Change matrix format to CSC in depletion

[eepeterson]

Description

This PR is related to #2703, but is just looking at changing the matrix format (no change to the solver method) since in my test case this reduces the time spent in CRAM by more than 25% (for IndependentOperator calculations). The majority of the speed up is actually just from setting the matrix format of ident = sp.eye(A.shape[0], format='csc') to be compatible with A prior to looping over the residues and also works for CSR format. The motivation to change to CSC is to avoid SparseEfficiencyWarnings and repeated conversions from CSR to CSC once we introduced explicit LU factorization as outlined in #2703. My idea here was to work through restructuring any necessary regression tests here to make sure we aren't making depletion less accurate. Interestingly enough the CSC format change results in fewer negative density warnings as shown in the files attached (it's not the addition of the factorization like I originally thought)

One test case didn't pass locally, although I did confirm that the resulting atom numbers coming out of CRAM agree to within a relative tolerance of 1e-14 between this patch and develop. I believe the error is resulting from the calculated reaction rates in the transport run done when final_step=True.

Below are the profile outputs for this problem:

no_patch.txt
csc_patch.txt

Update after merging #2771 and #2779: This PR offers negligible speed up (but at least no slow down) while reducing the number of negative density warnings, plus is more efficient for future work to be carried out in #2703 (see updated outputs below).

with_no_csc_patch.txt
with_csc_patch.txt

Checklist

• I have performed a self-review of my own code
  - [ ] I have run clang-format (version 15) on any C++ source files (if applicable)
• I have followed the style guidelines for Python source files (if applicable)
• I have made corresponding changes to the documentation (if applicable)
  - [ ] I have added tests that prove my fix is effective or that my feature works (if applicable)

[drewejohnson]

Thanks for breaking this out.

If the performance improvement is really due to having csc layout everywhere, then this feels better. But if we can get similar speedup by ensuring that all the matrices used are the same layout, even existing csr, and we don't get the same changes to the regression suite, that is preferable to me.

I know the change to csc also influences the LU factorization from #2703, so that's another thing to contend with. And I know there are potential some CI / local machine differences that are not easy to solve. And we have a whole bevy of other tests that pass without updates. I'm being kind of a wet blanket to try to understand sources of benefit and potential problems.