Support for xp.linalg.lu (not yet part of the Array API spec)

[ogrisel]

Context adding LU factorization to the Array API spec:

• RFC: add support for LU factorization in the linalg extension array-api#627

Since numpy.linalg.lu does not exist yet (but scipy.linalg.lu does), @rgommers suggested working out an API candidate as part of array-api-compat first by reviewing the API choices and options implemented in various libraries targeting Array API support.

A short term implementation for numpy could probably delegate the work to scipy.linalg.lu in a first iteration.

Based on this work, numpy.linalg could subsequently be extended to directly implement the correct API to be submitted for a future revision of the spec.

Motivation: this is needed to add Array API support to the randomized linear algebra solver for the Principal Component Analysis estimator in scikit-learn:

• ENH Array API support for PCA scikit-learn/scikit-learn#26315

Non exhaustive list of available implementations:

• scipy.linalg.lu
• cupyx.scipy.linalg.lu
• torch.linalg.lu
• jax.scipy.linalg.lu
• dask.array.linalg.lu
• ...

Related methods in scipy:

• scipy.linalg.lu_factor
• scipy.linalg.lu_solve

[rgommers]

Thanks @ogrisel! It looks like you only have a single usage in scikit-learn (here), with lu(x, permute_l=True), so if that is covered you should be good for now, right?

I think for the API design decisions, it's best to put them on data-apis/array-api#627. And then let's implement it here. I'll try to post some thoughts there within the next few hours.

[ogrisel]

It looks like you only have a single usage in scikit-learn (here), with lu(x, permute_l=True), so if that is covered you should be good for now, right?

Yes, this is also what I found out via git grep.

[ntessore]

If numpy support relied scipy.linalg.lu(), could this be implemented by conditionally adding lu() to numpy-compat's linalg namespace only when scipy is installed, and not making scipy a requirement?

[rgommers]

That sounds like the right thing to do to me, we don't want this package to have a direct dependency on scipy.

[asmeurer]

Based on the scope of array-api-compat, lu should be added first to a draft version of the standard. Then we can add it here. It's better to discuss design specifics of it in the array-api repo. For actual implementations, it would be better to discuss that with specific libraries.

Regarding the scipy question, if lu were added, I wouldn't see an issue with making only that function (in the numpy wrapper) depend on scipy.

[asmeurer]

Closing this as it's out of scope here as long as lu isn't in the standard. The better place for it to go as long as it isn't is the array-api-extra package https://github.com/data-apis/array-api-extra