ENH: new function `interp`

[ev-br]

suggested at scipy/scipy#22343 (comment)

[lucascolley]

first bit of due diligence: https://github.com/data-apis/array-api/issues?q=interp is blank

[rgommers]

That definitely won't fly as part of the standard.

[lucascolley]

The NumPy implementation is in C at https://github.com/numpy/numpy/blob/c23886c226012a50da11066d3be98fd94e571101/numpy/_core/src/multiarray/compiled_base.c#L552-L719

[ev-br]

Linear interpolation is certainly possible to write in pure python, here's one implementation (most likely, quite overengineered): https://github.com/scipy/scipy/blob/v1.15.2/scipy/interpolate/_interpolate.py#L457

One np.interp's feature to be careful about is its left and right arguments. Naively they are basically, out[x > x[-1]] = right; out[x < x[0]] = left, so need to take care of immutable arrays.

[lucascolley]

This sounds like a perfect candidate for a Python implementation in array-api-extra, then, for as long as https://scipy.github.io/devdocs/tutorial/interpolate/1D.html#piecewise-linear-interpolation continues to direct to NumPy.

[lucascolley]

next question: would interp be the best name @ev-br ? Or is there anything else that is more clear and doesn't clash with existing (semantically-different) functions?

[ev-br]

IMO, yes.

xpx.pad is a drop-in replacement for np.pad; xpx.kron is a drop-in replacement for np.kron, xpx.interp is a drop-in replacement for np.interp.

The ecosystem is already too crowded with variant functions for linear interpolation, which are almost but not completely unlike each other.