Developer Reference

ID 766877
Date 3/31/2023
Public

## LAPACKE_zheevx Example Program in C for Row Major Data Layout

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

LAPACKE_zheevx (row-major, high-level) 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>
#include "mkl_lapacke.h"

/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* a, MKL_INT lda );
extern void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );

/* Parameters */
#define N 4
#define LDA N
#define LDZ N

/* Main program */
int main() {
/* Locals */
MKL_INT n = N, lda = LDA, ldz = LDZ, il, iu, m, info;
double abstol, vl, vu;
/* Local arrays */
MKL_INT ifail[N];
double w[N];
MKL_Complex16 z[LDZ*N];
MKL_Complex16 a[LDA*N] = {
{ 6.51,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00},
{-5.92, -9.53}, {-1.73,  0.00}, { 0.00,  0.00}, { 0.00,  0.00},
{-2.46, -2.91}, { 6.50, -2.09}, { 6.90,  0.00}, { 0.00,  0.00},
{ 8.84, -3.21}, { 1.32, -8.81}, {-0.59, -2.47}, {-2.85,  0.00}
};
/* Executable statements */
printf( "LAPACKE_zheevx (row-major, high-level) 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;
/* Solve eigenproblem */
info = LAPACKE_zheevx( LAPACK_ROW_MAJOR, 'V', 'V', 'L', n, a, lda,
vl, vu, il, iu, abstol, &m, w, z, ldz, ifail );
/* 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 );
exit( 0 );
} /* End of LAPACKE_zheevx Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* a, MKL_INT lda ) {
MKL_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*lda+j].real, a[i*lda+j].imag );
printf( "\n" );
}
}

/* Auxiliary routine: printing a real matrix */
void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) {
MKL_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*lda+j] );
printf( "\n" );
}
}