From Werner KRAUTH

Revision as of 21:41, 22 September 2015 Werner (Talk | contribs) ← Previous diff		Current revision Werner (Talk | contribs)
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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.	+	This page presents the program gauss_test.py, a direct-sampling algorithm for two independent Gaussian random numbers. This algorithm is used to illustrate the concept of "sample transformation"
	__FORCETOC__		__FORCETOC__
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	=Program=		=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
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	[x, y] = gauss_test(1.0)		[x, y] = gauss_test(1.0)
	print x, y		print x, y
		+	=Version=
		+	See history for version information.
		+
		+	[[Category:Python]] [[Category:Honnef_2015]] [[Category:MOOC_SMAC]]

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Current revision

This page presents the program gauss_test.py, a direct-sampling algorithm for two independent Gaussian random numbers. This algorithm is used to illustrate the concept of "sample transformation"

Contents 1 Description 2 Program 3 Version

Description

Program

import random, math

def gauss_test(sigma):
    phi = random.uniform(0.0, 2.0 * math.pi)
    Upsilon = random.uniform(0.0, 1.0)
    Psi = - math.log(Upsilon)
    r = sigma * math.sqrt(2.0 * Psi)
    x = r * math.cos(phi)
    y = r * math.sin(phi)
    return [x, y]

nsamples = 50
for sample in range(nsamples):
    [x, y] = gauss_test(1.0)
    print x, y

Version

See history for version information.