## Developer Reference

• 2022.1
• 12/20/2021
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Contents

# LAPACKE_dgesvd Example Program in C for Column Major Data Layout

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/*
LAPACKE_dgesvd Example.
=======================

Program computes the singular value decomposition of a general
rectangular matrix A:

8.79   9.93   9.83   5.45   3.16
6.11   6.91   5.04  -0.27   7.98
-9.15  -7.93   4.86   4.85   3.01
9.57   1.64   8.83   0.74   5.80
-3.49   4.02   9.80  10.00   4.27
9.84   0.15  -8.99  -6.02  -5.31

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. 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.
========================

LAPACKE_dgesvd (column-major, high-level) Example Program Results

Singular values
27.47  22.64   8.56   5.99   2.01

Left singular vectors (stored columnwise)
-0.59   0.26   0.36   0.31   0.23
-0.40   0.24  -0.22  -0.75  -0.36
-0.03  -0.60  -0.45   0.23  -0.31
-0.43   0.24  -0.69   0.33   0.16
-0.47  -0.35   0.39   0.16  -0.52
0.29   0.58  -0.02   0.38  -0.65

Right singular vectors (stored rowwise)
-0.25  -0.40  -0.69  -0.37  -0.41
0.81   0.36  -0.25  -0.37  -0.10
-0.26   0.70  -0.22   0.39  -0.49
0.40  -0.45   0.25   0.43  -0.62
-0.22   0.14   0.59  -0.63  -0.44
*/
#include <stdlib.h>
#include <stdio.h>
#include "mkl_lapacke.h"

#define min(a,b) ((a)>(b)?(b):(a))

/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );

/* Parameters */
#define M 6
#define N 5
#define LDA M
#define LDU M
#define LDVT N

/* Main program */
int main() {
/* Locals */
MKL_INT m = M, n = N, lda = LDA, ldu = LDU, ldvt = LDVT, info;
double superb[min(M,N)-1];
/* Local arrays */
double s[N], u[LDU*M], vt[LDVT*N];
double a[LDA*N] = {
8.79,  6.11, -9.15,  9.57, -3.49,  9.84,
9.93,  6.91, -7.93,  1.64,  4.02,  0.15,
9.83,  5.04,  4.86,  8.83,  9.80, -8.99,
5.45, -0.27,  4.85,  0.74, 10.00, -6.02,
3.16,  7.98,  3.01,  5.80,  4.27, -5.31
};
/* Executable statements */
printf( "LAPACKE_dgesvd (column-major, high-level) Example Program Results\n" );
/* Compute SVD */
info = LAPACKE_dgesvd( LAPACK_COL_MAJOR, 'A', 'A', m, n, a, lda,
s, u, ldu, vt, ldvt, superb );
/* 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 );
exit( 0 );
} /* End of LAPACKE_dgesvd Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( 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+j*lda] );
printf( "\n" );
}
}``````

#### Product and Performance Information

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