kappa_SQ: A Matlab package for randomized sampling of matrices with orthonormal columns

TL;DR

kappa_SQ is a Matlab package with GUI tools for experimenting with randomized row sampling and analyzing the two-norm condition number of sampled matrices with orthonormal columns.

Contribution

It provides an integrated platform for generating test matrices, performing row sampling, measuring condition numbers, and visualizing results, facilitating research in randomized matrix sampling.

Findings

Enables easy experimentation with row sampling methods.

Provides tools to analyze the condition number of sampled matrices.

Includes features for plotting and bounding condition numbers.

Abstract

The kappa_SQ software package is designed to assist researchers working on randomized row sampling. The package contains a collection of Matlab functions along with a GUI that ties them all together and provides a platform for the user to perform experiments. In particular, kappa_SQ is designed to do experiments related to the two-norm condition number of a sampled matrix, $\kappa(SQ)$, where $S$ is a row sampling matrix and $Q$ is a tall and skinny matrix with orthonormal columns. Via a simple GUI, kappa_SQ can generate test matrices, perform various types of row sampling, measure $\kappa(SQ)$, calculate bounds and produce high quality plots of the results. All of the important codes are written in separate Matlab function files in a standard format which makes it easy for a user to either use the codes by themselves or incorporate their own codes into the kappa_SQ package.