Introduction to Sparse Matrices In Scilab - Projects

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