DOC: interpolate: Extrapolation tips and tricks

[ev-br]

Reference issue

closes gh-16338, closes gh-14386, closes gh-14472

What does this implement/fix?

Add a tutorial page with several worked examples of extrapolation--- handling out-of-bounds data --- in several interpolators. In general, extrapolation is not entirely consistent in scpy.interpolate, default modes are not always useful, and in some cases manual work on the user side is needed. There are four examples, of both using the existing keyword switches etc, and DIY implementations.

Additional information

Two out of four examples are provided by users, in gh-14386 and gh-14472. Am crediting the users in the commit messages, will comment on the issues to see if they want to be listed as commit co-authors.

[ev-br]

CI failures are unrelated, as it is a pure DOC change.

[mdhaber]

Since this is all new and the information is correct/useful, I think we can merge this pretty quickly.

I agree that this closes the issues if you think it would make the API too messy to include options for these things.

I've only made it halfway through. Next pass I'll start from "Manually implement the asymptotic".

[ev-br]

I think the last commit addresses all review suggestions.

[j-bowhay]

A few minor comments

[ev-br]

Thanks Jake for the review, I tried to address your comments in the last commit in this branch.

[mdhaber]

I wanted to finish my review, but the rendered artifacts are not available right now for some reason (looks like a CircleCI issue). Since I'm not very familiar with these functions, the rendered documentation is important, so I'll have to come back. I'll try to look at the rest (starting at "Manually Implement the Asymptotics") on Thursday.

[j-bowhay]

Thanks @ev-br that is my comments addressed

[mdhaber]

My original comments have been resolved, I don't have any new ones, and this is very useful. Thanks @ev-br @j-bowhay!

[mdhaber]

Oh, the only question is what we should do about co-authorship of @chausies. I see you asked whether they'd like to be credited, but there is no response. What would you like to do? Besides #14472 (comment), you can usually find real email addresses by adding .patch to the URL of any commit. e.g., https://github.com/chausies/myconfigs/commit/b33ded48276f9bcdfcee667c4b7c9dad783cc9e0.patch .

[ev-br]

I think the lack of response on GH for a reasonable time can be interpreted as a lazy agreement to the attribution in the commit message of 4237531 --- this used the information which is already made public by @chausies.

The comment on gh-14386 has two weeks, we can probably wait some more.

[ev-br]

Thanks Matt, Jake for the reviews!