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Feature Wishlist
- Modified Clenshaw recurrence for all special functions governed by 3-term recurrence relations.
- Higher dimensional interpolation (Akima has a natural generalization to higher dimensions, but there's some work on getting the API correct.)
- Prolate spheroidal wavefunctions
- Higher dimensional quadrature; sparse grids for medium dimensionality, extensions of Gaussian quadrature in lower dimensions.
- Wavelet transforms, shearlets
- Bivariate interpolation and quadrature at the Padua points
What else is a natural fit for the library, and is useful?
What else is a natural fit for the library, and is useful?
- Make further progress on zeta, phi and friends (Lerch phi transcendent, polylog, and more).
- Extend constants to higher precision such as 10,000 decimal digits and get them tested.
- Evaluate recent progress in the literature on Bernoulli number generation (can we save memory and/or time compared with extracting Bn from tangent numbers?).
What else is a natural fit for the library, and is useful?
- Legendre functions and associated Legendre functions of arbitrary (non-integer real) order and degree.
- More special functions of complex argument, particularly on the unit disk. Gamma should be a reasonable place to start. Perhaps complex orthogonal polynomials if these are calculated from straightforward recursion.
- FFT
Friends, if you don't mind, I'm going to clean up this thread since it kinda got off topic and many of the off-topic issues have been resolved.
- fixed sized polynomials without allocation
- corresponding polynomial solvers, e.g. analytic, bairstow, companion matrix
Did you notice recent discussion about FFT in mailing list? I think it would be great if math supported FFT for all multiprecision types, especially quad-double, which is currently in the works. And please note that it's not possible to use libfftw as a backend for quad-double.
first and second derivative for interpolations (exist sometimes) 2d interpolation
I think every interpolator has the first derivative implemented. Second derivatives of the quintic B-spline are implemented. Other interpolators have the wrong spectral properties and perform poorly on second derivatives.
2D interpolation is coming! (Akima + pchip)
@cosurgi : Totally agree it would be useful, but I really like FFTW and it satisfies all my needs, so other things are a higher priority. I don't know who has the skillset to take on such a difficult task . . .
What else is a natural fit for the library, and is useful?
- Dirichlet Distribution #317
From discussion with the SciPy Maintainers:
- Symplectic ODE solver https://github.com/scipy/scipy/issues/12690
- logcdf for statistical distributions #946
- entropy for statistical distributions
- Add support for complex arguments to appropriate statistical distributions
- Make develop branch work with Scipy https://github.com/scipy/scipy/pull/17432
