# test_matrix

test_matrix, an Octave code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.

A wide range of matrix dimensions, forms and properties are available. These matrices may be useful in testing an algorithm for correctness on a variety of problems.

Many of the matrices can be rectangular, with the user specifying the number of rows and columns. Almost all the matrices can be made of arbitrary size, with the user specifying the dimension.

Many different matrix zero structures are available, including diagonal, bidiagonal, tridiagonal, pentadiagonal, banded, upper and lower triangular, and Hessenberg.

Many different matrix symmetry patterns are available, including symmetric, antisymmetric, persymmetric, circulant, Toeplitz, and Hankel.

Matrices are available with known inverses, condition numbers, determinants, rank, eigenvalues, and characteristic polynomials. Other matrix properties include positive definiteness, positivity, zero/one, and adjacency matrices.

Many of the matrices come from a MATLAB M file collection developed by Nicholas Higham, Department of Mathematics, University of Manchester.

An earlier version of the collection is available, again as MATLAB M files, in ACM TOMS Algorithm 694, in the TOMS directory of the NETLIB web site.

Many of these matrices, and many other matrices, are available at https://math.nist.gov, the Matrix Market web site.

### Languages:

test_matrix is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

companion_matrix, an Octave code which computes the companion matrix for a polynomial, in a variety of bases.

magic_matrix, an Octave code which computes a magic matrix, for any odd order n, such that all rows and columns have the same sum.

polynomial_conversion, an Octave code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Hermite, Lagrange, Laguerre and other forms.

risk_matrix, an Octave code which computes the transition and adjacency matrix for the game of risk.

snakes_matrix, an Octave code which computes the transition matrix for Snakes and Ladders.

tennis_matrix, an Octave code which computes the transition matrix for a game of tennis, which has 17 distinct states.

wathen_matrix, an Octave code which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

web_matrix, an Octave code which stores sample matrices describing a web page network. These matrices are typically very sparse, and the examples here are stored using the sparse triplet (ST) format. They can be used to demonstrate pagerank and other graph algorithms.

wishart_matrix, an Octave code which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.

### Source Code:

Last revised on 05 April 2024.