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  • 12/20/2021
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ZGELSD 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. * ******************************************************************************** */ /* ZGELSD Example. ============== Program computes the minimum norm-solution to a complex linear least squares problem using the singular value decomposition of A, where A is the coefficient matrix: ( 4.55, -0.32) ( -4.36, -4.76) ( 3.99, -6.84) ( 8.03, -6.47) ( 8.87, -3.11) ( 0.02, 8.43) ( 5.43, -9.30) ( 2.28, 8.94) ( -0.74, 1.16) ( 3.80, -6.12) ( -7.24, 0.72) ( 2.21, 9.52) and B is the right-hand side matrix: ( -8.25, 7.98) ( 2.91, -8.81) ( -5.04, 3.33) ( 6.19, 0.19) ( 7.98, -4.38) ( -5.96, 7.18) Description. ============ The routine computes the minimum-norm solution to a complex linear least squares problem: minimize ||b - A*x|| using the singular value decomposition (SVD) of A. A is an m-by-n matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the m-by-nrhs right hand side matrix B and the n-by-nrhs solution matrix X. The effective rank of A is determined by treating as zero those singular values which are less than rcond times the largest singular value. Example Program Results. ======================== ZGELSD Example Program Results Minimum norm solution ( -0.08, 0.09) ( 0.04, 0.16) ( -0.17, 0.10) ( 0.17, -0.47) ( -0.92, -0.01) ( 0.71, -0.41) ( -0.47, -0.26) ( 0.69, 0.02) Effective rank = 3 Singular values 20.01 18.21 7.88 */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZGELSD prototype */ extern void zgelsd( int* m, int* n, int* nrhs, dcomplex* a, int* lda, dcomplex* b, int* ldb, double* s, double* rcond, int* rank, dcomplex* work, int* lwork, double* rwork, int* iwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ); extern void print_rmatrix( char* desc, int m, int n, double* a, int lda ); /* Parameters */ #define M 3 #define N 4 #define NRHS 2 #define LDA M #define LDB N /* Main program */ int main() { /* Locals */ int m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork, rank; /* Negative rcond means using default (machine precision) value */ double rcond = -1.0; dcomplex wkopt; dcomplex* work; /* Local arrays */ /* iwork dimension should be at least 3*min(m,n)*nlvl + 11*min(m,n), rwork dimension should be at least 10*min(m,n)+2*min(m,n)*smlsiz+ +8*min(m,n)*nlvl+3*smlsiz*nrhs+(smlsiz+1)^2, where nlvl = max( 0, int( log_2( min(m,n)/(smlsiz+1) ) )+1 ) and smlsiz = 25 */ int iwork[3*M*0+11*M]; double s[M], rwork[10*M+2*M*25+8*M*0+3*25*NRHS+26*26]; dcomplex a[LDA*N] = { { 4.55, -0.32}, { 8.87, -3.11}, {-0.74, 1.16}, {-4.36, -4.76}, { 0.02, 8.43}, { 3.80, -6.12}, { 3.99, -6.84}, { 5.43, -9.30}, {-7.24, 0.72}, { 8.03, -6.47}, { 2.28, 8.94}, { 2.21, 9.52} }; dcomplex b[LDB*NRHS] = { {-8.25, 7.98}, {-5.04, 3.33}, { 7.98, -4.38}, { 0.00, 0.00}, { 2.91, -8.81}, { 6.19, 0.19}, {-5.96, 7.18}, { 0.00, 0.00} }; /* Executable statements */ printf( " ZGELSD Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; zgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, &wkopt, &lwork, rwork, iwork, &info ); lwork = (int)wkopt.re; work = (dcomplex*)malloc( lwork*sizeof(dcomplex) ); /* Solve the equations A*X = B */ zgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, work, &lwork, rwork, iwork, &info ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm computing SVD failed to converge;\n" ); printf( "the least squares solution could not be computed.\n" ); exit( 1 ); } /* Print minimum norm solution */ print_matrix( "Minimum norm solution", n, nrhs, b, ldb ); /* Print effective rank */ printf( "\n Effective rank = %6i\n", rank ); /* Print singular values */ print_rmatrix( "Singular values", 1, m, s, 1 ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of ZGELSD 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 real matrix */ void print_rmatrix( char* desc, int m, int n, double* 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", a[i+j*lda] ); printf( "\n" ); } }

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