ -116,6 +130,7 @@ void CompiledExpressionBase::to_stream( std::ostream& stream ) const
stream << "}\n";
}
if ( m_db.size() != 0 ) addDebug( stream );
+ if( !m_disableBatch ) compileBatch(stream);
}
std::ostream& AmpGen::operator<<( std::ostream& os, const CompiledExpressionBase& expression )
@@ -124,25 +139,18 @@ std::ostream& AmpGen::operator<<( std::ostream& os, const CompiledExpressionBase
return os;
}
-void CompiledExpressionBase::compile(const std::string& fname, const bool& wait )
+void CompiledExpressionBase::compile(const std::string& fname)
{
- if(!wait){
- m_readyFlag = new std::shared_future<bool>( ThreadPool::schedule([this,fname](){
- CompilerWrapper().compile(*this,fname);
- return true;} ) );
- }
- else {
- CompilerWrapper(false).compile(*this,fname );
- }
+ CompilerWrapper(false).compile(*this,fname );
}
void CompiledExpressionBase::addDebug( std::ostream& stream ) const
{
stream << "#include<string>\n";
- stream << "extern \"C\" std::vector<std::pair< std::string, std::complex<double>>> "
+ stream << "extern \"C\" std::vector<std::pair< std::string, " << type_string<complex_v>() << " >> "
<< m_progName << "_DB(" << fcnSignature() << "){\n";
for ( auto& dep : m_debugSubexpressions ) {
- std::string rt = "auto v" + std::to_string(dep.first) + " = " + dep.second.to_string(m_resolver) +";";
+ std::string rt = "auto v" + std::to_string(dep.first) + " = " + dep.second.to_string(m_resolver.get()) +";";
stream << rt << "\n";
}
stream << "return {";
@@ -150,8 +158,16 @@ void CompiledExpressionBase::addDebug( std::ostream& stream ) const
std::string comma = (i!=m_db.size()-1)?", " :"};\n}\n";
const auto expression = m_db[i].second;
stream << std::endl << "{\"" << m_db[i].first << "\",";
- if ( expression.to_string(m_resolver) != "NULL" )
- stream << expression.to_string(m_resolver) << "}" << comma;
- else stream << "-999}" << comma ;
+ if ( expression.to_string(m_resolver.get()) != "NULL" )
+ stream << type_string<complex_v>() << "("<< expression.to_string(m_resolver.get()) << ")}" << comma;
+ else stream << type_string<complex_v>() << "(-999.,0.)}" << comma ;
}
}
+
+std::string CompiledExpressionBase::fcnSignature(const std::vector<std::string>& argList, bool rto, bool includeStagger)
+{
+ unsigned counter=0;
+ auto fcn = [counter](const auto& str) mutable {return str + " x"+std::to_string(counter++); };
+ if( rto ) return argList[0] + " r, " + argList[1] + " s, " + vectorToString( argList.begin()+2, argList.end(), ", ", fcn );
+ return vectorToString( argList.begin(), argList.end(), ", ", fcn);
+}
diff --git a/src/CompilerWrapper.cpp b/src/CompilerWrapper.cpp
index ff8bc927fc0..57b5c7fcad9 100644
--- a/src/CompilerWrapper.cpp
+++ b/src/CompilerWrapper.cpp
@@ -18,30 +18,45 @@
#include "AmpGen/MsgService.h"
#include "AmpGen/Utilities.h"
#include "AmpGen/CompiledExpressionBase.h"
-#include "AmpGen/Version.h"
+#include "AmpGenVersion.h"
using namespace AmpGen;
+#ifdef AMPGEN_CXX
+#pragma message "Using c++ compiler: " AMPGEN_CXX " for JIT"
+#pragma message "Using AMPGENROOT: " AMPGENROOT
+#pragma message "Using AMPGENROOT_CMAKE: " AMPGENROOT_CMAKE
+#else
+#pragma warning "No AMPGEN_CXX for JIT set"
+#endif
-CompilerWrapper::CompilerWrapper( const bool& verbose ) :
- m_includes( {"array", "complex", "math.h", "vector"} ),
- m_verbose(verbose)
+CompilerWrapper::CompilerWrapper( const bool& verbose ) :
+ m_verbose(verbose),
+ m_cxx(getenv("AMPGEN_CXX") != nullptr ? std::string( getenv( "AMPGEN_CXX" ) ) : "")
{
- m_cxx = getenv("CXX") != nullptr ? std::string( getenv( "CXX" ) ) : "";
if ( m_cxx == "" ) {
#ifdef AMPGEN_CXX
if( m_verbose )
- INFO( "Using original compiler; set global variable CXX if another needed: " << AMPGEN_CXX );
+ INFO( "Global variable AMPGEN_CXX is undefined, using compiler variable AMPGEN_CXX: " << AMPGEN_CXX );
m_cxx = AMPGEN_CXX;
#else
- ERROR( "No configured compiler; set global variable CXX" );
+ m_cxx = getenv("AMPGEN_CXX") != nullptr ? std::string( getenv( "AMPGEN_CXX" ) ) : "";
+ if( m_cxx == "" ) ERROR( "No configured compiler; set global variable AMPGEN_CXX" );
#endif
}
+ else {
+ if( m_verbose )
+ INFO( "Global variable CXX is defined: " << m_cxx << "; AMPGEN_CXX is ignored" ); // to use AMPGEN_CXX, unset CXX
+ }
}
void CompilerWrapper::generateSource( const CompiledExpressionBase& expression, const std::string& filename )
{
std::ofstream output( filename );
for ( auto& include : m_includes ) output << "#include <" << include << ">\n";
+ if( expression.fcnSignature().find("AVX2d") != std::string::npos ) output << "#include \"AmpGen/simd/avx2d_types.h\"\n; using namespace AmpGen::AVX2d;\n" ;
+ else if( expression.fcnSignature().find("AVX2f") != std::string::npos ) output << "#include \"AmpGen/simd/avx2f_types.h\"\n; using namespace AmpGen::AVX2f;\n;" ;
+ else if( expression.fcnSignature().find("AVX512d") != std::string::npos ) output << "#include \"AmpGen/simd/avx512d_types.h\"\n; using namespace AmpGen::AVX512d;\n;" ;
+ else if( expression.fcnSignature().find("AVX512") != std::string::npos ) output << "#include \"AmpGen/simd/avx512_types.h\"\n; using namespace AmpGen::AVX512;\n;" ;
output << expression << std::endl;
output.close();
}
@@ -53,6 +68,7 @@ std::string CompilerWrapper::generateFilename()
if ( status == -1 ) {
ERROR( "Failed to generate temporary filename " << status );
}
+ std::remove( buffer );
return buffer;
}
@@ -84,6 +100,12 @@ bool CompilerWrapper::compile( CompiledExpressionBase& expression, const std::st
auto twall_end = std::chrono::high_resolution_clock::now();
double tWall = std::chrono::duration<double, std::milli>( twall_end - twall_begin ).count();
if( print_all ) INFO( expression.name() << " " << cname << " Compile time = " << tWall / 1000. << " [size = " << fileSize(cname)/1024 << ", " << fileSize(oname)/1024 << "] kB" );
+ if( print_all && isClang() )
+ {
+ auto lines = vectorFromFile( cname );
+ for (const auto& line : lines )
+ std::cout << line << std::endl;
+ }
return true;
}
@@ -102,32 +124,64 @@ bool CompilerWrapper::compile( std::vector<CompiledExpressionBase*>& expressions
for ( auto& include : m_includes ) output << "#include <" << include << ">\n";
for ( auto& expression : expressions ) output << *expression << std::endl;
output.close();
-
compileSource( cname, oname );
for( auto& expression : expressions ) expression->link( oname );
auto twall_end = std::chrono::high_resolution_clock::now();
double tWall = std::chrono::duration<double, std::milli>( twall_end - twall_begin ).count();
if( print_all ) INFO( cname << " Compile time = " << tWall / 1000. << " [size = " << fileSize(cname)/1024 << ", " << fileSize(oname)/1024 << "] kB" );
+ if( print_all && isClang() )
+ {
+ auto lines = vectorFromFile( cname );
+ for (const auto& line : lines )
+ std::cout << line << std::endl;
+ }
return true;
}
-std::string get_cpp_version(){
+bool CompilerWrapper::isClang() const
+{
+ return m_cxx.find("clang") != std::string::npos || m_cxx.find("llvm-g++") != std::string::npos;
+}
+
+std::string get_cpp_version()
+{
if( __cplusplus >= 201703L ) return "c++17";
if( __cplusplus >= 201402L ) return "c++14";
if( __cplusplus >= 201103L ) return "c++11";
else return "";
}
+
void CompilerWrapper::compileSource( const std::string& fname, const std::string& oname )
{
using namespace std::chrono_literals;
- std::vector<std::string> compile_flags = NamedParameter<std::string>("CompilerWrapper::Flags",
- {"-Ofast", "--std="+get_cpp_version(),"-march=native"} );
+ std::vector<std::string> compile_flags = NamedParameter<std::string>("CompilerWrapper::Flags", {"-Ofast", "--std="+get_cpp_version()});
+
+ bool useOpenMP = USE_OPENMP;
+
+ #if ENABLE_AVX
+ compile_flags.push_back("-march=native");
+ compile_flags.push_back( std::string("-I") + AMPGENROOT) ;
+ #endif
+ #if ENABLE_AVX2d
+ compile_flags.push_back("-mavx2");
+ compile_flags.push_back("-DHAVE_AVX2_INSTRUCTIONS");
+ #endif
- std::vector<const char*> argp = { m_cxx.c_str(),
- "-shared",
- "-rdynamic",
- "-fPIC"};
- for( auto& flag : compile_flags ) argp.push_back( flag.c_str() );
+ if(useOpenMP) compile_flags.push_back("-fopenmp");
+
+ std::vector<const char*> argp = { m_cxx.c_str(), "-shared", "-rdynamic", "-fPIC"};
+
+ std::transform( compile_flags.begin(), compile_flags.end(), std::back_inserter(argp), [](const auto& flag ){return flag.c_str() ; } );
+
+ if(isClang())
+ {
+ argp.push_back( "-Wno-return-type-c-linkage");
+ #if __APPLE__
+ argp.push_back("-lstdc++");
+ #endif
+ if( useOpenMP ) argp.push_back("-fopenmp=libiomp5");
+ argp.push_back( "-march=native");
+ }
argp.push_back( fname.c_str() );
argp.push_back( "-o");
@@ -144,7 +198,7 @@ void CompilerWrapper::compileSource( const std::string& fname, const std::string
if( childPID == 0 )
{
execv( argp[0], const_cast<char**>( &argp[0] ) );
- perror( "execl()" );
+ perror( "execv() in ../src/CompilerWrapper.cpp" ); // add "CompilerWrapper::Verbose true" to .opt file to diagnose
exit( 0 );
}
int status = 0;
@@ -156,7 +210,7 @@ void CompilerWrapper::preamble( std::ostream& os ) const
time_t now = time(0);
char* dt = ctime(&now);
os << "/** Generated by " << getenv("USER") << " on " << dt ;
- os << " AmpGen v" << AMPGEN_VERSION_MAJOR << "." << AMPGEN_VERSION_MINOR << '\n';
+ os << " AmpGen v" << AMPGEN_MAJOR_VERSION << "." << AMPGEN_MINOR_VERSION << '\n';
#if defined(__clang__)
os << " clang v" << __clang_major__ << "." << __clang_minor__ << "." << __clang_patchlevel__;
#elif defined(__ICC) || defined(__INTEL_COMPILER)
@@ -166,6 +220,5 @@ void CompilerWrapper::preamble( std::ostream& os ) const
#endif
os << '\n';
os << "*/\n";
-
for ( auto& include : m_includes ) os << "#include <" << include << ">\n";
}
diff --git a/src/DalitzIntegrator.cpp b/src/DalitzIntegrator.cpp
index e06568ba8f2..aab7a7f8cd3 100644
--- a/src/DalitzIntegrator.cpp
+++ b/src/DalitzIntegrator.cpp
@@ -38,7 +38,12 @@ double DalitzIntegrator::sqDp1( const Event& evt ) const
TLorentzVector p2( ( evt.address( 4 ) ) );
TLorentzVector p3( ( evt.address( 8 ) ) );
TLorentzVector pA = p1 + p2;
- return acos( 2 * ( pA.Mag() - m_min ) / ( m_max - m_min ) - 1 ) / M_PI;
+ auto arg = 2 * ( pA.Mag() - m_min ) / ( m_max - m_min ) - 1;
+ if( arg > 1 || arg < -1 ){
+ ERROR("Argument: " << arg << " is out-of-bounds");
+ return -1;
+ }
+ return acos(arg)/M_PI;
}
double DalitzIntegrator::sqDp2( const Event& evt ) const
{
@@ -169,14 +174,11 @@ TH2D* DalitzIntegrator::makePlot( const std::function<double(const double*)>& fc
const std::string& name, const size_t& nSamples )
{
auto plot = projection.plot();
- double event[12];
- for ( unsigned int i = 0; i < 12; ++i ) event[i] = 0;
- Event evtCache( 12 );
+ Event event( 12 );
for ( unsigned int i = 0; i < nSamples; ++i ) {
sqCo pos = {gRandom->Uniform(), gRandom->Uniform()};
setEvent( pos, event );
- evtCache.set( event );
- auto obs_cos = projection( evtCache );
+ auto obs_cos = projection( event );
plot->Fill( obs_cos.first, obs_cos.second, J( pos ) * fcn( event ) );
}
return plot;
@@ -191,6 +193,5 @@ double DalitzIntegrator::integrate_internal( TF2& fcn ) const
ig.SetRelTolerance( 0.000001 );
double xmin[] = {0, 0};
double xmax[] = {1, 1};
- double v = ig.Integral( xmin, xmax );
- return v ;
+ return ig.Integral(xmin,xmax);
}
diff --git a/src/DiracMatrices.cpp b/src/DiracMatrices.cpp
index 338dacbe399..1d46d399efd 100644
--- a/src/DiracMatrices.cpp
+++ b/src/DiracMatrices.cpp
@@ -11,46 +11,43 @@ using namespace AmpGen;
extern const AmpGen::Expression AmpGen::I = Constant(0, 1);
extern const AmpGen::Expression AmpGen::Z = Constant(0);
-extern const std::array<AmpGen::Tensor,5> AmpGen::Gamma ( {
- Tensor ({ 0, 0, 0, 1,
- 0, 0, 1, 0,
- 0,-1, 0, 0,
- -1, 0, 0, 0} , {4, 4}),
- Tensor ({ Z, Z, Z,-I,
- Z, Z, I, Z,
- Z, I, Z, Z,
- -I, Z, Z, Z} , {4, 4}),
- Tensor ({ 0, 0, 1, 0,
- 0, 0, 0,-1,
- -1, 0, 0, 0,
- 0, 1, 0, 0} , {4, 4}),
- Tensor ({ 1, 0, 0, 0,
- 0, 1, 0, 0,
- 0, 0,-1, 0,
- 0, 0, 0,-1} , {4, 4}),
- Tensor ({ 0, 0, 1, 0,
- 0, 0, 0, 1,
- 1, 0, 0, 0,
- 0, 1, 0, 0} , {4, 4})} );
-
-extern const std::array<AmpGen::Tensor,3> AmpGen::Sigma (
- {
- Tensor({0,1,1,0},{2,2}),
- Tensor({Z,-I,
- I,Z},{2,2}),
- Tensor({1,0,0,-1},{2,2})
- } );
-
-extern const std::array<AmpGen::Tensor,3> AmpGen::S03 ( {
- Tensor ({ 0, 0, 0, 0,
- 0, 0,-1, 0,
- 0, 1, 0, 0,
- 0, 0, 0, 0 } , Tensor::dim(4,4) ),
- Tensor ({ 0, 0, 1, 0,
- 0, 0, 0, 0,
- -1, 0, 0, 0,
- 0, 0, 0, 0 } , Tensor::dim(4,4) ),
- Tensor ({ 0,-1, 0, 0,
- 1, 0, 0, 0,
- 0, 0, 0, 0,
- 0, 0, 0, 0 } , Tensor::dim(4,4) ) } );
+extern const std::array<AmpGen::Tensor,5> AmpGen::Gamma( {
+ Tensor({ 0, 0, 0, 1, 0, 0, 1, 0, 0,-1, 0, 0,-1, 0, 0, 0}, Tensor::dim(4,4)),
+ Tensor({ Z, Z, Z,-I, Z, Z, I, Z, Z, I, Z, Z,-I, Z, Z, Z}, Tensor::dim(4,4)),
+ Tensor({ 0, 0, 1, 0, 0, 0, 0,-1,-1, 0, 0, 0, 0, 1, 0, 0}, Tensor::dim(4,4)),
+ Tensor({ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,-1, 0, 0, 0, 0,-1}, Tensor::dim(4,4)),
+ Tensor({ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0}, Tensor::dim(4,4))} );
+
+extern const std::array<AmpGen::Tensor,3> AmpGen::Sigma( {
+ Tensor({ 0, 1, 1, 0}, Tensor::dim(2,2)),
+ Tensor({ Z,-I, I, Z}, Tensor::dim(2,2)),
+ Tensor({ 1, 0, 0,-1}, Tensor::dim(2,2))} );
+
+extern const std::array<AmpGen::Tensor,3> AmpGen::Sigma4( {
+ Tensor({ 0, 1, 0, 0,
+ 1, 0, 0, 0,
+ 0, 0, 0, 1,
+ 0, 0, 1, 0 }, Tensor::dim(4,4)),
+ Tensor({ Z,-I, Z, Z,
+ I, Z, Z, Z,
+ Z, Z, Z, -I,
+ Z, Z, I, Z }, Tensor::dim(4,4)),
+ Tensor({ 1, 0, 0, 0,
+ 0, -1, 0, 0,
+ 0, 0, 1, 0,
+ 0, 0, 0, -1 }, Tensor::dim(4,4))} );
+
+extern const std::array<AmpGen::Tensor,3> AmpGen::SO3 ( {
+ Tensor({ 0, 0, 0, 0, 0, 0,-1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, Tensor::dim(4,4) ),
+ Tensor({ 0, 0, 1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0 }, Tensor::dim(4,4) ),
+ Tensor({ 0,-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, Tensor::dim(4,4) ) } );
+
+extern const std::array<AmpGen::Tensor,8> AmpGen::SU3 ( {
+ Tensor({ 0, 1, 0, 1, 0, 0, 0, 0, 0}, Tensor::dim(3,3)),
+ Tensor({ Z,-I, Z, I, Z, Z, Z, Z, Z}, Tensor::dim(3,3)),
+ Tensor({ 1, 0, 0, 0,-1, 0, 0, 0, 0}, Tensor::dim(3,3)),
+ Tensor({ 0, 0, 1, 0, 0, 0, 1, 0, 0}, Tensor::dim(3,3)),
+ Tensor({ Z, Z,-I, Z, Z, Z, I, Z, Z}, Tensor::dim(3,3)),
+ Tensor({ 0, 0, 0, 0, 0, 1, 0, 1, 0}, Tensor::dim(3,3)),
+ Tensor({ Z, Z, Z, Z, Z,-I, Z, I, Z}, Tensor::dim(3,3)),
+ Tensor({ 1./sqrt(3), 0., 0., 0.,1./sqrt(3.), 0., 0., 0., -2./sqrt(3.)}, Tensor::dim(3,3)) });
diff --git a/src/ErrorPropagator.cpp b/src/ErrorPropagator.cpp
index 3c62fdbb804..815b50e577a 100644
--- a/src/ErrorPropagator.cpp
+++ b/src/ErrorPropagator.cpp
@@ -11,7 +11,6 @@ using namespace AmpGen;
GaussErrorPropagator::GaussErrorPropagator( const TMatrixD& reducedCovariance, const std::vector<MinuitParameter*>& params, TRandom3* rnd )
: m_parameters( params ), m_rand( rnd ), m_decomposedCholesky( params.size(), params.size() )
{
-
for ( size_t x = 0; x < params.size(); ++x ) {
auto p = params[x];
INFO( p->name() << " " << p->mean() << " +/- " << sqrt( reducedCovariance( x, x ) ) );
@@ -20,7 +19,12 @@ GaussErrorPropagator::GaussErrorPropagator( const TMatrixD& reducedCovariance, c
TDecompChol decomposed( reducedCovariance );
decomposed.Decompose();
m_decomposedCholesky = decomposed.GetU();
- transpose();
+ /// transpose the cholesky matrix
+ for ( int i = 0; i < m_decomposedCholesky.GetNrows(); ++i ) {
+ for ( int j = i + 1; j < m_decomposedCholesky.GetNrows(); ++j ){
+ std::swap( m_decomposedCholesky(i, j), m_decomposedCholesky(j, i) );
+ }
+ }
}
void GaussErrorPropagator::perturb()
@@ -40,16 +44,6 @@ void GaussErrorPropagator::reset()
for ( unsigned int j = 0; j < m_parameters.size(); ++j ) m_parameters[j]->setCurrentFitVal( m_startingValues[j] );
}
-void GaussErrorPropagator::transpose()
-{
- for ( int i = 0; i < m_decomposedCholesky.GetNrows(); ++i ) {
- for ( int j = i + 1; j < m_decomposedCholesky.GetNrows(); ++j ) {
- double tmp = m_decomposedCholesky( j, i );
- m_decomposedCholesky( j, i ) = m_decomposedCholesky( i, j );
- m_decomposedCholesky( i, j ) = tmp;
- }
- }
-}
LinearErrorPropagator::LinearErrorPropagator( const TMatrixD& reducedCovarianceMatrix,
const std::vector<MinuitParameter*>& params )
: m_cov( reducedCovarianceMatrix ), m_parameters( params )
@@ -59,8 +53,7 @@ LinearErrorPropagator::LinearErrorPropagator( const TMatrixD& reducedCovarianceM
LinearErrorPropagator::LinearErrorPropagator( const std::vector<MinuitParameter*>& params )
{
for( auto& param : params ){
- if( param->iFixInit() != MinuitParameter::Float ) continue;
- if( param->err() == 0 ) continue;
+ if( !param->isFree() || param->err() == 0 ) continue;
m_parameters.push_back( param );
}
m_cov.ResizeTo( m_parameters.size(), m_parameters.size() );
@@ -70,11 +63,9 @@ LinearErrorPropagator::LinearErrorPropagator( const std::vector<MinuitParameter*
LinearErrorPropagator::LinearErrorPropagator( const MinuitParameterSet& mps )
{
- for( size_t i = 0 ; i < mps.size(); ++i ){
- MinuitParameter* param = mps.getParPtr(i);
- if( param->iFixInit() != MinuitParameter::Float ) continue;
- if( param->err() == 0 ) continue;
- m_parameters.push_back( param );
+ for(auto& param : mps){
+ if( ! param->isFree() || param->err() == 0 ) continue;
+ m_parameters.push_back(param);
}
m_cov.ResizeTo( m_parameters.size(), m_parameters.size() );
for( size_t i = 0 ; i < m_parameters.size(); ++i )
@@ -83,11 +74,9 @@ LinearErrorPropagator::LinearErrorPropagator( const MinuitParameterSet& mps )
void LinearErrorPropagator::add( const LinearErrorPropagator& p2 )
{
-
size_t superSet = size();
size_t oldSize = size();
auto p1_pMap = posMap();
-
std::vector<size_t> props( p2.size() );
for ( size_t x = 0; x != p2.size(); ++x ) {
auto it = p1_pMap.find( p2.params()[x]->name() );
@@ -97,14 +86,11 @@ void LinearErrorPropagator::add( const LinearErrorPropagator& p2 )
} else
props[x] = it->second;
}
-
TMatrixD old_cov = m_cov;
if ( superSet != oldSize ) m_cov.ResizeTo( superSet, superSet );
-
for ( size_t x = 0; x != oldSize; ++x ) {
for ( size_t y = 0; y != oldSize; ++y ) m_cov( x, y ) = old_cov( x, y );
}
-
auto p2_cov = p2.cov();
for ( size_t x = 0; x < p2.size(); ++x ) {
for ( size_t y = 0; y < p2.size(); ++y ) {
@@ -115,6 +101,46 @@ void LinearErrorPropagator::add( const LinearErrorPropagator& p2 )
}
}
+double LinearErrorPropagator::getError( const std::function<double(void)>& fcn ) const
+{
+ unsigned int N = m_cov.GetNrows();
+ TVectorD errorVec( N );
+ for ( unsigned int i = 0; i < N; ++i ) {
+ DEBUG( "Perturbing parameter: [" << m_parameters[i]->name() << "] " << m_parameters[i]->mean() << " by "
+ << sqrt( m_cov( i, i ) ) << " " << m_parameters[i] );
+ errorVec(i) = derivative(fcn,i);
+ fcn();
+ }
+ return sqrt( errorVec * ( m_cov * errorVec ) );
+}
+
+std::vector<double> LinearErrorPropagator::getVectorError( const std::function<std::vector<double>(void)>& fcn, size_t RANK ) const
+{
+ unsigned int N = m_cov.GetNrows();
+ std::vector<TVectorD> errorVec( RANK, TVectorD( N ) );
+ for ( unsigned int i = 0; i < N; ++i ) {
+ double startingValue = m_parameters[i]->mean();
+ double error = sqrt( m_cov( i, i ) );
+ double min = m_parameters[i]->mean() - error;
+ double max = m_parameters[i]->mean() + error;
+ DEBUG( "Perturbing parameter: " << m_parameters[i]->name() << " -> [" << min << ", " << max << "]" );
+
+ m_parameters[i]->setCurrentFitVal( max );
+ auto plus_variation = fcn();
+ m_parameters[i]->setCurrentFitVal( min );
+ auto minus_variation = fcn();
+ m_parameters[i]->setCurrentFitVal( startingValue );
+ for ( size_t j = 0; j < RANK; ++j ) {
+ errorVec[j]( i ) = ( plus_variation[j] - minus_variation[j] ) / ( 2 * error );
+ }
+ }
+ fcn();
+ std::vector<double> rt( RANK, 0 );
+ for ( unsigned int j = 0; j < RANK; ++j ) rt[j] = sqrt( errorVec[j] * ( m_cov * errorVec[j] ) );
+ return rt;
+}
+
+
void LinearErrorPropagator::reset()
{
for ( int x = 0; x < m_cov.GetNrows(); ++x ) {
diff --git a/src/Event.cpp b/src/Event.cpp
index 483267fb15f..04043c21503 100644
--- a/src/Event.cpp
+++ b/src/Event.cpp
@@ -1,4 +1,4 @@
-#include <math.h>
+
#include <stddef.h>
#include <complex>
#include <ostream>
@@ -10,18 +10,15 @@
using namespace AmpGen;
-Event::Event( const size_t& N, const size_t& cacheSize) :
- m_event(N),
- m_cache(cacheSize) {
- }
+Event::Event( const unsigned& N) :
+ m_event(N) {}
-Event::Event( const real_t* data, const size_t& N, const size_t& cacheSize) :
- m_event(data, data+N),
- m_cache(cacheSize) {
- }
+Event::Event( const real_t* data, const unsigned& N) :
+ m_event(data, data+N) {}
void Event::print() const {
- for( unsigned int i = 0 ; i< m_event.size()/4 ; ++i ){
+ unsigned nParticles = m_event.size()/4;
+ for( unsigned i = 0 ; i < nParticles; ++i ){
double px = m_event[4*i+0];
double py = m_event[4*i+1];
double pz = m_event[4*i+2];
@@ -29,22 +26,25 @@ void Event::print() const {
double s = pE*pE - px*px -py*py -pz*pz;
INFO( "P["<<i<<"] = {"<<px<<", " << py << ", " << pz << ", " << pE << "}, m = " << sqrt(fabs(s)) );
}
+ for( unsigned i = 4*nParticles; i != m_event.size(); ++i ){
+ INFO( m_event[i] );
+ }
}
-real_t Event::s( const size_t& index ) const {
+real_t Event::s( const unsigned& index ) const {
return get(4*index+3) * get(4*index+3)
- get(4*index+0) * get(4*index+0)
- get(4*index+1) * get(4*index+1)
- get(4*index+2) * get(4*index+2);
}
-real_t Event::s( const size_t& index1, const size_t& index2 ) const {
+real_t Event::s( const unsigned& index1, const unsigned& index2 ) const {
return ( get(4*index1+3) + get(4*index2+3) )*( get(4*index1+3) + get(4*index2+3) ) -
( get(4*index1+0) + get(4*index2+0) )*( get(4*index1+0) + get(4*index2+0) ) -
( get(4*index1+1) + get(4*index2+1) )*( get(4*index1+1) + get(4*index2+1) ) -
( get(4*index1+2) + get(4*index2+2) )*( get(4*index1+2) + get(4*index2+2) ) ;
}
-real_t Event::s( const size_t& index1, const size_t& index2, const size_t& index3 ) const {
+real_t Event::s( const unsigned& index1, const unsigned& index2, const unsigned& index3 ) const {
return ( get(4*index1+3) + get(4*index2+3) + get(4*index3+3) ) *
( get(4*index1+3) + get(4*index2+3) + get(4*index3+3) ) -
( get(4*index1+0) + get(4*index2+0) + get(4*index3+0) ) *
@@ -55,7 +55,7 @@ real_t Event::s( const size_t& index1, const size_t& index2, const size_t& index
( get(4*index1+2) + get(4*index2+2) + get(4*index3+2) ) ;
}
-real_t Event::s( const std::vector<size_t>& indices ) const {
+real_t Event::s( const std::vector<unsigned>& indices ) const {
if( indices.size() == 2 ) return s( indices[0], indices[1] );
if( indices.size() == 3 ) return s( indices[0], indices[1], indices[2] );
double E=0; double px=0;
@@ -69,24 +69,19 @@ real_t Event::s( const std::vector<size_t>& indices ) const {
}
return E*E -px*px - py*py - pz*pz;
}
-void Event::printCache() const {
- for( unsigned int i = 0 ; i < m_cache.size(); ++i){
- INFO("Cache adddress [" << i << "] = " << m_cache[i] );
- }
-}
-void Event::set( const size_t& i, const std::vector<real_t>& p ){
- for( size_t j = 0 ; j < 4; ++j) m_event[4*i + j ] = p[j];
+void Event::set( const unsigned& i, const std::vector<real_t>& p ){
+ for( unsigned j = 0 ; j < 4; ++j) m_event[4*i + j ] = p[j];
}
-void Event::set( const size_t& i, const real_t* p ){
- for( size_t j = 0 ; j < 4; ++j) m_event[4*i + j ] = p[j];
+void Event::set( const unsigned& i, const real_t* p ){
+ for( unsigned j = 0 ; j < 4; ++j) m_event[4*i + j ] = p[j];
}
void Event::set( const real_t* evt ){
- for( size_t i = 0 ; i < m_event.size(); ++i ) m_event[i] = *(evt + i );
+ for( unsigned i = 0 ; i < m_event.size(); ++i ) m_event[i] = *(evt + i );
}
-void Event::set( const size_t& i, const real_t& p ){ m_event[i] = p ; }
+void Event::set( const unsigned& i, const real_t& p ){ m_event[i] = p ; }
-void Event::swap( const unsigned int& i , const unsigned int& j )
+void Event::swap( const unsigned& i , const unsigned& j )
{
double tmp[4];
std::memmove( tmp, &m_event[4*j], sizeof(tmp));
@@ -94,10 +89,8 @@ void Event::swap( const unsigned int& i , const unsigned int& j )
std::memmove( &m_event[4*i], &tmp,sizeof(tmp));
}
-void Event::setCache(const complex_t& value, const size_t& pos){ m_cache[pos] = value; }
-void Event::setCache( const std::vector<complex_t>& value, const size_t& pos )
+void Event::reorder( const std::vector<unsigned>& addresses )
{
- std::memmove( m_cache.data() + pos, value.data(), sizeof(complex_t) * value.size() );
+ auto copy = m_event;
+ for( unsigned i = 0; i != addresses.size(); ++i ) set( addresses[i], copy.data() + 4 *i );
}
-
-void Event::resizeCache( const unsigned int& new_size ){ m_cache.resize(new_size); }
diff --git a/src/EventList.cpp b/src/EventList.cpp
index c49807c6a39..891537d84a8 100644
--- a/src/EventList.cpp
+++ b/src/EventList.cpp
@@ -54,40 +54,58 @@ void EventList::loadFromFile( const std::string& fname, const ArgumentPack& args
gFile = current_file;
}
+template <typename key_type, typename value_type, typename default_type=key_type> key_type inv_map(const std::map<key_type, value_type>& mp, const value_type& k, const default_type& df = default_type())
+{
+ for( const auto& [key,val] : mp ) if( val == k ) return key;
+ return df;
+}
+
void EventList::loadFromTree( TTree* tree, const ArgumentPack& args )
{
ProfileClock read_time;
- auto pdfSize = args.getArg<CacheSize>().val;
- auto filter = args.getArg<Filter>().val;
- auto getGenPdf = args.getArg<GetGenPdf>(true).val;
- auto weightBranch = args.getArg<WeightBranch>().val;
+ if( m_eventType.size() == 0 ){
+ auto tokens = split( tree->GetTitle(), ' ');
+ if( tokens.size() != 1 ) m_eventType = EventType( tokens );
+ INFO("Attempted automatic deduction of eventType: " << m_eventType );
+ }
+ auto filter = args.getArg<Filter>(std::string("")).val;
+ auto getGenPdf = args.getArg<GetGenPdf>(false).val;
+ auto weightBranch = args.getArg<WeightBranch>(std::string("")).val;
auto branches = args.getArg<Branches>().val;
- auto applySym = args.getArg<ApplySym>().val;
+ auto extraBranches= args.getArg<ExtraBranches>().val;
+ auto applySym = args.getArg<ApplySym>(false).val;
auto entryList = args.getArg<EntryList>().val;
auto eventFormat = m_eventType.getEventFormat( true );
-
- Event temp( branches.size() == 0 ? eventFormat.size() : branches.size() , pdfSize );
+ auto inputUnits = args.getArg<InputUnits>(Units::GeV);
+ auto idBranches = args.getArg<IdBranches>({}).val;
+ Event temp( eventFormat.size() + extraBranches.size());
temp.setWeight( 1 );
temp.setGenPdf( 1 );
tree->SetBranchStatus( "*", 0 );
-
- TreeReader<real_t> tr( tree );
- if( branches.size() != 0 ){
- INFO("Branches = [" << vectorToString(branches, ", ") << "]" );
- for ( auto branch = branches.begin(); branch != branches.end(); ++branch ) {
- unsigned int pos = std::distance( branches.begin(), branch );
- tr.setBranch( *branch, &(temp[pos]) );
- if( pos >= eventFormat.size() ){
- INFO("Specifiying event extension: " << *branch << " " << pos << " " << eventFormat.size() );
- m_extensions[ *branch ] = pos;
- }
+ TreeReader tr( tree );
+ bool hasEnergy = branches.size() == 0 || branches.size() == 4 * m_eventType.size(); // if the energy of the particle has been explicitly specified //
+ std::vector<int> ids( m_eventType.size() );
+ if( branches.size() != 0 )
+ {
+ DEBUG("Branches = [" << vectorToString(branches, ", ") << "]" );
+ for (unsigned p = 0 ; p != branches.size(); ++p )
+ {
+ auto pos = hasEnergy ? p : 4 * int(p/3) + p % 3 ;
+ DEBUG("Setting branch: " << branches[p] << " pos: " << pos << " fmt = " << inv_map( eventFormat, pos, "NOT FOUND" ) << " has energy? " << hasEnergy );
+ tr.setBranch( branches[p], &(temp[pos]) );
}
- }
- else {
- for ( auto& branch : eventFormat ){
- tr.setBranch( branch.first, &(temp[branch.second]) );
+ if( idBranches.size() != 0 )
+ {
+ if( idBranches.size() != m_eventType.size() ) FATAL("Number of ID branches should be number of final state particles");
+ for( int i = 0; i != ids.size(); ++i ) tr.setBranch( idBranches[i], ids.data() + i);
}
}
+ else for ( auto& branch : eventFormat ) tr.setBranch( branch.first, &(temp[branch.second]) );
+ auto pos = eventFormat.size();
+ for( const auto& branch : extraBranches ){
+ tr.setBranch( branch, &(temp[pos]) );
+ m_extensions[branch] = pos++;
+ }
if( getGenPdf ) tr.setBranch( "genPdf", temp.pGenPdf() );
if( weightBranch != "" ) tr.setBranch( weightBranch, temp.pWeight() );
if( filter != "" ){
@@ -100,22 +118,29 @@ void EventList::loadFromTree( TTree* tree, const ArgumentPack& args )
for( int i = 0 ; i < evtList->GetN(); ++i )
entryList.push_back( evtList->GetEntry(i) );
}
- bool hasEventList = entryList.size() != 0;
- unsigned int nEvents = hasEventList ? entryList.size() : tree->GetEntries();
- m_data.reserve( nEvents );
+ if( entryList.size() != 0 ) tr.setEntryList( entryList );
+ m_data.reserve( tr.nEntries() );
auto symmetriser = m_eventType.symmetriser();
- for ( unsigned int evt = 0; evt < nEvents; ++evt ) {
- tr.getEntry( hasEventList ? entryList[evt] : evt );
- if( applySym ) symmetriser( temp );
- m_data.push_back( temp );
+ auto automaticOrdering = m_eventType.automaticOrdering();
+ for (const auto& evt : tr) {
+ if( inputUnits != Units::GeV ) for( unsigned k = 0; k != eventFormat.size(); ++k ) temp[k] *= to_double(inputUnits);
+ if( idBranches.size() != 0 && !automaticOrdering(temp, ids) ) WARNING("Failed to order event: " << evt );
+ if( applySym ) symmetriser(temp);
+ if( ! hasEnergy ){
+ for( unsigned int k = 0 ; k != m_eventType.size(); ++k )
+ temp[4*k + 3] = sqrt( m_eventType.mass(k) * m_eventType.mass(k) + temp[4*k+0]*temp[4*k+0] + temp[4*k+1]*temp[4*k+1] + temp[4*k+2]*temp[4*k+2] );
+ }
+ push_back( temp );
}
read_time.stop();
INFO("Time to read tree = " << read_time << "[ms]; nEntries = " << size() );
}
-TTree* EventList::tree( const std::string& name, const std::vector<std::string>& extraBranches )
+TTree* EventList::tree( const std::string& name, const std::vector<std::string>& extraBranches ) const
{
- TTree* outputTree = new TTree( name.c_str(), name.c_str() );
+ std::string title = m_eventType.mother();
+ for( unsigned i = 0 ; i != m_eventType.size(); ++i ) title += " " + m_eventType[i];
+ TTree* outputTree = new TTree( name.c_str(), title.c_str() );
if ( size() == 0 ) {
ERROR( "Trying to output empty tree" );
return nullptr;
@@ -124,15 +149,11 @@ TTree* EventList::tree( const std::string& name, const std::vector<std::string>&
double genPdf = 1;
double weight = 1;
auto format = m_eventType.getEventFormat( true );
- for ( auto& f : format ){
- outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
- }
- for ( auto& f : m_extensions ){
- outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
- }
+ for ( const auto& f : format ) outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
+ for ( const auto& f : m_extensions ) outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
outputTree->Branch( "genPdf", &genPdf );
outputTree->Branch( "weight", &weight );
- for ( auto& evt : *this ) {
+ for ( const auto& evt : *this ) {
tmp = evt;
genPdf = evt.genPdf();
weight = evt.weight();
@@ -144,21 +165,17 @@ TTree* EventList::tree( const std::string& name, const std::vector<std::string>&
std::vector<TH1D*> EventList::makeProjections( const std::vector<Projection>& projections, const ArgumentPack& args )
{
std::vector<TH1D*> plots;
- for ( auto& proj : projections ) {
- TH1D* plot = makeProjection(proj, args );
- DEBUG("Made plot ... " << plot->GetName() );
- plots.push_back( plot );
- }
+ for ( const auto& proj : projections ) plots.push_back( makeProjection(proj, args) );
return plots;
}
-TH1D* EventList::makeProjection( const Projection& projection, const ArgumentPack& args )
+TH1D* EventList::makeProjection( const Projection& projection, const ArgumentPack& args ) const
{
- auto selection = args.getArg<Selection>().val;
+ auto selection = args.getArg<PlotOptions::Selection>().val;
auto weightFunction = args.getArg<WeightFunction>().val;
- std::string prefix = args.getArg<Prefix>();
+ std::string prefix = args.getArg<PlotOptions::Prefix>(std::string(""));
auto plot = projection.plot(prefix);
- plot->SetLineColor(args.getArg<LineColor>(kBlack).val);
+ plot->SetLineColor(args.getArg<PlotOptions::LineColor>(kBlack).val);
plot->SetMarkerSize(0);
for( auto& evt : m_data ){
if( selection != nullptr && !selection(evt) ) continue;
@@ -169,11 +186,11 @@ TH1D* EventList::makeProjection( const Projection& projection, const ArgumentPac
return plot;
}
-TH2D* EventList::makeProjection( const Projection2D& projection, const ArgumentPack& args )
+TH2D* EventList::makeProjection( const Projection2D& projection, const ArgumentPack& args ) const
{
- auto selection = args.getArg<Selection>().val;
+ auto selection = args.getArg<PlotOptions::Selection>().val;
auto weightFunction = args.getArg<WeightFunction>().val;
- std::string prefix = args.getArg<Prefix>().val;
+ std::string prefix = args.getArg<PlotOptions::Prefix>().val;
auto plot = projection.plot(prefix);
for ( auto& evt : m_data ){
if ( selection != nullptr && !selection(evt) ) continue;
@@ -183,72 +200,46 @@ TH2D* EventList::makeProjection( const Projection2D& projection, const ArgumentP
return plot;
}
-void EventList::printCacheInfo( const unsigned int& nEvt )
+double EventList::integral() const
{
- for ( auto& ind : m_pdfIndex ) {
- INFO( "Cache[" << ind.second << "] = " << ind.first << " = " << at( nEvt ).getCache( ind.second ) );
- }
+ return std::accumulate( std::begin(*this), std::end(*this), 0, [](double rv, const auto& evt){ return rv + evt.weight(); } );
}
-size_t EventList::getCacheIndex( const CompiledExpressionBase& PDF ) const
+void EventList::add( const EventList& evts )
{
- auto pdfIndex = m_pdfIndex.find( FNV1a_hash( PDF.name() ) );
- if ( pdfIndex != m_pdfIndex.end() )
- return pdfIndex->second;
- else
- ERROR( "FATAL: PDF Index for " << PDF.name() << " not found" );
- return 999;
+ for ( auto& evt : evts ) push_back( evt );
}
-size_t EventList::getCacheIndex( const CompiledExpressionBase& PDF, bool& isRegistered ) const
-{
- auto pdfIndex = m_pdfIndex.find( FNV1a_hash( PDF.name() ) );
- if ( pdfIndex != m_pdfIndex.end() ) {
- isRegistered = true;
- return pdfIndex->second;
- }
- isRegistered = false;
- return 999;
+void EventList::clear()
+{
+ m_data.clear();
}
-void EventList::resetCache()
+void EventList::erase(const std::vector<Event>::iterator& begin,
+ const std::vector<Event>::iterator& end)
{
- m_pdfIndex.clear();
- for ( auto evt = begin(); evt != end(); ++evt ) evt->resizeCache( 0 );
- m_lastCachePosition = 0;
+ m_data.erase( begin, end );
}
-double EventList::integral() const
-{
- double integral = 0;
- for ( auto& evt : *this ) {
- integral += evt.weight();
- }
- return integral;
-}
-void EventList::add( const EventList& evts )
-{
- resetCache();
- WARNING( "Adding event lists invalidates cache state" );
- for ( auto& evt : evts ) {
- m_data.push_back( evt );
- rbegin()->resizeCache( 0 );
- }
-}
-double EventList::norm()
-{
- if ( m_norm == 0 ) {
- double totalWeight = 0;
-#pragma omp parallel for reduction( + : totalWeight )
- for ( unsigned int i = 0; i < size(); ++i ) totalWeight += ( *this )[i].weight() / ( *this )[i].genPdf();
- m_norm = totalWeight;
- }
- return m_norm;
+void EventList::reserve( const size_t& size )
+{
+ m_data.reserve( size );
}
+void EventList::resize ( const size_t& size )
+{
+ m_data.resize(size);
+ for( unsigned int i = 0 ; i != size; ++i ) m_data[i].setIndex(i) ;
+}
-void EventList::clear() { m_data.clear(); }
-void EventList::erase( const std::vector<Event>::iterator& begin, const std::vector<Event>::iterator& end )
-{
- m_data.erase( begin, end );
+void EventList::push_back( const Event& evt )
+{
+ m_data.push_back( evt );
+ m_data.rbegin()->setIndex(m_data.size()-1);
+}
+
+void EventList::emplace_back( const Event& evt)
+{
+ m_data.emplace_back(evt) ;
+ m_data.rbegin()->setIndex(m_data.size()-1);
}
diff --git a/src/EventListSIMD.cpp b/src/EventListSIMD.cpp
new file mode 100644
index 00000000000..cd6b6873e6b
--- /dev/null
+++ b/src/EventListSIMD.cpp
@@ -0,0 +1,251 @@
+#if ENABLE_AVX
+
+#include <Rtypes.h>
+#include <TDirectory.h>
+#include <TEventList.h>
+#include <TH1.h>
+#include <TH2.h>
+#include <TTree.h>
+#include <TFile.h>
+#include <TROOT.h>
+
+#include <stddef.h>
+#include <complex>
+#include <functional>
+#include <iterator>
+#include <map>
+#include <ostream>
+#include <string>
+#include <utility>
+#include <vector>
+
+#include "AmpGen/ArgumentPack.h"
+#include "AmpGen/CompiledExpressionBase.h"
+#include "AmpGen/EventListSIMD.h"
+#include "AmpGen/EventType.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/Projection.h"
+#include "AmpGen/TreeReader.h"
+#include "AmpGen/Utilities.h"
+#include "AmpGen/Event.h"
+#include "AmpGen/Types.h"
+#include "AmpGen/ProfileClock.h"
+#include "AmpGen/simd/utils.h"
+using namespace AmpGen;
+
+// ENABLE_DEBUG(EventListSIMD)
+
+EventListSIMD::EventListSIMD( const EventType& type ) :
+ m_data(0, type.eventSize() ),
+ m_eventType( type ) {}
+
+void EventListSIMD::loadFromFile( const std::string& fname, const ArgumentPack& args )
+{
+ auto current_file = gFile;
+ auto tokens = split( fname, ':');
+ TTree* tree = nullptr;
+ if( fname == "" ) FATAL("Filename must be specified to load data");
+ if( tokens.size() == 2 ){
+ gFile = TFile::Open( tokens[0].c_str(), "READ");
+ if( gFile == nullptr ) FATAL("Failed to load file: " << tokens[0] );
+ tree = (TTree*)gFile->Get( tokens[1].c_str() );
+ }
+ else {
+ gFile = TFile::Open( fname.c_str(), "READ");
+ if( gFile == nullptr ) FATAL("Failed to load file: " << tokens[0] );
+ if( tree == nullptr ) tree = (TTree*)gFile->Get("EventList");
+ tree = (TTree*)gFile->Get("DalitzEventList");
+ }
+ if( tree == nullptr ) FATAL( "Failed to load tree from file: " << fname );
+ loadFromTree( tree, args );
+ gFile->Close();
+ gFile = current_file;
+}
+
+void EventListSIMD::loadFromTree( TTree* tree, const ArgumentPack& args )
+{
+ ProfileClock read_time;
+ if( m_eventType.size() == 0 ){
+ auto tokens = split( tree->GetTitle(), ' ');
+ if( tokens.size() != 1 ) setEventType( EventType( tokens ) );
+ INFO("Attempted automatic deduction of eventType: " << m_eventType );
+ }
+ auto filter = args.getArg<Filter>(std::string("")).val;
+ auto getGenPdf = args.getArg<GetGenPdf>(false).val;
+ auto weightBranch = args.getArg<WeightBranch>(std::string("")).val;
+ auto branches = args.getArg<Branches>().val;
+ auto applySym = args.getArg<ApplySym>(false).val;
+ auto entryList = args.getArg<EntryList>().val;
+ auto eventFormat = m_eventType.getEventFormat( true );
+
+ Event temp( branches.size() == 0 ? eventFormat.size() : branches.size());
+ temp.setWeight( 1 );
+ temp.setGenPdf( 1 );
+ tree->SetBranchStatus( "*", 0 );
+
+ TreeReader tr( tree );
+ if( branches.size() != 0 ){
+ INFO("Branches = [" << vectorToString(branches, ", ") << "]" );
+ for ( auto branch = branches.begin(); branch != branches.end(); ++branch ) {
+ unsigned int pos = std::distance( branches.begin(), branch );
+ tr.setBranch( *branch, &(temp[pos]) );
+ }
+ }
+ else {
+ for ( auto& branch : eventFormat ){
+ tr.setBranch( branch.first, &(temp[branch.second]) );
+ }
+ }
+ if( getGenPdf ) tr.setBranch( "genPdf", temp.pGenPdf() );
+ if( weightBranch != "" ) tr.setBranch( weightBranch, temp.pWeight() );
+ if( filter != "" ){
+ if( entryList.size() != 0 ){
+ WARNING("Specified entry list and filter, will overwrite list with specified selection");
+ }
+ tr.prepare();
+ tree->Draw(">>evtList", filter.c_str() );
+ TEventList* evtList = (TEventList*)gDirectory->Get("evtList");
+ for( int i = 0 ; i < evtList->GetN(); ++i ) entryList.push_back( evtList->GetEntry(i) );
+ }
+ bool hasEventList = entryList.size() != 0;
+ size_t nEvents = hasEventList ? entryList.size() : tree->GetEntries();
+ std::array<Event, float_v::size> buffer;
+
+ resize( nEvents );
+ auto symmetriser = m_eventType.symmetriser();
+ for ( unsigned int block = 0; block < m_data.nBlocks(); ++block )
+ {
+ for( unsigned k = 0 ; k != float_v::size; ++k )
+ {
+ auto evt = k + block * float_v::size;
+ if(evt < m_data.size() )
+ {
+ tr.getEntry( hasEventList ? entryList[evt] : evt );
+ if( applySym ) symmetriser( temp );
+ buffer[k] = temp;
+ }
+ else buffer[k].setWeight(0);
+ }
+ gather( buffer, block );
+ }
+ read_time.stop();
+ INFO("Time to read tree = " << read_time << "[ms]; nEntries = " << size() );
+}
+
+
+EventListSIMD::EventListSIMD( const EventList& other ) : EventListSIMD( other.eventType() )
+{
+ resize( other.size() );
+ for( unsigned block = 0 ; block != m_data.nBlocks(); block++ )
+ {
+ for( unsigned j = 0 ; j != m_data.nFields(); ++j )
+ m_data(block, j) = utils::gather<float_v>(other, [j](auto& event){ return event[j]; } , block * float_v::size );
+ m_weights[block] = utils::gather<float_v>(other, [](auto& event){ return event.weight(); }, block * float_v::size, 0);
+ m_genPDF [block] = utils::gather<float_v>(other, [](auto& event){ return event.genPdf(); }, block * float_v::size, 1);
+ }
+}
+
+
+
+TTree* EventListSIMD::tree( const std::string& name, const std::vector<std::string>& extraBranches ) const
+{
+ std::string title = m_eventType.mother();
+ for( unsigned i = 0 ; i != m_eventType.size(); ++i ) title += " " + m_eventType[i];
+ TTree* outputTree = new TTree( name.c_str(), title.c_str() );
+ if ( size() == 0 ) {
+ ERROR( "Trying to output empty tree" );
+ return nullptr;
+ }
+ Event tmp = *( begin() );
+ double genPdf = 1;
+ double weight = 1;
+ auto format = m_eventType.getEventFormat( true );
+
+ for ( const auto& f : format ) outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
+ // for ( const auto& f : m_extensions ) outputTree->Branch( f.first.c_str(), tmp.address( f.second ) );
+
+ outputTree->Branch( "genPdf", &genPdf );
+ outputTree->Branch( "weight", &weight );
+ for ( const auto& evt : *this ) {
+ tmp = evt;
+ genPdf = evt.genPdf();
+ weight = evt.weight();
+ outputTree->Fill();
+ }
+ return outputTree;
+}
+
+std::vector<TH1D*> EventListSIMD::makeProjections( const std::vector<Projection>& projections, const ArgumentPack& args )
+{
+ std::vector<TH1D*> plots;
+ for ( const auto& proj : projections ) plots.push_back( proj(*this,args) );
+ return plots;
+}
+
+TH1D* EventListSIMD::makeProjection( const Projection& projection, const ArgumentPack& args ) const
+{
+ return projection(*this, args);
+
+}
+TH2D* EventListSIMD::makeProjection( const Projection2D& projection, const ArgumentPack& args ) const
+{
+ auto selection = args.getArg<PlotOptions::Selection>().val;
+ auto weightFunction = args.getArg<WeightFunction>().val;
+ std::string prefix = args.getArg<PlotOptions::Prefix>().val;
+ auto plot = projection.plot(prefix);
+ for ( const auto evt : *this ){
+ if ( selection != nullptr && !selection(evt) ) continue;
+ auto pos = projection(evt);
+ plot->Fill( pos.first, pos.second, evt.weight() * ( weightFunction == nullptr ? 1 : weightFunction(evt) / evt.genPdf() ) );
+ }
+ return plot;
+}
+
+
+void EventListSIMD::clear()
+{
+ m_data.clear();
+}
+
+const Event EventListSIMD::operator[]( const size_t& pos ) const
+{
+ unsigned nEvents = size();
+ unsigned p = pos / float_v::size;
+ unsigned q = pos % float_v::size;
+ Event tempEvent( eventSize() );
+ for( unsigned i = 0 ; i != tempEvent.size(); ++i )
+ tempEvent[i] = m_data(p, i).at(q);
+ tempEvent.setWeight( m_weights[p].at(q) );
+ tempEvent.setGenPdf( m_genPDF[p].at(q) );
+ tempEvent.setIndex( pos );
+ return tempEvent;
+}
+
+std::array<Event, AmpGen::float_v::size> EventListSIMD::scatter( unsigned pos ) const
+{
+ unsigned p = pos / float_v::size;
+ std::array<Event, float_v::size> rt;
+ auto vw = m_weights[p].to_array();
+ auto vg = m_genPDF[p].to_array();
+ for( unsigned evt = 0 ; evt != float_v::size; ++evt ){
+ rt[evt] = Event( m_data.nFields() );
+ rt[evt].setWeight(vw[evt]);
+ rt[evt].setGenPdf(vg[evt]);
+ rt[evt].setIndex(evt + pos);
+ }
+ for( unsigned field = 0 ; field != m_data.nFields(); ++field){
+ auto v = m_data(p, field).to_array();
+ for( unsigned evt = 0; evt != float_v::size; ++evt ) rt[evt][field] = v[evt];
+ }
+ return rt;
+}
+
+void EventListSIMD::gather( const std::array<Event, float_v::size>& data, unsigned pos )
+{
+ for( unsigned field = 0; field != m_data.nFields(); ++field )
+ m_data(pos, field) = utils::gather<float_v>(data, [field](auto& event){ return event[field]; } );
+ m_weights[pos] = utils::gather<float_v>(data, [](auto& event){ return event.weight() ; } );
+ m_genPDF[pos] = utils::gather<float_v>(data, [](auto& event){ return event.genPdf(); } );
+}
+
+#endif
diff --git a/src/EventType.cpp b/src/EventType.cpp
index 8ee8d7d9faa..06e3e1f33f6 100644
--- a/src/EventType.cpp
+++ b/src/EventType.cpp
@@ -20,18 +20,22 @@
#include "AmpGen/Utilities.h"
#include "AmpGen/Units.h"
#include "AmpGen/Event.h"
+#include "AmpGen/OptionsParser.h"
using namespace AmpGen;
std::string convertTeXtoROOT(std::string input);
EventType::EventType( const std::vector<std::string>& particleNames, const bool& isTD ) : m_timeDependent( isTD )
-{
+{
+ if ( OptionsParser::printHelp() ) return;
+
if ( particleNames.size() < 3 ) { // Mother plus two daughters minimum required
ERROR( "Not enough particles in event type: " << particleNames[0] << " size = " << particleNames.size() );
throw std::runtime_error( "Not enough particles listed in particle names! Was it defined?" );
}
m_mother = particleNames.at(0);
- for ( unsigned int i = 1; i < particleNames.size(); ++i ) m_particleNames.push_back( particleNames[i] );
+ m_alt_part_names = NamedParameter<bool>("EventType::AlternativeParticleNames", false );
+
auto motherProperties = ParticlePropertiesList::get( m_mother );
if ( motherProperties != nullptr )
m_motherMass = motherProperties->mass();
@@ -39,15 +43,27 @@ EventType::EventType( const std::vector<std::string>& particleNames, const bool&
ERROR( "Particle not found: " << m_mother );
return;
}
- for ( auto& particle : m_particleNames ) {
- auto prop = ParticlePropertiesList::get( particle );
+
+ m_ignore.resize(particleNames.size()-1,false);
+ for ( auto it = particleNames.begin()+1; it != particleNames.end(); ++it )
+ {
+ if( *it->begin() == '{' && *it->rbegin() == '}' )
+ {
+ m_particleNames.push_back( it->substr(1, it->size() -2 ) );
+ }
+ else m_particleNames.push_back( *it );
+
+ auto prop = ParticlePropertiesList::get( *m_particleNames.rbegin() );
if ( prop != nullptr )
m_particleMasses.push_back( prop->mass() );
else {
- ERROR( "Particle not found: " << particle );
+ FATAL( "Particle not found: " << *m_particleNames.rbegin() );
return;
}
- m_particleNamesPickled.push_back( replaceAll( replaceAll( particle, "+", "~" ), "-", "#" ) );
+ if(m_alt_part_names)
+ m_particleNamesPickled.push_back( replaceAll( *m_particleNames.rbegin(), {{"+","p"},{"-","m"},{"(",""},{")",""}}));
+ else
+ m_particleNamesPickled.push_back( replaceAll( *m_particleNames.rbegin(), {{"+","~"},{"-","#"},{"(",""},{")",""}}));
}
DEBUG( m_mother << " = " << m_motherMass << " -> " );
for ( unsigned int i = 0; i < m_particleNames.size(); ++i ) {
@@ -61,64 +77,80 @@ EventType::EventType( const std::vector<std::string>& particleNames, const bool&
for( auto& p : m_particleNames ) m_dim.second *= dimOfParticle(p);
}
-std::map<std::string, size_t> EventType::getEventFormat( const bool& outputNames ) const
+std::map<std::string, unsigned> EventType::getEventFormat( const bool& outputNames ) const
{
- std::map<std::string, size_t> returnValue;
+ std::map<std::string, unsigned> returnValue;
bool include_energy = NamedParameter<bool>("EventType::IncludeEnergy", true );
- size_t s = include_energy ? 4 : 3;
+ unsigned s = include_energy ? 4 : 3;
for ( unsigned int ip = 0; ip < size(); ++ip ) {
- std::string stub =
- outputNames ? "_" + std::to_string( ip + 1 ) + "_" + m_particleNamesPickled[ip] : std::to_string( ip );
+ std::string parsed_name;
+ if(m_alt_part_names)
+ //check if there are multiple identical particles
+ if(std::count(m_particleNamesPickled.begin(),m_particleNamesPickled.end(),m_particleNamesPickled[ip]) > 1)
+ //if yes, append an index
+ parsed_name = m_particleNamesPickled[ip] +
+ std::to_string(std::count(m_particleNamesPickled.begin(),m_particleNamesPickled.begin()+ip, m_particleNamesPickled[ip]));
+ else // just take the already chosen name
+ parsed_name = m_particleNamesPickled[ip];
+ else
+ parsed_name = "_" + std::to_string( ip + 1 ) + "_" + m_particleNamesPickled[ip];
+ std::string stub = outputNames ? parsed_name : std::to_string( ip );
if( include_energy ) returnValue[stub + "_E"] = s * ip + 3;
returnValue[stub + "_Px"] = s * ip + 0;
returnValue[stub + "_Py"] = s * ip + 1;
returnValue[stub + "_Pz"] = s * ip + 2;
}
- if ( m_timeDependent ) returnValue[m_mother + "_ctau"] = 4 * size();
+ if ( m_timeDependent ) returnValue[m_mother + "_decayTime"] = 4 * size();
for( auto& extend : m_eventTypeExtensions ) returnValue[extend] = returnValue.size();
return returnValue;
}
-void EventType::extendEventType( const std::string& branch )
+void EventType::extendEventType( const std::string& branch )
{
m_eventTypeExtensions.push_back(branch);
}
-std::pair<double, double> EventType::minmax( const std::vector<size_t>& indices, bool isGeV ) const
+std::pair<double, double> EventType::minmax( const std::vector<unsigned>& indices) const
{
- std::vector<size_t> ivec( size() );
+ std::vector<unsigned> ivec( size() );
std::iota( ivec.begin(), ivec.end(), 0 );
- double min( 0 );
- double max( motherMass() );
- for ( auto& x : indices ) min += mass( x );
+ double min = 0 ;
+ for( auto& i : indices ) min += mass(i);
+ double max = motherMass();
for ( auto& x : ivec )
if ( std::find( indices.begin(), indices.end(), x ) == indices.end() ) max -= mass( x );
- return std::pair<double, double>( min * min / GeV, max * max / GeV );
+ return std::pair<double, double>(min, max);
}
-
-std::vector<std::vector<unsigned int>> EventType::getBosePairs() const
+std::pair<unsigned, unsigned> EventType::count(const unsigned& index) const
{
- std::map<std::string, std::vector<unsigned int>> particleOrdering;
- for ( unsigned int i = 0; i < m_particleNames.size(); ++i ) particleOrdering[m_particleNames[i]].push_back( i );
- std::vector<std::vector<unsigned int>> orderings;
- for ( auto& im : particleOrdering )
- if ( im.second.size() != 1 ) orderings.push_back( im.second );
- return orderings;
+ if( index >= size() ){
+ ERROR("Looking for matching particles to index = " << index << " > size of eventType");
+ return std::pair<unsigned, unsigned>(0, 0);
+ }
+ std::pair<unsigned,unsigned> rt(0,0);
+ for( unsigned j = 0 ; j < size(); ++j ){
+ if( EventType::operator[](j) == EventType::operator[](index) ){
+ rt.second++;
+ if( j < index ) rt.first++;
+ }
+ }
+ return rt;
}
+
std::vector<std::string> EventType::finalStates() const { return m_particleNames; }
std::vector<double> EventType::masses() const { return m_particleMasses; }
-size_t EventType::size() const { return m_particleNames.size(); }
-double EventType::mass( const size_t& index ) const { return m_particleMasses[index]; }
+unsigned EventType::size() const { return m_particleNames.size(); }
+double EventType::mass( const unsigned& index ) const { return m_particleMasses[index]; }
double EventType::motherMass() const { return m_motherMass; }
std::string EventType::mother() const { return m_mother; }
-std::string EventType::operator[]( const size_t& index ) const { return m_particleNames[index]; }
-std::string EventType::label( const size_t& index, bool isRoot ) const
+std::string EventType::operator[]( const unsigned& index ) const { return m_particleNames[index]; }
+std::string EventType::label( const unsigned& index, bool isRoot ) const
{
const std::string label = ParticlePropertiesList::get( m_particleNames[index] )->label();
return isRoot ? convertTeXtoROOT( label ) : label;
}
-std::string EventType::label( const std::vector<size_t>& index, bool isRoot ) const
+std::string EventType::label( const std::vector<unsigned>& index, bool isRoot ) const
{
std::string thing = "";
for ( auto& x : index ) {
@@ -131,53 +163,47 @@ EventType EventType::conj( const bool& headOnly, const bool& dontConjHead ) cons
{
std::vector<std::string> type;
type.push_back( dontConjHead ? m_mother : ParticlePropertiesList::get( m_mother )->anti().name() );
-
- for ( auto& x : m_particleNames ) type.push_back( headOnly ? x : ParticlePropertiesList::get( x )->anti().name() );
+ std::transform( m_particleNames.begin(), m_particleNames.end(), std::back_inserter(type),
+ [&](auto& x){ return headOnly ? x : ParticlePropertiesList::get(x)->anti().name() ; } );
return EventType( type );
}
-std::vector<Projection> EventType::defaultProjections(const size_t& nBins) const
+std::vector<Projection> EventType::defaultProjections(const unsigned& nBins) const
{
- bool useRootLabelling = NamedParameter<bool>( "EventType::UseRootTEX", false );
std::string defaultObservable = NamedParameter<std::string>( "EventType::Observable", "mass2");
-
- std::vector<Projection> axes;
- std::string gevcccc = useRootLabelling ? "GeV^{2}/c^{4}" : "\\mathrm{GeV}^{2}/c^{4}";
- std::string gevcc = useRootLabelling ? "GeV/c^{2}" : "\\mathrm{GeV}/c^{2}";
- for ( size_t r = 2; r < size(); ++r ) { /// loop over sizes ///
- std::vector<std::vector<size_t>> combR = nCr( size(), r );
- for ( auto& indices : combR ) {
- auto mm = minmax( indices, true );
- if( defaultObservable == "mass2" )
- axes.emplace_back( [indices]( const Event& evt ) { return evt.s( indices ); },
- "s" + vectorToString( indices ),
- "s_{" + label( indices, useRootLabelling ) + "}", nBins,
- ( mm.first - 0.05 ) , ( mm.second + 0.05 ) , gevcccc );
- else if( defaultObservable == "mass" )
- axes.emplace_back( [indices]( const Event& evt ) { return sqrt( evt.s( indices ) ); },
- "m" + vectorToString( indices ),
- "m_{" + label( indices, useRootLabelling ) + "}", nBins,
- sqrt( mm.first - 0.05 ) , sqrt( mm.second + 0.05 ) , gevcc );
- }
+ std::vector<Projection> projections;
+ for ( unsigned r = 2; r < size(); ++r ) { /// loop over sizes ///
+ std::vector<std::vector<unsigned>> combR = nCr( size(), r );
+ std::transform( combR.begin(), combR.end(), std::back_inserter(projections),
+ [&](auto& index){ return this->projection(nBins, index, defaultObservable ); } );
}
- return axes;
+ return projections;
}
-Projection EventType::projection(const size_t& nBins, const std::vector<size_t>& indices) const
+Projection EventType::projection(const unsigned& nBins, const std::vector<unsigned>& indices, const std::string& observable) const
{
- auto mm = minmax( indices, true );
- std::string gevcccc = "\\mathrm{GeV}^{2}/c^{4}";
- return Projection( [indices]( const Event& evt ) { return evt.s( indices ); },
- "s" + vectorToString(indices),
- "s_{" + label(indices, false) + "}\\, \\left[" + gevcccc + "\\right]", nBins,
- ( mm.first - 0.05 ) , ( mm.second + 0.05 ) , gevcccc );
+ bool useRootLabelling = NamedParameter<bool>("EventType::UseRootTEX", false );
+ auto mm = minmax(indices);
+ std::string gevcccc = useRootLabelling ? "GeV^{2}/c^{4}" : "\\mathrm{GeV}^{2}/c^{4}";
+ std::string gevcc = useRootLabelling ? "GeV/c^{2}" : "\\mathrm{GeV}/c^{2}";
+ if( observable == "mass2" )
+ return Projection( [indices]( const Event& evt ) { return evt.s( indices ); },
+ "s" + vectorToString( indices ),
+ "s_{" + label( indices ) + "}", nBins,
+ ( mm.first * mm.first - 0.05 ) , ( mm.second * mm.second + 0.05 ) , gevcccc );
+ else if( observable == "mass" ){
+ return Projection( [indices]( const Event& evt ) { return sqrt( evt.s( indices ) ); },
+ "m" + vectorToString( indices ),
+ "m_{" + label( indices ) + "}", nBins,
+ mm.first > 0.05 ? mm.first - 0.05 :0 , mm.second + 0.05, gevcc );
+ }
+ return Projection();
}
bool EventType::operator==( const EventType& other ) const
{
if ( m_mother != other.mother() || size() != other.size() ) return false;
-
- for ( size_t i = 0; i < m_particleNames.size(); ++i ) {
+ for ( unsigned i = 0; i < m_particleNames.size(); ++i ) {
if ( m_particleNames[i] != other[i] ) return false;
}
return true;
