[WIP] Attempting to wrap randomized SVD

[kshyatt]

Attempted to wrap the randomized SVD method which relies on oversampling and the power method. Definitely open to some interface improvements here! Also, the ugly look of the tests suggests perhaps we should extend diagview a little...

[codecov]

Codecov Report

❌ Patch coverage is 97.64706% with 4 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/implementations/orthnull.jl	90.47%	2 Missing ⚠️
ext/MatrixAlgebraKitCUDAExt/yacusolver.jl	97.05%	1 Missing ⚠️
src/implementations/svd.jl	98.64%	1 Missing ⚠️

Files with missing lines	Coverage Δ
ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl	86.66% <100.00%> (ø)
...MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl	86.66% <100.00%> (+0.95%)	⬆️
src/MatrixAlgebraKit.jl	100.00% <ø> (ø)
src/common/gauge.jl	100.00% <100.00%> (ø)
src/implementations/eig.jl	100.00% <100.00%> (ø)
src/implementations/eigh.jl	98.41% <100.00%> (ø)
src/implementations/gen_eig.jl	100.00% <100.00%> (ø)
src/implementations/lq.jl	98.62% <100.00%> (ø)
src/implementations/polar.jl	100.00% <100.00%> (ø)
src/implementations/qr.jl	96.31% <100.00%> (ø)
... and 4 more

... and 1 file with indirect coverage changes

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[Jutho]

I haven't looked at this in detail yet. Do you think CUSOLVER_Randomized should be a valid argument for svd_full! given the warning note in the doc string? Wouldn't this make more sense as a svd_trunc! algorithm ?

[kshyatt]

Could well do better there since for best performance/accuracy k should be much much smaller than min(m,n). I can switch it in the morning.

[kshyatt]

The reason I didn't do this at first I think is that Xgesvdr expects U, S, and V to be full sized, which is rather annoying...

[lkdvos]

I do have somewhere on my todo list to make the check_input function also take the algorithm, would that help here?

I think I agree with Jutho though, that this might make more sense as an svd_trunc implementation, with some restrictions on the possible truncation strategies of course.

[kshyatt]

If we can modify check_input then that seems fine to me! I could do that as part of this PR, even?

[lkdvos]

Looks good to me! I left some minor comments, but otherwise I'm happy to merge. (GPU CI runs now right?)

[kshyatt]

CI does now run!