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  • 12/20/2021
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LAPACKE_zgesdd Example Program in C for Row Major Data Layout

/******************************************************************************* * 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. * ******************************************************************************** */ /* LAPACKE_zgesdd Example. ======================= Program computes the singular value decomposition of a general rectangular complex matrix A using a divide and conquer method, where A is: ( -5.40, 7.40) ( 6.00, 6.38) ( 9.91, 0.16) ( -5.28, -4.16) ( 1.09, 1.55) ( 2.60, 0.07) ( 3.98, -5.26) ( 2.03, 1.11) ( 9.88, 1.91) ( 4.92, 6.31) ( -2.11, 7.39) ( -9.81, -8.98) Description. ============ The routine computes the singular value decomposition (SVD) of a complex 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*VH 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 unitary matrix and VH (V conjugate transposed) is an n-by-n unitary 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 VH, not V. Example Program Results. ======================== LAPACKE_zgesdd (row-major, high-level) Example Program Results Singular values 21.76 16.60 3.97 Left singular vectors (stored columnwise) ( 0.55, 0.00) ( 0.76, 0.00) ( -0.34, 0.00) ( -0.04, -0.15) ( 0.27, -0.23) ( 0.55, -0.74) ( 0.81, 0.12) ( -0.52, -0.14) ( 0.13, -0.11) Right singular vectors (stored rowwise) ( 0.23, 0.21) ( 0.37, 0.39) ( 0.24, 0.33) ( -0.56, -0.37) ( -0.58, 0.40) ( 0.11, 0.17) ( 0.60, -0.27) ( 0.16, 0.06) ( 0.60, 0.12) ( -0.19, 0.30) ( 0.39, 0.20) ( 0.45, 0.31) */ #include <stdlib.h> #include <stdio.h> #include "mkl_lapacke.h" /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* a, MKL_INT lda ); extern void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ); /* Parameters */ #define M 3 #define N 4 #define LDA N #define LDU M #define LDVT N /* Main program */ int main() { /* Locals */ MKL_INT m = M, n = N, lda = LDA, ldu = LDU, ldvt = LDVT, info; /* Local arrays */ double s[M]; MKL_Complex16 u[LDU*M], vt[LDVT*N]; MKL_Complex16 a[LDA*M] = { {-5.40, 7.40}, { 6.00, 6.38}, { 9.91, 0.16}, {-5.28, -4.16}, { 1.09, 1.55}, { 2.60, 0.07}, { 3.98, -5.26}, { 2.03, 1.11}, { 9.88, 1.91}, { 4.92, 6.31}, {-2.11, 7.39}, {-9.81, -8.98} }; /* Executable statements */ printf( "LAPACKE_zgesdd (row-major, high-level) Example Program Results\n" ); /* Compute SVD */ info = LAPACKE_zgesdd( LAPACK_ROW_MAJOR, 'S', m, n, a, lda, s, u, ldu, vt, ldvt ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm computing SVD failed to converge.\n" ); exit( 1 ); } /* Print singular values */ print_rmatrix( "Singular values", 1, m, s, 1 ); /* Print left singular vectors */ print_matrix( "Left singular vectors (stored columnwise)", m, m, u, ldu ); /* Print right singular vectors */ print_matrix( "Right singular vectors (stored rowwise)", m, n, vt, ldvt ); exit( 0 ); } /* End of LAPACKE_zgesdd Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* a, MKL_INT lda ) { MKL_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*lda+j].real, a[i*lda+j].imag ); printf( "\n" ); } } /* Auxiliary routine: printing a real matrix */ void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) { MKL_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*lda+j] ); printf( "\n" ); } }

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