Walker.py

From Werner KRAUTH

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import random
def walker_setup (pi):
    """compute the lookup table for Walker's algorithm"""
    N_walker = len(pi)
    walker_mean = sum(a[0] for a in pi) / float(N_walker)
    long_s = []
    short_s = []
    for p in pi:
        if p[0] > walker_mean:
            long_s.append(p[:])
        else:
            short_s.append(p[:])
    walker_table = []
    for k in range(N_walker - 1):
        e_plus = long_s.pop()
        e_minus = short_s.pop()
        walker_table.append((e_minus[0], e_minus[1], e_plus[1]))
        e_plus[0] = e_plus[0] - (walker_mean - e_minus[0])
        if e_plus[0] < walker_mean:
            short_s.append(e_plus)
        else:
            long_s.append(e_plus)
    if long_s != []:
        walker_table.append((long_s[0][0], long_s[0][1], long_s[0][1]))
    else:
        walker_table.append((short_s[0][0], short_s[0][1], short_s[0][1]))
    return N_walker, walker_mean, walker_table

N = 12
pi = [random.uniform(0.1, 10.0) for i in range(N)]
pisum = sum(a for a in pi)
pi = [[pi[k] / pisum, k] for k in range(N)]

N_walker, walker_mean, walker_table = walker_setup (pi)

data = [0] * N
NSample = 100000 * N
for iter in range(NSample):
    i = random.randint (0, N - 1)
    Upsilon = random.uniform (0.0, walker_mean)
    if Upsilon < walker_table[i][0]:
        sample = walker_table[i][1]
    else:
        sample = walker_table[i][2]
    data[sample] += 1.0 / NSample
for i in range(N):
    print(pi[i], data[i])