Monte Carlo Methods Tutorial

cds.montecarlo estimates integrals, π, and random walks by sampling.

1. Estimating π

import math
from cds.montecarlo import estimate_pi

r = estimate_pi(samples=100_000, seed=42)
print(r.estimate, abs(r.estimate - math.pi))

2. Integrating by Sampling

from cds.montecarlo import mc_integrate

# ∫_0^1 x^2 dx = 1/3
print(mc_integrate(lambda x: x**2, a=0.0, b=1.0, samples=50_000, seed=7).value)

3. Random Walks

from cds.montecarlo import random_walk_1d, random_walk_2d

print(random_walk_1d(steps=100, seed=1).position)
w2 = random_walk_2d(steps=100, seed=2)
print(w2.x, w2.y)

4. Buffon's Needle

from cds.montecarlo import buffon_needle

print(buffon_needle(drops=10_000, needle_length=0.5, line_spacing=1.0, seed=3).pi_estimate)

Run the full demo with python examples/montecarlo_demo.py.