## Developer Reference

• 2022.1
• 12/20/2021
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Contents

# ZHEEVR Example Program in C

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/*
ZHEEVR Example.
==============

Program computes eigenvalues specified by a selected range of values
and corresponding eigenvectors of a complex Hermitian matrix A using the
Relatively Robust Representations, where A is:

( -2.16,  0.00) ( -0.16, -4.86) ( -7.23, -9.38) ( -0.04,  6.86)
( -0.16,  4.86) (  7.45,  0.00) (  4.39,  6.29) ( -8.11, -4.41)
( -7.23,  9.38) (  4.39, -6.29) ( -9.03,  0.00) ( -6.89, -7.66)
( -0.04, -6.86) ( -8.11,  4.41) ( -6.89,  7.66) (  7.76,  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.
========================

ZHEEVR Example Program Results

The total number of eigenvalues found: 2

Selected eigenvalues
-4.18   3.57

Selected eigenvectors (stored columnwise)
(  0.68,  0.00) (  0.38,  0.00)
(  0.03,  0.18) (  0.54, -0.57)
( -0.03,  0.21) ( -0.40,  0.04)
(  0.20,  0.64) ( -0.14, -0.26)
*/
#include <stdlib.h>
#include <stdio.h>

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

/* ZHEEVR prototype */
extern void zheevr( 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, int* isuppz, 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
#define LDZ N

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, ldz = LDZ, il, iu, m, info, lwork, lrwork, liwork;
double abstol, vl, vu;
int iwkopt;
int* iwork;
double rwkopt;
double* rwork;
dcomplex wkopt;
dcomplex* work;
/* Local arrays */
int isuppz[N];
double w[N];
dcomplex z[LDZ*N];
dcomplex a[LDA*N] = {
{-2.16,  0.00}, {-0.16,  4.86}, {-7.23,  9.38}, {-0.04, -6.86},
{ 0.00,  0.00}, { 7.45,  0.00}, { 4.39, -6.29}, {-8.11,  4.41},
{ 0.00,  0.00}, { 0.00,  0.00}, {-9.03,  0.00}, {-6.89,  7.66},
{ 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, { 7.76,  0.00}
};
/* Executable statements */
printf( " ZHEEVR 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 = -5.0;
vu = 5.0;
/* Query and allocate the optimal workspace */
lwork = -1;
lrwork = -1;
liwork = -1;
zheevr( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
&abstol, &m, w, z, &ldz, isuppz, &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 */
zheevr( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu,
&abstol, &m, w, z, &ldz, isuppz, work, &lwork, rwork, &lrwork,
iwork, &liwork, &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*)iwork );
free( (void*)rwork );
free( (void*)work );
exit( 0 );
} /* End of ZHEEVR 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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