## Developer Reference

• 2022.1
• 12/20/2021
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Contents

# ZGESVD Example Program in C

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

ZGESVD 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>

/* Complex datatype */
struct _dcomplex { double re, im; };
typedef struct _dcomplex dcomplex;

/* ZGESVD prototype */
extern void zgesvd( char* jobu, char* jobvt, int* m, int* n, dcomplex* a,
int* lda, double* s, dcomplex* u, int* ldu, dcomplex* vt, int* ldvt,
dcomplex* work, int* lwork, double* rwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda );
extern void print_rmatrix( char* desc, int m, int n, double* a, int lda );

/* Parameters */
#define M 3
#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;
dcomplex wkopt;
dcomplex* work;
/* Local arrays */
/* rwork dimension should be at least max( 1, 5*min(m,n) ) */
double s[M], rwork[5*M];
dcomplex u[LDU*M], vt[LDVT*N];
dcomplex a[LDA*N] = {
{ 5.91, -5.69}, {-3.15, -4.08}, {-4.89,  4.20},
{ 7.09,  2.72}, {-1.89,  3.27}, { 4.10, -6.70},
{ 7.78, -4.06}, { 4.57, -2.07}, { 3.28, -3.84},
{-0.79, -7.21}, {-3.88, -3.30}, { 3.84,  1.19}
};
/* Executable statements */
printf( " ZGESVD Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
zgesvd( "All", "All", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &wkopt, &lwork,
rwork, &info );
lwork = (int)wkopt.re;
work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
/* Compute SVD */
zgesvd( "All", "All", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork,
rwork, &info );
/* 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 );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of ZGESVD Example */

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

/* Auxiliary routine: printing a real matrix */
void print_rmatrix( 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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