Gauss test.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 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]]

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

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.

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