The Problem With Converting Long Int To Float In Python
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Entering edit mode
12.4 years ago
Gahoo ▴ 270

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?

python • 11k views
9
Entering edit mode
12.4 years ago
Will 4.5k

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.

0
Entering edit mode

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

0
Entering edit mode

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

8
Entering edit mode
12.4 years ago
brentp 24k

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

0
Entering edit mode

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

0
Entering edit mode

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

0
Entering edit mode

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