From Werner KRAUTH

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		+	This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.
		+
		+	__FORCETOC__
		+	=Description=
		+
		+	=Program=
		+
		+	import random
		+
		+	L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
		+	sigma = 0.15
		+	sigma_sq = sigma ** 2
		+	delta = 0.1
		+	n_steps = 1000
		+	for steps in range(n_steps):
		+	a = random.choice(L)
		+	b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
		+	min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
		+	box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
		+	if not (box_cond or min_dist < 4.0 * sigma ** 2):
		+	a[:] = b
		+	print L
		+
		+	=Version=
		+	See history for version information.
		+
		+	[[Category:Python]]
		+
	import random, math		import random, math

---

Revision as of 21:42, 22 September 2015

This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.

Contents 1 Description 2 Program 3 Version

Description

Program

import random

L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
sigma = 0.15
sigma_sq = sigma ** 2
delta = 0.1
n_steps = 1000
for steps in range(n_steps):
    a = random.choice(L)
    b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
    min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
    box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
    if not (box_cond or min_dist < 4.0 * sigma ** 2):
        a[:] = b
print L

Version

See history for version information.

import random, math

def event(a, b, dirc, sigma):
    d_perp = abs(b[not dirc] - a[not dirc]) % 1.0
    d_perp = min(d_perp, 1.0 - d_perp)
    if d_perp > 2.0 * sigma:
        return float("inf")
    else:
        d_para = math.sqrt(4.0 * sigma ** 2 - d_perp ** 2)
        return (b[dirc] - a[dirc] - d_para + 1.0) % 1.0

L = [[0.25, 0.25], [0.25, 0.75], [0.75, 0.25], [0.75, 0.75]]
ltilde = 0.819284; sigma = 0.15
for iter in xrange(20000):
    dirc = random.randint(0, 1)
    print iter, dirc, L
    distance_to_go = ltilde
    next_a = random.choice(L)
    while distance_to_go > 0.0:
        a = next_a
        event_min = distance_to_go
        for b in [x for x  in L if x != a]:
            event_b = event(a, b, dirc, sigma)
            if event_b < event_min:
                next_a = b
                event_min = event_b
        a[dirc] = (a[dirc] + event_min) % 1.0
        distance_to_go -= event_min