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  • 12/20/2021
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ZSYSV Example Program in C

/******************************************************************************* * Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* ZSYSV Example. ============== The program computes the solution to the system of linear equations with a complex symmetric matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( 9.99, -4.73) ( -5.68, -0.80) ( -8.94, 1.32) ( -9.42, 2.05) ( -5.68, -0.80) ( -8.01, 4.61) ( 1.64, -6.29) ( 6.79, -2.17) ( -8.94, 1.32) ( 1.64, -6.29) ( 9.04, 3.96) ( -4.51, -7.54) ( -9.42, 2.05) ( 6.79, -2.17) ( -4.51, -7.54) ( 0.40, 4.06) and B is the right-hand side matrix: ( 5.71, -1.20) ( 2.84, -0.18) ( -7.70, 6.47) ( -8.29, -1.72) ( 3.77, -7.40) ( -4.28, -8.25) ( -3.78, 0.33) ( -2.70, -0.39) Description. ============ The routine solves for X the complex system of linear equations A*X = B, where A is an n-by-n symmetric matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The diagonal pivoting method is used to factor A as A = U*D*UT or A = L*D*LT , where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A*X = B. Example Program Results. ======================== ZSYSV Example Program Results Solution ( 0.13, 0.13) ( 0.63, 0.34) ( 0.32, -0.07) ( 0.61, 0.21) ( -0.26, -0.44) ( -0.01, -0.10) ( -0.40, 0.51) ( 0.21, 0.02) Details of factorization (-16.42, 1.69) ( -0.53, 0.35) ( 0.36, 0.41) ( -0.78, 0.49) ( 0.00, 0.00) ( 3.69, 0.64) (-16.58, -1.61) ( -0.10, -0.65) ( 0.00, 0.00) ( 0.00, 0.00) ( 1.02, -3.74) ( -0.73, -0.52) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 9.04, 3.96) Pivot indices 1 -1 -1 3 */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZSYSV prototype */ extern void zsysv( char* uplo, int* n, int* nrhs, dcomplex* a, int* lda, int* ipiv, dcomplex* b, int* ldb, dcomplex* work, int* lwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ); extern void print_int_vector( char* desc, int n, int* a ); /* Parameters */ #define N 4 #define NRHS 2 #define LDA N #define LDB N /* Main program */ int main() { /* Locals */ int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork; dcomplex wkopt; dcomplex* work; /* Local arrays */ int ipiv[N]; dcomplex a[LDA*N] = { { 9.99, -4.73}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, {-5.68, -0.80}, {-8.01, 4.61}, { 0.00, 0.00}, { 0.00, 0.00}, {-8.94, 1.32}, { 1.64, -6.29}, { 9.04, 3.96}, { 0.00, 0.00}, {-9.42, 2.05}, { 6.79, -2.17}, {-4.51, -7.54}, { 0.40, 4.06} }; dcomplex b[LDB*NRHS] = { { 5.71, -1.20}, {-7.70, 6.47}, { 3.77, -7.40}, {-3.78, 0.33}, { 2.84, -0.18}, {-8.29, -1.72}, {-4.28, -8.25}, {-2.70, -0.39} }; /* Executable statements */ printf( " ZSYSV Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; zsysv( "Upper", &n, &nrhs, a, &lda, ipiv, b, &ldb, &wkopt, &lwork, &info ); lwork = (int)wkopt.re; work = (dcomplex*)malloc( lwork*sizeof(dcomplex) ); /* Solve the equations A*X = B */ zsysv( "Upper", &n, &nrhs, a, &lda, ipiv, b, &ldb, work, &lwork, &info ); /* Check for the exact singularity */ if( info > 0 ) { printf( "The element of the diagonal factor " ); printf( "D(%i,%i) is zero, so that D is singular;\n", info, info ); printf( "the solution could not be computed.\n" ); exit( 1 ); } /* Print solution */ print_matrix( "Solution", n, nrhs, b, ldb ); /* Print details of factorization */ print_matrix( "Details of factorization", n, n, a, lda ); /* Print pivot indices */ print_int_vector( "Pivot indices", n, ipiv ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of ZSYSV Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " (%6.2f,%6.2f)", a[i+j*lda].re, a[i+j*lda].im ); printf( "\n" ); } } /* Auxiliary routine: printing a vector of integers */ void print_int_vector( char* desc, int n, int* a ) { int j; printf( "\n %s\n", desc ); for( j = 0; j < n; j++ ) printf( " %6i", a[j] ); printf( "\n" ); }

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