Associated Legendre Polynomials

[raminammour]

Hello,

I was evaluating some spherical harmonics implementations and found the implementation here to be competitive with GSL for example (which is great!). Looking at the function sphevaluate it is easy to see that hidden inside would be an implementation of the associated Legendre polynomials.

The codes does a few extra flops (division/multiplication by pi, cos/sin) and the usual obscure normalization factors :)

It would be great the associated Legendre polynomial can be pulled out, and exported from this package. Maybe even contributed to some other julia package (SpecialFunctions?). It would be a very competitive pure julia implementation.

Any help is appreciated, and thanks for a nice package,

Cheers!

[raminammour]

Sorry about the noise, just found: JuliaMath/SpecialFunctions.jl#136

[dlfivefifty]

That PR looks like it’s going nowhere. If you wanted to pull this out and make a new PR that might fair better.

[raminammour]

Sorry, I meant this one JuliaMath/SpecialFunctions.jl#175, which looks more promising :)

[MikaelSlevinsky]

The Clenshaw--Smith recurrence relation (evaluating expansions with bases satisfying three-term recurrence relations) is a perfect candidate for vectorization since it costs O(mn) flops but only requires O(m+n) storage to evaluate an m-term expansion at n points. One day, I may add such generic code in the C library this wraps using Intel SIMD so that they're ccallable.