Event chain.py
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 |
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