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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