Complex balancing

[vyudu]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

A first pass at the complex-balance implementation. Does not seem like Graphs.jl has a matrix-tree implementation, so I have the matrix tree implementation here for now, but I'll work on adding it as a PR to Graphs.jl (and in particular implementing a method of generating the spanning trees that doesn't simply generate every combination of n-1 edges).

[isaacsas]

Let me start by saying this is a great first PR!

Here are a first set of comments -- these are more general Julia practices / Catalyst internals comments than method specifc or performance specific.

I need to finish going through the paper and then I will give a second review more focused on the algorithmic details, but you can at least address these for now.

[isaacsas]

@vyudu can you merge master into this? Do you know how to do that? (If not I can explain to you on Slack.)

I usually use Gitkraken to do that as I find it easier than merging via the commandline.

[TorkelE]

I second that GitKraken is a really nice tool, if you haven't checked it out yet.

[isaacsas]

Can you add one more test that uses a network that is complex balanced with multiple nonlinearities and non-trivial rate expressions (i.e. reactions like k1*k2, 3A + 2B --> 3*C)? Just to stress the code a bit more.

In terms of performance optimization I think that can be a followup. So I'm happy to merge once you address this last set of comments.

[isaacsas]

CI is still failing?

[isaacsas]

This looks like it might have been rebased on an older version of master?

[isaacsas]

Maybe try merging master into your PR?

[isaacsas]

(Generally I find it easier to merge instead of rebase to update a PR.)

[TorkelE]

@vyudu I tried to merge this onto master for you, but couldn't get it to work unfortunately. If you check the "Files changed" tab at the top of the PR you see that there are a very large number of changes:

What probably have happened is that this was a PR of some branch, and then it got rebased on an updated master, and somewhere some of the changes of the branches it originally was branched off of was carried through when this one was rebased on the master again.

Since you are developing on your own master branch, I would try (as Sam pointed out here, and to me earlier) to simply merge your master branch with Catalyst's master branch, and then push the PR again. If that does not work out, and the changes introduced here are very straightforward (i.e. just adds functions at the bottom of the network_analysis.jl file, and some tests) it might be easiest to simply copy these into a new, clean, branch and make a new PR from that.

[isaacsas]

Thanks @vyudu great first PR.

[TorkelE]

Thanks @vyudu great first PR.

Second that! And sorry for giving you poor advice on the rebase/merge thing. I tried @isaacsas's method properly now as well and it works great

[vyudu]

Thank you both!