Enhance numerical stability of Savitzky-Golay coefficient computation. #1
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Added a numerically stabilised version of the Savitzky Golay filter computation as described in Scipy Issue #20825 scipy/scipy#20825 (comment)
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The adaption mentioned here seems possible without loss of accuracy. |
…y avoiding the explicit computation of the pseudoinverse
…h `np.linalg.lstsq`
…tion for the super stabilised Savitzky Golay coefficients - in this context, the derivative pre-factor was incorporated into the correction factors as a single rather than multiple multiplications
…on coefficients of the super stabilised Savitzky Golay coefficients. It does not provide any benefit and `math.factorial` is more direct. Yet, it's a micro-optimization.
…this could ever be encountered in this context
…/ 2`` in super stabilised Savitzky Golay coefficient computation by using a simplified solution in this case - made relative error test in main truly insensitive to ZeroDivision (`inf` was never used in case of zero division because Python does not evaluate lazily) - added a more extensive test for the coefficients against the correct solution to main to avoid thing like the first bullet point happening
…Golay coefficients safe against floating point errors in the zero-check
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This PR adds a numerically stabilised version of the Savitzky Golay filter computation as described for the Scipy Issue #20825 in this comment.