I need to evaluate BesselK function at about ten million points. I know scipy.special supports this as scipy.special.kv(n, x), but I want a faster evaluation as well as a memory efficient evaluation. Ideally numexpr would be good, and I tried numexpr.evaluate("kv(n, x)") as well as numexpr.evaluate("besselk(n,x)") but both did not work. Does anyone know the exact command for BesselK in numexpr?
The numexpr docs list the supported functions, and, alas, Bessel functions are not in it.
http://numexpr.readthedocs.io/projects/NumExpr3/en/latest/user_guide.html
You can try looking around for alternative implementations, e.g. from GSL or boost, but frankly I doubt the speed difference is going to be non-trivial, if any at all.
What might be relevant is avoiding the loops over the points on the python side. Either just use array-valued arguments to scipy.special.kv or drop to Cython and use the cython_special version with looping in Cython.