I have been sampling random numbers from different distributions and just realized how slow are numpy binomial random numbers compared to other distributions. For instance
%timeit for x in range(100): np.random.binomial(100,0.5)
10000 loops, best of 3: 82.6 µs per loop
%timeit for x in range(100): np.random.uniform()
100000 loops, best of 3: 14.6 µs per loop
A binomial number takes 6 times more than a uniform one! This can be understandable, since binomial is discrete and requires a more complex transformation. But for instance if I ask for a binomial with a number of trials n=0 or n=1 the time spent is similar:
%timeit for x in range(100): np.random.binomial(0,0.5)
10000 loops, best of 3: 78.8 µs per loop
%timeit for x in range(100): np.random.binomial(1,0.5)
10000 loops, best of 3: 80.1 µs per loop
This does not seem very efficient because the result of these samplings should be trivial: For zero trials, the results should be always zero and for 1 trial it should be a simple Bernoulli trial. So for instance a faster implementation of the binomial would be:
import numpy as np
def custombinomial(n,p):
if n == 0:
return 0
if n == 1:
x = np.random.uniform()
if x<p:
return 1
else:
return 0
else:
return np.random.binomial()
And here is the timing:
%timeit for x in range(100): custombinomial(0,0.5)
100000 loops, best of 3: 11.8 µs per loop
%timeit for x in range(100): custombinomial(1,0.5)
10000 loops, best of 3: 31.2 µs per loop
I am sure this could be improved for even larger values of n. Is there any reason I am missing for numpy being so slow? Is there any other library that can give faster random numbers (even if it includes some sort of C/Cython)?
Also, additionally, I know that numpy is good if I want to create a bunch of random numbers at the same time i.e. get an array of binomially distributed numbers, but in many cases the parameters of the distribution n and p will change on the fly, so the call of individual random numbers would not be directly an option. Would it be possible an alternative in which an array of uniformly distributed random numbers is generated and they are transformed in the particular binomials as they are required?.
