Lambdify support

.gitignore

@@ -66,6 +66,9 @@ pip-wheel-metadata
 # VS Code
 .vscode
 
+# Emacs - projectile
+TAGS
+
 # default pytest cache directory
 */.pytest_cache
 .pytest_cache/

docs/Makefile

@@ -0,0 +1,177 @@
+# Makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS    =
+SPHINXBUILD   = sphinx-build
+PAPER         =
+BUILDDIR      = build
+
+# User-friendly check for sphinx-build
+ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1)
+$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/)
+endif
+
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
+# the i18n builder cannot share the environment and doctrees with the others
+I18NSPHINXOPTS  = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
+
+.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext
+
+help:
+	@echo "Please use \`make <target>' where <target> is one of"
+	@echo "  html       to make standalone HTML files"
+	@echo "  dirhtml    to make HTML files named index.html in directories"
+	@echo "  singlehtml to make a single large HTML file"
+	@echo "  pickle     to make pickle files"
+	@echo "  json       to make JSON files"
+	@echo "  htmlhelp   to make HTML files and a HTML help project"
+	@echo "  qthelp     to make HTML files and a qthelp project"
+	@echo "  devhelp    to make HTML files and a Devhelp project"
+	@echo "  epub       to make an epub"
+	@echo "  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+	@echo "  latexpdf   to make LaTeX files and run them through pdflatex"
+	@echo "  latexpdfja to make LaTeX files and run them through platex/dvipdfmx"
+	@echo "  text       to make text files"
+	@echo "  man        to make manual pages"
+	@echo "  texinfo    to make Texinfo files"
+	@echo "  info       to make Texinfo files and run them through makeinfo"
+	@echo "  gettext    to make PO message catalogs"
+	@echo "  changes    to make an overview of all changed/added/deprecated items"
+	@echo "  xml        to make Docutils-native XML files"
+	@echo "  pseudoxml  to make pseudoxml-XML files for display purposes"
+	@echo "  linkcheck  to check all external links for integrity"
+	@echo "  doctest    to run all doctests embedded in the documentation (if enabled)"
+
+clean:
+	rm -rf $(BUILDDIR)/*
+
+html:
+	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
+
+dirhtml:
+	$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
+
+singlehtml:
+	$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
+	@echo
+	@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
+
+pickle:
+	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
+	@echo
+	@echo "Build finished; now you can process the pickle files."
+
+json:
+	$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
+	@echo
+	@echo "Build finished; now you can process the JSON files."
+
+htmlhelp:
+	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
+	@echo
+	@echo "Build finished; now you can run HTML Help Workshop with the" \
+	      ".hhp project file in $(BUILDDIR)/htmlhelp."
+
+qthelp:
+	$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
+	@echo
+	@echo "Build finished; now you can run "qcollectiongenerator" with the" \
+	      ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
+	@echo "# qcollectiongenerator $(BUILDDIR)/qthelp/einsteinpy.qhcp"
+	@echo "To view the help file:"
+	@echo "# assistant -collectionFile $(BUILDDIR)/qthelp/einsteinpy.qhc"
+
+devhelp:
+	$(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
+	@echo
+	@echo "Build finished."
+	@echo "To view the help file:"
+	@echo "# mkdir -p $$HOME/.local/share/devhelp/einsteinpy"
+	@echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/einsteinpy"
+	@echo "# devhelp"
+
+epub:
+	$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
+	@echo
+	@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
+
+latex:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo
+	@echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
+	@echo "Run \`make' in that directory to run these through (pdf)latex" \
+	      "(use \`make latexpdf' here to do that automatically)."
+
+latexpdf:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through pdflatex..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+latexpdfja:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through platex and dvipdfmx..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf-ja
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+text:
+	$(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
+	@echo
+	@echo "Build finished. The text files are in $(BUILDDIR)/text."
+
+man:
+	$(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
+	@echo
+	@echo "Build finished. The manual pages are in $(BUILDDIR)/man."
+
+texinfo:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo
+	@echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
+	@echo "Run \`make' in that directory to run these through makeinfo" \
+	      "(use \`make info' here to do that automatically)."
+
+info:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo "Running Texinfo files through makeinfo..."
+	make -C $(BUILDDIR)/texinfo info
+	@echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
+
+gettext:
+	$(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
+	@echo
+	@echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
+
+changes:
+	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
+	@echo
+	@echo "The overview file is in $(BUILDDIR)/changes."
+
+linkcheck:
+	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
+	@echo
+	@echo "Link check complete; look for any errors in the above output " \
+	      "or in $(BUILDDIR)/linkcheck/output.txt."
+
+doctest:
+	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
+	@echo "Testing of doctests in the sources finished, look at the " \
+	      "results in $(BUILDDIR)/doctest/output.txt."
+
+xml:
+	$(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml
+	@echo
+	@echo "Build finished. The XML files are in $(BUILDDIR)/xml."
+
+pseudoxml:
+	$(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml
+	@echo
+	@echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml."

