Introduction to Sparse Matrices In Scilab - Projects

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Sparse matrices can be managed in Scilab since 1989 [2]. In Scilab 5.0(i.e. in 2008), the UMFPACK module was added.The Scibench external module :http://atoms.scilab.org/toolboxes/scibenchprovides a collection of benchmark scripts to measure the performanceof Scilab. For example, it contains benchmarks for the dense matrix-matrixproduct, the dense backslash operator, the Cholesky decomposition or 2DLattice Boltzmann simulations.In order to install this module, we use the statement :atomsInstall (" scibench ")and restart Scilab.The version 0.6 includes benchmarks for sparse matrices, based on thePoisson equation. The performance presented in this document are measuredwith Scilab 5.3.2 on Windows XP with a 4GB computer using Intel XeonE5410 4*2.33 GHz processors.The script that we are going to use is poisson.sce, which is provided inthe demos directory of the module.11.2 The sparse matrixThe scibench_poissonA(n) statement creates a sparse matrix equationassociated with n cells in the X coordinate and n cells in the Y coordinate.Before calling this session, we call the stacksize function in order to let Scilaballocate as much memory as possible. Then we call the PlotSparse functionto plot the sparsity pattern of the matrix.stacksize (" max ");A = scibench_poissonA (50);PlotSparse (A)The previous script produces the plot in the figure 12.We emphasize that the previous matrix is a n 2 -by-n 2 sparse matrix. Evenfor moderate values of n, this creates huge matrices. Fortunately, only nonzeroentries are stored, so that Scilab has no problem to store it, provided thatthe nonzero entries can be stored in the memory.--> size (A)ans =2500. 2500.28
Figure 12 – Sparsity pattern of the Poisson matrix.The Kronecker operator is used, so that the computation of the matrix isvectorized. To edit the code, we just run the following code.--> edit scibench_poissonAAt the core of the algorithm, we find the statementA = I .*. T + T .*. Iwhere T is a sparse matrix and I is the sparse n-by-n identity matrix. Hence,creating the whole matrix is done with only one statement.11.3 The Poisson SolverThe scibench_poisson function solves the 2D Poisson equation. Its callingsequence isscibench_poisson ( N , plotgraph , verbose , solver )where N is the number of cells, plotgraph is a boolean to plot the graphics,verbose is a boolean to print messages and solver is a function which solvesthe linear equation A*x=b.29
Page 2: 4 Cholesky factorizations 155 Funct
Page 6 and 7: sp2adjspeyesponessprandspzerosfulls
Page 8 and 9: -->D= sparse (C)D =( 3, 5) sparse m
Page 10 and 11: lufactlusolvelugetludelchfactchsolv
Page 12 and 13: -->x= lusolve (h,b)x =1.0.50.333333
Page 14 and 15: 0 0 0 0 28 20 71 39 0 00 10 0 0 32
Page 16 and 17: PlotSparseReadHBSparsecond2spcondes
Page 18 and 19: umf licenseumf ludelumf lufactumf l
Page 20 and 21: Read sparse doubles matrices in gat
Page 22 and 23: int read_sparse ( char * fname , un
Page 24 and 25: dnaupddneupddsaupddsaupdznaupdzneup
Page 26 and 27: Information about MatrixMarket file
Page 30 and 31: The solver argument is designed so
Page 32 and 33: function u = mysolverTAUCS (N,b)A =
Page 34 and 35: -->A = scibench_poissonA ( 500 );--

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