Fix type promote in case b is complex

[ma-sadeghi]

Fixes #398

[codecov[bot]]

Codecov Report

Merging #399 (d3bc1ce) into main (1c679c6) will increase coverage by 0.20%. Report is 2 commits behind head on main. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #399      +/-   ##
==========================================
+ Coverage   69.72%   69.92%   +0.20%     
==========================================
  Files          26       26              
  Lines        1965     1965              
==========================================
+ Hits         1370     1374       +4     
+ Misses        595      591       -4     

Files	Coverage Δ
src/common.jl	89.28% <100.00%> (-1.79%)	:arrow_down:
src/factorization.jl	75.86% <ø> (+0.43%)	:arrow_up:

... and 1 file with indirect coverage changes

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[ChrisRackauckas]

add a test?

[ma-sadeghi]

add a test?

Sure! Just to clarify, do you want to test the "complex" part or the "tol-type-mismatch"? If the former, I was thinking of adding a complex prob3 to basictests.jl

[ChrisRackauckas]

It would be nice to catch both things, but at least showing the behavior on complex should be done since that's a non-trivial interaction I didn't immediately guess.

[ChrisRackauckas]

Tests are failing

[ma-sadeghi]

All tests are passing except for MKL and SVD. From the error messages, I think the MKL wrapper doesn't support complex systems, but not sure what's going on with SVD.

[ChrisRackauckas]

Yes the MKL_jll direct wrapper doesn't support complex, so mark that as broken.

SVD, mark as broken and open a Base Julialang issue.

[ChrisRackauckas]

oh actually that seems like an issue with the cache construction, so ArrayInterface should get some updates and tests for SVD initialization on complex

[ChrisRackauckas]

https://github.com/JuliaArrays/ArrayInterface.jl/blob/master/src/ArrayInterface.jl#L669

The SVD instance creation is only based on A, so the arrays are all complex typed. Should we just always convert b? I think that in order to hit the fast LAPACK functions it's required that b is complex as well and converts internally?

[ma-sadeghi]

Thanks for the fixes. Quick question: Should we fix formatting here or in a separate PR (formatter complains about ext/LinearSolveEnzymeExt.jl, ext/LinearSolveIterativeSolversExt.jl, src/appleaccelerate.jl, src/default.jl, src/mkl.jl, test/basictests.jl, test/default_algs.jl, test/enzyme.jl, test/resolve.jl).

[ChrisRackauckas]

in a separate PR. Right now we're checking if the new format is sufficient and will format all of SciML at the same time.