Automatic differentiation of pfaffian

[Gertian]

As mentioned in #142 we implemented backwards differentiation for the pfaffian in this PR.

To do this we created a package extension stored which is automatically loaded when chainsrulecore is. This way there is minimal overhead when the user does not need this functionality.

Special thank to @https://github.com/lkdvos for figuring out a proper test using the build in ChainsRuleTestUtils package !

[Gertian]

For now I marked this PR as a draft since I'm still figuring out if all required functionality has been added.

In particular I'm still struggling with things such as : ``gradient(x->pfaffian(x), skewhermitian(rand(4,4))[ [1,2],[1,2] ])'' this might however not be a problem.

[codecov]

Codecov Report

❌ Patch coverage is 84.61538% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.60%. Comparing base (01329c0) to head (5fd7793).
⚠️ Report is 11 commits behind head on main.

Files with missing lines	Patch %	Lines
ext/SkewLinearAlgebraChainRulesCoreExt.jl	84.61%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #143      +/-   ##
==========================================
- Coverage   89.82%   88.60%   -1.22%     
==========================================
  Files          10       10              
  Lines        1572     1659      +87     
==========================================
+ Hits         1412     1470      +58     
- Misses        160      189      +29     

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[Gertian]

The 1.6 versions are failing because we are using package extensions which were not yet included before v1.9.
This does not affect the performance apart from the AD part though !

Nightly fails for unknown reasons.

Codecov is slightly lowered but I don't see a way to get it back to where it was.

I'll put this PR into ready for review now.

[Gertian]

I just noticed that something is still wrong with the constructor. I'll try to figure this out tomorrow.

[Gertian]

@stevengj , thanks for your input.

I'll use the extension for a few days to see if any more unexpected bugs pop up. If not I think this is ready for merging if you also agree.

[Gertian]

I've been using this for a few days now and don't seem to notice any bugs , I'll tag this ready for review.

[Gertian]

@stevengj so what do we do with this ? :)

[stevengj]

Some failing CI tests, but the logs have expired and they need to be re-run.

[stevengj]

package extensions require Julia 1.9, I think?

[stevengj]

should be a version bump to 1.1 for a new feature.