Monte Carlo integration

Faisal Qureshi
faisal.qureshi@ontariotechu.ca
http://www.vclab.ca

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© Faisal Qureshi

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

import random
import numpy as np
import matplotlib.pyplot as plt

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

def f(x):
    return x**2

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)

<matplotlib.collections.FillBetweenPolyCollection at 0x10aa697f0>

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: 0.3200380458458901
Exact Integral of f: 0.3333333333333333