## Developer Reference

• 2022.1
• 12/20/2021
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Contents

# 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" );
}
}``````

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