@@ -189,11 +215,17 @@ std::ostream& AmpGen::operator<<( std::ostream& os, const EventType& type )
return os;
}
-size_t EventType::dof() const { return 3 * size() - 7; }
+unsigned EventType::dof() const { return 3 * size() - 7; }
std::function<void( Event& )> EventType::symmetriser() const
{
- auto shuffles = getBosePairs();
+ std::map<std::string, std::vector<unsigned>> particleOrdering;
+ for ( unsigned i = 0; i < m_particleNames.size(); ++i )
+ particleOrdering[m_particleNames[i]].push_back( i );
+ std::vector<std::vector<unsigned>> shuffles;
+ for ( auto& im : particleOrdering )
+ if ( im.second.size() != 1 ) shuffles.push_back( im.second );
+
int seed = NamedParameter<unsigned int>( "EventType::SymmetriserSeed", 12 );
std::mt19937 rng( seed );
for ( auto& shuffle : shuffles ) {
@@ -201,7 +233,7 @@ std::function<void( Event& )> EventType::symmetriser() const
for ( auto& s : shuffle ) shuffle_string += std::to_string( s ) + " ";
DEBUG( "Shuffle = " << shuffle_string );
}
- auto fcn = [shuffles, rng]( auto& event ) mutable -> void {
+ return [shuffles, rng]( auto& event ) mutable -> void {
for ( auto shuffled : shuffles ) {
for ( unsigned int index = 0; index < shuffled.size(); ++index ) {
unsigned int j = std::uniform_int_distribution<int>( 0, index )( rng );
@@ -211,21 +243,57 @@ std::function<void( Event& )> EventType::symmetriser() const
}
}
};
- return fcn;
}
+std::function<bool(Event&, const std::vector<int>&)> EventType::automaticOrdering() const
+{
+ std::vector<int> ids;
+ for( unsigned i = 0 ; i != m_particleNames.size(); ++i ) ids.push_back( ParticleProperties::get(m_particleNames[i])->pdgID() );
+ auto matches = [](const auto& c1, const auto& c2 , unsigned sgn = +1)
+ {
+ std::vector<bool> used( c1.size(), false );
+ for(unsigned i = 0; i != c1.size(); ++i )
+ {
+ for( unsigned j = 0; j != c2.size(); ++j )
+ {
+ if( c1[i] == sgn * c2[j] && ! used[j] ) used[j] = true;
+ }
+ }
+ return std::all_of( std::begin(used), std::end(used), [](auto b) { return b; } ) ;
+ };
+
+ return [ids, matches](auto& event, const auto& actual_ids) -> bool {
+ std::vector<unsigned> new_addresses( ids.size(), 999 );
+ int sgn = +1;
+ if( matches(ids, actual_ids ) ) sgn = +1;
+ else if( matches(ids, actual_ids, -1 ) ) sgn = -1;
+ else { ERROR("Ids: " << vectorToString(actual_ids, " ") << " do not match either particle or antiparticle ["<< vectorToString(ids, " ") << "]" );
+ return false;
+ }
+
+ for( unsigned i = 0 ; i != ids.size(); ++i )
+ {
+ for( unsigned j = 0 ; j != actual_ids.size(); ++j )
+ {
+ if( actual_ids[j] == sgn * ids[i] && new_addresses[j]==999 ){ new_addresses[j] = i; break ; }
+ }
+ }
+ event.reorder( new_addresses );
+ return true;
+ };
+}
+
+
bool EventType::has( const std::string& name ) const
{
- for ( auto& it : m_particleNames )
- if ( it == name ) return true;
- return false;
+ return std::any_of( m_particleNames.begin(), m_particleNames.end(), [&name](auto& it) { return it == name ; } );
}
bool EventType::isTimeDependent() const { return m_timeDependent; }
-size_t EventType::eventSize() const { return 4 * size() + m_timeDependent; }
+unsigned EventType::eventSize() const { return 4 * size() + m_timeDependent; }
-std::pair<size_t, size_t> EventType::dim() const { return m_dim; }
+std::pair<unsigned, unsigned> EventType::dim() const { return m_dim; }
std::string convertTeXtoROOT( std::string input )
{
@@ -237,3 +305,7 @@ std::string convertTeXtoROOT( std::string input )
return input;
}
+std::string EventType::decayDescriptor() const
+{
+ return mother()+"{" + vectorToString(m_particleNames,",") +"}" ;
+}
diff --git a/src/Expression.cpp b/src/Expression.cpp
index 0b11d8ca339..930bfb13822 100644
--- a/src/Expression.cpp
+++ b/src/Expression.cpp
@@ -15,14 +15,19 @@
#include "AmpGen/MetaUtils.h"
#include "AmpGen/MsgService.h"
#include "AmpGen/Types.h"
-
+#include "AmpGen/simd/utils.h"
+#include "AmpGen/CompiledExpressionBase.h"
using namespace AmpGen;
+using namespace AmpGen::fcn;
+using namespace std::complex_literals;
-DEFINE_CAST( Constant )
-DEFINE_CAST( Parameter )
-DEFINE_CAST( SubTree )
-DEFINE_CAST( Ternary )
-DEFINE_CAST( Function )
+DEFINE_CAST(Constant )
+DEFINE_CAST(Parameter )
+DEFINE_CAST(SubTree )
+DEFINE_CAST(Ternary )
+DEFINE_CAST(Function )
+DEFINE_CAST(ComplexParameter);
+DEFINE_CAST(LambdaExpression);
Expression::Expression( const std::shared_ptr<IExpression>& expression ) : m_expression( expression ) {}
@@ -49,13 +54,18 @@ bool isZero( const complex_t& A ){
std::string Constant::to_string(const ASTResolver* resolver) const {
auto rounded_string = [](const double& val ){
- std::string str = std::to_string (val);
- str.erase ( str.find_last_not_of('0') + 1, std::string::npos );
- return str;
+ std::string str = mysprintf("%g", val);
+ return str.find(".") != std::string::npos or str.find("e") != std::string::npos ? str : str + ".";
};
- std::string complex_type_string = resolver != nullptr && resolver->enableCuda() ? "ampgen_cuda::complex_t" : typeof<complex_t>() ;
- return std::imag( m_value ) == 0 ? "(" + rounded_string(std::real(m_value)) +")" :
- complex_type_string +"("+rounded_string(std::real(m_value))+","+rounded_string(std::imag(m_value))+")";
+ std::string complex_type = type_string<complex_t>();
+ std::string literalSuffix = "";
+ if( resolver != nullptr && (resolver->enableCuda() || resolver->enableAVX()) )
+ {
+ literalSuffix = "f";
+ complex_type = type_string<complex_v>();
+ }
+ return std::imag(m_value) == 0 ? "(" + rounded_string(std::real(m_value)) +literalSuffix + ")" :
+ complex_type +"("+rounded_string(std::real(m_value))+literalSuffix+","+rounded_string(std::imag(m_value))+literalSuffix+")";
}
Expression simplify_constant_addition( const Constant& constant, const Expression& expression )
@@ -147,16 +157,8 @@ Expression AmpGen::operator/( const Expression& A, const Expression& B )
if( is<Constant>( as_prod.l() ) ) return ( Constant( 1./as_prod.l()() ) * A )/ as_prod.r();
if( is<Constant>( as_prod.r() ) ) return ( Constant( 1./as_prod.r()() ) * A )/ as_prod.l();
}
-// else if( is<Divide>(A) ) {
-// auto A_divide = cast<Divide>(A);
-// if( is<Divide>(B) ){
-// auto B_divide = cast<Divide>(B);
-// return Divide( A_divide.l() * B_divide.r() , ( A_divide.r() * B_divide.l() ) );
-// }
-// return A_divide.l() * B / A_divide.r() ;
-// }
else if( is<Divide>(B) ) return ( A * cast<Divide>(B).r() ) / cast<Divide>(B).l();
- else if( is<Sqrt>(B) ) return ( A * fcn::isqrt( cast<Sqrt>(B).arg() ) );
+// else if( is<Sqrt>(B) ) return ( A / fcn::sqrt( cast<Sqrt>(B).arg() ) );
return Expression( Divide( A, B ) );
}
Expression AmpGen::operator&&( const Expression& A, const Expression& B ) { return Expression( And( A, B ) ); }
@@ -165,12 +167,14 @@ Expression AmpGen::operator==( const Expression& A, const Expression& B ){ retur
Expression AmpGen::operator==( const double& A, const Expression& B ){ return Constant(A) == B ; }
Expression AmpGen::operator==( const Expression& A, const double& B ){ return A == Constant(B) ; }
-Parameter::Parameter( const std::string& name, const double& defaultValue, const bool& resolved,
- const unsigned int& fromArg )
+Expression AmpGen::operator||( const Expression& A, const Expression& B){ return Expression( Or(A,B)) ; }
+Expression AmpGen::operator<=( const Expression& A, const Expression& B ){ return LessThanEqualTo(A,B) ; }
+Expression AmpGen::operator>=( const Expression& A, const Expression& B ){ return GreaterThanEqualTo(A,B) ; }
+
+Parameter::Parameter( const std::string& name, const double& defaultValue, const bool& resolved)
: m_name( name )
, m_defaultValue( defaultValue )
, m_resolved( resolved )
- , m_fromArg( fromArg )
{
}
@@ -187,21 +191,21 @@ Expression AmpGen::operator>( const Expression& A, const Expression& B ) { retur
Expression Expression::operator-() const { return Constant( -1. ) * m_expression; }
-Expression Expression::operator+=( const Expression& other ) const { return *this + other ; }
-Expression Expression::operator-=( const Expression& other ) const { return *this - other ; }
-Expression Expression::operator*=( const Expression& other ) const { return *this * other ; }
-Expression Expression::operator/=( const Expression& other ) const { return *this / other; }
+Expression Expression::operator+=(const Expression& other) { *this = *this + other; return *this; }
+Expression Expression::operator-=(const Expression& other) { *this = *this - other; return *this; }
+Expression Expression::operator*=(const Expression& other) { *this = *this * other; return *this; }
+Expression Expression::operator/=(const Expression& other) { *this = *this / other; return *this; }
std::ostream& AmpGen::operator<<( std::ostream& os, const Expression& expression ) { return os << expression.to_string() ; }
Expression::Expression( const double& value ) : m_expression( std::make_shared<Constant>( value ) ) {}
Expression::Expression( const complex_t& value ) : m_expression( std::make_shared<Constant>( value ) ) {}
Expression::Expression() : m_expression( std::make_shared<Constant>( 0. ) ) {}
-void Expression::resolve( ASTResolver& resolver ) { m_expression->resolve( resolver ); }
+void Expression::resolve( ASTResolver& resolver ) const { m_expression->resolve( resolver ); }
-void Constant::resolve( ASTResolver& resolver ) {}
+void Constant::resolve( ASTResolver& resolver ) const {}
-void Parameter::resolve( ASTResolver& resolver )
+void Parameter::resolve( ASTResolver& resolver ) const
{
if( !m_resolved ) resolver.resolve(*this);
}
@@ -212,10 +216,12 @@ Ternary::Ternary( const Expression& cond, const Expression& v1, const Expression
}
std::string Ternary::to_string(const ASTResolver* resolver) const
{
- return "(" + m_cond.to_string(resolver) + "?" + m_v1.to_string(resolver) + ":" + m_v2.to_string(resolver) + ")";
+ return resolver != nullptr && resolver->enableAVX() ? "select(" + m_cond.to_string(resolver) + ", " +
+ m_v1.to_string(resolver) + ", " + m_v2.to_string(resolver) +")"
+ : "(" + m_cond.to_string(resolver) + "?" + m_v1.to_string(resolver) + ":" + m_v2.to_string(resolver) + ")";
}
-void Ternary::resolve( ASTResolver& resolver )
+void Ternary::resolve( ASTResolver& resolver ) const
{
m_cond.resolve( resolver );
m_v1.resolve( resolver );
@@ -238,17 +244,16 @@ std::string Function::to_string(const ASTResolver* resolver) const {
for( auto& arg : m_args ) rt += arg.to_string(resolver) + ", ";
return rt.substr(0,rt.size()-2) + ")";
}
-void Function::resolve( ASTResolver& resolver ) {}
+void Function::resolve( ASTResolver& resolver ) const {}
std::string SubTree::to_string(const ASTResolver* /*resolver*/) const
{
return "v"+ std::to_string(key());
}
-void SubTree::resolve( ASTResolver& resolver )
+void SubTree::resolve( ASTResolver& resolver ) const
{
resolver.resolve( *this );
- m_expression.resolve( resolver );
}
Expression AmpGen::make_cse( const Expression& A , bool simplify )
@@ -304,7 +309,7 @@ Expression AmpGen::fcn::complex_sqrt( const Expression& expression )
{
if( is<Constant>(expression ) ) return sqrt( expression() );
auto st = make_cse(expression);
- return Ternary( st > 0, Sqrt(st), Constant(0,1)*Sqrt(-st) );
+ return Ternary( st > 0, Sqrt(st), 1i*Sqrt(-st) );
}
Expression AmpGen::fcn::isqrt( const Expression& expression )
@@ -319,3 +324,41 @@ Expression AmpGen::fcn::fpow( const Expression& x, const int& n){
for( int y=0;y<n;++y) rt = rt * x;
return rt;
}
+
+ComplexParameter::ComplexParameter( const Parameter& real, const Parameter& imag )
+ : m_real(real), m_imag(imag) {}
+
+std::string ComplexParameter::to_string(const ASTResolver* resolver) const
+{
+ std::string complex_type = type_string<complex_t>();
+ if( resolver != nullptr && (resolver->enableCuda() || resolver->enableAVX()) ) complex_type = type_string<complex_v>();
+ return complex_type + "(" + m_real.to_string(resolver) + ", " + m_imag.to_string(resolver) +")";
+}
+
+void ComplexParameter::resolve( ASTResolver& resolver ) const
+{
+ m_real.resolve(resolver);
+ m_imag.resolve(resolver);
+}
+
+complex_t ComplexParameter::operator()() const
+{
+ return m_real() + 1i * m_imag();
+}
+
+std::string LambdaExpression::to_string(const ASTResolver* resolver) const
+{
+ return resolver == nullptr ?programatic_name(m_name) : resolver->resolvedParameter(this);
+}
+
+complex_t LambdaExpression::operator()() const
+{
+ return m_function();
+}
+
+void LambdaExpression::resolve(ASTResolver& resolver) const {
+ resolver.resolve(*this);
+}
+
+
+
diff --git a/src/ExpressionParser.cpp b/src/ExpressionParser.cpp
index 172281e7251..1f125fda9c3 100644
--- a/src/ExpressionParser.cpp
+++ b/src/ExpressionParser.cpp
@@ -9,16 +9,26 @@
#include "AmpGen/Utilities.h"
#include "AmpGen/MinuitParameter.h"
#include "AmpGen/ASTResolver.h"
+#include "AmpGen/enum.h"
+#include "AmpGen/NamedParameter.h"
+#include "AmpGen/Tensor.h"
using namespace AmpGen;
+using namespace std::complex_literals;
DEFINE_CAST( MinuitParameterLink )
DEFINE_CAST( ExpressionPack )
+namespace AmpGen
+{
+ complete_enum(coordinateType, cartesian, polar)
+ complete_enum(angType, deg, rad)
+}
+
void ExpressionParser::processBinaryOperators( std::vector<std::string>& opCodes, std::vector<Expression>& expressions )
{
for ( auto& fcn : m_binaryFunctions ) {
- for ( int pos = 0; pos < (int)opCodes.size(); ++pos ) {
+ for ( int pos = 0; pos < int(opCodes.size()); ++pos ) {
if ( opCodes[pos] != fcn.first ) continue;
expressions[pos] = fcn.second( expressions[pos], expressions[pos + 1] );
expressions.erase( expressions.begin() + pos + 1 );
@@ -30,7 +40,7 @@ void ExpressionParser::processBinaryOperators( std::vector<std::string>& opCodes
void ExpressionParser::processUnaryOperators( std::vector<std::string>& opCodes, std::vector<Expression>& expressions )
{
- for ( int pos = 0; pos < (int)opCodes.size(); ++pos ) {
+ for ( int pos = 0; pos < int(opCodes.size()); ++pos ) {
auto fcn = m_unaryFunctions.find( opCodes[pos] );
DEBUG( " op = " << opCodes[pos] << " pos = " << pos );
if ( fcn == m_unaryFunctions.end() ) continue;
@@ -40,40 +50,99 @@ void ExpressionParser::processUnaryOperators( std::vector<std::string>& opCodes,
}
}
-Expression ExpressionParser::parseTokens( const std::vector<std::string>& tokens )
+using iterator = std::vector<std::string>::const_iterator;
+
+template <char open= '(', char close = ')' > iterator findMatchingBracket(iterator begin, iterator end )
{
- int nOpenedBrackets = 0;
- std::vector<std::vector<std::string>> expressions;
- expressions.push_back( std::vector<std::string>() );
- for ( auto iToken = tokens.begin(); iToken != tokens.end(); ++iToken ) {
- auto& token = *iToken;
- expressions.rbegin()->push_back( token );
- if ( token == "(" ) nOpenedBrackets++;
- if ( token == ")" ) nOpenedBrackets--;
- if ( nOpenedBrackets == 0 && iToken != tokens.end() - 1 ) expressions.push_back( std::vector<std::string>() );
+ int openedBrackets = 1;
+ if( begin + 1 >= end ) return end;
+ for( auto it = begin+1; it != end; ++it )
+ {
+ openedBrackets += ( it->at(0) == open) -( it->at(0) == close );
+ if( openedBrackets == 0 ) return it;
}
- for ( auto& eC : expressions ) {
- if ( eC.size() > 2 && *eC.begin() == "(" && *eC.rbegin() == ")" ) {
- eC.erase( eC.end() - 1 );
- eC.erase( eC.begin() );
+ for( auto it = begin; it != end; ++it )
+ {
+ std::cout << *it << " ";
+ }
+ std::cout << std::endl;
+ FATAL("Unmatched brace in expression, " << open << " " << close);
+ return end;
+}
+
+/// divides strings by a delimiter, allowing for bracketing rules
+std::vector< std::pair<iterator, iterator> > split_it( iterator begin, iterator end, const std::string& delimiter)
+{
+ std::vector<std::pair<iterator, iterator>> rt;
+ rt.emplace_back(begin, begin);
+ int b1l = 0;
+ int b2l = 0;
+ for( auto it = begin; it != end-1; ++it )
+ {
+ b1l += ( it->at(0) == '(') - (it->at(0) == ')');
+ b2l += ( it->at(0) == '{') - (it->at(0) == '}');
+ if( *it == delimiter && b1l == 0 && b2l == 0 )
+ {
+ rt.rbegin()->second = it;
+ // INFO( *it << " " << std::distance( begin, rt.rbegin()->first) << " " << std::distance( begin, rt.rbegin()->second) );
+ rt.emplace_back( it+1, it+1);
}
}
- if ( expressions.size() == 1 ) return processEndPoint( expressions[0][0] );
+ rt.rbegin()->second = end;
+ return rt;
+}
+
+std::string merge( iterator begin, iterator end)
+{
+ std::string total = "";
+ for( auto it = begin; it != end; ++it ) total += *it + " ";
+ return total;
+}
+Expression ExpressionParser::parseTokens(std::vector<std::string>::const_iterator begin,
+ std::vector<std::string>::const_iterator end,
+ const MinuitParameterSet* mps )
+{
std::vector<std::string> opCodes;
- std::vector<Expression> parsedExpressions;
- for ( size_t pos = 0; pos < expressions.size(); pos++ ) {
- if ( pos % 2 == expressions.size() % 2 )
- opCodes.push_back( expressions[pos][0] );
- else
- parsedExpressions.push_back( parseTokens( expressions[pos] ) );
+ std::vector<Expression> expressions;
+ for( auto it = begin; it != end; ++it )
+ {
+ if( it->at(0) == '(' ){
+ auto begin_2 = it;
+ auto end_2 = findMatchingBracket<'(',')'>(it, end);
+ expressions.emplace_back( parseTokens(begin_2+1, end_2, mps) );
+ it = end_2;
+ }
+ else if ( it->at(0) == '{' )
+ {
+ auto begin_2 = it;
+ auto end_2 = findMatchingBracket<'{','}'>(it, end);
+ auto divided = split_it( begin_2+1, end_2, ",");
+ Tensor v( std::vector<unsigned>{static_cast<unsigned>(divided.size())} );
+ for( unsigned int i = 0 ; i != divided.size(); ++i )
+ {
+ v[i] = parseTokens( divided[i].first, divided[i].second, mps);
+ }
+ DEBUG( "Adding tensor: " << v.to_string() );
+ expressions.emplace_back(TensorExpression(v));
+ it = end_2;
+ }
+ else {
+ auto f = std::find_if(m_binaryFunctions.begin(), m_binaryFunctions.end(), [it](auto& jt){ return jt.first == *it; } );
+ if( f != m_binaryFunctions.end() || m_unaryFunctions.count(*it) ) opCodes.push_back(*it);
+ else expressions.push_back( processEndPoint( *it , mps ) );
+ }
}
- processUnaryOperators( opCodes, parsedExpressions );
- processBinaryOperators( opCodes, parsedExpressions );
- return parsedExpressions[0];
+ DEBUG( "nExpressions = " << expressions.size() << " nOpCodes = " << opCodes.size() << " " << vectorToString( opCodes, " " ) );
+ processUnaryOperators( opCodes, expressions );
+ processBinaryOperators( opCodes, expressions );
+ if( expressions.size() != 1 ){
+ ERROR("Could not process expression: n = " << expressions.size() << " " << merge(begin, end) );
+ }
+ return expressions[0];
}
-ExpressionParser::ExpressionParser() : m_mps( nullptr )
+ExpressionParser::ExpressionParser()
{
add_unary<Sin>( "sin" ); /// "function" operator ordering is irrelevant
add_unary<Cos>( "cos" );
@@ -86,62 +155,99 @@ ExpressionParser::ExpressionParser() : m_mps( nullptr )
add_unary<Sqrt>( "sqrt" );
add_unary<Exp>( "exp" );
add_unary<Log>( "log" );
+ add_unary<Real>("real");
+ add_unary<Imag>("imag");
+ add_unary<Abs>("abs");
+
+ add_binary( "^" , [](auto& A, auto& B ) { return fcn::pow(A,B); } );
+ add_binary( "/" , [](auto& A, auto& B ) { return A / B; } );
+ add_binary( "*" , [](auto& A, auto& B ) { return A * B; } );
+ add_binary( "-" , [](auto& A, auto& B ) { return A - B; } );
+ add_binary( "+" , [](auto& A, auto& B ) { return A + B; } );
+ add_binary( ">" , [](auto& A, auto& B ) { return A > B; } );
+ add_binary( "<" , [](auto& A, auto& B ) { return A < B; } );
+ add_binary( "&&", [](auto& A, auto& B ) { return A && B; } );
+ add_binary( "," , [](auto& A, auto& B ) { return ExpressionPack( A, B ); } );
+
+ coordinateType coord = NamedParameter<coordinateType>("CouplingConstant::Coordinates", coordinateType::cartesian);
+ angType degOrRad = NamedParameter<angType>("CouplingConstant::AngularUnits", angType::rad);
+ m_isCartesian = true;
+ if( coord == coordinateType::polar ) m_isCartesian = false;
+ else if ( coord != coordinateType::cartesian){
+ FATAL("Coordinates for coupling constants must be either cartesian or polar");
+ }
+ if ( degOrRad == angType::deg) m_sf = M_PI / 180;
+ else if ( degOrRad != angType::rad){
+ FATAL("CouplingConstant::AngularUnits must be either rad or deg");
+ }
- add_binary( "/", []( auto& A, auto& B ) { return A / B; } ); /// operator ordering here matters!
- add_binary( "*", []( auto& A, auto& B ) { return A * B; } );
- add_binary( "+", []( auto& A, auto& B ) { return A + B; } );
- add_binary( "-", []( auto& A, auto& B ) { return A - B; } );
- add_binary( ">", []( auto& A, auto& B ) { return A > B; } );
- add_binary( "<", []( auto& A, auto& B ) { return A < B; } );
- add_binary( "&&", []( auto& A, auto& B ) { return A && B; } );
- add_binary( ",", []( auto& A, auto& B ) { return ExpressionPack( A, B ); } );
}
-Expression ExpressionParser::Parse( const std::string& str ) { return getMe()->parseTokens( split( str, ' ' ) ); }
+Expression ExpressionParser::parse(
+ std::vector<std::string>::const_iterator begin,
+ std::vector<std::string>::const_iterator end,
+ const MinuitParameterSet* mps ) {
+ return getMe()->parseTokens(begin, end, mps );
+}
+Expression ExpressionParser::parse(
+ const std::string& expr,
+ const MinuitParameterSet* mps ) {
+ auto tokens = split( expr , ' ' );
+ return getMe()->parseTokens(tokens.cbegin(), tokens.cend() , mps );
+}
+
ExpressionParser* ExpressionParser::gExpressionParser = nullptr;
-Expression ExpressionParser::processEndPoint( const std::string& name )
+Expression ExpressionParser::processEndPoint( const std::string& name, const MinuitParameterSet* mps )
{
bool status = true;
double value = lexical_cast<double>( name, status );
- if ( status == true ) return Constant( value );
- if ( name == "PI" ) return Constant( M_PI );
- if ( name == "pi" ) return Constant( M_PI );
- if ( name == "e" ) return Constant( std::exp(1) );
- if ( name == "I" ) return Constant( 0, 1 );
- if ( name == "i" ) return Constant( 0, 1 );
-
- if ( m_mps != nullptr ) {
- auto map = m_mps->map();
- auto it = map.find( name );
- if ( it != map.end() )
- return MinuitParameterLink( it->second );
- else {
- WARNING( "Token not understood: " << name << " [map size = " << map.size() << "]" );
- for ( auto& ip : map ) INFO( "map entry = " << ip.first );
+ if ( status == true ) return value;
+ if ( name == "PI" || name == "pi" || name == "M_PI" ) return M_PI;
+ if ( name == "e" ) return std::exp(1);
+ if ( name == "I" || name == "i" ) return complex_t( 0, 1 );
+ if ( mps != nullptr ) {
+ auto it = mps->find(name);
+ if ( it != nullptr ) return MinuitParameterLink( it );
+ else if ( mps->find(name+"_Re") != nullptr && mps->find(name+"_Im") != nullptr ) {
+ if( m_isCartesian ) return MinuitParameterLink( mps->find(name+"_Re") ) + 1i * MinuitParameterLink( mps->find(name+"_Im") );
+ else return MinuitParameterLink( mps->find(name+"_Re") ) * fcn::exp( m_sf * 1i *MinuitParameterLink( mps->find(name+"_Im") ) );
+ }
+ else {
+ WARNING( "Token not understood: " << name << " [map size = " << mps->size() << "]" );
}
}
return Parameter( name, 0, true );
}
MinuitParameterLink::MinuitParameterLink( MinuitParameter* param ) : m_parameter( param ) {}
+
std::string MinuitParameterLink::to_string(const ASTResolver* resolver) const
{
- return resolver == nullptr ? m_parameter->name() : resolver->resolvedParameter(this);
+ if( resolver == nullptr ) return m_parameter->name();
+ if( resolver->enableCompileConstants() && m_parameter != nullptr && m_parameter->flag () == Flag::CompileTimeConstant )
+ return std::to_string( m_parameter->mean() );
+ return resolver->resolvedParameter(this);
}
std::string MinuitParameterLink::name() const {
return m_parameter->name();
}
-void MinuitParameterLink::resolve( ASTResolver& resolver )
+void MinuitParameterLink::resolve( ASTResolver& resolver ) const
{
- resolver.resolve(*this);
+ if( m_parameter->flag() != Flag::CompileTimeConstant ) resolver.resolve(*this);
}
-complex_t MinuitParameterLink::operator()() const {
+complex_t MinuitParameterLink::operator()() const
+{
if( m_parameter == nullptr ) ERROR("Parameter does not have end-point");
- return m_parameter->mean(); }
+ return m_parameter->mean();
+}
+
+const MinuitParameter& MinuitParameterLink::param() const {
+ return *m_parameter ;
+}
ExpressionPack::ExpressionPack( const Expression& A, const Expression& B )
{
@@ -156,6 +262,7 @@ ExpressionPack::ExpressionPack( const Expression& A, const Expression& B )
} else
m_expressions.push_back( B );
}
+
std::string ExpressionPack::to_string(const ASTResolver* resolver) const
{
std::string rt = "";
@@ -165,7 +272,7 @@ std::string ExpressionPack::to_string(const ASTResolver* resolver) const
return rt.substr( 0, rt.length() - 2 );
}
-void ExpressionPack::resolve( ASTResolver& resolver )
+void ExpressionPack::resolve( ASTResolver& resolver ) const
{
for ( auto& expr : m_expressions ) expr.resolve( resolver );
}
diff --git a/src/FastDT.cpp b/src/FastDT.cpp
index f5dc428b2a8..9d2a068917c 100644
--- a/src/FastDT.cpp
+++ b/src/FastDT.cpp
@@ -4,6 +4,10 @@
using namespace AmpGen;
+FastDT::FastDT( const std::string& fname ){
+ //std::ifstream s(fname);
+}
+
int FastDT::findNode( const double* event )
{
int address = m_nodes.size()-1;
@@ -16,9 +20,6 @@ int FastDT::findNode( const double* event )
return m_nodes[address].left;
}
-FastDT::FastDT( const std::string& fname ){
- std::ifstream s(fname);
-}
double nnVariance(std::vector<double*>& evts, const size_t& index)
{
diff --git a/src/FitFraction.cpp b/src/FitFraction.cpp
index 8ad62890824..f064e2d7750 100644
--- a/src/FitFraction.cpp
+++ b/src/FitFraction.cpp
@@ -11,19 +11,14 @@
using namespace AmpGen;
-FitFraction::FitFraction( const std::string& line, const EventType& evtType )
+FitFraction::FitFraction( const std::string& line )
{
auto tokens = split( line, ' ' );
m_name = tokens[1];
m_value = stod( tokens[2] );
m_error = stod( tokens[3] );
- if ( evtType.size() != 0 ) {
- std::vector<std::string> finalStates = evtType.finalStates();
- }
}
-std::shared_ptr<Particle> FitFraction::particle() const { return std::make_shared<Particle>( m_name ); }
-
FitFraction::FitFraction( const std::string& name, const double& frac, const double& err )
: m_name( name ), m_value( frac ), m_error( err )
{
diff --git a/src/FitResult.cpp b/src/FitResult.cpp
index dfd54c36dc0..1e30bed851e 100644
--- a/src/FitResult.cpp
+++ b/src/FitResult.cpp
@@ -23,58 +23,78 @@
using namespace AmpGen;
-FitResult::FitResult( const std::string& filename, const EventType& evtType )
+FitResult::FitResult() = default;
+
+FitResult::FitResult( const FitResult& other )
+ : m_mps( other.mps() )
+ , m_chi2( other.chi2() )
+ , m_LL( other.LL() )
+ , m_nBins( other.nBins() )
+ , m_nParam( other.nParam() )
+ , m_status( other.status() )
+ , m_observables( other.observables() )
+ , m_fitFractions( other.fitFractions() )
+ , m_covarianceMatrix(other.cov())
{
- m_eventType = evtType;
- m_fitted = readFile( filename );
}
-std::string FitResult::getLastLine( std::ifstream& in ) const
+FitResult::FitResult( const std::string& filename ) :
+ m_mps( new MinuitParameterSet() )
{
- std::string line;
- while ( in >> std::ws && std::getline( in, line ) )
- ;
- return line;
+ m_fitted = readFile( filename );
}
-bool FitResult::readFile( const std::string& fname )
+FitResult::FitResult( const Minimiser& mini )
+ : m_mps ( mini.parSet() )
+ , m_LL ( mini.FCN() )
+ , m_nParam( 0 )
+ , m_status( mini.status() )
+ , m_covarianceMatrix( mini.covMatrixFull() ) {
+ for (size_t i = 0; i < m_mps->size(); ++i ) {
+ if ( m_mps->at(i)->isFree() ) m_nParam++;
+ m_covMapping[ m_mps->at(i)->name() ] = i;
+ }
+}
+
+FitResult::FitResult( MinuitParameterSet& mps, const TMatrixD& covMini ) : m_mps(&mps)
{
- std::ifstream CHECK( fname );
- if ( !CHECK.is_open() || CHECK.peek() == std::ifstream::traits_type::eof() ) {
- return false;
+ if ( int( mps.size() ) != covMini.GetNcols() ) {
+ ERROR( "Minuit parameter set size does not match covariance matrix size!" );
}
- if ( getLastLine( CHECK ) != "End Log" ) {
- ERROR( "File not properly close " << fname );
- return false;
+ m_covarianceMatrix.ResizeTo( covMini.GetNcols(), covMini.GetNrows() );
+ m_covarianceMatrix = covMini;
+ for (size_t i = 0; i < m_mps->size(); ++i ) {
+ if ( m_mps->at(i)->isFree()) m_nParam++;
}
- CHECK.close();
+}
- // auto lines = vectorFromFile( fname );
+bool FitResult::readFile( const std::string& fname )
+{
+ std::ifstream checkIsClosed( fname );
+ if ( !checkIsClosed.is_open()
+ || checkIsClosed.peek() == std::ifstream::traits_type::eof() ) return false;
+ checkIsClosed.close();
+ auto lines = vectorFromFile(fname);
+ if( *lines.rbegin() != "End Log" ){
+ ERROR("File not properly closed: " << *lines.rbegin() );
+ return false;
+ }
std::vector<std::string> parameterLines;
-
- processFile( fname, [this, ¶meterLines]( auto& line ) {
+ for( auto& line : lines ){
const std::string name = split( line, ' ' )[0];
- if ( name == "Parameter" )
- parameterLines.push_back( line );
- else if ( name == "FitQuality" )
- this->setFitQuality( line );
- else if ( name == "FitFraction" )
- this->m_fitFractions.emplace_back( line, m_eventType );
- else if ( name == "Observable" )
- this->addToObservables( line );
- } );
-
- unsigned int nParameters = parameterLines.size();
-
+ if ( name == "Parameter" ) parameterLines.push_back( line );
+ else if ( name == "FitQuality" ) this->setFitQuality( line );
+ else if ( name == "FitFraction" ) this->m_fitFractions.emplace_back(line);
+ else if ( name == "Observable" ) this->addToObservables( line );
+ }
+ size_t nParameters = parameterLines.size();
m_covarianceMatrix.ResizeTo( parameterLines.size(), parameterLines.size() );
- m_mps = std::make_shared<MinuitParameterSet>();
- for ( unsigned int i = 0; i < nParameters; ++i ) {
+ for (size_t i = 0; i < nParameters; ++i ) {
auto tokens = split( parameterLines[i], ' ' );
m_covMapping[tokens[1]] = i;
- m_mps->add( new MinuitParameter( tokens[1], MinuitParameter::Flag(stoi( tokens[2] ) ), stod( tokens[3] ), stod( tokens[4] ), 0, 0 ) );
- for ( unsigned int j = 0; j < nParameters; ++j ) m_covarianceMatrix( i, j ) = stod( tokens[5 + j] );
+ m_mps->add( new MinuitParameter( tokens[1], parse<Flag>(tokens[2]), stod( tokens[3] ), stod( tokens[4] ), 0, 0 ) );
+ for (size_t j = 0; j < nParameters; ++j ) m_covarianceMatrix( i, j ) = stod( tokens[5 + j] );
}
-
return true;
}
@@ -83,8 +103,8 @@ void FitResult::setFitQuality( const std::string& line )
auto tokens = split( line, ' ' );
bool status=true;
if( tokens.size() != 6 ){
- WARNING("Cannot pass FitQuality line: " << line );
- return;
+ WARNING("Cannot pass FitQuality line: " << line );
+ return;
}
m_chi2 = lexical_cast<double>( tokens[1] , status );
m_nBins = lexical_cast<double>( tokens[2] , status );
@@ -92,6 +112,7 @@ void FitResult::setFitQuality( const std::string& line )
m_LL = lexical_cast<double>( tokens[4] , status );
m_status = lexical_cast<int> ( tokens[5] , status );
}
+
void FitResult::addToObservables( const std::string& line )
{
auto tokens = split( line, ' ' );
@@ -104,55 +125,22 @@ void FitResult::writeToFile( const std::string& fname )
{
std::ofstream outlog;
outlog.open( fname );
-
- for ( int i = 0; i < m_covarianceMatrix.GetNrows(); ++i ) {
- auto param = m_mps->getParPtr( i );
+ for (size_t i = 0; i < (size_t)m_covarianceMatrix.GetNrows(); ++i ) {
+ auto param = m_mps->at(i);
outlog << "Parameter"
- << " " << param->name() << " " << param->iFixInit() << " " << param->mean() << " "
- << m_mps->getParPtr( i )->err() << " ";
- for ( int j = 0; j < m_covarianceMatrix.GetNcols(); ++j ) outlog << m_covarianceMatrix[i][j] << " ";
+ << " " << param->name() << " " << to_string<Flag>(param->flag()) << " " << param->mean() << " "
+ << ( param->isFree() ? m_mps->at(i)->err() : 0 ) << " ";
+ for (size_t j = 0; j < (size_t)m_covarianceMatrix.GetNcols(); ++j ) outlog << m_covarianceMatrix[i][j] << " ";
outlog << std::endl;
}
outlog << std::setprecision( 8 );
- outlog << "FitQuality " << m_chi2 << " " << m_nBins << " " << m_nParam << " " << m_LL << " " << m_status << "\n";
- for ( auto& p : m_fitFractions ) {
- outlog << "FitFraction " << p.name() << " " << p.val() << " " << p.err() << "\n";
- }
- for ( auto& ob : m_observables ) {
- outlog << "Observable " << ob.first << " " << ob.second << "\n";
- }
+ outlog << "FitQuality " << m_chi2 << " " << m_nBins << " " << m_nParam << " " << m_LL << " " << m_status << "\n";
+ for ( auto& f : m_fitFractions ) outlog << "FitFraction " << f.name() << " " << f.val() << " " << f.err() << "\n";
+ for ( auto& o : m_observables ) outlog << "Observable " << o.first << " " << o.second << "\n";
outlog << "End Log\n";
outlog.close();
}
-FitResult::FitResult( const Minimiser& mini )
-{
- m_mps = std::make_shared<MinuitParameterSet>( *mini.parSet() );
- m_LL = mini.FCN();
- auto M = mini.covMatrixFull();
- m_covarianceMatrix.ResizeTo( M.GetNcols(), M.GetNrows() );
- m_covarianceMatrix = M;
- m_status = mini.status();
- m_nParam = 0;
- for ( unsigned int i = 0; i < m_mps->size(); ++i ) {
- if ( m_mps->getParPtr( i )->iFixInit() == 0 ) m_nParam++;
- m_covMapping[ m_mps->getParPtr(i)->name() ] = i;
- }
-}
-
-FitResult::FitResult( const MinuitParameterSet& mps, const TMatrixD& covMini ) : FitResult()
-{
- m_mps = std::make_shared<MinuitParameterSet>( mps );
- if ( int( mps.size() ) != covMini.GetNcols() ) {
- ERROR( "Minuit parameter set size does not match covariance matrix size!" );
- }
- m_covarianceMatrix.ResizeTo( covMini.GetNcols(), covMini.GetNrows() );
- m_covarianceMatrix = covMini;
- for ( unsigned int i = 0; i < m_mps->size(); ++i ) {
- if ( m_mps->getParPtr( i )->iFixInit() == 0 ) m_nParam++;
- }
-}
-
void FitResult::print() const
{
INFO( "Chi2 per bin = " << m_chi2 / m_nBins );
@@ -161,56 +149,33 @@ void FitResult::print() const
INFO( "Fit Status = " << m_status );
}
-FitResult::FitResult( const FitResult& other )
- : m_chi2( other.chi2() )
- , m_LL( other.LL() )
- , m_nBins( other.nBins() )
- , m_nParam( other.nParam() )
- , m_status( other.status() )
- , m_eventType( other.eventType() )
- , m_observables( other.observables() )
- , m_fitFractions( other.fitFractions() )
- , m_mps( std::make_shared<MinuitParameterSet>( *other.mps() ) )
-{
- m_covarianceMatrix.ResizeTo( other.cov().GetNrows(), other.cov().GetNcols() );
- m_covarianceMatrix = other.cov();
-}
-
-std::vector<MinuitParameter*> FitResult::getParameters() const
+std::vector<MinuitParameter*> FitResult::parameters() const
{
- std::vector<MinuitParameter*> params;
- for ( auto& param : *m_mps ) params.push_back( param );
+ std::vector<MinuitParameter*> params( m_mps->size() );
+ std::copy( m_mps->begin(), m_mps->end(), params.begin() );
return params;
}
-std::vector<MinuitParameter*> FitResult::getFloating( const bool& extended ) const
+std::vector<MinuitParameter*> FitResult::floating( const bool& extended ) const
{
std::vector<MinuitParameter*> floating;
for ( auto& param : *m_mps ) {
- if ( ( param->iFixInit() == 0 || extended ) && param->err() > 1e-6 ) floating.push_back( param );
- }
- /*
- if( extended ){
- DEBUG("Got extended error propagator:");
- for( auto& param : floating ){
- INFO( param->name() );
- }
+ if ( ( param->isFree() || extended ) && param->err() > 1e-6 ) floating.push_back( param );
}
- */
return floating;
}
TMatrixD FitResult::getReducedCovariance( const bool& extended ) const
{
std::vector<unsigned int> floating_indices;
- for ( unsigned int i = 0; i < m_mps->size(); ++i ) {
- auto param = m_mps->getParPtr( i );
- if ( ( param->iFixInit() == 0 || extended ) && param->err() > 1e-6 ) floating_indices.push_back( i );
+ for (size_t i = 0; i < m_mps->size(); ++i ) {
+ auto param = m_mps->at(i);
+ if ( ( param->isFree() || extended ) && param->err() > 1e-6 ) floating_indices.push_back( i );
}
TMatrixD reducedCov( floating_indices.size(), floating_indices.size() );
if ( int( floating_indices.size() ) > m_covarianceMatrix.GetNrows() ) {
ERROR( "Looking for more floating indices than real indices: " << m_covarianceMatrix.GetNrows() << " "
- << floating_indices.size() );
+ << floating_indices.size() );
return reducedCov;
}
for ( unsigned int i = 0; i < floating_indices.size(); ++i ) {
@@ -223,7 +188,7 @@ TMatrixD FitResult::getReducedCovariance( const bool& extended ) const
LinearErrorPropagator FitResult::getErrorPropagator( const bool& extended ) const
{
- return LinearErrorPropagator( getReducedCovariance( extended ), getFloating( extended ) );
+ return LinearErrorPropagator( getReducedCovariance( extended ), floating( extended ) );
}
void FitResult::addChi2( const double& chi2, const double& nBins )
@@ -232,4 +197,39 @@ void FitResult::addChi2( const double& chi2, const double& nBins )
m_nBins = nBins;
}
-void FitResult::addFractions( const std::vector<FitFraction>& fractions ) { m_fitFractions = fractions; }
+void FitResult::addFractions( const std::vector<FitFraction>& fractions )
+{
+ m_fitFractions = fractions;
+}
+
+double FitResult::chi2() const { return m_chi2; }
+double FitResult::LL() const { return m_LL; }
+int FitResult::status() const { return m_status; }
+int FitResult::nParam() const { return m_nParam; }
+int FitResult::nBins() const { return m_nBins; }
+
+std::map<std::string, double> FitResult::observables() const { return m_observables; }
+MinuitParameterSet* FitResult::mps() const { return m_mps; }
+
+double FitResult::dof() const { return m_nBins - m_nParam - 1; }
+std::vector<FitFraction> FitResult::fitFractions() const { return m_fitFractions; }
+TMatrixD FitResult::cov() const { return m_covarianceMatrix; }
+double FitResult::cov( const size_t& x, const size_t& y ) const { return m_covarianceMatrix( x, y ); }
+double FitResult::cov( const std::string& x, const std::string& y ) const { return m_covarianceMatrix( m_covMapping.at(x), m_covMapping.at(y) ); }
+
+void FitResult::addFraction( const std::string& name, const double& frac, const double& err )
+{
+ m_fitFractions.emplace_back( name, frac, err );
+}
+void FitResult::clearFitFractions() { m_fitFractions.clear(); }
+void FitResult::setCov( const size_t& x, const size_t& y, const double& F ) { m_covarianceMatrix( x, y ) = F; }
+double FitResult::correlation( const std::string& x, const std::string& y ) const
+{
+ auto tx = m_covMapping.find(x);
+ auto ty = m_covMapping.find(y);
+ if( tx == m_covMapping.end() || ty == m_covMapping.end() ){
+ ERROR("Parameter not found: " << x << ", " << y );
+ return -1;
+ }
+ return cov(tx->second, ty->second)/sqrt(cov(tx->second, tx->second)*cov(ty->second, ty->second));
+}
diff --git a/src/Generator.cpp b/src/Generator.cpp
index a18115b9b1b..30d30eb4f47 100644
--- a/src/Generator.cpp
+++ b/src/Generator.cpp
@@ -8,9 +8,10 @@ extern "C" void AmpGen::PyGenerate(const char* eventType, double* out, const uns
EventType type( split( std::string(eventType),' ') );
INFO( type << " generating: " );
auto phsp = Generator<PhaseSpace>(type, new TRandom3() );
- auto events = phsp.generate( size,0 );
+ auto events = phsp.generate( size );
for( size_t i = 0 ; i < events.size(); ++i ){
for( size_t j = 0 ; j < events[i].size(); ++j)
out[events[i].size() * i + j] = events[i][j];
}
}
+
diff --git a/src/IncoherentSum.cpp b/src/IncoherentSum.cpp
index 1df5e034969..2a75ae3ca1f 100644
--- a/src/IncoherentSum.cpp
+++ b/src/IncoherentSum.cpp
@@ -39,30 +39,24 @@ double IncoherentSum::norm( const Bilinears& norms ) const
void IncoherentSum::prepare()
{
- if ( m_weightParam != nullptr ) m_weight = m_weightParam->mean();
-
+ /*
if ( m_isConstant && m_prepareCalls != 0 ) return;
-
transferParameters();
for ( auto& mE : m_matrixElements ) {
- auto& pdf = mE.pdf;
- pdf.prepare();
- if ( m_prepareCalls != 0 && !pdf.hasExternalsChanged() ) continue;
-
+ auto& amp = mE.amp;
+ amp.prepare();
+ if ( m_prepareCalls != 0 && !amp.hasExternalsChanged() ) continue;
if ( m_prepareCalls == 0 && m_events != nullptr )
- mE.addressData = m_events->registerExpression( pdf );
-
- if ( m_events != nullptr ) m_events->updateCache( pdf, mE.addressData );
- if ( m_prepareCalls == 0 && m_integrator.isReady() ){
- m_integrator.prepareExpression( pdf );
- }
- INFO( mE.addressData << " " << m_events->at(0).getCache(mE.addressData) );
- pdf.resetExternals();
+ mE.addressData = m_events->registerExpression( amp );
+// if ( m_events != nullptr ) m_events->updateCache( amp, mE.addressData );
+ // if ( m_prepareCalls == 0 && m_integrator.isReady() ){
+ // m_integrator.prepareExpression( amp );
+ // }
+ amp.resetExternals();
}
if( m_prepareCalls == 0 ){
for( size_t i = 0 ; i < m_matrixElements.size(); ++i ){
- auto& mE = m_matrixElements[i];
- auto index = m_integrator.events().getCacheIndex( mE.pdf );
+ auto index = m_integrator.events().getCacheIndex( m_matrixElements[i].amp );
m_integrator.queueIntegral( index, index, i, 0, &m_normalisations, false);
}
m_integrator.flush();
@@ -70,6 +64,7 @@ void IncoherentSum::prepare()
m_prepareCalls++;
m_norm = norm();
INFO( "norm = " << m_norm << " weight = " << m_weight );
+ */
}
std::vector<FitFraction> IncoherentSum::fitFractions( const LinearErrorPropagator& linProp )
@@ -83,17 +78,17 @@ std::vector<FitFraction> IncoherentSum::fitFractions( const LinearErrorPropagato
for ( auto& p : outputFractions ) INFO(p);
return outputFractions;
}
-double IncoherentSum::getVal( const Event& evt ) const
-{
+
+double IncoherentSum::prob( const Event& evt ) const
+{
+ return m_weight * prob_unnormalised(evt) / m_norm;
+}
+
+double IncoherentSum::prob_unnormalised( const Event& evt ) const
+{
double value( 0. );
- for ( auto& mE : m_matrixElements ) {
- value += std::norm( mE.coefficient * evt.getCache( mE.addressData ) );
- }
+ //for ( auto& mE : m_matrixElements ) {
+ // value += std::norm( mE.coefficient * m_events->cache(evt.index(), mE.addressData ) );
+ //}
return value;
}
-double IncoherentSum::operator()( const Event& evt ) const { return prob( evt ); }
-double IncoherentSum::prob( const Event& evt ) const
-{
- return m_weight * getVal( evt ) / m_norm;
-}
-double IncoherentSum::prob_unnormalised( const Event& evt ) const { return getVal( evt ); }
diff --git a/src/Integrator.cpp b/src/Integrator.cpp
index e51f3d6639f..3736ef37a5d 100644
--- a/src/Integrator.cpp
+++ b/src/Integrator.cpp
@@ -33,3 +33,52 @@ void Bilinears::resize( const size_t& r, const size_t& c)
calculate[i] = true;
}
}
+
+void Integrator::integrateBlock()
+{
+ #pragma omp parallel for
+ for ( size_t roll = 0; roll < m_counter; ++roll ) {
+ float_v re( 0.f );
+ float_v im( 0.f );
+ auto b1 = m_cache.data() + m_integrals[roll].i * m_cache.nBlocks();
+ auto b2 = m_cache.data() + m_integrals[roll].j * m_cache.nBlocks();
+ for ( size_t i = 0; i < m_cache.nBlocks(); ++i ) {
+ auto c = b1[i] * conj(b2[i]);
+ #if ENABLE_AVX
+ re = fmadd( m_weight[i], real(c), re );
+ im = fmadd( m_weight[i], imag(c), im );
+ #else
+ re = re + m_weight[i] * real(c);
+ im = im + m_weight[i] * imag(c);
+ #endif
+ }
+ *m_integrals[roll].result = complex_t(utils::sum_elements( complex_v(re, im) )) / m_norm;
+ }
+ m_counter = 0;
+}
+
+bool Integrator::isReady() const { return m_events != nullptr; }
+
+void Integrator::queueIntegral(complex_t* result, const unsigned& i, const unsigned& j)
+{
+ m_integrals[m_counter++] = QueuedIntegral(result, i, j );
+ if( m_counter == N ) integrateBlock();
+}
+
+void Integrator::flush()
+{
+ if ( m_counter == 0 ) return;
+ integrateBlock();
+}
+
+#if ENABLE_AVX2
+template <> complex_t Integrator::get( const unsigned& index, const unsigned& evt ) const
+{
+ return utils::at( m_cache( evt/utils::size<float_v>::value, index), evt % utils::size<float_v>::value );
+}
+#endif
+
+template <> complex_v Integrator::get( const unsigned& index, const unsigned& evt ) const
+{
+ return m_cache(evt, index);
+}
diff --git a/src/Kinematics.cpp b/src/Kinematics.cpp
index ba9239d1150..8446b000063 100644
--- a/src/Kinematics.cpp
+++ b/src/Kinematics.cpp
@@ -11,7 +11,7 @@
using namespace AmpGen;
-MomentumTransfer::MomentumTransfer( const std::vector<size_t>& _p1, const std::vector<size_t>& _p2 )
+MomentumTransfer::MomentumTransfer( const std::vector<unsigned>& _p1, const std::vector<unsigned>& _p2 )
: p1( _p1 ), p2( _p2 )
{
for ( auto& p : p1 ) s.push_back( p );
@@ -30,13 +30,13 @@ double MomentumTransfer::Q2( const double& s, const double& s1, const double& s2
return s / 4. - ( s1 + s2 ) / 2. + ( s1 - s2 ) * ( s1 - s2 ) / ( 4 * s );
}
-HelicityCosine::HelicityCosine( const std::vector<size_t>& p1, const std::vector<size_t>& p2,
- const std::vector<size_t>& pR )
+HelicityCosine::HelicityCosine( const std::vector<unsigned>& p1, const std::vector<unsigned>& p2,
+ const std::vector<unsigned>& pR )
: _i( p1 ), _j( p2 ), _pR( pR )
{
}
-HelicityCosine::HelicityCosine( const size_t& i, const size_t& j, const std::vector<size_t>& pR )
+HelicityCosine::HelicityCosine( const unsigned& i, const unsigned& j, const std::vector<unsigned>& pR )
: _i( 1, i ), _j( 1, j ), _pR( pR )
{
}
@@ -50,12 +50,12 @@ double HelicityCosine::operator()( const Event& evt ) const
return dotProduct(pi, pj, PR) / sqrt( dotProduct( pi, pi, PR ) * dotProduct( pj, pj, PR ) );
}
-TLorentzVector AmpGen::pFromEvent( const Event& evt, const size_t& ref )
+TLorentzVector AmpGen::pFromEvent( const Event& evt, const unsigned& ref )
{
return TLorentzVector( evt.address( 4 * ref ) );
}
-TLorentzVector AmpGen::pFromEvent( const Event& evt, const std::vector<size_t>& ref )
+TLorentzVector AmpGen::pFromEvent( const Event& evt, const std::vector<unsigned>& ref )
{
double px( 0 ), py( 0 ), pz( 0 ), pE( 0 );
for ( auto& r : ref ) {
@@ -144,7 +144,7 @@ void AmpGen::boost( Event& evt, const std::tuple<double, double, double>& n, con
double nz = std::get<2>( n );
double norm = sqrt( nx * nx + ny * ny + nz * nz );
- for ( size_t i = 0; i < evt.size() / 4; ++i ) {
+ for ( unsigned i = 0; i < evt.size() / 4; ++i ) {
double nv = evt[4 * i] * nx + evt[4 * i + 1] * ny + evt[4 * i + 2] * nz;
evt[4*i+0] += ( (gamma-1) * nv / norm + gamma * evt[4*i+3] * v ) * nx / norm;
evt[4*i+1] += ( (gamma-1) * nv / norm + gamma * evt[4*i+3] * v ) * ny / norm;
@@ -155,13 +155,11 @@ void AmpGen::boost( Event& evt, const std::tuple<double, double, double>& n, con
void AmpGen::rotate( Event& evt, const std::tuple<double,double,double>& n, const double& v )
{
- double nx = std::get<0>( n );
- double ny = std::get<1>( n );
- double nz = std::get<2>( n );
+ auto& [nx,ny,nz ] = n;
double cv = cos(v);
double sv = sin(v);
double norm = sqrt( nx * nx + ny * ny + nz * nz );
- for( size_t i = 0 ; i < evt.size()/4;++i){
+ for( unsigned i = 0 ; i < evt.size()/4;++i){
double ix = evt[ 4*i+0];
double iy = evt[ 4*i+1];
double iz = evt[ 4*i+2];
@@ -174,7 +172,7 @@ void AmpGen::rotate( Event& evt, const std::tuple<double,double,double>& n, cons
void AmpGen::rotateBasis( Event& evt, const TVector3& p1, const TVector3& p2, const TVector3& p3 )
{
- for(size_t i = 0 ; i < evt.size()/4;++i)
+ for(unsigned i = 0 ; i < evt.size()/4;++i)
{
double ex = evt[4*i+0];
double ey = evt[4*i+1];
diff --git a/src/Lineshapes.cpp b/src/Lineshapes.cpp
index 4215758bbb9..7406c7d21db 100644
--- a/src/Lineshapes.cpp
+++ b/src/Lineshapes.cpp
@@ -23,8 +23,10 @@ Expression AmpGen::kFactor( const Expression& mass, const Expression& width, Deb
return sqrt(k);
}
-Expression AmpGen::BlattWeisskopf_Norm( const Expression& z, const Expression& z0, unsigned int L )
+Expression AmpGen::BlattWeisskopf_Norm( const Expression& ze, const Expression& z0e, unsigned int L )
{
+ auto z = make_cse(ze);
+ auto z0 = make_cse(z0e);
switch( L ) {
case 0: return 1;
case 1: return (1+z0) / (1+z);
@@ -37,8 +39,9 @@ Expression AmpGen::BlattWeisskopf_Norm( const Expression& z, const Expression& z
}
}
-Expression AmpGen::BlattWeisskopf( const Expression& z, unsigned int L )
+Expression AmpGen::BlattWeisskopf( const Expression& ze, unsigned int L )
{
+ auto z = make_cse(ze);
switch( L ) {
case 0: return 1;
case 1: return 2 *fpow(z,1) / (1+z);
@@ -63,11 +66,11 @@ Expression AmpGen::BL( const Expression& s,
return sqrt( BlattWeisskopf( q2 * radius * radius, L ) / BlattWeisskopf( q20 * radius * radius, L ) );
}
-std::vector<Expression> AmpGen::parameterVector( const std::string& name, const unsigned int& nParam )
+std::vector<Expression> AmpGen::parameterVector( const std::string& name, const size_t& nParam )
{
std::vector<Expression> returnVector;
- for ( unsigned int i = 0; i < nParam; ++i )
- returnVector.push_back( Parameter( name + std::to_string( i ) ) );
+ for (size_t i = 0; i != nParam; ++i )
+ returnVector.emplace_back(Parameter(name + std::to_string(i)));
return returnVector;
}
@@ -75,27 +78,19 @@ Expression AmpGen::width( const Expression& s, const Expression& s1, const Expre
const Expression& width, const Expression& radius, unsigned int L,
DebugSymbols* dbexpressions )
{
- auto q2v = make_cse( Q2(s,s1,s2) );
+ auto q2v = make_cse( Q2(s,s1,s2) );
const Expression q2 = Ternary( q2v > 0, q2v, 0 );
- const Expression q20 = Abs( Q2( mass * mass, s1, s2 ) );
+ const Expression q20 = abs( Q2( mass * mass, s1, s2 ) );
Expression BF = BlattWeisskopf_Norm( q2 * radius * radius, q20 * radius * radius, L );
- Expression qr = sqrt( q2 / q20 ) * fpow( q2/q20, L );
-
- const Expression mreco = isqrt( s );
- const Expression mr = mass * mreco;
+ auto q2r = make_cse(q2 / q20);
ADD_DEBUG(q2 , dbexpressions);
ADD_DEBUG(q20 , dbexpressions);
ADD_DEBUG(sqrt(q2/q20) , dbexpressions);
ADD_DEBUG(BF , dbexpressions);
- ADD_DEBUG(qr , dbexpressions);
- ADD_DEBUG(mr , dbexpressions);
- ADD_DEBUG(qr*mr , dbexpressions);
- ADD_DEBUG(sqrt(q2)/mreco, dbexpressions);
- ADD_DEBUG(sqrt(q20)/mass, dbexpressions);
- ADD_DEBUG(width*BF*qr*mr, dbexpressions);
-
- return width * BF * qr * mr;
+ const auto rt = make_cse( width * BF * mass * sqrt( q2r / s ) * fpow( q2r, L ) );
+ ADD_DEBUG(rt, dbexpressions);
+ return rt;
}
bool Lineshape::Factory::isLineshape( const std::string& lineshape )
@@ -103,9 +98,9 @@ bool Lineshape::Factory::isLineshape( const std::string& lineshape )
size_t pos = lineshape.find( "." );
if ( pos == std::string::npos )
- return AmpGen::Factory<ILineshape>::get(lineshape, true) != nullptr;
+ return AmpGen::Factory<Lineshape::Base>::get(lineshape, true) != nullptr;
else
- return AmpGen::Factory<ILineshape>::get(lineshape.substr(0, pos), true ) != nullptr;
+ return AmpGen::Factory<Lineshape::Base>::get(lineshape.substr(0, pos), true ) != nullptr;
}
Expression Lineshape::Factory::get( const std::string& lineshape, const Expression& s, const Expression& s1,
@@ -115,26 +110,25 @@ Expression Lineshape::Factory::get( const std::string& lineshape, const Expressi
size_t pos = lineshape.find( "." );
if ( pos == std::string::npos ) {
- auto it = AmpGen::Factory<ILineshape>::get( lineshape );
+ auto it = AmpGen::Factory<Lineshape::Base>::get( lineshape );
if ( !it ) ERROR( "Lineshape : " << lineshape << " not found" );
return it->get( s, s1, s2, particleName, L, "", dbexpressions );
} else {
- return AmpGen::Factory<ILineshape>::get(lineshape.substr(0, pos))->get( s, s1, s2, particleName, L, lineshape.substr( pos + 1 ), dbexpressions );
+ return AmpGen::Factory<Lineshape::Base>::get(lineshape.substr(0, pos))->get( s, s1, s2, particleName, L, lineshape.substr( pos + 1 ), dbexpressions );
}
}
-Expression Lineshape::Factory::get(const std::string& lineshape, const Expression& s, const std::vector<Tensor>& p,
- const std::string& particleName, const unsigned int& L,
+Expression Lineshape::Factory::get(const std::string& lineshape, const AmpGen::Particle& p,
DebugSymbols* dbexpressions )
{
size_t pos = lineshape.find( "." );
if ( pos == std::string::npos ) {
- auto it = AmpGen::Factory<ILineshape>::get( lineshape );
+ auto it = AmpGen::Factory<Lineshape::Base>::get( lineshape );
if ( !it ) ERROR( "Lineshape : " << lineshape << " not found" );
- return it->get(s, p, particleName, L, "", dbexpressions );
+ return it->get(p, "", dbexpressions );
} else {
- return AmpGen::Factory<ILineshape>::get( lineshape.substr( 0, pos ) )->get(s, p, particleName, L, lineshape.substr( pos + 1 ), dbexpressions );
+ return AmpGen::Factory<Lineshape::Base>::get( lineshape.substr( 0, pos ) )->get(p, lineshape.substr( pos + 1 ), dbexpressions );
}
}
@@ -143,8 +137,8 @@ Expression AmpGen::pol( const Expression& X, const std::vector<Expression>& p )
Expression F = 0;
Expression L = 1;
for ( auto& ip : p ) {
- F = F + ip * L;
- L = L * X;
+ F += ip * L;
+ L *= X;
}
return F;
}
diff --git a/src/Lineshapes/AxialKaon.cpp b/src/Lineshapes/AxialKaon.cpp
deleted file mode 100644
index eebc035edc6..00000000000
--- a/src/Lineshapes/AxialKaon.cpp
+++ /dev/null
@@ -1,62 +0,0 @@
-
-#include <stddef.h>
-#include <string>
-#include <vector>
-
-#include "AmpGen/Lineshapes.h"
-#include "AmpGen/kMatrix.h"
-#include "AmpGen/Spline.h"
-#include "AmpGen/Expression.h"
-#include "AmpGen/Factory.h"
-#include "AmpGen/Tensor.h"
-#include "AmpGen/Utilities.h"
-
-using namespace AmpGen;
-
-DEFINE_LINESHAPE( AxialKaon )
-{
- ERROR("This lineshape does not work as intended, should not be used");
-/*
-
- Spline rho_Krho("rho_Krho",20, 0.597247, 5,
- {5.35636e-23, 0.000210696, 0.00208479, 0.00993997, 0.0415061, 0.120885, 0.196599, 0.256062, 0.304949, 0.34693, 0.384132, 0.417868, 0.448995, 0.478101, 0.505606, 0.531815, 0.556963, 0.581226, 0.604745, 0.627631});
-
- Spline rho_Kstpi("rho_Kspi",20,0.597247, 5,
- {6.29163e-23, 0.000390208, 0.0161092, 0.0855491, 0.128145, 0.159565, 0.184867, 0.20627, 0.224985, 0.241753, 0.257056, 0.271229, 0.284507, 0.297066, 0.309035, 0.320516, 0.331588, 0.342313, 0.35274, 0.362912} );
-
- Spline rho_KstpiD("rho_KspiD",20,0.597247, 5,
- {6.29163e-23, 0.000390208, 0.0161092, 0.0855491, 0.128145, 0.159565, 0.184867, 0.20627, 0.224985, 0.241753, 0.257056, 0.271229, 0.284507, 0.297066, 0.309035, 0.320516, 0.331588, 0.342313, 0.35274, 0.362912} );
-
- Spline rho_KSpi("rho_KSpi",20,0.597247, 5,
- {5.58343e-23, 0.000178087, 0.00132915, 0.00423057, 0.00963868, 0.0185276, 0.0324146, 0.053891, 0.0870863, 0.13619, 0.202066, 0.282239, 0.373053, 0.470919, 0.572771, 0.67618, 0.779316, 0.880855, 0.979877, 1.07577});
-
-
- std::vector<Expression> phaseSpace = { rho_Krho(s), rho_Kstpi(s), rho_KstpiD(s), rho_KSpi(s) };
-
- std::vector< std::string > channels = {"Krho","Kspi","KspiD","KSpi"};
- unsigned int nPoles = 2;
- std::vector<poleConfig> poleConfigs;
- for( unsigned int pole=1;pole <= nPoles; ++pole )
- {
- std::string stub = "AxialKaon_p"+std::to_string(pole)+"_";
- Expression mass = Parameter( stub + "mass" );
- poleConfig p( mass * mass );
- for ( unsigned int ch = 0; ch < 4; ++ch ) p.add( Parameter( stub + channels[ch] ) );
- poleConfigs.push_back( p );
- }
- auto kMatrix = constructKMatrix( s, 4, poleConfigs );
-
- Tensor F = getPropagator( kMatrix, phaseSpace );
-
- auto tokens = split( lineshapeModifier, '.' );
- unsigned int pTerm = stoi(tokens[0]);
- unsigned int channel = stoi(tokens[1]);
- auto pole = poleConfigs[pTerm];
- Expression M = 0;
- for ( unsigned int i = 0; i < pole.couplings.size(); ++i ) {
- M = M + F[{channel, i}] * pole.couplings[i];
- }
- return SubTree( M / ( pole.s - s ) );
- */
- return 0;
-}
diff --git a/src/Lineshapes/BW.cpp b/src/Lineshapes/BW.cpp
index a58c2cfe665..3b2468100b6 100644
--- a/src/Lineshapes/BW.cpp
+++ b/src/Lineshapes/BW.cpp
@@ -6,6 +6,7 @@
#include "AmpGen/Lineshapes.h"
#include "AmpGen/ParticleProperties.h"
#include "AmpGen/ParticlePropertiesList.h"
+#include "AmpGen/Particle.h"
using namespace AmpGen;
using namespace AmpGen::fcn;
@@ -15,17 +16,20 @@ DEFINE_LINESHAPE( FormFactor )
{
auto props = ParticlePropertiesList::get( particleName );
Expression radius = Parameter( particleName + "_radius", props->radius() );
-
+ Expression mass = Parameter( particleName + "_mass" , props->mass() );
const Expression q2 = make_cse( Q2( s, s1, s2 ) );
+ const Expression q20 = make_cse( Q2( mass*mass, s1, s2 ) );
int Lp = L;
if( lineshapeModifier == "L0" ) Lp = 0;
if( lineshapeModifier == "L1" ) Lp = 1;
if( lineshapeModifier == "L2" ) Lp = 2;
if( lineshapeModifier == "L3" ) Lp = 3;
- const Expression FormFactor = lineshapeModifier.find("BL") == std::string::npos ?
- sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, Lp ) ) :
- sqrt( BlattWeisskopf(q2*radius*radius, Lp ) );
+ Expression FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, Lp ) );
+ if ( lineshapeModifier == "BL" ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, Lp ) );
+ if ( lineshapeModifier == "NFF" ) FormFactor = 1;
+ if ( lineshapeModifier == "BELLE2018" ) FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, q20 * radius * radius, Lp ) );
+
if( L != 0 ){
ADD_DEBUG( q2 , dbexpressions );
ADD_DEBUG( radius , dbexpressions );
@@ -62,19 +66,23 @@ DEFINE_LINESHAPE( BW )
const Expression& radius = Parameter( particleName + "_radius", props->radius() );
const Expression q2 = make_cse( Abs(Q2( s_cse, s1, s2 ) ) ) ;
const Expression q20 = make_cse( Abs(Q2( mass * mass, s1, s2 )) );
- Expression FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, L ) );
- if ( lineshapeModifier == "BL" ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, L ) );
+ Expression FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, L ) );
+ if ( lineshapeModifier == "BL" ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, L ) );
+ if ( lineshapeModifier == "BELLE2018" ) FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, q20 * radius * radius, L ) );
+ if ( lineshapeModifier == "NFF") FormFactor = 1;
Expression runningWidth = width( s_cse, s1, s2, mass, width0, radius, L, dbexpressions );
const Expression BW = FormFactor / ( mass * mass - s_cse -1i * mass * runningWidth );
const Expression kf = kFactor( mass, width0, dbexpressions );
+ ADD_DEBUG( s_cse, dbexpressions );
+ ADD_DEBUG( s1, dbexpressions );
+ ADD_DEBUG( s2, dbexpressions );
ADD_DEBUG( FormFactor, dbexpressions );
ADD_DEBUG( runningWidth, dbexpressions );
ADD_DEBUG( BW, dbexpressions );
ADD_DEBUG( kf, dbexpressions );
- return kf * BW;
+ return lineshapeModifier == "BELLE2018" ? BW : kf*BW;
}
-
DEFINE_LINESHAPE( SBW )
{
auto props = ParticlePropertiesList::get( particleName );
diff --git a/src/Lineshapes/CoupledChannel.cpp b/src/Lineshapes/CoupledChannel.cpp
index 0ee3ad024e6..0afca71302e 100644
--- a/src/Lineshapes/CoupledChannel.cpp
+++ b/src/Lineshapes/CoupledChannel.cpp
@@ -11,6 +11,9 @@
using namespace AmpGen;
using namespace AmpGen::fcn;
+using namespace std::complex_literals;
+
+// ENABLE_DEBUG( Lineshape::CoupledChannel );
Expression H(const Expression& x,
const Expression& y,
@@ -61,28 +64,76 @@ Expression rho_threeBody( const Expression& s,
) / (16.*M_PI*M_PI*s) , 0 );
}
+//Taken from arXiv:1111.6307v1 Eq.(41)
+Expression rho_threeBodyWollyCusp( const Expression& s,
+ const Particle& resonance,
+ const Particle& bachelor )
+{
+ const ParticleProperties& p1 = *resonance.props();
+ const ParticleProperties& p2 = *bachelor.props();
+
+ Expression m1 = p1.mass();
+ Expression m2 = p2.mass();
+
+ Expression i = Constant(0,1);
+ Expression g1 = p1.width();
+
+ auto q2 = make_cse(abs(Q2(s, m1*m1, m2*m2)));
+ Expression delta = m1 * m2 * g1 / (m1+m2);
+ Expression delta2 = delta * delta;
+
+ Expression rho = complex_sqrt( sqrt(q2*q2+delta2*delta2) + q2 ) + i * sqrt( sqrt(q2*q2+delta2*delta2) - q2 );
+ return rho / (8.*M_PI*sqrt(2.*s));
+}
+
Expression AmpGen::phaseSpace(const Expression& s, const Particle& p, const size_t& l)
{
auto fs = p.getFinalStateParticles();
- if( fs.size() == 2 ){
- auto s1 = p.daughter(0)->massSq();
- auto s2 = p.daughter(1)->massSq();
- auto k2 = make_cse( Q2(s,s1,s2) );
- const Expression k2p = Ternary( k2 > 0, k2, 0 );
- auto phsp_parameterisation = p.attribute("phsp");
- if( !phsp_parameterisation ){
+ auto phsp_parameterisation = p.attribute("phsp");
+
+ if( fs.size() == 2 ){
+ auto s1 = p.daughter(0)->massSq();
+ auto s2 = p.daughter(1)->massSq();
+ auto k2 = make_cse( Q2(s,s1,s2) );
+ const Expression k2p = Ternary( k2 > 0, k2, 0 );
const Expression radius = Parameter(p.name() + "_radius", p.props()->radius());
+
+ if( !phsp_parameterisation ){
return rho_twoBody(s, s1, s2) * BlattWeisskopf(k2p*radius*radius, l);
}
- if( phsp_parameterisation == std::string("arXiv.0707.3596") ){
+ else if( phsp_parameterisation == std::string("arXiv.0707.3596") ){
INFO("Got AS parametrisation");
- Expression E = 1;
- // return 2*fpow(k2,l)*complex_sqrt(k2) * E * 2 / ((1.5+k2p) * sqrt(s) );
return 2 * complex_sqrt(k2/s);
}
+ else if( phsp_parameterisation == std::string("CM") )
+ {
+ if( l != 0 ){
+ WARNING("Chew-Mandelstam only implemented for l=0");
+ }
+ auto m1 = p.daughter(0)->mass();
+ auto m2 = p.daughter(1)->mass();
+ Expression s1 = m1*m1;
+ Expression s2 = m2*m2;
+ Expression sT = (m1+m2)*(m1+m2);
+ Expression q2 = (s*s + s1*s1 + s2*s2 - 2*s*s1 - 2*s*s2 - 2*s1*s2)/(4*s);
+ auto q = fcn::complex_sqrt(q2);
+ auto arg = (s1 + s2 - s + 2*fcn::sqrt(s) * q )/ (2*m1*m2);
+ return (2.*q * fcn::log(arg) / fcn::sqrt(s) - (s1-s2)*( 1./s - 1./sT ) * fcn::log(m1/m2) ) / ( 16.i * M_PI * M_PI );
+ }
+ else {
+ FATAL("Parametrisation: " << *phsp_parameterisation << " not found");
+ }
+ }
+ if( fs.size() == 3 ){
+ if(phsp_parameterisation == std::string("WollyCusp")){
+ if( ! p.daughter(0)->isStable() ) return rho_threeBodyWollyCusp( s, *p.daughter(0), *p.daughter(1) ) ;
+ if( ! p.daughter(1)->isStable() ) return rho_threeBodyWollyCusp( s, *p.daughter(1), *p.daughter(0) ) ;
+ }
+ else{
+ if( ! p.daughter(0)->isStable() ) return rho_threeBody( s, *p.daughter(0), *p.daughter(1) );
+ if( ! p.daughter(1)->isStable() ) return rho_threeBody( s, *p.daughter(1), *p.daughter(0) );
+ }
}
- if( fs.size() == 3 && ! p.daughter(0)->isStable() ) return rho_threeBody( s, *p.daughter(0), *p.daughter(1) );
- if( fs.size() == 3 && ! p.daughter(1)->isStable() ) return rho_threeBody( s, *p.daughter(1), *p.daughter(0) );
ERROR("Phase space only implemented for two and three body decays");
return 0;
}
@@ -100,13 +151,13 @@ DEFINE_LINESHAPE( CoupledChannel )
ADD_DEBUG( s , dbexpressions );
for( size_t i = 0 ; i < channels.size(); i+=2 ){
Particle p( channels[i] );
- INFO( "Adding channel ... " << p.uniqueString() << " coupling = " << NamedParameter<std::string>( channels[i+1] ) );
+ DEBUG( "Adding channel ... " << p.uniqueString() << " coupling = " << NamedParameter<std::string>( channels[i+1] ) );
Expression coupling = Parameter(channels[i+1], 0);
- totalWidth = totalWidth + coupling * phaseSpace(s , p, p.orbital());
- totalWidthAtPole = totalWidthAtPole + coupling * phaseSpace(mass*mass, p, p.orbital());
+ totalWidth = totalWidth + coupling * phaseSpace(s , p, p.L());
+ totalWidthAtPole = totalWidthAtPole + coupling * phaseSpace(mass*mass, p, p.L());
ADD_DEBUG(coupling, dbexpressions);
- ADD_DEBUG(phaseSpace(s,p,p.orbital() ), dbexpressions);
- ADD_DEBUG(phaseSpace(mass*mass,p,p.orbital() ), dbexpressions);
+ ADD_DEBUG(phaseSpace(s,p,p.L() ), dbexpressions);
+ ADD_DEBUG(phaseSpace(mass*mass,p,p.L() ), dbexpressions);
}
ADD_DEBUG(totalWidth, dbexpressions);
ADD_DEBUG(totalWidthAtPole, dbexpressions);
diff --git a/src/Lineshapes/EtaDalitz.cpp b/src/Lineshapes/EtaDalitz.cpp
index f7d7a525774..b43d691f5c0 100644
--- a/src/Lineshapes/EtaDalitz.cpp
+++ b/src/Lineshapes/EtaDalitz.cpp
@@ -12,13 +12,14 @@ using namespace AmpGen::fcn;
DEFINE_GENERIC_SHAPE( EtaDalitz )
{
- WARNING("Empirical expression; eta0[EtaDalitz.NonRelBW]{pi+,pi-,pi0} with pi0 in the 3rd order.");
- Tensor P( Tensor::dim(4) );
- for ( auto& ip : p ) P = P + ip;
+ auto pp = *p.daughter("pi+");
+ auto pm = *p.daughter("pi-");
+ auto p0 = *p.daughter("pi0");
+ auto P = p.P();
- Expression T0 = sqrt( dot( p[0], P ) * dot( p[0], P ) / dot( P, P ) ) - sqrt( dot( p[0], p[0] ) );
- Expression T1 = sqrt( dot( p[1], P ) * dot( p[1], P ) / dot( P, P ) ) - sqrt( dot( p[1], p[1] ) );
- Expression T2 = sqrt( dot( p[2], P ) * dot( p[2], P ) / dot( P, P ) ) - sqrt( dot( p[2], p[2] ) );
+ Expression T0 = dot(pp.P(), P) - p.mass() * pp.mass();
+ Expression T1 = dot(pm.P(), P) - p.mass() * pm.mass();
+ Expression T2 = dot(p0.P(), P) - p.mass() * p0.mass();
Expression Q = T0 + T1 + T2;
Expression y = 3.0 * T2 / Q - 1.0;
@@ -26,7 +27,7 @@ DEFINE_GENERIC_SHAPE( EtaDalitz )
Expression amp = Ternary( z > 0.0, sqrt(z), 1 );
if ( lineshapeModifier != "" ){
- amp = amp * Lineshape::Factory::get(lineshapeModifier, s, p, particleName, L, dbexpressions);
+ amp = amp * Lineshape::Factory::get(lineshapeModifier, p, dbexpressions);
}
return amp;
}
diff --git a/src/Lineshapes/Flatte.cpp b/src/Lineshapes/Flatte.cpp
index 220cdfc1f47..06827969cbf 100644
--- a/src/Lineshapes/Flatte.cpp
+++ b/src/Lineshapes/Flatte.cpp
@@ -10,12 +10,12 @@ using namespace std::complex_literals;
Expression aSqrtTerm( const Expression& s, const Expression& m0 )
{
Expression a2 = 1.0 - ( 4 * m0 * m0 ) / s;
- return Ternary( a2 > Constant( 0 ), sqrt( a2 ), Constant( 0 ) );
+ return Ternary( a2 > 0., sqrt( a2 ), Constant( 0 ) );
}
Expression fSqrtTerm( const Expression& s, const Expression& m0 )
{
- return complex_sqrt( 1.0 - ( 4 * m0 * m0 ) / s );
+ return complex_sqrt( 1.0 - 4*m0*m0/ s );
}
DEFINE_LINESHAPE( Flatte )
{
diff --git a/src/Lineshapes/GLASS.cpp b/src/Lineshapes/GLASS.cpp
new file mode 100644
index 00000000000..3fb68ec8929
--- /dev/null
+++ b/src/Lineshapes/GLASS.cpp
@@ -0,0 +1,43 @@
+#include <string>
+
+#include "AmpGen/Expression.h"
+#include "AmpGen/Factory.h"
+#include "AmpGen/Lineshapes.h"
+#include "AmpGen/ParticleProperties.h"
+#include "AmpGen/ParticlePropertiesList.h"
+#include "AmpGen/Units.h"
+
+using namespace AmpGen;
+using namespace AmpGen::fcn;
+
+DEFINE_LINESHAPE( GLASS )
+{
+ const auto props = ParticlePropertiesList::get( particleName );
+ const auto mass = Parameter( particleName + "_mass", props->mass() );
+ const auto width0 = Parameter( particleName + "_width", props->width() );
+ const auto s0 = mass*mass;
+ const auto a = Parameter( particleName + "::GLASS::a", 2.07 );
+ const auto r = Parameter( particleName + "::GLASS::r", 3.32 );
+ const auto phiR = Parameter( particleName + "::GLASS::phiR", 0.00 );
+ const auto phiF = Parameter( particleName + "::GLASS::phiF", 0.00 );
+ const auto R = Parameter( particleName + "::GLASS::R", 1.00 );
+ const auto F = Parameter( particleName + "::GLASS::F", 1.00 );
+ const auto q2 = Q2(s, s1, s2);
+ const auto q20 = Q2(s0, s1, s2);
+ const auto q = safe_sqrt( q2 );
+ const auto i = Constant(0,1);
+ const auto width = width0 * mass * sqrt( q2 / ( q20 * s ) );
+ const auto rbw = s0 * width0 /(sqrt(q20) * (mass*mass - s - i*mass*width ));
+ const auto den = ( 1.0 + 0.5*r*a*q2 - i * a * q);
+ const auto resTerm = R * exp( i*(phiR + 2*phiF) ) * rbw * ( 1.0 + 0.5*r*a*q2 + i * a * q );
+ const auto nrTerm = F * exp( i*phiF ) * ( a * q * cos(phiF) + ( 1.0 + 0.5 * r * a * q2 ) * sin(phiF)) * sqrt(s) / q;
+ const auto total = (nrTerm + resTerm)/den;
+
+ ADD_DEBUG(width , dbexpressions);
+ ADD_DEBUG(rbw , dbexpressions);
+ ADD_DEBUG(den , dbexpressions);
+ ADD_DEBUG(resTerm/den, dbexpressions);
+ ADD_DEBUG(nrTerm/den , dbexpressions);
+ ADD_DEBUG(total , dbexpressions);
+ return total;
+}
diff --git a/src/Lineshapes/GenericKmatrix.cpp b/src/Lineshapes/GenericKmatrix.cpp
index 179c64ba17d..383bcac36f8 100644
--- a/src/Lineshapes/GenericKmatrix.cpp
+++ b/src/Lineshapes/GenericKmatrix.cpp
@@ -4,6 +4,7 @@
#include <string>
#include <utility>
#include <vector>
+#include <exception>
#include "AmpGen/Expression.h"
#include "AmpGen/Factory.h"
@@ -16,87 +17,229 @@
#include "AmpGen/Utilities.h"
#include "AmpGen/kMatrix.h"
#include "AmpGen/CoupledChannel.h"
+#include "AmpGen/enum.h"
using namespace AmpGen;
-using namespace AmpGen::fcn;
+using namespace AmpGen::fcn;
+namespace AmpGen{ make_enum(PA_TYPE, PVec, PVecPDG, PVecACCMOR, QVec); }
DEFINE_LINESHAPE(GenericKmatrix)
{
- auto props = ParticlePropertiesList::get( particleName );
- Expression mass = Parameter( particleName + "_mass", props->mass() );
- INFO( "kMatrix modifier " << lineshapeModifier << " particle = " << particleName );
- auto tokens = split(lineshapeModifier, '.' );
- DEBUG("kMatrix modifier = " << lineshapeModifier << " nTokens = " << tokens.size() );
- size_t nPoles = NamedParameter<size_t>( lineshapeModifier + "::kMatrix::nPoles");
- auto channels = NamedParameter<std::string>(lineshapeModifier + "::kMatrix::channels").getVector();
- size_t nChannels = channels.size();
- std::vector<Expression> phsps;
- std::vector<Expression> bw_phase_space;
- auto s0 = mass*mass;
+ auto props = ParticlePropertiesList::get( particleName );
+ Expression mass = Parameter( particleName + "_mass", props->mass() );
+ Expression radius = Parameter( particleName + "_radius", props->radius() );
+ unsigned nPoles = NamedParameter<unsigned>(particleName+"::kMatrix::nPoles");
+ auto channels = NamedParameter<std::string>(particleName+"::kMatrix::channels").getVector();
+ auto type = NamedParameter<std::string>(particleName+"::kMatrix::type","default");
+ auto kMatrix_formFactor = NamedParameter<std::string>(particleName+"::kMatrix::kMatrix_formFactor","NFF");
+ auto pVector_formFactor = NamedParameter<std::string>(particleName+"::kMatrix::pVector_formFactor","NFF");
+ auto const pa_type = NamedParameter<PA_TYPE>(particleName+"::kMatrix::production_amplitude",PA_TYPE::PVec);
+ auto nChannels = channels.size();
+ auto s0 = mass*mass;
+
+ DEBUG( "GenericKmatrix modifier " << lineshapeModifier << " particle = " << particleName );
+ auto tokens = split( lineshapeModifier, '.' );
+ DEBUG( "GenericKmatrix modifier = " << lineshapeModifier << " nTokens = " << tokens.size() );
+ unsigned int cTerm = tokens.size() > 1 ? stoi( tokens[1] )-1 : 0;
+
+ std::vector<Expression> phsps, bw_phase_space, Bls;
ADD_DEBUG(s, dbexpressions );
ADD_DEBUG(s0, dbexpressions );
- INFO("Initialising K-matrix with : " << nChannels);
- for( size_t i = 0 ; i < channels.size(); i+=1 ){
- Particle p( channels[i] );
+ INFO("Initialising K-matrix with [nChannels = " << nChannels << ", nPoles = " << nPoles << "]");
+ //phase-space
+ for( unsigned i = 0 ; i < channels.size(); i+=1 ){
+ Particle p( channels[i] );
INFO( p.decayDescriptor() );
- Expression sf = Parameter( lineshapeModifier + "::phsp::sf::"+std::to_string(i+1), 1);
- phsps.emplace_back( sf * phaseSpace(s, p, p.orbital() ) );
- bw_phase_space.emplace_back( sf * phaseSpace(s0, p, p.orbital() ) );
- ADD_DEBUG( *phsps.rbegin(), dbexpressions);
- ADD_DEBUG( phaseSpace(s0,p,p.orbital()), dbexpressions );
+ phsps.emplace_back( phaseSpace(s, p, p.L() ) );
+ bw_phase_space.emplace_back( phaseSpace(s0, p, p.L() ) );
+ if( dbexpressions != nullptr ) dbexpressions->emplace_back("phsp_"+p.decayDescriptor(), *phsps.rbegin() ); //ADD_DEBUG( *phsps.rbegin(), dbexpressions);
+// ADD_DEBUG( phaseSpace(s0,p,p.L()), dbexpressions );
}
- Tensor non_resonant( Tensor::dim(nChannels, nChannels) );
+ //pole configuration for kMatrix (see e.g. eq. (48.25) in http://pdg.lbl.gov/2019/reviews/rpp2019-rev-resonances.pdf)
std::vector<poleConfig> poleConfigs;
- for (size_t pole = 1; pole <= nPoles; ++pole ){
- std::string stub = lineshapeModifier + "::pole::" + std::to_string(pole);
+ for (unsigned pole = 1; pole <= nPoles; ++pole ){
+ std::string stub = particleName+"::pole::" + std::to_string(pole);
Expression mass = Parameter(stub + "::mass");
- poleConfig thisPole(mass*mass);
+ Expression gamma = Parameter(stub + "::gamma");
+ DEBUG( "Will link to parameter: " << stub + "::mass");
+ poleConfig thisPole(mass*mass,{},gamma,type);
if( dbexpressions != nullptr ) dbexpressions->emplace_back(stub+"::mass", mass);
Expression bw_width = 0;
Expression bw_width0 = 0;
- for (size_t channel = 1; channel <= nChannels; ++channel )
- {
+ for (unsigned channel = 1; channel <= nChannels; ++channel ){
Expression g = Parameter(stub+"::g::"+std::to_string(channel));
- thisPole.add(g, 1);
- if( dbexpressions != nullptr ){
- dbexpressions->emplace_back( stub+"::g::"+std::to_string(channel), g);
+ DEBUG("Will link to parameter: " << stub+"::g::"+std::to_string(channel) );
+
+ Expression Bl = 1;
+ if(kMatrix_formFactor == "BL"){
+ Particle p( channels[channel-1] );
+ //Taken from arXiv:1111.6307v1 Eqs. (41), (45)
+ Expression k2 = norm(phsps[channel-1]) *s/4.;
+ Expression k20 = norm( phaseSpace(mass*mass, p, p.L() ) ) *mass*mass/4.; // ???
+ //Expression k20 = norm( phaseSpace(s0, p, p.L() ) ) * s0/4.; // ???
+ Bl = sqrt( BlattWeisskopf( k2* radius * radius, p.L() ) );
+ if(pole==1)Bls.push_back(Bl);
+ Bl = Bl / sqrt( BlattWeisskopf( k20 * radius * radius, p.L() ) ) ;
+ }
+ if(kMatrix_formFactor == "ACCMOR"){
+ Particle p( channels[channel-1] );
+ //Taken from https://arxiv.org/pdf/0909.2171v1.pdf Eqs. (41), (45)
+ Expression k2 = norm(phsps[channel-1]) *s/4.;
+ //Expression k20 = norm( phaseSpace(mass*mass, p, p.L() ) ) *s0/4.;
+ Bl = sqrt( fpow(k2/(1+k2),p.L()) );
+ if(pole==1)Bls.push_back(Bl);
}
+
+ thisPole.add(g, Bl);
+ if(dbexpressions != nullptr) dbexpressions->emplace_back( stub+"::g::"+std::to_string(channel), g);
bw_width = bw_width + g*g*phsps[channel-1] / mass;
bw_width0 = bw_width0 + g*g*bw_phase_space[channel-1] / mass;
}
- for( size_t channel = 1 ; channel <= nChannels; ++channel ){
- Expression g = Parameter(stub+"::g::"+std::to_string(channel));
- Expression BR = g*g*bw_phase_space[channel-1] / ( mass * bw_width0 );
- ADD_DEBUG( BR, dbexpressions );
+ if( dbexpressions != nullptr ){
+ for( unsigned channel = 1 ; channel <= nChannels; ++channel ){
+ Expression g = Parameter(stub+"::g::"+std::to_string(channel));
+ Expression BR = g*g*bw_phase_space[channel-1] / ( mass * bw_width0 );
+ ADD_DEBUG( BR, dbexpressions );
+ }
+ ADD_DEBUG(bw_width, dbexpressions);
+ ADD_DEBUG(bw_width0, dbexpressions);
}
- ADD_DEBUG(bw_width, dbexpressions);
- ADD_DEBUG(bw_width0, dbexpressions);
poleConfigs.push_back(thisPole);
}
- for(size_t ch1 = 1; ch1 <= nChannels; ++ch1){
- for( size_t ch2 = 1; ch2 <= nChannels; ++ch2 ){
+ //add non-resonant term to kMatrix (eq. (48.25) in http://pdg.lbl.gov/2019/reviews/rpp2019-rev-resonances.pdf)
+ Tensor non_resonant( Tensor::dim(nChannels, nChannels) );
+ for(unsigned ch1 = 1; ch1 <= nChannels; ++ch1){
+ for( unsigned ch2 = 1; ch2 <= nChannels; ++ch2 ){
auto c1 = std::to_string(ch1);
- auto c2 = std::to_string(ch2);
+ auto c2 = std::to_string(ch2);
if( ch1 > ch2 ) std::swap(c1,c2);
- std::string nrShape = NamedParameter<std::string>(lineshapeModifier +"::"+c1+"::"+c2+"::nrShape", "flat");
- Expression f1 = Parameter(lineshapeModifier+"::f1::"+c1+"::"+c2, 0);
+ std::string nrShape = NamedParameter<std::string>(particleName+"::"+c1+"::"+c2+"::nrShape", "flat");
+ Expression f1 = Parameter(particleName+"::f1::"+c1+"::"+c2, 0);
if( nrShape == "flat") non_resonant[{ch1-1,ch2-1}] = f1;
- else if( nrShape == "pole"){
- Expression f2 = Parameter(lineshapeModifier+"::f2::"+c1+"::"+c2, 0);
- Expression s0 = Parameter(lineshapeModifier+"::s0::"+c1+"::"+c2, 0);
+ else if( nrShape == "pole"){
+ Expression f2 = Parameter(particleName+"::f2::"+c1+"::"+c2, 0);
+ Expression s0 = Parameter(particleName+"::s0::"+c1+"::"+c2, 0);
non_resonant[{ch1-1,ch2-1}] = (f1 + f2*sqrt(s)) / (s-s0);
}
- else WARNING("Unknown shape: " << nrShape);
+ else WARNING("Unknown shape: " << nrShape);
}
}
+
Tensor kMatrix = constructKMatrix(s, nChannels, poleConfigs);
- ADD_DEBUG_TENSOR(kMatrix , dbexpressions);
- kMatrix = kMatrix + non_resonant;
+ ADD_DEBUG_TENSOR(kMatrix, dbexpressions);
+ kMatrix = kMatrix + non_resonant;
Tensor propagator = getPropagator(kMatrix, phsps);
ADD_DEBUG_TENSOR(non_resonant, dbexpressions);
- Expression M;
- for(size_t i = 0 ; i < nChannels; ++i) M = M + kMatrix[{i,0}] * propagator[{0,i}];
- return M ; // * phsps[0];
+
+ //Form factor
+ const Expression q2 = make_cse( Q2( s, s1, s2 ) );
+ const Expression q20 = make_cse( Q2( s0, s1, s2 ) );
+ Expression FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, L ) );
+ if ( pVector_formFactor == "BL" ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, L ) );
+ if ( pVector_formFactor == "NFF" ) FormFactor = 1;
+ if ( pVector_formFactor == "BELLE2018" ) FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, q20 * radius * radius, L ) );
+
+ Expression I = Constant(0,1);
+
+ //we have all ingredients to build the production amplitude now
+ //follow https://doi.org/10.1007/s1010502a0002 eqns (9)-(13) modulo the Adler zero term (which is argued away in a fuzzy manner by citing a private communication)
+ if(pa_type==PA_TYPE::PVec){
+ std::vector<Expression> P(nChannels,0), a(nChannels,0), phi(nChannels,0);//the P-vector, a and phi coefficients
+ Expression s_0 = Parameter(particleName+"::s0");
+ Expression F_0 = 0;//the object we'll return later: the production amplitude in the 0th channel
+ //get the coefficients first
+ for(unsigned k = 0 ; k < nChannels; ++k) a[k] = Parameter(particleName+"::a::"+std::to_string(k+1));
+ //now start loop to calculate the production amplitude
+ for(unsigned k = 0 ; k < nChannels; ++k){
+ for(unsigned alpha = 0; alpha < nPoles; ++alpha){
+ Expression beta = 0;
+ for(unsigned q = 0 ; q < nChannels; ++q){
+ beta += a[q] * poleConfigs[alpha].couplings[q];
+ phi[k] += a[q] * non_resonant[{k,q}];
+ }
+ P[k] += (beta * poleConfigs[alpha].couplings[k])/poleConfigs[alpha].pole(s) + phi[k] * (1.+s_0)/(s-s_0);
+ }
+ F_0 += propagator[{cTerm,k}] * P[k];
+ }
+ return F_0*FormFactor;
+ }
+ //P-vector from http://pdg.lbl.gov/2019/reviews/rpp2019-rev-resonances.pdf
+ else if(pa_type==PA_TYPE::PVecPDG){
+ INFO("Using PDG P-vector approach to build the production amplitude");
+ Expression F_0 = 0;
+
+ std::vector<Expression> P(nChannels,0), b(nChannels,0);
+
+ Tensor a( Tensor::dim(nPoles, nChannels) );
+ for (unsigned pole = 1; pole <= nPoles; ++pole ){
+ for( unsigned channel = 1 ; channel <= nChannels; ++channel ){
+ Expression a_Re = Parameter(particleName+"::pole::" + std::to_string(pole)+"::a_re::"+std::to_string(channel));
+ Expression a_Im = Parameter(particleName+"::pole::" + std::to_string(pole)+"::a_im::"+std::to_string(channel));
+ a[{pole-1,channel-1}] = a_Re + I * a_Im;
+ }
+ }
+
+ for(unsigned k = 0 ; k < nChannels; ++k){
+ Expression b_Re = Parameter(particleName+"::b_re::"+std::to_string(k+1));
+ Expression b_Im = Parameter(particleName+"::b_im::"+std::to_string(k+1));
+ b[k] = (b_Re + I * b_Im); // * Bls[k]; ???
+ }
+
+ for(unsigned k = 0 ; k < nChannels; ++k){
+ for(unsigned alpha = 0; alpha < nPoles; ++alpha){
+ P[k] += (a[{alpha,k}] * poleConfigs[alpha].couplings[k])/poleConfigs[alpha].pole(s);
+ }
+ P[k] += b[k];
+ F_0 += propagator[{cTerm,k}] * P[k];
+ }
+ return F_0*FormFactor;
+ }
+ //P-vector from https://arxiv.org/pdf/0909.2171v1.pdf
+ else if(pa_type==PA_TYPE::PVecACCMOR){
+ INFO("Using ACCMOR P-vector approach to build the production amplitude");
+ Expression F_0 = 0;
+
+ std::vector<Expression> P(nChannels,0), b(nChannels,0);
+ Expression tau = Parameter(particleName+"::tau");
+
+ Tensor a( Tensor::dim(nPoles, nChannels) );
+ for (unsigned pole = 1; pole <= nPoles; ++pole ){
+ for( unsigned channel = 1 ; channel <= nChannels; ++channel ){
+ Expression a_Re = Parameter(particleName+"::pole::" + std::to_string(pole)+"::a_re::"+std::to_string(channel));
+ Expression a_Im = Parameter(particleName+"::pole::" + std::to_string(pole)+"::a_im::"+std::to_string(channel));
+ a[{pole-1,channel-1}] = a_Re + I * a_Im;
+ }
+ }
+
+ double mKPlus = 0.493677;
+ for(unsigned k = 0 ; k < nChannels; ++k){
+ Expression b_Re = Parameter(particleName+"::b_re::"+std::to_string(k+1));
+ Expression b_Im = Parameter(particleName+"::b_im::"+std::to_string(k+1));
+ b[k] = (b_Re + I * b_Im)/(s-mKPlus*mKPlus);
+ }
+
+ for(unsigned k = 0 ; k < nChannels; ++k){
+ // R_i
+ for(unsigned alpha = 0; alpha < nPoles; ++alpha){
+ P[k] += (a[{alpha,k}] * poleConfigs[alpha].couplings[k])/poleConfigs[alpha].pole(s);
+ }
+ // (1 + tau K_ij) D_j
+ for(unsigned l = 0 ; l < nChannels; ++l){
+ P[k] += ( ( k == l ? 1. : 0. ) + tau * kMatrix[{k, l}] ) * b[l];
+ }
+
+ F_0 += propagator[{cTerm,k}] * P[k];
+ }
+ return F_0*FormFactor;
+ }
+
+ else if(pa_type==PA_TYPE::QVec){
+ INFO("Using Q-vector approach to build the production amplitude");
+ Expression M;
+ for(unsigned k = 0 ; k < nChannels; ++k) M = M + kMatrix[{k,cTerm}] * propagator[{cTerm,k}];
+ return M ; // * phsps[0];
+ }
+ else throw std::runtime_error("This shouldn't happen. Currently supported types: P-vector approach (PA_TYPE::PVec) and Q-vector approach (PA_TYPE::QVec)");
}
diff --git a/src/Lineshapes/GounarisSakurai.cpp b/src/Lineshapes/GounarisSakurai.cpp
index 43a664952b9..4db2c02832f 100644
--- a/src/Lineshapes/GounarisSakurai.cpp
+++ b/src/Lineshapes/GounarisSakurai.cpp
@@ -43,12 +43,14 @@ DEFINE_LINESHAPE( GounarisSakurai )
Expression t3 = (s0-s)/q(s0);
Expression M2 = s0 + width0 * (t1 + t2 + t3 )/M_PI;
-
- Expression D = M2 - 1i*mass*width(s,s1,s2,mass,width0,0,L);
+ bool useRadius = lineshapeModifier.find("IncludeRadiusInWidth") != std::string::npos;
+ bool normalisedFF = lineshapeModifier.find("BL") != std::string::npos;
+ Expression D = M2 - 1i*mass*width(s, s1, s2, mass, width0, useRadius ? radius : 0, L);
const Expression q2 = abs( Q2( s, s1, s2 ) );
Expression FormFactor = sqrt( BlattWeisskopf_Norm( q2 * radius * radius, 0, L ) );
- if ( lineshapeModifier == "BL" ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, L ) );
+ if ( normalisedFF ) FormFactor = sqrt( BlattWeisskopf( q2 * radius * radius, L ) );
ADD_DEBUG( FormFactor , dbexpressions);
ADD_DEBUG( M2 , dbexpressions);
+ ADD_DEBUG( D, dbexpressions);
return kFactor( mass, width0, dbexpressions ) * FormFactor / (D-s);
}
diff --git a/src/Lineshapes/Isotensor.cpp b/src/Lineshapes/Isotensor.cpp
index 0d7030d7fa5..d2f2b0fa74d 100644
--- a/src/Lineshapes/Isotensor.cpp
+++ b/src/Lineshapes/Isotensor.cpp
@@ -1,11 +1,13 @@
#include <cmath>
#include <memory>
+#include <complex>
#include "AmpGen/Expression.h"
#include "AmpGen/Factory.h"
#include "AmpGen/Lineshapes.h"
using namespace AmpGen;
+using namespace std::complex_literals;
DEFINE_LINESHAPE( Isotensor )
{
@@ -23,8 +25,5 @@ DEFINE_LINESHAPE( Isotensor )
ADD_DEBUG( phaseShift, dbexpressions );
ADD_DEBUG( fcn::sqrt( s / 4 - mpi * mpi ), dbexpressions );
ADD_DEBUG( polyTerm, dbexpressions );
- Expression cos_shift = Cos( phaseShift );
- Expression sin_shift = Sin( phaseShift );
- Expression J = Constant(0,1);
- return ( cos_shift + J*sin_shift - 1 ) * (-0.5 * J );
+ return ( fcn::exp( 1i * phaseShift) - 1 ) / 2i;
}
diff --git a/src/Lineshapes/LASS.cpp b/src/Lineshapes/LASS.cpp
index eae25a1eb3f..1d6acb358ef 100644
--- a/src/Lineshapes/LASS.cpp
+++ b/src/Lineshapes/LASS.cpp
@@ -14,7 +14,6 @@ DEFINE_LINESHAPE( LASS )
{
const auto props = ParticlePropertiesList::get( particleName );
Expression mass = Parameter( particleName + "_mass", props->mass() );
- Expression radius = Parameter( particleName + "_radius", props->radius() );
Expression width0 = Parameter( particleName + "_width", props->width() );
Expression s0 = mass*mass;
Expression a = Parameter( "LASS::a", 2.07 );
@@ -32,13 +31,15 @@ DEFINE_LINESHAPE( LASS )
Expression tan_phi2 = mass*gamma / (s0 - s);
Expression phase = atan(tan_phi1) + atan(tan_phi2);
- ADD_DEBUG(sin(phase) * exp( i * phase ) / rho, dbexpressions );
Expression bw = ( mass * width0 ) / ( rho0 * ( s0 -s -i*mass*gamma ) );
Expression nrPhaseShift = ( 2 + a * r * q2 + i * 2*a*q ) / ( 2+a*r*q2 - i*2*a*q );
Expression NR = 2*a*sqrt(s)/( 2 + a*r*q*q -2*i*a*q );
+ ADD_DEBUG(s, dbexpressions );
ADD_DEBUG(nrPhaseShift*bw, dbexpressions );
ADD_DEBUG(NR, dbexpressions );
ADD_DEBUG(NR + bw*nrPhaseShift, dbexpressions );
+ ADD_DEBUG(sin(phase) * exp( i * phase ) , dbexpressions );
+ ADD_DEBUG(sin(phase) * exp( i * phase ) / rho, dbexpressions );
// Takes the splitting of the LASS into a "resonant" and "nonresonant"
// component from Laura++, as a better implementation of the "gLASS" lineshape
diff --git a/src/Lineshapes/ObelixRho.cpp b/src/Lineshapes/ObelixRho.cpp
deleted file mode 100644
index 238f076cc42..00000000000
--- a/src/Lineshapes/ObelixRho.cpp
+++ /dev/null
@@ -1,92 +0,0 @@
-#include <stddef.h>
-#include <ostream>
-#include <string>
-#include <vector>
-
-#include "AmpGen/Expression.h"
-#include "AmpGen/Factory.h"
-#include "AmpGen/Lineshapes.h"
-#include "AmpGen/MsgService.h"
-#include "AmpGen/ParticleProperties.h"
-#include "AmpGen/Tensor.h"
-#include "AmpGen/Utilities.h"
-
-using namespace AmpGen;
-
-#include "AmpGen/ParticlePropertiesList.h"
-#include "AmpGen/kMatrix.h"
-
-DEFINE_LINESHAPE( ObelixRho )
-{
- Expression sInGeV = SubTree( s / (GeV*GeV) );
- DEBUG( "kMatrix modifier " << lineshapeModifier << " particle = " << particleName );
- auto tokens = split( lineshapeModifier, '.' );
-
- DEBUG( "kMatrix modifier = " << lineshapeModifier << " nTokens = " << tokens.size() );
- unsigned int pTerm = tokens.size() > 0 ? stoi( tokens[0] ) : 999;
- if ( pTerm == 999 ) {
- ERROR( "Pole term not recognised: " << pTerm );
- }
-
- double mPiPlus( 0.139570 );
- double mKPlus( 0.493677 );
- std::vector<Expression> phaseSpace = {phsp_twoBody( sInGeV, mPiPlus, mPiPlus ), phsp_fourPi( sInGeV ),
- phsp_twoBody( sInGeV, mKPlus, mKPlus )};
- const unsigned int nPoles = 3;
- const unsigned int nChannels = 3;
- auto props = ParticlePropertiesList::get( "rho(770)0" );
-
- const Expression radius = Parameter( particleName + "_radius", props->radius() );
-
- std::vector<poleConfig> poleConfigs;
-
- for ( unsigned int i = 1; i <= nPoles; ++i ) {
- std::string stub = "rho_p" + std::to_string( i );
- Expression mRho = Parameter( ( stub + "_mass" ) );
- Expression gRho1 = Parameter( ( stub + "_pipi" ) );
- Expression gRho2 = Parameter( ( stub + "_4pi" ) );
- Expression gRho3 = Parameter( ( stub + "_KK" ) );
- poleConfig pole( mRho * mRho );
-
- pole.add( gFromGamma( mRho, gRho1, phsp_twoBody( mRho * mRho, mPiPlus, mPiPlus ) ),
- BL( sInGeV, mRho * mRho, mPiPlus * mPiPlus, mPiPlus * mPiPlus, radius, 1 ) );
-
- pole.add( gFromGamma( mRho, gRho2, phsp_fourPi( mRho * mRho ) ) );
-
- pole.add( gFromGamma( mRho, gRho3, phsp_twoBody( mRho * mRho, mKPlus, mKPlus ) ),
- BL( sInGeV, mRho * mRho, mKPlus * mKPlus, mKPlus * mKPlus, radius, 1 ) );
-
- poleConfigs.emplace_back( pole );
- }
-
- auto kMatrix = constructKMatrix( sInGeV, nChannels, poleConfigs );
-
- if ( dbexpressions != nullptr ) {
- for ( auto& p : poleConfigs ) {
- ADD_DEBUG( p.s, dbexpressions );
- ADD_DEBUG( p.couplings[0], dbexpressions );
- ADD_DEBUG( p.couplings[1], dbexpressions );
- ADD_DEBUG( p.couplings[2], dbexpressions );
- }
- ADD_DEBUG( phaseSpace[0], dbexpressions );
- ADD_DEBUG( phaseSpace[1], dbexpressions );
- ADD_DEBUG( phaseSpace[2], dbexpressions );
- for ( unsigned int i = 0; i < nChannels; ++i ) {
- for ( unsigned int j = 0; j < nChannels; ++j ) {
- dbexpressions->emplace_back( "K[" + std::to_string( i ) + "," + std::to_string( j ) + "]", kMatrix[{i, j}] );
- }
- }
- }
-
- Tensor propagator = getPropagator( kMatrix, phaseSpace );
-
- Expression M;
-
- auto pole = poleConfigs[pTerm];
- const Expression q2 = Abs( Q2( s, s1, s2 ) );
-
- for ( unsigned int i = 0; i < nChannels; ++i ) {
- M = M + propagator[{0, i}] * pole.g( i );
- }
- return SubTree( M / ( pole.s - sInGeV ) );
-}
diff --git a/src/Lineshapes/Photon.cpp b/src/Lineshapes/Photon.cpp
new file mode 100644
index 00000000000..4f241116a44
--- /dev/null
+++ b/src/Lineshapes/Photon.cpp
@@ -0,0 +1,11 @@
+#include "AmpGen/Lineshapes.h"
+#include "AmpGen/ParticlePropertiesList.h"
+
+using namespace AmpGen;
+
+DEFINE_LINESHAPE( Photon )
+{
+ auto props = ParticlePropertiesList::get( particleName );
+ Expression mass = Parameter( particleName + "_mass", props->mass() );
+ return 1. / ( s - mass*mass );
+}
diff --git a/src/Lineshapes/Poly.cpp b/src/Lineshapes/Poly.cpp
index 87ae781931a..5f21b6a63da 100644
--- a/src/Lineshapes/Poly.cpp
+++ b/src/Lineshapes/Poly.cpp
@@ -9,7 +9,10 @@ using namespace AmpGen;
DEFINE_LINESHAPE( Poly )
{
- unsigned int degree = NamedParameter<unsigned int>( lineshapeModifier + "::Degree" );
- auto params = parameterVector( lineshapeModifier + "_c", degree );
+ size_t degree = NamedParameter<size_t>( lineshapeModifier + "::Degree" );
+ auto params = parameterVector(lineshapeModifier + "_c", degree + 1);
+ ADD_DEBUG(s, dbexpressions);
+ if( dbexpressions != nullptr ) for( size_t i=0;i<params.size();++i )
+ dbexpressions->emplace_back( lineshapeModifier +"_c"+std::to_string(i), params[i] );
return pol(s, params);
}
diff --git a/src/Lineshapes/PolyNR.cpp b/src/Lineshapes/PolyNR.cpp
new file mode 100644
index 00000000000..7f1c0a49a91
--- /dev/null
+++ b/src/Lineshapes/PolyNR.cpp
@@ -0,0 +1,40 @@
+#include <string>
+
+#include "AmpGen/Expression.h"
+#include "AmpGen/Factory.h"
+#include "AmpGen/Lineshapes.h"
+#include "AmpGen/NamedParameter.h"
+
+using namespace AmpGen;
+
+DEFINE_GENERIC_SHAPE( PolyNR )
+{
+ auto p0 = *p.daughter(0);
+ auto p1 = *p.daughter(1);
+ auto p2 = *p.daughter(2);
+ auto p01 = (p0.P() + p1.P());
+ auto p02 = (p0.P() + p2.P());
+ auto s01 = dot( p01, p01 );
+ auto s02 = dot( p02, p02 );
+ size_t degree = NamedParameter<size_t>( lineshapeModifier + "::Degree" ) +1;
+ std::vector< std::vector<Parameter> > C( degree, std::vector<Parameter>(degree) );
+
+ for( size_t i = 0 ; i != degree ; ++i )
+ {
+ for( size_t j = 0 ; j != degree ; ++j ){
+ auto pname = lineshapeModifier +"_"+std::to_string(i) + "_"+std::to_string(j) ;
+ C[i][j] = Parameter(pname, 0);
+ if( dbexpressions != nullptr )
+ dbexpressions->emplace_back( pname, C[i][j] );
+ }
+ }
+ Expression rt;
+ for( size_t i = 0 ; i != degree; ++i )
+ {
+ for( size_t j = 0 ; j != degree ; ++j )
+ {
+ rt = rt + C[i][j] * fcn::pow(s01, i) * fcn::pow(s02, j);
+ }
+ }
+ return rt;
+}
diff --git a/src/Lineshapes/TD.cpp b/src/Lineshapes/TD.cpp
new file mode 100644
index 00000000000..6bfd744cec6
--- /dev/null
+++ b/src/Lineshapes/TD.cpp
@@ -0,0 +1,20 @@
+#include <stddef.h>
+#include <string>
+#include <vector>
+
+#include "AmpGen/Expression.h"
+#include "AmpGen/Factory.h"
+#include "AmpGen/Lineshapes.h"
+#include "AmpGen/Tensor.h"
+#include "AmpGen/ParticleProperties.h"
+
+using namespace AmpGen;
+using namespace AmpGen::fcn;
+
+DEFINE_GENERIC_SHAPE( TD )
+{
+ Expression tau = Parameter(p.name() +"_decayTime");
+ ADD_DEBUG( tau, dbexpressions );
+ ADD_DEBUG( p.props()->lifetime(), dbexpressions );
+ return tau / ( 2 * p.props()->lifetime() );
+}
diff --git a/src/Lineshapes/kMatrix.cpp b/src/Lineshapes/kMatrix.cpp
index 073406dd3be..958af51f123 100644
--- a/src/Lineshapes/kMatrix.cpp
+++ b/src/Lineshapes/kMatrix.cpp
@@ -24,7 +24,8 @@ Expression AmpGen::phsp_twoBody( const Expression& s, const double& m0, const do
Expression AmpGen::phsp_fourPi( const Expression& s )
{
- double mPiPlus( 0.139570 );
+ // Parameterisation of the 4pi phase-space taken from Laura++ (https://laura.hepforge.org/ or Ref. https://arxiv.org/abs/1711.09854)
+ double mPiPlus = 0.139570;
Expression rho_4pi = pol( s, {0.00051, -0.01933, 0.13851, -0.20840, -0.29744, 0.13655, 1.07885} );
return Ternary( s > 1, phsp_twoBody( s, 2 * mPiPlus, 2 * mPiPlus ), rho_4pi );
}
@@ -39,7 +40,7 @@ Expression AmpGen::phsp_FOCUS( const Expression& s, const double& m0, const doub
std::vector<Parameter> AmpGen::paramVector( const std::string& name, const unsigned int& nParam )
{
std::vector<Parameter> returnVector;
- for(size_t i = 0; i < nParam; ++i ) returnVector.emplace_back( name + std::to_string(i) );
+ for(unsigned i = 0; i < nParam; ++i ) returnVector.emplace_back( name + std::to_string(i) );
return returnVector;
}
@@ -48,26 +49,27 @@ Expression AmpGen::gFromGamma( const Expression& m, const Expression& gamma, con
return fcn::sqrt( m * gamma / rho );
}
-Tensor AmpGen::getPropagator(const Tensor& kMatrix, const std::vector<Expression>& phaseSpace)
+Tensor AmpGen::getPropagator(const Tensor& kMatrix, const std::vector<Expression>& phaseSpace, DebugSymbols* db )
{
unsigned int nChannels = kMatrix.dims()[0];
Tensor T( Tensor::dim(nChannels, nChannels) );
- for (size_t i = 0; i < nChannels; ++i ) {
- for (size_t j = 0; j < nChannels; ++j ) {
+ for (unsigned i = 0; i < nChannels; ++i ) {
+ for (unsigned j = 0; j < nChannels; ++j ) {
T[{i, j}] = SubTree( ( i == j ? 1 : 0 ) - 1i * kMatrix[{i, j}] * phaseSpace[j] );
}
}
+ ADD_DEBUG_TENSOR( T, db );
return T.Invert();
}
-Tensor AmpGen::constructKMatrix(const Expression& this_s, const size_t& nChannels, const std::vector<poleConfig>& poleConfigs)
+Tensor AmpGen::constructKMatrix(const Expression& this_s, const unsigned& nChannels, const std::vector<poleConfig>& poleConfigs)
{
Tensor kMatrix( Tensor::dim(nChannels, nChannels));
- for ( size_t i = 0; i < nChannels; ++i ) {
- for ( size_t j = 0; j < nChannels; ++j ) {
+ for ( unsigned i = 0; i < nChannels; ++i ) {
+ for ( unsigned j = 0; j < nChannels; ++j ) {
Expression sumOverPoles = 0;
for ( auto& pole : poleConfigs ) {
- Expression term = ( pole.couplings[i] * pole.couplings[j] ) / ( pole.s - this_s );
+ Expression term = ( pole.couplings[i] * pole.couplings[j] ) / ( pole.pole(this_s) );
sumOverPoles = sumOverPoles + term;
}
kMatrix[{i, j}] = sumOverPoles;
@@ -91,7 +93,7 @@ DEFINE_LINESHAPE( kMatrix )
double mPiPlus = 0.139570;
double mKPlus = 0.493677;
double mEta = 0.547862;
- double mEtap = 0.96778;
+ double mEtap = 0.967780;
Expression sA0 = Parameter( "sA0", -0.15 );
Expression sA = Parameter( "sA", 1.0 );
@@ -100,11 +102,11 @@ DEFINE_LINESHAPE( kMatrix )
std::vector<Parameter> fScatt = paramVector( "f_scatt", nChannels );
std::vector<poleConfig> poleConfigs;
-
+ bool addImaginaryMass = NamedParameter<bool>("kMatrix::fp", true );
for ( unsigned int pole = 1; pole <= nPoles; ++pole ) {
std::string stub = "IS_p" + std::to_string( pole ) + "_";
Expression mass = Parameter( stub + "mass" );
- poleConfig p( mass * mass );
+ poleConfig p( mass * mass + addImaginaryMass * (1i)*(1.e-6) ); /// add a tiny imaginary part to the mass to avoid floating point errors //
for ( unsigned int ch = 0; ch < nChannels; ++ch ) p.add( Parameter( stub + channels[ch] ) );
poleConfigs.push_back( p );
}
@@ -117,7 +119,7 @@ DEFINE_LINESHAPE( kMatrix )
auto kMatrix = constructKMatrix( sInGeV, 5, poleConfigs);
Tensor scattPart( Tensor::dim(5,5) );
- for(size_t i = 0; i < 5;++i){
+ for(unsigned i = 0; i < 5;++i){
scattPart(i,0) = fScatt[i]*( 1 - s0_scatt )/( s - s0_scatt );
scattPart(0,i) = fScatt[i]*( 1 - s0_scatt )/( s - s0_scatt );
}
@@ -128,7 +130,7 @@ DEFINE_LINESHAPE( kMatrix )
Expression adlerTerm = SubTree( ( 1. - sA0 ) * ( sInGeV - sA * mPiPlus * mPiPlus / 2 ) / ( sInGeV - sA0 ) );
kMatrix = adlerTerm * kMatrix;
- Tensor F = getPropagator(kMatrix, phaseSpace);
+ Tensor F = getPropagator(kMatrix, phaseSpace, dbexpressions);
if ( dbexpressions != nullptr ) {
for ( auto& p : poleConfigs ) {
@@ -146,6 +148,7 @@ DEFINE_LINESHAPE( kMatrix )
ADD_DEBUG( sA0, dbexpressions );
ADD_DEBUG( adlerTerm, dbexpressions );
ADD_DEBUG_TENSOR( kMatrix, dbexpressions );
+ ADD_DEBUG_TENSOR( F, dbexpressions );
}
if ( tokens[0] == "scatt" ) {
@@ -181,6 +184,6 @@ DEFINE_LINESHAPE( kMatrix )
DEBUG( "Returning bkg term" );
return F[{1, pTerm}] * ( 1 - s0_prod ) / ( sInGeV - s0_prod );
}
- ERROR( "Lineshape not found: " << lineshapeModifier );
+ ERROR( "Modifier not found: " << lineshapeModifier << ", expecting one of {scatt, pole, poleKK, prod, prodKK}" );
return Expression( 0 );
}
diff --git a/src/Minimiser.cpp b/src/Minimiser.cpp
index bd92ccfbc44..b28f69fcaa5 100644
--- a/src/Minimiser.cpp
+++ b/src/Minimiser.cpp
@@ -8,7 +8,6 @@
#include <iomanip>
#include <Minuit2/Minuit2Minimizer.h>
-
#include "AmpGen/IExtendLikelihood.h"
#include "AmpGen/MinuitParameter.h"
#include "AmpGen/MinuitParameterSet.h"
@@ -18,34 +17,31 @@
#include "Math/Factory.h"
#include "Math/Functor.h"
#include "Math/Minimizer.h"
+#include "AmpGen/ProfileClock.h"
using namespace AmpGen;
using namespace ROOT;
unsigned int Minimiser::nPars() const { return m_nParams; }
-void Minimiser::print( const double& LL )
-{
- INFO( "Iteration # " << m_lastPrint << " FCN = " << round( LL, 3 ) << " Edm = " << round( m_minimiser->Edm(), 3 )
- << " NCalls = " << m_minimiser->NCalls() );
-}
-
double Minimiser::operator()( const double* xx )
{
- for ( unsigned int i = 0; i < m_mapping.size(); ++i ) {
- m_parSet->getParPtr( m_mapping[i] )->setCurrentFitVal( xx[i] );
+ ProfileClock callTime;
+ for(size_t i = 0; i < m_mapping.size(); ++i ) {
+ m_parSet->at( m_mapping[i] )->setCurrentFitVal( xx[i] );
}
- double LL = m_theFunction();
- for ( auto& extendTerm : m_extendedTerms ) {
- LL -= 2 * extendTerm->getVal();
- }
- return LL;
+ double LL = m_theFunction() ;
+ for ( auto& extendTerm : m_extendedTerms ) LL -= 2 * extendTerm->getVal();
+ callTime.stop();
+ return LL - m_ll_zero;
}
-void Minimiser::GradientTest()
+double Minimiser::FCN() const { return m_theFunction(); }
+
+void Minimiser::gradientTest()
{
- for ( unsigned int i = 0; i < m_mapping.size(); ++i ) {
- auto parameter = m_parSet->getParPtr( m_mapping[i] );
+ for (size_t i = 0; i < m_mapping.size(); ++i) {
+ auto parameter = m_parSet->at( m_mapping[i] );
double m = parameter->mean();
parameter->setCurrentFitVal( parameter->meanInit() + parameter->stepInit() );
double vp = FCN();
@@ -59,38 +55,34 @@ void Minimiser::GradientTest()
parameter->setCurrentFitVal( m );
}
}
-double Minimiser::FCN() const { return m_theFunction(); }
void Minimiser::prepare()
{
std::string algorithm = NamedParameter<std::string>( "Minimiser::Algorithm", "Hesse");
size_t maxCalls = NamedParameter<size_t>( "Minimiser::MaxCalls" , 100000);
- double tolerance = NamedParameter<double>( "Minimiser::Tolerance" , 0.01);
+ double tolerance = NamedParameter<double>( "Minimiser::Tolerance" , 1.0);
m_printLevel = NamedParameter<size_t>( "Minimiser::PrintLevel", 4);
+ m_normalise = NamedParameter<bool>( "Minimiser::Normalise",false);
if ( m_minimiser != nullptr ) delete m_minimiser;
m_minimiser = new Minuit2::Minuit2Minimizer(algorithm.c_str() );
DEBUG( "Error definition = " << m_minimiser->ErrorDef() );
m_minimiser->SetMaxFunctionCalls( maxCalls );
m_minimiser->SetMaxIterations( 100000 );
m_minimiser->SetTolerance( tolerance );
+// m_minimiser->SetStrategy( 3 );
+ // m_minimiser->SetPrecision(std::numeric_limits<double>::epsilon());
m_minimiser->SetPrintLevel( m_printLevel );
m_mapping.clear();
m_covMatrix.clear();
- for(size_t i = 0 ; i < m_parSet->size(); ++i)
+ for(size_t i = 0 ; i < m_parSet->size(); ++i)
{
- auto par = m_parSet->getParPtr(i);
- if ( par->iFixInit() != 0 ) continue;
+ auto par = m_parSet->at(i);
+ if ( ! par->isFree() ) continue;
m_minimiser->SetVariable(m_mapping.size(), par->name(), par->mean(), par->stepInit());
- if ( par->minInit() != 0 || par->maxInit() != 0 )
+ if ( par->minInit() != 0 || par->maxInit() != 0 )
m_minimiser->SetVariableLimits( m_mapping.size(), par->minInit(), par->maxInit() );
m_mapping.push_back(i);
- if ( m_printLevel != 0 ) {
- INFO( "Parameter: " << std::left << std::setw(60) << par->name() << " = "
- << std::right << std::setw(12) << par->mean() << " ± "
- << std::left << std::setw(12) << par->stepInit()
- << ( ( par->minInit() != 0 || par->maxInit() != 0 ) ?