src/riccipy/__init__.py

@@ -1,5 +1,4 @@
 """
-=======
 RicciPy
 =======
 
@@ -9,4 +8,5 @@
 
 __version__ = "0.1.dev0"
 from .metric import Metric, SpacetimeMetric
+from .numerical import lambdify_tensor
 from .tensor import Index, Tensor, expand_tensor, indices

src/riccipy/numerical.py

@@ -0,0 +1,114 @@
+from functools import partial
+from itertools import starmap
+from types import FunctionType
+
+import numpy as np
+
+from sympy import Array, lambdify
+from sympy.tensor.tensor import TensExpr
+
+from .tensor import expand_tensor
+
+
+class NumericalArray(object):
+    """
+    Class for representing an array of symbolic expressions as lambdified functions.
+
+    Calling instances of this class will result in the evaluation of a lambda function
+    that returns a numerically valued array representing the results of the individual
+    component expressions.
+
+    Furthermore, instances may also be used to access specific components in a manner
+    identical to accessing the components of an numpy array.
+
+    """
+
+    def __init__(self, args, array, **kwargs):
+        """
+        Create a new NumericalArray.
+
+        Parameters
+        ----------
+        args : (list, tuple)
+            Iterable of ~sympy.Symbol objects that specifcy the order of the arguments
+            for the lambda functions that will be generated.
+        array : (list, tuple, ~sympy.Matrix, ~sympy.Array)
+            The array of symbolic expressions to be lambdified.
+
+        """
+        array = Array(array)
+        self._vars = args
+        self._objstr = str(array)
+        self._array = array
+        self._modules = kwargs.pop("modules", None)
+        self._lambda = lambdify(self._vars, self._array, modules=self._modules)
+        self._generator = self._build_generator()
+
+    def _build_generator(self):
+        shape = self._array.shape
+        ndarr = np.ndarray(shape, dtype=FunctionType)
+        lfunc = partial(lambdify, modules=self._modules)
+        generator = starmap(lfunc, [(self._vars, elem) for elem in self._array])
+        ndarr.put(range(len(self._array)), list(generator))
+        return ndarr
+
+    def __getitem__(self, key):
+        return self._generator.__getitem__(key)
+
+    def __call__(self, *args):
+        return np.asarray(self._lambda(*args))
+
+    def __getattr__(self, attr):
+        if hasattr(self._array, attr):
+            return getattr(self._array, attr)
+        raise AttributeError("%s has no attribute: %s", self.__class__.__name__, attr)
+
+    def __repr__(self):
+        return "NumericalArray(%s)" % self._objstr
+
+    def __str__(self):
+        return self.__repr__()
+
+
+def lambdify_tensor(args, expr, idxs=None, **kwargs):
+    """
+    Generate a numerical array representation for the result of a tensor expression.
+
+    When the tensor expression passed results in an instance of ~sympy.Array, a
+    NumericalArray object is returned.
+    A NumericalArray can be used to access lambda functions for either the array
+    as a whole or for individual components. See the example below.
+
+    Parameters
+    ----------
+    args : (list, tuple)
+        Iterable of ~sympy.Symbol objects that specifcy the order of the arguments
+        for the lambda functions that will be generated.
+    expr : (~sympy.tensor.tensor.TensExpr, ~sympy.Expr)
+        The tensor expression to be lambdified. If this is an ordinary expression
+        this function defaults to ~sympy.lambdify.
+    idxs : (list, tuple)
+        Iterable of Index objects to specify the indices for the result of ``expr``.
+
+    Examples
+    --------
+    >>> t, r, th, ph = symbols('t r theta phi', real=True)
+    >>> schw = diag(1-1/r, -1/(1-1/r), -r**2, -r**2*sin(th)**2)
+    >>> g = Metric('g', (t, r, th, ph), schw)
+    >>> narr = lambdify_tensor((r, th), g(-mu,-nu))
+    >>> narr(2, 0)
+    array([[ 0.5,  0. ,  0. ,  0. ],
+            [ 0. , -2. ,  0. ,  0. ],
+            [ 0. ,  0. , -4. ,  0. ],
+            [ 0. ,  0. ,  0. , -0. ]])
+    >>> narr[0,0]
+    <function _lambdifygenerated(r, theta)>
+    >>> narr[0,0](2, 0)
+    0.5
+
+    """
+    if isinstance(expr, TensExpr):
+        expr = expand_tensor(expr, idxs)
+    if isinstance(expr, Array):
+        return NumericalArray(args, expr, **kwargs)
+    return lambdify(args, expr, **kwargs)

