rmt 0.1.0

Random matrix theory: Marchenko-Pastur, Wigner semicircle, eigenvalue statistics
Documentation

rmt

Random Matrix Theory primitives for spectral analysis and signal detection. Implements Marchenko-Pastur law, Wigner semicircle law, and eigenvalue spacing statistics.

Dual-licensed under MIT or Apache-2.0.

crates.io | docs.rs

use rmt::{marchenko_pastur_density, wigner_semicircle_density, sample_wishart};

// Marchenko-Pastur: eigenvalue density of sample covariance
let ratio = 0.5;  // p/n
let density = marchenko_pastur_density(1.5, ratio, 1.0);

// Wigner semicircle: symmetric random matrix eigenvalues
let density = wigner_semicircle_density(0.5, 1.0);

// Sample a Wishart matrix
let wishart = sample_wishart(100, 50);

Functions

Function Purpose
marchenko_pastur_density MP law density
marchenko_pastur_support MP support bounds
wigner_semicircle_density Wigner law density
sample_wishart Sample X^T X
sample_goe Gaussian Orthogonal Ensemble
level_spacing_ratios Eigenvalue spacing statistics
empirical_spectral_density Histogram-based density
stieltjes_transform m(z) transform

Why RMT?

  • Covariance matrix eigenvalues follow MP distribution
  • Neural network weight spectra reveal training dynamics
  • Distinguish signal from noise in PCA