Developer Reference

ID 766877
Date 12/20/2021
Public

ZHEEVD Example Program in C

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/*
ZHEEVD Example.
==============

Program computes all eigenvalues and eigenvectors of a complex Hermitian
matrix A using divide and conquer algorithm, where A is:

(  3.40,  0.00) ( -2.36, -1.93) ( -4.68,  9.55) (  5.37, -1.23)
( -2.36,  1.93) (  6.94,  0.00) (  8.13, -1.47) (  2.07, -5.78)
( -4.68, -9.55) (  8.13,  1.47) ( -2.14,  0.00) (  4.68,  7.44)
(  5.37,  1.23) (  2.07,  5.78) (  4.68, -7.44) ( -7.42,  0.00)

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

The routine computes all eigenvalues and, optionally, eigenvectors of an
n-by-n complex Hermitian matrix A. The eigenvector v(j) of A satisfies

A*v(j) = lambda(j)*v(j)

where lambda(j) is its eigenvalue. The computed eigenvectors are
orthonormal.
If the eigenvectors are requested, then this routine uses a divide and
conquer algorithm to compute eigenvalues and eigenvectors.

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

ZHEEVD Example Program Results

Eigenvalues
-21.97  -0.05   6.46  16.34

Eigenvectors (stored columnwise)
(  0.41,  0.00) ( -0.34,  0.00) ( -0.69,  0.00) (  0.49,  0.00)
(  0.02, -0.30) (  0.32, -0.21) ( -0.57, -0.22) ( -0.59, -0.21)
(  0.18,  0.57) ( -0.42, -0.32) (  0.06,  0.16) ( -0.35, -0.47)
( -0.62, -0.09) ( -0.58,  0.35) ( -0.15, -0.31) ( -0.10, -0.12)
*/
#include <stdlib.h>
#include <stdio.h>

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

/* ZHEEVD prototype */
extern void zheevd( char* jobz, char* uplo, int* n, dcomplex* a, int* lda,
double* w, dcomplex* work, int* lwork, double* rwork, int* lrwork,
int* iwork, int* liwork, 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 N 4
#define LDA N

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, info, lwork, lrwork, liwork;
int iwkopt;
int* iwork;
double rwkopt;
double* rwork;
dcomplex wkopt;
dcomplex* work;
/* Local arrays */
double w[N];
dcomplex a[LDA*N] = {
{ 3.40,  0.00}, {-2.36,  1.93}, {-4.68, -9.55}, { 5.37,  1.23},
{ 0.00,  0.00}, { 6.94,  0.00}, { 8.13,  1.47}, { 2.07,  5.78},
{ 0.00,  0.00}, { 0.00,  0.00}, {-2.14,  0.00}, { 4.68, -7.44},
{ 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, {-7.42,  0.00}
};
/* Executable statements */
printf( " ZHEEVD Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
lrwork = -1;
liwork = -1;
zheevd( "Vectors", "Lower", &n, a, &lda, w, &wkopt, &lwork, &rwkopt,
&lrwork, &iwkopt, &liwork, &info );
lwork = (int)wkopt.re;
work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
lrwork = (int)rwkopt;
rwork = (double*)malloc( lrwork*sizeof(double) );
liwork = iwkopt;
iwork = (int*)malloc( liwork*sizeof(int) );
/* Solve eigenproblem */
zheevd( "Vectors", "Lower", &n, a, &lda, w, work, &lwork, rwork,
&lrwork, iwork, &liwork, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm failed to compute eigenvalues.\n" );
exit( 1 );
}
/* Print eigenvalues */
print_rmatrix( "Eigenvalues", 1, n, w, 1 );
/* Print eigenvectors */
print_matrix( "Eigenvectors (stored columnwise)", n, n, a, lda );
/* Free workspace */
free( (void*)iwork );
free( (void*)rwork );
free( (void*)work );
exit( 0 );
} /* End of ZHEEVD 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" );
}
}