\ does not work for sparse matrices with Float32 elements

[ViralBShah]

As discussed in https://stackoverflow.com/questions/70648351/getting-an-error-when-using-backslash-operator-on-sparse-matrix-and-dense-vector/70662601#70662601, \ does not work for sparse matrices with Float32 elements.

It would be nice to bring back Float32 support in sparse solvers. The issue is that \ calls lu!, which does not have a matching method. Naturally lu! should not promote, but \ should check and promote.

[KristofferC]

I think the core problem is that you cannot change between float32 and float64 support in suitesparse during runtime.

Edit: Actually JuliaLang/julia#14076 (comment) says that it's not even supported.

[rayegun]

It's not supported in at least UMFPACK and KLU. I think there's promotions to Float64 somewhere, they just may not be available in the \ interface. I'm not sure about CHOLMOD.

[dkarrasch]

The issue with the given problem is that the sparse matrix is recognized as Hermitian, so it gets wrapped as Hermitian(A). The next step would be that SuiteSparse.jl takes over, but it doesn't because this signature is too narrow:

https://github.com/JuliaLang/SuiteSparse.jl/blob/2f355a266ac3439c98c531f0fc774bcccb2dd43d/src/cholmod.jl#L1568-L1585

It should perhaps be widened to include all those nzval-types that get promoted to Float64 if necessary.

[ViralBShah]

Note that CHOLMOD does not support Float32, but UMFPACK does (and Julia should probably as well).

We do emit the warning for CHOLMOD

┌ Warning: 2022-06-21 14:36:17 : CHOLMOD only works with double precision. Converting single precision matrix to double
└ @ Circuitscape ~/.julia/packages/Circuitscape/XpftG/src/logging.jl:25

So what we need to do is what @dkarrasch suggests above.