Introduction to Sparse Matrices In Scilab - Projects
Introduction to Sparse Matrices In Scilab - Projects
Introduction to Sparse Matrices In Scilab - Projects
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1.2 Overview<strong>In</strong> this section, we make an overview of the features provided by <strong>Scilab</strong>for sparse matrices.The current set of <strong>to</strong>ols available in <strong>Scilab</strong> for sparse matrices are thefollowing :– management of sparse matrices of arbitrary size,– basic algebra on sparse matrices, including, sum, dot product, transpose,matrix-matrix product,– sparse LU decomposition and resolution of linear equations from thisdecomposition based on the <strong>Sparse</strong> package written by Kenneth S. Kundertand Alber<strong>to</strong> Sangiovanni-Vincentelli,– sparse Cholesky decomposition and resolution of linear equations fromthis decomposition, based on a sparse Cholesky fac<strong>to</strong>rization packagedeveloped by Esmond Ng and Barry Pey<strong>to</strong>n at ORNL and a multipleminimun-degree ordering package by Joseph Liu at University of Waterloo,– iterative methods of linear systems of equations, including PreconditionnedConjugate Gradient (pcg), Generalized Minimum Residual method(gmres), Quasi Minimal Residual method with preconditionning(qmr),– sparse LU decomposition and resolution of linear equations from thisdecomposition based on the UMFPACK library,– sparse Cholesky decomposition and resolution of linear equations fromthis decomposition based on the TAUCS library,– sparse eigenvalue computations, based on the Arpack library, using theImplicitly Restarted Arnoldi Method.Several file formats allows <strong>to</strong> manage sparse matrices.– <strong>Scilab</strong> is able <strong>to</strong> read matrices in the Harwell-Boeing format, thanks <strong>to</strong>the ReadHB<strong>Sparse</strong> function of the Umfpack module.– The Matrix Market external module (available in ATOMS) providesfunctions <strong>to</strong> read and write matrices in the Matrix Market format.2 Basic features<strong>In</strong> this section, we present the basic sparse matrix features. <strong>In</strong> the firstpart, we review how <strong>to</strong> create a sparse matrix. Then we analyze how a sparse5