implement in-place ldiv! for Cholesky factorization

[ranocha]

I have implemented an in-place ldiv! for Cholesky factorizations of sparse matrices.

Closes #319
Closes #275
Closes #123
Xref https://discourse.julialang.org/t/is-there-no-ldiv-for-choleski-factorization-of-a-sparse-matrix/114806

Caveats

The method works locally but is not as elegant as the UMFPack/LU version or the other code in the CHOLMOD wrapper:

• UMFPack accepts arrays/pointers directly whereas CHOLMOD uses cholmod_dense structs.
• The Dense wrappers in the Julia CHOLMOD module allocate new arrays.

Thus, the code looks a bit different from the remaining code in the file.

The current method still allocates some memory on my system since we do not provide the workspace vectors Handle_Y and Handle_E. We could store them in the CHOLMOD.Factor struct. I tried that, but they were still C_NULL after the call to solve2 (when initialized with C_NULL). Thus, re-using them is not working as I understand the docs. Thus, I have not added this complexity to this PR.
Maybe related: DrTimothyAldenDavis/SuiteSparse#45

Questions

Shall we announce this somewhere in some form of NEWS.md so that people can adopt to this change?

[codecov]

Codecov Report

Attention: Patch coverage is 84.78261% with 7 lines in your changes missing coverage. Please review.

Project coverage is 84.16%. Comparing base (4141e8a) to head (fcf34fb).
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/solvers/cholmod.jl	84.78%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #547      +/-   ##
==========================================
+ Coverage   84.07%   84.16%   +0.09%     
==========================================
  Files          12       12              
  Lines        9067     9106      +39     
==========================================
+ Hits         7623     7664      +41     
+ Misses       1444     1442       -2     

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[ViralBShah]

cc @dkarrasch @rayegun

[ranocha]

@ViralBShah @dkarrasch @rayegun Does any of you have some time to review this PR?

[ViralBShah]

I will take a look today. Also hoping someone else can in addition.

[rayegun]

With the exception that I'm not clear if Dense inputs are tested sgtm. Will merge once that has an answer

[ViralBShah]

This looks straightforward. Merging. The PR just looked much bigger because of all the whitespace changes.

I'd like to hold this PR until I resolve a couple of docs issues that need to get backported into 1.11 - which I hope will be in a day or two.

[ranocha]

Thanks a lot! I'm sorry for the confusing with the whitespace changes - VSCode did all that for me and I didn't notice before

[ViralBShah]

Is it possible to add a docstring?

[ranocha]

It does not differ from the standard ldiv! behavior, so I didn't add a docstring - many people expect it to just work as discussed in the issues linked above. Would you prefer an explicit docstring? If so, I can add one

[ViralBShah]

Yeah good point. Not necessary.

[ranocha]

Thanks a lot for your reviews! Do you know which Julia version will include this patch?

[ViralBShah]

It will go on Julia master when we bump SparseArrays.jl - happens every few days, and then go into 1.12.

[ranocha]

Thanks!