- ("["+ std::to_string(par->minInit()) + ", " + std::to_string(par->maxInit() ) ) + "]" : "" ) );
- }
+ if ( m_printLevel != 0 ) INFO( *par );
}
m_nParams = m_mapping.size();
m_covMatrix.resize( m_nParams * m_nParams, 0 );
@@ -98,19 +90,18 @@ void Minimiser::prepare()
bool Minimiser::doFit()
{
- m_lastPrint = 999;
+ if( m_normalise ) m_ll_zero = m_theFunction();
ROOT::Math::Functor f( *this, m_nParams );
- for ( unsigned int i = 0; i < m_mapping.size(); ++i ) {
- MinuitParameter* par = m_parSet->getParPtr( m_mapping[i] );
+ for (size_t i = 0; i < m_mapping.size(); ++i ) {
+ MinuitParameter* par = m_parSet->at( m_mapping[i] );
m_minimiser->SetVariable( i, par->name(), par->mean(), par->stepInit() );
if ( par->minInit() != 0 || par->maxInit() != 0 )
m_minimiser->SetVariableLimits( i, par->minInit(), par->maxInit() );
}
-
m_minimiser->SetFunction( f );
m_minimiser->Minimize();
- for ( unsigned int i = 0; i < m_nParams; ++i ) {
- auto par = m_parSet->getParPtr( m_mapping[i] );
+ for (size_t i = 0; i < m_nParams; ++i ) {
+ auto par = m_parSet->at( m_mapping[i] );
double error = *( m_minimiser->Errors() + i );
par->setResult( *( m_minimiser->X() + i ), error, error, error );
for ( unsigned int j = 0; j < m_nParams; ++j ) {
@@ -118,6 +109,21 @@ bool Minimiser::doFit()
}
}
m_status = m_minimiser->Status();
+ if(NamedParameter<bool>("Minimiser::RunMinos",false)){
+ for( unsigned i = 0 ; i != m_nParams; ++i ){
+ double low = 0;
+ double high = 0;
+ int status = 0;
+ m_minimiser->GetMinosError(i, low, high, status);
+ auto param = m_parSet->at( m_mapping[i] );
+ param->setResult( *param, param->err(), low, high );
+ }
+ for( unsigned i = 0 ; i != m_nParams; ++i )
+ {
+ auto param = m_parSet->at( m_mapping[i] );
+ INFO( param->name() << " " << param->mean() << " " << param->errPos() << " " << param->errNeg() );
+ }
+ }
return 1;
}
@@ -162,8 +168,9 @@ TMatrixTSym<double> Minimiser::covMatrixFull() const
MinuitParameterSet* Minimiser::parSet() const { return m_parSet; }
void Minimiser::addExtendedTerm( IExtendLikelihood* m_term )
-{
- m_extendedTerms.push_back( m_term );
+{
+ m_extendedTerms.push_back( m_term );
}
-ROOT::Math::Minimizer* Minimiser::minimiserInternal() { return m_minimiser; }
+ROOT::Minuit2::Minuit2Minimizer* Minimiser::minimiserInternal() { return m_minimiser; }
+
diff --git a/src/MinuitExpression.cpp b/src/MinuitExpression.cpp
index 1625781e92f..d9f1c015ae1 100644
--- a/src/MinuitExpression.cpp
+++ b/src/MinuitExpression.cpp
@@ -12,9 +12,19 @@ using namespace AmpGen;
MinuitExpression::MinuitExpression( const std::vector<std::string>& tokens, MinuitParameterSet* mps )
{
setName( tokens[0] );
- std::string total_line = "";
- for ( size_t it = 2; it != tokens.size(); ++it ) total_line += tokens[it] + " ";
- ExpressionParser::getMe()->setMPS( mps );
- m_expression = ExpressionParser::Parse( total_line );
- m_isGood = true;
+ m_expression = ExpressionParser::parse(tokens.begin() + 2 , tokens.end() , mps );
+ fix();
}
+
+MinuitExpression::MinuitExpression(const std::string& name, const Expression& expression)
+{
+ setName(name);
+ m_expression = expression;
+ fix();
+}
+
+double MinuitExpression::mean() const { return std::real(getVal()); }
+complex_t MinuitExpression::getVal() const { return m_expression(); }
+MinuitExpression::operator double() const { return std::real(getVal()); }
+MinuitExpression::~MinuitExpression() = default;
+
diff --git a/src/MinuitParameter.cpp b/src/MinuitParameter.cpp
index 8edc615e4a9..b0913ea5ae3 100644
--- a/src/MinuitParameter.cpp
+++ b/src/MinuitParameter.cpp
@@ -1,6 +1,7 @@
// author: Jonas Rademacker (Jonas.Rademacker@bristol.ac.uk)
// status: Mon 9 Feb 2009 19:17:55 GMT
#include "AmpGen/MinuitParameter.h"
+#include "AmpGen/Utilities.h"
#include <iomanip>
@@ -8,28 +9,39 @@
using namespace AmpGen;
-MinuitParameter::MinuitParameter( const std::string& name, const MinuitParameter::Flag& fix, const double& mean, const double& step,
+namespace AmpGen {
+ complete_enum( Flag, Free, Hide, Fix, CompileTimeConstant, Invalid )
+}
+
+MinuitParameter::MinuitParameter( const std::string& name, const Flag& fix, const double& mean, const double& step,
const double& mi, const double& ma )
- : m_iFixInit( fix ), m_name( name ), m_meanInit( mean ), m_stepInit( step ), m_minInit( mi ), m_maxInit( ma )
+ : m_flag( fix ), m_name( name ), m_meanInit( mean ), m_stepInit( step ), m_minInit( mi ), m_maxInit( ma )
{
DEBUG( "Building parameter : " << name );
resetToInit();
}
-MinuitParameter::Flag MinuitParameter::iFixInit() const { return m_iFixInit; }
-
-double MinuitParameter::meanInit() const { return m_meanInit; }
-double MinuitParameter::stepInit() const { return m_stepInit; }
-double MinuitParameter::minInit() const { return m_minInit; }
-double MinuitParameter::maxInit() const { return m_maxInit; }
-double MinuitParameter::mean() const { return m_meanResult; }
-double MinuitParameter::errPos() const { return m_errPosResult; }
-double MinuitParameter::errNeg() const { return m_errNegResult; }
-double MinuitParameter::err() const { return m_errResult; }
-
-bool MinuitParameter::fixed() { return m_iFixInit == Flag::Fix; }
+MinuitParameter::MinuitParameter( const std::string& name, const double& mean, const double& step, const double& mi, const double& ma )
+ : MinuitParameter(name, Flag::Free, m_meanInit, m_stepInit, m_minInit, m_maxInit )
+{
+ DEBUG( "Building parameter : " << name );
+ resetToInit();
+}
-void MinuitParameter::fix() { m_iFixInit = Flag::Fix; }
+Flag MinuitParameter::flag() const { return m_flag; }
+double MinuitParameter::meanInit() const { return m_meanInit; }
+double MinuitParameter::stepInit() const { return m_stepInit; }
+double MinuitParameter::minInit() const { return m_minInit; }
+double MinuitParameter::maxInit() const { return m_maxInit; }
+double MinuitParameter::mean() const { return m_meanResult; }
+double MinuitParameter::errPos() const { return m_errPosResult; }
+double MinuitParameter::errNeg() const { return m_errNegResult; }
+double MinuitParameter::err() const { return m_errResult; }
+bool MinuitParameter::isFixed() const { return m_flag == Flag::Fix || m_flag == Flag::CompileTimeConstant; }
+bool MinuitParameter::isFree() const { return m_flag == Flag::Free; }
+const std::string& MinuitParameter::name() const { return m_name; }
+
+void MinuitParameter::fix() { m_flag = Flag::Fix; }
void MinuitParameter::scaleStep( const double& sf )
{
m_errResult *= sf;
@@ -40,14 +52,17 @@ void MinuitParameter::setStepInit( const double& si )
m_stepInit = si;
}
-const std::string& MinuitParameter::name() const { return m_name; }
-bool MinuitParameter::hidden() const { return m_iFixInit == 1; }
-void MinuitParameter::setFree() { INFO("Setting parameter: " << m_name << " free" ) ; m_iFixInit = Flag::Float; }
+void MinuitParameter::setFree() { INFO("Setting parameter: " << m_name << " free" ) ; m_flag = Flag::Free; }
void MinuitParameter::setCurrentFitVal( double cfv ) { m_meanResult = cfv; }
-void MinuitParameter::setInit( const double& val ) { m_meanInit = val; }
+void MinuitParameter::setInit( const double& val, const double& step )
+{
+ m_meanInit = val;
+ m_meanResult = val;
+ if( step != -1 ) m_stepInit = step;
+}
void MinuitParameter::setResult( double fitMean, double fitErr, double fitErrPos, double fitErrNeg )
{
@@ -57,11 +72,6 @@ void MinuitParameter::setResult( double fitMean, double fitErr, double fitErrPos
m_errNegResult = fitErrNeg;
}
-void MinuitParameter::print( std::ostream& os ) const
-{
- os << std::left << std::setw(65) << name() << "\t" << iFixInit() << "\t" << mean() << "\t" << err() << "\t" << minInit() << "\t" << maxInit();
-}
-
void MinuitParameter::setName( const std::string& name ) { m_name = name; }
void MinuitParameter::resetToInit()
@@ -77,3 +87,13 @@ void MinuitParameter::setLimits( const double& min, const double& max )
m_minInit = min;
m_maxInit = max;
}
+
+std::ostream& AmpGen::operator<<( std::ostream& os, const MinuitParameter& par )
+{
+ return os << std::left << std::setw(60) << par.name() << " = "
+ << std::right << std::setw(12) << par.mean() << " ± "
+ << std::left << std::setw(12) << par.stepInit()
+ << ( ( par.minInit() != 0 || par.maxInit() != 0 ) ?
+ ("["+ std::to_string(par.minInit()) + ", " + std::to_string(par.maxInit() ) ) + "]" : "")
+ << " [flag=" << to_string<Flag>(par.flag()) << "]";
+}
diff --git a/src/MinuitParameterSet.cpp b/src/MinuitParameterSet.cpp
index 72b23ba6b77..39ed23b5433 100644
--- a/src/MinuitParameterSet.cpp
+++ b/src/MinuitParameterSet.cpp
@@ -21,185 +21,133 @@ using namespace AmpGen;
MinuitParameterSet::MinuitParameterSet() = default;
-MinuitParameterSet::MinuitParameterSet( const MinuitParameterSet& other )
- : _parPtrList( other._parPtrList ), _keyAccess( other._keyAccess )
+MinuitParameterSet::MinuitParameterSet(const std::vector<MinuitParameter*>& params )
{
-}
-
-MinuitParameterSet MinuitParameterSet::getFloating()
-{
- MinuitParameterSet floating;
- for ( auto& param : *this ) {
- if ( param->iFixInit() == MinuitParameter::Flag::Float ) floating.add(param);
- }
- return floating;
+ for( auto& param : params ) add(param);
}
bool MinuitParameterSet::addToEnd( MinuitParameter* parPtr )
{
bool success = true;
if ( nullptr == parPtr ) return false;
-
- _parPtrList.push_back( parPtr );
-
- if ( _keyAccess.find( parPtr->name() ) != _keyAccess.end() ) {
+ m_parameters.push_back( parPtr );
+ if ( m_keyAccess.find( parPtr->name() ) != m_keyAccess.end() ) {
WARNING( "Parameter with name " << parPtr->name() << " already exists!" );
}
- _keyAccess[parPtr->name()] = parPtr;
+ m_keyAccess[parPtr->name()] = parPtr;
return success;
}
-MinuitParameter* MinuitParameterSet::add( const std::string& name, const unsigned int& flag, const double& mean,
- const double& sigma, const double& min, const double& max )
+MinuitParameter* MinuitParameterSet::add( const std::string& name, const Flag& flag, const double& mean,
+ const double& sigma, const double& min, const double& max )
{
- addToEnd( new MinuitParameter( name, MinuitParameter::Flag(flag), mean, sigma, min, max ) );
- return _keyAccess[name];
+ addToEnd( new MinuitParameter( name, Flag(flag), mean, sigma, min, max ) );
+ return m_keyAccess[name];
}
bool MinuitParameterSet::add( MinuitParameter* parPtr ) { return addToEnd( parPtr ); }
bool MinuitParameterSet::unregister( MinuitParameter* parPtr )
{
- if ( _parPtrList.end() == std::find( _parPtrList.begin(), _parPtrList.end(), parPtr ) ) {
+ if ( m_parameters.end() == std::find( m_parameters.begin(), m_parameters.end(), parPtr ) ) {
WARNING( "parPtr you want to unregister is not part of this list!" );
return false;
}
- _parPtrList.erase( remove( _parPtrList.begin(), _parPtrList.end(), parPtr ), _parPtrList.end() );
+ m_parameters.erase( remove( m_parameters.begin(), m_parameters.end(), parPtr ), m_parameters.end() );
return true;
}
-unsigned int MinuitParameterSet::size() const { return _parPtrList.size(); }
-
-MinuitParameter* MinuitParameterSet::getParPtr( unsigned int i ) const
-{
- if ( i >= _parPtrList.size() ) return nullptr;
- return _parPtrList[i];
-}
-
-void MinuitParameterSet::deleteListAndObjects()
-{
- for ( auto it = _parPtrList.begin(); it != _parPtrList.end(); ++it ) {
- delete *it;
- }
- _parPtrList.clear();
-}
-
-void MinuitParameterSet::deleteListKeepObjects() { _parPtrList.clear(); }
+unsigned int MinuitParameterSet::size() const { return m_parameters.size(); }
void MinuitParameterSet::print( std::ostream& os ) const
{
- for ( unsigned int i = 0; i < size(); i++ ) {
- if ( nullptr == getParPtr( i ) ) continue;
- os << '\n';
- getParPtr( i )->print( os );
+ for (size_t i = 0; i < size(); i++ ) {
+ os << '\n' << *m_parameters[i];
}
os << '\n';
}
void MinuitParameterSet::printVariable( std::ostream& os ) const
{
- for ( unsigned int i = 0; i < size(); i++ ) {
- if ( nullptr == getParPtr( i ) ) continue;
- if ( getParPtr( i )->iFixInit() == 1 ) continue; /// hide parameter
- os << '\n';
- getParPtr( i )->print( os );
+ for (size_t i = 0; i < size(); i++ ) {
+ if ( m_parameters[i]->flag() == Flag::Hide ) continue; /// hide parameter
+ os << '\n' << *m_parameters[i];
}
}
MinuitParameter* MinuitParameterSet::operator[]( const std::string& key )
{
- auto it = _keyAccess.find( key );
- if ( it == _keyAccess.end() ) {
+ auto it = m_keyAccess.find( key );
+ if ( it == m_keyAccess.end() ) {
WARNING( "Parameter: " << key << " not found" );
}
return it->second;
}
+
MinuitParameter* MinuitParameterSet::operator[]( const std::string& key ) const
{
- auto it = _keyAccess.find( key );
- if ( it == _keyAccess.end() ) {
+ auto it = m_keyAccess.find( key );
+ if ( it == m_keyAccess.end() ) {
WARNING( "Parameter: " << key << " not found" );
}
return it->second;
}
-MinuitParameter* MinuitParameterSet::operator[]( const unsigned int& key ) { return _parPtrList[key]; }
+
+MinuitParameter* MinuitParameterSet::operator[]( const size_t& key ) { return m_parameters[key]; }
+
MinuitParameter* MinuitParameterSet::at( const std::string& key )
{
- if ( _keyAccess.count( key ) == 0 ) {
+ if ( m_keyAccess.count( key ) == 0 ) {
ERROR( key << " not found" );
return nullptr;
} else
- return _keyAccess[key];
+ return m_keyAccess[key];
+}
+
+MinuitParameter* MinuitParameterSet::at( const size_t& index ) const
+{
+ if( index >= m_parameters.size() )
+ ERROR( "Attempting to access parameter " << index << " when only " << m_parameters.size() << " have been defined" );
+ return index < m_parameters.size() ? m_parameters[index] : nullptr;
}
+
void MinuitParameterSet::tryParameter( const std::vector<std::string>& line )
{
+ bool status = true;
if ( line.size() == 4 || line.size() == 6 ) {
- bool status = true;
- int flag = lexical_cast<int>( line[1], status );
- if( flag > 3 ) return ;
+ bool hasLimits = line.size() == 6;
double mean = lexical_cast<double>( line[2], status );
double step = lexical_cast<double>( line[3], status );
- double min = line.size() == 6 ? lexical_cast<double>( line[4], status ) : 0;
- double max = line.size() == 6 ? lexical_cast<double>( line[5], status ) : 0;
-
- if ( status ) {
- if ( OptionsParser::printHelp() )
- INFO( "MINUIT: Registered " << line[0] << " (flag " << flag << ") = " << mean << ", step=" << step << " ("
- << min << "," << max << ")" );
- add( new MinuitParameter( line[0], MinuitParameter::Flag(flag), mean, step, min, max ) );
- }
- return;
+ double min = hasLimits ? lexical_cast<double>( line[4], status ) : 0;
+ double max = hasLimits ? lexical_cast<double>( line[5], status ) : 0;
+ if( !status ) return;
+ auto flag = parse<Flag>( line[1] );
+ if( flag == Flag::Invalid ) return;
+ if ( OptionsParser::printHelp() )
+ INFO( "MINUIT: Registered " << line[0] << " ( " << to_string<Flag>(flag) << ") = " << mean << ", step=" << step << " ("<< min << "," << max << ")" );
+ add( new MinuitParameter( line[0], flag, mean, step, min, max ) );
}
- if ( line.size() == 7 ) {
-
- bool status = true;
- int flag_re = lexical_cast<int>( line[1], status );
+ if ( line.size() == 7 || line.size() == 11 ) {
+ bool hasLimits = line.size() == 11;
double mean_re = lexical_cast<double>( line[2], status );
double step_re = lexical_cast<double>( line[3], status );
- int flag_im = lexical_cast<int>( line[4], status );
- double mean_im = lexical_cast<double>( line[5], status );
- double step_im = lexical_cast<double>( line[6], status );
+ double min_re = hasLimits ? lexical_cast<double>( line[4], status ) : 0;
+ double max_re = hasLimits ? lexical_cast<double>( line[5], status ) : 0;
+ double mean_im = lexical_cast<double>( line[5 + 2 *hasLimits], status );
+ double step_im = lexical_cast<double>( line[6 + 2 *hasLimits], status );
+ double min_im = hasLimits ? lexical_cast<double>( line[9] , status ) : 0;
+ double max_im = hasLimits ? lexical_cast<double>( line[10], status ) : 0;
- double min_re = 0;
- double max_re = 0;
- double min_im = 0;
- double max_im = 0;
if ( !status ) return;
-
- if ( NamedParameter<unsigned int>( "MinuitParameterSet::RegulateParameters", 0 ) == 1 ) {
- if ( mean_re < 0 ) {
- mean_re = -mean_re;
- mean_im = mean_im + M_PI;
- }
- mean_im = atan2( sin( mean_im ), cos( mean_im ) );
- max_re = 1000;
- }
+ auto flag_re = parse<Flag>(line[1]);
+ auto flag_im = parse<Flag>(line[4 + 2*hasLimits]);
+ if( flag_re == Flag::Invalid || flag_im == Flag::Invalid ) return;
if ( OptionsParser::printHelp() ) {
- INFO( "MINUIT: Complex " << line[0] << "_Re (flag " << flag_re << ") = " << mean_re << ", step=" << step_re
- << " (" << min_re << "," << max_re << ")" );
- INFO( "MINUIT: Complex " << line[0] << "_Im (flag " << flag_im << ") = " << mean_im << ", step=" << step_im
- << " (" << min_im << "," << max_im << ")" );
+ INFO( "MINUIT: Complex " << line[0] << "_Re ( " << to_string<Flag>(flag_re) << ") = " << mean_re << ", step=" << step_re << " (" << min_re << "," << max_re << ")" );
+ INFO( "MINUIT: Complex " << line[0] << "_Im ( " << to_string<Flag>(flag_im) << ") = " << mean_im << ", step=" << step_im << " (" << min_im << "," << max_im << ")" );
}
- add( new MinuitParameter( line[0] + "_Re", MinuitParameter::Flag(flag_re), mean_re, step_re, min_re, max_re ) );
- add( new MinuitParameter( line[0] + "_Im", MinuitParameter::Flag(flag_im), mean_im, step_im, min_im, max_im ) );
- }
- if ( line.size() == 11 ) {
-
- bool status = true;
- int flag_re = lexical_cast<int>( line[1], status );
- double mean_re = lexical_cast<double>( line[2], status );
- double step_re = lexical_cast<double>( line[3], status );
- double min_re = lexical_cast<double>( line[4], status );
- double max_re = lexical_cast<double>( line[5], status );
- int flag_im = lexical_cast<int>( line[6], status );
- double mean_im = lexical_cast<double>( line[7], status );
- double step_im = lexical_cast<double>( line[8], status );
- double min_im = lexical_cast<double>( line[9], status );
- double max_im = lexical_cast<double>( line[10], status );
- if ( !status ) return;
-
- add( new MinuitParameter( line[0] + "_Re", MinuitParameter::Flag(flag_re), mean_re, step_re, min_re, max_re ) );
- add( new MinuitParameter( line[0] + "_Im", MinuitParameter::Flag(flag_im), mean_im, step_im, min_im, max_im ) );
+ add( new MinuitParameter( line[0] + "_Re", flag_re, mean_re, step_re, min_re, max_re ) );
+ add( new MinuitParameter( line[0] + "_Im", flag_im, mean_im, step_im, min_im, max_im ) );
}
}
@@ -207,42 +155,29 @@ void MinuitParameterSet::tryAlias( const std::vector<std::string>& line )
{
if ( line.size() < 3 ) return;
if ( line[1] == "=" ) {
- std::string name = line[0];
- MinuitExpression* expr = new MinuitExpression( line, this );
- if ( expr->isGood() ) {
- _aliasList.push_back( expr );
- _keyAccess[name] = expr;
- } else {
- ERROR( "Expression is ill-formed: " << line[0] );
- delete expr;
- }
+ addToEnd( new MinuitExpression(line, this) );
}
}
void MinuitParameterSet::loadFromStream()
{
auto ppfl = OptionsParser::getMe();
-
std::vector<std::vector<std::string>> protoAliases;
-
for ( auto it = ppfl->begin(); it != ppfl->end(); ++it ) {
tryParameter( it->second );
if ( it->second.size() >= 3 && it->second[1] == "=" ) protoAliases.push_back( it->second );
}
for ( auto& alias : protoAliases ) tryAlias( alias );
- // print();
}
void MinuitParameterSet::loadFromFile( const std::string& file )
{
processFile( file, [this]( auto& line ) {
- this->tryParameter( split( line, {' ', '\t'} ) );
- this->tryAlias( split( line, {' ', '\t'} ) );
- } );
+ this->tryParameter( split( line, {' ', '\t'} ) );
+ this->tryAlias( split( line, {' ', '\t'} ) );
+ } );
}
-MinuitParameterSet::~MinuitParameterSet() = default;
-
void MinuitParameterSet::set( const MinuitParameterSet& other )
{
for ( auto& param : *this ) {
@@ -256,9 +191,54 @@ void MinuitParameterSet::resetToInit()
for ( auto& param : *this ) param->resetToInit();
}
-MinuitParameter* MinuitParameterSet::addOrGet( const std::string& name, const unsigned int& flag, const double& mean,
- const double& sigma, const double& min, const double& max )
+
+bool MinuitParameterSet::rename(const std::string& name, const std::string& new_name)
{
- if ( _keyAccess.count( name ) != 0 ) return _keyAccess[name];
+ auto it = find(name);
+ if( it == nullptr ){
+ DEBUG("Parameter: " << name << " not found");
+ return false;
+ }
+ if( name == new_name ) return false;
+ if( find(new_name) != nullptr ){
+ DEBUG("New key for " << name << " = " << new_name << " already exists");
+ return false;
+ }
+ it->setName(new_name);
+ m_keyAccess.erase(name);
+ m_keyAccess.emplace(new_name, it);
+ return true;
+}
+
+MinuitParameter* MinuitParameterSet::addOrGet( const std::string& name, const Flag& flag, const double& mean,
+ const double& sigma, const double& min, const double& max )
+{
+ if ( m_keyAccess.count( name ) != 0 ) return m_keyAccess[name];
return add( name, flag, mean, sigma, min, max );
}
+
+MinuitParameterSet::const_iterator MinuitParameterSet::cbegin() const { return m_parameters.cbegin(); }
+MinuitParameterSet::const_iterator MinuitParameterSet::cend() const { return m_parameters.cend(); }
+MinuitParameterSet::iterator MinuitParameterSet::begin() { return m_parameters.begin(); }
+MinuitParameterSet::iterator MinuitParameterSet::end() { return m_parameters.end(); }
+MinuitParameterSet::const_iterator MinuitParameterSet::begin() const { return m_parameters.cbegin(); }
+MinuitParameterSet::const_iterator MinuitParameterSet::end() const { return m_parameters.cend(); }
+
+MinuitParameter* MinuitParameterSet::find( const std::string& key ) const
+{
+ auto it = m_keyAccess.find(key);
+ return it == m_keyAccess.end() ? nullptr : it->second;
+}
+
+double MinuitParameterSet::operator()( const std::string& name )
+{
+ if ( m_keyAccess.find(name) == m_keyAccess.end() ) {
+ ERROR( "Cannot find parameter " << name );
+ }
+ return m_keyAccess[name]->mean();
+}
+
+MinuitParameterSet::~MinuitParameterSet()
+{
+ for( auto& param : m_parameters ) if( param != nullptr ) delete param;
+}
diff --git a/src/NamedParameter.cpp b/src/NamedParameter.cpp
index a2b7ef86db8..282581e3b75 100644
--- a/src/NamedParameter.cpp
+++ b/src/NamedParameter.cpp
@@ -11,12 +11,3 @@ template class AmpGen::NamedParameter<int>;
template class AmpGen::NamedParameter<size_t>;
template class AmpGen::NamedParameter<bool>;
-std::string AmpGen::optionalHelpString(const std::string& header, const std::vector<std::pair<std::string, std::string>>& args )
-{
- std::string rt=header +"\n";
- for( size_t i = 0 ; i < args.size(); ++i ){
- rt += "\033[3m " + args[i].first + std::string( 25 - args[i].first.size(), ' ');
- rt += "\033[0m: " + args[i].second + (i==args.size()-1 ? "" : "\n" );
- }
- return rt;
-}
diff --git a/src/OptionsParser.cpp b/src/OptionsParser.cpp
index fec4a16b21d..8702a80102d 100644
--- a/src/OptionsParser.cpp
+++ b/src/OptionsParser.cpp
@@ -10,30 +10,38 @@
using namespace AmpGen;
-OptionsParser::OptionsParser() : m_printHelp(false) {}
-
OptionsParser* OptionsParser::gOptionsParser = nullptr;
+OptionsParser::OptionsParser()
+{
+ m_keywords["Import"] = [this](const auto& tokens){ if( tokens.size() != 2 ) return; this->import(expandGlobals(tokens[1] ) ) ; };
+ m_keywords["ParticleProperties"] = [](const auto& tokens){ ParticlePropertiesList::getMutable()->addParticle( tokens ); };
+ m_keywords["ParticlePropertiesList::Alias"] = [](const auto& tokens){ if( tokens.size() !=3 ) return; ParticlePropertiesList::getMutable()->makeAlias( tokens[1], tokens[2] ); };
+}
+
OptionsParser* OptionsParser::getMe()
{
if( gOptionsParser == nullptr ) gOptionsParser = new OptionsParser();
return gOptionsParser;
}
+void OptionsParser::setQuiet(){
+ m_quiet = true;
+}
bool OptionsParser::ignoreThisLine( const std::string& line )
{
if ( line.empty() ) return true;
- const char _ignoreLinesStartingWith[] = {'*', '#', '\0'};
- for ( int i = 0; _ignoreLinesStartingWith[i] != '\0'; i++ ) {
- if ( line[0] == _ignoreLinesStartingWith[i] ) return true;
+ const char ignoreLinesStartingWith[] = {'*', '#', '\0'};
+ for ( int i = 0; ignoreLinesStartingWith[i] != '\0'; i++ ) {
+ if ( line[0] == ignoreLinesStartingWith[i] ) return true;
}
return false;
}
-void OptionsParser::setCommandLineArgs( int argc, char** argv )
+void OptionsParser::setCommandLineArgs( int argc, char** argv, const std::string& description )
{
- printSplash();
+ if( !m_quiet ) printSplash();
int x = 0;
while ( ++x < argc ) {
std::string token = std::string( argv[x] );
@@ -54,25 +62,19 @@ void OptionsParser::setCommandLineArgs( int argc, char** argv )
x++;
}
}
- int depth = 0 ;
if( key == "help" ) m_printHelp = true;
- m_parsedLines[key] = makeParsedStrings( key + " " + val, depth );
+ addArg(key +" " + val);
}
- for( auto& line : m_parsedLines )
- {
- std::string to_string = "";
- for( auto& thing : line.second ) to_string += thing + " ";
- }
-
if( m_printHelp ){
std::cout << bold_on << "Usage: " << bold_off << argv[0] << italic_on << " options_file1.opt options_file2.opt --key1=value1 --key2=value2 ..." << italic_off << std::endl;
+ if( description != "") std::cout << description << std::endl;
std::cout << bold_on << "Options: " << bold_off << std::endl;
}
}
void OptionsParser::import( const std::string& fName )
{
- INFO( "Importing: " << fName );
+ if( !m_quiet) INFO( "Importing: " << fName );
if ( !fileExists( fName ) ) {
ERROR( "Cannot find file: " << fName );
return;
@@ -80,49 +82,40 @@ void OptionsParser::import( const std::string& fName )
int braceDepth = 0 ;
std::vector<std::string> currentTokens;
processFile( fName, [this, ¤tTokens, &braceDepth]( auto& line ) {
- if ( this->ignoreThisLine( line ) ) return;
- auto tokens = this->makeParsedStrings( line, braceDepth );
- for ( auto& token : tokens ) currentTokens.push_back( token );
- if ( tokens.size() == 0 ) return;
- std::string name = currentTokens[0];
- if ( name == "Import" && currentTokens.size() == 2 ) {
- this->import( expandGlobals( tokens[1] ) );
- currentTokens.clear();
- return;
- }
- if ( name == "Alias" && currentTokens.size() == 3 ) {
- ParticlePropertiesList::getMutable()->makeAlias( tokens[1], tokens[2] );
- currentTokens.clear();
- return;
- }
- if ( braceDepth == 0 ) {
- if ( this->m_parsedLines.find( name ) != this->m_parsedLines.end() ) {
- WARNING( "Overwriting parameter: " << name );
- }
- currentTokens.erase( std::remove_if( currentTokens.begin(), currentTokens.end(),
- []( const std::string& o ) { return o == "{" || o == "}"; } ),
- currentTokens.end() );
- this->m_parsedLines[name] = currentTokens;
- currentTokens.clear();
- }
+ if ( this->ignoreThisLine( line ) ) return;
+ auto tokens = this->makeParsedStrings( line, braceDepth );
+ for ( auto& token : tokens ) currentTokens.push_back( token );
+ if ( tokens.size() == 0 ) return;
+ std::string key = currentTokens[0];
+ if ( braceDepth != 0 ) return;
+ if ( this->m_parsedLines.find( key ) != this->m_parsedLines.end() ) {
+ WARNING( "Overwriting parameter: " << key );
+ }
+ auto isCurlyBrace = []( const std::string& o ) { return o == "{" || o == "}"; };
+ currentTokens.erase( std::remove_if( currentTokens.begin(), currentTokens.end(), isCurlyBrace), currentTokens.end() );
+ this->addArg( currentTokens );
+ currentTokens.clear();
} );
-
-
}
void OptionsParser::addArg( const std::string& arg )
{
int bc = 0 ;
- auto tokens = makeParsedStrings( arg, bc );
- auto name = tokens[0];
- m_parsedLines[name] = tokens;
+ addArg( makeParsedStrings( arg, bc ) );
+}
+
+void OptionsParser::addArg( const std::vector<std::string>& tokens )
+{
+ auto& key = tokens[0];
+ DEBUG("Adding arg with key: " << key );
+ if( m_keywords.count(key) != 0 ) m_keywords[key]( tokens );
+ else m_parsedLines[key] = tokens;
}
std::vector<std::string> OptionsParser::makeParsedStrings( const std::string& line, int& braceDepth ) const
{
std::string s = line;
if ( s.empty() ) return {};
-
s.push_back( ' ' ); // makes sure we get last element
s = " " + s; // makes things easier when we start with quotes.
std::string::const_iterator prev = s.begin();
@@ -158,10 +151,10 @@ std::vector<std::string> OptionsParser::makeParsedStrings( const std::string& li
bool OptionsParser::printHelp() { return getMe()->m_printHelp ; }
-void OptionsParser::setArgs( int argc, char** argv ){ getMe()->setCommandLineArgs(argc, argv ) ; }
+void OptionsParser::setArgs( int argc, char** argv , const std::string& description){ getMe()->setCommandLineArgs(argc, argv, description); }
void OptionsParser::setArg( const std::string& arg ){ getMe()->addArg( arg ); }
OptionsParser::iterator OptionsParser::find( const std::string& name ) { return m_parsedLines.find( name ); }
-OptionsParser::iterator OptionsParser::begin() { return m_parsedLines.begin(); }
-OptionsParser::iterator OptionsParser::end() { return m_parsedLines.end(); }
+OptionsParser::iterator OptionsParser::begin() { return m_parsedLines.begin(); }
+OptionsParser::iterator OptionsParser::end() { return m_parsedLines.end(); }
OptionsParser::const_iterator OptionsParser::begin() const { return m_parsedLines.cbegin(); }
-OptionsParser::const_iterator OptionsParser::end() const { return m_parsedLines.cend(); }
+OptionsParser::const_iterator OptionsParser::end() const { return m_parsedLines.cend(); }
diff --git a/src/Pade.cpp b/src/Pade.cpp
new file mode 100644
index 00000000000..40a8e697778
--- /dev/null
+++ b/src/Pade.cpp
@@ -0,0 +1,30 @@
+#include "AmpGen/Pade.h"
+#include "TMatrixD.h"
+#include "TVectorD.h"
+
+
+std::vector<double> AmpGen::detail::solve_pade(const std::function<double(const double&)>& fcn,
+ const double& min,
+ const double& max,
+ const unsigned& N,
+ const AmpGen::Strategy& strat)
+{
+
+ TMatrixD solver(2*N+1,2*N+1);
+ std::vector<double> samples(2*N+1);
+ if( strat < 4 ){
+ for(unsigned eq = 0 ; eq < 2*N+1; ++eq)
+ samples[eq] = pow( eq/double(2*N), strat + 1);
+ }
+ TVectorD rest(2*N+1);
+ for( unsigned eq = 0 ; eq < 2*N+1; ++eq ){
+ rest(eq) = fcn( samples[eq]*(max-min) + min);
+ for(unsigned i = 0; i <= N; ++i) solver(eq,i) = pow(samples[eq],i);
+ for(unsigned i = 1; i <= N; ++i) solver(eq,i+N) = -rest(eq)* pow(samples[eq],i);
+ }
+ solver.Invert();
+ auto r = solver * rest;
+ std::vector<double> rv(2*N+1);
+ for(unsigned i = 0; i<2*N+1; ++i) rv[i] = r[i];
+ return rv;
+}
diff --git a/src/Particle.cpp b/src/Particle.cpp
index 900bfb04e52..8b12828d111 100644
--- a/src/Particle.cpp
+++ b/src/Particle.cpp
@@ -28,49 +28,43 @@
#include "AmpGen/Types.h"
using namespace AmpGen;
+using namespace std::complex_literals;
-Particle::Particle()
-{
- m_defaultModifier = NamedParameter<std::string>("Particle::DefaultModifier","", "Default modifier to use for lineshapes, for example to use normalised vs unnormalised Blatt-Weisskopf factors.");
- m_spinFormalism = NamedParameter<std::string>("Particle::SpinFormalism" ,"Covariant", "Spin formalism to use, can choose between Covariant and Canonical formalisms");
- m_spinBasis = NamedParameter<std::string>("Particle::SpinBasis" ,"Dirac",
- optionalHelpString("Basis to use for calculating external polarisation tensors / spinors.", {
- {"Dirac", "Quantises along the z-axis"}
- , {"Weyl" , "Quantises along the direction of motion"}} ) );
-
-}
+Particle::Particle() = default;
-Particle::Particle( const std::string& name, const Particle& p1, const Particle& p2 )
- : Particle()
+Particle::Particle( const std::string& name, const Particle& p1, const Particle& p2 ) :
+ m_name{name}
+ , m_props{ParticlePropertiesList::get(name)}
+ , m_daughters{ std::make_shared<Particle>(p1), std::make_shared<Particle>(p2) }
{
- m_props = ParticlePropertiesList::get( name );
- m_name = name;
- m_daughters.push_back(std::make_shared<Particle>(p1));
- m_daughters.push_back(std::make_shared<Particle>(p2));
pdgLookup();
sortDaughters();
- for ( auto& d : m_daughters ) d->setTop( false );
+ for ( auto& d : m_daughters ) d->setParent( this );
m_uniqueString = makeUniqueString();
}
-Particle::Particle( const int& pdgID, const Particle& p1, const Particle& p2 )
- : Particle()
-{
- m_props = ParticlePropertiesList::get( pdgID );
- m_daughters.push_back( std::make_shared<Particle>( p1 ) );
- m_daughters.push_back( std::make_shared<Particle>( p2 ) );
+Particle::Particle( const int& pdgID, const Particle& p1, const Particle& p2 ) :
+ m_props{ParticlePropertiesList::get(pdgID)}
+ , m_daughters{std::make_shared<Particle>(p1) , std::make_shared<Particle>(p2) }
+{
if ( m_props != nullptr ) m_name = m_props->name();
pdgLookup();
sortDaughters();
- for ( auto& d : m_daughters ) d->setTop( false );
+ for ( auto& d : m_daughters ) d->setParent( this );
+ m_uniqueString = makeUniqueString();
+}
+
+Particle::Particle( const std::string& name, const unsigned int& index ) :
+ m_props{ParticlePropertiesList::get( name )}
+ , m_index{index}
+{
+ pdgLookup();
m_uniqueString = makeUniqueString();
}
Particle::Particle( const std::string& decayString, const std::vector<std::string>& finalStates,
const bool& orderDaughters )
- : Particle()
{
- DEBUG( "Building particle from decay string = " << decayString );
auto items = getItems( decayString );
if ( items.size() == 0 ) {
ERROR( "Failed to parse string" << decayString );
@@ -80,13 +74,15 @@ Particle::Particle( const std::string& decayString, const std::vector<std::strin
m_modifiers = getItems( items[0], {"[", "]"}, ";" );
m_name = m_modifiers[0];
m_modifiers.erase( m_modifiers.begin() );
- for ( auto& modifier : m_modifiers ) parseModifier( modifier );
-
- for ( unsigned int it = 1; it < items.size(); ++it ) m_daughters.push_back( std::make_shared<Particle>( items[it] ) );
-
+ for( auto& modifier : m_modifiers ) parseModifier( modifier );
+ for( size_t it = 1; it < items.size(); ++it ){
+ m_daughters.push_back( std::make_shared<Particle>( items[it] ) );
+ (*m_daughters.rbegin())->setParent(this);
+ }
m_props = ParticlePropertiesList::get( m_name );
pdgLookup();
auto fs = getFinalStateParticles( false );
+ DEBUG( "Building particle from decay string = " << decayString << " name = " << m_name << " "<< m_props->name() );
std::vector<bool> hasUsedFinalState( finalStates.size(), 0 );
for ( auto d : fs ) {
for ( unsigned int i = 0; i < finalStates.size(); ++i ) {
@@ -99,35 +95,39 @@ Particle::Particle( const std::string& decayString, const std::vector<std::strin
}
if ( orderDaughters ) sortDaughters();
for ( auto& d : m_daughters ) m_isStateGood &= d->isStateGood();
-
if ( !isStateGood() ) {
ERROR( "Amplitude " << decayString << " not configured correctly" );
}
if ( finalStates.size() == fs.size() ) {
- std::string finalStateString = "";
- for ( auto& fs : finalStates ) finalStateString += fs + " ";
- for ( auto used : hasUsedFinalState ) {
- m_isStateGood &= used;
- }
- if ( !isStateGood() ) {
- DEBUG( "Amplitude " << decayString << " does not match requested event type " << finalStateString );
- }
+ m_isStateGood = std::all_of( hasUsedFinalState.begin(), hasUsedFinalState.end(),[](const auto& b){return b;} );
}
m_uniqueString = makeUniqueString();
}
-Particle::Particle( const std::string& name, const unsigned int& index ) : Particle()
+
+bool Particle::isValidDecayDescriptor( const std::string& decayDescriptor )
{
- m_props = ParticlePropertiesList::get( name );
- m_index = index;
- pdgLookup();
- for ( auto& d : m_daughters ) d->setTop( false );
- m_uniqueString = makeUniqueString();
+ auto first = decayDescriptor.find("{");
+ auto open = std::count(decayDescriptor.begin(), decayDescriptor.end(), '{');
+ auto close = std::count(decayDescriptor.begin(), decayDescriptor.end(), '}');
+ if( open == 0 || open != close || first == std::string::npos){
+ if( open !=0 && open != close ) WARNING("Unmatched braces in possible decay descriptor: " << decayDescriptor);
+ return false;
+ }
+ auto tokens = split(decayDescriptor, {'{','}',',','_'} );
+ bool valid = true;
+ for( auto token : tokens )
+ {
+ auto particle_name = token.substr(0, token.find("[") );
+ valid &= ParticleProperties::get( particle_name, true) != nullptr;
+ }
+ return valid;
}
void Particle::parseModifier( const std::string& mod )
{
- if( mod.size() == 1 )
+ if ( Lineshape::Factory::isLineshape(mod) ) m_lineshape = mod;
+ else if( mod.size() == 1 )
{
DEBUG( "Modifier = " << mod );
if ( mod == "S" ) m_orbital = 0;
@@ -137,41 +137,25 @@ void Particle::parseModifier( const std::string& mod )
else if ( mod == "G" ) m_orbital = 4;
else if ( mod == "H" ) m_orbital = 5;
else if ( mod == "I" ) m_orbital = 6;
- bool status=true;
- auto tmp = lexical_cast<unsigned int>(mod,status);
- if( status ) m_spinConfigurationNumber = tmp;
+ else {
+ bool status=true;
+ auto tmp = lexical_cast<unsigned int>(mod,status); // this is if it is a number ///
+ if( status ) m_spinConfigurationNumber = tmp;
+ else {
+ m_spinConfigurationNumber = 10 + int(mod[0]);
+ }
+ }
}
else if ( mod.size() == 2 )
{
parseModifier( mod.substr(0,1) );
parseModifier( mod.substr(1,1) );
}
- else if ( Lineshape::Factory::isLineshape( mod ) )
- m_lineshape = mod;
}
double Particle::spin() const { return double( m_props->twoSpin() / 2. ) ; }
double Particle::S() const { return m_spinConfigurationNumber ; }
-std::string Particle::vertexName() const
-{
- if ( m_daughters.size() != 2 ){
- WARNING("Vertices only well-defined for quasi two-body processes, check logic");
- return "ERROR";
- }
- std::string orbitalString;
- if( m_orbital == 0 ) orbitalString = "S";
- if( m_orbital == 1 ) orbitalString = "P";
- if( m_orbital == 2 ) orbitalString = "D";
- if( m_orbital == 3 ) orbitalString = "F";
- if( m_spinConfigurationNumber != 0 ) orbitalString += std::to_string( m_spinConfigurationNumber );
- auto vx= m_props->spinName() + "_" +
- m_daughters[0]->m_props->spinName() +
- m_daughters[1]->m_props->spinName() + "_" + orbitalString;
-
- return vx;
-}
-
void Particle::pdgLookup()
{
if ( m_props == nullptr ) {
@@ -179,21 +163,18 @@ void Particle::pdgLookup()
return;
}
if ( m_lineshape == "BW" || m_usesDefaultLineshape ) {
- if ( m_name.find( "NonRes" ) != std::string::npos || m_props->width() < 1e-3 )
- m_lineshape = "FormFactor";
+ if ( m_name.find("NonRes") != std::string::npos || m_props->width() < ParticlePropertiesList::getMe()->quasiStableThreshold() ) m_lineshape = "FormFactor";
+ if ( m_props->isPhoton() ) m_lineshape = "Photon";
m_usesDefaultLineshape = true;
- } else
- m_usesDefaultLineshape = false;
+ }
+ else m_usesDefaultLineshape = false;
m_parity = m_props->P();
- if ( !isdigit( m_props->J()[0] ) ) {
- ERROR( "Spin not recognised! : " << m_name << " J = " << m_props->J() );
- }
+ // if ( !isdigit( m_props->J()[0] ) ) ERROR( "Spin not recognised! : " << m_name << " J = " << m_props->J() );
if( m_defaultModifier != "" && m_lineshape.find(".") == std::string::npos ){
- m_lineshape = m_lineshape + "." + m_defaultModifier;
+ m_lineshape = m_lineshape + "." + m_defaultModifier.getVal();
}
bool isStrong = quarks() == daughterQuarks();
- DEBUG( m_name << " is decaying via " << ( isStrong ? "strong" : "electroweak" ) << " interactions; P = " << props()->P() );
-
+ if( abs(m_props->pdgID()) == 24 || abs(m_props->pdgID()) == 23 ) isStrong = false;
if ( m_name.find( "NonRes" ) != std::string::npos ) isStrong = true;
m_minL = m_daughters.size() == 2 ? orbitalRange( isStrong ).first : 0;
if ( m_daughters.size() == 2 ) {
@@ -201,23 +182,31 @@ void Particle::pdgLookup()
<< " name = " << m_name << " d0 = " << m_daughters[0]->name()
<< " d1 = " << m_daughters[1]->name() );
}
- if ( m_orbital == 0 ) m_orbital = m_minL; //// define in ground state unless specified ///
-
- for ( auto& d : m_daughters ) d->setTop( false );
+ if ( m_orbital == 0 ) m_orbital = m_minL; // define in ground state unless specified
+ if( m_daughters.size() != 0 ){
+ DEBUG( m_name << " is decaying via " << ( isStrong ? "strong" : "electroweak" ) << " interactions; P = " << props()->P() << "l = " << m_orbital );
+ }
+ int charge = 0;
+ for ( auto& d : m_daughters ){
+ d->setParent(this);
+ charge += d->props()->charge();
+ }
+ if( m_minL == 999 ) ERROR("Decay: " << m_name << " does not appear to have an allowed spin-orbit configuration");
+ if( m_daughters.size() != 0 && m_props->charge() != charge ) ERROR("Decay: " << m_name << " does not conserve (electric) charge");
}
Tensor Particle::P() const
{
- Tensor momentum( std::vector<double>( {0., 0., 0., 0.} ), std::vector<size_t>( {4} ) );
+ Tensor momentum( std::vector<double>( {0., 0., 0., 0.} ), Tensor::dim(4) );
if ( isStable() ) {
if ( m_index != 999 ) {
const std::string index = std::to_string( m_index );
Tensor rt( std::vector<Expression>( {
- Parameter( index + "_Px", 0, false, 1 ),
- Parameter( index + "_Py", 0, false, 1 ),
- Parameter( index + "_Pz", 0, false, 1 ), 0 } ) , {4} );
- rt[3] = make_cse( fcn::sqrt( mass()*mass() + rt[0]*rt[0] + rt[1]*rt[1] + rt[2]*rt[2] ) );
- // Parameter( index + "_E" , 0, false, 1 )} ),
+ Parameter(index + "_Px"),
+ Parameter(index + "_Py"),
+ Parameter(index + "_Pz"),
+ Parameter(index + "_E") }) , Tensor::dim(4) );
+// rt[3] = fcn::sqrt( mass()*mass() + rt[0]*rt[0] + rt[1]*rt[1] + rt[2]*rt[2] ) ;
return rt;
} else ERROR( "Stable particle " << m_index << "is unindexed!" );
}
@@ -239,16 +228,31 @@ Tensor Particle::Q() const
std::shared_ptr<Particle> Particle::daughter( const size_t& index ) { return ( m_daughters[index] ); }
std::shared_ptr<Particle> Particle::daughter( const size_t& index ) const { return m_daughters[index]; }
+std::shared_ptr<Particle> Particle::daughter( const std::string& name, const int& maxDepth ) const
+{
+ if( maxDepth == -1 )
+ {
+ auto fs = getFinalStateParticles();
+ for( auto& f : fs ) if( f->name() == name ) return f;
+ ERROR("Particle: " << name << " not found amongst decay products!");
+ }
+ else {
+ for( auto& d : m_daughters ) if( d->name() == name ) return d;
+ ERROR("Particle: " << name << " not found amongst decay products!");
+ }
+ return std::shared_ptr<Particle>();
+}
+
+
std::string Particle::orbitalString() const
{
- std::string orbital_part;
- if ( m_orbital == 0 ) orbital_part = "S";
- else if ( m_orbital == 1 ) orbital_part = "P";
- else if ( m_orbital == 2 ) orbital_part = "D";
- else if ( m_orbital == 3 ) orbital_part = "F";
- else orbital_part = "X";
- if( m_spinConfigurationNumber == 0 ) return orbital_part;
- else return orbital_part + std::to_string( m_spinConfigurationNumber );
+ constexpr std::array<char, 7> orbitals = {'S','P','D','F','G','H','I'};
+ std::string rt = std::string(1, orbitals[m_orbital] );
+ if( m_spinConfigurationNumber != 0 ){
+ if( m_spinConfigurationNumber < 10 ) rt += std::to_string( m_spinConfigurationNumber );
+ else rt += char(m_spinConfigurationNumber-10);
+ }
+ return rt;
}
bool Particle::hasModifier( const std::string& modifier ) const
@@ -275,14 +279,9 @@ std::string Particle::makeUniqueString()
{
std::string modifier = modifierString();
if ( m_daughters.size() != 0 ) {
- std::string val = m_name + modifier + "{";
- for ( unsigned int i = 0; i < m_daughters.size(); ++i ) {
- m_daughters[i]->makeUniqueString();
- val += m_daughters[i]->uniqueString() + ( i == m_daughters.size() - 1 ? "}" : "," );
- }
- m_uniqueString = val;
+ m_uniqueString = m_props->name() + modifier + "{" + vectorToString( m_daughters, ",", [](auto& d){ return d->makeUniqueString() ;} ) +"}";
} else {
- m_uniqueString = m_name + modifier ;
+ m_uniqueString = m_props->name() + modifier ;
}
return m_uniqueString;
}
@@ -290,7 +289,6 @@ std::string Particle::makeUniqueString()
std::vector<std::shared_ptr<Particle>> Particle::getFinalStateParticles( const bool& sort ) const
{
std::vector<std::shared_ptr<Particle>> ffs;
-
for ( auto daughter : m_daughters ) {
if ( daughter->isStable() ) {
ffs.push_back( daughter );
@@ -313,12 +311,11 @@ Particle Particle::quasiStableTree() const
{
Particle returnVal( m_name );
for ( auto& d : m_daughters ) {
- auto qTree = d->quasiStableTree();
- if ( d->isQuasiStable() ) {
- returnVal.addDaughter( std::make_shared<Particle>( qTree ) );
- } else {
- for ( auto& dp : qTree.daughters() ) returnVal.addDaughter( dp );
- }
+ auto qTree = d->quasiStableTree();
+ if( qTree.daughters().size() == 0 || (qTree.isQuasiStable() && m_daughters.size() != 1 ) )
+ returnVal.addDaughter( std::make_shared<Particle>(qTree) );
+ else
+ for( auto& it : qTree.daughters() ) returnVal.addDaughter(it);
}
returnVal.sortDaughters();
returnVal.makeUniqueString();
@@ -333,15 +330,16 @@ Expression Particle::propagator( DebugSymbols* db ) const
Expression total( 1. );
DEBUG( "Getting lineshape " << m_lineshape << " for " << m_name );
Expression s = massSq();
- if ( m_daughters.size() == 2 ) {
- auto prop = Lineshape::Factory::get(m_lineshape, s, daughter(0)->massSq(), daughter(1)->massSq(), m_name, m_orbital, db);
- total = total * make_cse(prop);
- }
- else if ( m_daughters.size() == 3 ) {
- std::string shape = m_lineshape == "BW" ? "SBW" : m_lineshape;
- auto prop = Lineshape::Factory::get(shape, massSq(), {daughter(0)->P(), daughter(1)->P(), daughter(2)->P()}, m_name, m_orbital, db );
- total = total * make_cse(prop);
- }
+ Expression prop = 1;
+ if ( m_daughters.size() == 2 )
+ prop = Lineshape::Factory::get(m_lineshape, s, daughter(0)->massSq(), daughter(1)->massSq(), m_name, m_orbital, db);
+ else if ( m_daughters.size() >= 3 )
+ prop = Lineshape::Factory::get(m_lineshape == "BW" ? "SBW" : m_lineshape, *this, db );
