Direct surface.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.+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]]

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

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.

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