Metropolis X2X4.py
From Werner KRAUTH
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| ==Further information== | ==Further information== | ||
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| ==References== | ==References== | ||
| + | * Tartero, G., Krauth, W. Concepts in Monte Carlo sampling, Am. J. Phys. 92, 65–77 (2024) [https://arxiv.org/pdf/2309.03136 arXiv:2309.03136 | ||
Revision as of 13:46, 11 June 2024
Contents |
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 math
import random
import matplotlib.pyplot as plt
def u(x):
return x ** 2 / 2.0 + x ** 4 / 4.0
x = 0.0
delta = 0.1
data = []
n_samples = 10 ** 6
for i in range(n_samples):
new_x = x + random.uniform(-delta, delta)
delta_u = u(new_x) - u(x)
if random.random() < math.exp(-delta_u): x = new_x
data.append(x)
plt.title('Metropolis algorithm, anharmonic oscillator' )
plt.xlabel('$x$')
plt.ylabel('$\pi(x)$')
plt.hist(data, bins=100, density=True,label='data')
XValues = []
YValues = []
for i in range(-1000,1000):
x = i / 400.0
XValues.append(x)
YValues.append(math.exp(- u(x)) / 1.93525)
plt.plot(XValues, YValues, label='theory')
plt.legend(loc='upper right')
plt.show()
Further information
References
- Tartero, G., Krauth, W. Concepts in Monte Carlo sampling, Am. J. Phys. 92, 65–77 (2024) [https://arxiv.org/pdf/2309.03136 arXiv:2309.03136
