Separate Algorithm and Driver - part II (SVD)

[lkdvos]

Follow-up on #178 to improve on #176.

This consists of quite a few more opinionated changes that I think are warranted but might not be completely fair.

I have renamed a bunch of the LAPACK-like functions across YALAPACK/YAROCSOLVER/YACUSOLVER in an attempt to make life slightly easier, and simply merge all of the implementations into a single big @eval loop.

In the meantime, I also changed the GLA implementations to actually copy in-place, as this is something that has come up quite a few times already and I think overall this is probably more convenient anyways.

The jacobi-svd algorithm that only worked for LAPACK with m >= n is now also implemented for m < n by making use of the same svd_via_adjoint pattern that was already present in some of the GPU solvers, which is now also shared.

---

I think overall this manages to delete quite a bit of code, but the eval loops are also somewhat hard to follow so I'm not sure if this is all that much "simpler" implementation-wise, but at least it does allow selecting DivideAndConquer in a driver-agnostic way.

[Jutho]

Some suggestions but otherwise looks great.

[lkdvos]

@kshyatt I think this one is good to go, only CUDA seems to somehow go out of memory and I'm confused why this is only now happening. I reduced the sizes a bit, but if this doesn't end up helping I might just call this unrelated to this PR and we should go ahead with merging this one.

[github-actions]

After the build completes, the updated documentation will be available here

[codecov]

Codecov Report

❌ Patch coverage is 90.83333% with 11 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms.jl	44.44%	5 Missing ⚠️
src/implementations/svd.jl	92.85%	4 Missing ⚠️
...ixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl	92.85%	1 Missing ⚠️
src/interface/svd.jl	50.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
...MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl	74.13% <100.00%> (+4.13%)	⬆️
ext/MatrixAlgebraKitCUDAExt/yacusolver.jl	96.12% <100.00%> (+0.37%)	⬆️
ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl	84.84% <100.00%> (-1.07%)	⬇️
src/MatrixAlgebraKit.jl	100.00% <ø> (ø)
src/common/defaults.jl	64.28% <ø> (ø)
src/common/gauge.jl	100.00% <100.00%> (ø)
src/implementations/lq.jl	95.06% <ø> (ø)
src/implementations/qr.jl	95.08% <ø> (ø)
src/interface/decompositions.jl	76.19% <ø> (+5.82%)	⬆️
src/yalapack.jl	85.37% <100.00%> (ø)
... and 4 more

... and 1 file with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.