Introduction to Sparse Matrices In Scilab - Projects

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The solver argument is designed so that we can customize the linear equationsolver which we want to use. For example, if we want to use the sparsebackslash operator, all we have to do is to create the mysolverBackslashfunction as below.function u= mysolverBackslash (N, b)A = scibench_poissonA (N);u = A\b;endfunctionThe following script solves the Poisson equation with N = 50.scf ();scibench_poisson (50 , %t , %t , mysolverBackslash );The previous script produces the following output, where h is the dimensionnalspacee step and enorminf is the value of the infinite norm of the error.-> scibench_poisson (50 , %t , %t , mysolverBackslash );N = 50h = 1.9607843137254902 e -002h^2 = 3.8446751249519417 e -004enorminf = 1.2634082165868810 e -003C = enorminf / h^2 = 3.2861247713424775 e +000wall clock time = 0.15 secondsThe previous script also produces the plot in the figure 13.It is then easy to use the pcg function built in Scilab, which uses a preconditionnedconjugate gradient algorithm. We use the scibench_poissonAufunction, which computes the A*u product without actually storing the matrixA.function u= mysolverPCG (N, b)tol = 0.000001;maxit = 9999;u = zeros (N ^2 ,1);[u,flag ,iter , res ] = ..pcg ( scibench_poissonAu ,b,tol , maxit ,[] ,[] ,u);endfunctionscf ();[ timesec , enorminf ,h] = ..scibench_poisson (50 , %f , %t , mysolverPCG );30
Figure 13 – Approximate solution and numerical error of the Poisson equation.11.4 The benchmarkBased on the scibench module, it is easy to compare various sparse linearequation solvers in Scilab. We compared the following functions :– sparse backslash (which internally use a sparse LU decomposition),– pcg function,– UMPFACK module,– the TAUCS module.Both the UMFPACK and TAUCS modules were created by Bruno Pincon[7].In order to use the UMFPACK module, we created the following mysolverUMFfunction which solves the A*u=b equation.function u = mysolverUMF (N,b)A = scibench_poissonA (N);humf = umf_lufact (A);u = umf_lusolve (humf ,b)umf_ludel ( humf )endfunctionWe also created the following wrapper for the TAUCS module.31
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 28 and 29: Sparse matrices can be managed in S
Page 32 and 33: function u = mysolverTAUCS (N,b)A =
Page 34 and 35: -->A = scibench_poissonA ( 500 );--

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