Let’s get back to the statistical module, that will calculate an Hypergeometric Distribution (HD) p value so we can define the overrepresented motifs. Last time we saw it, we just had defined the factorial function, which is immensely helpful in this case due to the number of factorial calculations needed in the HD. The factorial function was the one below


def fac(n):
    value = reduce(lambda i, j : i * j, range(1, n + 1))
    return value

but as mentioned in the comments by Dave and by Mike via email the method used is not the best method to calculate factorial in Python. The best approach in this case is to use operator.mul. All functions in the operator modules are in implemented in pure C and they mimic the same operators in Python. So in this module we can find mul for multiplication, sub for subtraction, add for additions, etc.

The operator.mul needs two arguments to multiply, and in our case we still need to use reduce to sum all the results from a series of multiplications. As parameters we should use a range, that can start with 2, that should go up to the number we want the factorial plus one. Finally our function would be 


import operator

def fac(n):
    value = reduce(operator.mul, xrange(2, n+1))
    return value

The time gain, quickly measured in a non-scientific fashion in my system, is around 5 to 15%, depending on the factorial being calculated. It may seem a small gain, but when you need to calculate almost a million factorials for all possible motifs the amount of time saved is crucial. Next time we will be back with more statistics, expanding the module.

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