Introduction to Sparse Matrices In Scilab - Projects

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function u = mysolverTAUCS (N,b)A = scibench_poissonA (N);hchol = taucs_chfact (A);u = taucs_chsolve ( hchol ,b)taucs_chdel ( hchol )endfunctionWe were unable to use the TAUCS solver, which makes Scilab unstablein this case. This problem was reported in the following bug report :http://bugzilla.scilab.org/show_bug.cgi?id=8824It is straightforward to created increasingly large matrices and to measurethe time required to solve the Poisson equation. The script is provided withinthe demos of the scibench module. The plot in the figure 14 compares thevarious solvers.It is obvious that, in this case, the UMFPACK module is much faster.The fact that we use the pcg function without actually preconditionningthe matrix is an obvious limitation of this benchmark. This is why we workon updating the sparse ILU preconditionners in the following Forge project :http://forge.scilab.org/index.php/p/spilu/The current work is based on the former Scilin project.This benchmark shows that we can solve really large systems of equations.The table in the figure 15 displays the performance measures.For matrices larger than approximately 400, the UMFPACK functionsfails to solve the equation because they require more memory than Scilabcan provide to it.--> scibench_poisson (400 , %t , %t , mysolverUMF )!-- error 999umf_lufact : An error occurred :symbolic factorization : not enough memoryat line 3 of function mysolverUMF called by :at line 95 of function scibench_poisson called by :scibench_poisson (400 , %t , %t , mysolverUMF )We emphasize that the actual size of the matrix does not matter. Whatmatters is the number of nonzero terms in the matrix. For example, withN=500, the matrix is 250000-by-250000 but has only 1 248 000 nonzero entries.32
0.300.25Solving 2D Poisson equation with Sparse solversBackslashPCGUMF0.20Time (s)0.150.100.050.000 5000 10000 15000Number of equationsFigure 14 – Comparison of solvers for the sparse linear system of equationsof the Poisson equation.Solver N Matrix Size Time (s)Backslash 50 2500-by-2500 0.15PCG 50 2500-by-2500 0.09Backslash 100 10000-by-10000 4.32PCG 100 10000-by-10000 0.32Backslash 200 40000-by-40000 88.89PCG 200 40000-by-40000 2.03UMFPACK 200 40000-by-40000 0.81PCG 300 90000-by-90000 7.27UMFPACK 300 90000-by-90000 2.35PCG 500 250000-by-250000 44.77Figure 15 – The Poisson benchmark for various size of matrices.33
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 30 and 31: The solver argument is designed so
Page 34 and 35: -->A = scibench_poissonA ( 500 );--

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