Adapt to TensorKit v0.15

[lkdvos]

This is a minimal set of changes needed to make this package compatible with TK v0.15.

In the long run, it might be nice to consider making some more substantial changes to further reduce the required code here, while migrating some of it to MatrixAlgebraKit.
I'm listing some of these suggestions here as a reminder:

• PolarNewton is an algorithm for computing the polar decomposition, which we can directly implement in MatrixAlgebraKit.
• _left_polar! could be replaced with MatrixAlgebraKit.left_polar! if we adopt a strategy that is similar to the one we have for QR decompositions -- providing an empty R to indicate that we do not wish to compute R.
• The various project(anti)hermitian functions might also be reasonable in MatrixAlgebraKit.

For now though, I'd prefer to just leave that for the future and get this merged, so also MPSKit can be updated.
Before tagging a new release, we could consider switching the formatter, and optionally migrating the repository to use the shared github actions.

[codecov]

Codecov Report

❌ Patch coverage is 78.12500% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.28%. Comparing base (fdc9112) to head (950fcad).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/TensorKitManifolds.jl	37.50%	5 Missing ⚠️
src/auxiliary.jl	94.11%	1 Missing ⚠️
src/unitary.jl	66.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #17      +/-   ##
==========================================
+ Coverage   73.38%   74.28%   +0.89%     
==========================================
  Files           5        5              
  Lines         620      591      -29     
==========================================
- Hits          455      439      -16     
+ Misses        165      152      -13     

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[Jutho]

Why not use MAK.qr_compact! for this?

[Jutho]

same for the other qr! calls below.

[lkdvos]

Because this is the compact form that is immediately in-place multiplied into a different matrix below, so technically that's doing an additional multiplication lmul! below. I'm not sure if it really matters, but it felt a bit weird to change this into something slower if it was working before :)

[Jutho]

On this evening's flight, I will try to spend some time on TensorKitManifolds.jl, to indeed properly migrate some functionality to MatrixAlgebraKit and update it to TensorKit 0.15. Let's see where I land (hopefully Krakow, but you get the point).

[lkdvos]

@Jutho, do you mind if I tag and release this as a patch version already? I think this counts as non-breaking, and it is holding back MPSKit from using the new TensorKit version (and therefore also PEPSKit and TNRKit). Definitely happy to improve to more MatrixAlgebraKit implementations afterwards.

[Jutho]

Ok sure.