src/riccipy/tests/test_metric.py

@@ -1,8 +1,7 @@
-from sympy import Expr, diag, eye, sin, symbols, tensorproduct, zeros
-
 from riccipy.metric import *
 from riccipy.partial import *
 from riccipy.tensor import *
+from sympy import Expr, diag, eye, sin, symbols, tensorproduct, zeros
 
 
 def _generate_schwarzschild():

src/riccipy/tests/test_numerical.py

@@ -0,0 +1,29 @@
+import numpy as np
+from types import FunctionType
+from riccipy.tensor import *
+from riccipy.metric import *
+from riccipy.numerical import *
+
+from sympy import diag, sin, symbols
+
+def _generate_schwarzschild():
+    coords = symbols("t r theta phi", real=True)
+    t, r, th, ph = coords
+    schw = diag(1 - 1 / r, -1 / (1 - 1 / r), -r ** 2, -r ** 2 * sin(th) ** 2)
+    g = Metric("g", coords, schw)
+    mu, nu = indices("mu nu", g)
+    return (coords, t, r, th, ph, schw, g, mu, nu)
+
+def test_NumericalArray():
+    (coords, t, r, th, ph, schw, g, mu, nu) = _generate_schwarzschild()
+    narr = NumericalArray((r, th), g.as_array())
+    expect = [[0.5, 0, 0, 0], [0, -2, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0]]
+    assert isinstance(narr(2,0), np.ndarray)
+    assert (narr(2, 0) == expect).all()
+    assert isinstance(narr[0,0], FunctionType)
+    assert narr[0,0](2,0) == 0.5
+
+def test_lambdify_tensor():
+    (coords, t, r, th, ph, schw, g, mu, nu) = _generate_schwarzschild()
+    narr = lambdify_tensor((r, th), g(-mu,-nu))
+    assert isinstance(narr, NumericalArray)

src/riccipy/tests/test_partial.py

@@ -1,8 +1,7 @@
-from sympy import diag, sin, symbols
-
 from riccipy.metric import *
 from riccipy.partial import *
 from riccipy.tensor import *
+from sympy import diag, sin, symbols
 
 
 def _generate_schwarzschild():

src/riccipy/tests/test_tensor.py

@@ -1,8 +1,7 @@
-from sympy import Array, diag, eye, simplify, sin, symbols
-from sympy.tensor.tensor import TensExpr, TensMul
-
 from riccipy.metric import *
 from riccipy.tensor import *
+from sympy import Array, diag, eye, simplify, sin, symbols
+from sympy.tensor.tensor import TensExpr, TensMul
 
 
 def _generate_simple():