Cache some properties

[Illviljan]

Cache some small properties that are rather slow to calculate but doesn't change that often.

Questions that needs to be resolved:

• Can these properties change during the lifetime of the class? If so the cache needs to be reset when that happens.

• Related to Should we cache some small properties? #3514
• Tests added
• Passes pre-commit run --all-files
• User visible changes (including notable bug fixes) are documented in whats-new.rst
• New functions/methods are listed in api.rst

Notes

• Mixin classes makes it difficult to cache properties. For example ndim in NdimSizeLenMixin cannot be easily be replaced with cache_readonly.

[github-actions]

Unit Test Results

         6 files           6 suites   53m 11s ⏱️
16 200 tests 14 465 ✔️ 1 735 💤 0 ❌
90 396 runs  82 221 ✔️ 8 175 💤 0 ❌

Results for commit 59bd433.

♻️ This comment has been updated with latest results.

[max-sixty]

Thanks for kicking this off @Illviljan .

My concern with this is that adding the _cache nullifies the benefits of slots. @keewis do you have any thoughts?

It also sounds like the speed-ups I was seeing might not be real. Probably we should have an ASV so there's a benchmark we're all looking at.

[Illviljan]

The case I'm optimizing is dataset interpolation with many variables. Although it's not the bottleneck there I halved the shape time from ~180ms to ~92ms with this change.

[max-sixty]

Resurrecting this, as discussed on the dev call.

Could we replace the pandas decorator with the one from the standard library? That may require adding __dict__ as a slot.

Then as long as the benchmarks still look good, there was consensus that we should merge.