Factor Metropolis X2X4 patch.py
From Werner KRAUTH
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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). | ||
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| + | ==Python program== | ||
| + | |||
| + | |||
| import math | import math | ||
| import random | import random | ||
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| plt.legend(loc='upper right') | plt.legend(loc='upper right') | ||
| plt.show() | plt.show() | ||
| + | |||
| + | ==Further information== | ||
| + | ==References== | ||
Revision as of 07:00, 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
def u2(pos): return 0.5 * pos ** 2
def u4(pos): return 0.25 * pos ** 4
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_u2 = u2(new_x) - u2(x)
delta_u4 = u4(new_x) - u4(x)
Upsilon2 = random.uniform(0.0, 1.0)
Upsilon4 = random.uniform(0.0, 1.0)
if Upsilon2 < math.exp(-delta_u2) and Upsilon4 < math.exp(-delta_u4):
x = new_x
data.append(x)
plt.title('Factorized Metropolis algorithm (patch), 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()
