Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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

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/*
LAPACKE_sgesdd 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.
========================

LAPACKE_sgesdd (column-major, high-level) 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>
#include "mkl_lapacke.h"

/* 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 4
#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;
/* Local arrays */
float s[N], u[LDU*M], vt[LDVT*N];
float a[LDA*N] = {
7.52f, -0.76f,  5.13f, -4.75f,  1.33f, -2.40f,
-1.10f,  0.62f,  6.62f,  8.52f,  4.91f, -6.77f,
-7.95f,  9.34f, -5.66f,  5.75f, -5.49f,  2.34f,
1.08f, -7.10f,  0.87f,  5.30f, -3.52f,  3.95f
};
/* Executable statements */
printf( "LAPACKE_sgesdd (column-major, high-level) Example Program Results\n" );
/* Compute SVD */
info = LAPACKE_sgesdd( LAPACK_COL_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_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_sgesdd 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+j*lda] );
printf( "\n" );
}
}