entropy.py

#!/usr/bin/env python

from letters import file2prob, file2pairs
from math import log

def entropy(dist):
    """
    Calculate the entropy of a probability distribution. The
    probability distribution is given as a dictionary where
    the keys are the support and the values are the probabilities
    """
    return -sum(p*log(p, 2) for p in dist.values() if p > 0)

if __name__ == '__main__':
    import sys
    
    if len(sys.argv) != 2:
        print("Usage: %s filename" % sys.argv[0])
        sys.exit(-1)
        
    filename = sys.argv[1]

    probs = file2prob(filename)
    conds = file2pairs(filename)

    cc = sum([ [probs[c]*d for d in conds[c].values()]
               for c in conds ], [])
    centropy = -sum(p*log(p,2) for p in cc if p > 0)
    print(entropy(probs)/-log(1/len(probs),2), centropy/-log(1/len(cc),2))