id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
557627188,MDExOlB1bGxSZXF1ZXN0MzY5MTg0Mjk0,3733,Implementation of polyfit and polyval,20629530,closed,0,,,9,2020-01-30T16:58:51Z,2020-03-26T00:22:17Z,2020-03-25T17:17:45Z,CONTRIBUTOR,,0,pydata/xarray/pulls/3733," - [x] Closes #3349
 - [x] Tests added
 - [x] Passes `isort -rc . && black . && mypy . && flake8`
 - [x] Fully documented, including `whats-new.rst` for all changes and `api.rst` for new API

Following discussions in #3349, I suggest here an implementation of `polyfit` and `polyval` for xarray. However, this is still work in progress, a lot of testing is missing, all docstrings are missing. But, mainly, I have questions on how to properly conduct this.

My implementation mostly duplicates the code of `np.polyfit`, but making use of `dask.array.linalg.lstsq` and `dask.array.apply_along_axis` for dask arrays. The same method as in `xscale.signal.fitting.polyfit`, but I add NaN-awareness in a 1-D manner. 
The version with numpy is also slightly different of `np.polyfit` because of the NaN skipping, but I wanted the function to replicate its behaviour. It returns a variable number of DataArrays, depending on the keyword arguments (coefficients, [ residuals, matrix rank, singular values ] / [covariance matrix]).
Thus giving a medium-length function that has a lot of duplicated code from `numpy.polyfit`.  I thought of simply using a `xr.apply_ufunc`, but that makes chunking along the fitted dimension forbidden and difficult to return the ancillary results (residuals, rank, covariance matrix...).

Questions: 
1 ) Are the functions where they should go?
2 ) Should xarray's implementation really replicate the behaviour of numpy's? A lot of extra code could be removed if we'd say we only want to compute and return the residuals and the coefficients. All the other variables are a few lines of code away for the user that really wants them, and they don't need the power of xarray and dask anyway.","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/3733/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,pull