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## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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## CGESDD Example Program in C

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/*
CGESDD Example.
==============

Program computes the singular value decomposition of a general
rectangular complex matrix A using a divide and conquer method, where A is:

( -5.40,  7.40) (  6.00,  6.38) (  9.91,  0.16) ( -5.28, -4.16)
(  1.09,  1.55) (  2.60,  0.07) (  3.98, -5.26) (  2.03,  1.11)
(  9.88,  1.91) (  4.92,  6.31) ( -2.11,  7.39) ( -9.81, -8.98)

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. If singular vectors are desired, it uses a divide and conquer
algorithm. 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.
========================

CGESDD Example Program Results

Singular values
21.76  16.60   3.97

Left singular vectors (stored columnwise)
(  0.55,  0.00) (  0.76,  0.00) ( -0.34,  0.00)
( -0.04, -0.15) (  0.27, -0.23) (  0.55, -0.74)
(  0.81,  0.12) ( -0.52, -0.14) (  0.13, -0.11)

Right singular vectors (stored rowwise)
(  0.23,  0.21) (  0.37,  0.39) (  0.24,  0.33) ( -0.56, -0.37)
( -0.58,  0.40) (  0.11,  0.17) (  0.60, -0.27) (  0.16,  0.06)
(  0.60,  0.12) ( -0.19,  0.30) (  0.39,  0.20) (  0.45,  0.31)
*/
#include <stdlib.h>
#include <stdio.h>

/* Complex datatype */
struct _fcomplex { float re, im; };
typedef struct _fcomplex fcomplex;

/* CGESDD prototype */
extern void cgesdd( char* jobz, int* m, int* n, fcomplex* a,
int* lda, float* s, fcomplex* u, int* ldu, fcomplex* vt, int* ldvt,
fcomplex* work, int* lwork, float* rwork, int* iwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda );
extern void print_rmatrix( char* desc, int m, int n, float* 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;
fcomplex wkopt;
fcomplex* work;
/* Local arrays */
/* iwork dimension should be at least 8*min(m,n) */
int iwork[8*M];
/* rwork dimension should be at least 5*(min(m,n))**2 + 7*min(m,n)) */
float s[M], rwork[5*M*M+7*M];
fcomplex u[LDU*M], vt[LDVT*N];
fcomplex a[LDA*N] = {
{-5.40f,  7.40f}, { 1.09f,  1.55f}, { 9.88f,  1.91f},
{ 6.00f,  6.38f}, { 2.60f,  0.07f}, { 4.92f,  6.31f},
{ 9.91f,  0.16f}, { 3.98f, -5.26f}, {-2.11f,  7.39f},
{-5.28f, -4.16f}, { 2.03f,  1.11f}, {-9.81f, -8.98f}
};
/* Executable statements */
printf( " CGESDD Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
cgesdd( "Singular vectors", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &wkopt,
&lwork, rwork, iwork, &info );
lwork = (int)wkopt.re;
work = (fcomplex*)malloc( lwork*sizeof(fcomplex) );
/* Compute SVD */
cgesdd( "Singular vectors", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work,
&lwork, rwork, iwork, &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 CGESDD Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, int m, int n, fcomplex* 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, float* 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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