TEST_MATRIX
Higham's Test Matrices
TEST_MATRIX
is a MATLAB library which
defines a set of test 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 of the matrices come from a MATLAB M file collection developed by
Nicholas Higham, Department of Mathematics, University of Manchester, and
maintained in the "testmatrix" file somewhere at
the MATLAB web site.
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.
Languages:
TEST_MATRIX is available in
a MATLAB version.
Related Data and Programs:
LINPACK,
a MATLAB library which
provides some linear algebra operations for certain standard storage formats.
LINPLUS,
a MATLAB library which
provides some simple linear algebra operations for a number of storage formats.
TEST_MAT,
a MATLAB library which
defines a number of test matrices.
Reference:

TS Chow,
A class of Hessenberg matrices with known eigenvalues and
inverses,
SIAM Review,
Volume 11, Number 3, July 1969, pages 391395.

Robert Gregory, David Karney,
A Collection of Matrices for Testing Computational Algorithms,
Wiley, 1969,
ISBN: 0882756494,
LC: QA263 G862.

Nicholas Higham,
Algorithm 694: A Collection of Test Matrices in MATLAB,
ACM Transactions on Mathematical Software,
Volume 17, Number 3, September 1991, pages 289305.

Morris Newman, John Todd,
The evaluation of matrix inversion programs,
Journal of the Society for Industrial and Applied Mathematics,
Volume 6, Number 4, 1958, pages 466476.

Andrew Wathen,
Realistic eigenvalue bounds for the Galerkin mass matrix,
IMA Journal of Numerical Analysis,
Volume 7, 1987, pages 449457.

Joan Westlake,
A Handbook of Numerical Matrix Inversion and Solution of
Linear Equations,
John Wiley, 1968.

James Wilkinson,
Rounding Errors in Algebraic Processes,
Prentice Hall, 1963,
ISBN: 0486679993.

James Wilkinson,
The Algebraic Eigenvalue Problem,
Oxford University Press, 1988,
ISBN: 0198534183.

James Wilkinson, Christian Reinsch,
Handbook for Automatic Computation,
Volume II, Linear Algebra, Part 2,
Springer, 1971,
ISBN: 0387054146.
Source Code:

adsmax.m, alternating directions
direct search method.

augment.m, augmented system matrix.

bandred.m, band reduction by twosided
unitary transformation.

cauchy.m, the Cauchy matrix.

cgs.m, classical GramScmdidt QR
orthogonalization.

chebspec.m, Chebyshev spectral
differentiation matrix.

chebvand.m, Vandermondelike
matrix for the Chebyshev polynomials.

cholp.m, Cholesky factorization with
pivoting;

chop.m, round matrix elements.

chow.m, the Chow matrix.

circul.m, a circulant matrix.

clement.m, the Clement matrix.

cod.m, complete orthogonal decomposition.

comp.m, comparison matrices.

compan.m, companion matrix.

cond.m, compute matrix condition number.

condex.m, Linpack condition number
estimate counterexamples.

contents.m, contents.

cpltaxes.m, determines suitable
axis for plot of complex vector.

cycol.m, matrix with cyclically repeating
columns.

diagpiv.m, diagonal pivoting factorization
with partial pivoting.

dingdong.m, the Dingdong matrix.

dorr.m, the Dorr matrix.

dramadah.m, the Dramadah matrix
(inverse Hadamard).

dual.m, dual vector in Hoelder Pnorm.

eigsens.m, eigenvalue condition numbers.

fdemo.m, demonstration function for
direct search maximizers.

fiedler.m, the Fiedler matrix.

forsythe.m, the Forsythe matrix.

frank.m, the Frank matrix.

fv.m, field of values.

gallery.m, a gallery of test matrices.

ge.m, Gaussian elimination without pivoting.

gearm.m, the Gear matrix.

gecp.m, Gaussian elimination with complete
pivoting.

gersh.m, Gershgorin eigenvalue estimates.

gfpp.m, matrix with maximal pivot growth
factor for Gaussian elimination.

gj.m, GaussJordan elimination.

grcar.m, the Grcar matrix.

hadamard.m, the Hadamard matrix.

hilb.m, the Hilbert matrix.

house.m, the Householder matrix.

invhess.m, inverse of an upper
Hessenberg matrix.

invol.m, an involutory matrix.

ipjfact.m, a Hankel matrix with
factorial elements.

jordbloc.m, Jordan block matrix.

kahan.m, the Kahan matrix.

kms.m, the KMS matrix.

krylov.m, a Krylov matrix.

lauchli.m, the Lauchli matrix.

lehmer.m, the Lehmer matrix.

lesp.m, the Lesp matrix.

lotkin.m, the Lotkin matrix.

makejcf.m, a matrix with given
Jordan canonical form.

matrix.m, access matrix toolbox
matrices by number.

matsignt.m, matrix sign function
for a triangular matrix.

mdsmax.m, multidirectional search
method for direct search optimization.

mgs.m, modified GramSchmidt QR
orthogonalization.

minij.m, the min(i,j) matrix.

moler.m, the Moler matrix.

neumann.m, the Neumann matrix.

nmsmax.m, the NelderMead simplex
method for direct search optimization.

ohess.m, random orthogonal upper
Hessenberg matrix.

orthog.m, some orthogonal and
nearly orthogonal matrices.

parter.m, the Parter matrix.

pascal.m, the Pascal matrix.

pdtoep.m, a positive definite
Toeplitz matrix.

pei.m, the Pei matrix.

pentoep.m, a pentadiagonal Toeplitz
matrix.

pnorm.m, estimate of matrix Pnorm.

poisson.m, the Poisson matrix.

poldec.m, polar decomposition of a matrix.

prolate.m, the prolate matrix.

ps.m, dot plot of a pseudospectrum.

pscont.m, contour plots of pseudospectrum.

qmult.m, premultiply by a random
orthogonal matrix.

rando.m, random matrix with elements
of 1, 0 and 1.

randsvd.m, random matrix with given
singular values.

redheff.m, the Redheffer matrix.

riemann.m, the Riemann matrix.

rq.m, the Rayleigh quotient.

rschur.m, an upper quasitriangular
matrix.

see.m, pictures of a matrix and
its pseudoinverse.

seqa.m, additive sequence.

seqcheb.m, sequence of points
related to Chebyshev polynomials.

seqm.m, multiplicative sequence.

show.m, display signs of matrix elements.

signm.m, matrix sign decomposition.

skewpart.m, skewsymmetric part
of a matrix.

smoke.m, the Smoke matrix.

sparsify.m, randomly set matrix
elements to 0.

sub.m, principal submatrix.

symmpart.m, symmetric part of matrix.

timestamp.m,
prints the current HMSDMY date as a timestamp.

tmtdemo.m, demonstration of test
matrix toolbox.

trap2tri.m, unitary reduction of
trapezoidal matrix to triangular form.

tridiag_dense.m,
tridiagonal matrix, dense form.

tridiag_sparse.m,
tridiagonal matrix, sparse form.

triw.m, upper triangular Wilkinson matrix.

vand.m, Vandermonde matrix.

wathen.m, the Wathen matrix.

wilk.m, the Wilkinson matrix.
Examples and Tests:
You can go up one level to
the MATLAB source codes.
Last revised on 01 September 2005.