Random Matrix Analysis Toolkit

Simulate random matrices and ensembles and compute their eigenvalue spectra and dispersions.

RMAT: Random Matrix Analysis Toolkit

RMAT is an R package for simulating random matrices and ensembles as well as computing and analyzing their eigenvalue spectra and dispersions.

Installation

NOTE: This package has been submitted to CRAN and is pending release.

You can install the package in one of two ways:

# Through CRAN
install.packages("RMAT")
# Through Github
devtools::install_github(repo = "ataqi23/RMAT")

Usage

The package can be thought to contain two priamry modules: the matrix module and spectral statistics module.

Matrices

Included in the package are various wrapper functions for generating random matrices very efficiently. They follow the RM_xxx format in allusion to the stats sampling functions like rnorm. Every matrix sampling function has an ensemble counterpart in the RME_xxx format.

Consider the following example:

library(RMAT)
# Generate an ensemble of 50x50 Complex Hermitian Standard Normal matrices
ens <- RME_norm(N = 20, cplx = T, herm = T, size = 50)

The matrices included are:

• Uniform Matrices
• Normal Matrices
• Tridiagonal Matrices
• Beta Ensemble for b = 1,2,4
• Generalized Beta Ensemble for b > 0
• Stochastic Matrices
• Erdos-Renyi Graph Transition Matrices

Spectral Statistics

The two primary functions in the spectral statistics module are spectrum and dispersion. These two functions take either a matrix or an ensemble, and return the respective eigenvalue spectrum or dispersion. Consider the following example:

library(RMAT)
# Generate a random matrix ensemble
ens <- RME_beta(N = 20, beta = 4, size = 50)
# Compute the spectral statistics of the ensemble
ens_spectrum <- spectrum(ens, sort_norms = FALSE)
ens_dispersion <- dispersion(ens, pairs = "consecutive", sort_norms = FALSE)

About

This package was developed as a part of my Reed senior thesis in the Spring of 2021.