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Add comments to network analysis file #906

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124 changes: 104 additions & 20 deletions src/network_analysis.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,8 @@
function filter_constspecs(specs, stoich::AbstractVector{V}, smap) where {V <: Integer}
isempty(specs) && (return Vector{Int}(), Vector{V}())

# If any species are constant, go through these manually and add their indices and
# stoichiometries to `ids` and `filtered_stoich`.
if any(isconstant, specs)
ids = Vector{Int}()
filtered_stoich = Vector{V}()
Expand Down Expand Up @@ -44,11 +46,15 @@ function reactioncomplexmap(rn::ReactionSystem)
!isempty(nps.complextorxsmap) && return nps.complextorxsmap
complextorxsmap = nps.complextorxsmap

# Retrieves system reactions and a map from species to their index in the species vector.
rxs = reactions(rn)
smap = speciesmap(rn)
numreactions(rn) > 0 ||
error("There must be at least one reaction to find reaction complexes.")

for (i, rx) in enumerate(rxs)
# Create the `ReactionComplex` corresponding to the reaction's substrates. Adds it
# to the reaction complex dictionary (recording it as the substrates of the i'th reaction).
subids, substoich = filter_constspecs(rx.substrates, rx.substoich, smap)
subrc = sort!(ReactionComplex(subids, substoich))
if haskey(complextorxsmap, subrc)
Expand All @@ -57,6 +63,8 @@ function reactioncomplexmap(rn::ReactionSystem)
complextorxsmap[subrc] = [i => -1]
end

# Create the `ReactionComplex` corresponding to the reaction's products. Adds it
# to the reaction complex dictionary (recording it as the products of the i'th reaction).
prodids, prodstoich = filter_constspecs(rx.products, rx.prodstoich, smap)
prodrc = sort!(ReactionComplex(prodids, prodstoich))
if haskey(complextorxsmap, prodrc)
Expand Down Expand Up @@ -94,7 +102,10 @@ function reactioncomplexes(rn::ReactionSystem; sparse = false)
isempty(get_systems(rn)) ||
error("reactioncomplexes does not currently support subsystems.")
nps = get_networkproperties(rn)

# If the complexes have not been cached, or the cached complexes uses a different sparsity.
if isempty(nps.complexes) || (sparse != issparse(nps.complexes))
# Computes the reaction complex dictionary. Use it to create a sparse/dense matrix.
complextorxsmap = reactioncomplexmap(rn)
nps.complexes, nps.incidencemat = if sparse
reactioncomplexes(SparseMatrixCSC{Int, Int}, rn, complextorxsmap)
Expand All @@ -105,8 +116,11 @@ function reactioncomplexes(rn::ReactionSystem; sparse = false)
nps.complexes, nps.incidencemat
end

# Creates a *sparse* reaction complex matrix.
function reactioncomplexes(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSystem,
complextorxsmap)
# Computes the I, J, and V vectors used for the sparse matrix (read about sparse matrix
# representation for more information).
complexes = collect(keys(complextorxsmap))
Is = Int[]
Js = Int[]
Expand All @@ -122,6 +136,7 @@ function reactioncomplexes(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSystem
complexes, B
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Here, and in a lot more cases, I wonder if there are more descriptive names for the matrices? I am really not familiar with standards for network analysis though, and I only think it happened like once or twice that I had to do a actual retake to go around to look what kind of matrix I was dealing with.
(I have no strong opinions, but a general thought I had)

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Maybe we could go through and use incidencemat, complexstoichmat, netstoichmat, etc. for these variable names, or maybe standardize the letters we use for each of the matrices and have that somewhere in the documentation (I believe the most common I have seen are Y or Z for the complex stoichiometry matrix, D for the incidence matrix, and S or \Gamma for the reaction stoichiometry matrix)

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Except you don't want a variable name to be the same as function names we provide so they should be something different.

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Perhaps we should have made the functions get_netstoichmat and such but it is too late now for that as it would be breaking. (And our naming is not inconsistent with how base Julia names many functions.)

end

# Creates a *dense* reaction complex matrix.
function reactioncomplexes(::Type{Matrix{Int}}, rn::ReactionSystem, complextorxsmap)
complexes = collect(keys(complextorxsmap))
B = zeros(Int, length(complexes), numreactions(rn))
Expand Down Expand Up @@ -158,6 +173,9 @@ function complexstoichmat(rn::ReactionSystem; sparse = false)
isempty(get_systems(rn)) ||
error("complexstoichmat does not currently support subsystems.")
nps = get_networkproperties(rn)

