[Numpy-discussion] Change in default behavior of np.polyfit

[Andreas Nußbaumer]

Hi,

in [1] the scaling factor for the covariance matrix of `np.polyfit` was
discussed. The conclusion was, that it is non-standard and a patch might be
in order to correct this. Pull request [2] changes the factor from
chisq(popt)/(M-N-2) to chisq(popt)/(M-N) (with M=number of point, N=number
of parameters) essentially removing the "-2". Clearly, this changes the
result for the covariance matrix (but not the result for the polynomial
coefficients) and therefore the current behavior if `cov=True` is set.

It should be noted, that `scipy.optimize.curve_fit` also uses the
chisq(popt)/(M-N) as scaling factor (without "-2"). Therefore, the change
would remove a discrepancy.

Additionally, patch [2] adds an option that sets the scaling factor of the
covariance matrix to 1 . This can be useful in occasions, where the weights
are given by 1/sigma with sigma being the (known) standard errors of
(Gaussian distributed) data points, in which case the un-scaled matrix is
already a correct estimate for the covariance matrix.

Best,
Andreas

[1]
http://numpy-discussion.10968.n7.nabble.com/Inconsistent-results-for-the-covariance-matrix-between-scipy-optimize-curve-fit-and-numpy-polyfit-td45582.html
[2] https://github.com/numpy/numpy/pull/11197
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