Developer Reference

ID 766877
Date 12/20/2021
Public

## ZHEEVX Example Program in C

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/*
ZHEEVX Example.
==============

Program computes eigenvalues specified by a selected range of values
and corresponding eigenvectors of a complex Hermitian matrix A:

(  6.51,  0.00) ( -5.92,  9.53) ( -2.46,  2.91) (  8.84,  3.21)
( -5.92, -9.53) ( -1.73,  0.00) (  6.50,  2.09) (  1.32,  8.81)
( -2.46, -2.91) (  6.50, -2.09) (  6.90,  0.00) ( -0.59,  2.47)
(  8.84, -3.21) (  1.32, -8.81) ( -0.59, -2.47) ( -2.85,  0.00)

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

The routine computes selected 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.
Eigenvalues and eigenvectors can be selected by specifying either a range
of values or a range of indices for the desired eigenvalues.

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

ZHEEVX Example Program Results

The total number of eigenvalues found: 3

Selected eigenvalues
0.09   9.53  18.75

Selected eigenvectors (stored columnwise)
(  0.18,  0.00) ( -0.54,  0.00) (  0.67,  0.00)
( -0.40, -0.31) ( -0.21, -0.17) ( -0.30, -0.43)
(  0.60,  0.40) ( -0.35, -0.28) ( -0.39, -0.34)
( -0.34,  0.26) ( -0.57,  0.35) (  0.05,  0.05)
*/
#include <stdlib.h>
#include <stdio.h>

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

/* ZHEEVX prototype */
extern void zheevx( char* jobz, char* range, char* uplo, int* n, dcomplex* a,
int* lda, double* vl, double* vu, int* il, int* iu, double* abstol,
int* m, double* w, dcomplex* z, int* ldz, dcomplex* work, int* lwork,
double* rwork, int* iwork, int* ifail, 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
#define LDZ N

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, ldz = LDZ, il, iu, m, info, lwork;
double abstol, vl, vu;
dcomplex wkopt;
dcomplex* work;
/* Local arrays */
/* iwork dimension should be at least 5*n */
int iwork[5*N], ifail[N];
/* rwork dimension should be at least 7*n */
double w[N], rwork[7*N];
dcomplex z[LDZ*N];
dcomplex a[LDA*N] = {
{ 6.51,  0.00}, {-5.92, -9.53}, {-2.46, -2.91}, { 8.84, -3.21},
{ 0.00,  0.00}, {-1.73,  0.00}, { 6.50, -2.09}, { 1.32, -8.81},
{ 0.00,  0.00}, { 0.00,  0.00}, { 6.90,  0.00}, {-0.59, -2.47},
{ 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, {-2.85,  0.00}
};
/* Executable statements */
printf( " ZHEEVX Example Program Results\n" );
/* Negative abstol means using the default value */
abstol = -1.0;
/* Set VL, VU to compute eigenvalues in half-open (VL,VU] interval */
vl = 0.0;
vu = 100.0;
/* Query and allocate the optimal workspace */
lwork = -1;
zheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
&abstol, &m, w, z, &ldz, &wkopt, &lwork, rwork, iwork, ifail, &info );
lwork = (int)wkopt.re;
work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
/* Solve eigenproblem */
zheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
&abstol, &m, w, z, &ldz, work, &lwork, rwork, iwork, ifail, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm failed to compute eigenvalues.\n" );
exit( 1 );
}
/* Print the number of eigenvalues found */
printf( "\n The total number of eigenvalues found:%2i\n", m );
/* Print eigenvalues */
print_rmatrix( "Selected eigenvalues", 1, m, w, 1 );
/* Print eigenvectors */
print_matrix( "Selected eigenvectors (stored columnwise)", n, m, z, ldz );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of ZHEEVX 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" );
}
}