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Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 3/31/2023
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DGESDD Example Program in C

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/*
   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" );
        }
}