If you are interested in the hypergeometric numerical evaluation, it's > probably a good idea to take a look at this recent master's thesis > written on the problem: > > http://people.maths.ox.ac.uk/porterm/research/pearson_final.pdf<http://bl-1.com/click/load/BDEKOABvUWAAYgNhATc-b0231> > > The thesis is really comprehensive and detailed with quite convincing conclusions on the methods to be used with varying a,b,x (though I am yet to read the thesis properly enough understand and validate each of the multitude of the cases for the boundaries for the parameters). It seems to be an assuring and reliable walk through for the project.
> This may give some systematic overview on the range of methods > available. (Note that for copyright reasons, it's not a good idea to > look closely at the source codes linked from that thesis, as they are > not available under a compatible license.) > > It may well be that the best approach for evaluating these functions, > if accuracy in the whole parameter range is wanted, in the end turns > out to require arbitrary-precision computations. In that case, it > would be a very good idea to look at how the problem is approached in > mpmath. There are existing multiprecision packages written in C, and > using one of them in scipy.special could bring better evaluation > performance even if the algorithm is the same. > Yeah, this seems to be brilliant idea. mpmath too, I assume, must have used some of the methods mentioned in the thesis. I ll look through the code and get back. I am still unaware of the complexity of project expected at GSoC. This project looks engaging to me. Will an attempt to improve both Spherical harmonic functions ( improving the present algorithm to avoid the calculation for lower n's and m's) and hypergeometric functions be too ambitious or is it doable? Regards Jennifer > -- > Pauli Virtanen > >
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