I'd like to be able to get a quicker low accuracy computation of the argument of the complex-valued JacobiTheta1 function.
I only need as much accuracy as to get a decent plot, which means... I don't know... about 1e-3 relative accuracy?
If I can get a formula or approach that is "evalhf'able" then I can construct a procedure which does this action and writes results inplace to a float Matrix.
The naive approach in the code below takes about 6min to compute on a fast Intel i7. I'm hoping for something closer to 5sec.
I confess that I haven't yet studied the topic in any depth. I was wondering if anyone had any suggestions, before I waste time on the wrong tracks.
Digits:=5: # Not a big speedup, and maybe not wise.