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