Python module that contains functionality to calculate a FUNKY collection of distribution functions, that sum to 1 over M sample points.

probdistro.py

#!/usr/bin/env python

import numpy, pandas, pylab

def _return_prob_dist_sub(M = 5, N = 1000000):
    us = numpy.random.random_sample((M-1, N))
    ainits = numpy.zeros((M, N))
    #
    z = numpy.ones( N )
    ainits[0,:] = z * us[0,:]
    for jdx in xrange(1, M - 1):
        z = z * (1 - us[jdx-1,:] )
        ainits[jdx,:] = z * us[jdx,:]
    z = z * (1 - us[M-2,:] )
    ainits[M-1,:] = z
    #
    alpha_shuffle = numpy.zeros((M, N))
    idx_shuffle = numpy.zeros((M, N), dtype=int)
    for jdx in xrange(N):
        a0 = ainits[:,jdx]
        vals = numpy.random.permutation( numpy.linspace( 0, M-1, M, dtype=int))
        alpha_shuffle[:,jdx] = a0[vals]
    return alpha_shuffle
        
def calc_prob_dist(M = 5, N = 1000000):
    assert(isinstance(M, int))
    assert(isinstance(N, int))
    assert(M >= 1)
    assert(N >= 1)
    #
    nums, rem = divmod( N, 1000000)
    alpha_shuffle = numpy.zeros((M, N))
    for idx in xrange(nums):
        alpha_shuffle[:,idx*1000000:(idx+1)*1000000] = _return_prob_dist_sub(M, 1000000)
    if rem != 0:
        alpha_shuffle[:,nums*1000000:] = _return_prob_dist_sub(M, rem)
    return alpha_shuffle

def draw_data( alpha_shuffle ):
    vars, lengths = alpha_shuffle.shape
    df = pandas.DataFrame({ r'alpha_%d' % (idx + 1) : pandas.Series( alpha_shuffle[idx,:] ) for
                            idx in xrange(vars) })
    df.plot(kind = 'hist', bins = 1000, normed = True, alpha = 0.1, linewidth = 0)
    pylab.savefig('distrib_%d_%d.pdf' % (vars, lengths), bbox_inches = 'tight')