A Test Matrix Generation Suite

We discuss the design and implementation of a suite of test matrix generators for testing linear algebra software. These routines generate random matrices with certain properties which are useful for testing linear equation solving, least squares, and eigendecomposition software. These properties include the spectrum, symmetry, bandwidth, norm, sparsity, conditioning (with respect to inversion or for the eigenproblem), type (real or complex), and storage scheme (dense, packed, or banded). 1 Introduction Testing a large numerical linear algebra library such as LAPACK [3] requires generating many different kinds of test matrices. For example, LAPACK contains linear equation solving routines for real and complex matrices which may be symmetric, Hermitian, or nonsymmetric, banded or dense, packed or unpacked, positive definite or indefinite, and so on. Thorough testing requires test matrices with a range of condition numbers and scalings (i.e., with norms near the overflow and underflow t..