Feature Wishlist

[NAThompson]

• 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?

[ckormanyos]

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?).

[ckormanyos]

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

[NAThompson]

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.

[octopus-prime]

• fixed sized polynomials without allocation
• corresponding polynomial solvers, e.g. analytic, bairstow, companion matrix

[NAThompson]

@octopus-prime : Yup. Also that reminds me: Jenkins-Traub.

[cosurgi]

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.

[sebweb3r]

first and second derivative for interpolations (exist sometimes)
2d interpolation

[NAThompson]

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)

[NAThompson]

@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 . . .

[mrityunjay-tripathi]

What else is a natural fit for the library, and is useful?

• Dirichlet Distribution Dirichlet Distribution #317

[mborland]

From discussion with the SciPy Maintainers:

• Symplectic ODE solver The case for Symplectic Solvers in ODE Solver scipy/scipy#12690
• logcdf for statistical distributions Add logcdf to distributions  #946
• entropy for statistical distributions
• Add support for complex arguments to appropriate statistical distributions
• Make develop branch work with Scipy BLD: Boost.Math standalone submodule scipy/scipy#17432