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  • 2022.1
  • 12/20/2021
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DGESDD 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. * ******************************************************************************** */ /* DGESDD Example. ============== Program computes the singular value decomposition of a general rectangular matrix A using a divide and conquer method, where A is: 7.52 -1.10 -7.95 1.08 -0.76 0.62 9.34 -7.10 5.13 6.62 -5.66 0.87 -4.75 8.52 5.75 5.30 1.33 4.91 -5.49 -3.52 -2.40 -6.77 2.34 3.95 Description. ============ The routine computes the singular value decomposition (SVD) of a real m-by-n matrix A, optionally computing the left and/or right singular vectors. If singular vectors are desired, it uses a divide and conquer algorithm. The SVD is written as A = U*SIGMA*VT where SIGMA is an m-by-n matrix which is zero except for its min(m,n) diagonal elements, U is an m-by-m orthogonal matrix and VT (V transposed) is an n-by-n orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m, n) columns of U and V are the left and right singular vectors of A. Note that the routine returns VT, not V. Example Program Results. ======================== DGESDD Example Program Results Singular values 18.37 13.63 10.85 4.49 Left singular vectors (stored columnwise) -0.57 0.18 0.01 0.53 0.46 -0.11 -0.72 0.42 -0.45 -0.41 0.00 0.36 0.33 -0.69 0.49 0.19 -0.32 -0.31 -0.28 -0.61 0.21 0.46 0.39 0.09 Right singular vectors (stored rowwise) -0.52 -0.12 0.85 -0.03 0.08 -0.99 -0.09 -0.01 -0.28 -0.02 -0.14 0.95 0.81 0.01 0.50 0.31 */ #include <stdlib.h> #include <stdio.h> /* DGESDD prototype */ extern void dgesdd( char* jobz, int* m, int* n, double* a, int* lda, double* s, double* u, int* ldu, double* vt, int* ldvt, double* work, int* lwork, int* iwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, double* a, int lda ); /* Parameters */ #define M 6 #define N 4 #define LDA M #define LDU M #define LDVT N /* Main program */ int main() { /* Locals */ int m = M, n = N, lda = LDA, ldu = LDU, ldvt = LDVT, info, lwork; double wkopt; double* work; /* Local arrays */ /* iwork dimension should be at least 8*min(m,n) */ int iwork[8*N]; double s[N], u[LDU*M], vt[LDVT*N]; double a[LDA*N] = { 7.52, -0.76, 5.13, -4.75, 1.33, -2.40, -1.10, 0.62, 6.62, 8.52, 4.91, -6.77, -7.95, 9.34, -5.66, 5.75, -5.49, 2.34, 1.08, -7.10, 0.87, 5.30, -3.52, 3.95 }; /* Executable statements */ printf( " DGESDD Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; dgesdd( "Singular vectors", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &wkopt, &lwork, iwork, &info ); lwork = (int)wkopt; work = (double*)malloc( lwork*sizeof(double) ); /* Compute SVD */ dgesdd( "Singular vectors", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &info ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm computing SVD failed to converge.\n" ); exit( 1 ); } /* Print singular values */ print_matrix( "Singular values", 1, n, s, 1 ); /* Print left singular vectors */ print_matrix( "Left singular vectors (stored columnwise)", m, n, u, ldu ); /* Print right singular vectors */ print_matrix( "Right singular vectors (stored rowwise)", n, n, vt, ldvt ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of DGESDD Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( 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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