More sparse operations support

[alyst]

This PR adds support for more SparseMKL operations:

• dense := sparse * sparse (sp2md!())
• sparse := sparse * sparse (including the in-place one that can optionally disable checks for the sparsity structure) (sp2m(), sp2m!())
• dense := X * A * X^T (syprd!())
• dense := X * X^T (syrk!())

Implementation Details

• while Intel MKL sp2m() supports
  reusing the sparsity structure in principle, it only supports the sparsity structure allocated by Intel MKL.
  It is therefore not possible to directly update the existing SparseMatrixCSC object, reusing the colptr, rowval and updating the nzval only.
  Instead, each sp2m!() call has to recalculate the sparsity structure, so it is not efficient as it could have been.
• Intel MKL syrkd() and
  syprd() routines only support the CSR format and only fill the upper triangular part of the matrix.
  So, while MKLSparse.jl wrappers (syrkd!() and syprd!()) implement CSC support by treating it as a transpose/adjoint of the CSR matrix, it
  does not work for complex numbers and operations like C := a * A^H A + b * C, because transposition trick messes with which half of the hermitian C
  is used. So complex support for syrkd!() and syprd!() is disabled
• Because of these complications, syrkd!() and syprd!() were not "plugged" into mul!() calls like low rank dense BLAS counterparts.
  Also, copytri!() is actually very expensive for large matrices due to cache misses, so doing it by default may result in degraded performance.
• For syprd!() there is also no direct LinearAlgebra call to overload.
  Potentially, MKLSparse.jl may support PDMats.jl via extension mechanism to implement X_A_Xt!() via syprd!().
• syrk() only returns the upper triangular part of the resulting sparse matrix. Since allocating and computing the lower triangular part in that case could be even more expensive than
  for the dense case, syrk(..., copytri=true) is not allowed.
• spmm() and spmmd!() wrappers were added, but as they are just more limited versions of sp2m!() and sp2md!(), they were not tested

[amontoison]

@alyst Can you split the PR to add what is already working?

[alyst]

@amontoison I will rebase it on top of the 2 PRs I have submitted today. I think all of the new operations should be working (I use them in my code), but I would need to fix/add the tests.

[amontoison]

Perfect, thanks @alyst 👍
What we should also try to interface in the future is the sparse preconditioner.

[codecov]

Codecov Report

Attention: Patch coverage is 80.44280% with 53 lines in your changes missing coverage. Please review.

Project coverage is 44.39%. Comparing base (cb0852e) to head (4a7c463).
Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
src/generic.jl	79.50%	25 Missing ⚠️
src/types.jl	40.90%	13 Missing ⚠️
src/interface.jl	80.85%	9 Missing ⚠️
src/mklsparsematrix.jl	93.65%	4 Missing ⚠️
src/utils.jl	88.23%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           master      #50       +/-   ##
===========================================
+ Coverage   32.98%   44.39%   +11.40%     
===========================================
  Files           7        8        +1     
  Lines        1258     1489      +231     
===========================================
+ Hits          415      661      +246     
+ Misses        843      828       -15     

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[alyst]

@amontoison Finally I was able to add the tests for this PR, so it should be ready for review. I've also added "Implementation Notes" section to the PR description to provide some context about what was implemented and what are the limitations.

[amontoison]

@alyst I will review that :)
Do you need the release v2025.0.0 of MKL_jll.jl?

[alyst]

I will review that :) Do you need the release v2025.0.0 of MKL_jll.jl?

Thank you! I think v2025.0 is not required, any v2024 should work as well (v2025 is subject to the same restrictions I've mentioned in the implementation notes).

[amontoison]

LGTM, I merged and tagged a new release 👍