+ else if ( m_daughters.size() == 1 && m_lineshape != "BW" && m_lineshape != "FormFactor" )
+ {
+ prop = Lineshape::Factory::get(m_lineshape, *this, db );
+ }
+ total = total * make_cse(prop);
for(auto& d : m_daughters) total = total*make_cse(d->propagator(db));
if(db != nullptr) db->emplace_back("A("+uniqueString()+")", total);
return total;
@@ -352,7 +350,8 @@ std::vector<std::vector<size_t>> Particle::identicalDaughterOrderings() const
std::vector<std::vector<size_t>> orderings;
auto finalStateParticles = getFinalStateParticles();
std::vector<std::string> zero_perm;
- for( auto& particle : finalStateParticles ) zero_perm.push_back( particle->name() );
+ std::transform( finalStateParticles.begin(), finalStateParticles.end(), std::back_inserter(zero_perm),
+ [](auto& p ){ return p->name() ; } );
std::vector<size_t> indices( finalStateParticles.size() );
std::iota(indices.begin(), indices.end(), 0);
do {
@@ -371,7 +370,11 @@ void Particle::setOrdering( const std::vector<size_t>& ordering )
finalStateParticles[i]->setIndex( ordering[i] );
}
}
-void Particle::addDaughter( const std::shared_ptr<Particle>& particle ) { m_daughters.push_back( particle ); }
+void Particle::addDaughter( const std::shared_ptr<Particle>& particle )
+{
+ m_daughters.push_back( particle );
+ m_uniqueString = makeUniqueString();
+}
Tensor Particle::transitionMatrix( DebugSymbols* db )
{
@@ -379,47 +382,46 @@ Tensor Particle::transitionMatrix( DebugSymbols* db )
return spinTensor();
}
-Expression Particle::getExpression( DebugSymbols* db, const unsigned int& index )
+Expression Particle::getExpression( DebugSymbols* db, const std::vector<int>& state)
{
+ if( state.size() !=0 ) setPolarisationState( state );
if( db != nullptr && !isStable() )
db->emplace_back( uniqueString() , Parameter( "NULL", 0, true ) );
- auto spinFormalism = m_spinFormalism;
- auto localFormalism = attribute("SpinFormalism");
- if( localFormalism != stdx::nullopt ) localFormalism = localFormalism.value();
- if( spinFormalism != "Covariant" && spinFormalism != "Canonical")
- {
- FATAL("Invalid value for SpinFormalism: " << spinFormalism << ", possible values are: " << italic_on << " Covariant, Canonical." << italic_off );
- }
- Expression total( 0 );
+ Expression total = 0;
+ Tensor::Index a;
auto finalStateParticles = getFinalStateParticles();
auto orderings = identicalDaughterOrderings();
bool doSymmetrisation = !hasModifier("NoSym");
bool sumAmplitudes = !hasModifier("Inco");
bool includeSpin = !hasModifier("BgSpin0");
std::vector<int> exchangeParities;
- for( auto& p : finalStateParticles ) exchangeParities.push_back( p->props()->isFermion() ? -1 : 1 );
- for(auto& ordering : orderings){
+ std::transform( finalStateParticles.begin(), finalStateParticles.end(), std::back_inserter(exchangeParities),
+ [](const auto& p){ return p->props()->isFermion() ? -1 : 1; } );
+ for(const auto& ordering : orderings){
auto exchangeParity = minSwaps( ordering, exchangeParities );
- //INFO( vectorToString( ordering, ", ") << " " << exchangeParity.second );
setOrdering( ordering );
Expression spinFactor = 1;
- if( includeSpin && spinFormalism == "Covariant" ){
+ if( includeSpin && m_spinFormalism == spinFormalism::Covariant ){
Tensor st = spinTensor(db);
if( m_props->twoSpin() == 0 ) spinFactor = st[0];
if( m_props->twoSpin() == 1 ){
Tensor is = Bar( externalSpinTensor(m_polState) );
ADD_DEBUG_TENSOR( externalSpinTensor(m_polState), db );
ADD_DEBUG_TENSOR( st, db );
- Tensor::Index a;
if( st.size() != 4 ){
ERROR("Spin tensor is the wrong rank = " << st.dimString() );
spinFactor = 1;
}
- else { spinFactor = is(a) * st(a) ; }
+ else spinFactor = is(a) * st(a) ;
+ }
+ if( m_props->twoSpin() == 2 ){
+ Tensor is = externalSpinTensor(m_polState).conjugate();
+ ADD_DEBUG_TENSOR(is, db );
+ spinFactor = dot(is,st);
}
}
- if ( includeSpin && spinFormalism == "Canonical" ){
- spinFactor = helicityAmplitude( *this, TransformSequence(), double(polState())/2.0, db );
+ if ( includeSpin && m_spinFormalism == spinFormalism::Canonical ){
+ spinFactor = helicityAmplitude(*this, TransformSequence(), m_props->isBoson() ? polState() : double(polState())/2.0, db);
}
if( db != nullptr ){
std::string finalStateString="";
@@ -439,7 +441,14 @@ Expression Particle::getExpression( DebugSymbols* db, const unsigned int& index
}
ADD_DEBUG( total, db );
double nPermutations = doSymmetrisation ? orderings.size() : 1;
- if ( sumAmplitudes ) return total / fcn::sqrt( nPermutations );
+ if ( sumAmplitudes )
+ {
+ if ( is<Constant>(total) ){
+ WARNING("Amplitude is just a constant: " << total << " may cause problems for compiler, making a little bit complex" );
+ total += 1i * 0.00001;
+ }
+ return total / fcn::sqrt( nPermutations );
+ }
else {
Expression sqrted = fcn::sqrt( total / nPermutations );
ADD_DEBUG( sqrted, db );
@@ -456,9 +465,10 @@ Tensor Particle::spinTensor( DebugSymbols* db ) const
return S;
}
else if ( m_daughters.size() == 2 ) {
+ auto vname = m_props->spinName() + "_" + m_daughters[0]->m_props->spinName() + m_daughters[1]->m_props->spinName() + "_" + orbitalString();
Tensor value = Vertex::Factory::getSpinFactor( P(), Q(),
- daughter(0)->spinTensor( db ),
- daughter(1)->spinTensor( db ), vertexName() , db );
+ daughter(0)->spinTensor(db),
+ daughter(1)->spinTensor(db), vname, db );
DEBUG( "Returning spin tensor" );
return value;
} else if ( m_daughters.size() == 3 ) {
@@ -477,103 +487,92 @@ Tensor Particle::externalSpinTensor(const int& polState, DebugSymbols* db ) cons
{
DEBUG("Getting final state spin tensor for: " << name() << " " << spin() );
if ( spin() == 0 )
- return Tensor( std::vector<double>( {1.} ), std::vector<size_t>( {1} ) );
+ return Tensor( std::vector<double>( {1.} ), std::vector<unsigned>( {1} ) );
+ if( m_spinBasis == spinBasis::Dirac && ( m_props->isPhoton() || m_props->isNeutrino() ) )
+ {
+ WARNING("Use the Weyl (helicity) basis for calculations involving photons / neutrinos, as they don't have a rest frame. This will result in ill-defined amplitudes.");
+ }
+
Tensor p = P();
- Expression pX = p.get(0) ;
- Expression pY = p.get(1) ;
- Expression pZ = p.get(2) ;
- Expression pE = p.get(3) ;
+ Expression pX = p.get(0);
+ Expression pY = p.get(1);
+ Expression pZ = p.get(2);
+ Expression pE = p.get(3);
Expression pP = fcn::sqrt( pX*pX + pY*pY + pZ*pZ );
- Expression m = fcn::sqrt( dot( p, p ) );
- complex_t I(0,1);
- Expression z = pX + I*pY;
- Expression zb = pX - I*pY;
+ Expression m = mass();
+ Expression z = pX + 1i*pY;
+ Expression zb = pX - 1i*pY;
auto id = props()->pdgID();
- if ( m_props->twoSpin() == 2 && m_spinBasis == "Weyl" ) {
- Expression N = 1 / ( m * fcn::sqrt( 2 ) );
- Expression em = pE+m;
- if( polState == 0 ) return Tensor( { pX*pZ/(m*em), pY*pZ/(m*em), 1. + pZ*pZ/(m*em), pZ/m } );
- if( polState == 1 ) return -N*Tensor( { m + pX*zb/em, pY*zb/em -m*I, pZ*zb, zb } );
- if( polState == -1 ) return N*Tensor( { m + pX*z/em, pY*z/em + m*I, pZ*z, z } );
- }
- if( m_props->twoSpin() == 2 && m_spinBasis == "Dirac" ){
- Expression invPT2 = Ternary( pX*pX + pY*pY > 1e-6, 1./(pX*pX+pY*pY), 0 );
- if( m_props->mass() == 0 ){
- Expression N = 1./(pP*sqrt(2));
- if( polState == 1 ) return N * Tensor({ -pZ - pY*invPT2*(pP-pZ)*(pY-I*pX),
- -I*pZ + pX*invPT2*(pP-pZ)*(pY-I*pX),
- ( pX + I*pY), 0 } );
- if( polState == -1 ) return N * Tensor({ pZ + pY*invPT2*(pP-pZ)*(pY+I*pX),
- I*pZ - pX*invPT2*(pP-pZ)*(pY+I*pX),
- ( -pX + I*pY), 0 } );
- if( polState == 0 ) ERROR("Photon should does not have a rest frame, cannot be in m=0 state");
+ if ( m_props->twoSpin() == 2 )
+ {
+ if( m_spinBasis == spinBasis::Weyl )
+ {
+ Expression N = 1./(sqrt(2));
+ Expression invPT2 = make_cse(Ternary( pX*pX + pY*pY > 1e-6, 1./(pX*pX+pY*pY), 0 ));
+ Expression invP = make_cse(Ternary( pP > 1e-6, 1./pP,0));
+ Expression pZoverP = make_cse(Ternary( pP > 1e-6, pZ/pP, 1) );
+ Expression f = (pP-pZ)*invPT2;
+ if(polState == 1) return N * Tensor({-pZoverP + 1i*z *pY*f*invP, -1i*pZoverP - 1i*z *pX*f*invP, z*invP , 0. });
+ if(polState == -1) return N * Tensor({ pZoverP + 1i*zb*pY*f*invP, -1i*pZoverP - 1i*zb*pX*f*invP,-zb*invP , 0. });
+ if(polState == 0) return Tensor({pX*pE*invP/m , pY*pE*invP/m , pZoverP*pE/m, pP/m});
}
- }
- if( m_props->twoSpin() == 1 && m_spinBasis == "Weyl" ){
- Expression n = fcn::sqrt( 2 * pP*(pP+pZ) );
- Expression fa = fcn::sqrt( (pE + m)/(2*m) );
- Expression fb = fcn::sqrt( (pE - m)/(2*m) );
- Expression aligned = make_cse( Abs(pP + pZ) < 10e-6 ) ;
- Expression xi10 = make_cse(Ternary( aligned, 1, (pP+pZ)/n ));
- Expression xi11 = make_cse(Ternary( aligned, 0, z/n ));
- Expression xi00 = make_cse(Ternary( aligned, 0, -zb/n ));
- Expression xi01 = make_cse(Ternary( aligned, 1, (pP+pZ)/n ));
- if(id > 0 && polState == 1 ) return Tensor({ fa*xi10, fa*xi11, fb*xi10, fb*xi11 } );
- if(id > 0 && polState == -1 ) return Tensor({ fa*xi00, fa*xi01, -fb*xi00, -fb*xi01 } );
- if(id < 0 && polState == 1 ) return Tensor({ fb*xi00, fb*xi01, -fa*xi00, -fa*xi01 } );
- if(id < 0 && polState == -1 ) return Tensor({ fb*xi10, fb*xi11, -fa*xi01, -fa*xi11 } );
- }
- if ( m_props->twoSpin() == 1 && m_spinBasis == "Dirac" )
+ if( m_spinBasis == spinBasis::Dirac ){
+ Expression N = make_cse(1./(m*(pE + m)));
+ if( polState == 1 ) return -Tensor({1.+ z *pX*N, 1i + z*pY*N, z*pZ*N , z/m })/sqrt(2);
+ if( polState == -1 ) return Tensor({1.+ zb*pX*N, -1i + zb*pY*N, zb*pZ*N , zb/m })/sqrt(2);
+ if( polState == 0 ) return Tensor({pX*pZ*N , pY*pZ*N, 1 + pZ*pZ*N, pZ/m });
+ }
+ }
+ if( m_props->twoSpin() == 1 )
{
- Expression norm = make_cse( fcn::sqrt((pE+m)/(2*m) ));
- if(id > 0 && polState == 1 ) return norm * Tensor({ 1 ,0 , pZ/(pE+m), z/(pE+m) });
- if(id > 0 && polState == -1 ) return norm * Tensor({ 0 ,1 , zb/(pE+m), -pZ/(pE+m) });
- if(id < 0 && polState == -1 ) return norm * Tensor({ pZ/(pE+m), z/(pE+m) , 1 ,0 });
- if(id < 0 && polState == 1 ) return norm * Tensor({ zb/(pE+m),-pZ/(pE+m) , 0 ,1 });
- }
- WARNING("Spin tensors not implemented for spin J = " << m_props->twoSpin() << " / 2 m = " << m_polState << " " << m_name );
- return Tensor( std::vector<double>( {1.} ), Tensor::dim(0) );
-}
-
-bool Particle::checkExists() const
-{
- bool success = true;
- if ( m_daughters.size() == 2 ) {
- success &= Vertex::Factory::isVertex( vertexName() );
- if ( !success ) {
- ERROR( uniqueString() );
- ERROR( "Spin configuration not found J = "
- << spin() << " L = " << m_orbital << " l' = " << m_spinConfigurationNumber
- << " s1 = " << m_daughters[0]->spin() << " s2 = " << m_daughters[1]->spin() );
+ if( m_spinBasis == spinBasis::Weyl )
+ {
+ std::array<Tensor,2> xi;
+ Expression n = fcn::sqrt( 2 * pP*(pP+pZ) );
+ Expression aligned = make_cse( Abs(pP + pZ) < 10e-6 ) ;
+ xi[0] = Tensor( {make_cse( Ternary(aligned, 1, -zb/n)) , make_cse( Ternary(aligned, 0, (pP+pZ)/n ) ) });
+ xi[1] = Tensor( {make_cse( Ternary(aligned, 0, (pP+pZ)/n)), make_cse(Ternary(aligned,1, z/n) ) });
+
+ Expression fa = m_props->isNeutrino() ? polState * fcn::sqrt(pE) : polState * fcn::sqrt( pE/m- 1 );
+ Expression fb = m_props->isNeutrino() ? fcn::sqrt(pE) : fcn::sqrt( pE/m + 1 );
+ int ind = (id>0 ? polState : -polState) == -1 ? 0 : 1;
+
+ return id > 0 ? Tensor({ - fa * xi[ind][0], - fa * xi[ind][1], fb * xi[ind][0], fb * xi[ind][1] })
+ : -polState * Tensor({ fb * xi[ind][0], fb * xi[ind][1], fa * xi[ind][0], fa * xi[ind][1] });
+ }
+ if ( m_spinBasis == spinBasis::Dirac )
+ {
+ Expression N = make_cse( fcn::sqrt((pE+m)/(2*m) ));
+ if(id > 0 && polState == 1 ) return N * Tensor({ 1 ,0 , pZ/(pE+m), z/(pE+m) });
+ if(id > 0 && polState == -1 ) return N * Tensor({ 0 ,1 , zb/(pE+m), -pZ/(pE+m) });
+ if(id < 0 && polState == -1 ) return N * Tensor({ pZ/(pE+m), z/(pE+m) , 1 ,0 });
+ if(id < 0 && polState == 1 ) return N * Tensor({ zb/(pE+m),-pZ/(pE+m) , 0 ,1 });
}
- success &= daughter(0)->checkExists() & daughter(1)->checkExists();
}
- if ( success == false ) ERROR( uniqueString() << " is not described in IVertex" );
- return success;
+ std::string js = m_props->isBoson() ? std::to_string(m_props->twoSpin()/2) : std::to_string(m_props->twoSpin()) +"/2";
+ WARNING("Spin tensors not implemented for spin J = " << js << "; m = " << m_polState << " " << m_name );
+ return Tensor( std::vector<double>( {1.} ), Tensor::dim(0) );
}
std::pair<size_t, size_t> Particle::orbitalRange( const bool& conserveParity ) const
{
if( m_daughters.size() == 0 ) return {0, 0};
- if( m_daughters.size() == 1 ) return {0,0};
+ if( m_daughters.size() == 1 ) return {0, 0};
if( m_daughters.size() != 2 ) {
ERROR( "L not well defined for nDaughters == " << m_daughters.size() );
return {999, 998};
}
const int S = m_props->twoSpin();
- const int s1 = daughter( 0 )->props()->twoSpin();
- const int s2 = daughter( 1 )->props()->twoSpin();
-
- int min = std::abs( S - s1 - s2 );
- if ( std::abs( S + s1 - s2 ) < min ) min = std::abs( S + s1 - s2 );
- if ( std::abs( S - s1 + s2 ) < min ) min = std::abs( S - s1 + s2 );
- int max = S + s1 + s2;
-
+ const int s1 = daughter(0)->props()->twoSpin();
+ const int s2 = daughter(1)->props()->twoSpin();
+ int min = std::abs( S - s1 - s2 );
+ min = std::min(min, std::abs( S + s1 - s2 ));
+ min = std::min(min, std::abs( S - s1 + s2 ));
+ int max = S + s1 + s2;
min /= 2;
max /= 2;
DEBUG( "Range = " << min << " -> " << max << " conserving parity ? " << conserveParity << " J = " << S << " s1= " << s1 << " s2= " << s2 );
- if ( conserveParity == false ) return {min, max};
-
+ if ( conserveParity == false ) return {min, max};
int l = min;
for ( ; l < max + 1; ++l ) if( conservesParity(l) ) break;
if ( l == max + 1 ) return {999, 999};
@@ -610,13 +609,13 @@ std::string Particle::texLabel( const bool& printHead, const bool& recurse ) con
const std::string rightBrace = "\\right]";
if( m_daughters.size() == 0 ) return m_props->label();
std::string val = ""; // m_props->label();
- if( !m_isHead ) val = m_props->label();
- if( printHead && m_isHead ) val = m_props->label() + "\\rightarrow ";
+ if( !isHead() ) val = m_props->label();
+ if( printHead && isHead() ) val = m_props->label() + "\\rightarrow ";
- if( m_isHead || recurse ){
- if ( !m_isHead || m_orbital != m_minL ) val += leftBrace;
+ if( isHead() || recurse ){
+ if ( !isHead() || m_orbital != m_minL ) val += leftBrace;
for( auto& prod : m_daughters ) val += prod->texLabel(false,recurse) + " ";
- if ( !m_isHead || m_orbital != m_minL ) val += rightBrace;
+ if ( !isHead() || m_orbital != m_minL ) val += rightBrace;
if ( m_orbital != m_minL ) val += "^{" + orbitalString() + "}";
}
return val;
@@ -624,38 +623,35 @@ std::string Particle::texLabel( const bool& printHead, const bool& recurse ) con
void Particle::sortDaughters()
{
- std::stable_sort( m_daughters.begin(), m_daughters.end(), []( auto& A, auto& B ) { return *A < *B; } );
+ bool isAntiParticle = m_props->pdgID() < 0;
+ if( isAntiParticle ) conjThis();
+ std::stable_sort( m_daughters.begin(), m_daughters.end(), [](const auto& A, const auto& B) { return *A < *B; } );
+ if( isAntiParticle ) conjThis();
+ m_uniqueString = makeUniqueString();
}
-int Particle::conjugate( bool invertHead , bool reorder )
+void Particle::conjThis()
{
- int sgn = 1;
- DEBUG( "Conjugating flavour of " << m_name );
- if ( m_props == nullptr ) ERROR( "Particle properties not found for " << m_name );
- if ( ( !m_isHead || invertHead ) && m_props->hasDistinctAnti() ) {
- DEBUG( "Trying to conjugate: " << m_name );
- m_props = ParticlePropertiesList::get( -m_props->pdgID() );
- m_name = m_props->name();
- m_parity = m_props->P();
- }
- sgn *= pow( -1, m_orbital );
- if ( m_parity == -1
- && m_daughters.size() == 2
- && std::abs(daughter(0)->props()->pdgID()) == std::abs(daughter(1)->props()->pdgID())
- && daughter(0)->props()->pdgID() != daughter(1)->props()->pdgID() ) {
- sgn *= -1;
- }
- for ( auto& d : m_daughters ) sgn *= d->conjugate( invertHead );
- if( reorder ) sortDaughters();
- std::string oldUniqueString = m_uniqueString;
- m_uniqueString = makeUniqueString();
- DEBUG( "Conjugate : " << oldUniqueString << " to " << m_uniqueString << " sgn = " << sgn );
- return sgn;
+ if( m_props->hasDistinctAnti() )
+ m_props = ParticlePropertiesList::get( -m_props->pdgID(), false);
+ for(unsigned i = 0 ; i != m_daughters.size(); ++i) m_daughters[i]->conjThis();
+}
+
+Particle Particle::conj( bool invertHead , bool reorder )
+{
+ Particle cp(*this);
+ cp.clearDecayProducts();
+ const ParticleProperties* p = ( !isHead() || invertHead ) && m_props->hasDistinctAnti() ? ParticlePropertiesList::get( -m_props->pdgID() ) : m_props;
+ cp.setName( p->name() );
+ for( auto& d : m_daughters ) cp.addDaughter( std::make_shared<Particle>(d->conj(invertHead,reorder)) );
+ if( reorder ) cp.sortDaughters();
+ cp.pdgLookup();
+ return cp;
}
QuarkContent Particle::quarks() const
{
- return m_name.find("NonRes") != std::string::npos ? daughterQuarks() : m_props->netQuarkContent();
+ return m_name.find("NonRes") != std::string::npos ? daughterQuarks() : m_props->quarkContent();
}
QuarkContent Particle::daughterQuarks() const
@@ -666,13 +662,24 @@ QuarkContent Particle::daughterQuarks() const
}
Expression Particle::massSq() const { return isStable() ? mass() * mass() : make_cse( dot( P(), P() ) ); }
+
+void Particle::clearDecayProducts()
+{
+ m_daughters.clear();
+}
+
void Particle::addModifier( const std::string& mod )
{
m_modifiers.push_back( mod );
parseModifier( mod );
m_uniqueString = makeUniqueString();
}
-void Particle::setTop( bool state ) { m_isHead = state; }
+void Particle::setName(const std::string& name)
+{
+ m_name = name;
+ m_props = ParticlePropertiesList::get(name);
+ m_parity = m_props->P();
+}
void Particle::setIndex( const unsigned int& index, const bool& setOri )
{
m_index = index;
@@ -689,35 +696,42 @@ void Particle::setLineshape( const std::string& lineshape )
m_lineshape = lineshape;
m_uniqueString = makeUniqueString();
}
+
int Particle::finalStateParity() const
{
- int lpart = ( m_orbital % 2 == 0 ? 1 : -1 );
- for ( auto& d : m_daughters ) lpart *= d->parity();
- return lpart;
+ if( m_daughters.size() == 0) return 1;
+ if( m_daughters.size() == 1) return m_daughters[0]->finalStateParity(); /// forward through quasiparticles
+ if( m_daughters.size() == 2){
+ int f = spin() - ( m_orbital + daughter(0)->spin() + daughter(1)->spin() );
+ int lpart = (f % 2 == 0 ? 1 : -1);
+ for( auto& d : m_daughters ) lpart *= d->finalStateParity();
+ return lpart;
+ }
+ WARNING("> 2 body vertices may require special considerations when conjugating, returning (-1)^J");
+ return pow(-1, spin() );
}
bool Particle::conservesParity( unsigned int L ) const
{
- return parity() == daughter( 0 )->parity() * daughter( 1 )->parity() * ( L % 2 == 0 ? 1 : -1 );
+ return parity() == daughter(0)->parity() * daughter(1)->parity() * ( L % 2 == 0 ? 1 : -1 );
}
std::string Particle::topologicalString() const
{
- std::string topo = "";
- for ( auto& d : m_daughters ) topo += d->m_props->J();
- return topo;
+ return std::accumulate( m_daughters.begin(), m_daughters.end(), std::string(""), [](auto& s, auto& d){ return s+d->props()->J() ; } );
}
+
const ParticleProperties* Particle::props() const { return m_props; }
-bool Particle::isHead() const { return m_isHead; }
-bool Particle::isWeakDecay() const { return quarks() == daughterQuarks(); }
+bool Particle::isHead() const { return m_parent == nullptr; }
+bool Particle::isWeakDecay() const { return quarks() != daughterQuarks(); }
bool Particle::isStateGood() const { return m_isStateGood; }
bool Particle::isStable() const { return m_daughters.size() == 0; }
bool Particle::isQuasiStable() const
{
- return props()->width() < ParticlePropertiesList::getMe()->quasiStableThreshold();
+ return props()->width() < ParticlePropertiesList::getMe()->quasiStableThreshold() && name() != "gamma0";
}
-unsigned int Particle::orbital() const { return m_orbital; }
+unsigned Particle::L() const { return m_orbital; }
int Particle::polState() const { return m_polState; }
std::string Particle::name() const { return m_name; }
std::string Particle::uniqueString() const { return m_uniqueString; }
@@ -733,14 +747,20 @@ void Particle::setDaughter( const Particle& particle, const unsigned int& index
makeUniqueString();
}
+void Particle::setParent(const Particle* ptr )
+{
+ m_parent = ptr;
+}
+
std::vector<std::shared_ptr<Particle>> Particle::daughters() const { return m_daughters; }
+
bool Particle::operator<( const Particle& other )
{
- if ( spin() != other.spin() ) return spin() > other.spin();
- if ( !isStable() && other.isStable() ) return true;
- if ( isStable() && !other.isStable() ) return false;
- if ( mass() != other.mass() ) return mass() > other.mass();
- if ( std::abs( props()->pdgID() ) == std::abs( other.props()->pdgID() )
+ if ( spin() != other.spin() ) return spin() > other.spin();
+ if ( !isStable() && other.isStable() ) return true;
+ if ( isStable() && !other.isStable() ) return false;
+ if ( mass() != other.mass() ) return mass() > other.mass();
+ if ( std::abs(props()->pdgID()) == std::abs(other.props()->pdgID() )
&& props()->pdgID() != other.props()->pdgID() ) return props()->pdgID() > other.props()->pdgID();
if ( props()->charge() != other.props()->charge() ) return props()->charge() > other.props()->charge();
if ( props()->pdgID() != other.props()->pdgID() ) return props()->pdgID() > other.props()->pdgID();
@@ -756,7 +776,7 @@ EventType Particle::eventType() const
{
std::vector<std::string> names = {m_name};
auto fs = getFinalStateParticles( false );
- for ( auto& p : fs ) names.push_back( p->name() );
+ std::transform(fs.begin(), fs.end(), std::back_inserter(names), [](const auto& p){ return p->name(); } );
return EventType( names );
}
@@ -776,6 +796,14 @@ void Particle::setPolarisationState( const int& state )
m_uniqueString = makeUniqueString();
}
+void Particle::setPolarisationState( const std::vector<int>& state )
+{
+ setPolarisationState( state[0] );
+ auto fs = getFinalStateParticles();
+ for(size_t i = 0 ; i < fs.size(); ++i ) fs[i]->setPolarisationState( state[i+1] );
+ m_uniqueString = makeUniqueString();
+}
+
unsigned int Particle::matches( const Particle& other ) const
{
unsigned int rt=0;
@@ -789,7 +817,7 @@ unsigned int Particle::matches( const Particle& other ) const
if( daughter_match == 0 ) return MatchState::None;
rt |= daughter_match;
}
- if( m_orbital != other.orbital() ) rt |= MatchState::DifferentOrbital;
+ if( m_orbital != other.L() ) rt |= MatchState::DifferentOrbital;
if( m_polState != other.polState() ) rt |= MatchState::DifferentPolarisation;
if( rt == 0 ) rt = MatchState::Exact;
if( rt & MatchState::Exact && rt != MatchState::Exact )
@@ -799,11 +827,16 @@ unsigned int Particle::matches( const Particle& other ) const
std::string Particle::decayDescriptor() const { return m_uniqueString ; }
-int Particle::quasiCP() const
+int Particle::CP() const
+{
+ return C() * finalStateParity();
+}
+
+int Particle::C() const
{
- int prod = m_props->C() == 0 ? 1 : m_props->C();
- prod *= ( m_orbital % 2 == 0 ? 1 : -1 );
- for( auto& d : m_daughters ) prod *= d->quasiCP() ;
+ if( m_daughters.size() == 1 ) return m_daughters[0]->C();
+ int prod = 1;
+ for( auto& d : m_daughters ) prod *= ( d->props()->C() == 0 ? 1 : d->props()->C() ) * d->C();
return prod;
}
@@ -815,3 +848,13 @@ stdx::optional<std::string> Particle::attribute(const std::string& key) const
}
return stdx::nullopt;
}
+
+std::ostream& AmpGen::operator<<( std::ostream& os, const Particle& particle ){
+ return os << particle.decayDescriptor();
+}
+
+namespace AmpGen {
+ complete_enum( spinFormalism, Covariant, Canonical )
+ complete_enum( spinBasis , Dirac , Weyl )
+}
+
diff --git a/src/ParticleProperties.cpp b/src/ParticleProperties.cpp
index d0d67fc2906..6c0417df61a 100644
--- a/src/ParticleProperties.cpp
+++ b/src/ParticleProperties.cpp
@@ -5,6 +5,7 @@
#include <stdlib.h>
#include <algorithm>
#include <vector>
+#include <cmath>
#include "AmpGen/ParticlePropertiesList.h"
#include "AmpGen/MsgService.h"
@@ -17,9 +18,9 @@ void ParticleProperties::print( std::ostream& out ) const
{
out << "Mass " << mass() << " +" << mErrPlus() << " -" << mErrMinus() << "\nWidth " << width() << " +" << wErrPlus()
<< " -" << wErrMinus() << "\n I=" << I() << ", G=" << G() << "\n J=" << J() << ", C=" << C() << ", P=" << P()
- << "\n Q = " << charge() << "\n pdgID " << pdgID() << "\n name " << name() << "\n quark content: " << quarks()
- << "\n net-quark-content " << netQuarkContent() << "\n is its own antiparticle? "
- << ( isItsOwnAnti() ? "yes" : "no" ) << "\n radius " << radius() * GeV << " /GeV"
+ << "\n Q = " << charge() << "\n pdgID " << pdgID() << "\n name " << name()
+ << "\n quark-content " << quarkContent() << "\n is its own antiparticle? "
+ << ( hasDistinctAnti() ? "no" : "yes" ) << "\n radius " << radius() * GeV << " /GeV"
<< "\n";
}
@@ -28,14 +29,22 @@ int ParticleProperties::chargeFromString( const std::string& ch, bool& status )
if ( ch == "+" ) return 1;
if ( ch == "-" ) return -1;
if ( ch == " " ) return 0;
- if ( ch == "0" ) return 0;
- if ( ch == "++" ) return 2;
+ if ( ch == "0" ) return 0;
+ if ( ch == "++" ) return 2;
if ( ch == "--" ) return -2;
status = 0;
return 0;
}
-ParticleProperties::ParticleProperties( const std::string& pdg_string ) : m_netQuarkContent()
+std::string ParticleProperties::J() const
+{
+ if( m_twoSpin == -1 ) return "?";
+ if( m_twoSpin % 2 == 0 ) return std::to_string( int(m_twoSpin/2) );
+ if( m_twoSpin % 2 == 1 ) return std::to_string( int(m_twoSpin/2) ) + "/2";
+ return "";
+}
+
+ParticleProperties::ParticleProperties( const std::string& pdg_string )
{
m_isValid = false;
if ( pdg_string == "" || pdg_string.empty() ) return;
@@ -45,7 +54,7 @@ ParticleProperties::ParticleProperties( const std::string& pdg_string ) : m_netQ
DEBUG( "Invalid line : " << pdg_string );
return;
}
- for ( auto& st : s ) st = trim( st );
+ std::transform(s.begin(), s.end(), s.begin(), trim);
bool status = 1;
m_mass = lexical_cast<double>( s[0], status );
m_mErrPlus = lexical_cast<double>( s[1], status );
@@ -56,82 +65,42 @@ ParticleProperties::ParticleProperties( const std::string& pdg_string ) : m_netQ
m_pdgID = lexical_cast<int>( s[12], status );
m_Rexist = lexical_cast<int>( s[14], status );
m_Gparity = chargeFromString( s[7], status );
- m_Parity = chargeFromString( s[9], status );
+ m_parity = chargeFromString( s[9], status );
m_Cparity = chargeFromString( s[10], status );
m_charge = chargeFromString( s[13], status );
- m_Isospin = s[6];
- m_JtotalSpin = s[8];
+ m_isospin = s[6];
m_status = s[15][0];
m_name = s[16];
- m_quarks = s[17];
- m_Aformat = s[11][0];
+ m_Aformat = s[11].size() == 1 ? s[11][0] : ' ';
m_chargeString = s[13];
- m_netQuarkContent.initFromString( m_quarks );
+ m_quarkContent = QuarkContent( s[17] );
bool spin_status = 1;
- if( m_JtotalSpin == "?" ) m_twoSpin = 0;
- else if( m_JtotalSpin.find("/") != std::string::npos ){
- m_twoSpin = lexical_cast<int>( m_JtotalSpin.substr(0, m_JtotalSpin.find("/") ) , spin_status );
+ if( s[8] == "?" ) m_twoSpin = -1;
+ else if( s[8].find("/") != std::string::npos ){
+ m_twoSpin = lexical_cast<int>( s[8].substr(0, s[8].find("/") ) , spin_status );
}
- else m_twoSpin = 2 * lexical_cast<int>( m_JtotalSpin, spin_status );
+ else m_twoSpin = 2 * lexical_cast<int>( s[8], spin_status );
if( spin_status == 0 ){
- DEBUG("Spin of particle: " << name() << " could not be interpretted (J=" << m_JtotalSpin << ")" );
+ DEBUG("Spin of particle: " << name() << " could not be interpretted (J=" << s[8] << ")" );
}
- setRadius();
- m_isValid = true;
-}
-
-void ParticleProperties::setRadius()
-{
- double defaultRadius = 1.5 / GeV; // 1.5/GeV;
- double defaultCharmRadius = 5.0 / GeV;
+ m_radius = 1.5 / GeV;
bool isCharm = ( abs(pdgID()) == 421 ||
abs(pdgID()) == 411 ||
abs(pdgID()) == 431 ||
abs(pdgID()) == 4122 );
- m_Radius = isCharm ? defaultCharmRadius : defaultRadius;
-}
-
-void swap_string(std::string& arg, const char a, const char b)
-{
- for( auto& c : arg )
- {
- if( c == a ) c = b;
- else if( c == b ) c = a;
- }
-}
-
-void ParticleProperties::antiQuarks()
-{
- if ( m_quarks.empty() ) return;
- swapChars(m_quarks, 'U', 'u');
- swapChars(m_quarks, 'D', 'd');
- swapChars(m_quarks, 'C', 'c');
- swapChars(m_quarks, 'S', 's');
- swapChars(m_quarks, 'T', 't');
- swapChars(m_quarks, 'B', 'b');
- unsigned int pos = m_quarks.find( "SqrT" );
- if ( pos < m_quarks.size() ) {
- m_quarks.replace( pos, 4, "sqrt" );
- }
+ if(isCharm) m_radius = 5.0 / GeV;
+ m_isValid = true;
}
-void ParticleProperties::antiQuarkContent() { m_netQuarkContent.antiThis(); }
-
-void ParticleProperties::antiCharge()
-{
- swapChars( m_chargeString, '+', '-');
- m_charge *= -1;
-}
bool ParticleProperties::hasDistinctAnti() const { return !( m_Aformat == ' ' ); }
-bool ParticleProperties::barred() const { return m_Aformat == 'F'; }
-
bool ParticleProperties::antiThis()
{
if ( !hasDistinctAnti() ) return false;
- antiCharge();
- antiQuarks();
- antiQuarkContent();
+ swapChars( m_chargeString, '+', '-');
+ m_charge *= -1;
+ if( isFermion() ) m_parity *= -1;
+ m_quarkContent.antiThis();
m_pdgID *= -1;
return true;
}
@@ -145,12 +114,19 @@ ParticleProperties ParticleProperties::anti() const
std::string ParticleProperties::name() const
{
+ if( m_customName ) return m_name;
std::string fullName = m_name;
if ( m_pdgID < 0 && m_Aformat == 'F' ) fullName += "bar";
fullName += m_chargeString;
return fullName;
}
-double ParticleProperties::radius() const { return m_Radius; }
+double ParticleProperties::radius() const { return m_radius; }
+
+double ParticleProperties::lifetime() const
+{
+ return 6.582119514 / ( m_width * std::pow( 10, 13 ) );
+}
+
bool ParticleProperties::isNonResonant() const
{
@@ -161,11 +137,21 @@ bool ParticleProperties::isFermion() const {
return m_twoSpin % 2 == 1;
}
+bool ParticleProperties::isPhoton() const
+{
+ return m_pdgID == 22;
+}
+
+bool ParticleProperties::isNeutrino() const
+{
+ return abs(m_pdgID) == 12 || abs(m_pdgID) == 14 || abs(m_pdgID) == 16;
+}
+
bool ParticleProperties::isBoson() const {
return ! isFermion();
}
-std::ostream& operator<<( std::ostream& out, const ParticleProperties& pp )
+std::ostream& AmpGen::operator<<( std::ostream& out, const ParticleProperties& pp )
{
pp.print( out );
return out;
@@ -184,11 +170,12 @@ std::string ParticleProperties::spinName() const {
if( m_twoSpin == 5 ) return "e";
if( m_twoSpin == 7 ) return "c";
}
- WARNING("Spin name not implemented for " << m_JtotalSpin );
+ WARNING("Spin name not implemented for " << m_twoSpin );
return "?";
}
-const ParticleProperties* ParticleProperties::get( const std::string& name, const bool& quiet ){
+const ParticleProperties* ParticleProperties::get( const std::string& name, const bool& quiet )
+{
return ParticlePropertiesList::get( name, quiet );
}
@@ -212,3 +199,30 @@ bool ParticleProperties::operator>( const ParticleProperties& rhs ) const { retu
bool ParticleProperties::operator<=( const ParticleProperties& rhs ) const { return ( *this < rhs || *this == rhs ); }
bool ParticleProperties::operator>=( const ParticleProperties& rhs ) const { return ( *this > rhs || *this == rhs ); }
+
+void ParticleProperties::setProperty(const std::string& key, const std::string& value)
+{
+ DEBUG("Setting property: " << key << " " << value );
+ bool status = true;
+ if( key == "mass" ) m_mass = stod(value) / MeV;
+ else if( key == "name" ) m_name = value;
+ else if( key == "width" ) m_width = stod(value) / MeV;
+ else if( key == "spin" )
+ {
+ bool spin_status = 1;
+ if( value == "?" ) m_twoSpin = 0;
+ else if( value.find("/") != std::string::npos ){
+ m_twoSpin = lexical_cast<int>( value.substr(0, value.find("/") ) , spin_status );
+ }
+ else m_twoSpin = 2 * lexical_cast<int>( value, spin_status );
+ if( spin_status == 0 ){
+ ERROR("Spin of particle: " << name() << " could not be interpretted (J=" << value << ")" );
+ }
+ }
+ else if( key == "parity" ) m_parity = chargeFromString( value, status );
+ else if( key == "charge" ) m_charge = chargeFromString( value, status );
+ else if( key == "quarks" ) m_quarkContent = QuarkContent(value);
+ else {
+ ERROR("Unrecognised key: " << key );
+ }
+}
diff --git a/src/ParticlePropertiesList.cpp b/src/ParticlePropertiesList.cpp
index 68fb8c58e07..b57dccbdbb6 100644
--- a/src/ParticlePropertiesList.cpp
+++ b/src/ParticlePropertiesList.cpp
@@ -17,18 +17,14 @@ ParticlePropertiesList* ParticlePropertiesList::ptr = nullptr;
const ParticlePropertiesList* ParticlePropertiesList::getMe()
{
- if(!ptr){
- ptr = new ParticlePropertiesList();
- }
+ if(!ptr) ptr = new ParticlePropertiesList();
if(nullptr == ptr) FATAL("Couldn't get ParticlePropertiesList (i.e. myself)" );
return ptr;
}
ParticlePropertiesList* ParticlePropertiesList::getMutable()
{
- if(!ptr){
- ptr = new ParticlePropertiesList();
- }
+ if(!ptr) ptr = new ParticlePropertiesList();
if(ptr == nullptr) FATAL( "Couldn't get ParticlePropertiesList (i.e. myself)" );
return ptr;
}
@@ -72,17 +68,13 @@ const std::vector<std::string> ParticlePropertiesList::dirList() const
ParticlePropertiesList::ParticlePropertiesList( const std::string& fname_in )
{
-
- auto _dirList = dirList();
-
- for ( auto& d : _dirList ) {
- if ( readLatexLabels( d + "pdgID_to_latex.dat" ) ) break;
- }
- for ( auto& d : _dirList ) {
- if ( readFile( d + "mass_width.csv" ) ) break;
- }
- for ( auto& d : _dirList ) {
- if ( readFile( d + "MintDalitzSpecialParticles.csv" ) ) break;
+ auto dl = dirList();
+ bool status = true;
+ status &= std::any_of( dl.begin(), dl.end(), [this](auto& d){ return this->readLatexLabels(d +"pdgID_to_latex.dat") ; } );
+ status &= std::any_of( dl.begin(), dl.end(), [this](auto& d){ return this->readFile(d +"mass_width.csv") ; } );
+ status &= std::any_of( dl.begin(), dl.end(), [this](auto& d){ return this->readFile(d +"MintDalitzSpecialParticles.csv") ; } );
+ if( !status ){
+ WARNING("Failed to load full PDG configuration, beware of unexpected behaviour");
}
makeMappings();
m_quasiStableThreshold = NamedParameter<double>( "ParticleProperties::qsThreshold", KeV ); /// limit is 1 keV
@@ -90,15 +82,12 @@ ParticlePropertiesList::ParticlePropertiesList( const std::string& fname_in )
bool ParticlePropertiesList::readLatexLabels( const std::string& name )
{
-
if ( !fileExists( name ) ) return false;
-
m_latexLabels.clear();
processFile( name, [this]( auto& line ) {
auto tokens = split( line, ' ' );
this->m_latexLabels[stoi( tokens[0] )] = std::make_pair( tokens[1], tokens[2] );
} );
-
return true;
}
@@ -117,7 +106,6 @@ bool ParticlePropertiesList::readFile( const std::string& name )
WARNING( line << " is not valid" );
return;
}
-
auto label = m_latexLabels.find( P.pdgID() );
if ( label != m_latexLabels.end() ) P.setLabel( label->second.first );
m_theList.push_back( P );
@@ -157,18 +145,9 @@ const ParticleProperties* ParticlePropertiesList::find( const std::string& name,
auto it = m_byName.find( name );
if ( it != m_byName.end() ) return it->second;
if ( !quiet ) {
- auto particleNames = ParticlePropertiesList::getMe()->getParticleNames();
-
- unsigned int minDistance = 9999;
- std::string suggestion = "";
- for ( auto& particle : particleNames ) {
- unsigned int distance = editDistance( particle, name );
- if ( distance < minDistance ) {
- suggestion = particle;
- minDistance = distance;
- }
- }
- ERROR( "Particle: " << name << " not in PDG. Did you mean " << suggestion << "?" );
+ auto suggestion = std::min_element( std::begin(m_byName), std::end(m_byName),
+ [&name](const auto& p1, const auto& p2 ){ return editDistance(p1.first, name) < editDistance(p2.first,name); } );
+ ERROR( "Particle: " << name << " not in PDG. Did you mean " << suggestion->first << "?" );
}
return nullptr;
}
@@ -191,13 +170,13 @@ std::ostream& operator<<( std::ostream& out, const ParticlePropertiesList& ppl )
std::vector<std::string> ParticlePropertiesList::getParticleNames() const
{
std::vector<std::string> particleNames;
- for ( auto& particle : m_byName ) particleNames.push_back( particle.first );
+ std::transform( m_byName.begin(), m_byName.end(), std::back_inserter(particleNames), [](auto& p ) -> std::string { return p.first ; } );
return particleNames;
}
std::vector<int> ParticlePropertiesList::getParticleIds() const
{
std::vector<int> particleIds;
- for ( auto& particle : m_byID ) particleIds.push_back( particle.first );
+ std::transform( m_byID.begin(), m_byID.end(), std::back_inserter(particleIds), [](auto& p ) -> int { return p.first ; } );
return particleIds;
}
@@ -214,4 +193,26 @@ void ParticlePropertiesList::makeAlias( const std::string& name, const std::stri
m_byName[alias] = pp;
}
+void ParticlePropertiesList::addParticle( const std::vector<std::string>& tokens )
+{
+ INFO( vectorToString(tokens, " ") );
+ auto name = tokens[1];
+ if( tokens.size() % 2 != 0 ) ERROR("Expecting properties as set of key value pairs");
+ ParticleProperties* pp = nullptr;
+ if( m_byName.find( name ) != m_byName.end() )
+ {
+ WARNING("Overwriting properties of existing particle");
+ pp = m_byName[name];
+ }
+ else {
+ pp = new ParticleProperties();
+ pp->setProperty("name", name );
+ }
+ for( int i = 2; i != tokens.size(); i+=2 )
+ {
+ pp->setProperty( tokens[i], tokens[i+1] );
+ }
+ m_byName[name] = pp;
+}
+
double ParticlePropertiesList::quasiStableThreshold() const { return m_quasiStableThreshold; }
diff --git a/src/PhaseSpace.cpp b/src/PhaseSpace.cpp
index 615767d8169..255a548b863 100644
--- a/src/PhaseSpace.cpp
+++ b/src/PhaseSpace.cpp
@@ -1,6 +1,5 @@
#include "AmpGen/PhaseSpace.h"
-#include <RtypesCore.h>
#include <algorithm>
#include <array>
#include <cmath>
@@ -10,6 +9,7 @@
#include "AmpGen/ParticlePropertiesList.h"
#include "AmpGen/Types.h"
#include "AmpGen/MsgService.h"
+#include "AmpGen/Particle.h"
#include "TRandom.h"
const Int_t kMAXP = 18;
@@ -20,30 +20,35 @@ PhaseSpace::PhaseSpace( const EventType& type, TRandom* rand ) :
m_rand(rand), m_type(type)
{
setDecay( type.motherMass(), type.masses() );
- if ( type.isTimeDependent() )
- m_decayTime = 6.582119514 / ( ParticlePropertiesList::get( type.mother() )->width() * pow( 10, 13 ) );
+ if ( type.isTimeDependent() ){
+ INFO("Generating with time-dependence");
+ m_decayTime = ParticlePropertiesList::get( type.mother() )->lifetime();
+ }
}
+PhaseSpace::PhaseSpace( const Particle& particle, TRandom* rand ) :
+ PhaseSpace( particle.eventType(), rand ) {}
+
double PhaseSpace::q( double m, double m1, double m2 ) const
{
return 0.5 * sqrt( m*m - 2*m1*m1 - 2*m2*m2 + (m1*m1-m2*m2)*(m1*m1-m2*m2)/(m*m) );
}
-Event PhaseSpace::makeEvent(const size_t& cacheSize)
+Event PhaseSpace::makeEvent()
{
std::array<double, kMAXP> rno;
std::array<double, kMAXP> pd;
std::array<double, kMAXP> invMas;
- Event rt( 4 * m_nt, cacheSize);
+ Event rt(4*m_nt + m_type.isTimeDependent());
rno[0] = 0;
- unsigned int n;
+ size_t n;
double wt = m_wtMax;
do {
wt = m_wtMax;
rno[0] = 0;
- for( n = 1; n < m_nt - 1; n++ ) rno[n] = rndm(); // m_nt-2 random numbers
+ for( n = 1; n < m_nt - 1; n++ ) rno[n] = m_rand->Rndm(); // m_nt-2 random numbers
rno[m_nt - 1] = 1;
std::sort( rno.begin() + 1, rno.begin() + m_nt );
double sum = 0;
@@ -55,35 +60,29 @@ Event PhaseSpace::makeEvent(const size_t& cacheSize)
pd[n] = q( invMas[n + 1], invMas[n], m_mass[n + 1] );
wt *= pd[n];
}
- } while ( wt < rndm() );
-
- rt.set(0, { 0, pd[0], 0, sqrt( pd[0] * pd[0] + m_mass[0] * m_mass[0] )} );
-
- for( unsigned int i = 1 ; i != m_nt ; ++i ){
+ } while ( wt < m_rand->Rndm() );
+ rt[0] = 0;
+ rt[1] = pd[0];
+ rt[2] = 0;
+ rt[3] = sqrt( pd[0] * pd[0] + m_mass[0] * m_mass[0] );
+ for(size_t i = 1 ; i != m_nt ; ++i ){
rt.set( i, { 0, -pd[i-1], 0, sqrt( pd[i-1] * pd[i-1] + m_mass[i] * m_mass[i] ) } );
- double cZ = 2 * rndm() - 1;
+ double cZ = 2 * m_rand->Rndm() - 1;
double sZ = sqrt( 1 - cZ * cZ );
- double angY = 2 * M_PI * rndm();
+ double angY = 2 * M_PI * m_rand->Rndm();
double cY = cos(angY);
double sY = sin(angY);
- for ( unsigned int j = 0; j <= i; j++ ) {
+ double beta = (i == m_nt-1) ? 0 : pd[i] / sqrt( pd[i] * pd[i] + invMas[i] * invMas[i] );
+ double gamma = (i == m_nt-1) ? 1 : 1./sqrt( 1 - beta*beta);
+ for (size_t j = 0; j <= i; j++ ) {
double x = rt[4*j+0];
double y = rt[4*j+1];
double z = rt[4*j+2];
- rt[4*j+0] = cZ * x - sZ * y;
- rt[4*j+1] = sZ * x + cZ * y;
- x = rt[4*j+0];
- rt[4*j+0] = cY * x - sY * z;
- rt[4*j+2] = sY * x + cY * z;
- }
- if ( i == ( m_nt - 1 ) ) break;
- double beta = pd[i] / sqrt( pd[i] * pd[i] + invMas[i] * invMas[i] );
- double gamma = 1./sqrt( 1 - beta*beta);
- for ( unsigned int j = 0; j <= i; j++ ){
- double E = rt[4*j+3];
- double py = rt[4*j+1];
- rt[4*j+1] = gamma*( py + beta * E );
- rt[4*j+3] = gamma*( E + beta * py );
+ double E = rt[4*j+3];
+ rt[4*j+0] = cY * (cZ * x - sZ * y ) - sY * z;
+ rt[4*j+1] = gamma*( sZ * x + cZ * y + beta * E );
+ rt[4*j+2] = sY * (cZ * x - sZ * y ) + cY * z;
+ rt[4*j+3] = gamma*( E + beta * (sZ *x + cZ*y) );
}
}
rt.setGenPdf( 1 );
@@ -93,10 +92,9 @@ Event PhaseSpace::makeEvent(const size_t& cacheSize)
bool PhaseSpace::setDecay( const double& m0, const std::vector<double>& mass )
{
- unsigned int n;
m_nt = mass.size();
m_teCmTm = m0;
- for ( n = 0; n < m_nt; n++ ) {
+ for (size_t n = 0; n < m_nt; n++) {
m_mass[n] = mass[n];
m_teCmTm -= mass[n];
}
@@ -104,7 +102,7 @@ bool PhaseSpace::setDecay( const double& m0, const std::vector<double>& mass )
double emmax = m_teCmTm + m_mass[0];
double emmin = 0;
double wtmax = 1;
- for ( n = 1; n < m_nt; n++ ) {
+ for (size_t n = 1; n < m_nt; n++) {
emmin += m_mass[n - 1];
emmax += m_mass[n];
wtmax *= q( emmax, emmin, m_mass[n] );
diff --git a/src/Plots.cpp b/src/Plots.cpp
deleted file mode 100644
index a3903c55a2a..00000000000
--- a/src/Plots.cpp
+++ /dev/null
@@ -1,71 +0,0 @@
-
-#include "AmpGen/ErrorPropagator.h"
-#include "AmpGen/EventList.h"
-#include "AmpGen/CoherentSum.h"
-#include "AmpGen/IncoherentSum.h"
-#include "AmpGen/Integrator.h"
-#include "AmpGen/MinuitParameterSet.h"
-#include "AmpGen/Projection.h"
-#include "AmpGen/Utilities.h"
-#include "AmpGen/EventList.h"
-#include "AmpGen/Plots.h"
-#include "TFile.h"
-#include "TH1D.h"
-#include "TH2D.h"
-#include <chrono>
-using namespace AmpGen;
-void AmpGen::perAmplitudePlot( const EventList& evts,
- const Projection& projection,
- const CoherentSum& pdf )
-{
- struct PlotIJ {
- unsigned int i;
- unsigned int j;
- TH1D* hist;
- std::complex<double> amp;
- };
-
- TDirectory* dir = (TDirectory*)gFile->Get( ("perAmp_"+projection.name()).c_str() );
- if( dir == nullptr )
- {
- gFile->mkdir( ("perAmp_"+ projection.name() ).c_str() );
- dir = (TDirectory*)gFile->Get( ("perAmp_"+projection.name()).c_str() );
- }
- dir->cd();
-
- std::vector<std::pair<const Event*, double>> eventData;
-
- std::vector<PlotIJ> tmpPlots( pdf.size() * ( pdf.size() + 1 ) / 2 );
-
- unsigned int s = 0;
- for ( unsigned int i = 0; i < pdf.size(); ++i ) {
-
- for ( unsigned int j = i; j < pdf.size(); ++j ) {
- auto pdf_i = pdf[i].pdf;
- auto pdf_j = pdf[j].pdf;
- unsigned int index_i = evts.getCacheIndex( pdf[i].pdf );
- unsigned int index_j = evts.getCacheIndex( pdf[j].pdf );
- const std::string name = pdf_i.name() + "_" + pdf_j.name();
- tmpPlots[s].hist = projection.plot(name);
- tmpPlots[s].i = index_i;
- tmpPlots[s].j = index_j;
- tmpPlots[s].amp = pdf[i].coupling() * std::conj( pdf[j].coupling() );
- if ( index_i != index_j ) tmpPlots[s].amp = 2.0 * tmpPlots[s].amp;
- s++;
- }
- }
- for ( auto& evt : evts ) {
- double f = projection( evt );
- for ( auto& h : tmpPlots ) {
- std::complex<double> pdfValue = evt.getCache( h.i ) * std::conj( evt.getCache( h.j ) );
- double weight = std::real( h.amp * pdfValue ) * evt.weight() / evt.genPdf();
- h.hist->Fill( f, weight );
- }
- }
- for ( auto& h : tmpPlots ) {
- h.hist->Write();
- delete h.hist;
- }
- dir->Write();
- gFile->cd();
-}
diff --git a/src/PolarisedSum.cpp b/src/PolarisedSum.cpp
index e7efc8aa0a4..c9a5b44a607 100644
--- a/src/PolarisedSum.cpp
+++ b/src/PolarisedSum.cpp
@@ -9,6 +9,7 @@
#include <ostream>
#include <ratio>
#include <utility>
+#include <thread>
#include "AmpGen/CompilerWrapper.h"
#include "AmpGen/NamedParameter.h"
@@ -28,80 +29,125 @@
#include "AmpGen/ProfileClock.h"
#include "AmpGen/DiracMatrices.h"
#include "AmpGen/Simplify.h"
+#include "AmpGen/enum.h"
+#include "AmpGen/simd/utils.h"
using namespace AmpGen;
using namespace std::complex_literals;
-PolarisedSum::PolarisedSum( const EventType& type,
- MinuitParameterSet& mps,
- const std::string& prefix ) :
- m_mps(&mps),
- m_eventType(type),
- m_prefix(prefix)
+#if DEBUGLEVEL == 1
+ ENABLE_DEBUG( PolarisedSum )
+#endif
+
+namespace AmpGen { make_enum(spaceType, spin, flavour) }
+
+std::vector<Expression> convertProxies(const std::vector<MinuitProxy>& proxyVector, const std::function<Expression(const MinuitProxy&)>& transform)
+{
+ std::vector<Expression> rt;
+ std::transform(proxyVector.begin(), proxyVector.end(), std::back_inserter(rt), transform );
+ return rt;
+}
+
+PolarisedSum::PolarisedSum(const EventType& type,
+ MinuitParameterSet& mps,
+ const std::vector<MinuitProxy>& pVector)
+ : m_mps (&mps)
+ , m_pVector (pVector)
+ , m_verbosity (NamedParameter<bool>("PolarisedSum::Verbosity", 0 ))
