Fix torch linalg cholesky_ex

[Daniel4078]

PR Description

Related Issue

Closes #28772

Checklist

• Did you add a function?
• Did you add the tests?
• Did you run your tests and are your tests passing?
• Did pre-commit not fail on any check?
• Did you follow the steps we provided?

Socials

[Daniel4078]

@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.

[Sam-Armstrong]

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!

[Sam-Armstrong]

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

[Daniel4078]

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 (

ivy/ivy/functional/ivy/linear_algebra.py

Line 2143 in 5665437

ret

) and they seem to work fine.

[Sam-Armstrong]

Ah yeah, I think this is fine on second thought. Thanks a lot @Daniel4078!