The Problem With Converting Long Int To Float In Python

Question

[Gahoo]

I want to implement the equation(cumulative hypergeometric distribution) in this article with python.

Here are the codes:

from math import factorial

def Binomial(n,k):
    if n > k:
        return factorial(n) / (factorial(k)*factorial(n-k))
    elif n == k:
        return 1

def Hypergeometric(x,m,n,N):
    return 1.0*Binomial(m,x)*Binomial(N-m,n-x)/Binomial(N,n)

def HypergeometricCDF(x,m,n,N):
    cdf=0
    for i in range(x,min(m,n)+1):
        cdf+=Hypergeometric(i,m,n,N)
    return cdf

print HypergeometricCDF(5,40,50,500)
print HypergeometricCDF(50,400,500,5000)

It will raise "OverflowError: long int too large to convert to float". But without converting to float,you would get 0.How to deal with large numbers like this in python? Are there any better ways to calculate cumulative hypergeometric distribution in python?

Answer 1

[Will]

The problem is that with genomic scales the NchooseK operation produces giant numbers that often cause overflows in python. The trick is to use the log-nchoosek operations since this will keep even th elargest numbers within a reasonable range.

You can check out my gist here: git://gist.github.com/1051335.git

or this:

from math import log, exp
from mpmath import loggamma

def logchoose(ni, ki):
    try:
        lgn1 = loggamma(ni+1)
        lgk1 = loggamma(ki+1)
        lgnk1 = loggamma(ni-ki+1)
    except ValueError:
        #print ni,ki
        raise ValueError

    return lgn1 - (lgnk1 + lgk1)

def gauss_hypergeom(X, n, m, N):
    """Returns the probability of drawing X successes of m marked items
     in n draws from a bin of N total items."""

    assert N >= m, 'Number of items %i must be larger than the number of marked items %i' % (N, m)
    assert m >= X, 'Number of marked items %i must be larger than the number of sucesses %i' % (m, X)
    assert n >= X, 'Number of draws %i must be larger than the number of sucesses %i' % (n, X)
    assert N >= n, 'Number of draws %i must be smaller than the total number of items %i' % (n, N)

    r1 = logchoose(m, X)
    try:
        r2 = logchoose(N-m, n-X)
    except ValueError:
        return 0
    r3 = logchoose(N,n)

    return exp(r1 + r2 - r3)

def hypergeo_cdf(X, n, m, N):

    assert N >= m, 'Number of items %i must be larger than the number of marked items %i' % (N, m)
    assert m >= X, 'Number of marked items %i must be larger than the number of sucesses %i' % (m, X)
    assert n >= X, 'Number of draws %i must be larger than the number of sucesses %i' % (n, X)
    assert N >= n, 'Number of draws %i must be smaller than the total number of items %i' % (n, N)
    assert N-m >= n-X, 'There are more failures %i than unmarked items %i' % (N-m, n-X)

    s = 0
    for i in range(1, X+1):
        s += max(gauss_hypergeom(i, n, m, N), 0.0)
    return min(max(s,0.0), 1)

Everything should be self-explanitory.

[brentp]

Thanks @Will, that's very helpful! and good to know.

[Gahoo]

Thanks a lot.I have thought log function, but don't know how.

Answer 2

[brentp]

The short answer is use scipy.stats.

I had the same problem and ended up with this https://github.com/brentp/bio-playground/blob/master/utils/list_overlap_p.py#L35

[Will]

even that won't work when N is very large ... You need to use a log-hypercdf

[Will]

nice, last time I checked scipy.stats would return overflow errors on large-N hypergeocdfs ... they must've updated things since then.

[Gahoo]

This looks more decent.But it required Scipy and Numpy.