How does this compare to Scipy's implementation?

[jorenham]

Scipy has scipy.special.hyp2f1, which is implemented in cython: https://github.com/scipy/scipy/blob/v1.11.3/scipy/special/_hyp2f1.pxd.

So just out of curiousity; how does this specfunc implementation compare against Scipy's one?

[fedro4]

Hi,
Its bin a long time since I last used these, so take this with a grain of salt, but from looking at my README, I guess the main difference is that this implementation allows all arguments to be complex valued (which I needed for my usecase at the time), while the Scipy implementation only allows z, but not a, b, or c, to be complex:

I think mpmath did provide hypergeometric functions with complex-valued arguements, and I use it as a fallback, but it was too slow for my usecase.

So if you need complex valued arguments, this might be something for you. Otherwise, you're probably better of just using the Scipy variant.

[Didou09]

@fedro4 thanks for implementing this, I'll probably need to use it.
I've used mpmath python library to handle complex arguments thus far, but it is indeed slow.

How much faster would you estimate this implementation to be on large numpy arrays ?

[fedro4]

I don’t recall specific numbers, as it has been years ago… but i think for my usecase, it was at least an order of magnitude faster, if not several… unlike mpmath (at the time?), it directly operates on numpy arrays.
If I recall correctly, it’s really a rather straightforward calculation of the sums, basically just hoping they converge without further tricks, which worked susprisingly well for hypergeometric functions (but not so much for parabolic cylinder functions).
My Suggestion would be that, should you decide to use it, you start by implementing this in a way that let’s you switch between this and mpmath, so you can compare the Speed and ensure consistent results.