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@ogrisel @glemaitre this is the per-test setting PR.

By the way I can also review this PR as is (as an internal refactoring) without thinking about third party developer API first and defer the third party estimator API to a later PR.

@ogrisel I plan to write a new page for "how to write your estimator" anyway, but a bit later. These will certainly find their way there.

I also plan to expose this functionality to third party devs, but first prefer to be mostly done with test refactoring, since during this phase we're gonna add/remove/rename a lot of tests. But I added a note in the code to remember this point.

allow registering custom test data generators per-estimators

Yeah I was happy that, that part of the code could be removed, but when we get to supporting non-numerical data for estimators, that test-generator-registration is gonna be necessary anyway. So it'll come.

Maybe you might want to see if test_pca_array_api_compliance could be refactored as part of this PR to check that the new infra is expressive enough for this use case?

Alternatively we can do it in a follow-up.

I see. That's easy to include, but needs a tiny bit of restructuring. Happy to do that, but rather keep these PRs as small as it gets so that we move forward fast. I can work on that once we merge this PR.

@ogrisel note that the test you mention has two issues:

test_pca_array_api_compliance basically is running two tests:

• check_array_api_input_and_values: This somehow lives under estimator_checks.py but is NOT a part of the common tests. It's an alias for check_array_api_input(..., check_values=True), while check_array_api_input(..., check_values=False) is in common tests.
• check_array_api_get_precision: This is in test_pca.py and is not a part of the common tests, so I'm not sure if it's relevant here.

This seems like something we should tackle separate from this PR.