The Test Matrix Toolbox for Matlab (Version 3.0)
Nicholas John Higham, Nicholas John Higham · OpenGrey (Institut de l'Information Scientifique et Technique) · 2013
We describe version 3.0 of the Test Matrix Toolbox for Matlab 4.2. The toolbox contains a collection of test matrices, routines for visualizing matrices, routines for direct search optimization, and miscellaneous routines that provide useful additions to Matlab’s existing set of functions. There are 58 parametrized test matrices, which are mostly square, dense, nonrandom, and of arbitrary dimension. The test matrices include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involutary, and totally positive matrices. The visualization routines display surface plots of a matrix and its (pseudo-) inverse, the field of values, Gershgorin disks, and twoand three-dimensional views of pseudospectra. The direct search optimization routines implement the alternating directions method, the multidirectional search method and the Nelder–Mead simplex method. We explain the need for collections of test matrices and summarize the features of the collection in the toolbox. We give examples of the use of the toolbox and explain some of the interesting properties of the Frank matrix and magic square matrices. The leading comment lines from all the toolbox routines are listed.