Speeding up a big a loop with a logarithm in Python

Question

I'm trying to speed up the following code:

from math import log
from random import random

def logtest1(N):
    tr=0
    for i in range(1,N):
        T= 40 + 10*random()
        tr += -log(random())/T

I'm fairly new to python (coming from matlab)... and this same code runs 5x slower in python than matlab (and Julia), which got my attention.

I tried using a numba and a parakeet wrapper, and numpy functions instead of python ones, but didn't get any improvement at all.

I'd appreciate any help. Thanks.

edit: the whole thing is a Monte Carlo simulation, so N is very large... 10e6 for testing purposes

Answer 1

You should really be looking into numpy. And Scipy, while you're at it. Numpy is a speed-optimized package for N-dimensional array numerics, and Scipy is a collection of scientific computing stuff built upon numpy.

If you write the function using numpy arrays, it looks like this:

def logtest2(N):
    T = 40. + 10. * np.random.rand(N)
    return np.sum(-1*np.log(np.random.rand(N)) / T)

It's also a lot faster. Testing with N = 1000000 gave me a runtime of 500ms for your version and 75ms for this one.