Developer Reference

## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 3/31/2023
Public

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## CHEEV Example Program in C

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/*
CHEEV Example.
==============

Program computes all eigenvalues and eigenvectors of a complex Hermitian
matrix A:

(  9.14,  0.00) ( -4.37, -9.22) ( -1.98, -1.72) ( -8.96, -9.50)
( -4.37,  9.22) ( -3.35,  0.00) (  2.25, -9.51) (  2.57,  2.40)
( -1.98,  1.72) (  2.25,  9.51) ( -4.82,  0.00) ( -3.24,  2.04)
( -8.96,  9.50) (  2.57, -2.40) ( -3.24, -2.04) (  8.44,  0.00)

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

The routine computes all 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.

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

CHEEV Example Program Results

Eigenvalues
-16.00  -6.76   6.67  25.51

Eigenvectors (stored columnwise)
(  0.34,  0.00) ( -0.55,  0.00) (  0.31,  0.00) ( -0.70,  0.00)
(  0.44, -0.54) (  0.26,  0.18) (  0.45,  0.29) (  0.22, -0.28)
( -0.48, -0.37) ( -0.52, -0.02) ( -0.05,  0.57) (  0.15,  0.08)
(  0.10, -0.12) ( -0.50,  0.28) ( -0.23, -0.48) (  0.34, -0.49)
*/
#include <stdlib.h>
#include <stdio.h>

/* Complex datatype */
struct _fcomplex { float re, im; };
typedef struct _fcomplex fcomplex;

/* CHEEV prototype */
extern void cheev( char* jobz, char* uplo, int* n, fcomplex* a, int* lda,
float* w, fcomplex* work, int* lwork, float* rwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda );
extern void print_rmatrix( char* desc, int m, int n, float* a, int lda );

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

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, info, lwork;
fcomplex wkopt;
fcomplex* work;
/* Local arrays */
/* rwork dimension should be at least max(1,3*n-2) */
float w[N], rwork[3*N-2];
fcomplex a[LDA*N] = {
{ 9.14f,  0.00f}, {-4.37f,  9.22f}, {-1.98f,  1.72f}, {-8.96f,  9.50f},
{ 0.00f,  0.00f}, {-3.35f,  0.00f}, { 2.25f,  9.51f}, { 2.57f, -2.40f},
{ 0.00f,  0.00f}, { 0.00f,  0.00f}, {-4.82f,  0.00f}, {-3.24f, -2.04f},
{ 0.00f,  0.00f}, { 0.00f,  0.00f}, { 0.00f,  0.00f}, { 8.44f,  0.00f}
};
/* Executable statements */
printf( " CHEEV Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
cheev( "Vectors", "Lower", &n, a, &lda, w, &wkopt, &lwork, rwork, &info );
lwork = (int)wkopt.re;
work = (fcomplex*)malloc( lwork*sizeof(fcomplex) );
/* Solve eigenproblem */
cheev( "Vectors", "Lower", &n, a, &lda, w, work, &lwork, rwork, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm failed to compute eigenvalues.\n" );
exit( 1 );
}
/* Print eigenvalues */
print_rmatrix( "Eigenvalues", 1, n, w, 1 );
/* Print eigenvectors */
print_matrix( "Eigenvectors (stored columnwise)", n, n, a, lda );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of CHEEV Example */

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