Use AbstractSparseMatrixCSC for sparse factorizations

[j-fu]

This e.g. would allow to supply a matrix type with multithreaded factorization etc. Would solve #190.

However, see https://github.com/JuliaSparse/SparseArrays.jl/issues/265 .

[codecov[bot]]

Codecov Report

Merging #273 (82da413) into main (a7b7d2b) will decrease coverage by 35.12%. The diff coverage is 47.05%.

@@             Coverage Diff             @@
##             main     #273       +/-   ##
===========================================
- Coverage   70.97%   35.86%   -35.12%     
===========================================
  Files          14       11        -3     
  Lines         858      764       -94     
===========================================
- Hits          609      274      -335     
- Misses        249      490      +241     

Impacted Files	Coverage Δ
src/LinearSolve.jl	60.00% <ø> (-36.56%)	:arrow_down:
src/factorization.jl	33.63% <46.66%> (-49.49%)	:arrow_down:
src/default.jl	38.55% <50.00%> (-15.67%)	:arrow_down:
src/factorization_sparse.jl	0.00% <0.00%> (-100.00%)	:arrow_down:
ext/LinearSolveHYPRE.jl	0.00% <0.00%> (-92.60%)	:arrow_down:
src/preconditioners.jl	21.42% <0.00%> (-58.58%)	:arrow_down:
src/solve_function.jl	63.63% <0.00%> (-36.37%)	:arrow_down:
src/iterative_wrappers.jl	53.88% <0.00%> (-23.44%)	:arrow_down:
... and 5 more

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[ChrisRackauckas]

Anywhere that assumes it's a sparsematrixcsc should not remove the conversion because that could concrete things like MatrixOperators of SparseMatrixCSC. For things that are already concrete matrices it should be a no-op so that's fine, and then afterwards it should assert it's an AbstractSparseMatrixCSC and use the sparse matrix functions on it.

[j-fu]

:+1:

[j-fu]

Hi,I think we need a version update for LinearSolvePardiso.jl as well to bring this in place there.

[ChrisRackauckas]

It should probably be changed into an extension package in the near future.