ZigZag X2X4.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). | ||
| + | |||
| + | ==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 07:02, 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
time_ev = 0.0
sigma = 1 if x <= 0.0 else -1
data = []
n_samples = 10 ** 6
while len(data) < n_samples:
delta_u = -math.log(random.random())
new_x = sigma * math.sqrt(-1.0 + math.sqrt(1.0 + 4.0 * delta_u))
new_time_ev = time_ev + abs(new_x - x)
for t in range(math.ceil(time_ev), math.floor(new_time_ev) + 1):
data.append(x + sigma * (t - time_ev))
x = new_x
time_ev = new_time_ev
sigma *= -1
plt.title('Zig-Zag 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()
