Add svdsolve AD rule

[pbrehmer]

This PR adds a reverse-rule for svdsolve which implements the truncated SVD adjoint recently derived in this pre-print. See also PR #83.

[pbrehmer]

For the first commit I mostly copied the code from QuantumKitHub/PEPSKit.jl#15 and adapted it a bit to KrylovKit. As of now, this is untested but the PEPSKit version runs correctly and produces results that are consistent with the TensorKit SVD reverse-rule. However, this PR does need a bit of help to get it fully running @lkdvos.

[lkdvos]

Great, thanks!
( I had in mind merging it into #83 first, such that I can immediately make it part of the package extension 😄 )
I'll try and have a look at this later this week!

[Jutho]

Am I correct that this only works for the case where A is an explicit matrix?

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 98 lines in your changes are missing coverage. Please review.

Project coverage is 75.16%. Comparing base (4e8e1fa) to head (d9779c4).

Files	Patch %	Lines
ext/KrylovKitChainRulesCoreExt/svdsolve.jl	0.00%	49 Missing ⚠️
src/adrules/svdsolve.jl	0.00%	49 Missing ⚠️

Additional details and impacted files

@@               Coverage Diff                @@
##           ad-extension      #84      +/-   ##
================================================
- Coverage         77.40%   75.16%   -2.25%     
================================================
  Files                30       31       +1     
  Lines              2957     2851     -106     
================================================
- Hits               2289     2143     -146     
- Misses              668      708      +40     

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[pbrehmer]

Am I correct that this only works for the case where A is an explicit matrix?

Yes, I forgot to add that. I wasn't sure how KrylovKit internally handles the abstract vector types and what would be the best way to rewrite things like U = hcat(lvecs...) as well as the matrix multiplications that are performed.

[lkdvos]

@pbrehmer , I edited this PR so it now points to the branch on the main repository. Can you still move the implementation to the extension folder? I think I can merge after

[pbrehmer]

I think this should do the job? I hope this is mergeable now.

[Jutho]

Ok, I pushed some updates to the ad-extension branch, but now there is a conflict again. Can I resolve it (this will also push to your master) or do you want to rebase from your side?

[pbrehmer]

Can I resolve it (this will also push to your master) or do you want to rebase from your side?

Yes sure, you can go ahead and resolve it (and push), thanks!