Developer Reference

ID 766877
Date 12/20/2021
Public

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

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/*
LAPACKE_zgesvd Example.
=======================

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

(  5.91, -5.69) (  7.09,  2.72) (  7.78, -4.06) ( -0.79, -7.21)
( -3.15, -4.08) ( -1.89,  3.27) (  4.57, -2.07) ( -3.88, -3.30)
( -4.89,  4.20) (  4.10, -6.70) (  3.28, -3.84) (  3.84,  1.19)

Description.
============

The routine computes the singular value decomposition (SVD) of a complex
m-by-n matrix A, optionally computing the left and/or right singular
vectors. The SVD is written as

A = U*SIGMA*VH

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 unitary matrix and VH (V conjugate
transposed) is an n-by-n unitary 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 VH, not V.

Example Program Results.
========================

LAPACKE_zgesvd (row-major, high-level) Example Program Results

Singular values
17.63  11.61   6.78

Left singular vectors (stored columnwise)
( -0.86,  0.00) (  0.40,  0.00) (  0.32,  0.00)
( -0.35,  0.13) ( -0.24, -0.21) ( -0.63,  0.60)
(  0.15,  0.32) (  0.61,  0.61) ( -0.36,  0.10)

Right singular vectors (stored rowwise)
( -0.22,  0.51) ( -0.37, -0.32) ( -0.53,  0.11) (  0.15,  0.38)
(  0.31,  0.31) (  0.09, -0.57) (  0.18, -0.39) (  0.38, -0.39)
(  0.53,  0.24) (  0.49,  0.28) ( -0.47, -0.25) ( -0.15,  0.19)
*/
#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, MKL_Complex16* a, MKL_INT lda );
extern void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );

/* Parameters */
#define M 3
#define N 4
#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;
/* Local arrays */
double s[M];
double superb[min(M,N)-1];
MKL_Complex16 u[LDU*M], vt[LDVT*N];
MKL_Complex16 a[LDA*M] = {
{ 5.91, -5.69}, { 7.09,  2.72}, { 7.78, -4.06}, {-0.79, -7.21},
{-3.15, -4.08}, {-1.89,  3.27}, { 4.57, -2.07}, {-3.88, -3.30},
{-4.89,  4.20}, { 4.10, -6.70}, { 3.28, -3.84}, { 3.84,  1.19}
};
/* Executable statements */
printf( "LAPACKE_zgesvd (row-major, high-level) Example Program Results\n" );
/* Compute SVD */
info = LAPACKE_zgesvd( 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_rmatrix( "Singular values", 1, m, s, 1 );
/* Print left singular vectors */
print_matrix( "Left singular vectors (stored columnwise)", m, m, u, ldu );
/* Print right singular vectors */
print_matrix( "Right singular vectors (stored rowwise)", m, n, vt, ldvt );
exit( 0 );
} /* End of LAPACKE_zgesvd Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* 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,%6.2f)", a[i*lda+j].real, a[i*lda+j].imag );
printf( "\n" );
}
}

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