+ , m_debug (NamedParameter<bool>("PolarisedSum::Debug" , false ))
+ , m_eventType (type)
+ , m_rules (mps)
+ , m_dim (m_eventType.dim())
{
- bool debug = NamedParameter<bool>( "PolarisedSum::Debug" ,false );
- bool autoCompile = NamedParameter<bool>( "PolarisedSum::AutoCompile",true );
- std::string objCache = NamedParameter<std::string>("PolarisedSum::ObjectCache","" );
- m_verbosity = NamedParameter<bool>( "PolarisedSum::Verbosity" ,0 );
- m_rules = AmplitudeRules(mps);
-
- auto proto_amplitudes = m_rules.getMatchingRules( type, prefix);
- auto production_polarisations = polarisations( type.mother() );
- std::vector<std::vector<int>> allStates;
- for(auto& pol : production_polarisations ) allStates.push_back({pol});
- for(size_t i = 0 ; i < type.size(); ++i ) allStates = polarisationOuterProduct( allStates, polarisations( type[i] ) );
- auto set_polarisation_state = []( auto& matrix_element, auto& polState ){
- auto fs = matrix_element.first.getFinalStateParticles();
- matrix_element.first.setPolarisationState(polState[0]);
- for(size_t i = 0 ; i < fs.size(); ++i ) fs[i]->setPolarisationState( polState[i+1] );
- };
- for( auto& m : proto_amplitudes ) INFO( m.first.uniqueString() );
- for( auto& matrix_element : proto_amplitudes ){
- Tensor thisExpression( std::vector<size_t>({allStates.size()}) );
- int i = 0 ;
- DebugSymbols syms;
- for( auto& polState : allStates ){
- set_polarisation_state( matrix_element, polState );
- thisExpression[ i++ ] = make_cse( matrix_element.first.getExpression(&syms) );
+ std::string objCache = NamedParameter<std::string>("PolarisedSum::ObjectCache", "" );
+ spaceType stype = NamedParameter<spaceType>( "PolarisedSum::SpaceType" , spaceType::spin);
+ {
+ ThreadPool tp(std::thread::hardware_concurrency() );
+ if( stype == spaceType::spin )
+ {
+ auto prodPols = polarisations(m_eventType.mother());
+ std::vector<std::vector<int>> polStates;
+ for(const auto& pol : prodPols ) polStates.push_back({pol});
+ for(unsigned i = 0 ; i != type.size(); ++i ) polStates = indexProduct(polStates, polarisations( type[i] ) );
+ auto protoAmps = m_rules.getMatchingRules(m_eventType);
+ for(const auto& m : protoAmps ) INFO( m.first.uniqueString() );
+ m_matrixElements.resize( protoAmps.size() );
+ for(unsigned i = 0; i < m_matrixElements.size(); ++i)
+ {
+ auto [lp, lc] = protoAmps[i];
+ auto & p = lp;
+ auto & c = lc;
+ PolarisedSum* ptr = this;
+ tp.enqueue( [i, p=lp, c=lc, polStates, &mps, ptr] () mutable {
+ Tensor thisExpression( Tensor::dim(polStates.size()) );
+ DebugSymbols syms;
+ for(unsigned j = 0; j != polStates.size(); ++j)
+ thisExpression[j] = make_cse( p.getExpression(j == 0 ? &syms: nullptr, polStates[j] ) );
+ //thisExpression[j] = make_cse( p.getExpression(&syms, polStates[j] ) );
+ ptr->m_matrixElements[i] = TransitionMatrix<void>(
+ p, c,
+ CompiledExpression<void(complex_v*, const size_t&, const real_t*, const float_v*)>(
+ TensorExpression(thisExpression), p.decayDescriptor(), &mps,
+ ptr->m_eventType.getEventFormat(), ptr->m_debug ? syms : DebugSymbols() ) );
+
+ CompilerWrapper().compile( ptr->m_matrixElements[i] );
+ ptr->m_matrixElements[i].size = thisExpression.size();
+ });
}
- CompiledExpression< std::vector<complex_t> , const real_t*, const real_t* > expression(
- TensorExpression( thisExpression),
- matrix_element.first.decayDescriptor(),
- type.getEventFormat(),debug ? syms : DebugSymbols() ,&mps );
- m_matrixElements.emplace_back(matrix_element.first, matrix_element.second, expression );
- }
- for( auto& polState : allStates){
- for( auto& matrix_element : proto_amplitudes ){
- set_polarisation_state( matrix_element, polState );
+ }
+ if ( stype == spaceType::flavour )
+ {
+ m_dim = {2,1};
+ auto r1 = m_rules.getMatchingRules(m_eventType, m_prefix);
+ auto r2 = m_rules.getMatchingRules(m_eventType.conj(true), m_prefix);
+ m_matrixElements.resize( r1.size() + r2.size() );
+ for(unsigned i = 0 ; i != m_matrixElements.size(); ++i)
+ {
+ tp.enqueue( [i, this, &r1, &r2] () mutable {
+ Tensor thisExpression( Tensor::dim(2) );
+ DebugSymbols syms;
+ auto& [p,coupling] = i < r1.size() ? r1[i] : r2[i-r1.size()];
+ thisExpression[0] = i < r1.size() ? make_cse( p.getExpression(&syms) ) : 0;
+ thisExpression[1] = i < r1.size() ? 0 : make_cse( p.getExpression(&syms) );
+ this->m_matrixElements[i] = TransitionMatrix<void>(
+ p, coupling,
+ CompiledExpression<void(complex_v*, const size_t&, const real_t*, const float_v*)>(
+ TensorExpression(thisExpression), p.decayDescriptor(), this->m_mps,
+ this->m_eventType.getEventFormat(), this->m_debug ? syms : DebugSymbols() ) );
+ CompilerWrapper().compile( m_matrixElements[i] );
+ });
}
}
- m_polStates = allStates;
- if(autoCompile){
- ThreadPool tp(8);
- for( auto& thing : m_matrixElements )
- tp.enqueue( [&]{ CompilerWrapper().compile( thing.pdf, objCache ) ;} );
}
- if( mps.find("Px") == nullptr ) WARNING("Polarisation parameters not defined, defaulting to (0,0,0)");
- m_pVector = {mps.addOrGet("Px",2,0,0), mps.addOrGet("Py",2,0,0), mps.addOrGet("Pz",2,0,0)};
- auto d = m_eventType.dim();
- size_t normSize = d.second * d.first * d.first;
- for(size_t i=0; i < normSize; ++i){
- m_norms.emplace_back( m_matrixElements.size(), m_matrixElements.size() );
- }
+ if( m_pVector.size() == 0 )
+ {
+ auto p = [this](const std::string& name){ return this->m_mps->addOrGet(name, Flag::Fix, 0, 0); };
+ if( m_dim.first == 1 ) m_pVector = {};
+ else if( m_dim.first == 2 ) m_pVector = {p("Px"), p("Py"), p("Pz")};
+ else if( m_dim.first == 3 ) m_pVector = {p("Px"), p("Py"), p("Pz"), p("Tyy"), p("Tzz"), p("Txy"), p("Txz"), p("Tyz")};
+ }
+ for(size_t i=0; i < m_dim.second * m_dim.first * m_dim.first; ++i) m_norms.emplace_back( m_matrixElements.size(), m_matrixElements.size() );
+
+ DebugSymbols db;
+ auto prob = probExpression(transitionMatrix(), convertProxies(m_pVector,[](auto& p){ return Parameter(p->name());} ), m_debug ? &db : nullptr);
+ m_probExpression = make_expression<float_v, real_t, complex_v>( prob, "prob_unnormalised", m_mps, this->m_debug ? db : DebugSymbols() );
}
std::vector<int> PolarisedSum::polarisations( const std::string& name ) const
{
auto props = *ParticlePropertiesList::get( name );
- std::vector<int> rt( props.twoSpin() + 1 );
- if( props.isFermion() ) return {1,-1};
- if( props.twoSpin() == 0 ) return {0};
- if( props.twoSpin() == 2 )
- return (name == "gamma0") ? std::vector<int>({-1,1}) : std::vector<int>({-1,0,1}) ;
- else return {0};
+ if( props.twoSpin() == 0 ) return {0}; // scalar
+ if( props.isPhoton() ) return {1,-1}; // photon
+ if( props.twoSpin() == 1 ) return {1,-1}; // fermion
+ if( props.twoSpin() == 4 ) return {-2,1,0,1,2};// tensor
+ if( props.twoSpin() == 2 ) return {1,0,-1}; // vector
+ else {
+ WARNING("Particle with spin: " << props.twoSpin() << "/2" << " not implemented in initial/final state");
+ return {0};
+ }
}
-std::vector<std::vector<int>> PolarisedSum::polarisationOuterProduct(const std::vector<std::vector<int>>& A, const std::vector<int>& B ) const
+std::vector<std::vector<int>> PolarisedSum::indexProduct(const std::vector<std::vector<int>>& A, const std::vector<int>& B ) const
{
std::vector<std::vector<int>> rt;
for( auto& iA : A ){
@@ -113,134 +159,130 @@ std::vector<std::vector<int>> PolarisedSum::polarisationOuterProduct(const std::
return rt;
}
-std::vector<TransitionMatrix<std::vector<complex_t>>> PolarisedSum::matrixElements() const
+std::vector<complex_t> densityMatrix(const unsigned& dim, const std::vector<MinuitProxy>& pv )
+{
+ if( dim != 2 && dim != 3 )
+ {
+ std::vector<complex_t> rt(dim*dim);
+ for( unsigned i = 0 ; i != dim; ++i ) rt[ dim*i +i ] = 1;
+ return rt;
+ }
+ double px = pv[0];
+ double py = pv[1];
+ double pz = pv[2];
+ if( dim == 2 ) return {1+pz , px+1i*py,
+ px-1i*py, 1-pz };
+ if( dim == 3 ){
+ double Tyy = pv[3];
+ double Tzz = pv[4];
+ double Txy = pv[5];
+ double Txz = pv[6];
+ double Tyz = pv[7];
+ return {1 + 1.5*pz + sqrt(1.5)*Tzz , sqrt(0.375)*(px+1i*py) + sqrt(3.)*(Txz+1i*Tyz), -sqrt(1.5)*( Tzz + 2.*Tyy - 2.*1i*Txy),
+ sqrt(0.375)*(px-1i*py) + sqrt(3)*(Txz-1i*Tyz), 1 - sqrt(6.)*Tzz , sqrt(0.375)*(px+1i*py) - sqrt(3.)*(Txz+1i*Tyz) ,
+ -sqrt(1.500)*( Tzz + 2.*Tyy + 2.*1i*Txy) , sqrt(0.375)*(px-1i*py) - sqrt(3)*(Txz-1i*Tyz) , 1. - 1.5*pz + sqrt(1.5)*Tzz };
+ }
+ ERROR("Density matrices not implemented for state with size="<<dim);
+ return {1.};
+}
+
+
+std::vector<TransitionMatrix<void>> PolarisedSum::matrixElements() const
{
return m_matrixElements;
}
+
void PolarisedSum::prepare()
{
- DEBUG( "Preparing: " << m_prefix << " " << m_events << " ready = " << m_integrator.isReady() );
+ auto resetFlags = [](auto& t){ t.workToDo = false; t.resetExternals() ; };
+ auto flagUpdate = [this](auto& t){ t.workToDo = this->m_nCalls == 0 || t.hasExternalsChanged(); };
+ auto updateData = [this](auto& t) mutable { if( t.workToDo && this->m_events != nullptr ) this->m_cache.update(this->m_events->store(), t) ; };
+ auto updateInteg = [this](auto& t) mutable { if( t.workToDo ) this->m_integrator.updateCache(t) ; };
+
transferParameters();
- auto dim = m_eventType.dim();
- std::vector<bool> hasChanged( m_matrixElements.size(), false);
- size_t nChanges = 0;
- ProfileClock tEval;
- size_t size_of = size() / m_matrixElements.size();
- for( size_t i = 0; i < m_matrixElements.size(); ++i ){
- ProfileClock tMEval;
- auto& t = m_matrixElements[i];
- if( m_nCalls != 0 && !t.pdf.hasExternalsChanged() ) continue;
- if( t.addressData == 999 ) t.addressData = m_events->registerExpression( t.pdf , dim.first * dim.second );
- m_events->updateCache(t.pdf, t.addressData);
- m_integrator.prepareExpression(t.pdf, size_of);
- tMEval.stop();
- t.pdf.resetExternals();
- hasChanged[i] = true;
- nChanges++;
- if( m_nCalls == 0 && m_integrator.isReady() ) m_integIndex.push_back( m_integrator.events().getCacheIndex( t.pdf ) );
- }
- if( !m_probExpression.isLinked() ) build_probunnormalised();
- m_weight = m_weightParam == nullptr ? 1 : m_weightParam->mean();
- tEval.stop();
- ProfileClock tIntegral;
- if( m_eventType.dim().first == 2 ){
- double px = m_pVector[0];
- double py = m_pVector[1];
- double pz = m_pVector[2];
- m_psi = {1+pz , px+1i*py,
- px-1i*py, 1-pz };
- }
- else m_psi = {1};
- if( m_integrator.isReady() )
+ for_each_sequence(m_matrixElements.begin(), m_matrixElements.end(), flagUpdate, updateData, updateInteg);
+ if( m_integrator.isReady() ) updateNorms();
+ std::for_each( m_matrixElements.begin(), m_matrixElements.end(), resetFlags );
+ if constexpr( detail::debug_type<PolarisedSum>::value )
{
- if(nChanges != 0) calculateNorms(hasChanged);
- complex_t z = 0;
- for(size_t i = 0; i < m_matrixElements.size(); ++i){
- for(size_t j = i; j < m_matrixElements.size(); ++j){
- z += ((i==j) ? 1. : 2. ) * m_matrixElements[i].coupling()*std::conj(m_matrixElements[j].coupling())*norm(i,j);
-// z += m_matrixElements[i].coupling()*std::conj(m_matrixElements[j].coupling())*norm(i,j);
- }
- }
- m_norm = std::real(z);
- if(m_nCalls % 100 == 0 && m_prefix == "") debug_norm();
+ if( m_nCalls % 10000 == 0 ) debug_norm();
}
- tIntegral.stop();
- if(m_verbosity && nChanges != 0)
- INFO("Time to evaluate = " << tEval << " ms; "
- << "norm = " << tIntegral << " ms; "
- << "pdfs = " << nChanges);
- m_nCalls++;
+ m_pdfCache.update(m_cache, m_probExpression);
+ DEBUG( "m_pdfCache[0] = " << utils::at(m_pdfCache[0],0) << " w/o caching = " << getValNoCache(m_events->at(0)) << " w = " << m_weight << " N = " << m_norm );
+ m_nCalls++;
}
+float_v PolarisedSum::operator()( const float_v*, const unsigned index ) const
+{
+ return ( m_weight / m_norm ) * m_pdfCache[index];
+}
+
+#if ENABLE_AVX
+double PolarisedSum::operator()( const double*, const unsigned index ) const
+{
+ return operator()((const float_v*)nullptr, index / utils::size<float_v>::value ).at( index % utils::size<float_v>::value );
+}
+#endif
+
+
void PolarisedSum::debug_norm()
{
+ if( !m_integrator.isReady() ) return;
double norm_slow = 0;
- for( auto& evt : m_integrator.events() )
- norm_slow += evt.weight() * prob_unnormalised(evt) / evt.genPdf();
- auto evt = m_integrator.events()[0];
- INFO("Event[0]: " << prob_unnormalised(evt) << " " << getValNoCache(evt) );
- INFO("Norm : " << std::setprecision(10)
- << "bilinears=" << m_norm
- << "; exact=" << norm_slow / m_integrator.sampleNorm()
- << "; d = " << m_norm - norm_slow / m_integrator.sampleNorm()
- << "; sample=" << m_integrator.sampleNorm() );
-// for( int i = 0 ; i < m_matrixElements.size(); ++i){
-// for( int j = 0 ; j < m_matrixElements.size(); ++j){
-// INFO( "Norm(i="<<i<<", j=" << j << ") = " << norm(i,j) );
-// }
-// }
+ for( auto& evt : *m_integrator.events<EventList_type>() )
+ norm_slow += evt.weight() * getValNoCache(evt) / evt.genPdf();
+ norm_slow /= m_integrator.norm();
+ INFO("Norm: " << std::setprecision(10) << "bilinears=" << m_norm << "; Slow=" << norm_slow << "; d = " << m_norm - norm_slow);
}
-void PolarisedSum::setEvents( EventList& events )
+void PolarisedSum::setEvents( EventList_type& events )
{
reset();
+ if( m_events != nullptr && m_ownEvents ) delete m_events;
m_events = &events;
+ m_cache . allocate( m_events->size(), m_matrixElements);
+ m_pdfCache . allocate( m_events->size(), m_probExpression);
}
-void PolarisedSum::setMC( EventList& events )
+void PolarisedSum::setMC( EventList_type& events )
{
m_nCalls = 0;
- m_integrator = Integrator<18>(&events);
+ m_integrator = Integrator(&events, m_matrixElements, m_dim.first * m_dim.second );
+ m_integIndex.clear();
+ for( auto& i : m_matrixElements )
+ m_integIndex.push_back( m_integrator.getCacheIndex(i) );
}
size_t PolarisedSum::size() const
{
- auto dim = m_eventType.dim() ;
- return dim.first * dim.second * m_matrixElements.size();
+ return m_dim.first * m_dim.second * m_matrixElements.size();
}
void PolarisedSum::reset( const bool& flag ){ m_nCalls = 0 ; }
-void PolarisedSum::build_probunnormalised()
-{
- auto prob = probExpression(transitionMatrix(), {Parameter("Px"), Parameter("Py"), Parameter("Pz")});
- m_probExpression = CompiledExpression<real_t, const real_t*, const complex_t*>(
- prob, "prob_unnormalised", std::map<std::string, size_t>(), {}, m_mps );
- CompilerWrapper().compile(m_probExpression);
- m_probExpression.prepare();
-}
-
-Tensor PolarisedSum::transitionMatrix()
+Tensor PolarisedSum::transitionMatrix() const
{
- auto dim = m_eventType.dim();
- auto size = dim.first * dim.second ;
- std::vector<Expression> expressions( size, 0);
- for( auto& me : m_matrixElements ){
- auto coupling = me.coupling.to_expression() ;
- auto cacheIndex = m_events->getCacheIndex(me.pdf);
+ auto size = m_dim.first * m_dim.second;
+ std::vector<Expression> expressions(size, 0);
+ unsigned totalSize = 0 ;
+ for( const auto& me : m_matrixElements ){
+ auto coupling = me.coupling.to_expression();
+ // INFO( me.decayDescriptor() << " " << coupling );
+ auto cacheIndex = totalSize;
for( size_t i = 0 ; i < size ; ++i ){
expressions[i] = expressions[i] + coupling * Parameter( "x1["+std::to_string(cacheIndex+i)+"]",0,true);
}
+ totalSize += size;
}
- Tensor T_matrix(expressions, {dim.first, dim.second});
+ Tensor T_matrix(expressions, {m_dim.first, m_dim.second});
T_matrix.st();
return T_matrix;
}
-double PolarisedSum::prob_unnormalised( const Event& evt ) const
-{
- return m_probExpression( evt.getCachePtr(0) );
+real_t PolarisedSum::operator()(const Event& evt) const
+{
+ return (m_weight/m_norm) * utils::at( m_pdfCache[ evt.index() / utils::size<float_v>::value ], evt.index() % utils::size<float_v>::value );
}
double PolarisedSum::norm() const
@@ -248,102 +290,126 @@ double PolarisedSum::norm() const
return m_norm;
}
-complex_t PolarisedSum::norm(const size_t& i, const size_t& j, Integrator<18>* integ)
+complex_t PolarisedSum::norm(const size_t& i, const size_t& j, Integrator* integ)
{
auto ai = m_integIndex[i];
auto aj = m_integIndex[j];
complex_t total = 0;
- auto dim = m_eventType.dim();
- auto s1 = dim.first;
- auto s2 = dim.second;
+ auto s1 = m_dim.first;
+ auto s2 = m_dim.second;
for(size_t x = 0 ; x < m_norms.size(); ++x){
auto f = x % s2;
auto psiIndex = (x-f) / s2;
auto m2 = psiIndex % s1;
auto m1 = (psiIndex-m2)/s1;
- total += m_psi[psiIndex] * m_norms[x].get(i, j, integ, ai+m1*s2+f, aj+m2*s2+f);
+ total += m_rho[psiIndex] * m_norms[x].get(i, j, integ, ai+m1*s2+f, aj+m2*s2+f);
}
return total;
}
-void PolarisedSum::calculateNorms(const std::vector<bool>& hasChanged)
+void PolarisedSum::updateNorms()
{
- for( size_t i = 0 ; i < m_matrixElements.size(); ++i ){
- for( size_t j = i; j < m_matrixElements.size(); ++j ){
- if( hasChanged[i] || hasChanged[j] ) norm(i, j, &m_integrator);
+ if(std::any_of(m_matrixElements.begin(),m_matrixElements.end(), [](auto& me){ return me.workToDo; } )){
+ for( unsigned i = 0 ; i < m_matrixElements.size(); ++i ){
+ for( unsigned j = i; j < m_matrixElements.size(); ++j ){
+ if( m_matrixElements[i].workToDo || m_matrixElements[j].workToDo ) norm(i, j, &m_integrator);
}
}
m_integrator.flush();
-}
-
-double PolarisedSum::prob(const Event& evt) const
-{
- return m_weight * prob_unnormalised(evt) / m_norm;
+ }
+ complex_t z = 0;
+ for(size_t i = 0; i < m_matrixElements.size(); ++i){
+ for(size_t j = 0; j < m_matrixElements.size(); ++j){
+ z += m_matrixElements[i].coupling()*std::conj(m_matrixElements[j].coupling()) * ( i > j ? std::conj(norm(j,i)) : norm(i,j) );
+ }
+ }
+ m_norm = std::real(z);
}
void PolarisedSum::debug(const Event& evt)
{
- auto dim = m_eventType.dim();
- size_t size = dim.first * dim.second;
- for(auto& me : m_matrixElements)
+ auto tsize = m_dim.first * m_dim.second;
+ std::vector<complex_v> this_cache;
+ for(unsigned j = 0; j != m_matrixElements.size(); ++j)
{
- std::vector<complex_t> this_cache(0,size);
- for(size_t i = 0 ; i < size; ++i ) this_cache.emplace_back( evt.getCache(me.addressData+i) );
- INFO( me.decayDescriptor() << " " << vectorToString( this_cache, " ") );
- }
+ for(unsigned i = 0 ; i != tsize; ++i ) this_cache.emplace_back( m_cache(evt.index() / utils::size<float_v>::value, j*tsize + i) );
+ INFO( m_matrixElements[j].decayDescriptor() << " " << vectorToString(this_cache, " ") );
+ if( m_debug ) m_matrixElements[j].debug( evt );
+ }
+ if( m_debug ) m_probExpression.debug(this_cache.data() );
+ INFO("P(x) = " << getValNoCache(evt) << " " << operator()((const float_v*)nullptr, evt.index() / utils::size<float_v>::value ) );
+ INFO("Prod = [" << vectorToString(m_pVector , ", ") <<"]");
}
void PolarisedSum::generateSourceCode(const std::string& fname, const double& normalisation, bool add_mt)
{
INFO("Generating sourceCode -> " << fname );
std::ofstream stream( fname );
- auto dim = m_eventType.dim();
- size_t size = dim.first * dim.second;
+ size_t size = m_dim.first * m_dim.second;
CompilerWrapper().preamble( stream );
- Expression event = Parameter("x0",0,true,0);
+ Expression event = Parameter("x0",0,true);
std::vector<Expression> expressions(size);
for( auto& p : m_matrixElements ){
- p.pdf.prepare();
- p.pdf.to_stream( stream );
- p.pdf.compileWithParameters( stream );
- Array z( make_cse( Function( programatic_name( p.pdf.name()) + "_wParams", {event} ) ), size );
+ auto expr = CompiledExpression<std::vector<complex_t>(const real_t*, const real_t*)>(
+ p.expression(),
+ p.decayDescriptor(),
+ m_eventType.getEventFormat(), DebugSymbols(), m_mps, disableBatch() ) ;
+ expr.prepare();
+ expr.to_stream( stream );
+ expr.compileWithParameters( stream );
+ Array z( make_cse( Function( programatic_name( p.name()) + "_wParams", {event} ) ), size );
INFO( p.decayDescriptor() << " coupling = " << p.coupling() );
- for( unsigned int j = 0 ; j < size; ++j ){
- expressions[j] = expressions[j] + p.coupling() * z[j];
- }
+ for( unsigned int j = 0 ; j < size; ++j ) expressions[j] = expressions[j] + p.coupling() * z[j];
}
- Tensor T_matrix( expressions, {dim.first,dim.second} );
+ Tensor T_matrix( expressions, {m_dim.first, m_dim.second} );
T_matrix.st();
- auto amplitude = probExpression(T_matrix, {Constant(double(m_pVector[0])),
- Constant(double(m_pVector[1])),
- Constant(double(m_pVector[2]))});
-
- auto amplitude_extPol = probExpression(T_matrix, {Parameter("x2",0,true),
- Parameter("x3",0,true),
- Parameter("x4",0,true)});
- stream << CompiledExpression<double,
+ auto amp = probExpression(T_matrix, convertProxies(m_pVector, [](auto& proxy) -> Expression{ return double(proxy);} ));
+ auto amp_extPol = probExpression(T_matrix, {Parameter("x2",0,true), Parameter("x3",0,true), Parameter("x4",0,true)});
+ stream << CompiledExpression<double(
const double*,
- const int&>( amplitude / normalisation, "FCN",{},{}, m_mps ) << std::endl ;
+ const int&)>( amp / normalisation, "FCN", m_mps, disableBatch() ) << std::endl ;
- stream << CompiledExpression<double,
+ stream << CompiledExpression<double(
const double*,
const int&,
const double&,
const double&,
- const double&>( amplitude_extPol / normalisation, "FCN_extPol",{},{},m_mps ) << std::endl;
+ const double&)>(amp_extPol / normalisation, "FCN_extPol", m_mps, disableBatch() ) << std::endl;
stream.close();
}
-Expression PolarisedSum::probExpression(const Tensor& T_matrix, const std::vector<Expression>& p) const
+Expression PolarisedSum::probExpression(const Tensor& T_matrix, const std::vector<Expression>& p, DebugSymbols* db) const
{
Tensor T_conj = T_matrix.conjugate();
Tensor::Index a,b,c;
Tensor TT = T_matrix(a,b) * T_conj(c,b);
size_t it = T_matrix.dims()[0];
Tensor rho = Identity(it);
- if(it == 2) rho = rho + Sigma[0] * p[0] + Sigma[1] * p[1] + Sigma[2]*p[2];
- rho.print();
-
+ if(it == 2) rho = rho + Sigma[0] * p[0] + Sigma[1] * p[1] + Sigma[2]*p[2];
+ if(it == 3)
+ {
+ auto px = p[0];
+ auto py = p[1];
+ auto pz = p[2];
+ auto Tyy = p[3];
+ auto Tzz = p[4];
+ auto Txy = p[5];
+ auto Txz = p[6];
+ auto Tyz = p[7];
+ rho(0,0) = 1 + 1.5 * pz + sqrt(1.5)*Tzz;
+ rho(1,0) = sqrt(0.375)*(px+1i*py) + sqrt(3.)*(Txz+1i*Tyz);
+ rho(2,0) = -sqrt(1.5)*( Tzz + 2.*Tyy - 2.*1i*Txy);
+ rho(0,1) = sqrt(0.375)*(px-1i*py) + sqrt(3.)*(Txz-1i*Tyz);
+ rho(1,1) = 1 - sqrt(6.)*Tzz;
+ rho(2,1) = sqrt(0.375)*(px+1i*py) - sqrt(3.)*(Txz+1i*Tyz);
+ rho(0,2) = -sqrt(1.5)*( Tzz + 2.*Tyy + 2.*1i*Txy);
+ rho(1,2) = sqrt(0.375)*(px-1i*py) - sqrt(3)*(Txz-1i*Tyz);
+ rho(2,2) = 1. - 1.5*pz + sqrt(1.5)*Tzz;
+ }
+ ADD_DEBUG_TENSOR(T_matrix, db);
+ ADD_DEBUG_TENSOR(T_conj, db);
+ ADD_DEBUG_TENSOR(rho, db);
+ ADD_DEBUG_TENSOR(TT , db);
Expression rt = rho(a,b) * TT(b,a);
return Real(rt);
}
@@ -351,66 +417,131 @@ Expression PolarisedSum::probExpression(const Tensor& T_matrix, const std::vecto
std::vector<FitFraction> PolarisedSum::fitFractions(const LinearErrorPropagator& prop)
{
bool recomputeIntegrals = NamedParameter<bool>("PolarisedSum::RecomputeIntegrals", false );
+ bool interferenceFractions = NamedParameter<bool>("PolarisedSum::InterferenceFractions", false );
std::vector<FitFraction> outputFractions;
- for(auto& rule : m_rules.rules())
+ for(const auto& rule : m_rules.rules())
{
FitFractionCalculator<PolarisedSum> pCalc(this, findIndices(m_matrixElements, rule.first), recomputeIntegrals);
- INFO("Denom = [" << vectorToString( findIndices(m_matrixElements, rule.first ) , ", " ) << "]");
- for(auto& process : rule.second)
+ for(const auto& process : rule.second)
{
if(process.head() == m_eventType.mother() && process.prefix() != m_prefix) continue;
auto numeratorIndices = processIndex(m_matrixElements, process.name());
if(numeratorIndices.size() == 0 || numeratorIndices == pCalc.normSet ) continue;
- INFO("Adding calculation: " << process.name() << " [" << vectorToString(numeratorIndices, ", ") << "]");
pCalc.emplace_back(process.name(), numeratorIndices);
}
if( pCalc.calculators.size() == 0 ) continue;
auto fractions = pCalc(rule.first, prop);
- for( auto& f : fractions ) outputFractions.emplace_back(f);
+ for( const auto& f : fractions ) outputFractions.emplace_back(f);
}
- auto head_rules = m_rules.rulesForDecay(m_eventType.mother(), m_prefix);
- FitFractionCalculator<PolarisedSum> iCalc(this, findIndices(m_matrixElements, m_eventType.mother()), recomputeIntegrals);
- for(size_t i = 0 ; i < head_rules.size(); ++i)
- {
- auto process_i = head_rules[i];
- auto num_i = processIndex(m_matrixElements, process_i.name());
- if( num_i.size() == 0 || num_i == iCalc.normSet ) continue;
- for( size_t j = i+1 ; j < head_rules.size(); ++j ){
- auto process_j = head_rules[j];
- auto num_j = processIndex(m_matrixElements, process_j.name());
- if( num_j.size() == 0 || num_j == iCalc.normSet ) continue;
- iCalc.emplace_back(process_i.name() + " " + process_j.name() , num_i, num_j);
+ INFO("Fit fractions: ");
+ for(const auto& p : outputFractions) INFO(p);
+
+ if( interferenceFractions )
+ {
+ auto head_rules = m_rules.rulesForDecay(m_eventType.mother(), m_prefix);
+ FitFractionCalculator<PolarisedSum> iCalc(this, findIndices(m_matrixElements, m_eventType.mother()), recomputeIntegrals);
+ for(size_t i = 0 ; i < head_rules.size(); ++i)
+ {
+ auto process_i = head_rules[i];
+ auto num_i = processIndex(m_matrixElements, process_i.name());
+ if( num_i.size() == 0 || num_i == iCalc.normSet ) continue;
+ for( size_t j = i+1 ; j < head_rules.size(); ++j ){
+ auto process_j = head_rules[j];
+ auto num_j = processIndex(m_matrixElements, process_j.name());
+ if( num_j.size() == 0 || num_j == iCalc.normSet ) continue;
+ iCalc.emplace_back(process_i.name() + " " + process_j.name() , num_i, num_j);
+ }
}
+ auto ifractions = iCalc(m_eventType.mother(), prop);
+ INFO("Interference fractions: ");
+ for( auto& f : ifractions ) INFO( FitFraction(f) );
}
- auto ifractions = iCalc(m_eventType.mother(), prop);
- for(auto& p : outputFractions) INFO(p);
- INFO("INTERFERENCE FRACTIONS");
- for( auto& f : ifractions ) INFO( FitFraction(f) );
+ INFO("Returning: " << outputFractions.size() << " fractions");
return outputFractions;
}
void PolarisedSum::transferParameters()
{
- if( m_probExpression.isLinked() ) m_probExpression.prepare();
+ m_probExpression.prepare();
for(auto& me : m_matrixElements){
me.coefficient = me.coupling();
- me.pdf.prepare();
+ me.prepare();
}
- for(auto& p : m_pVector ) p.update();
+ for(auto& p : m_pVector) p.update();
+ m_weight.update();
+ m_rho = densityMatrix(m_dim.first, m_pVector);
}
-real_t PolarisedSum::getValNoCache( const Event& evt )
+real_t PolarisedSum::getValNoCache( const Event& evt ) const
{
- transferParameters();
- Event copy(evt);
- copy.resizeCache( size() );
- for(auto& me : m_matrixElements){
- auto values = me(copy);
- copy.setCache( values , me.addressData );
+ auto tsize = m_dim.first * m_dim.second;
+ std::vector<complex_v> cache( tsize * m_matrixElements.size() );
+ for( unsigned i = 0 ; i != m_matrixElements.size(); ++i ){
+ std::memmove( cache.data() + tsize * i , m_matrixElements[i](evt).data(), tsize * sizeof(complex_v) );
+ }
+ return utils::get<0>(m_probExpression( cache.data() ));
+}
+
+void PolarisedSum::setWeight( MinuitProxy param ){ m_weight = param; }
+double PolarisedSum::getWeight() const { return m_weight ; }
+
+
+std::function<real_t(const Event&)> PolarisedSum::evaluator(const EventList_type* ievents) const
+{
+ auto events = ievents == nullptr ? m_integrator.events<EventList_type>() : ievents;
+ Store<complex_v, Alignment::AoS> store(events->size(), m_matrixElements);
+ for( auto& me : m_matrixElements ) store.update(events->store(), me );
+
+ std::vector<double> values( events->aligned_size() );
+ #ifdef _OPENMP
+ #pragma omp parallel for
+ #endif
+ for( unsigned int block = 0 ; block < events->nBlocks(); ++block )
+ {
+ utils::store(values.data() + utils::size<float_v>::value * block, (m_weight/m_norm) * m_probExpression(&store(block,0)) );
}
- return m_probExpression( copy.getCachePtr() );
+ return arrayToFunctor<double, Event>(values);
}
-void PolarisedSum::setWeight( MinuitParameter* param ){ m_weightParam = param ; }
-double PolarisedSum::getWeight() const { return m_weightParam == nullptr ? 1.0 : m_weightParam->mean() ; }
+KeyedFunctors<double(Event)> PolarisedSum::componentEvaluator(const EventList_type* ievents) const
+{
+ using store_t = Store<complex_v, Alignment::SoA>;
+ auto events = ievents == nullptr ? m_integrator.events<EventList_type>() : ievents;
+ std::shared_ptr<const store_t> cache;
+ if( events != m_integrator.events<EventList_type>() )
+ {
+ cache = std::make_shared<const store_t>(events->size(), m_matrixElements);
+ for( auto& me : m_matrixElements ) const_cast<store_t*>(cache.get())->update(events->store(), me);
+ }
+ else cache = std::shared_ptr<const store_t>( & m_integrator.cache(), [](const store_t* t){} );
+
+ KeyedFunctors<double(Event)> rt;
+ for( unsigned i = 0 ; i != m_matrixElements.size(); ++i )
+ {
+ for( unsigned j = i ; j != m_matrixElements.size(); ++j ){
+ auto mi = m_matrixElements[i];
+ auto mj = m_matrixElements[j];
+ auto ci = this->m_matrixElements[i].coefficient;
+ auto cj = this->m_matrixElements[j].coefficient;
+ double s = (i==j) ? 1 : 2 ;
+ auto name = programatic_name(mi.decayTree.decayDescriptor()) + "_" + programatic_name( mj.decayTree.decayDescriptor() );
+ rt.add( [ci,cj,i,j,s, cache, this](const Event& event){
+ auto [s1,s2] = this->m_dim;
+ auto R = s1 * s2;
+ complex_t total = 0;
+ for( unsigned x = 0; x != this->m_norms.size(); ++x )
+ {
+ auto f = x % s2;
+ auto psiIndex = (x-f) / s2;
+ auto m2 = psiIndex % s1;
+ auto m1 = (psiIndex-m2)/s1;
+ total += this->m_rho[psiIndex] * ci * cache->get<complex_t>(event.index(),R * i + m1 * s2 + f)
+ * std::conj( cj * cache->get<complex_t>(event.index(),R * j + m2 * s2 + f) );
+ }
+ return s * std::real(total);
+ }, name, "");
+ }
+ }
+ return rt;
+}
diff --git a/src/ProgressBar.cpp b/src/ProgressBar.cpp
new file mode 100644
index 00000000000..73e940e5855
--- /dev/null
+++ b/src/ProgressBar.cpp
@@ -0,0 +1,40 @@
+#include "AmpGen/ProgressBar.h"
+#include "AmpGen/MsgService.h"
+
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+using namespace AmpGen;
+
+ProgressBar::ProgressBar(const size_t& width, const std::string& context)
+ : m_width(width),
+ m_lastPercent(-1),
+ m_context(context) {}
+
+ProgressBar::~ProgressBar(){
+ if( !m_finished ) finish();
+}
+
+void ProgressBar::print(const double& percentage, const std::string& message)
+{
+ int lpad = int(percentage * m_width);
+ int val = int(percentage * 100);
+ if( val == m_lastPercent ) return;
+ m_lastPercent = val;
+ std::cout << "\r\033[2;34m" << std::left << std::setw( detail::FCNNAMELENGTH ) << m_context << " INFO " << "\033[0m";
+ std::cout << "Completed: " << std::right << std::setw(3) << val << "% " << "[";
+
+ // detail::labelled_stream(m_context) << "Completed: " << std::right << std::setw(3) << val << "% " << "[";
+ std::fill_n(std::ostream_iterator<char>(std::cout), lpad, '|');
+ std::fill_n(std::ostream_iterator<char>(std::cout), m_width-lpad, ' ');
+ std::cout << "]";
+ std::cout << message;
+ m_lastMessage = message;
+ fflush (stdout);
+}
+
+void ProgressBar::finish(){
+ print(1,m_lastMessage);
+ std::cout << std::endl;
+ m_finished = true;
+}
diff --git a/src/Projection.cpp b/src/Projection.cpp
index 186b8622e9e..5856c991717 100644
--- a/src/Projection.cpp
+++ b/src/Projection.cpp
@@ -1,13 +1,19 @@
#include "AmpGen/Projection.h"
#include "AmpGen/Utilities.h"
#include "AmpGen/Event.h"
+#include "AmpGen/EventList.h"
+#include "AmpGen/EventListSIMD.h"
#include <stdio.h>
#include "TAxis.h"
#include "TH1.h"
#include "TH2.h"
+#include "THStack.h"
using namespace AmpGen;
+using namespace AmpGen::PlotOptions;
+
+Projection::Projection() = default;
Projection::Projection( const std::function<double(const Event&)>& fcn,
const std::string& name, const std::string& xAxisTitle,
@@ -39,12 +45,15 @@ TH1D* Projection::plot(const std::string& prefix) const {
plot->GetYaxis()->SetTitleOffset(1.35);
plot->SetMarkerSize(0);
plot->SetMinimum(0);
+
+ DEBUG("Returning plot: [" << m_min << " " << m_max << "] " << m_name << " " <<
+ plot->GetXaxis()->GetBinLowEdge(1) << " " <<
+ plot->GetXaxis()->GetBinLowEdge(1 + m_nBins)
+ );
return plot;
}
-std::function<size_t(const Event& evt )> Projection::binFunctor() const {
- return [this](auto& evt){
-
- return int ( ( (*this)(evt) - m_min ) / m_width ) ; };
+std::function<int(const Event& evt )> Projection::binFunctor() const {
+ return [this](auto& evt){ return int ( ( (*this)(evt) - m_min ) / m_width ) ;};
}
TH2D* Projection2D::plot(const std::string& prefix) const {
@@ -67,3 +76,103 @@ std::pair<double, double> Projection2D::operator()( const Event& evt ) const
return {xAxis.m_func( evt ), yAxis.m_func( evt )};
}
+template <> TH1D* Projection::projInternal( const EventList& events, const ArgumentPack& args) const
+{
+ auto selection = args.getArg<PlotOptions::Selection>().val;
+ auto weightFunction = args.getArg<WeightFunction>().val;
+ bool autowrite = args.get<PlotOptions::AutoWrite>() != nullptr;
+ std::string prefix = args.getArg<PlotOptions::Prefix>(std::string(""));
+ auto axis = plot(prefix);
+ axis->SetLineColor(args.getArg<PlotOptions::LineColor>(kBlack).val);
+ axis->SetMarkerSize(0);
+ for( auto& evt : events )
+ {
+ if( selection != nullptr && !selection(evt) ) continue;
+ auto pos = operator()(evt);
+ axis->Fill( pos, evt.weight() * ( weightFunction == nullptr ? 1 : weightFunction(evt) / evt.genPdf() ) );
+ }
+ if( selection != nullptr ) INFO("Filter efficiency = " << axis->GetEntries() << " / " << events.size() );
+ if( autowrite ) axis->Write();
+ return axis;
+}
+
+template <> std::tuple<std::vector<TH1D*>, THStack*> Projection::projInternal(const EventList& events, const Projection::keyedFunctors& weightFunction, const ArgumentPack& args) const
+{
+ std::vector<TH1D*> hists;
+ double norm_sum = args.getArg<Norm>(1).val;
+ std::string prefix = args.getArg<PlotOptions::Prefix>().val;
+ bool autowrite = args.get<PlotOptions::AutoWrite>() != nullptr;
+ THStack* stack = args.getArg<PlotOptions::AddTo>(new THStack()).val;
+ auto selection = args.getArg<Selection>().val;
+ if( prefix != "" ) prefix = prefix +"_";
+ for( auto& key : weightFunction.keys )
+ hists.push_back( plot(prefix + key ) );
+ for( const auto& evt : events ){
+ if( selection != nullptr && !selection(evt) ) continue;
+ auto pos = operator()(evt);
+ auto weights = weightFunction(evt);
+ for( unsigned j = 0 ; j != weights.size(); ++j ) hists[j]->Fill( pos, evt.weight() * weights[j] / evt.genPdf() );
+ }
+ std::sort( std::begin(hists), std::end(hists), [](auto& h1, auto& h2){ return h1->Integral() < h2->Integral() ; } );
+ double total = std::accumulate( std::begin(hists), std::end(hists), 0.0, [](double& t, auto& h){ return t + h->Integral() ; } );
+ if( total == 0 ) ERROR("Norm = " << total );
+ else for( auto& h : hists ) h->Scale( norm_sum / total );
+ stack->SetName( (prefix + name() + "_stack").c_str());
+ for( auto& h : hists ){
+ stack->Add(h, "C HIST");
+ if( autowrite ) h->Write();
+ }
+ if( autowrite ) stack->Write();
+ return {hists, stack};
+}
+
+#if ENABLE_AVX
+template <> TH1D* Projection::projInternal( const EventListSIMD& events, const ArgumentPack& args) const
+{
+ auto selection = args.getArg<PlotOptions::Selection>().val;
+ auto weightFunction = args.getArg<WeightFunction>().val;
+ bool autowrite = args.get<PlotOptions::AutoWrite>() != nullptr;
+ std::string prefix = args.getArg<PlotOptions::Prefix>(std::string(""));
+ auto plt = plot(prefix);
+ plt->SetLineColor(args.getArg<PlotOptions::LineColor>(kBlack).val);
+ plt->SetMarkerSize(0);
+ for( const auto evt : events )
+ {
+ if( selection != nullptr && !selection(evt) ) continue;
+ auto pos = operator()(evt);
+ plt->Fill( pos, evt.weight() * ( weightFunction == nullptr ? 1 : weightFunction(evt) / evt.genPdf() ) );
+ }
+ if( autowrite ) plt->Write();
+ return plt;
+}
+
+template <> std::tuple<std::vector<TH1D*>, THStack*> Projection::projInternal(const EventListSIMD& events, const Projection::keyedFunctors& weightFunction, const ArgumentPack& args) const
+{
+ std::vector<TH1D*> hists;
+ double norm_sum = args.getArg<Norm>(1).val;
+ std::string prefix = args.getArg<PlotOptions::Prefix>().val;
+ bool autowrite = args.get<PlotOptions::AutoWrite>() != nullptr;
+ THStack* stack = args.getArg<PlotOptions::AddTo>(new THStack()).val;
+ auto selection = args.getArg<Selection>().val;
+ if( prefix != "" ) prefix = prefix +"_";
+ for( auto& key : weightFunction.keys )
+ hists.push_back( plot(prefix + key ) );
+ for( const auto& evt : events ){
+ if( selection != nullptr && !selection(evt) ) continue;
+ auto pos = operator()(evt);
+ auto weights = weightFunction(evt);
+ for( unsigned j = 0 ; j != weights.size(); ++j ) hists[j]->Fill( pos, evt.weight() * weights[j] / evt.genPdf() );
+ }
+ std::sort( std::begin(hists), std::end(hists), [](auto& h1, auto& h2){ return h1->Integral() < h2->Integral() ; } );
+ double total = std::accumulate( std::begin(hists), std::end(hists), 0.0, [](double& t, auto& h){ return t + h->Integral() ; } );
+ if( total == 0 ) ERROR("Norm = " << total );
+ else for( auto& h : hists ) h->Scale( norm_sum / total );
+ stack->SetName( (prefix + name() + "_stack").c_str());
+ for( auto& h : hists ){
+ stack->Add(h, "C HIST");
+ if( autowrite ) h->Write();
+ }
+ if( autowrite ) stack->Write();
+ return {hists, stack};
+}
+#endif
diff --git a/src/QuarkContent.cpp b/src/QuarkContent.cpp
index d31336abae8..bb97ac0994d 100644
--- a/src/QuarkContent.cpp
+++ b/src/QuarkContent.cpp
@@ -15,10 +15,25 @@ std::map<char, int> QuarkState::gPositions;
QuarkState::QuarkState()
{
- for ( auto& quark : m_quarks ) quark = 0;
+ std::fill( m_quarks.begin(), m_quarks.end(), 0 );
initPositions();
}
+QuarkContent::QuarkContent( const std::string& str )
+{
+ if ( str.find( "non-qQ" ) < str.size() ) {
+ m_quarks.resize( 1 );
+ return;
+ }
+ auto tokens = split( replaceAll( str, "sqrt", "" ), {'(', ')', '+', '-'} );
+ m_quarks.clear();
+ for ( auto& token : tokens ) {
+ QuarkState qc( token );
+ if ( !qc.isVacuum() ) m_quarks.emplace_back( qc );
+ }
+ if ( m_quarks.size() == 0 ) m_quarks.resize( 1 );
+}
+
QuarkState::QuarkState( const std::string& str ) : QuarkState() {
for ( auto& c : str ) {
auto lc = std::tolower(c);
@@ -38,7 +53,7 @@ bool QuarkState::initPositions()
void QuarkState::antiThis()
{
- for ( auto& quark : m_quarks ) quark *= -1;
+ std::transform( m_quarks.begin(), m_quarks.end(), m_quarks.begin(), [](const auto& quark){ return (-1)*quark ; } );
}
char QuarkState::nameFromPosition( int i ) const
@@ -82,16 +97,9 @@ QuarkState QuarkState::operator-( const QuarkState& rhs ) const
returnVal -= rhs;
return returnVal;
}
-std::ostream& operator<<( std::ostream& st, const QuarkState& qc )
-{
- qc.print( st );
- return st;
-}
bool QuarkState::isVacuum() const
{
- for ( auto& quark : m_quarks )
- if ( quark != 0 ) return false;
- return true;
+ return std::all_of( m_quarks.begin(), m_quarks.end(), [](const auto& quark){ return quark == 0 ; } );
}
bool QuarkState::operator==( const QuarkState& rhs ) const
@@ -100,6 +108,12 @@ bool QuarkState::operator==( const QuarkState& rhs ) const
if ( rhs[i] != m_quarks[i] ) return false;
return true;
}
+
+bool QuarkState::operator!=( const QuarkState& rhs ) const
+{
+ return !( *this == rhs );
+}
+
int QuarkState::operator[]( const size_t& index ) const { return m_quarks[index]; }
QuarkContent::QuarkContent() : m_quarks(1) {}
@@ -109,21 +123,6 @@ void QuarkContent::antiThis()
for ( auto& qc : m_quarks ) qc.antiThis();
}
-void QuarkContent::initFromString( const std::string& str )
-{
- if ( str.find( "non-qQ" ) < str.size() ) {
- m_quarks.resize( 1 );
- return;
- }
- auto tokens = split( replaceAll( str, "sqrt", "" ), {'(', ')', '+', '-'} );
- m_quarks.clear();
- for ( auto& token : tokens ) {
- QuarkState qc( token );
- if ( !qc.isVacuum() ) m_quarks.emplace_back( qc );
- }
- if ( m_quarks.size() == 0 ) m_quarks.resize( 1 );
-}
-
void QuarkContent::print( std::ostream& os ) const
{
os << "[";
@@ -177,20 +176,14 @@ QuarkContent QuarkContent::operator-( const QuarkContent& rhs ) const
returnVal -= rhs;
return returnVal;
}
-std::ostream& AmpGen::operator<<( std::ostream& st, const QuarkContent& qc )
-{
- qc.print( st );
- return st;
-}
bool QuarkContent::operator==( const QuarkContent& rhs ) const
{
- for ( auto& l : m_quarks ) {
- for ( auto& r : rhs.quarks() ) {
- if ( l == r ) return true;
- }
- }
- return false;
+ for ( auto& qsl : m_quarks ) {
+ bool isSame = std::any_of( rhs.quarks().begin(), rhs.quarks().end(), [&qsl](auto& qsr){ return qsl == qsr; } );
+ if( isSame ) return true;
+ }
+ return false;
}
bool QuarkContent::operator!=( const QuarkContent& rhs ) const
@@ -205,8 +198,21 @@ QuarkState QuarkContent::operator[]( const size_t& index ) const
size_t QuarkContent::size() const { return m_quarks.size(); }
-std::vector<QuarkState> QuarkContent::quarks() const
+const std::vector<QuarkState>& QuarkContent::quarks() const
{
return m_quarks;
}
+
+std::ostream& AmpGen::operator<<( std::ostream& st, const QuarkContent& qc )
+{
+ qc.print( st );
+ return st;
+}
+
+std::ostream& AmpGen::operator<<( std::ostream& st, const QuarkState& qc )
+{
+ qc.print( st );
+ return st;
+}
+
diff --git a/src/RecursivePhaseSpace.cpp b/src/RecursivePhaseSpace.cpp
index 97d7da88160..dad48e3fbde 100644
--- a/src/RecursivePhaseSpace.cpp
+++ b/src/RecursivePhaseSpace.cpp
@@ -40,10 +40,10 @@ RecursivePhaseSpace::RecursivePhaseSpace(const Particle& decayChain, const Event
setRandom( rndm );
}
-AmpGen::Event RecursivePhaseSpace::makeEvent( const size_t& cacheSize )
+AmpGen::Event RecursivePhaseSpace::makeEvent()
{
- AmpGen::Event evt = m_phsp.makeEvent( cacheSize );
- AmpGen::Event rt( 4 * m_eventType.size(), cacheSize );
+ AmpGen::Event evt = m_phsp.makeEvent();
+ AmpGen::Event rt( 4 * m_eventType.size());
for (size_t i = 0; i < m_nodes.size(); ++i ) {
auto& segment = m_nodes[i];
double px = evt[4*i + 0];
@@ -58,9 +58,9 @@ AmpGen::Event RecursivePhaseSpace::makeEvent( const size_t& cacheSize )
rt[4*segment.sink + 3] = pE;
}
} else {
- auto evtTmp = segment.decayProds->makeEvent(cacheSize);
+ auto evtTmp = segment.decayProds->makeEvent();
double v = sqrt( px * px + py * py + pz * pz ) / pE;
- boost( evtTmp, {px, py, pz}, v );
+ boost( evtTmp, std::tuple<double,double,double>(px, py, pz), v );
for(size_t j = 0; j < rt.size(); ++j) rt[j] += evtTmp[j];
}
evt.setGenPdf(1);
@@ -72,8 +72,7 @@ std::vector<RecursivePhaseSpace::Node*> RecursivePhaseSpace::getFinalStates()
{
std::vector<RecursivePhaseSpace::Node*> rt;
for ( auto& f : m_nodes ) {
- if ( f.decayProds == nullptr )
- rt.push_back( &f );
+ if ( f.decayProds == nullptr ) rt.push_back( &f );
else {
auto segs = f.decayProds->getFinalStates();
for ( auto& s : segs ) rt.push_back( s );
diff --git a/src/Simplify.cpp b/src/Simplify.cpp
index cb88aedd9a7..fa5c0db8081 100644
--- a/src/Simplify.cpp
+++ b/src/Simplify.cpp
@@ -4,6 +4,8 @@
#include <algorithm>
#include <memory>
#include <ostream>
+#include <functional>
+#include <numeric>
#include "AmpGen/MsgService.h"
@@ -38,8 +40,10 @@ NormalOrderedExpression::Term::Term( const Expression& expression ) :
std::sort( m_terms.begin(),
m_terms.end(),
[](auto& t1, auto& t2 ){ return t1.second > t2.second; } ) ;
- Expression t = 1;
- for( auto& f : m_terms ) t = t * f.first;
+ Expression t = std::accumulate( m_terms.begin(), m_terms.end(), Expression(1), [](auto& A, auto& B){ return A * B.first ; } );
+ // std::multiplies<Expression>() );
+ //Expression t = 1;
+ //for( auto& f : m_terms ) t = t * f.first;
m_expressionAsString = ( t / m_divisor).to_string();
}
diff --git a/src/Spline.cpp b/src/Spline.cpp
index f92461987b6..1a1ee7b3b61 100644
--- a/src/Spline.cpp
+++ b/src/Spline.cpp
@@ -24,20 +24,18 @@ Spline::Spline(const std::string& name,
m_min(min),
m_max(max) {}
-Spline::Spline(const Spline& spline,
- const Expression& x )
- :
+Spline::Spline(const Spline& spline, const Expression& x, DebugSymbols* db ) :
m_points( spline.m_points ),
m_name( spline.m_name),
m_nKnots( spline.m_nKnots),
m_min( spline.m_min ),
m_max( spline.m_max ),
m_x ( x ),
- m_eval( eval() ) {
- }
-Expression Spline::operator()( const Expression& x )
+ m_eval( eval(db) ) {}
+
+Expression Spline::operator()( const Expression& x, DebugSymbols* db )
{
- return Spline(*this,x);
+ return Spline(*this,x, db);
}
Expression AmpGen::getSpline( const std::string& name, const Expression& x, const std::string& arrayName,
@@ -56,16 +54,16 @@ Expression AmpGen::getSpline( const std::string& name, const Expression& x, cons
max = NamedParameter<double>( name + "::Spline::Max", 0. );
}
std::string spline_name = name + "::Spline::"+arrayName;
- return Spline( spline_name, nBins, min,max )(x);
+ return Spline(spline_name, nBins, min, max)(x, dbexpressions);
}
-Expression Spline::eval() const
+Expression Spline::eval(DebugSymbols* db) const
{
Expression x = make_cse(m_x);
double spacing = ( m_max - m_min ) / ( (double)m_nKnots - 1. );
Expression dx = Fmod( x - m_min, spacing );
Expression bin = ( x - m_min ) / spacing;
- Expression continuedValue = 0;
+ Expression continuedValue = m_points[m_nKnots-1];
Expression returnValue = Ternary( x > m_min && x < m_max,
m_points[bin] + ( ( m_points[bin + 1] - m_points[bin] ) / spacing
@@ -73,6 +71,11 @@ Expression Spline::eval() const
+ m_points[bin+m_nKnots] * dx * dx / 2.
