Naive surface 2d.py

From Werner KRAUTH

Revision as of 12:47, 6 June 2024 Werner (Talk | contribs) ← Previous diff		Current revision Werner (Talk | contribs)
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		+	==Context==
		+	This page is part of my [[BegRohu_Lectures_2024|2024 Beg Rohu Lectures]] on "The second Markov chain revolution" at the [https://www.ipht.fr/Meetings/BegRohu2024/index.html Summer School] "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).
		+
		+	==Python program==
		+
	import random, math		import random, math
	import matplotlib.pyplot as plt		import matplotlib.pyplot as plt

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Current revision

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import random, math
import matplotlib.pyplot as plt
N_trials = 1000000
data = []
twopi = 2.0 * math.pi
for iter in range(N_trials):
    x = random.uniform(-1.0, 1.0)
    y = random.uniform(-1.0, 1.0)
    r = math.sqrt(x ** 2 + y ** 2)
    if r < 1.0:
        x = x / r; y = y / r # uniform sample on the surface of unit sphere
        phi = (math.atan2(y, x) + twopi) % twopi
        data.append(phi)
plt.title('naive_surface_2d.py (histogram of angles)')
plt.xlabel('angle')
plt.ylabel('histogram')
plt.hist(data, bins=100, density=True)
plt.show()