Simone Carlo Surace

The issue is that currently [this](#1320) fails, so the easiest would be to write two rules, one for `cholesky` and one for `cholesky!`, but I'd rather first merge this in...

> The in place reverse mode cholesky rule is going to be harder because the out of place one from Michel makes an assumption about the aliasing usage of the...

See #1320, i.e. writing a rule for `cholesky!` won't be sufficient because the stuff in `cholcopy` fails to differentiate.

I would suggest merging this now, keeping the focus to the correctness, and making the `cholesky!` rule in another PR. As for tooling, two things would be helpful in my...

> > See #1320, i.e. writing a rule for `cholesky!` won't be sufficient because the stuff in `cholcopy` fails to differentiate. > > Seems like that's an Enzyme issue that...

> FWIW, I think the safest way to go is to only define the rules only for `LAPACK.potrf!`, which are necessary until Enzyme can differentiate through LAPACK code. I don't...

Please add your questions as comments to specific lines and I'll try to answer to the best of my knowledge. Edit: I won't be able to really explain `_cholesky_pullback_shared_code` beyond...

@sethaxen I wrote some tests from scratch using EnzymeTestUtils. They have the known limitations. I'm not sure that is better than the previous situation. We still have some disagreements about...

That's great, looking forward to it.

I'll look into it