Developer Reference

ID 766877
Date 12/20/2021
Public

## LAPACKE_sgesvd Example Program in C for Row Major Data Layout

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/*
LAPACKE_sgesvd 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_sgesvd (row-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, float* a, MKL_INT lda );

/* Parameters */
#define M 6
#define N 5
#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;
float superb[min(M,N)-1];
/* Local arrays */
float s[N], u[LDU*M], vt[LDVT*N];
float a[LDA*M] = {
8.79f,  9.93f,  9.83f, 5.45f,  3.16f,
6.11f,  6.91f,  5.04f, -0.27f,  7.98f,
-9.15f, -7.93f,  4.86f, 4.85f,  3.01f,
9.57f,  1.64f,  8.83f, 0.74f,  5.80f,
-3.49f,  4.02f,  9.80f, 10.00f,  4.27f,
9.84f,  0.15f, -8.99f, -6.02f, -5.31f
};
/* Executable statements */
printf( "LAPACKE_sgesvd (row-major, high-level) Example Program Results\n" );
/* Compute SVD */
info = LAPACKE_sgesvd( LAPACK_ROW_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_sgesvd Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, float* 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" );
}
}