EDIT(lucascolley): please keep the conversation below for higher-level topics, and use https://github.com/scipy/scipy/wiki/Array-types-support-information-tracker to jot down notes related to implementing these changes.

See gh-18286 for the proposed design changes, and gh-18668 for the main PR that laid the foundations (it supported all of scipy.cluster, added a CI job that used both pytorch-cpu and numpy.array_api, and documented the design patterns).

This issue is to track the current status of support across submodules, and other larger tasks/TODOs. Submodules:

• scipy.cluster ENH: add machinery to support Array API #18668
• scipy.constants ENH: constants: add array api support #20593
• scipy.datasets ENH: datasets: array API standard support #20594 (no changes needed)
• scipy.fft ENH: fft: support array API standard #19005
• scipy.fftpack # Don't do, fftpack is legacy
• scipy.integrate (see ENH: integrate: add array API standard support #20930 - PRs welcome!)
• scipy.interpolate
• scipy.io (no changes needed - all functions involve I/O through host memory)
• scipy.linalg (in progress, see ENH: linalg: array library interoperability #19068)
• scipy.misc # Don't do, will be removed
• scipy.ndimage (initial conversion done in ENH: ndimage: add array API standard support #21150, follow-up tracked in TST/MAINT: ndimage: follow-ups for array API standard support #21280)
• scipy.odr
• scipy.optimize
• scipy.signal ENH: signal: add array API standard support #20678
• scipy.sparse # TBD on whether to update functions in that namespace; the data structures are a different type of task, see ENH: sparse: first pass at array API standard compat #20190
• scipy.sparse.csgraph
• scipy.sparse.linalg
• scipy.spatial
• scipy.special (initial set of functions done in ENH: special: dispatch to array library #19023)
• scipy.stats (see ENH: stats: add array API-support #20544 - PRs welcome!)

Desirable for later:

• Once we're more confident that everything is in good shape, see if we should start emitting warnings for input types that may see a change in behavior (see this comment).
• Write a policy for cases where one wants to change existing pure Python code with array API support to compiled code (for performance improvements with numpy). See this comment).
• Figure out if and how to deal with mixing multiple array types coming from the same library (see this comment).
• Once JAX and/or Dask are supported in the array-api-compat package, add support for them in SciPy (both can be tested in CI too). (JAX done in ENH: array types: add JAX support #20085, Dask WIP at ENH: array types: add dask.array support #20956)
• CuPy isn't testable in (free) CI easily, but it could be done (e.g. https://betatim.github.io/posts/github-action-with-gpu/ or with https://cirun.io/). Shouldn't be done before all this becomes stable/supported. Update 22 Oct 2024: it's about time now, see CI: adding a GPU-enabled CI job #21740.