# If the complexes stoichiometry matrix has not been cached, or the cached one uses a
# different sparsity, computes (and caches) it.
if isempty(nps.complexstoichmat) || (sparse != issparse(nps.complexstoichmat))
nps.complexstoichmat = if sparse
complexstoichmat(SparseMatrixCSC{Int, Int}, rn, keys(reactioncomplexmap(rn)))
Expand All @@ -168,7 +186,10 @@ function complexstoichmat(rn::ReactionSystem; sparse = false)
nps.complexstoichmat
end

# Creates a *sparse* reaction complex stoichiometry matrix.
function complexstoichmat(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSystem, rcs)
# Computes the I, J, and V vectors used for the sparse matrix (read about sparse matrix
# representation for more information).
Is = Int[]
Js = Int[]
Vs = Int[]
Expand All @@ -182,6 +203,7 @@ function complexstoichmat(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSystem,
Z = sparse(Is, Js, Vs, numspecies(rn), length(rcs))
end

# Creates a *dense* reaction complex stoichiometry matrix.
function complexstoichmat(::Type{Matrix{Int}}, rn::ReactionSystem, rcs)
Z = zeros(Int, numspecies(rn), length(rcs))
for (i, rc) in enumerate(rcs)
Expand Down Expand Up @@ -213,6 +235,9 @@ function complexoutgoingmat(rn::ReactionSystem; sparse = false)
isempty(get_systems(rn)) ||
error("complexoutgoingmat does not currently support subsystems.")
nps = get_networkproperties(rn)

# If the outgoing complexes matrix has not been cached, or the cached one uses a
# different sparsity, computes (and caches) it.
if isempty(nps.complexoutgoingmat) || (sparse != issparse(nps.complexoutgoingmat))
B = reactioncomplexes(rn, sparse = sparse)[2]
nps.complexoutgoingmat = if sparse
Expand All @@ -224,16 +249,22 @@ function complexoutgoingmat(rn::ReactionSystem; sparse = false)
nps.complexoutgoingmat
end

# Creates a *sparse* outgoing reaction complex stoichiometry matrix.
function complexoutgoingmat(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSystem, B)
# Computes the I, J, and V vectors used for the sparse matrix (read about sparse matrix
# representation for more information).
n = size(B, 2)
rows = rowvals(B)
vals = nonzeros(B)
Is = Int[]
Js = Int[]
Vs = Int[]

# Allocates space to the vectors (so that it is not done incrementally in the loop).
sizehint!(Is, div(length(vals), 2))
sizehint!(Js, div(length(vals), 2))
sizehint!(Vs, div(length(vals), 2))

for j in 1:n
for i in nzrange(B, j)
if vals[i] != one(eltype(vals))
Expand All @@ -246,6 +277,7 @@ function complexoutgoingmat(::Type{SparseMatrixCSC{Int, Int}}, rn::ReactionSyste
sparse(Is, Js, Vs, size(B, 1), size(B, 2))
end

# Creates a *dense* outgoing reaction complex stoichiometry matrix.
function complexoutgoingmat(::Type{Matrix{Int}}, rn::ReactionSystem, B)
Δ = copy(B)
for (I, b) in pairs(Δ)
Expand Down Expand Up @@ -284,10 +316,14 @@ function incidencematgraph(rn::ReactionSystem)
nps.incidencegraph
end

# Computes the incidence graph from an *dense* incidence matrix.
function incidencematgraph(incidencemat::Matrix{Int})
@assert all(∈([-1, 0, 1]), incidencemat)
n = size(incidencemat, 1) # no. of nodes/complexes
graph = Graphs.DiGraph(n)

# Walks through each column (corresponds to reactions). For each, find the input and output
# complex and add an edge representing these to the incidence graph.
for col in eachcol(incidencemat)
src = 0
dst = 0
Expand All @@ -301,12 +337,16 @@ function incidencematgraph(incidencemat::Matrix{Int})
return graph
end

# Computes the incidence graph from an *sparse* incidence matrix.
function incidencematgraph(incidencemat::SparseMatrixCSC{Int, Int})
@assert all(∈([-1, 0, 1]), incidencemat)
m, n = size(incidencemat)
graph = Graphs.DiGraph(m)
rows = rowvals(incidencemat)
vals = nonzeros(incidencemat)