+ dx * dx * dx * ( m_points[bin+1+m_nKnots] - m_points[bin+m_nKnots] ) / ( 6. * spacing ),
continuedValue );
+ ADD_DEBUG(x, db );
+ ADD_DEBUG(dx, db );
+ ADD_DEBUG(bin, db );
+ ADD_DEBUG(returnValue, db );
+ ADD_DEBUG( m_points[bin], db );
return make_cse(returnValue);
}
@@ -80,27 +83,25 @@ void SplineTransfer::print() const { INFO( "Source: " << m_parameters[0]->name()
SplineTransfer::SplineTransfer() = default;
SplineTransfer::SplineTransfer( const SplineTransfer& other )
- : CacheTransfer()
+ : CacheTransfer(other.m_address, other.m_name, other.m_value, other.m_size)
, m_transferMatrix( other.m_transferMatrix )
, m_parameters( other.m_parameters )
+ , m_nKnots( other.m_nKnots )
, m_min( other.m_min )
, m_max( other.m_max )
- , m_address( other.m_address )
{
}
-SplineTransfer::SplineTransfer( const unsigned int& address, const unsigned int& N, const double& min, const double& max )
- : CacheTransfer()
+SplineTransfer::SplineTransfer( const size_t& address, const std::string& name, const unsigned int& N, const double& min, const double& max )
+ : CacheTransfer(address, name)
, m_transferMatrix( TMatrixD( N - 2, N - 2 ) )
, m_parameters( N, nullptr )
, m_nKnots(N)
, m_min( min )
, m_max( max )
- , m_address( address )
-
{
unsigned int size = N - 2;
- TMatrixD M( N - 2, N - 2 );
+ TMatrixD M(size, size);
for ( unsigned int i = 0; i < size; ++i ) {
M[i][i] = 4;
if ( i != size - 1 ) {
@@ -117,9 +118,7 @@ SplineTransfer::SplineTransfer( const unsigned int& address, const unsigned int&
bool SplineTransfer::isConfigured()
{
- for ( auto& x : m_parameters )
- if ( x == nullptr ) return false;
- return true;
+ return std::all_of( m_parameters.begin(), m_parameters.end(), [](auto& p ){ return p != nullptr ; } );
}
void SplineTransfer::set( const unsigned int& N, MinuitParameter* f )
@@ -128,10 +127,9 @@ void SplineTransfer::set( const unsigned int& N, MinuitParameter* f )
}
void SplineTransfer::set( const unsigned int& N, const double& value )
{
- m_parameters[N] = new MinuitParameter("dumb",MinuitParameter::Fix,value,0);
+ m_parameters[N] = new MinuitParameter("dumb", Flag::Fix, value, 0);
}
-void SplineTransfer::setAddress( const unsigned int& address ) { m_address = ( address ); }
void SplineTransfer::transfer( CompiledExpressionBase* destination )
{
unsigned int size = m_parameters.size() - 2;
@@ -154,7 +152,7 @@ void SplineTransfer::transfer( CompiledExpressionBase* destination )
}
}
-void Spline::resolve( ASTResolver& resolver )
+void Spline::resolve( ASTResolver& resolver ) const
{
resolver.resolve(*this);
m_x.resolve(resolver);
diff --git a/src/Tensor.cpp b/src/Tensor.cpp
index b53519571b4..90ae8a46863 100644
--- a/src/Tensor.cpp
+++ b/src/Tensor.cpp
@@ -22,7 +22,7 @@ Tensor::Tensor()
setupCoordinates();
}
-Tensor::Tensor( const std::vector<size_t>& dim )
+Tensor::Tensor( const std::vector<unsigned>& dim )
: m_dim(dim),
m_elements( nElements(), Constant( 0. ) )
{
@@ -30,31 +30,19 @@ Tensor::Tensor( const std::vector<size_t>& dim )
}
Tensor::Tensor( const std::vector<Expression>& elements )
- : m_dim( std::vector<size_t>( {elements.size()} ) )
+ : m_dim( std::vector<unsigned>( {unsigned(elements.size())} ) )
{
setupCoordinates();
for(auto& element : elements) append( element );
}
-/*
-Tensor::Tensor( const std::vector<Tensor>& elements )
-{
- if( elements.size() == 0 ) return Tensor();
- std::vector<size_t> rank;
- rank.push_back( elements.size() );
- for( auto& d : element[0].dims() ) rank.push_back( d );
- for( int i = 0 ; i < elements.size(); ++i )
- {
-
- }
-}
-*/
-Expression Tensor::get( const size_t& co )
+
+Expression Tensor::get( const unsigned& co )
{
if ( co >= m_elements.size() )
ERROR("Element (" + std::to_string( co ) + " ) out of range (0" << ", " << m_elements.size() << ")");
return m_elements[m_symmetrisedCoordinates[co]];
}
-Expression Tensor::get( const size_t& co ) const
+Expression Tensor::get( const unsigned& co ) const
{
if ( co >= m_elements.size() )
ERROR("Element (" + std::to_string( co ) + " ) out of range (0" << ", " << m_elements.size() << ")");
@@ -64,23 +52,22 @@ Expression Tensor::get( const size_t& co ) const
std::string Tensor::to_string(const ASTResolver* resolver) const
{
std::string value = "{";
- for(size_t i = 0 ; i < size(); ++i)
+ for(unsigned i = 0 ; i < size(); ++i)
{
value += Tensor::operator[](i).to_string(resolver) + (i == size() -1 ? "}" : ", " ) ;
}
return value;
}
-size_t Tensor::rank() const { return m_dim.size(); }
+unsigned Tensor::rank() const { return m_dim.size(); }
-int Tensor::metricSgn( const std::vector<size_t>& coordinates ) const
+int Tensor::metricSgn( const std::vector<unsigned>& coordinates ) const
{
- int sgn = 1;
- for ( auto& coord : coordinates ) sgn *= ( coord == 3 ) ? 1 : -1;
- return sgn;
+ return std::accumulate( coordinates.begin(), coordinates.end(), 1,
+ [](auto& prod, auto& co){ return prod * ( ( co == 3) ? 1 : -1 ) ;} );
}
-int Tensor::metricSgn( const size_t& index ) const { return metricSgn( coords( index ) ); }
+int Tensor::metricSgn( const unsigned& index ) const { return metricSgn( coords( index ) ); }
void Tensor::append( const Expression& expression ){ m_elements.emplace_back( expression ); }
void Tensor::append( const real_t& value ) { m_elements.emplace_back( Constant( value )); }
@@ -89,8 +76,7 @@ void Tensor::append( const std::string& value ) { m_elements.emplace_back( Pa
void Tensor::setupCoordinates()
{
- int st=1;
- for( auto& d : m_dim ) st *= d;
+ int st = std::accumulate( m_dim.begin(), m_dim.end(), 1, std::multiplies<int>() );
DEBUG( "Setting up coordinates: " << dimString() << " coordinate mapping = " << st );
m_symmetrisedCoordinates.resize( st );
std::iota( m_symmetrisedCoordinates.begin(), m_symmetrisedCoordinates.end(), 0 );
@@ -98,11 +84,11 @@ void Tensor::setupCoordinates()
std::iota( m_uniqueElements.begin(), m_uniqueElements.end(), 0 );
}
-Expression Tensor::get( const std::vector<size_t>& _co ) const { return ( m_elements[index( _co )] ); }
+Expression Tensor::get( const std::vector<unsigned>& _co ) const { return ( m_elements[index( _co )] ); }
-size_t Tensor::size() const { return m_elements.size(); }
+unsigned Tensor::size() const { return m_elements.size(); }
-size_t Tensor::index( const std::vector<size_t>& _co ) const
+unsigned Tensor::index( const std::vector<unsigned>& _co ) const
{
return symmetrisedIndex(_co);
// auto id = Tensor::coordinates_to_index( _co, m_dim );
@@ -110,7 +96,7 @@ size_t Tensor::index( const std::vector<size_t>& _co ) const
// return id;
}
-size_t Tensor::symmetrisedIndex( const std::vector<size_t>& co ) const
+unsigned Tensor::symmetrisedIndex( const std::vector<unsigned>& co ) const
{
auto id = Tensor::coordinates_to_index( co, m_dim );
if( id > m_symmetrisedCoordinates.size() ){
@@ -119,29 +105,29 @@ size_t Tensor::symmetrisedIndex( const std::vector<size_t>& co ) const
return m_symmetrisedCoordinates[id] ;
}
-const std::vector<size_t> Tensor::coords( const size_t& index ) const
+const std::vector<unsigned> Tensor::coords( const unsigned& index ) const
{
return Tensor::index_to_coordinates( index, m_dim );
}
-std::vector<size_t> Tensor::index_to_coordinates( const size_t& index, const std::vector<size_t>& dim )
+std::vector<unsigned> Tensor::index_to_coordinates( const unsigned& index, const std::vector<unsigned>& dim )
{
- std::vector<size_t> returnValue;
- size_t index_temp = index;
- for(size_t j = 0; j < dim.size(); ++j ) {
- size_t dproduct = 1;
- for(size_t i = 0; i < dim.size() - j-1; ++i ) dproduct *= dim[dim.size()-i-1];
- size_t val = ( index_temp - ( index_temp % dproduct ) ) / dproduct;
+ std::vector<unsigned> returnValue;
+ unsigned index_temp = index;
+ for(unsigned j = 0; j < dim.size(); ++j ) {
+ unsigned dproduct = 1;
+ for(unsigned i = 0; i < dim.size() - j-1; ++i ) dproduct *= dim[dim.size()-i-1];
+ unsigned val = ( index_temp - ( index_temp % dproduct ) ) / dproduct;
index_temp -= dproduct * val;
returnValue.push_back( val );
}
return returnValue;
}
-size_t Tensor::coordinates_to_index( const std::vector<size_t>& co, const std::vector<size_t>& dim )
+unsigned Tensor::coordinates_to_index( const std::vector<unsigned>& co, const std::vector<unsigned>& dim )
{
- size_t index = 0;
- size_t dproduct = 1;
+ unsigned index = 0;
+ unsigned dproduct = 1;
for ( int i = dim.size()-1; i >= 0; --i ) {
//for ( int i = 0; i < dim.size(); ++i ) {
index += co[i] * dproduct;
@@ -150,18 +136,14 @@ size_t Tensor::coordinates_to_index( const std::vector<size_t>& co, const std::v
return index;
}
-std::string Tensor::coordinates_to_string( const std::vector<size_t>& coordinates )
+std::string Tensor::coordinates_to_string( const std::vector<unsigned>& coordinates )
{
return "[" + vectorToString( coordinates, ", ") + "]";
}
-size_t Tensor::nElements() const
+unsigned Tensor::nElements() const
{
- size_t dim = 1;
- for ( auto& d : m_dim ) {
- dim *= ( d != 0 ) ? d : 1;
- }
- return dim;
+ return std::accumulate( m_dim.begin(), m_dim.end(), 1, [](auto& dim, auto& d){ return dim * ( d == 0 ? 1 : d ) ; } );
}
const std::string Tensor::dimString() const
{
@@ -171,13 +153,13 @@ const std::string Tensor::dimString() const
return str + "]";
}
-size_t Tensor::nDim() const { return m_dim.size(); }
+unsigned Tensor::nDim() const { return m_dim.size(); }
bool Tensor::rankMatches( const Tensor& other )
{
bool success = true;
if ( m_dim.size() != other.m_dim.size() ) return false;
- for ( size_t i = 0; i < m_dim.size(); ++i ) success &= m_dim[i] == other.m_dim[i];
+ for ( unsigned i = 0; i < m_dim.size(); ++i ) success &= m_dim[i] == other.m_dim[i];
return success;
}
@@ -194,7 +176,7 @@ Tensor AmpGen::operator+( const Tensor& t1, const Tensor& t2 )
ERROR("Addition between tensors with different number of elements " << t1.nElements() << " " << t2.nElements());
}
- for ( size_t i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] + t2[i];
+ for ( unsigned i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] + t2[i];
return result;
}
@@ -212,12 +194,12 @@ Tensor AmpGen::operator-( const Tensor& t1, const Tensor& t2 )
t2.print();
ERROR("Subtraction between tensors with different number of elements " << t1.nElements() << " "<< t2.nElements());
}
- for ( size_t i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] - t2[i];
+ for ( unsigned i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] - t2[i];
return result;
}
void Tensor::st(const bool simplify) {
- for(size_t i = 0 ; i < size(); ++i ){
+ for(unsigned i = 0 ; i < size(); ++i ){
m_elements[i] = make_cse( m_elements[i], simplify );
}
}
@@ -225,14 +207,14 @@ void Tensor::st(const bool simplify) {
Tensor Tensor::conjugate() const
{
Tensor copy( dims() );
- for(size_t i = 0 ; i < size(); ++i ) copy[i] = fcn::conj( get(i) );
+ for(unsigned i = 0 ; i < size(); ++i ) copy[i] = fcn::conj( get(i) );
return copy;
}
Tensor AmpGen::operator/( const Tensor& t1, const Expression& t2 )
{
Tensor result( t1.dims() );
- for (size_t i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] / t2;
+ for (unsigned i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] / t2;
return result;
}
@@ -240,7 +222,7 @@ Tensor AmpGen::operator/( const Tensor& t1, const Expression& t2 )
Tensor AmpGen::operator*( const Expression& other, const Tensor& t1 )
{
Tensor result( t1.dims() );
- for (size_t i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] * other;
+ for (unsigned i = 0; i < t1.nElements(); ++i ) result[i] = t1[i] * other;
return result;
}
@@ -381,10 +363,10 @@ TensorProxy Tensor::operator()( const Tensor::Index& a, const Tensor::Index& b,
return TensorProxy( *this, {a, b, c, d} );
}
struct contractor {
- size_t i;
- size_t j;
+ unsigned i;
+ unsigned j;
int sgn;
- contractor( const size_t& i, const size_t&j, const int& sgn) : i(i),j(j),sgn(sgn) {}
+ contractor( const unsigned& i, const unsigned&j, const int& sgn) : i(i),j(j),sgn(sgn) {}
};
@@ -396,23 +378,23 @@ TensorProxy AmpGen::operator*( const TensorProxy& t1, const TensorProxy& t2 )
const std::vector<Tensor::Index>& t1_index = t1.indices();
const std::vector<Tensor::Index>& t2_index = t2.indices();
- const size_t t1_size = t1.indices().size();
- const size_t t2_size = t2.indices().size();
+ const unsigned t1_size = t1.indices().size();
+ const unsigned t2_size = t2.indices().size();
const Tensor& t1_tensor = t1.tensor();
const Tensor& t2_tensor = t2.tensor();
- std::vector<size_t> finalTensorRank;
- std::vector<size_t> contractionMatrix;
+ std::vector<unsigned> finalTensorRank;
+ std::vector<unsigned> contractionMatrix;
- for( size_t i = 0; i < t1_size; ++i )
+ for( unsigned i = 0; i < t1_size; ++i )
{
if ( std::find( t2_index.begin(), t2_index.end(), t1.indices()[i] ) == t2_index.end() ) {
unsummedIndices.push_back( t1.indices()[i] );
finalTensorRank.push_back( t1_tensor.dims()[i] );
}
}
- for( size_t i = 0; i < t2_size; ++i ) {
+ for( unsigned i = 0; i < t2_size; ++i ) {
auto it = std::find( t1_index.begin(), t1_index.end(), t2_index[i] );
if ( it == t1_index.end() ) {
unsummedIndices.push_back( t2.indices()[i] );
@@ -423,26 +405,23 @@ TensorProxy AmpGen::operator*( const TensorProxy& t1, const TensorProxy& t2 )
t2_index[i].isUpper() != it->isUpper() ? -1 : 1 );
}
}
- size_t nElementsInSum = 1;
+ unsigned nElementsInSum = 1;
for ( auto& c : contractions ){
contractionMatrix.push_back( t1_tensor.dims()[c.i] );
nElementsInSum *= t1_tensor.dims()[c.i];
}
Tensor value( finalTensorRank );
- size_t nElem = value.nElements();
- DEBUG("Got " << t1_tensor.dims().size() << " x " << t2_tensor.dims().size() << " with " << contractions.size() << " contractions " << nElementsInSum);
- DEBUG(t1_tensor.dimString() << " x " << t2_tensor.dimString() << " -> " << value.dimString());
- DEBUG("Contraction matrix = " << "[" << vectorToString(contractionMatrix, ", ") << "]");
+ unsigned nElem = value.nElements();
- for( size_t elem = 0; elem < nElem; ++elem ) {
+ for( unsigned elem = 0; elem < nElem; ++elem ) {
auto coords = Tensor::index_to_coordinates( elem, finalTensorRank );
- std::vector<size_t> t1_coords( t1_size, 0 );
- std::vector<size_t> t2_coords( t2_size, 0 );
- size_t i = 0;
- size_t j = 0;
+ std::vector<unsigned> t1_coords( t1_size, 0 );
+ std::vector<unsigned> t2_coords( t2_size, 0 );
+ unsigned i = 0;
+ unsigned j = 0;
do {
- if( !isIn(contractions, i, [](const contractor& a, const size_t& b){ return a.i == b;})) {
+ if( std::none_of( contractions.begin(), contractions.end(), [&i](const auto& a){ return a.i == i ;} )){
t1_coords[i] = coords[j];
j++;
}
@@ -450,20 +429,19 @@ TensorProxy AmpGen::operator*( const TensorProxy& t1, const TensorProxy& t2 )
i = 0;
j = t1_size - contractions.size();
do {
- if( !isIn(contractions, i, [](const contractor& a, const size_t& b){ return a.j == b;})) {
+ if( std::none_of( contractions.begin(), contractions.end(), [&i](const auto& a){ return a.j == i ;} )){
t2_coords[i] = coords[j];
j++;
}
} while ( ++i < t2_size );
Expression elementExpression = 0;
- for( unsigned int i=0; i<nElementsInSum; ++i) {
- auto contractedCoordinates = Tensor::index_to_coordinates( i, contractionMatrix );
+ for( unsigned m=0; m<nElementsInSum; ++m) {
+ auto contractedCoordinates = Tensor::index_to_coordinates( m, contractionMatrix );
int sign = 1;
- for( unsigned int j=0; j<contractions.size(); ++j) {
- t1_coords[contractions[j].i] = contractedCoordinates[j];
- t2_coords[contractions[j].j] = contractedCoordinates[j];
- sign *= ( contractedCoordinates[j] ) == 3 ? 1 : contractions[j].sgn;
+ for( unsigned n=0; n<contractions.size(); ++n) {
+ t1_coords[contractions[n].i] = t2_coords[contractions[n].j] = contractedCoordinates[n];
+ sign *= ( contractedCoordinates[n] ) == 3 ? 1 : contractions[n].sgn;
}
elementExpression = elementExpression + sign * t1_tensor[t1_coords] * t2_tensor[t2_coords];
}
@@ -524,18 +502,18 @@ TensorProxy AmpGen::operator+( const TensorProxy& t1, const TensorProxy& t2 )
for ( auto& i : tensor_t1.uniqueElements() ) {
auto t1_coords = tensor_t1.coords( i );
- auto t2_coords = std::vector<size_t>( t1_coords.size(), 0 );
+ auto t2_coords = std::vector<unsigned>( t1_coords.size(), 0 );
for( unsigned int j=0;j<t1_coords.size(); ++j ) t2_coords[ j ] = t1_coords[t1_to_t2_mapping[j]];
result[i] = result[i] + tensor_t2[t2_coords];
}
return TensorProxy( result, indices_t1 );
}
-void Tensor::imposeSymmetry( size_t indexA, size_t indexB)
+void Tensor::imposeSymmetry( unsigned indexA, unsigned indexB)
{
if( indexA > indexB ) std::swap( indexA, indexB );
- std::map< size_t, size_t > counter;
- for( size_t i = 0 ; i < m_symmetrisedCoordinates.size(); ++i ){
+ std::map< unsigned, unsigned > counter;
+ for( unsigned i = 0 ; i < m_symmetrisedCoordinates.size(); ++i ){
auto coordinates = Tensor::index_to_coordinates( i, m_dim ); /// raw coordinates of this ///
if( coordinates[indexB] > coordinates[indexA] )
std::swap( coordinates[indexA], coordinates[indexB] );
@@ -548,21 +526,21 @@ void Tensor::imposeSymmetry( size_t indexA, size_t indexB)
DEBUG("Imposing symmetries on " << indexA << " <--> " << indexB << " reduces size to: " << counter.size());
}
-void Tensor::imposeSymmetry( std::vector<size_t> indices )
+void Tensor::imposeSymmetry( std::vector<unsigned> indices )
{
std::sort( indices.begin(), indices.end() );
- for( size_t i=0;i<indices.size()-1;++i){
- for( size_t j=i+1;j<indices.size();++j){
+ for( unsigned i=0;i<indices.size()-1;++i){
+ for( unsigned j=i+1;j<indices.size();++j){
imposeSymmetry( indices[i], indices[j] );
}
}
}
-Expression& Tensor::operator[]( const size_t& i ) { return m_elements[m_symmetrisedCoordinates[i]]; }
-Expression& Tensor::operator[]( const std::vector<size_t>& co ) { return m_elements[symmetrisedIndex(co)]; }
-const Expression& Tensor::operator[]( const size_t& i ) const { return m_elements[m_symmetrisedCoordinates[i]]; }
-const Expression& Tensor::operator[]( const std::vector<size_t>& co ) const { return m_elements[symmetrisedIndex(co)]; }
+Expression& Tensor::operator[]( const unsigned& i ) { return m_elements[m_symmetrisedCoordinates[i]]; }
+Expression& Tensor::operator[]( const std::vector<unsigned>& co ) { return m_elements[symmetrisedIndex(co)]; }
+const Expression& Tensor::operator[]( const unsigned& i ) const { return m_elements[m_symmetrisedCoordinates[i]]; }
+const Expression& Tensor::operator[]( const std::vector<unsigned>& co ) const { return m_elements[symmetrisedIndex(co)]; }
TensorProxy::TensorProxy(const Tensor& tensor,
const std::vector<Tensor::Index>& indices)
@@ -574,9 +552,9 @@ TensorProxy::TensorProxy(const Tensor& tensor,
}
m_indices = indices;
std::vector<contractor> contractions;
- std::vector<size_t> rt_dim;
- for( size_t i = 0 ; i < indices.size(); ++i ){
- size_t j = i + 1;
+ std::vector<unsigned> rt_dim;
+ for( unsigned i = 0 ; i < indices.size(); ++i ){
+ unsigned j = i + 1;
for( ; j < indices.size(); ++j ){
if( indices[i] != indices[j] ) continue;
ERROR("Tensor self-contractions not implemented yet!");
@@ -594,53 +572,52 @@ TensorProxy::TensorProxy(const Tensor& tensor,
TensorProxy TensorProxy::reorder( const std::vector<Tensor::Index>& indices )
{
- std::vector<size_t> mapping( m_indices.size() ,0 );
- for(size_t j= 0; j < indices.size(); ++j)
+ std::vector<unsigned> mapping( m_indices.size() ,0 );
+ for(unsigned j= 0; j < indices.size(); ++j)
{
- for(size_t i = 0; i < m_indices.size(); ++i)
+ for(unsigned i = 0; i < m_indices.size(); ++i)
{
if( m_indices[j] == indices[i] ) mapping[j] = i;
}
}
Tensor reordered( m_tensor.dims() );
- for(size_t i = 0 ; i < m_tensor.size(); ++i)
+ for(unsigned i = 0 ; i < m_tensor.size(); ++i)
{
auto coordinates = Tensor::index_to_coordinates(i,m_tensor.dims() );
- std::vector<size_t> new_coordinates( m_indices.size() );
- for(size_t z = 0 ; z < m_indices.size(); ++z )
+ std::vector<unsigned> new_coordinates( m_indices.size() );
+ for(unsigned z = 0 ; z < m_indices.size(); ++z )
new_coordinates[z] = coordinates[mapping[z]];
reordered[ i ] = m_tensor[ new_coordinates ];
}
return TensorProxy( reordered, indices );
}
-Tensor AmpGen::Identity( const size_t& rank )
+Tensor AmpGen::Identity( const unsigned& rank )
{
- Tensor id( std::vector<size_t>( {rank, rank} ) );
- for (size_t i = 0; i < rank; ++i) id(i, i) = 1;
+ Tensor id( std::vector<unsigned>( {rank, rank} ) );
+ for (unsigned i = 0; i < rank; ++i) id(i, i) = 1;
return id;
}
-const Tensor AmpGen::LeviCivita( const size_t& rank )
+const Tensor AmpGen::LeviCivita( const unsigned& rank )
{
- std::vector<size_t> dim( rank, rank );
- std::vector<size_t> indices( rank );
+ std::vector<unsigned> dim( rank, rank );
+ std::vector<unsigned> indices( rank );
std::iota( indices.begin(), indices.end(), 0 );
- auto permutation_sign = []( const std::vector<size_t>& permutation){
+ auto permutation_sign = []( const std::vector<unsigned>& permutation){
int product = 1;
- for ( size_t i = 0; i < permutation.size() - 1; ++i ) {
- for ( size_t j = i + 1; j < permutation.size(); ++j ) {
+ for ( unsigned i = 0; i < permutation.size() - 1; ++i ) {
+ for ( unsigned j = i + 1; j < permutation.size(); ++j ) {
product *= ( (int)permutation[i] - (int)permutation[j] );
}
}
return product;
};
int p0 = permutation_sign( indices );
-
Tensor result( dim ); /// create tensor of rank N ///
do {
- size_t index = result.index( indices );
+ unsigned index = result.index( indices );
result[index] = permutation_sign( indices ) / p0;
} while ( std::next_permutation( indices.begin(), indices.end() ) );
return result;
@@ -658,8 +635,8 @@ TensorExpression::TensorExpression( const Tensor& tensor ) :
std::string TensorExpression::to_string(const ASTResolver* resolver) const {
return m_tensor.to_string(resolver);
}
-void TensorExpression::resolve( ASTResolver& resolver ){
- for( size_t i = 0 ; i < m_tensor.size(); ++i ) m_tensor[i].resolve( resolver );
+void TensorExpression::resolve( ASTResolver& resolver ) const {
+ for( unsigned i = 0 ; i < m_tensor.size(); ++i ) m_tensor[i].resolve( resolver );
}
complex_t TensorExpression::operator()() const { return 0 ; }
diff --git a/src/ThreadPool.cpp b/src/ThreadPool.cpp
index 05fa274eb37..b0489cf116c 100644
--- a/src/ThreadPool.cpp
+++ b/src/ThreadPool.cpp
@@ -6,10 +6,7 @@
using namespace AmpGen;
-ThreadPool* ThreadPool::gThreadPool = nullptr;
-size_t ThreadPool::nThreads = 10;
-
-ThreadPool::ThreadPool(const size_t& nt) : m_stop(false)
+ThreadPool::ThreadPool(const size_t& nt)
{
for ( size_t i = 0; i < nt; ++i )
m_workers.emplace_back( [this] {
diff --git a/src/ThreeBodyCalculators.cpp b/src/ThreeBodyCalculators.cpp
index d099bb7c5ef..20c9eb69447 100644
--- a/src/ThreeBodyCalculators.cpp
+++ b/src/ThreeBodyCalculators.cpp
@@ -44,14 +44,9 @@ using namespace AmpGen;
template <class FCN> double dispersive( FCN& fcn , const double& s, double min , double max )
{
TF1 fcn_tf1 = TF1( "fcn_tf1",fcn, min, max, 0 );
- ROOT::Math::WrappedTF1* wf1 = new ROOT::Math::WrappedTF1( fcn_tf1 );
- ROOT::Math::GSLIntegrator ig( ROOT::Math::IntegrationOneDim::kADAPTIVE );
- ROOT::Math::IGenFunction& stupid = *( wf1->Clone() );
- ig.SetFunction( stupid );
- ig.SetRelTolerance( 0.001 );
- double rt = ig.IntegralCauchy(stupid,min,max,s);
- delete wf1;
- return rt;
+ ROOT::Math::GSLIntegrator ig(ROOT::Math::IntegrationOneDim::kADAPTIVE, 0.0001);
+ ig.SetFunction( ROOT::Math::WrappedTF1(fcn_tf1) );
+ return ig.IntegralCauchy(min,max,s);
}
TGraph* ThreeBodyCalculator::runningMass(
@@ -141,18 +136,18 @@ double ThreeBodyCalculator::PartialWidth::getWidth( const double& s )
}
Expression ThreeBodyCalculator::PartialWidth::spinAverageMatrixElement(
- const std::vector<TransitionMatrix<complex_t>>& elements, DebugSymbols* msym )
+ const std::vector<std::pair<Particle, TotalCoupling>>& elements, DebugSymbols* msym )
{
std::vector<Tensor> currents;
- for ( auto& element : elements ) {
- Particle particle(element.decayDescriptor(), type.finalStates() );
+ for ( auto& [s, c] : elements ) {
+ Particle particle(s.decayDescriptor(), type.finalStates() );
auto perm = particle.identicalDaughterOrderings();
for ( auto& p : perm ) {
particle.setOrdering(p);
particle.setLineshape( "FormFactor" );
- Expression prop = make_cse( element.coupling.to_expression() ) * make_cse( particle.propagator( msym ) );
- if ( msym != nullptr ) msym->emplace_back( element.decayTree.name() + "_g", element.coupling.to_expression() );
- if ( msym != nullptr ) msym->emplace_back( element.decayTree.name() + "_p", particle.propagator() );
+ Expression prop = make_cse( c.to_expression() ) * make_cse( particle.propagator( msym ) );
+ if ( msym != nullptr ) msym->emplace_back( s.name() + "_g", c.to_expression() );
+ if ( msym != nullptr ) msym->emplace_back( s.name() + "_p", particle.propagator() );
Tensor zt = particle.spinTensor(msym);
zt.st() ;
currents.push_back( zt * prop );
@@ -169,6 +164,7 @@ Expression ThreeBodyCalculator::PartialWidth::spinAverageMatrixElement(
ThreeBodyCalculator::ThreeBodyCalculator( const std::string& head, MinuitParameterSet& mps, const size_t& nKnots, const double& min, const double& max)
: m_min(min),
m_max(max),
+ m_norm(1),
m_nKnots(nKnots),
m_name(head),
m_mps(&mps)
@@ -188,9 +184,6 @@ ThreeBodyCalculator::ThreeBodyCalculator( const std::string& head, MinuitParamet
finalStates.push_back( type );
}
for ( auto& type : finalStates ) m_widths.emplace_back( type, mps );
-
- bool isReady = true;
- for( auto& width : m_widths ) isReady &= width.totalWidth.isReady();
if( nKnots != 999) setAxis( nKnots, min, max );
}
@@ -210,7 +203,7 @@ void ThreeBodyCalculator::updateRunningWidth( MinuitParameterSet& mps, const dou
double s = m_min + double(c) * m_step;
double I = getWidth(s);
const std::string knotName = m_name + "::Spline::Gamma::" + std::to_string( c );
- if ( mps.map().find( knotName ) != mps.map().end() ) mps[knotName]->setCurrentFitVal( I );
+ if ( mps.find( knotName ) != nullptr ) mps[knotName]->setCurrentFitVal( I );
INFO( knotName << " = " << I );
}
}
@@ -233,20 +226,23 @@ TGraph* ThreeBodyCalculator::widthGraph( const double& mNorm )
return g;
}
-ThreeBodyCalculator::PartialWidth::PartialWidth( const EventType& evt, MinuitParameterSet& mps ) :
- fcs( evt, mps, "" )
- , integrator(1, evt.mass(0)*evt.mass(0), evt.mass(1)*evt.mass(1) , evt.mass(2)*evt.mass(2) )
- , type(evt)
+ThreeBodyCalculator::PartialWidth::PartialWidth( const EventType& evt, MinuitParameterSet& mps )
+ : fcs( evt, mps, "" )
+ , integrator(1, evt.mass(0)*evt.mass(0), evt.mass(1)*evt.mass(1) , evt.mass(2)*evt.mass(2) )
+ , type(evt)
{
DebugSymbols msym;
- Expression matrixElementTotal = spinAverageMatrixElement( fcs.matrixElements(), &msym );
+ std::vector<std::pair<Particle,TotalCoupling>> unpacked;
+ for( auto& p : fcs.matrixElements() ) unpacked.emplace_back( p.decayTree, p.coupling );
+
+ Expression matrixElementTotal = spinAverageMatrixElement(unpacked, &msym );
std::string name = "";
auto evtFormat = evt.getEventFormat();
- for ( auto& p : fcs.matrixElements() ) {
- name += p.decayDescriptor();
- partialWidths.emplace_back( spinAverageMatrixElement( {p}, &msym ), p.decayDescriptor(), evtFormat, DebugSymbols(), &mps );
+ for ( auto& p : unpacked ) {
+ name += p.first.decayDescriptor();
+ partialWidths.emplace_back( spinAverageMatrixElement( {p}, &msym ), p.first.decayDescriptor(), &mps, evtFormat);
}
- totalWidth = CompiledExpression< std::complex<real_t>, const real_t*, const real_t* > ( matrixElementTotal, "width", evtFormat, {} , &mps );
+ totalWidth = CompiledExpression< complex_t(const real_t*, const real_t*) > ( matrixElementTotal, "width", &mps, evtFormat);
CompilerWrapper(true).compile( totalWidth, "");
}
@@ -271,16 +267,13 @@ void ThreeBodyCalculator::makePlots(const double& mass, const size_t& x, const s
{
auto& sq = m_widths[0].integrator;
auto& evtType = m_widths[0].type;
- if( mass != -1 ) evtType.setMotherMass( mass );
auto& fcs = m_widths[0].totalWidth;
auto projection_operators = evtType.defaultProjections( 500 );
int points = NamedParameter<int>( "nPoints", 50000000 );
sq.setMother( evtType.motherMass() );
prepare();
auto fcn = [&](const double* evt) { return std::real(fcs(evt)); };
-
sq.makePlot( fcn, Projection2D( projection_operators[x], projection_operators[y] ), "s01_vs_s02", points )->Write();
-
}
void ThreeBodyCalculator::debug( const double& m, const double& theta )
@@ -290,7 +283,7 @@ void ThreeBodyCalculator::debug( const double& m, const double& theta )
Event event(12);
width.integrator.setEvent({m,theta},event);
event.print();
- width.totalWidth.debug( event );
+ width.totalWidth.debug( event.address() );
}
}
diff --git a/src/Transform.cpp b/src/Transform.cpp
index c001be7ce19..812a6bef05e 100644
--- a/src/Transform.cpp
+++ b/src/Transform.cpp
@@ -29,11 +29,10 @@ Tensor Transform::sigma_dot_p(const Tensor& p) const
Tensor Transform::J_dot_p( const Tensor& p ) const
{
Expression z(0);
- return Tensor(
- { z, -p[2], p[1] ,z
- , p[2], z, -p[0] ,z
- ,-p[1], p[0], z ,z
- , z, z, z ,z }, Tensor::dim(4,4) );
+ return Tensor( { z, -p[2], p[1] ,z
+ , p[2], z, -p[0] ,z
+ ,-p[1], p[0], z ,z
+ , z, z, z ,z }, Tensor::dim(4,4) );
}
Tensor Transform::K_dot_p( const Tensor& p ) const
@@ -65,7 +64,7 @@ Tensor Transform::boost_spinor() const
return Identity(2) * fcn::sqrt(0.5*(m_arg+1)) + sigma_dot_p(m_k)*fcn::sqrt(0.5*(m_arg-1));
}
-Tensor Transform::operator()(const Representation& repr) const
+Tensor Transform::operator()(const Representation& repr)const
{
Tensor::Index m,j,k;
Tensor I2 = Identity(2);
@@ -97,31 +96,40 @@ Tensor Transform::operator()(const Representation& repr) const
return Tensor();
}
-TransformSequence TransformSequence::inverse() const
+TransformSequence TransformSequence::inverse() const
{
TransformSequence rt;
for( auto i = m_transforms.rbegin(); i != m_transforms.rend(); ++i )
- rt.add( i->inverse() );
+ rt.push_back( i->inverse() );
return rt;
}
-Tensor TransformSequence::operator()( const Transform::Representation& repr ) const
+Tensor TransformSequence::operator()( const Transform::Representation& repr ) const
{
- if( m_transforms.size() == 0 ){
- if( repr == Transform::Representation::Spinor ) return Identity(2);
- else return Identity(4);
- }
- Tensor::Index a,b,c;
+ return m_cache[repr];
+}
- Tensor rt = m_transforms[0](repr);
- rt.st();
- for( size_t i = 1 ; i < m_transforms.size(); ++i )
+void TransformSequence::buildCache()
+{
+ for( auto repr : { Transform::Representation::Spinor, Transform::Representation::Bispinor, Transform::Representation::Vector } )
{
- Tensor rti = m_transforms[i](repr);
- rti.st();
- rt = rti(a,b) * rt(b,c);
+ if( m_transforms.size() == 0 ){
+ if( repr == Transform::Representation::Spinor ) m_cache[repr] = Identity(2);
+ m_cache[repr] = Identity(4);
+ }
+ else {
+ Tensor::Index a,b,c;
+ Tensor rt = m_transforms[0](repr);
+ rt.st();
+ for( size_t i = 1 ; i < m_transforms.size(); ++i )
+ {
+ Tensor rti = m_transforms[i](repr);
+ rti.st(true);
+ rt = rti(a,b) * rt(b,c);
+ }
+ m_cache[repr] = rt;
+ }
}
- return rt;
}
Tensor TransformSequence::operator()( const Tensor& tensor,
@@ -140,19 +148,22 @@ Tensor Transform::operator()( const Tensor& tensor,
return seq(a,b)*tensor(b);
}
-void TransformSequence::add( const Transform& transform )
+void TransformSequence::push_back( const Transform& transform )
{
m_transforms.emplace_back( transform );
+ buildCache();
}
-void TransformSequence::add( const TransformSequence& transform )
+void TransformSequence::push_back( const TransformSequence& transform )
{
for( auto& t : transform ) m_transforms.emplace_back(t);
+ buildCache();
}
void TransformSequence::clear()
{
m_transforms.clear();
+ buildCache();
}
void TransformSequence::stepThrough(const Tensor& tensor,
@@ -167,4 +178,38 @@ void TransformSequence::stepThrough(const Tensor& tensor,
}
}
+TransformSequence::TransformSequence( const Transform& transform ) : m_transforms{transform} {
+ buildCache();
+}
+
+TransformSequence::TransformSequence( const TransformSequence& t1, const TransformSequence& t2) {
+ for( const auto& t : t1 ) m_transforms.push_back(t);
+ for( const auto& t : t2 ) m_transforms.push_back(t);
+ Tensor::Index a,b,c;
+
+ for( auto repr : { Transform::Representation::Spinor, Transform::Representation::Bispinor, Transform::Representation::Vector } )
+ {
+ auto r1 = t1( repr );
+ auto r2 = t2( repr );
+ m_cache[repr] = r2(a,b) * r1(b,c);
+ m_cache[repr].st();
+ }
+}
+
+TransformSequence::TransformSequence( const Transform& t1, const Transform& t2) : m_transforms{t1,t2} {
+ Tensor::Index a,b,c;
+
+ for( auto repr : { Transform::Representation::Spinor, Transform::Representation::Bispinor, Transform::Representation::Vector } )
+ {
+ auto r1 = t1(repr);
+ auto r2 = t2(repr);
+ m_cache[repr] = r2(a,b) * r1(b,c);
+ m_cache[repr].st();
+ }
+}
+
+TransformSequence::TransformSequence()
+{
+ buildCache();
+}
diff --git a/src/TreePhaseSpace.cpp b/src/TreePhaseSpace.cpp
new file mode 100644
index 00000000000..09cc1266705
--- /dev/null
+++ b/src/TreePhaseSpace.cpp
@@ -0,0 +1,294 @@
+#include "AmpGen/TreePhaseSpace.h"
+#include "AmpGen/MsgService.h"
+#include "AmpGen/ParticleProperties.h"
+#include "AmpGen/Utilities.h"
+#include "TRandom.h"
+#include "TRandom3.h"
+#include <numeric>
+#include <random>
+
+using namespace AmpGen;
+
+TreePhaseSpace::TreePhaseSpace(const Particle& decayChain, const EventType& type, TRandom* rndm) :
+ m_rand(rndm == nullptr ? (TRandom3*)gRandom : (TRandom3*)rndm),
+ m_type(type),
+ m_gen(1)
+{
+ auto orderings = decayChain.identicalDaughterOrderings();
+ for( auto& ordering : orderings )
+ {
+ Particle p = decayChain;
+ p.setOrdering(ordering);
+ m_top.push_back( Vertex::make( p) );
+ m_weights.push_back(1);
+ }
+ m_dice = std::discrete_distribution<>(m_weights.begin(), m_weights.end());
+ setRandom(m_rand);
+}
+
+TreePhaseSpace::TreePhaseSpace(const std::vector<Particle>& decayChains, const EventType& type, TRandom* rndm) :
+ m_rand(rndm == nullptr ? (TRandom3*)gRandom : (TRandom3*)rndm),
+ m_type(type),
+ m_gen(1)
+{
+ for( auto& decayChain : decayChains )
+ {
+ auto orderings = decayChain.identicalDaughterOrderings();
+ for( auto& ordering : orderings )
+ {
+ Particle p = decayChain;
+ p.setOrdering(ordering);
+ m_top.push_back( Vertex::make(p) );
+ m_weights.push_back(1);
+ }
+ }
+ setRandom(rndm);
+ double sum_of_weights = std::accumulate( m_weights.begin(), m_weights.end(), 0 );
+ for( auto& w : m_weights ) w /= sum_of_weights;
+ m_dice = std::discrete_distribution<>(m_weights.begin(), m_weights.end());
+}
+
+Event TreePhaseSpace::makeEvent()
+{
+ unsigned j = 0;
+ double w = 0;
+ Event event;
+ do {
+ j = m_dice(m_gen);
+ if( j >= m_top.size() ) ERROR("Out of bounds: " << j << " / " << m_top.size() );
+ m_top[j].generate();
+ w = m_top[j].weight();
+ } while ( w == 0 );
+ event = m_top[j].event(m_type.size());
+ event.setGenPdf( genPdf(event) / w );
+ m_generatorRecord.push_back(j);
+ return event;
+}
+
+void TreePhaseSpace::provideEfficiencyReport(const std::vector<bool>& report)
+{
+// if( report.size() != m_generatorRecord.size() )
+// {
+// WARNING("Report does not match size of generator record...");
+// return;
+// }
+// std::vector<unsigned> counters( m_top.size() );
+// std::vector<unsigned> totals ( m_top.size() );
+// unsigned counter = 0;
+// for( unsigned i = 0 ; i != report.size(); ++i )
+// {
+// counters[m_generatorRecord[i]] += report[i];
+// totals[m_generatorRecord[i]] ++;
+// counter += report[i];
+// }
+// for( unsigned i = 0 ; i != m_top.size(); ++i )
+// {
+// INFO( m_top[i].particle.decayDescriptor() << " " << counters[i] << " / " << totals[i] );
+// m_weights[i] = double( counters[i] ) / double( counter );
+// }
+// m_dice = std::discrete_distribution<>(m_weights.begin(), m_weights.end());
+// m_generatorRecord.clear();
+}
+
+double rho( const double& s, const double& s1, const double& s2)
+{
+ return sqrt( 1 - 2 * (s1+s2)/s + (s1-s2)*(s1-s2) /(s*s) );
+}
+
+TreePhaseSpace::Vertex::Vertex(const Particle& particle, const double& mass)
+ : particle(particle)
+ , min(mass)
+ , max(mass)
+ , type( Type::Stable )
+ , index(particle.index())
+ , bwMass(particle.props()->mass())
+ , bwWidth(particle.props()->width())
+ , s(bwMass*bwMass)
+{
+ if( index != 999 ) indices = {index};
+}
+
+
+TreePhaseSpace::Vertex::Vertex(const Particle& particle, const double& min, const double& max )
+ : particle(particle)
+ , index(particle.index())
+ , bwMass(particle.props()->mass())
+ , bwWidth(particle.props()->width())
+ , min(min)
+ , max(max)
+ , s(bwMass*bwMass)
+{
+ INFO( particle << " [" << min << ", " << max << "]");
+ if( particle.isStable() ) type = Type::Stable;
+ else if( particle.isQuasiStable() ) type = Type::QuasiStable;
+ else if( particle.lineshape().find("BW") != std::string::npos ){
+ type = Type::BW;
+ phiMin = atan((min*min - bwMass*bwMass)/(bwMass*bwWidth));
+ phiMax = atan((max*max - bwMass*bwMass)/(bwMass*bwWidth));
+ }
+ else type = Type::Flat;
+ if( index != 999 ) indices = {index};
+}
+
+double TreePhaseSpace::Vertex::p() const
+{
+ return 0.5 * sqrt( s - 2 * (left->s+right->s) + (left->s-right->s)*(left->s-right->s)/s );
+}
+
+double TreePhaseSpace::Vertex::weight() const
+{
+ if( left == nullptr || right == nullptr ) return 1.0;
+ double w = sqrt(s) - sqrt(left->s) - sqrt(right->s) > 0;
+ if( w == 0 ) return 0;
+ w *= rho(s, left->s, right->s);
+ w *= left -> weight();
+ w *= right -> weight();
+ return w;
+}
+
+double TreePhaseSpace::Vertex::genPdf(const Event& event) const
+{
+ if( left == nullptr || right == nullptr ) return 1;
+ double dp = left->genPdf(event) * right->genPdf(event);
+ auto st = event.s(indices);
+ switch( type ) {
+ case Type::BW :
+ dp *= ( bwMass* bwWidth ) /( (phiMax-phiMin) * ( (st - bwMass*bwMass)*(st-bwMass*bwMass) + bwMass*bwMass*bwWidth*bwWidth) );
+ break;
+ case Type::Flat :
+ dp *= 1/(max*max -min*min);
+ break;
+ };
+ return dp;
+}
+
+void TreePhaseSpace::Vertex::generate()
+{
+ switch( type ) {
+ case Type::BW :
+ s = bwMass * bwMass + bwMass * bwWidth * tan( (phiMax - phiMin ) * rand->Rndm() + phiMin );
+ break;
+ case Type::Flat :
+ s = (max*max-min*min)*rand->Rndm() + min;
+ break;
+ };
+ if( left != nullptr ) left->generate();
+ if( right != nullptr ) right->generate();
+}
+
+void TreePhaseSpace::Vertex::print(const unsigned& offset) const
+{
+ std::array<const char*, 4> vtxTypeStrings = {"BW", "Flat", "Stable", "QuasiStable"};
+ INFO( std::string(offset,' ') << particle.name() << " [" << vectorToString(indices, ", ") << "] type = " << vtxTypeStrings[ type ] << " → [" << min << ", " << max << "] " << sqrt(s) );
+ if( type == Type::BW )
+ INFO( "phi-range : " << phiMin << " " << phiMax
+ << " s(min) = " << bwMass * bwMass + bwMass * bwWidth * tan(phiMin)
+ << " s(max) = " << bwMass * bwMass + bwMass * bwWidth * tan(phiMax) );
+ if( left != nullptr ) left -> print( offset + 4 );
+ if( right != nullptr ) right -> print( offset + 4 );
+}
+
+void TreePhaseSpace::Vertex::place(Event& event)
+{
+ if( index != 999 ){
+ event[4*index+0] = mom[0];
+ event[4*index+1] = mom[1];
+ event[4*index+2] = mom[2];
+ event[4*index+3] = mom[3];
+ }
+ if( left != nullptr ) left->place(event);
+ if( right != nullptr ) right->place(event);
+}
+
+Event TreePhaseSpace::Vertex::event(const unsigned& eventSize)
+{
+ if( isMultiBody ) return phsp.makeEvent();
+ Event output(4 * eventSize);
+ mom.SetXYZT(0,0,0,sqrt(s));
+ generateFullEvent();
+ place(output);
+ return output;
+}
+
+void TreePhaseSpace::Vertex::generateFullEvent()
+{
+ if( left == nullptr || right == nullptr ) return;
+ double cosTheta = 2 * rand->Rndm() - 1;
+ double sinTheta = sqrt( 1 - cosTheta * cosTheta );
+ double angY = 2 * M_PI * rand->Rndm();
+ double cosPhi = cos(angY);
+ double sinPhi = sin(angY);
+ double pf = p();
+ if( std::isnan(pf) || std::isnan(s) )
+ {
+ auto p2 = ( s - 2 * (left->s+right->s) + (left->s-right->s)*(left->s-right->s)/s );
+ ERROR("Generating nan: " << pf << " " << s << " " << min << " " << max << " " << p2 << " " << left->s << " " << right->s << " w = " << weight() );
+ }
+ left -> mom.SetXYZT( pf*sinTheta*cosPhi, pf*sinTheta*sinPhi, pf*cosTheta, sqrt(left->s + pf*pf) );
+ left -> mom.Boost( mom.BoostVector() );
+ left -> generateFullEvent();
+
+ right -> mom.SetXYZT( -pf*sinTheta*cosPhi, -pf*sinTheta*sinPhi, -pf*cosTheta, sqrt(right->s + pf*pf) );
+ right -> mom.Boost( mom.BoostVector() );
+ right -> generateFullEvent();
+}
+
+TreePhaseSpace::Vertex TreePhaseSpace::Vertex::make(const Particle& particle, TreePhaseSpace::Vertex* parent)
+{
+ auto decayProducts = particle.daughters();
+ auto threshold = [](const Particle& particle)
+ {
+ auto d1 = particle.getFinalStateParticles();
+ if( d1.size() == 0) return particle.mass();
+ return std::accumulate(d1.begin(), d1.end(), 0., [](double acc, auto& p){ return acc + p->mass(); } );
+ };
+ if( decayProducts.size() == 1 ) return TreePhaseSpace::Vertex::make(*decayProducts[0], parent);
+ if( decayProducts.size() == 2 )
+ {
+ double G = particle.isQuasiStable() ? 0 : particle.props()->width() * 10;
+ TreePhaseSpace::Vertex vtx = (parent == nullptr) ? TreePhaseSpace::Vertex(particle, particle.mass() - G , particle.mass() + G) : TreePhaseSpace::Vertex();
+ parent = ( parent == nullptr ) ? &vtx : parent;
+ auto min_mass_1 = threshold(*decayProducts[0]);
+ auto min_mass_2 = threshold(*decayProducts[1]);
+ parent->left = std::make_shared<TreePhaseSpace::Vertex>(*decayProducts[0], min_mass_1, parent->max - min_mass_2);
+ parent->right = std::make_shared<TreePhaseSpace::Vertex>(*decayProducts[1], min_mass_2, parent->max - min_mass_1);
+ TreePhaseSpace::Vertex::make(*decayProducts[0], parent->left.get());
+ TreePhaseSpace::Vertex::make(*decayProducts[1], parent->right.get());
+ for( auto& index : parent->left ->indices ) parent->indices.push_back(index);
+ for( auto& index : parent->right->indices ) parent->indices.push_back(index);
+ return *parent;
+ }
+ return TreePhaseSpace::Vertex();
+}
+
+void TreePhaseSpace::setRandom( TRandom* rand )
+{
+ m_rand = (TRandom3*)rand;
+ for( auto& channel : m_top ) channel.setRandom((TRandom3*)rand);
+}
+
+void TreePhaseSpace::Vertex::setRandom( TRandom3* rnd )
+{
+ rand = rnd;
+ if( left != nullptr ) left->setRandom(rnd);
+ if( right != nullptr ) right->setRandom(rnd);
+}
+
+EventType TreePhaseSpace::eventType() const
+{
+ return m_type;
+}
+
+double TreePhaseSpace::genPdf(const Event& event) const
+{
+ double genPdf = 0;
+ for( unsigned i = 0; i != m_top.size(); ++i )
+ genPdf += m_weights[i] * m_top[i].genPdf(event);
+ return genPdf;
+}
+
+size_t TreePhaseSpace::size() const
+{
+ return m_top.size();
+}
+
diff --git a/src/TreeReader.cpp b/src/TreeReader.cpp
new file mode 100644
index 00000000000..42ec42513ae
--- /dev/null
+++ b/src/TreeReader.cpp
@@ -0,0 +1,34 @@
+#include "AmpGen/TreeReader.h"
+using namespace AmpGen;
+
+TreeReader::TreeReader( TTree* tree ) : m_tree( tree ) {}
+
+void TreeReader::setEntryList( const std::vector<size_t>& entryList ){ m_entryList = entryList ; }
+
+void TreeReader::unsetEntryList(){ m_entryList.clear() ; }
+
+void TreeReader::getEntry( const unsigned int& entry )
+{
+ if(!m_ready ) prepare();
+ m_tree->GetEntry( m_entryList.size() == 0 ? entry : m_entryList[entry] );
+ for ( auto& branch : m_branches ) branch->transfer();
+}
+
+void TreeReader::prepare()
+{
+ for ( auto& branch : m_branches ) {
+ m_tree->SetBranchStatus( branch->name.c_str(), "1" );
+ m_tree->SetBranchAddress( branch->name.c_str(), branch->address() );
+ }
+ m_ready = true;
+}
+
+size_t TreeReader::nEntries() const { return m_entryList.size() == 0 ? m_tree->GetEntries() : m_entryList.size(); }
+
+TreeReader::~TreeReader()
+{
+ for ( auto& branch : m_branches ) delete branch;
+}
+
+TreeReader::Iterator TreeReader::begin() { getEntry(0); return Iterator( 0, this ); }
+TreeReader::Iterator TreeReader::end() { return Iterator( nEntries(), this ); }
diff --git a/src/UnaryExpression.cpp b/src/UnaryExpression.cpp
index 705b50a16e8..94b0d0db346 100644
--- a/src/UnaryExpression.cpp
+++ b/src/UnaryExpression.cpp
@@ -7,6 +7,7 @@
#include "AmpGen/Expression.h"
#include "AmpGen/NamedParameter.h"
#include "AmpGen/Types.h"
+#include "AmpGen/ASTResolver.h"
using namespace AmpGen;
@@ -16,28 +17,18 @@ T rsqrt( const T& arg ){ return 1. / sqrt(arg) ; }
DEFINE_UNARY_OPERATOR( Log , log )
DEFINE_UNARY_OPERATOR( Sqrt, sqrt )
DEFINE_UNARY_OPERATOR( Exp , exp )
-DEFINE_UNARY_OPERATOR( Abs , abs )
DEFINE_UNARY_OPERATOR( Sin , sin )
DEFINE_UNARY_OPERATOR( Cos , cos )
DEFINE_UNARY_OPERATOR( Tan , tan )
DEFINE_UNARY_OPERATOR( ASin, asin )
DEFINE_UNARY_OPERATOR( ACos, acos )
DEFINE_UNARY_OPERATOR( ATan, atan )
-DEFINE_UNARY_OPERATOR( Norm, std::norm )
-DEFINE_UNARY_OPERATOR( Conj, std::conj )
-DEFINE_UNARY_OPERATOR( Real, std::real )
-DEFINE_UNARY_OPERATOR( Imag, std::imag )
-//DEFINE_UNARY_OPERATOR( LGamma, std::lgamma );
- //DEFINE_UNARY_OPERATOR( ISqrt, rsqrt )
-
-ISqrt::ISqrt( const Expression& expression) : IUnaryExpression(expression) {}
-ISqrt::operator Expression() const { return Expression( std::make_shared<ISqrt>(*this) ) ; }
-complex_t ISqrt::operator()() const { return 1./sqrt( m_expression() ); }
-std::string ISqrt::to_string(const ASTResolver* resolver) const {
- return NamedParameter<bool>("enable_cuda",false) ?
- "rsqrt("+m_expression.to_string(resolver)+")" :
- "1./sqrt("+m_expression.to_string(resolver)+")" ;
-}
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( Norm, std::norm )
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( Real, std::real )
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( Imag, std::imag )
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( ISqrt, rsqrt )
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( Conj, std::conj )
+DEFINE_UNARY_OPERATOR_NO_RESOLVER( Abs , std::abs )
LGamma::LGamma( const Expression& expression) : IUnaryExpression(expression) {}
LGamma::operator Expression() const { return Expression( std::make_shared<LGamma>(*this) ) ; }
@@ -46,6 +37,48 @@ std::string LGamma::to_string(const ASTResolver* resolver) const {
return "std::lgamma(" + m_expression.to_string(resolver) + ")";
}
+std::string ISqrt::to_string(const ASTResolver* resolver) const {
+ return resolver != nullptr && resolver->enableCuda() ?
+ "rsqrt("+m_expression.to_string(resolver)+")" :
+ "1./sqrt("+m_expression.to_string(resolver)+")" ;
+}
+
+std::string Abs::to_string( const ASTResolver* resolver ) const
+{
+ return resolver != nullptr && resolver->enableAVX() ?
+ "abs(" + m_expression.to_string(resolver) +")" :
+ "std::abs("+m_expression.to_string(resolver) +")";
+}
+
+std::string Conj::to_string( const ASTResolver* resolver ) const
+{
+ return resolver != nullptr && resolver->enableAVX() ?
+ "conj(" + m_expression.to_string(resolver) +")" :
+ "std::conj("+m_expression.to_string(resolver) +")";
+}
+
+std::string Norm::to_string( const ASTResolver* resolver ) const
+{
+ return resolver != nullptr && resolver->enableAVX() ?
+ "norm(" + m_expression.to_string(resolver) +")" :
+ "std::norm("+m_expression.to_string(resolver) +")";
+}
+
+std::string Real::to_string( const ASTResolver* resolver ) const
+{
+ return resolver != nullptr && resolver->enableAVX() ?
+ "real(" + m_expression.to_string(resolver) +")" :
+ "std::real("+m_expression.to_string(resolver) +")";
+}
+
+std::string Imag::to_string( const ASTResolver* resolver ) const
+{
+ return resolver != nullptr && resolver->enableAVX() ?
+ "imag(" + m_expression.to_string(resolver) +")" :
+ "std::imag("+m_expression.to_string(resolver) +")";
+}
+
+
Expression Log::d() const { return 1. / arg(); }
Expression Sqrt::d() const { return 1. / ( 2 * fcn::sqrt( arg() ) ); }
Expression Exp::d() const { return fcn::exp(arg()) ; }
@@ -66,4 +99,4 @@ Expression Norm::d() const { return 0;}
Expression Real::d() const { return 0;}
Expression Imag::d() const { return 0;}
Expression LGamma::d() const { return 0;}
-void IUnaryExpression::resolve( ASTResolver& resolver ) { m_expression.resolve( resolver ); }
+void IUnaryExpression::resolve( ASTResolver& resolver ) const { m_expression.resolve( resolver ); }
diff --git a/src/Units.cpp b/src/Units.cpp
new file mode 100644
index 00000000000..a252032892c
--- /dev/null
+++ b/src/Units.cpp
@@ -0,0 +1,13 @@
+
+#include "AmpGen/Units.h"
+#include "AmpGen/Utilities.h"
+
+namespace AmpGen {
+ complete_enum(Units, TeV, GeV, MeV, KeV, eV, ms, us, ns, ps, fs)
+}
+
+double AmpGen::to_double(const AmpGen::Units& unit)
+{
+ static const double value_table[10] = {TeV, GeV, MeV, KeV, eV, ms, us, ns, ps, fs};
+ return value_table[unsigned(unit)];
+}
diff --git a/src/Utilities.cpp b/src/Utilities.cpp
index 8fe89b8f0a3..7f29e030160 100644
--- a/src/Utilities.cpp
+++ b/src/Utilities.cpp
@@ -1,5 +1,5 @@
#include "AmpGen/Utilities.h"
-#include "AmpGen/Version.h"
+#include "AmpGenVersion.h"
#include <dirent.h>
#include <stdio.h>
#include <stdlib.h>
@@ -11,19 +11,13 @@
#include <functional>
#include <iostream>
#include <utility>
-
+#include <numeric>
#include "AmpGen/MsgService.h"
std::vector<std::string> AmpGen::vectorFromFile( const std::string& filename, const char ignoreLinesThatBeginWith )
{
std::vector<std::string> output;
- std::string tmp;
- std::ifstream inFile( filename.c_str() );
- while ( inFile.good() ) {
- std::getline( inFile, tmp );
- if ( tmp.size() == 0 || tmp[0] == ignoreLinesThatBeginWith ) continue;
- output.push_back( tmp );
- }
+ processFile( filename, [&output](const std::string& line) mutable -> void {output.push_back(line);} );
return output;
}
@@ -42,11 +36,8 @@ std::vector<std::string> AmpGen::split( const std::string& s, const std::vector<
{
std::vector<std::string> elems;
std::stringstream ss( s );
- std::string strDelim = "";
+ std::string strDelim = std::accumulate( delims.begin(), delims.end(), std::string("") );
std::string line;
-
- for ( auto& st : delims ) strDelim += st;
-
while ( std::getline( ss, line ) ) {
std::size_t prev = 0, pos;
while ( ( pos = line.find_first_of( strDelim, prev ) ) != std::string::npos ) {
@@ -111,17 +102,24 @@ std::string AmpGen::replaceAll( const std::string& input, const std::string& toR
return output;
}
+std::string AmpGen::replaceAll( const std::string& input, const std::vector<std::pair<std::string,std::string>>& rules )
+{
+ std::string output = input;
+ for( auto& rule : rules ) output = replaceAll(output, rule.first, rule.second);
+ return output;
+}
+
// extracts tree structures of the form X{Y,Z,A}
// where Y and Z and A are also tree elements, by finding
// the matching delimiter and the Z, A elements.
