Introduction to Sparse Matrices In Scilab - Projects

1.2 OverviewIn this section, we make an overview of the features provided by Scilabfor sparse matrices.The current set of tools available in Scilab 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 Sparse package written by Kenneth S. Kundertand Alberto Sangiovanni-Vincentelli,– sparse Cholesky decomposition and resolution of linear equations fromthis decomposition, based on a sparse Cholesky factorization packagedeveloped by Esmond Ng and Barry Peyton 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 to manage sparse matrices.– Scilab is able to read matrices in the Harwell-Boeing format, thanks tothe ReadHBSparse function of the Umfpack module.– The Matrix Market external module (available in ATOMS) providesfunctions to read and write matrices in the Matrix Market format.2 Basic featuresIn this section, we present the basic sparse matrix features. In the firstpart, we review how to create a sparse matrix. Then we analyze how a sparse5