Monte Carlo integration¶
Faisal Qureshi
faisal.qureshi@ontariotechu.ca
http://www.vclab.ca
Copyright information¶
© Faisal Qureshi
License¶
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
In [17]:
import random
import numpy as np
import matplotlib.pyplot as plt
In [ ]:
def monte_carlo_integration(func, num_samples):
total = 0
for _ in range(num_samples):
x = random.random()
total += func(x)
average = total / num_samples
return average
In [15]:
def f(x):
return x**2
In [23]:
plt.figure(figsize=(5,5))
x_all = np.linspace(-2,2,1024)
y_all = f(x_all)
x = np.linspace(0,1,256)
y = f(x)
plt.plot(x_all,y_all,'r')
plt.fill_between(x,y)
Out[23]:
<matplotlib.collections.PolyCollection at 0x140f72790>
In [16]:
estimated_integral = monte_carlo_integration(f, num_samples=100)
exact_integral = 1/3 # Exact value of the integral
print("Estimated Integral of f:", estimated_integral)
print("Exact Integral of f:", exact_integral)
Estimated Integral of f: 0.33188938082730607 Exact Integral of f: 0.3333333333333333
In [ ]: