Sparse representation of stoichiometric matrices functions and matrices in complex-based functions

[yewalenikhil65]

from #386 (comment)

example. We use a second function argument of type Bool to switch sparsity on or off. Default is dense representation as earlier, i.e.sparsity=false

rn = @reaction_network begin
    k₁, 2A --> B
    k₂, A --> C
    k₃, C --> D
    k₄, B + D --> E
end k₁ k₂ k₃ k₄

julia> substoichmat(rn)   # usual function or substoichmat(rn,false)
4×5 Matrix{Int64}:
 2  0  0  0  0
 1  0  0  0  0
 0  0  1  0  0
 0  1  0  1  0

julia> substoichmat(rn,true)     # sparse representation
4×5 SparseMatrixCSC{Int64, Int64} with 5 stored entries:
 2  ⋅  ⋅  ⋅  ⋅
 1  ⋅  ⋅  ⋅  ⋅
 ⋅  ⋅  1  ⋅  ⋅
 ⋅  1  ⋅  1  ⋅

[yewalenikhil65]

I think conservationlaws also needs a sparse version.

[isaacsas]

@yewalenikhil65 have a deadline today for a report I need to submit -- I'll review both your PRs this weekend. (And yes, the conservation law methods should get a sparse version at some point too, but we can save that for a separate PR just to keep this easier to review.)

[yewalenikhil65]

@yewalenikhil65 have a deadline today for a report I need to submit -- I'll review both your PRs this weekend. (And yes, the conservation law methods should get a sparse version at some point too, but we can save that for a separate PR just to keep this easier to review.)

No problem!

[isaacsas]

@yewalenikhil65 take a look and let me know your thoughts on the changes. Mainly I made sparse=true a keyword to use for picking a sparse matrix. This is consistent with some of the usage in ModelingToolkit functions.

[isaacsas]

I also should have made all matrices have columns = reactions now.

[yewalenikhil65]

@yewalenikhil65 take a look and let me know your thoughts on the changes. Mainly I made sparse=true a keyword to use for picking a sparse matrix. This is consistent with some of the usage in ModelingToolkit functions.

This looks nice, exactly how i imagined.. Thanks!
I was also little concerned of https://github.com/yewalenikhil65/Catalyst.jl/blob/6a2b79eafac8376586c5483491d8980d5da7dd17/src/networkapi.jl#L473
does transposing here add any considerable computational cost ? I remember conversation thread regarding SNF to be made optimized later or searching for alternative LinearAlgebra based methods

Anyway, i will get back to fixing PR In ReactionNetworkImporters after you release new Catalyst version

[yewalenikhil65]

Is it good idea to be using SparseMatrixCSC{Int,Int} entries ? i also remember some conversation thread in Catalyst issues to leave scope for non-integer stoichiometries later probablt in furture

[isaacsas]

For now it's fine. When we get generalized stoichiometry we'll have to think about what to do here. We don't want it to be type Any, so we may need some extra preprocessing to figure out the type, or we just error and don't allow these functions when there is symbolic stoichiometry.

[isaacsas]

@yewalenikhil65 take a look and let me know your thoughts on the changes. Mainly I made sparse=true a keyword to use for picking a sparse matrix. This is consistent with some of the usage in ModelingToolkit functions.

This looks nice, exactly how i imagined.. Thanks!
I was also little concerned of https://github.com/yewalenikhil65/Catalyst.jl/blob/6a2b79eafac8376586c5483491d8980d5da7dd17/src/networkapi.jl#L473
does transposing here add any considerable computational cost ? I remember conversation thread regarding SNF to be made optimized later or searching for alternative LinearAlgebra based methods

Anyway, i will get back to fixing PR In ReactionNetworkImporters after you release new Catalyst version

I don't think this should be a big cost relative to computing the SNF, so using the transpose shouldn't be an issue. I think what @YingboMa was maybe suggesting is that we should implement and use the Bareiss method instead of SNF for finding the nullspace basis.