Factor Metropolis X2X4 patch.py

From Werner KRAUTH

Revision as of 23:00, 10 June 2024 Werner (Talk | contribs) ← Previous diff		Revision as of 23:01, 10 June 2024 Werner (Talk | contribs) Next diff →
Line 2:		Line 2:
	import random		import random
	import matplotlib.pyplot as plt		import matplotlib.pyplot as plt
-		+
	def u(x): return x ** 2 / 2.0 + x ** 4 / 4.0		def u(x): return x ** 2 / 2.0 + x ** 4 / 4.0
-		+
	def u2(pos): return 0.5 * pos ** 2		def u2(pos): return 0.5 * pos ** 2
-		+
	def u4(pos): return 0.25 * pos ** 4		def u4(pos): return 0.25 * pos ** 4
-		+
	x = 0.0		x = 0.0
	delta = 0.1		delta = 0.1
-		+
	data = []		data = []
	n_samples = 10 ** 6		n_samples = 10 ** 6
Line 23:		Line 23:
	x = new_x		x = new_x
	data.append(x)		data.append(x)
-
	plt.title('Factorized Metropolis algorithm (patch), anharmonic oscillator' )		plt.title('Factorized Metropolis algorithm (patch), anharmonic oscillator' )
	plt.xlabel('$x$')		plt.xlabel('$x$')

---

Revision as of 23:01, 10 June 2024

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()