From Werner KRAUTH

Revision as of 21:05, 22 September 2015 Werner (Talk | contribs) ← Previous diff		Revision as of 21:43, 22 September 2015 Werner (Talk | contribs) Next diff →
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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 numpy		import numpy

---

Revision as of 21:43, 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 numpy

neighbor =  [[1, 3, 0, 0], [2, 4, 0, 1], [2, 5, 1, 2],
             [4, 6, 3, 0], [5, 7, 3, 1], [5, 8, 4, 2],
             [7, 6, 6, 3], [8, 7, 6, 4], [8, 8, 7, 5]]
transfer = numpy.zeros((9, 9))
for k in range(9):
    for neigh in range(4): transfer[neighbor[k][neigh], k] += 0.25
position = numpy.zeros(9)
position[8] = 1.0
for t in range(100):
    print t,'  ',["%0.5f" % i for i in position]
    position = numpy.dot(transfer, position)