florisvb / PyNumDiff / 33272953939

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Make waveletdiff's derivative an FFT, and stop integer input truncating derivatives

Phi and Phi_prime are both circulant, so the DFT diagonalizes them and Phi_prime @ Phi^-1 becomes multiplication by the single transfer function fft(phi')/fft(phi), replacing a sparse LU on a (3N-2)-square matrix with an FFT pair: 20-41x faster and identical to 5e-13. Five methods allocated outputs with np.empty_like, inheriting an integer input's dtype and silently truncating derivatives, and the five taking dt_or_t now require it strictly increasing rather than accepting reversed or repeated timestamps. polydiff hands polyfit sqrt(kernel), since polyfit weights the unsquared residual, so a sample weighs the same fitting a window as blending windows; its test settings move to degree 5 and window 15, tightening five bounds by a decade.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

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