SJSU Singular Matrix Database
Software links, sources of some matrices and other links
Links to software designed to work with numerically singular matrices:
 ACM Algorithm 782 by C. H. Bischof and G. QuintanaOrti
has codes for rankrevealing QR factorizations of dense matrices. Matlab interfaces to the code are
here and also
here.
 ACM Algorithm 853 by L. Foster and R. Kommu
is a modification of the LAPACK routine xGELSY for solving rank deficient least squares problems using
a complete orthogonal decomposition. For low rank matrices the code is
faster than LAPACK code. A Matlab interface to the code is
here.
 Apalab  A Matlab toolbox for Approximate Polynomial
Algebra
by Zhonggang Zeng provides routines for estimating numerical rank, calculating numerical null spaces and
updating the calculations. They are part of a package of routines for polynomial algebra calculations.
The routines target matrices with a low dimensional
null space.
 Code for Rank Revealing Factorizations
contains Matlab interfaces to 9 routines for constructing rank revealing factorizations of dense
matrices and 3 routines for other common matrix factorizations.
 LAPACK has rank revealing algorithms using the QR
factorization with column interchanges (xGEQP3), complete orthogonal decomposition (xGELSY), and the
singular value decomposition (xGESVD, xGESDD). Mathematical programming languages such as Matlab, Maple
and Mathematica incorporate LAPACK
routines and will contain interfaces to some of the LAPACK code.
 Regularization Tools by Per Christian Hansen
(source of the Regtools group) can be used to experiment with different
regularization strategies. Regularization can aid in the choice of an appropriate
numerical rank. See also this link.
 spnrank (see
spnrank.pdf) by L. Foster is used to identify the
numerical rank of larger matrices in this database. The routine works for real or complex full matrices
in Matlab 7.3 or higher and for real (but not complex) sparse matrices in Matlab 7.5 or higher.
 SuiteSparseQR
by Tim Davis is an implementation of the multifrontal sparse
QR factorization method. It detects numerical rank using Heath's
technique.
 UTV Tools and Expansion Pack
by Per Christian Hansen and Ricardo Fierro provides Matlab
functions for computing and modifying rankrevealing UTV decompositions and rank revealing QR
decomposition. The routines
generally target matrices with either a low rank or a low dimensional null space.
At the current time most of the matrices for the SJsingular collection come from
University of Florida Sparse Matrix Collection. The following list of web sites
is from
University of Florida Sparse Matrix Collection.
Many of these matrices come from original
sources  computational scientists with a matrix problem to solve.
Others come from researchers, who work on algorithms for
singular matrices, sparse matrices or related graph problems. Researchers of both types
who maintain their own web pages or ftp sites for their matrices include:
 Harwell/Boeing Collection,
Iain Duff, Roger Grimes, John Lewis.
Click here for a description of
the matrices in the original Harwell/Boeing Collection.
 Matrix Market,
Roldan Pozo, Karen Remington, Ron Boisvert, Richard Barrett,
Jack Dongarra.

University of Basil collection, Olaf Schenk.
 Pajek networks,
V. Batagelj and A. Mrvar.

Oberwolfach model reduction benchmarks, E. Rudnyi, and many others.
 the
Gould, Hu, Scott collection
 NETLIB LP test problems,
David Gay.

SPARSKIT collection, Yousef Saad.
 NEP collection,
Zhaojun Bai, David Day, Jim Demmel, Jack Dongarra.
Click here for a description of the matrices in
this collection.
 Hans Mittelman's
LP test set
 C. Meszaros'
LP test set

Parasol matrices, Jacko Koster.
 Sep Kamvar's
web matrices.
 Reijo Kouhia's set
(source of the Cylshell group).
 JeanClaude
maintains a
Sparse Integer Matrices Collection.