How to use Matrix Market matrices in Matlab

The Matrix Market is an interesting collection of matrices from a variety of applications

Purpose

• To illustrate the use of Matrix Market matrices in Matlab

• To learn a bit about sparse matrices

• To use some of the tools available in Matlab for working with sparse matrices

Preliminary Steps• Locate a matrix at the Matrix Market web site

math.nist.gov/MatrixMarket (see the “Introduction to the Matrix Market” tutorial)

• Download and uncompress a file describing the matrix (see the “Downloading matrices from the Matrix Market” tutorial)

• Load the matrix into Matlab (see “Converting Matrix Market matrices to Matlab” tutorial and this tutorial)

In Matlab we will illustrate

• The structure of sparse matrices (using spy)• Solving large linear systems (using \)• The time required (using tic and toc)• The accuracy of the calculated solution (using

norm and condest)• Fill-in in the factorization (using lu, nnz and spy)• The effect of column reordering on fill-in (using

colmmd, lu, nnz and spy)• The time required for the solution when sparsity is

not used (using full)

The structure of sparse matrices

Time and accuracy of solving a system of equations

Non-zero structure of A

Fill-in

Fill-in

Column reordering

The value of sparsity

Other tutorials available at www.math.sjsu.edu/~foster

• Introduction to the Matrix Market

• Downloading matrices from the Matrix Market

• Converting Matrix Market matrices to Matlab format

• Iterative methods in Matlab with Matrix Market matrices