Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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

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/*
LAPACKE_cheevr 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_cheevr (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_Complex8* a, MKL_INT lda );
extern void print_rmatrix( char* desc, MKL_INT m, MKL_INT n, float* 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;
float abstol, vl, vu;
/* Local arrays */
MKL_INT isuppz[N];
float w[N];
MKL_Complex8 z[LDZ*N];
MKL_Complex8 a[LDA*N] = {
{-2.16f,  0.00f}, {-0.16f,  4.86f}, {-7.23f,  9.38f}, {-0.04f, -6.86f},
{ 0.00f,  0.00f}, { 7.45f,  0.00f}, { 4.39f, -6.29f}, {-8.11f,  4.41f},
{ 0.00f,  0.00f}, { 0.00f,  0.00f}, {-9.03f,  0.00f}, {-6.89f,  7.66f},
{ 0.00f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f}, { 7.76f,  0.00f}
};
/* Executable statements */
printf( "LAPACKE_cheevr (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_cheevr( 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_cheevr Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex8* 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, float* 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" );
}
}