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pdfrand.py

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#!/usr/bin/env python
# from http://mail.python.org/pipermail/python-list/2008-August/502750.html

from __future__ import division
from random import random

def integrate(f, lo, hi, steps=1000):
    dx = (hi - lo) / steps
    lo += dx / 2
    return sum(f(i*dx + lo) * dx for i in range(steps))

def make_cdf(f, lo, hi, steps=1000):
    total_area = integrate(f, lo, hi, steps)
    def cdf(x):
        assert lo <= x <= hi
        return integrate(f, lo, x, steps) / total_area
    return cdf

def bisect(target, f, lo, hi, n=20):
    'Find x between lo and hi where f(x)=target'
    for i in range(n):
        mid = (hi + lo) / 2.0
        if target < f(mid):
            hi = mid
        else:
            lo = mid
    return (hi + lo) / 2.0

def make_user_distribution(f, lo, hi, steps=1000, n=20):
    cdf = make_cdf(f, lo, hi, steps)
    return lambda: bisect(random(), cdf, lo, hi, n)

if __name__ == '__main__':
    def linear(x):
        return 3 * x - 6
    lo, hi = 2, 10
    r = make_user_distribution(linear, lo, hi)
    for i in range(20):
        print r()

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