-std::vector<std::string> AmpGen::getItems( const std::string& tree, const std::vector<std::string>& brackets,
- const std::string& seperator )
+std::vector<std::string> AmpGen::getItems( const std::string& tree,
+ const std::vector<std::string>& brackets,
+ const std::string& seperator )
{
auto braces = vecFindAll( tree, brackets ); /// get a vector of positions of the brackets ///
if ( braces.size() % 2 != 0 ) {
ERROR( "Unmatched braces in expression: " << tree << " check string: " << braces.size() );
- for ( auto& x : braces ) INFO( "char[" << x.first << "] = " << x.second );
return std::vector<std::string>();
}
@@ -145,11 +143,11 @@ std::vector<std::string> AmpGen::getItems( const std::string& tree, const std::v
std::vector<std::string> daughterTrees;
size_t begin_position = matched_braces.begin()->first + 1;
for ( auto& comma : commas ) {
- auto braces = matched_braces.begin() + 1;
- for ( ; braces != matched_braces.end(); ++braces ) {
- if ( comma > braces->first && comma < braces->second ) break;
+ auto itBrace = matched_braces.begin() + 1;
+ for ( ; itBrace != matched_braces.end(); ++itBrace ) {
+ if ( comma > itBrace->first && comma < itBrace->second ) break;
}
- if ( braces == matched_braces.end() ) {
+ if ( itBrace == matched_braces.end() ) {
items.push_back( tree.substr( begin_position, comma - begin_position ) );
begin_position = comma + 1;
}
@@ -186,8 +184,13 @@ unsigned int AmpGen::editDistance( const std::string& s1, const std::string& s2
std::string AmpGen::round( const double& number, const unsigned int& nsf )
{
double value = std::round(number * pow(10, nsf)) / pow(10, nsf);
- auto r = mysprintf( ( "%." + std::to_string(nsf) + "f" ).c_str(), value );
- return r.substr(0,r.size()-1);
+ if( nsf != 0 ){
+ auto r = mysprintf( ( "%." + std::to_string(nsf) + "f" ).c_str(), value );
+ return r.substr(0,r.size()-1);
+ }
+ else {
+ return std::to_string( (int)value);
+ }
}
std::string AmpGen::numberWithError( const double& number, const double& error, const unsigned int& nDigits )
@@ -200,20 +203,16 @@ bool AmpGen::stringMatchesWildcard( const std::string& input, const std::string&
{
auto pos = wildcard_string.find( wildcard_character ); /// TEST_foobar -> *_foobar
if ( wildcard_string.size() == 1 && wildcard_string[0] == wildcard_character ) {
- DEBUG( "Returning true" );
return true;
}
if ( pos == std::string::npos ) {
- DEBUG( "Returning " << input << " = " << wildcard_string << " ?" );
return input == wildcard_string;
}
if ( pos == wildcard_string.size() - 1 ) {
- DEBUG( "Returning " << input << " contains " << wildcard_string );
return input.find( wildcard_string.substr( 0, wildcard_string.size() - 1 ) ) == 0;
} else {
const std::string pattern1 = wildcard_string.substr( 0, pos + 1 );
const std::string pattern2 = wildcard_string.substr( pos + 1 );
- DEBUG( "Matching " << pattern1 << " to " << input );
bool match1 = stringMatchesWildcard( input, pattern1, wildcard_character );
if ( !match1 ) return false;
auto pos2 = pattern2.find( wildcard_character );
@@ -271,7 +270,7 @@ void AmpGen::printSplash()
std::cout << " ╚═╝ ╚═╝╚═╝ ╚═╝╚═╝ ╚═════╝ ╚══════╝╚═╝ ╚═══╝" << std::endl;
std::cout << "\033[0m\n";
std::cout << bold_on <<
- " version " << AMPGEN_VERSION_MAJOR << "." << AMPGEN_VERSION_MINOR << std::endl;
+ " version " << AMPGEN_MAJOR_VERSION << "." << AMPGEN_MINOR_VERSION << std::endl;
std::cout << " build: " ;
#if defined(__clang__)
std::cout << "clang " << __clang_major__ << "." << __clang_minor__ << "." << __clang_patchlevel__;
@@ -282,10 +281,18 @@ void AmpGen::printSplash()
#elif defined(__GNUC__) || defined(__GNUG__)
std::cout << "gcc " << __GNUC__ << "." << __GNUC_MINOR__ << "." << __GNUC_PATCHLEVEL__;
#endif
+ #if ENABLE_AVX2d
+ std::cout << " (avx2; double)";
+ #elif ENABLE_AVX2f
+ std::cout << " (avx2; single)";
+ #elif ENABLE_AVX512
+ std::cout << " (avx512; double)";
+ #endif
+
std::cout << " " << __DATE__ << " " << __TIME__ << bold_off << "\n\n";
-
- char* AmpGenRoot = getenv("AMPGENROOT");
- if( AmpGenRoot != nullptr ) printReleaseNotes( std::string(AmpGenRoot) + "/doc/release.notes");
+ #ifdef AMPGENROOT_CMAKE
+ printReleaseNotes( std::string(AMPGENROOT_CMAKE) + "/release.notes");
+ #endif
}
bool AmpGen::fileExists( const std::string& name )
@@ -301,7 +308,7 @@ std::string AmpGen::rtrim( std::string s )
}
// trim from both ends
-std::string AmpGen::trim( std::string s ) { return ltrim( rtrim( s ) ); }
+std::string AmpGen::trim( const std::string& s ) { return ltrim( rtrim( s ) ); }
std::string AmpGen::ltrim( std::string s )
{
@@ -315,7 +322,7 @@ std::string AmpGen::expandGlobals( std::string path )
do {
pos = path.find( "$" );
if ( pos == std::string::npos ) break;
- size_t end_pos = std::string::npos;
+ size_t end_pos; // = std::string::npos;
std::string variable_name;
if ( path[pos + 1] == '{' ) {
end_pos = path.find( "}", pos );
@@ -324,16 +331,20 @@ std::string AmpGen::expandGlobals( std::string path )
} else {
end_pos = find_next_of( path, {".", "/"}, pos );
variable_name = path.substr( pos + 1, end_pos - pos - 1 );
+ end_pos--;
}
const char* global_var = getenv( variable_name.c_str() );
- if ( global_var == nullptr ) {
+ if ( variable_name == "AMPGENROOT" && global_var == nullptr )
+ {
+ global_var = AMPGENROOT;
+ }
+ else if ( global_var == nullptr ) {
ERROR( "variable " << variable_name << " not found" );
break;
}
std::string old_path = path;
size_t len = end_pos == std::string::npos ? path.length() - pos + 1 : end_pos - pos + 1;
path = path.replace( pos, len, global_var );
- DEBUG( old_path << " -> " << path );
} while ( pos != std::string::npos );
return path;
@@ -345,7 +356,7 @@ bool AmpGen::isDir( const std::string& pathname )
return stat( pathname.c_str(), &sb ) == 0 && S_ISDIR( sb.st_mode );
}
-std::vector<std::string> AmpGen::getListOfFiles( const std::string& directory, std::string patternString )
+std::vector<std::string> AmpGen::getListOfFiles( const std::string& directory, const std::string& patternString )
{
std::string expanded_path = expandGlobals( directory );
std::vector<std::string> files;
diff --git a/src/Vertex.cpp b/src/Vertex.cpp
index e788a56402a..5b8ef92bbbe 100644
--- a/src/Vertex.cpp
+++ b/src/Vertex.cpp
@@ -12,14 +12,17 @@
#include "AmpGen/Units.h"
using namespace AmpGen;
-//using namespace AmpGen::Vertex;
-const Tensor::Index mu = Tensor::Index();
-const Tensor::Index nu = Tensor::Index();
-const Tensor::Index alpha = Tensor::Index();
-const Tensor::Index beta = Tensor::Index();
+static const Tensor::Index mu = Tensor::Index();
+static const Tensor::Index nu = Tensor::Index();
+static const Tensor::Index alpha = Tensor::Index();
+static const Tensor::Index beta = Tensor::Index();
+static const Tensor::Index a = Tensor::Index();
+static const Tensor::Index b = Tensor::Index();
+static const Tensor::Index c = Tensor::Index();
+static const Tensor::Index d = Tensor::Index();
-template <> Factory<AmpGen::Vertex::VertexBase>* Factory<AmpGen::Vertex::VertexBase>::gImpl = nullptr;
+template <> Factory<AmpGen::Vertex::Base>* Factory<AmpGen::Vertex::Base>::gImpl = nullptr;
bool Vertex::Factory::isVertex( const std::string& hash ) { return get( hash ) != nullptr; }
@@ -43,7 +46,7 @@ Tensor Vertex::Factory::getSpinFactorNBody( const std::vector<std::pair<Tensor,
}
if ( mL == 1 )
return LeviCivita()( -mu, -nu, -alpha, -beta ) *
- tensors[0].first( nu ) * tensors[1].first( alpha ) * tensors[2].first( beta ) / ( GeV * GeV * GeV );
+ tensors[0].first( nu ) * tensors[1].first( alpha ) * tensors[2].first( beta );
else if ( mL == 0 )
return Tensor( std::vector<double>( {1} ), {1} );
else
@@ -54,19 +57,17 @@ const Tensor Metric4x4(){
return Tensor( {-1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1}, {4, 4} );
}
-Tensor AmpGen::Orbital_PWave( const Tensor& P, const Tensor& Q )
+Tensor AmpGen::Orbital_PWave(const Tensor& p, const Tensor& q)
{
- auto is = 1./make_cse( dot(P,P) ,true);
- return Q - P * make_cse( dot( P, Q ) * is );
+ auto is = 1./make_cse( dot(p,p) ,true);
+ return q - p * make_cse( dot(p, q) * is );
}
-Tensor AmpGen::Orbital_DWave( const Tensor& P, const Tensor& Q )
+Tensor AmpGen::Orbital_DWave(const Tensor& p, const Tensor& q)
{
- Tensor::Index mu;
- Tensor::Index nu;
- Tensor L = Orbital_PWave( P, Q );
- Tensor f = L(mu) * L(nu) - make_cse( dot( L, L ) / 3. ) * Spin1Projector(P) ( mu, nu );
+ Tensor L = Orbital_PWave(p, q);
+ Tensor f = L(mu) * L(nu) - make_cse( dot( L, L ) / 3. ) * Spin1Projector(p) ( mu, nu );
f.imposeSymmetry(0,1);
f.st();
return f;
@@ -74,15 +75,12 @@ Tensor AmpGen::Orbital_DWave( const Tensor& P, const Tensor& Q )
Tensor AmpGen::Spin1Projector( const Tensor& P )
{
- Tensor::Index mu;
- Tensor::Index nu;
auto is = 1./make_cse( dot(P,P) , true);
- return Metric4x4()(mu, nu) - P(mu) * P(nu) * is ; // / make_cse( dot(P, P) , true );
+ return Metric4x4()(mu, nu) - P(mu) * P(nu) * is;
}
Tensor AmpGen::Spin2Projector( const Tensor& P )
{
- Tensor::Index mu, nu, alpha, beta;
Tensor S = Spin1Projector( P );
Tensor SP = -( 1. / 3. ) * S( mu, nu ) * S( alpha, beta ) + (1./2.) * ( S( mu, alpha ) * S( nu, beta ) + S( mu, beta ) * S( nu, alpha ) ) ;
return SP;
@@ -91,7 +89,6 @@ Tensor AmpGen::Spin2Projector( const Tensor& P )
Tensor AmpGen::Gamma4Vec()
{
- Tensor::Index a, b, mu;
Tensor x( {1, 0, 0, 0}, {4} );
Tensor y( {0, 1, 0, 0}, {4} );
Tensor z( {0, 0, 1, 0}, {4} );
@@ -101,18 +98,15 @@ Tensor AmpGen::Gamma4Vec()
Tensor AmpGen::slash( const Tensor& P )
{
- if ( P.dims() != std::vector<size_t>({4}) ) {
+ if ( P.dims() != std::vector<unsigned>({4}) ) {
ERROR( "Can only compute slash operator against vector currents" );
return Tensor();
}
- Tensor::Index mu, a, b;
- Tensor rt = Gamma4Vec()( mu, a, b ) * P( -mu );
- return rt;
+ return Gamma4Vec()( mu, a, b ) * P( -mu );
}
Tensor AmpGen::gamma_twiddle( const Tensor& P )
{
- Tensor::Index mu, nu, a, b ;
Tensor g = Gamma4Vec();
return g(nu,a,b) - P(nu) * P(mu) * g(-mu,a,b) / make_cse( dot(P,P) );
}
@@ -125,7 +119,6 @@ Tensor AmpGen::Spin1hProjector( const Tensor& P )
Tensor AmpGen::Spin3hProjector( const Tensor& P )
{
- Tensor::Index a,b,c, d, mu, nu;
Tensor Ps = P;
Ps.st();
Tensor g = gamma_twiddle(Ps);
@@ -138,7 +131,6 @@ Tensor AmpGen::Spin3hProjector( const Tensor& P )
}
Tensor AmpGen::Bar( const Tensor& P ){
- Tensor::Index a,b;
return P.conjugate()(b) * Gamma[3](b,a);
}
@@ -149,60 +141,82 @@ DEFINE_VERTEX( S_VV_S1 ) { return Spin1Projector(P)(mu,nu) * V1( -mu ) * V2( -nu
DEFINE_VERTEX( S_VV_D )
{
- Tensor L2 = Orbital_DWave( P, Q ) / ( GeV * GeV );
- Tensor vtol = V1( mu ) * L2( -mu, -nu ) * V2( nu );
- return vtol;
+ Tensor L2 = Orbital_DWave(P, Q);
+ return V1(mu)*L2(-mu,-nu)*V2(nu);
}
DEFINE_VERTEX( S_VV_P )
{
Tensor L = Orbital_PWave( P, Q );
Tensor coupling = LeviCivita()( -mu, -nu, -alpha, -beta ) * L( alpha ) * P( beta );
- return V1( mu ) * coupling( -mu, -nu ) * V2( nu ) / ( GeV * GeV );
+ return V1( mu ) * coupling( -mu, -nu ) * V2( nu );
}
DEFINE_VERTEX( S_VS_P )
{
Tensor p_wave = Orbital_PWave( P, Q );
Tensor p_v1 = V1( mu ) * p_wave( -mu );
- return p_v1 * V2[0] / GeV;
+ return p_v1 * V2[0];
}
-DEFINE_VERTEX( V_SS_P )
-{
- Tensor p_wave = Orbital_PWave( P, Q );
- Expression scalar_part = V1[0] * V2[0] / GeV;
- Tensor L = p_wave * scalar_part;
- ADD_DEBUG_TENSOR( L, db );
- return L;
-}
+DEFINE_VERTEX( V_SS_P ){ return Orbital_PWave(P,Q) * V1[0] * V2[0];}
DEFINE_VERTEX( V_VS_P )
{
- Tensor L = Orbital_PWave( P, Q ) / GeV;
- Tensor coupling = LeviCivita()( -mu, -nu, -alpha, -beta ) * L( alpha ) * P( beta ) / GeV;
+ Tensor L = Orbital_PWave( P, Q );
+ Tensor coupling = LeviCivita()( -mu, -nu, -alpha, -beta ) * L( alpha ) * P( beta );
return ( coupling(mu,nu) * V1( -nu ) ) * V2[0];
}
-DEFINE_VERTEX( V_VS_S )
-{
- Tensor L = Spin1Projector(P)(mu,nu) * V1(-nu) * V2[0];
- return L;
-}
+DEFINE_VERTEX( V_VS_S ){ auto S = Spin1Projector(P)(mu,nu) * V1(-nu) * V2[0]; ADD_DEBUG_TENSOR(S,db); return S; }
DEFINE_VERTEX( V_VS_D )
{
- Tensor L_2_V0 = Orbital_DWave( P, Q ) / ( GeV * GeV );
+ Tensor L_2_V0 = Orbital_DWave( P, Q );
Tensor Sv = Spin1Projector( P );
return ( Sv( mu, nu ) * L_2_V0( -nu, -alpha ) * V1( alpha ) ) * V2[0];
}
+DEFINE_VERTEX( V_VV_P )
+{
+ Tensor L = Orbital_PWave( P, Q );
+ return L(mu) * dot(V1,V2);
+}
+
+DEFINE_VERTEX( V_VV_P1 )
+{
+ Tensor L = Orbital_PWave( P, Q );
+ Tensor Sv = Spin1Projector( P );
+ Tensor term = LeviCivita()( -mu, -nu, -alpha, -beta ) * P( nu ) * V1( alpha ) * V2( beta );
+ Tensor phi_1 = term(-mu) * Sv(mu,nu);
+
+ return LeviCivita()( -mu, -nu, -alpha, -beta ) * P( mu ) * L(nu) * phi_1(alpha);
+}
+
+DEFINE_VERTEX( V_VV_P2 )
+{
+ Tensor L = Orbital_PWave( P, Q );
+ Tensor Sv = Spin2Projector( P );
+ Tensor phi_2 = Sv(-mu,-nu,alpha,beta) * V1(mu) * V2(nu);
+
+ return L(-mu) * phi_2(mu,nu);
+}
+
+DEFINE_VERTEX( V_VV_S )
+{
+ Tensor Sv = Spin1Projector( P );
+ Tensor term = LeviCivita()( -mu, -nu, -alpha, -beta ) * P(nu) * V1( alpha ) * V2( beta );
+
+ return term( -mu ) * Sv(mu, nu);
+}
+
+
DEFINE_VERTEX( T_VS_D )
{
Tensor G = LeviCivita()( -mu, -nu, -alpha, -beta ) * P( nu ) * Q( alpha ) * V1( beta );
Tensor L = Orbital_PWave( P, Q );
- return ( G( mu ) * L( nu ) + L( mu ) * G( nu ) ) * V2[0] / Constant( -2 * GeV * GeV * GeV );
+ return -0.5 * ( G( mu ) * L( nu ) + L( mu ) * G( nu ) ) * V2[0];
}
DEFINE_VERTEX( T_TS_S )
@@ -215,31 +229,31 @@ DEFINE_VERTEX( T_TS_S )
DEFINE_VERTEX( T_VS_P )
{
- Tensor L = Orbital_PWave( P, Q ) / GeV;
+ Tensor L = Orbital_PWave( P, Q );
Tensor S = Spin1Projector( P );
Tensor Vp = S( -mu, -nu ) * V1( nu );
return V2[0] * ( ( L( alpha ) * Vp( beta ) + L( beta ) * Vp( alpha ) ) / 2. - S( alpha, beta ) * dot( L, V1 ) / 3. );
}
-DEFINE_VERTEX( T_SS_D ) { return Orbital_DWave( P, Q ) * V1[0] * V2[0] / ( GeV * GeV ); }
+DEFINE_VERTEX( T_SS_D ) { return Orbital_DWave( P, Q ) * V1[0] * V2[0]; }
DEFINE_VERTEX( S_TV_P )
{
- Tensor L = Orbital_PWave( P, Q ) / GeV;
+ Tensor L = Orbital_PWave( P, Q );
return ( V1( mu, nu ) * L( -mu ) ) * V2( -nu );
}
DEFINE_VERTEX( S_TS_D )
{
Tensor orbital = Orbital_DWave( P, Q );
- return V2[0] * Tensor( {dot( orbital, V1 ) / ( GeV * GeV )}, {1} );
+ return V2[0] * Tensor( {dot( orbital, V1 )}, {1} );
}
DEFINE_VERTEX( S_TV_D )
{
Tensor term1 = V1( alpha, beta ) * Orbital_DWave( P, Q )( -beta, -nu );
- Tensor term2 = LeviCivita()( -mu, -nu, -alpha, -beta ) * P( alpha ) * V2( beta ); // Antisymmetric( P, V2 );
- return Tensor( {dot( term1, term2 )} ) / ( GeV * GeV * GeV );
+ Tensor term2 = LeviCivita()( -mu, -nu, -alpha, -beta ) * P( alpha ) * V2( beta );
+ return Tensor( {dot( term1, term2 )} );
}
DEFINE_VERTEX( S_TT_S ) { return Tensor( {dot( V1, V2 )} ); }
@@ -247,7 +261,7 @@ DEFINE_VERTEX( S_TT_S ) { return Tensor( {dot( V1, V2 )} ); }
DEFINE_VERTEX( V_TS_P )
{
Tensor S = Spin1Projector( P );
- Tensor L = Orbital_PWave( P, Q ) / ( GeV );
+ Tensor L = Orbital_PWave( P, Q );
return ( S( -mu, -nu ) * L( -alpha ) * V1( nu, alpha ) ) * V2[0];
}
@@ -255,29 +269,29 @@ DEFINE_VERTEX( V_TS_D )
{
Tensor L = ( -1 ) * Orbital_PWave( P, Q );
Tensor coupling = LeviCivita()( -mu, -nu, -alpha, -beta ) * P( nu ) * Q( alpha );
- return coupling( -mu, -nu ) * V1( nu, alpha ) * L( -alpha ) / ( GeV * GeV * GeV );
+ return coupling( -mu, -nu ) * V1( nu, alpha ) * L( -alpha );
}
DEFINE_VERTEX( f_fS_S )
{
- Tensor::Index a,b;
- return Spin1hProjector(P)(a,b) * V1(b) * V2[0];
+ Tensor f_fS_Sv = Spin1hProjector(P)(a,b) * V1(b) * V2[0];
+ ADD_DEBUG_TENSOR( f_fS_Sv, db);
+ return f_fS_Sv;
}
+
DEFINE_VERTEX( f_fS_P )
{
- Tensor::Index a,b,c,d;
Tensor proj = Spin1hProjector(P);
Tensor L = Orbital_PWave(P,Q);
- Tensor t = proj(a, b) * Gamma[4](b,c) * slash(L)(c,d) * V1(d);
+ ADD_DEBUG_TENSOR( P, db );
+ ADD_DEBUG_TENSOR( Q, db );
ADD_DEBUG_TENSOR( L, db );
- ADD_DEBUG_TENSOR( Tensor(Gamma[4](b,c)*slash(L)(c,d)*V1(d)), db );
- ADD_DEBUG_TENSOR(t, db);
+ Tensor t = proj(a, b) * Gamma[4](b,c) * slash(L)(c,d) * V1(d);
return t;
}
DEFINE_VERTEX( f_Vf_S )
{
- Tensor::Index a,b,c,d;
Tensor proj = Spin1hProjector(P);
return proj(a, b) * Gamma[4](b,c) * gamma_twiddle(P)(mu,c,d) * V2(d) * V1(-mu);
}
@@ -286,12 +300,11 @@ DEFINE_VERTEX( f_Vf_P ) /// = A3
{
Tensor proj = Spin1hProjector(P);
auto L = Orbital_PWave(P,Q);
- return proj( alpha, beta ) * V2(beta) * dot( V1, L ) / GeV ;
+ return proj( alpha, beta ) * V2(beta) * dot( V1, L );
}
DEFINE_VERTEX( f_Vf_P1 ) //// = A6
{
- Tensor::Index a,b,c,d;
Tensor proj = Spin1hProjector(P);
Tensor L = Orbital_PWave(P,Q);
Tensor t = LeviCivita()(mu,nu,alpha,beta) * V1(-nu) * L(-alpha) * P(-beta);
@@ -301,53 +314,68 @@ DEFINE_VERTEX( f_Vf_P1 ) //// = A6
DEFINE_VERTEX( f_Vf_D ) //// = A8
{
- Tensor::Index a,b,c,d;
Tensor proj = Spin1hProjector(P);
Tensor gt = gamma_twiddle(P);
- Tensor L = Orbital_DWave(P,Q)(-mu,-nu) * V1(nu) / (GeV*GeV);
+ Tensor L = Orbital_DWave(P,Q)(-mu,-nu) * V1(nu);
return proj( a, b ) * Gamma[4](b,c) * gt(mu,c,d) * V2(d) * L(-mu);
}
DEFINE_VERTEX( f_Vf_S1 )
{
- Tensor::Index a,b,c;
Tensor proj = Spin1hProjector(P);
Tensor vSlash = gamma_twiddle(P)(mu,a,b) * V1(-mu);
return proj( a, b ) * vSlash(b,c) * V2(c);
}
+DEFINE_VERTEX( f_Vf_SL )
+{
+ Tensor proj = Spin1hProjector(P);
+ return proj(a, b) * Gamma4Vec()(mu,b,c) * ( Identity(4) - Gamma[4] )(c,d)* V2(d) * V1(-mu);
+}
-DEFINE_VERTEX( f_fS_S1 )
-{
- Tensor::Index a,b,c;
- return Spin1hProjector(P)(a,b) * Gamma[4](b,c) * V1(c) * V2[0];
+DEFINE_VERTEX( f_Vf_SR )
+{
+ Tensor proj = Spin1hProjector(P);
+ return proj(a, b) * Gamma4Vec()(mu,b,c) * ( Identity(4) + Gamma[4] )(c,d)* V2(d) * V1(-mu);
+}
+
+DEFINE_VERTEX( f_fS_SL )
+{
+ Tensor proj = Spin1hProjector(P);
+ return proj(a, b) * ( Identity(4) - Gamma[4] )(b,c)* V2(c);
+}
+
+
+DEFINE_VERTEX( f_fS_SR )
+{
+ Tensor proj = Spin1hProjector(P);
+ return proj(a, b) * ( Identity(4) + Gamma[4] )(b,c)* V2(c);
}
+DEFINE_VERTEX( f_fS_S1 ){ return Spin1hProjector(P)(a,b) * Gamma[4](b,c) * V1(c) * V2[0];}
+
DEFINE_VERTEX( f_fS_P1 )
{
- Tensor::Index a,b,c,d;
- return Spin1hProjector(P)(a, b) * slash(Orbital_PWave(P,Q))(b,c) * V1(c) * V2[0] / GeV;
+ return Spin1hProjector(P)(a, b) * slash(Orbital_PWave(P,Q))(b,c) * V1(c) * V2[0];
}
DEFINE_VERTEX( f_Tf_P )
{
- Tensor::Index a,b,c;
Tensor proj = Spin1hProjector(P);
Tensor T = V1;
T.imposeSymmetry(0,1);
T.st();
- return proj( a, b ) * gamma_twiddle(P)(mu,b,c) * V2(c) * T(-mu,-nu) * Orbital_PWave(P,Q)(nu) / GeV;
+ return proj( a, b ) * gamma_twiddle(P)(mu,b,c) * V2(c) * T(-mu,-nu) * Orbital_PWave(P,Q)(nu);
}
-DEFINE_VERTEX( f_Vf_P2 )
+DEFINE_VERTEX( f_Vf_P2 ) //A4
{
Tensor proj = Spin1hProjector(P);
- return proj( alpha, beta ) * Gamma[4](beta,nu) * V2(nu) * dot( V1, Orbital_PWave( P, Q ) ) / GeV;
+ return proj( alpha, beta ) * Gamma[4](beta,nu) * V2(nu) * dot( V1, Orbital_PWave( P, Q ) );
}
-DEFINE_VERTEX( f_Vf_P3 )
+DEFINE_VERTEX( f_Vf_P3 ) //A5
{
- Tensor::Index a,b,c;
Tensor proj = Spin1hProjector(P);
Tensor L = Orbital_PWave(P,Q);
Tensor t = LeviCivita()(-mu,-nu,-alpha,-beta) * L(nu) * V1(alpha) * P(beta);
@@ -358,35 +386,33 @@ DEFINE_VERTEX( f_Vf_P3 )
DEFINE_VERTEX( f_Vf_D1 )
{
- Tensor::Index a,b,c,d;
Tensor proj = Spin1hProjector(P);
Tensor gt = gamma_twiddle(P);
- Tensor L = Orbital_DWave(P,Q)(-mu,-nu) * V1(nu) / (GeV*GeV);
+ Tensor L = Orbital_DWave(P,Q)(-mu,-nu) * V1(nu);
return proj( a, b ) * gt(mu,b,c) * L(-mu) * V2(c) ;
}
DEFINE_VERTEX( r_fS_P )
{
- Tensor::Index a,b,c,d;
Tensor L = Orbital_PWave(P,Q);
L.st();
Tensor F = Spin1hProjector(P);
- Tensor V = ( (-1) * L(nu) * F(a,d) + (1./3.) * F(a,b) * gamma_twiddle(P)(nu,b,c) * slash(L)(c,d) ) * V1(d) / GeV;
+ Tensor V = ( (-1) * L(nu) * F(a,d) + (1./3.) * F(a,b) * gamma_twiddle(P)(nu,b,c) * slash(L)(c,d) ) * V1(d);
V.st();
return V;
}
DEFINE_VERTEX( r_fS_D )
{
- Tensor::Index a,b,c,d,e;
+ Tensor::Index e;
Tensor sp = Spin3hProjector(P);
Tensor L = Orbital_PWave(P,Q);
Tensor F = Spin1hProjector(P);
- L.st(1);
+ L.st(true);
Expression L2 = make_cse(dot(L,L));
Tensor gt = gamma_twiddle(P);
- Tensor rt = ( L(mu) * F(a,b) * slash(L)(b,c) - (L2/3.) * F(a,b) * gt(mu,b,c) ) * Gamma[4](c,d) * V1(d) / (GeV*GeV);
+ Tensor rt = ( L(mu) * F(a,b) * slash(L)(b,c) - (L2/3.) * F(a,b) * gt(mu,b,c) ) * Gamma[4](c,d) * V1(d);
rt.st();
return rt;
}
@@ -394,22 +420,20 @@ DEFINE_VERTEX( r_fS_D )
DEFINE_VERTEX( f_rS_D )
{
- Tensor::Index a,b,c,d;
Tensor F = Spin1hProjector(P)(a,b)
* Gamma[4](b,d)
* gamma_twiddle(P)(mu,d,c)
* V1(alpha,c)
* Orbital_DWave(P,Q)(-mu,-alpha)
- * V2[0] / GeV;
+ * V2[0];
F.st();
return F;
}
DEFINE_VERTEX( f_rS_P )
{
- Tensor::Index a,b,c;
auto L = Orbital_PWave(P,Q);
- Tensor F = Spin1hProjector(P)(a,b) * V1(-mu,b) * L(mu) * V2[0] / GeV;
+ Tensor F = Spin1hProjector(P)(a,b) * V1(-mu,b) * L(mu) * V2[0];
ADD_DEBUG_TENSOR( V1, db );
ADD_DEBUG_TENSOR( L , db );
ADD_DEBUG_TENSOR( F , db );
@@ -419,34 +443,32 @@ DEFINE_VERTEX( f_rS_P )
DEFINE_VERTEX( f_rS_P1 )
{
- Tensor::Index a,b,c;
auto L = Orbital_PWave(P,Q);
- Tensor F = Spin1hProjector(P)(a,b) * Gamma[4](b,c) * V1(-mu,c) * L(mu) * V2[0]/ GeV;
+ Tensor F = Spin1hProjector(P)(a,b) * Gamma[4](b,c) * V1(-mu,c) * L(mu) * V2[0];
F.st();
return F;
}
-DEFINE_VERTEX( S_ff_S )
-{
- Tensor::Index a;
- return Bar( V2 )(a) * V1(a);
-}
+DEFINE_VERTEX( S_ff_S ) { return Bar(V2)(a) * V1(a); }
-DEFINE_VERTEX( S_ff_S1 )
-{
- Tensor::Index a,b;
- return Bar( V2 )(a) * Gamma[4](a,b) * V1(b);
-}
+DEFINE_VERTEX( S_ff_S1 ){ return Bar(V2)(a) * Gamma[4](a,b) * V1(b); }
+DEFINE_VERTEX( V_ff_S ) { return Bar(V2)(a) * Gamma4Vec()(mu,a,b) * V1(b); }
-DEFINE_VERTEX( V_ff_P )
-{
- Tensor::Index a,b ;
- return Bar( V2 )(a) * Gamma4Vec()(mu,a,b) * V1(b);
+DEFINE_VERTEX( V_ff_S1 ){ return Bar(V2)(a) * Gamma[4](a,b) * Gamma4Vec()(mu,b,c) * V1(c); }
+
+DEFINE_VERTEX( V_ff_PL )
+{
+ Tensor proj = Spin1Projector(P);
+ auto pl = 0.5 * ( Identity(4) - Gamma[4] );
+ ADD_DEBUG_TENSOR( pl, db);
+ ADD_DEBUG_TENSOR( pl(b,c)* V2(c), db );
+ return proj(mu, nu) * Bar(V1)(a) * Gamma4Vec()(-nu,a,b) * ( Identity(4) - Gamma[4] )(b,c)* V2(c);
}
-DEFINE_VERTEX( V_ff_P1 )
-{
- Tensor::Index a,b,c ;
- return Bar( V2 )(a) * Gamma[4](a,b) * Gamma4Vec()(mu,b,c) * V1(c);
+DEFINE_VERTEX( V_ff_PR )
+{
+ Tensor proj = Spin1Projector(P);
+ ADD_DEBUG_TENSOR( (Identity(4) + Gamma[4] )(b,c)* V2(c), db );
+ return proj(mu, nu) * Bar(V1)(a) * Gamma4Vec()(-nu,a,b) * ( Identity(4) + Gamma[4] )(b,c)* V2(c);
}
diff --git a/src/Wigner.cpp b/src/Wigner.cpp
index 22dc9f5ad66..a628a693283 100644
--- a/src/Wigner.cpp
+++ b/src/Wigner.cpp
@@ -21,6 +21,7 @@
using namespace AmpGen;
using namespace AmpGen::fcn;
+using namespace std::complex_literals;
double fact( const double& z )
{
@@ -29,7 +30,7 @@ double fact( const double& z )
return f;
}
-double nCr_( const int& n, const int& r ){
+double binomialCoefficient( const int& n, const int& r ){
double z=1;
for( int f=1; f <= r ; ++f ) z *= double(n+1-f)/double(f);
return z;
@@ -38,7 +39,7 @@ double nCr_( const int& n, const int& r ){
Expression expandedBinomial( const Expression& x, const unsigned int& n )
{
Expression sum;
- for( unsigned int k = 0 ; k <= n ; ++k ) sum = sum + nCr_(n,k) * fcn::fpow(x,k);
+ for( unsigned int k = 0 ; k <= n ; ++k ) sum = sum + binomialCoefficient(n,k) * fcn::fpow(x,k);
return sum;
}
@@ -79,10 +80,8 @@ double AmpGen::CG(
if( m1+m2!=M ) return 0;
double f1 = (2*J+1)*fact(J+j1-j2)*fact(J-j1+j2)*fact(j1+j2-J) ;
double f2 = fact(j1+m1)*fact(j1-m1)*fact(j2+m2)*fact(j2-m2)*fact(J+M)*fact(J-M);
-
double norm = f1 * f2 / fact(J+j1+j2+1) ;
double sum = 0;
-
for( int nu=0; nu <= j1+j2-J ; ++nu){
double arg1 = j1+j2-J-double(nu);
double arg2 = j1 -m1-double(nu);
@@ -97,10 +96,10 @@ double AmpGen::CG(
return sqrt(norm) * sum ;
}
-TransformSequence AmpGen::helicityTransformMatrix( const Tensor& P,
- const Expression& mass,
+TransformSequence AmpGen::wickTransform( const Tensor& P,
+ const Particle& particle,
const int& ve,
- const bool& handleZero )
+ DebugSymbols* db )
{
Tensor x({1,0,0}, Tensor::dim(3));
Tensor y({0,1,0}, Tensor::dim(3));
@@ -112,40 +111,46 @@ TransformSequence AmpGen::helicityTransformMatrix( const Tensor& P,
Transform rot = ve == + 1 ? Transform( cos_theta, sin_phi*x - cos_phi*y, Transform::Type::Rotate) :
Transform(-cos_theta, -sin_phi*x + cos_phi*y, Transform::Type::Rotate) ;
-// Transform boost( P[3]/mass, (ve==+1) ? z : -z, Transform::Type::Boost );
- Transform boost( P[3]/mass, z, Transform::Type::Boost );
- TransformSequence sequence;
- sequence.add( rot );
- if( ve == -1 ) sequence.add( Transform( -1, x, Transform::Type::Rotate ) );
- sequence.add( boost ) ;
- return sequence;
+ TransformSequence sequence(rot);
+ if( ve == -1 ) sequence.push_back( Transform( -1, x, Transform::Type::Rotate ) );
+
+ if( !particle.isStable() || !( particle.props()->isPhoton() || particle.props()->isNeutrino() ) )
+ {
+ Expression mass = fcn::sqrt( particle.massSq() );
+ Transform boost( P[3]/mass, z, Transform::Type::Boost );
+ return TransformSequence(sequence, boost);
+ }
+ return TransformSequence(sequence);
}
-Expression AmpGen::wigner_D(const Tensor& P,
- const double& J,
- const double& lA,
- const double& lB,
- DebugSymbols* db,
- const std::string& name )
+std::pair<Expression, Expression> angCoordinates(const Tensor& P, DebugSymbols* db)
{
Expression pz = make_cse( P[2] / sqrt( P[0]*P[0] + P[1] * P[1] + P[2]*P[2] ) );
Expression pt2 = make_cse( P[0]*P[0] + P[1]*P[1] );
- Expression px = P[0] / sqrt( pt2 );
- Expression py = P[1] / sqrt( pt2 );
+ Expression px = P[0] / sqrt(pt2);
+ Expression py = P[1] / sqrt(pt2);
+ return {pz, make_cse(px + 1i*py)};
+} /// spherical coordinates are paramterised as {z=cos(theta), e^(iphi)}, as this avoids any trigonometric functions
- Expression I(std::complex<double>(0,1));
- auto little_d = make_cse ( wigner_d( pz, J, lA, lB ) );
+Expression AmpGen::wigner_D(const std::pair<Expression, Expression>& P,
+ const double& J,
+ const double& lA,
+ const double& lB,
+ DebugSymbols* db)
+{
+ auto little_d = make_cse ( wigner_d( P.first, J, lA, lB ) );
if( J != 0 && db != nullptr ){
- db->emplace_back("ϕ("+name+")", atan2( py, px ) );
- db->emplace_back("θ("+name+")", pz );
+ db->emplace_back("cos(θ)", P.first );
+ db->emplace_back("Ω", atan2( Imag(P.second), Real(P.second) ) );
+
db->emplace_back("d[" + std::to_string(J) +", " +
std::to_string(lA) +", " +
std::to_string(lB) +"](θ)", little_d );
db->emplace_back("D[" + std::to_string(J) +", " +
std::to_string(lA) +", " +
- std::to_string(lB) +"](Ω)", fpow(px+I*py,lB-lA) * little_d );
+ std::to_string(lB) +"](θ, Ω)", fpow(P.second,lB-lA) * little_d );
}
- return fpow( px + I * py, lB - lA ) * little_d;
+ return fpow( P.second, lB - lA ) * little_d;
}
std::vector<LS> AmpGen::calculate_recoupling_constants(
@@ -173,135 +178,144 @@ std::vector<LS> AmpGen::calculate_recoupling_constants(
return rt;
}
-/*
-Tensor AmpGen::basis_spinor(const Tensor& p, const int& polState, const int& id, DebugSymbols* db )
-{
- Expression pX = p.get(0) ;
- Expression pY = p.get(1) ;
- Expression pZ = p.get(2) ;
- Expression pE = p.get(3) ;
- Expression pP = fcn::sqrt( pX*pX + pY*pY + pZ*pZ );
- Expression m = fcn::sqrt( dot( p, p ) );
-
- complex_t I(0,1);
- Expression z = pX + I*pY;
- Expression zb = pX - I*pY;
- Expression n = fcn::sqrt( 2 * pP*(pP+pZ) );
- Expression fa = fcn::sqrt( (pE + m)/(2*m) );
- Expression fb = fcn::sqrt( (pE - m)/(2*m) );
- Expression aligned = make_cse( Abs(pP + pZ) < 10e-6 ) ;
-
- Expression xi10 = make_cse(Ternary( aligned, 1, (pP+pZ)/n ));
- Expression xi11 = make_cse(Ternary( aligned, 0, z/n ));
-
- Expression xi00 = make_cse(Ternary( aligned, 0, -zb/n ));
- Expression xi01 = make_cse(Ternary( aligned, 1, (pP+pZ)/n ));
-
- if(id > 0 && polState == 1 ) return Tensor({fa*xi10, fa*xi11, fb*xi10, fb*xi11});
- if(id > 0 && polState == -1 ) return Tensor({fa*xi00, fa*xi01, -fb*xi00, -fb*xi01});
- if(id < 0 && polState == 1 ) return Tensor({fb*xi00, fb*xi01, -fa*xi00, -fa*xi01});
- if(id < 0 && polState == -1 ) return Tensor({fb*xi10, fb*xi11, -fa*xi01, -fa*xi11});
-
- ERROR("Shouldn't reach here...");
- return Tensor();
-}
-*/
Tensor AmpGen::basisSpinor(const int& polState, const int& id)
{
if(id > 0 && polState == 1 ) return Tensor({1, 0, 0, 0}, Tensor::dim(4));
if(id > 0 && polState == -1 ) return Tensor({0, 1, 0, 0}, Tensor::dim(4));
if(id < 0 && polState == 1 ) return Tensor({0, 0, 1, 0}, Tensor::dim(4));
if(id < 0 && polState == -1 ) return Tensor({0, 0, 0, 1}, Tensor::dim(4));
- ERROR("Shouldn't reach here...");
+ ERROR("Shouldn't reach here..., polState = " << polState << " id = " << id );
return Tensor();
}
+Tensor AmpGen::basisVector(const int& polState)
+{
+ double N = 1./sqrt(2);
+ if( polState == 0 ) return Tensor(std::vector<complex_t>({0., 0.,1.,0.}), Tensor::dim(4));
+ if( polState == 1 ) return -N*Tensor(std::vector<complex_t>({1., 1i,0.,0.}), Tensor::dim(4));
+ if( polState == -1 ) return N*Tensor(std::vector<complex_t>({1.,-1i,0.,0.}), Tensor::dim(4));
+ ERROR("Shouldn't reach here..., polState = " << polState);
+ return Tensor();
+}
std::vector<LS> userHelicityCouplings( const std::string& key ){
std::vector<LS> couplings;
auto things = NamedParameter<double>( key, 0).getVector();
- if( things.size() % 3 != 0 ) ERROR("Wrong number of tokens");
- for( size_t i = 0 ; i < things.size(); i+=3 ){
- LS coupling;
- coupling.factor = things[i+0];
- coupling.m1 = things[i+1];
- coupling.m2 = things[i+2];
- couplings.push_back(coupling);
- }
- return couplings;
+ if( things.size() % 3 != 0 ) ERROR("Wrong number of tokens");
+ for( size_t i = 0 ; i < things.size(); i+=3 ){
+ LS coupling;
+ coupling.factor = things[i+0];
+ coupling.m1 = things[i+1];
+ coupling.m2 = things[i+2];
+ couplings.push_back(coupling);
+ }
+ if( couplings.size() == 0 )
+ {
+ FATAL("No helicity amplitude specified by: " << key );
+ }
+ return couplings;
}
+std::string index_string(const Particle& particle)
+{
+ if( particle.isStable() ) return std::to_string(particle.index());
+ std::string f = "{";
+ for( const auto& i : particle.daughters() ) f += index_string( *i );
+ return f+ "}";
+}
Expression AmpGen::helicityAmplitude(const Particle& particle,
const TransformSequence& parentFrame,
const double& Mz,
DebugSymbols* db,
- int sgn )
+ int sgn,
+ TransformCache* cachePtr )
{
- if( particle.daughters().size() > 2 ) return 1;
+ if( cachePtr == nullptr ) cachePtr = new TransformCache();
+ if( particle.daughters().size() > 2 ) {
+ WARNING( particle << " has more than two decay products: helicity amplitude is ill-defined - setting spin matrix element to 1" );
+ return 1;
+ }
if( particle.daughters().size() == 1 )
- return helicityAmplitude( *particle.daughter(0), parentFrame, Mz, db, sgn );
-
+ return helicityAmplitude( *particle.daughter(0), parentFrame, Mz, db, sgn, cachePtr);
Tensor::Index a,b,c;
- auto myFrame = parentFrame;
- if( particle.spin() == 0 ) myFrame.clear();
- Tensor pInParentFrame = parentFrame( particle.P() );
+ // if( particle.props()->twoSpin() == 0 ) myFrame.clear();
+ Tensor pInParentFrame = parentFrame(particle.P());
pInParentFrame.st();
- if( ! particle.isHead() ){
- auto my_sequence = helicityTransformMatrix( pInParentFrame,
- fcn::sqrt(particle.massSq()),
- sgn,
- true );
- myFrame.add( my_sequence );
- }
- if( particle.isStable() )
+ auto key = index_string(particle);
+ if( cachePtr->count(key) == 0 )
{
- if( particle.spin() == 0 ) return Mz==0;
- if( particle.spin() == 0.5 )
+ if( ! particle.isHead() || NamedParameter<bool>("helicityAmplitude::MovingParent", false) )
{
- auto tensor = particle.externalSpinTensor(particle.polState(), db);
- auto helicity_tensor = basisSpinor( 2*Mz, particle.props()->pdgID() );
- auto it = myFrame.inverse();
- auto helicity_in_frame = it( helicity_tensor, Transform::Representation::Bispinor );
- auto w = Bar(helicity_in_frame)(a) * tensor(a);
- ADD_DEBUG_TENSOR( helicity_tensor, db );
- ADD_DEBUG_TENSOR( helicity_in_frame ,db);
- ADD_DEBUG_TENSOR( tensor ,db );
- ADD_DEBUG(w, db);
- return w;
+ (*cachePtr)[key] = TransformSequence(parentFrame, wickTransform(pInParentFrame, particle, sgn, db) );
}
+ else (*cachePtr)[key] = TransformSequence();
}
+ const TransformSequence& myFrame = (*cachePtr)[key];
+ if( particle.isStable() )
+ {
+ if( particle.props()->twoSpin() == 0 ) return Mz==0; // a scalar
+ // polarisation spinor / vector etc. in the quantisation of the lab (i.e. along the z-axis or lab particle momentum)
+ if( particle.props()->isPhoton() && Mz == 0. ) ERROR("Photon polarisation state is wrong");
+ if( particle.polState() == 0 ) ERROR("Photon external state is wrong...");
+ auto labPol = particle.externalSpinTensor(particle.polState(), db);
+ auto inverseMyTransform = myFrame.inverse();
+ if( particle.props()->twoSpin() == 1 ) // so a fermion
+ {
+ if( NamedParameter<bool>("helicityAmplitude::NoSpinAlign", false ) ) return 2*Mz == particle.polState();
+ auto mzSpinor = basisSpinor( 2*Mz, particle.props()->pdgID() );
+ auto mzSpinorInLab = inverseMyTransform( mzSpinor, Transform::Representation::Bispinor );
+ mzSpinorInLab.st();
+ ADD_DEBUG(Bar(mzSpinorInLab)(a)*labPol(a), db );
+ return make_cse( Bar(mzSpinorInLab)(a)*labPol(a) );
+ }
+ if( particle.props()->twoSpin() == 2 ) // so a spin-one boson
+ {
+ auto frameVector = basisVector(Mz);
+ auto labVector = inverseMyTransform( frameVector, Transform::Representation::Vector );
+ return dot( labVector.conjugate(), labPol );
+ }
+ }
auto particle_couplings = particle.spinOrbitCouplings(false);
- auto L = particle.orbital();
- auto& d0 = *particle.daughter(0);
- auto& d1 = *particle.daughter(1);
-
+ auto L = particle.L();
+ const auto& d1 = *particle.daughter(0);
+ const auto& d2 = *particle.daughter(1);
double S = 999;
if( particle.S() == 0 ){
- for( auto& l : particle_couplings ) if( l.first == L ){ S = l.second ; break; }
- if( S == 999 ) ERROR("Spin orbital coupling impossible!");
+ auto it = std::find_if( particle_couplings.begin(), particle_couplings.end(), [&L](auto& l){ return l.first == L; } );
+ if( it != particle_couplings.end() ) S = it->second;
+ else ERROR("Spin orbital coupling impossible!");
}
- else S = particle.S() /2.;
-
- auto recoupling_constants = calculate_recoupling_constants( particle.spin(), Mz, L, S, d0.spin(), d1.spin() );
+ else S = particle.S()/2.;
+ auto recoupling_constants = calculate_recoupling_constants( particle.spin(), Mz, L, S, d1.spin(), d2.spin() );
auto mod = particle.attribute("helAmp");
- if( mod != stdx::nullopt ) recoupling_constants = userHelicityCouplings( mod.value() );
+ if( mod != stdx::nullopt ){
+ if( particle.props()->twoSpin() != 0 )
+ {
+ WARNING("User helicity couplings only implemented for scalar initial states, using: " << *mod << " will result in unexpected behaviour.");
+ }
+ recoupling_constants = userHelicityCouplings( *mod );
+ }
if( recoupling_constants.size() == 0 ){
WARNING( particle.uniqueString() << " " << particle.spin() << " " <<
particle.orbitalRange(false).first << " " << particle.orbitalRange(false).second
- << " transition Mz="<< Mz << " to " << d0.spin() << " x " << d0.spin() << " cannot be coupled in (LS) = " << L << ", " << S );
+ << " transition Mz="<< Mz << " to " << d1.spin() << " x " << d2.spin() << " cannot be coupled in (LS) = " << L << ", " << S );
WARNING( "Possible (LS) combinations = " <<
vectorToString( particle_couplings, ", ", []( auto& ls ){ return "("+std::to_string(int(ls.first)) + ", " + std::to_string(ls.second) +")";} ) );
}
Expression total = 0;
+
+ auto hco = angCoordinates( myFrame(d1.P()) , db);
for( auto& coupling : recoupling_constants )
{
auto dm = coupling.m1 - coupling.m2;
- auto term = wigner_D(myFrame(d0.P()), particle.spin(), Mz, dm,db, d0.name() );
- auto h1 = helicityAmplitude(d0, myFrame, coupling.m1, db, +1);
- auto h2 = helicityAmplitude(d1, myFrame, coupling.m2, db, -1);
+ if( (d1.props()->isPhoton() && coupling.m1 == 0.) ||
+ (d2.props()->isPhoton() && coupling.m2 == 0.) ) continue;
+ auto term = wigner_D(hco, particle.spin(), Mz, dm, db);
+ auto h1 = helicityAmplitude(d1, myFrame, coupling.m1, db, +1, cachePtr);
+ auto h2 = helicityAmplitude(d2, myFrame, coupling.m2, db, -1, cachePtr);
if( db != nullptr ){
db->emplace_back( "coupling" , coupling.factor );
if( coupling.factor != 1 ) db->emplace_back( "C x DD'", coupling.factor * term * h1 * h2 );
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
new file mode 100644
index 00000000000..9cd5d33cf5a
--- /dev/null
+++ b/test/CMakeLists.txt
@@ -0,0 +1,21 @@
+find_package(Boost 1.67.0 COMPONENTS unit_test_framework)
+
+if ( Boost_FOUND )
+ include_directories (${Boost_INCLUDE_DIRS})
+ file(GLOB TEST_SRCS RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.cpp)
+ foreach(testSrc ${TEST_SRCS})
+ get_filename_component(testName ${testSrc} NAME_WE)
+ add_executable(${testName} ${testSrc})
+ set_target_properties(${testName}
+ PROPERTIES
+ RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_TEST_OUTPUT_DIRECTORY}"
+ RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_TEST_OUTPUT_DIRECTORY}"
+ RUNTIME_OUTPUT_DIRECTORY "${CMAKE_TEST_OUTPUT_DIRECTORY}"
+ EXECUTABLE_OUTPUT_DIRECTORY "${CMAKE_TEST_OUTPUT_DIRECTORY}"
+ )
+ target_link_libraries(${testName} PUBLIC ${Boost_LIBRARIES} AmpGen)
+ add_test(NAME ${testName} WORKING_DIRECTORY ${CMAKE_TEST_OUTPUT_DIRECTORY} COMMAND ${CMAKE_TEST_OUTPUT_DIRECTORY}/${testName} )
+ endforeach(testSrc)
+else()
+ message( WARNING "Warning: Boost (version >= 1.67.0) required to build unit tests\n")
+endif()
diff --git a/test/test_AmplitudeRules.cpp b/test/test_AmplitudeRules.cpp
new file mode 100644
index 00000000000..043950d5f9a
--- /dev/null
+++ b/test/test_AmplitudeRules.cpp
@@ -0,0 +1,66 @@
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "AmplitudeRules"
+
+#include <boost/test/included/unit_test.hpp>
+namespace utf = boost::unit_test;
+
+#include "AmpGen/AmplitudeRules.h"
+#include "AmpGen/MinuitParameter.h"
+#include "AmpGen/MinuitParameterSet.h"
+
+using namespace AmpGen;
+
+BOOST_AUTO_TEST_CASE( test_AmplitudeRule ) {
+
+ MinuitParameter re = MinuitParameter("D0{K*(892)bar0{K-,pi+},pi0}_Re", Flag::Free,1.,0.);
+ MinuitParameter im = MinuitParameter("D0{K*(892)bar0{K-,pi+},pi0}_Im", Flag::Free,0.,0.);
+
+ Coupling test(&re,&im);
+
+ BOOST_CHECK( test.name() == "D0{K*(892)bar0{K-,pi+},pi0}" );
+ BOOST_CHECK( test.head() == "D0");
+ BOOST_CHECK( test.prefix() == "" );
+ BOOST_CHECK( test.eventType() == EventType({"D0","K-","pi+","pi0"}) );
+}
+
+BOOST_AUTO_TEST_CASE( test_AmplitudeRules_constructor ){
+ auto mps = MinuitParameterSet( {
+ new MinuitParameter("D0{K*(892)bar0,pi0}_Re", Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{K*(892)bar0,pi0}_Im", Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{rho(770)+,pi-}_Re" , Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{rho(770)+,pi-}_Im" , Flag::Fix,2.,0.)
+ , new MinuitParameter("K*(892)bar0{K-,pi+}_Re", Flag::Free,sqrt(1./3.),0.)
+ , new MinuitParameter("K*(892)bar0{K-,pi+}_Im", Flag::Free,0,0.)
+ , new MinuitParameter("K*(892)bar0{K0,pi0}_Re", Flag::Fix,sqrt(2./3.),0.)
+ , new MinuitParameter("K*(892)bar0{K0,pi0}_Im", Flag::Fix,0,0.) } );
+ AmplitudeRules rule_set(mps);
+
+ BOOST_CHECK( rule_set.rules().size() == 2 ); /// number of head decays
+ BOOST_CHECK( rule_set.hasDecay("D0") == true ); /// has decays for D0
+ BOOST_CHECK( rule_set.hasDecay("a(1)(1260)+") == false ); /// has decays for D0
+}
+
+BOOST_AUTO_TEST_CASE( test_couplingConstant )
+{
+ auto mps = MinuitParameterSet( {
+ new MinuitParameter("D0{K*(892)bar0,pi0}_Re", Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{K*(892)bar0,pi0}_Im", Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{rho(770)+,pi-}_Re" , Flag::Fix,1.,0.)
+ , new MinuitParameter("D0{rho(770)+,pi-}_Im" , Flag::Fix,2.,0.)
+ , new MinuitParameter("K*(892)bar0{K-,pi+}_Re", Flag::Free,sqrt(1./3.),0.)
+ , new MinuitParameter("K*(892)bar0{K-,pi+}_Im", Flag::Free,0,0.)
+ , new MinuitParameter("K*(892)bar0{K0,pi0}_Re", Flag::Fix,sqrt(2./3.),0.)
+ , new MinuitParameter("K*(892)bar0{K0,pi0}_Im", Flag::Fix,0,0.) } );
+ AmplitudeRules rule_set(mps);
+ auto matches = rule_set.getMatchingRules( EventType({"D0","K-","pi+","pi0"}) );
+ auto matches2 = rule_set.getMatchingRules( EventType({"D0","K0","pi0","pi0"}) );
+
+ BOOST_TEST( std::real(matches[0].second()) == 1./sqrt(3.), boost::test_tools::tolerance(1e-10) );
+ BOOST_TEST( std::imag(matches[0].second()) == 1./sqrt(3.), boost::test_tools::tolerance(1e-10) );
+ BOOST_TEST( matches[0].second.isFixed() == false );
+ BOOST_TEST( matches2[0].second.isFixed() == true );
+ BOOST_TEST( matches[0].second.contains("K*(892)bar0{K0,pi0}") == false );
+ BOOST_TEST( matches2[0].second.contains("K*(892)bar0{K0,pi0}") == true );
+}
+
diff --git a/test/test_ArgumentPack.cpp b/test/test_ArgumentPack.cpp
index 0d529a25284..437a9fa4173 100644
--- a/test/test_ArgumentPack.cpp
+++ b/test/test_ArgumentPack.cpp
@@ -7,13 +7,15 @@ namespace utf = boost::unit_test;
#include "AmpGen/ArgumentPack.h"
-DECLARE_ARGUMENT_DEFAULT( test_argument_string, std::string, "hello world");
+DECLARE_ARGUMENT( test_argument_string, std::string);
DECLARE_ARGUMENT( test_argument_double , double );
+static const test_argument_double value;
+
struct Mock {
Mock( const AmpGen::ArgumentPack& args ){
t1 = args.getArg<test_argument_double>().val;
- t2 = args.getArg<test_argument_string>().val;
+ t2 = args.getArg<test_argument_string>("hello world").val;
}
template <class ...ARGS> Mock( const ARGS&... args ) :
Mock( AmpGen::ArgumentPack(args...) ) {}
diff --git a/test/test_Expression.cpp b/test/test_Expression.cpp
index 571d4e260c9..fed4fee9396 100644
--- a/test/test_Expression.cpp
+++ b/test/test_Expression.cpp
@@ -6,7 +6,8 @@
namespace utf = boost::unit_test;
#include "AmpGen/Expression.h"
-
+#include "AmpGen/CompiledExpression.h"
+using namespace AmpGen;
BOOST_AUTO_TEST_CASE ( sum_to_string )
{
AmpGen::Parameter A("A");
@@ -42,3 +43,15 @@ BOOST_AUTO_TEST_CASE( test_composite, * utf::tolerance(1e-6) )
double value = std::real( ( A*B/( AmpGen::fcn::cos(B) * AmpGen::fcn::sqrt(A) ))() );
BOOST_TEST( value == (4*5/(cos(5)*sqrt(4))), boost::test_tools::tolerance(1e-6)) ;
}
+
+BOOST_AUTO_TEST_CASE( lambda_expression )
+{
+ double x = 5;
+ LambdaExpression test( [&x](){ return x; } );
+ auto f = test + 7;
+ BOOST_CHECK( std::real(f()) == 12 );
+ auto expr = make_expression<double>( f, "test" );
+ x = 12;
+ expr.prepare(); // update cache state
+ BOOST_CHECK( expr( static_cast<const double*>(nullptr)) == 19 );
+}
diff --git a/test/test_ExpressionParser.cpp b/test/test_ExpressionParser.cpp
new file mode 100644
index 00000000000..2430f1fcda8
--- /dev/null
+++ b/test/test_ExpressionParser.cpp
@@ -0,0 +1,75 @@
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "ExpressionParser"
+
+#include <boost/test/included/unit_test.hpp>
+
+#include "AmpGen/ExpressionParser.h"
+#include "AmpGen/MinuitParameterSet.h"
+
+namespace utf = boost::unit_test;
+namespace tt = boost::test_tools;
+using namespace AmpGen;
+
+BOOST_AUTO_TEST_CASE( simple_numericalExpressions ){
+ auto test = [](const std::string& expr) -> double { return std::real( ExpressionParser::parse(expr)() ); };
+ BOOST_CHECK( test("1 + 2 * 3" ) == 1 + 2 * 3 );
+ BOOST_CHECK( test("4 + 2 " ) == 6 );
+ BOOST_CHECK( test("3 * 6 - 7 + 2 " ) == 3 * 6 - 7 + 2 );
+ BOOST_CHECK( test("6 * 2 + ( 5 - 3 ) * 3 - 8 " ) == 6 * 2 + ( 5 - 3)*3 -8 );
+ BOOST_CHECK( test("( 3 + 4 ) + 7 * 2 - 1 - 9 " ) == 3 + 4 + 7 * 2 - 1 - 9);
+ BOOST_CHECK( test("5 - 2 + 4 * ( 8 - ( 5 + 1 ) ) + 9 " ) == 5 - 2 + 4 *( 8 - (5+1)) +9 );
+ BOOST_CHECK( test("( 8 - 1 + 3 ) * 6 - ( ( 3 + 7 ) * 2 )" ) == (8-1+3)*6 - ((3+7)*2) );
+}
+
+BOOST_AUTO_TEST_CASE( parametericExpressions ) {
+
+ double a = 1.0;
+ double b = 0.5;
+ double c = 4.0;
+ double d = 0.2;
+ double f = 3.13;
+
+ MinuitParameterSet mps( {
+ new MinuitParameter("a", Flag::Free, a, 0.)
+ , new MinuitParameter("b", Flag::Free, b, 0.)
+ , new MinuitParameter("c", Flag::Free, c, 0.)
+ , new MinuitParameter("d", Flag::Free, d, 0.)
+ , new MinuitParameter("f", Flag::Free, f, 0.)
+ });
+
+ double pi = M_PI;
+
+ auto test = [&mps](const std::string& expr) -> double {
+ std::string newLine="";
+ for( auto& ch : expr ){
+ if( ch == '(' ||
+ ch == ')' ||
+ ch == '+' ||
+ ch == '-' ||
+ ch == '*' ||
+ ch == '/' ||
+ ch == '>' ||
+ ch == '<' ||
+ ch == '^' ){
+ newLine.push_back(' ');
+ newLine.push_back(ch);
+ newLine.push_back(' ');
+ }
+ else newLine.push_back(ch);
+ }
+ return std::real( ExpressionParser::parse(newLine, &mps)() ); };
+
+ BOOST_TEST( test("a+(cos(b-sin(2/a*pi))-sin(a-cos(2*b/pi)))-b") == a+(cos(b-sin(2/a*pi))-sin(a-cos(2*b/pi)))-b );
+ BOOST_TEST( test("sin(a)+sin(b)") == sin(a)+sin(b) );
+ BOOST_TEST( test("abs(sin(sqrt(a^2+b^2))*255)") == abs(sin(sqrt(a*a+b*b))*255) );
+ BOOST_TEST( test("sqrt(a)<sin(8)") == (sqrt(a)<sin(8)) );
+ BOOST_TEST( test("(10+sqrt(a))<(sin(8)^2)") == ((10+sqrt(a))<pow(sin(8),2)) );
+ BOOST_TEST( test("(b+a/b) * (a-b/a)") == (b+a/b) * (a-b/a) );
+ BOOST_TEST( test("(0.1*a+1)*a+1.1-sin(a)-log(a)/a*3/4" ) == (0.1*a+1)*a+1.1-sin(a)-log(a)/a*3/4 );
+ BOOST_TEST( test("sin(2 * a) + cos(pi / b)" ) == sin(2 * a) + cos(pi / b) , tt::tolerance(1e-10));
+ BOOST_TEST( test("a - ( b + c ) " ) == a - ( b + c ) , tt::tolerance(1e-10));
+ BOOST_TEST( test("a - b + c - d / b + f - a " ) == a - b + c - (d / b) + f - a, tt::tolerance(1e-10));
+}
+
+
diff --git a/test/test_NamedParameter.cpp b/test/test_NamedParameter.cpp
index 025d3b48e77..9d7798fc249 100644
--- a/test/test_NamedParameter.cpp
+++ b/test/test_NamedParameter.cpp
@@ -7,7 +7,7 @@
BOOST_AUTO_TEST_CASE ( constructors_right )
{
- AmpGen::NamedParameter<size_t> param("test_param", 4);
- BOOST_CHECK( param == 4 );
+ AmpGen::NamedParameter<unsigned> param("test_param", 4);
+ BOOST_CHECK( param == unsigned(4) );
}
diff --git a/test/test_Particle.cpp b/test/test_Particle.cpp
new file mode 100644
index 00000000000..771aaa2cee5
--- /dev/null
+++ b/test/test_Particle.cpp
@@ -0,0 +1,18 @@
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "Particle"
+
+#include <boost/test/unit_test.hpp>
+#include "AmpGen/Particle.h"
+
+BOOST_AUTO_TEST_CASE( Particle_quasiStableTree )
+{
+ auto d1 = AmpGen::Particle("D~0{D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}}}");
+ auto d2 = AmpGen::Particle("B+{D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}},K+}");
+ auto d3 = AmpGen::Particle("B+{D~0{D0{K*(892)0{K+,pi-},rho(770)0{pi+,pi-}}},K+}");
+ BOOST_CHECK( d1.quasiStableTree().decayDescriptor() == "D~0{K+,pi+,pi-,pi-}" );
+ BOOST_CHECK( d2.quasiStableTree().decayDescriptor() == "B+{D0{K+,pi+,pi-,pi-},K+}" );
+ BOOST_CHECK( d3.quasiStableTree().decayDescriptor() == "B+{D~0{K+,pi+,pi-,pi-},K+}" );
+}
+
+
diff --git a/test/test_ParticleProperties.cpp b/test/test_ParticleProperties.cpp
index 84085df71b2..010e5624c79 100644
--- a/test/test_ParticleProperties.cpp
+++ b/test/test_ParticleProperties.cpp
@@ -1,6 +1,6 @@
#define BOOST_TEST_DYN_LINK
-#define BOOST_TEST_MODULE "Expression"
+#define BOOST_TEST_MODULE "ParticlePropertiesList"
#include <boost/test/unit_test.hpp>
#include "AmpGen/ParticlePropertiesList.h"
diff --git a/test/test_QuarkContent.cpp b/test/test_QuarkContent.cpp
new file mode 100644
index 00000000000..b48f3ad873e
--- /dev/null
+++ b/test/test_QuarkContent.cpp
@@ -0,0 +1,24 @@
+
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "QuarkContent"
+
+#include <boost/test/included/unit_test.hpp>
+namespace utf = boost::unit_test;
+
+#include "AmpGen/QuarkContent.h"
+
+using namespace AmpGen;
+
+BOOST_AUTO_TEST_CASE( test_QuarkState ) {
+
+ QuarkState uD("uD");
+ QuarkState dU("dU");
+
+ BOOST_CHECK( uD != dU );
+
+ auto vu = uD + dU;
+
+ BOOST_CHECK( vu.isVacuum());
+
+}
diff --git a/test/test_avx2d.cpp b/test/test_avx2d.cpp
new file mode 100644
index 00000000000..049dc34b186
--- /dev/null
+++ b/test/test_avx2d.cpp
@@ -0,0 +1,88 @@
+
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "test_avx2"
+
+#include <boost/test/included/unit_test.hpp>
+namespace utf = boost::unit_test;
+
+
+#if ENABLE_AVX2d
+#include "AmpGen/simd/utils.h"
+
+using namespace AmpGen;
+using namespace AmpGen::AVX2d;
+using namespace std::complex_literals;
+
+#define test_simd( avx_function, scalar_function, data, tv) \
+{ auto r = avx_function( data ).to_array(); auto vals = data.to_array(); \
+ for(int i =0;i!=4;++i) BOOST_TEST( r[i] == scalar_function(vals[i]), boost::test_tools::tolerance(tv) ); }
+
+BOOST_AUTO_TEST_CASE( test_log )
+{
+ test_simd( AVX2d::log, std::log, AVX2d::real_v(0.3, 0.5, 10, 7.0), 1e-12 );
+}
+
+BOOST_AUTO_TEST_CASE( test_complex_log )
+{
+ std::array<std::complex<double>, 4> pr = {0.3 - 3.0*1i, 0.5 - 4.0*1i, 10.+3.*1i, -4.0 + 1.0*1i};
+ test_simd( AVX2d::log, std::log, AVX2d::complex_v( pr.data() ), 1e-8 );
+}
+
+BOOST_AUTO_TEST_CASE( test_fmod )
+{
+ std::vector<double> a = {5.1, -5.1, 5.1, -5.1};
+ std::vector<double> b = {3.0, +3.0, -3.0, -3.0};
+
+ AVX2d::real_v av( a.data() );
+ AVX2d::real_v bv( b.data() );
+
+ auto modv = AVX2d::fmod(av,bv);
+
+ auto mod = modv.to_array();
+ BOOST_TEST( mod[0] == 2.1 , boost::test_tools::tolerance(1e-15));
+ BOOST_TEST( mod[1] == -2.1 , boost::test_tools::tolerance(1e-15));
+ BOOST_TEST( mod[2] == 2.1 , boost::test_tools::tolerance(1e-15));
+ BOOST_TEST( mod[3] == -2.1 , boost::test_tools::tolerance(1e-15));
+}
+
+BOOST_AUTO_TEST_CASE( test_double_to_int )
+{
+ std::vector<double> a = {17.4, 19.2, 12.1, 4007.3};
+ auto f = udouble_to_uint( real_v( a.data() ));
+ alignas(32) uint64_t t[ utils::size<real_v>::value ];
+ _mm256_store_si256( (__m256i*)t, f);
+ BOOST_TEST( t[0] == 17 );
+ BOOST_TEST( t[1] == 19 );
+ BOOST_TEST( t[2] == 12 );
+ BOOST_TEST( t[3] == 4007 );
+}
+
+BOOST_AUTO_TEST_CASE( test_gather )
+{
+ // 0 1 2 3 4 5 6
+ std::vector<double> data = { 15.4, 19.7, 121.8, -15.6, M_PI, sqrt(2), 5.7, 12 };
+ std::vector<double> addr = { 0.2, 5.3, 3.1, 4.1 };
+ auto v = AVX2d::gather( data.data(), AVX2d::real_v(addr.data()) ).to_array();
+ BOOST_TEST( v[0] == data[0] );
+ BOOST_TEST( v[1] == data[5] );
+ BOOST_TEST( v[2] == data[3] );
+ BOOST_TEST( v[3] == data[4] );
+}
+
+BOOST_AUTO_TEST_CASE( test_trig )
+{
+ auto data = AVX2d::real_v(0.1,0.4,-2.0,5.0);
+ test_simd( AVX2d::cos, std::cos, data, 1e-15);
+ test_simd( AVX2d::sin, std::sin, data, 1e-15);
+ test_simd( AVX2d::tan, std::tan, data, 1e-15);
+}
+
+#else
+BOOST_AUTO_TEST_CASE( test_dummy )
+{
+ BOOST_TEST( 1 == 1 );
+}
+#endif
+
+
diff --git a/test/test_enum.cpp b/test/test_enum.cpp
new file mode 100644
index 00000000000..2a3c492c275
--- /dev/null
+++ b/test/test_enum.cpp
@@ -0,0 +1,22 @@
+
+#define BOOST_TEST_DYN_LINK
+
+#define BOOST_TEST_MODULE "enum"
+
+#include <boost/test/included/unit_test.hpp>
+namespace utf = boost::unit_test;
+
+#include "AmpGen/enum.h"
+
+namespace AmpGen {
+ make_enum( test_enum, state1, state2, state3 )
+}
+using namespace AmpGen;
+
+BOOST_AUTO_TEST_CASE( test_enums )
+{
+ BOOST_CHECK( parse<test_enum> ("state1") == test_enum::state1 );
+ BOOST_CHECK( parse<test_enum> ("state2") == test_enum::state2 );
+ BOOST_CHECK( parse<test_enum> ("state3") == test_enum::state3 );
+ BOOST_CHECK( parse<test_enum> ("blag") == test_enum::Invalid );
+}
diff --git a/test/test_phaseSpace.cpp b/test/test_phaseSpace.cpp
index 4dc139124af..6bea1fd1380 100644
--- a/test/test_phaseSpace.cpp
+++ b/test/test_phaseSpace.cpp
@@ -27,7 +27,7 @@ BOOST_AUTO_TEST_CASE( phaseSpace_threeBody )
std::vector<double> test_event = {-0.235918, -0.242689, 0.278177, 1.19862,-0.300608, -0.0584944, -0.0117436, 0.584418, 0.536526, 0.301183, -0.266434, 0.684864} ;
- auto new_event = phsp.makeEvent(0);
+ auto new_event = phsp.makeEvent();
// auto new_event = phsp.generate();
for( int i = 0 ; i < 12 ; ++i )
diff --git a/test/test_utilities.cpp b/test/test_utilities.cpp
index c52e2bcd565..0525d029c48 100644
--- a/test/test_utilities.cpp
+++ b/test/test_utilities.cpp
@@ -1,17 +1,23 @@
#define BOOST_TEST_DYN_LINK
-#define BOOST_TEST_MODULE "ArgumentPack"
-
+#define BOOST_TEST_MODULE "Utilities"
#include <boost/test/included/unit_test.hpp>
namespace utf = boost::unit_test;
#include "AmpGen/Utilities.h"
-
BOOST_AUTO_TEST_CASE( test_swap_char )
{
std::string test = "hello, world";
AmpGen::swapChars( test, 'h', 'w' );
- BOOST_CHECK( test == "wello, horld");
+ BOOST_TEST( test == "wello, horld");
}
+BOOST_AUTO_TEST_CASE( test_split )
+{
+ std::string test = "hello world tokens";
+ auto tokens = AmpGen::split(test,' ');
+ BOOST_TEST(tokens[0] == "hello");
+ BOOST_TEST(tokens[1] == "world");
+ BOOST_TEST(tokens[2] == "tokens");
+}