# Loops through the (n) columns. For each column, directly find the index of the input
# and output complex and add an edge representing these to the incidence graph.
for j in 1:n
inds = nzrange(incidencemat, j)
row = rows[inds]
Expand Down Expand Up @@ -387,32 +427,43 @@ rcs,incidencemat = reactioncomplexes(sir)
```
"""
function deficiency(rn::ReactionSystem)
# Precomputes required information. `conservationlaws` caches the conservation laws in `rn`.
nps = get_networkproperties(rn)
conservationlaws(rn)
r = nps.rank
ig = incidencematgraph(rn)
lc = linkageclasses(rn)

# Computes deficiency using its formula. Caches and returns it as output.
nps.deficiency = Graphs.nv(ig) - length(lc) - r
nps.deficiency
end

# Used in the subsequent function.
# For a linkage class (set of reaction complexes that form an isolated sub-graph), and some
# additional information of the full network, find the reactions, species, and parameters
# that constitute the corresponding sub-reaction network.
function subnetworkmapping(linkageclass, allrxs, complextorxsmap, p)
# Finds the reactions that are part of teh sub-reaction network.
rxinds = sort!(collect(Set(rxidx for rcidx in linkageclass
for rxidx in complextorxsmap[rcidx])))
rxs = allrxs[rxinds]
specset = Set(s for rx in rxs for s in rx.substrates if !isconstant(s))
for rx in rxs
newrxs = allrxs[rxinds]

# Find the species that are part of the sub-reaction network.
specset = Set(s for rx in newrxs for s in rx.substrates if !isconstant(s))
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Mark as new line. It is not, it has simply been pushed down one step and uses newrxs instead of rxs.

for rx in newrxs
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rxs to newrxs. No other change to this function

for product in rx.products
!isconstant(product) && push!(specset, product)
end
end
specs = collect(specset)
newspecs = collect(specset)

# Find the parameters that are part of the sub-reaction network.
newps = Vector{eltype(p)}()
for rx in rxs
for rx in newrxs
Symbolics.get_variables!(newps, rx.rate, p)
end
rxs, specs, newps # reactions and species involved in reactions of subnetwork

newrxs, newspecs, newps
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New names, used in this and the next function, see it for clarity.

end

"""
Expand All @@ -436,18 +487,23 @@ subnetworks(sir)
"""
function subnetworks(rs::ReactionSystem)
isempty(get_systems(rs)) || error("subnetworks does not currently support subsystems.")

# Retrieves required components. `linkageclasses` caches linkage classes in `rs`.
lcs = linkageclasses(rs)
rxs = reactions(rs)
p = parameters(rs)
t = get_iv(rs)
spatial_ivs = get_sivs(rs)
complextorxsmap = [map(first, rcmap) for rcmap in values(reactioncomplexmap(rs))]
subnetworks = Vector{ReactionSystem}()

# Loops through each sub-graph of connected reaction complexes. For each, create a
# new `ReactionSystem` model and pushes it to the subnetworks vector.
for i in 1:length(lcs)
reacs, specs, newps = subnetworkmapping(lcs[i], rxs, complextorxsmap, p)
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Here, I found it weird that rxs was used for the old reactions, and reacs was used for the new reactions (while newps and p was used for the new/old parameters). In this, and the previous subnetworkmapping function, I propose we change to newrxs, newspecs, and newps for the new reactions, species, and parameters.

newrxs, newspecs, newps = subnetworkmapping(lcs[i], rxs, complextorxsmap, p)
newname = Symbol(nameof(rs), "_", i)
push!(subnetworks,
ReactionSystem(reacs, t, specs, newps; name = newname, spatial_ivs))
ReactionSystem(newrxs, t, newspecs, newps; name = newname, spatial_ivs))
end
subnetworks
end
Expand Down Expand Up @@ -475,6 +531,9 @@ function linkagedeficiencies(rs::ReactionSystem)
lcs = linkageclasses(rs)
subnets = subnetworks(rs)
δ = zeros(Int, length(lcs))

# For each sub-reaction network of the reaction network, compute its deficiency. Returns
# the full vector of deficiencies for each sub-reaction network.
for (i, subnet) in enumerate(subnets)
conservationlaws(subnet)
nps = get_networkproperties(subnet)
Expand Down Expand Up @@ -531,11 +590,16 @@ function isweaklyreversible(rn::ReactionSystem, subnets)
im = get_networkproperties(rn).incidencemat
isempty(im) &&
error("Error, please call reactioncomplexes(rn::ReactionSystem) to ensure the incidence matrix has been cached.")

# For each sub-reaction network, caches its reaction complexes.
sparseig = issparse(im)
for subnet in subnets
nps = get_networkproperties(subnet)
isempty(nps.incidencemat) && reactioncomplexes(subnet; sparse = sparseig)
end

