On Tue, Aug 4, 2020 at 4:55 AM Ralf Gommers <ralf.gomm...@gmail.com> wrote:
> > > On Tue, Aug 4, 2020 at 1:49 AM Chris Vavaliaris <cv1...@wildcats.unh.edu> > wrote: > >> PR #16999: https://github.com/numpy/numpy/pull/16999 >> >> Hello all, >> this PR adds the two 1D Chebyshev transform functions `chebyfft` and >> `ichebyfft` into the `numpy.fft` module, utilizing the real FFTs `rfft` >> and >> `irfft`, respectively. As far as I understand, `pockefft` does not support >> cosine transforms natively; for this reason, an even extension of the >> input >> vector is constructed, whose real FFT corresponds to a cosine transform. >> >> The motivation behind these two additions is the ability to quickly >> perform >> direct and inverse Chebyshev transforms with `numpy`, without the need to >> write scripts that do the necessary (although minor) modifications. >> Chebyshev transforms are used often e.g. in the spectral integration of >> PDE >> problems; thus, I believe having them implemented in `numpy` would be >> useful >> to many people in the community. >> >> I'm happy to get comments/feedback on this feature, and on whether it's >> something more people would be interested in. Also, I'm not entirely sure >> what part of this functionality is/isn't present in `scipy`, so that the >> two >> `fft` modules remain consistent with one another. >> > > Hi Chris, that's a good question. scipy.fft is a superset of numpy.fft, > and the functionality included in NumPy is really only the basics that are > needed in many fields. The reason for the duplication stems from way back > when we had no wheels and SciPy was very hard to install. So I don't think > there's anything we'd add to numpy.fft at this point. > > As I commented on your PR, it would be useful to add some references and > applications, and then make your proposal on the scipy-dev list. > > Chebfun <https://github.com/chebfun/chebfun> is based around this method, they use series with possibly thousands of terms. Trefethen is a big fan of Chebyshev polynomials. Chuck
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