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DOC: update testing docs for alternative backends #20844

@fancidev

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@fancidev

Is your feature request related to a problem? Please describe.

In a recent PR from me (gh-20766), 6/14 commits and 6/9 CI runs are used to address Array API incompatibility. This created unnecessary burden on the CI infrastructure and lengthens the development cycle.

Describe the solution you'd like.

I’d like to improve the situation by running those compatibility tests locally.

Ideally, I’d like to have the following:

  1. An option in dev.py to run all the backends for xp-compatible tests. (Or maybe, do this by default.) Update: the option (-b) already exists.
  2. Update the dev doc to advertise this option. Update: DOC/DEV: mention -b option in contributor guide on testing #20849
  3. Maybe update requirements.txt to include the alternative backends.

Describe alternatives you've considered.

The first thing I did after seeing the CI errors was to install Jax, array_api_strict, and pytorch. I looked at the CI log to learn how to install them. (Basically with the [cpu] option.) Then I played a bit with each of them in a Jupyter Notebook. This helps understanding some of the errors, and I tested that the fixes at least work with the numpy backend. However, because I don’t know how to run the tests with other backends, I leave to the CI to run them.

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    DXEverything related to making the experience of working on SciPy more pleasantDocumentationIssues related to the SciPy documentation. Also check https://github.com/scipy/scipy.orgarray typesItems related to array API support and input array validation (see gh-18286)

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