Pseudo-Random Number Generation

A pseudo-random number generator (PRNG) is a deterministic algorithm that produces sequences of numbers that appear statistically random. The sequence is fully determined by its initial seed, making simulations reproducible.

Usage in NumPy

Python

import numpy as np # Seed for reproducibility (legacy interface) np.random.seed(42) # Preferred: create a Generator object rng = np.random.default_rng(seed=0) # Uniform distribution on [a, b]: N samples uniform_samples: np.ndarray = rng.uniform(low=0.0, high=1.0, size=1000) # Gaussian (normal) distribution: mean mu, standard deviation sigma gaussian_samples: np.ndarray = rng.normal(loc=0.0, scale=1.0, size=1000) # Standard normal (mean 0, variance 1) standard_normal_samples: np.ndarray = rng.standard_normal(size=1000)

Output

Using the same seed always produces the same sequence, which is essential for debugging and reproducible results in Monte Carlo integration, Random walks, and Euler-Maruyama scheme simulations.

Monte Carlo integration | Random walks | Wiener process | Euler-Maruyama scheme