Implement weighted groupby

[dcherian]

• xref compose weighted with groupby, coarsen, resample, rolling etc. #3937
• 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

Initial proof-of-concept. Suggestions to improve this are very welcome.

Here's some convenient testing code

import xarray as xr

ds = xr.tutorial.open_dataset('rasm').load()
month_length = ds.time.dt.days_in_month
weights = month_length.groupby('time.season') / month_length.groupby('time.season').sum()

actual = ds.weighted(month_length).groupby("time.season").mean()
expected = (ds * weights).groupby('time.season').sum(skipna=False)
xr.testing.assert_allclose(actual, expected)

I've added info to the repr

ds.weighted(month_length).groupby("time.season")

WeightedDatasetGroupBy, grouped over 'season'
4 groups with labels 'DJF', 'JJA', 'MAM', 'SON'.
weighted along dimensions: time by 'days_in_month'

[dcherian]

Pulled out combine because the inheritance order is DatasetGroupBy → DatasetGroupByArithmetic → ImplementsDatasetReduce → IncludeReduceMethods . That last one overwrites the reductions on WeighedGroupBy if it inherits from DatasetGroupBy

[dcherian]

This attempt subclasses GroupBy and works as .weighted().groupby()

@shoyer let me know what you think