@Sam-Armstrong This experimental function is supposed to quckly and directly returning the LAPACK error codes (https://www.netlib.org/lapack/lug/node136.html) as its return when the normal cholesky would fail, by directly checking for the error before calcuating the cholesky value (https://pytorch.org/docs/stable/generated/torch.linalg.cholesky_ex.html). Though I don't know how to implement and test for that behavior. Though the tests are passing for now it seems.

I don't think you need to implement/test the LAPACK error codes right now, that's probably out of scope for the moment.

I think we can just return a regular tuple rather than a named tuple, I know the torch function returns a named tuple, but practically I don't think there would really be a difference and I'm concerned that the named tuple could possibly cause problems for the transpiler. Otherwise the changes look good. Thanks @Daniel4078!

The reason why I use named tuple is that some other backend functions like ivy.svd did already return named tuple (