cholesky factorization Hermitian non-real in diagonal

[KlausC]

Fixes #37356

In case a complex entry is stored in the parent matrix of an Hermitian, consider only the real part when doing Cholesky factorisation.
After change in the generic implementation now in line with LAPACK.

[codecov-commenter]

Codecov Report

Merging #37382 into master will decrease coverage by 0.00%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master   #37382      +/-   ##
==========================================
- Coverage   87.08%   87.07%   -0.01%     
==========================================
  Files         357      357              
  Lines       72058    72039      -19     
==========================================
- Hits        62751    62731      -20     
- Misses       9307     9308       +1     

Impacted Files	Coverage Δ
stdlib/LinearAlgebra/src/matmul.jl	95.73% <0.00%> (-0.83%)	⬇️
base/missing.jl	91.62% <0.00%> (-0.53%)	⬇️
base/promotion.jl	83.50% <0.00%> (-0.52%)	⬇️
stdlib/SparseArrays/src/linalg.jl	95.18% <0.00%> (-0.29%)	⬇️
base/gmp.jl	88.34% <0.00%> (-0.26%)	⬇️
base/loading.jl	83.42% <0.00%> (-0.03%)	⬇️
stdlib/SparseArrays/src/sparsevector.jl	95.60% <0.00%> (+0.17%)	⬆️
base/bitset.jl	92.85% <0.00%> (+0.44%)	⬆️
base/tuple.jl	94.86% <0.00%> (+0.72%)	⬆️
base/namedtuple.jl	95.41% <0.00%> (+0.72%)	⬆️
... and 2 more

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[stevengj]

Looks like you messed up a rebase/merge and got a whole bunch of unrelated commits into this branch.

You'll probably want to create a new branch on your machine off of master, cherry-pick your commits from this branch, and force push to this branch to clean up the PR.

[lkapelevich]

Is anything else needed to merge this?

[KlausC]

Is anything else needed to merge this?

Not from my side.