WIP¶

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Computational Projects¶

Monte Carlo Integration¶

Here is a comparison of how I implemented a simple Monte Carlo integration in both Python and C++.

PythonC++Result

import numpy as np

def monte_carlo_pi(n_samples):
    x = np.random.rand(n_samples)
    y = np.random.rand(n_samples)
    inside = (x**2 + y**2) <= 1.0
    return 4.0 * np.sum(inside) / n_samples

print(f"Pi is approx: {monte_carlo_pi(10000)}")

#include <iostream>
#include <random>

int main() {
    int n_samples = 10000;
    int inside = 0;
    // ... (implementation details)
    std::cout << "Pi is approx: " << (4.0 * inside) / n_samples << std::endl;
    return 0;
}

Pi is approx: 3.14159...

The convergence rate scales as \(1/\sqrt{N}\).

code annotation

def lagrangian(phi, dphi):
    kinetic = 0.5 * dphi**2 # (1)
    potential = 0.5 * m**2 * phi**2 # (2)
return kinetic - potential

1. This is the kinetic term \(\partial_\mu \phi \partial^\mu \phi\) \
2. This is the mass term

def test_function():
    print("Hello") # (1)