Developer Reference

ID 766877
Date 3/31/2023
Public

## LAPACKE_zheevr Example Program in C for Column Major Data Layout

/*******************************************************************************
*  The information and material ("Material") provided below is owned by Intel
*  Corporation or its suppliers or licensors, and title to such Material remains
*  with Intel Corporation or its suppliers or licensors. The Material contains
*  proprietary information of Intel or its suppliers and licensors. The Material
*  is protected by worldwide copyright laws and treaty provisions. No part of
*  the Material may be copied, reproduced, published, uploaded, posted,
*  transmitted, or distributed in any way without Intel's prior express written
*  property rights in the Material is granted to or conferred upon you, either
*  expressly, by implication, inducement, estoppel or otherwise. Any license
*  under such intellectual property rights must be express and approved by Intel
*  in writing.
*
********************************************************************************
*/
/*
LAPACKE_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.
========================

LAPACKE_zheevr (column-major, high-level) 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>
#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 isuppz[N];
double w[N];
MKL_Complex16 z[LDZ*N];
MKL_Complex16 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( "LAPACKE_zheevr (column-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 = -5.0;
vu = 5.0;
/* Solve eigenproblem */
info = LAPACKE_zheevr( LAPACK_COL_MAJOR, 'V', 'V', 'L', n, a, lda,
vl, vu, il, iu, abstol, &m, w, z, ldz, isuppz );
/* 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_zheevr 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+j*lda].real, a[i+j*lda].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+j*lda] );
printf( "\n" );
}
}