Introduction to Sparse Matrices In Scilab - Projects

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0 0 0 0 28 20 71 39 0 00 10 0 0 32 0 39 46 8 032 0 0 0 12 33 0 8 82 110 0 65 55 0 0 0 0 11 100];b= ones (10 ,1);Asparse = sparse (A);[x, fail , err , iter , res ]=..pcg ( Asparse ,b, maxIter =30 , tol =1d -12)The previous script produces the following output.-->[x, fail , err , iter , res ]=..--> pcg ( Asparse ,b, maxIter =30 , tol =1d -12)res =1.0.23027430.11021720.02234630.00964460.00520380.00375250.00069590.00002070.00000421.697D -13iter =10.err =1.697D -13fail =0.x =0.00717510.01344920.00676100.00503390.00737350.00652480.00420640.00934340.00446400.0023456We see that 10 iterations were required to get a residual close to 10 −13 .14
chfactchsolvespcholsparse Cholesky factorizationsparse Cholesky solversparse cholesky factorization with permutationsFigure 3 – Cholesky factorizations for sparse matrices.4 Cholesky factorizationsThe figure 3 presents the functions which allow to compute the Choleskydecomposition of sparse matrices.The chfact and chsolve functions can be combined in order to solvesparse linear systems of equations, if the matrix is symmetric positive definite.In the following example, we solve the equation Ax = b where A is a sparse5-by-5 symmetric definite positive matrix.Afull = [2 -1 0 0 0;-1 2 -1 0 0;0 -1 2 -1 0;0 0 -1 2 -1;0 0 0 -1 2];A = sparse ( Afull );h = chfact (A);b = [0 ; 0; 0; 0; 6];chsolve (h,b)The [R,P]=spchol(X) statement produces a sparse lower triangular matrixR and a sparse permutation matrix P such that P RR T P T = X. In thefollowing session, we use the spchol function to compute the sparse Choleskydecomposition of a symmetric definite positive matrix.--> Afull = [--> 2 -1 0 0 0;--> -1 2 -1 0 0;--> 0 -1 2 -1 0;--> 0 0 -1 2 -1;--> 0 0 0 -1 2-->];-->A = sparse ( Afull );-->[R,P]= spchol (A)P =( 5, 5) sparse matrix15
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 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 32 and 33: function u = mysolverTAUCS (N,b)A =
Page 34 and 35: -->A = scibench_poissonA ( 500 );--

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