Matrix Depot: an extensible test matrix collection for Julia

Matrix Depot is a Julia software package that provides easy access to a large and diverse collection of test matrices. Its novelty is threefold. First, it is extensible by the user, and so can be adapted to include the user's own test problems. In doing so it facilitates experimentation and makes it easier to carry out reproducible research. Second, it amalgamates in a single framework two different types of existing matrix collections, comprising parametrized test matrices (including Hansen's set of regularization test problems and Higham's Test Matrix Toolbox) and real-life sparse matrix data (giving access to the University of Florida Sparse Matrix Collection). Third, it fully exploits the Julia language. It uses multiple dispatch to help provide a simple interface and, in particular, to allow matrices to be generated in any of the numeric data types supported by the language.

[1]  Alan Edelman,et al.  Julia: A Fast Dynamic Language for Technical Computing , 2012, ArXiv.

[2]  P. Hansen.  Discrete Inverse Problems: Insight and Algorithms , 2010 .

[3]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

[4]  Nicholas J. Higham,et al.  NLEVP: A Collection of Nonlinear Eigenvalue Problems , 2013, TOMS.

[5]  Richard F. Barrett,et al.  Matrix Market: a web resource for test matrix collections , 1996, Quality of Numerical Software.

[6]  Desmond J. Higham,et al.  CONTEST: A Controllable Test Matrix Toolbox for MATLAB , 2009, TOMS.

[7]  P. Clement,et al.  A Class of Triple-Diagonal Matrices for Test Purposes , 1959 .

[8]  M. L. Pei.  A test matrix for inversion procedures , 1962, CACM.

[9]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[10]  Vincent Lefèvre,et al.  MPFR: A multiple-precision binary floating-point library with correct rounding , 2007, TOMS.

[11]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[12]  James Demmel,et al.  Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers , 2008, TOMS.

[13]  C. W. Gear,et al.  A simple set of test matrices for eigenvalue programs , 1969 .

[14]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[15]  Jack Dongarra,et al.  A Test Matrix Collection for Non-Hermitian Eigenvalue Problems , 1997 .

[16]  Per Christian Hansen,et al.  Regularization Tools version 4.0 for Matlab 7.3 , 2007, Numerical Algorithms.

[17]  Iain S. Duff,et al.  Sparse matrix test problems , 1982 .

[18]  R. F. Boisvert,et al.  The Matrix Market Exchange Formats: Initial Design | NIST , 1996 .

[19]  Nicholas J. Higham,et al.  The Test Matrix Toolbox for Matlab (Version 3.0) , 2013 .

[20]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[21]  Nicholas J. Higham,et al.  Algorithm 694: a collection of test matrices in MATLAB , 1991, TOMS.

[22]  Mark R. Dennis,et al.  The Princeton companion to applied mathematics , 2015 .

[23]  Robert Todd Gregory,et al.  A collection of matrices for testing computational algorithms , 1969 .

[24]  Nicholas J. Higham,et al.  Accuracy and stability of numerical algorithms, Second Edition , 2002 .