MKL Pardiso direct linear solver support.

[bodono]

Add interface for the MKL Pardiso direct linear solver, add some tests and docs.

[bodono]

@odow @kalmarek - I'm 99.9% sure this isn't a breaking change for Julia but PTAL and let me know.

BTW - the MKL version of the direct solver can be much faster, so if the user has MKL installed in their Julia it might be worth investigating how to link against it for all the LAPACK / BLAS usages as well as the linear solver after this lands.

[kalmarek]

@bodono thanks, this looks great, I'm eager to try it!

Does it need something special from oneAPI, or just MKL?
If it's just MKL, we could easily ship it via another @Requires as e.g. DirectSolverMKL by adding build-time dependancy to SCS_jll build @odow.

[bodono]

It only uses pardiso, so I believe it's just MKL but would need to be tested.

[kalmarek]

So I tried to make it work, and here is a proof of concept:
https://gist.github.com/kalmarek/50755885b33f6ffd9dba0959df03388f
(you will need to define JULIA_HOME and set mkldirect in SCS_MKL.jl to run it).

I managed to compile and locally deploy SCS_MKL_jll without problem, but due to "complicated relationships in mkllibs family" you can't just using MKL prior using SCS. TLDR: mklibs reference symbols which they don't define and don't link with libs that define those. Note the --no-as-needed flag. For more information you can amuse yourself by reading JuliaPackaging/Yggdrasil#1075.

Unfortunately I don't see a way around it (except manually dlopening the required libs) so I'm afraid we won't have a smooth experience with SCS & MKL in julia land. Maybe @odow has more ideas?

[bodono]

Hmmm, that's annoying. I also found it a bit tricky to get the install right on all machines that I tried, I needed quite a lot of flags, see here, and the link at the comment above that line. I'm a bit surprised that Julia isn't able to figure it out with using MKL and using SCS as you say, but you know better than I do.

[kalmarek]

As far as I understand that's something that needs to be done at runtime (by e.g. detecting the capabilities of the cpu). That's not what julia jll system is created for. Theoretically we could dlopen the necessary libs in package __init__, but I wouldn't dare to register it in this state ;)