ENH: Option to return covariance matrix of fitted coeffecients for polynomial fitters

[tom-bird]

This is for fitters in the polynomial module.

Implementation is the same as numpy.polyfit.

See issue #7780. Was sent round the mailing list last week - no complaints.

[maxnoe]

This would be really helpful for us moving from numpy.polyfit to the options recommended by the docs.

What's the status here?

[maxnoe]

why is cov and full mutually exclusive? Shouldn't it be something like if full and not cov , elif cov and not full ....

[tom-bird]

I suppose it is a little ambiguous. I was just copying the style of polyfit to keep it consistent: https://github.com/numpy/numpy/blob/d9b1e32cb8ef90d6b4a47853241db2a28146a57d/numpy/lib/polynomial.py#L639-L6419

[mattip]

We discussed this at a recent triage meeting and the general opinion was to add a function fit_with_covariance instead of adding another kwarg. It would be nice to move this forward for feature parity.

[charris]

The changes should be mostly be in polyutils._fit. Note that it is private, so you can add arguments.

la.inv(np.dot(lhs.T, lhs)) is not a great way to compute the covariance matrix, but probably OK for well posed problems.

Docstrings need .. versionadded:: lines for the cov argument.

Maybe we should add a slot for the covariance in the polynomial base class? That would allow transformation of domain and polynomial basis types to track it. The default value would be None.

Note that number of degrees of freedom used to estimate the measurement variance can become uncertain, depending on how the weights are used and whether some variables are lost due to the condition number.

[mattip]

I am going to close this since it has been inactive for nearly two years. It still would be nice to get a fit_with_covariance function. Please feel free to reopen and continue or open a new PR to move this forward.