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 direct_surface.py, a direct-sampling algorithm for uniform points on the surface of a d-dimensional unit sphere
	__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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	radius = math.sqrt(sum(x ** 2 for x in R))		radius = math.sqrt(sum(x ** 2 for x in R))
	print [x / radius for x in R]		print [x / radius for x in R]
		+	=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 direct_surface.py, a direct-sampling algorithm for uniform points on the surface of a d-dimensional unit sphere

Contents 1 Description 2 Program 3 Version

Description

Program

import random, math

dimensions = 5
nsamples = 20
for sample in xrange(nsamples):
    R = [random.gauss(0.0, 1.0) for d in xrange(dimensions)]
    radius = math.sqrt(sum(x ** 2 for x in R))
    print [x / radius for x in R]

Version

See history for version information.