Introduction to Sparse Matrices In Scilab - Projects

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dnaupddneupddsaupddsaupdznaupdzneupdcompute approximations to a few eigenpairs ofa real linear operatorcompute the converged approximations to eigenvaluesof Az = λBz, approximations to a few eigenpairsof a real linear operatorcompute approximations to a few eigenpairs of a real andsymmetric linear operatorcompute approximations to the converged approximations toeigenvalues of Az = λBzcompute a few eigenpairs of a complex linear operatorwith respect to a semi-inner product defined by ahermitian positive semi-definite real matrix B.compute approximations to the converged approximations toeigenvalues of Az = λBzFigure 10 – Functions from the Arnoldi Package.– Single and Double Precision Real Arithmetic Versions for Symmetric,Non-symmetric,– Standard or Generalized Problems.– Single and Double Precision Complex Arithmetic Versions for Standardor Generalized Problems.– Routines for Banded Matrices - Standard or Generalized Problems.– Routines for The Singular Value Decomposition.– Example driver routines that may be used as templates to implementnumerous Shift-Invert strategies for all problem types, data types andprecision.10 The Matrix Market moduleThe Matrix Market (MM) exchange formats provide a simple mechanismto facilitate the exchange of matrix data. In particular, the objective hasbeen to define a minimal base ASCII file format which can be very easilyexplained and parsed, but can easily adapted to applications with a morerigid structure, or extended to related data objects. The MM exchange formatfor matrices is really a collection of affiliated formats which share design24
mminfommreadmmwriteExtracts size and storage informationReads a Matrix Market fileWrites a sparse or dense matrixFigure 11 – Functions from the Matrix Market module.elements.In the specification, two matrix formats are defined.– Coordinate Format. A file format suitable for representing general sparsematrices. Only nonzero entries are provided, and the coordinates ofeach nonzero entry is given explicitly. This is illustrated in the examplebelow.– Array Format. A file format suitable for representing general densematrices. All entries are provided in a pre-defined (column-oriented)order.The Matrix Market file format can be used to manage dense or sparsematrices. MM coordinate format is suitable for representing sparse matrices.Only nonzero entries need be encoded, and the coordinates of each are givenexplicitly.http://atoms.scilab.org/toolboxes/MatrixMarketIn order to install the Matrix Market module, we use the atoms system,as in the following script.atomsInstall (" MatrixMarket ")The table 11 presents the functions provided by the Matrix Market module.In the following script, we create a sparse matrix with the sparse functionand save it into a file with the mmwrite function.A= sparse ([1 ,1;1 ,3;2 ,2;3 ,1;3 ,3;3 ,4;4 ,3;4 ,4] ,..[9;27+ %i ;16;27 - %i ;145;88;88;121] ,[4 ,4]) ;filename = TMPDIR +"/A. mtx ";mmwrite ( filename ,A);In the following session, we use the mminfo function to extract informationsfrom this file.--> mminfo ( filename );=====================================25
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 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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