Introduction to Sparse Matrices In Scilab - Projects

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-->D= sparse (C)D =( 3, 5) sparse matrix( 1, 1) 1. + 9.i( 1, 2) 2. + 10. i( 2, 1) 3. + 11. i( 2, 2) 4. + 12. i( 2, 3) 5. + 13. i( 3, 2) 6. + 14. i( 3, 3) 7. + 15. i( 3, 4) 8. + 16. i2.2 Storage formatThere are various ways of storing the nonzero entries of a sparse matrix.In this section, we review how sparse matrices are stored internally, at thelibrary level.As we are going to see, the format used in Scilab is very similar (butnot exactly identical) to the compressed sparse row format (CSR), in whichthe nonzero entries are stored row-by-row. While this detail does not changethe way a user user sparse matrices at the interpreter level, it does have animpact on the way the libraries are connected to Scilab. Hence, this is animportant feature of sparse matrices in Scilab and it is worthwhile to knowprecisely what is stored.In Scilab, a sparse matrix is defined in the modules/core/includes/sparse.h.This is a C struct with type scisparse and the following fields :– int m : the number of rows.– int n : the number of columns.– int it : is equal to 0 if the matrix is real, and 1 if the matrix is complex.– int nel : number of nonzero elements */– int *mnel : an array with m entries. The entry mnel[i] is the numberof non nul elements of the i-th row.– int *icol : an array with nel entries. The entry icol[j] is the columnof the j-th nonzero element.– double *R : an array with nel entries. The entry R[j] is the real partof the j-th nonzero element.– double *I : an array with nel entries. The entry I[j] is the imaginarypart of the j-th nonzero element.Consider the sparse matrix in the following example.8
-->A = [-->1 2 0-->3 4 5-->0 6 7-->];-->B = sparse (A);In this case, the fields are the following.B.m: 3B.n: 3B.it: 0B. nel : 7B. mnel : [2 , 3, 2]B. icol : [1 , 2, 1, 2, 3, 2, 3]B.R: [1.0 , 2.0 , 3.0 , 4.0 , 5.0 , 6.0 , 7.0]B.I: [ undefined ]This current storage is different from the CSR format, in the sense thatthere is no array containing the row indices corresponding to the values andno array containing the cumulated indexes where each column starts.2.3 Sparse arithmeticScilab provides arithmetic operators for sparse matrices.Indeed, most operators are defined for sparse matrices. For example, theoperators +, - and * can be used for sparse matrices, as shown in the followingexample.Afull = [2 3 0 0 0;3 0 4 0 6;0 -1 -3 2 0;0 0 1 0 0;0 4 2 0 1];A = sparse ( Afull );B = 2*AC = A+Bx = [1;2;3;4;5]b = A * xAnother operator is the backslash operator \, which is presented in thenext section.9
Page 2: 4 Cholesky factorizations 155 Funct
Page 6 and 7: sp2adjspeyesponessprandspzerosfulls
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 32 and 33: function u = mysolverTAUCS (N,b)A =
Page 34 and 35: -->A = scibench_poissonA ( 500 );--

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