Fastest way to calculate exponential [exp()] function of large complex array in Python

Question

I'm developing code that integrates an ODE using scipy's complex_ode, where the integrand includes a Fourier transform and exponential operator acting on a large array of complex values.

To optimize performance, I've profiled this and found the main bottleneck is (after optimizing FFTs using PyFFTW etc) in the line:

val = np.exp(float_value * arr)

I'm currently using numpy which I understand calls C code - and thus should be quick. But is there any way to further improve performance please?

I've looked into using Numba but since my main loop includes FFTs too, I don't think it can be compiled (nopython=True flag leads to errors) and thus, I suspect it offers no gain.

Here is a test example for the code I'd like to optimize:

arr = np.random.rand(2**14) + 1j *np.random.rand(2**14)
float_value = 0.5
%timeit np.exp(float_value * arr)

Any suggestions welcomed thanks.

Answer 1

We could leverage numexpr module, which works really efficiently on large data involving transcendental operations -

In [91]: arr = np.random.rand(2**14) + 1j *np.random.rand(2**14)
    ...: float_value = 0.5
    ...: 

In [92]: %timeit np.exp(float_value * arr)
1000 loops, best of 3: 739 µs per loop

In [94]: import numexpr as ne

In [95]: %timeit ne.evaluate('exp(float_value*arr)')
1000 loops, best of 3: 241 µs per loop

This seems to be coherent with the expected performance as stated in the docs.