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

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.