WIP: chainrules

[Jutho]

ChainRulesCore.jl implementation of the factorization rrules.

Work in progress: still to add LQ case, and maybe eig(h)_trunc support. Also qr_null and lq_null support. Maybe direct left/right_orth and left/right_null support?

[codecov]

Codecov Report

Attention: Patch coverage is 96.66667% with 9 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
ext/MatrixAlgebraKitChainRulesCoreExt.jl	90.81%	9 Missing ⚠️

Files with missing lines	Coverage Δ
src/MatrixAlgebraKit.jl	100.00% <ø> (ø)
src/common/pullbacks.jl	100.00% <100.00%> (ø)
src/common/safemethods.jl	100.00% <100.00%> (+33.33%)	⬆️
src/implementations/lq.jl	98.05% <100.00%> (ø)
src/implementations/qr.jl	97.16% <100.00%> (ø)
src/pullbacks/eig.jl	100.00% <100.00%> (+100.00%)	⬆️
src/pullbacks/eigh.jl	100.00% <100.00%> (+100.00%)	⬆️
src/pullbacks/lq.jl	100.00% <100.00%> (ø)
src/pullbacks/polar.jl	100.00% <100.00%> (ø)
src/pullbacks/qr.jl	100.00% <100.00%> (+100.00%)	⬆️
... and 2 more

... and 3 files with indirect coverage changes

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[Jutho]

I think this is more or less ready for a review.

[lkdvos]

It's a bit much for me to fully double check all of the math, but from what I can tell this definitely looks good. (and an absolute impressive amount of work, both on the implementations but also on the tests, hats off!)

Up to the minor comments I left, I think this would be okay to merge for me. I can't say that I am fully following the comments on all of the gauge warnings and tolerances close enough, but I see you left quite a bit of room for customization so I'm guessing we'll just have to play around with it.