# the network is weakly reversible if each sub-network's incidenc graph is strongl
# connec (i.e. each node is reachable from each node).
all(Graphs.is_strongly_connected ∘ incidencematgraph, subnets)
end

Expand Down Expand Up @@ -645,25 +709,43 @@ end

# Used in the subsequent function.
function cache_conservationlaw_eqs!(rn::ReactionSystem, N::AbstractMatrix, col_order)
# Retrieves nullity (the number of conservation laws). `r` is the rank of the netstoichmat.
nullity = size(N, 1)
r = numspecies(rn) - nullity # rank of the netstoichmat
sts = species(rn)
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sts kind of suggests states, which is no longer a thing. I would change to us, but since these are species specifically, I changed this (here and in two calls over the next few lines) to sps.

r = numspecies(rn) - nullity

# Creates vectors of all independent and dependent species (those that are not, and are,
# eliminated by the conservation laws). Get vectors both with their indexes and the actual
# species symbolic variables.
sps = species(rn)
indepidxs = col_order[begin:r]
indepspecs = sts[indepidxs]
indepspecs = sps[indepidxs]
depidxs = col_order[(r + 1):end]
depspecs = sts[depidxs]
depspecs = sps[depidxs]

# Declares the conservation law parameters.
constants = MT.unwrap.(MT.scalarize(only(
@parameters $(CONSERVED_CONSTANT_SYMBOL)[1:nullity] [conserved=true])))

# Computes the equations for (examples uses simple two-state system, `X1 <--> X2`):
# - The species eliminated through conservation laws (`conservedeqs`). E.g. `[X2 ~ X1 - Γ[1]]`.
# - The conserved quantity parameters (`constantdefs`). E.g. `[Γ[1] ~ X1 + X2]`.
conservedeqs = Equation[]
constantdefs = Equation[]

# For each conserved quantity.
for (i, depidx) in enumerate(depidxs)
# Finds the coefficient (in the conservation law) of the species that is eliminated
# by this conservation law.
scaleby = (N[i, depidx] != 1) ? N[i, depidx] : one(eltype(N))
(scaleby != 0) || error("Error, found a zero in the conservation law matrix where "
*
"one was not expected.")
* "one was not expected.")

# Creates, for this conservation law, the sum of all independent species (weighted by
# the ratio between the coefficient of the species and the species which is elimianted.
coefs = @view N[i, indepidxs]
terms = sum(p -> p[1] / scaleby * p[2], zip(coefs, indepspecs))
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This was probably the function i had to look the most at to understand what was going on. In the end I thought that

terms = sum(coef / scaleby * sp for (coef, sp) in zip(coefs, indepspecs))

(p[1] to coef and p[2] to sp)
was clearer enough that I figured I could propose the change.

terms = sum(coef / scaleby * sp for (coef, sp) in zip(coefs, indepspecs))

# Computes the two equations corresponding to this conserved quantity.
eq = depspecs[i] ~ constants[i] - terms
push!(conservedeqs, eq)
eq = constants[i] ~ depspecs[i] + terms
Expand Down Expand Up @@ -695,6 +777,8 @@ Notes:
function conservationlaws(rs::ReactionSystem)
nps = get_networkproperties(rs)
!isempty(nps.conservationmat) && (return nps.conservationmat)

# If the conservation law matrix is not computed, do so and caches the result.
nsm = netstoichmat(rs)
nps.conservationmat = conservationlaws(nsm; col_order = nps.col_order)
cache_conservationlaw_eqs!(rs, nps.conservationmat, nps.col_order)
Expand All @@ -708,13 +792,13 @@ Compute conserved quantities for a system with the given conservation laws.
"""
conservedquantities(state, cons_laws) = cons_laws * state

# If u0s are not given while conservation laws are present, throws an error.
# If u0s are not given while conservation laws are present, throw an error.
# Used in HomotopyContinuation and BifurcationKit extensions.
# Currently only checks if any u0s are given
# (not whether these are enough for computing conserved quantitites, this will yield a less informative error).
# Currently only checks if any u0s are given (not whether these are enough for computing
# conserved quantities, this will yield a less informative error).
function conservationlaw_errorcheck(rs, pre_varmap)
vars_with_vals = Set(p[1] for p in pre_varmap)
any(s -> s in vars_with_vals, species(rs)) && return
any(sp -> sp in vars_with_vals, species(rs)) && return
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We don't really use s as much throughout, changed this to sp which is more commonly used (and also more clearly a species).

isempty(conservedequations(Catalyst.flatten(rs))) ||
error("The system has conservation laws but initial conditions were not provided for some species.")
end
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