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## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 12/20/2021
Public

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## ZGEEV Example Program in C

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/*
ZGEEV Example.
==============

Program computes the eigenvalues and left and right eigenvectors of a general
rectangular matrix A:

( -3.84,  2.25) ( -8.94, -4.75) (  8.95, -6.53) ( -9.87,  4.82)
( -0.66,  0.83) ( -4.40, -3.82) ( -3.50, -4.26) ( -3.15,  7.36)
( -3.99, -4.73) ( -5.88, -6.60) ( -3.36, -0.40) ( -0.75,  5.23)
(  7.74,  4.18) (  3.66, -7.53) (  2.58,  3.60) (  4.59,  5.41)

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

The routine computes for an n-by-n complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors. The right
eigenvector v(j) of A satisfies

A*v(j)= lambda(j)*v(j)

where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies

u(j)H*A = lambda(j)*u(j)H

where u(j)H denotes the conjugate transpose of u(j). The computed
eigenvectors are normalized to have Euclidean norm equal to 1 and
largest component real.

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

ZGEEV Example Program Results

Eigenvalues
( -9.43,-12.98) ( -3.44, 12.69) (  0.11, -3.40) (  5.76,  7.13)

Left eigenvectors
(  0.24, -0.18) (  0.61,  0.00) ( -0.18, -0.33) (  0.28,  0.09)
(  0.79,  0.00) ( -0.05, -0.27) (  0.82,  0.00) ( -0.55,  0.16)
(  0.22, -0.27) ( -0.21,  0.53) ( -0.37,  0.15) (  0.45,  0.09)
( -0.02,  0.41) (  0.40, -0.24) (  0.06,  0.12) (  0.62,  0.00)

Right eigenvectors
(  0.43,  0.33) (  0.83,  0.00) (  0.60,  0.00) ( -0.31,  0.03)
(  0.51, -0.03) (  0.08, -0.25) ( -0.40, -0.20) (  0.04,  0.34)
(  0.62,  0.00) ( -0.25,  0.28) ( -0.09, -0.48) (  0.36,  0.06)
( -0.23,  0.11) ( -0.10, -0.32) ( -0.43,  0.13) (  0.81,  0.00)
*/
#include <stdlib.h>
#include <stdio.h>

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

/* ZGEEV prototype */
extern void zgeev( char* jobvl, char* jobvr, int* n, dcomplex* a,
int* lda, dcomplex* w, dcomplex* vl, int* ldvl, dcomplex* vr, int* ldvr,
dcomplex* work, int* lwork, double* rwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda );

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

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, ldvl = LDVL, ldvr = LDVR, info, lwork;
dcomplex wkopt;
dcomplex* work;
/* Local arrays */
/* rwork dimension should be at least 2*n */
double rwork[2*N];
dcomplex w[N], vl[LDVL*N], vr[LDVR*N];
dcomplex a[LDA*N] = {
{-3.84,  2.25}, {-0.66,  0.83}, {-3.99, -4.73}, { 7.74,  4.18},
{-8.94, -4.75}, {-4.40, -3.82}, {-5.88, -6.60}, { 3.66, -7.53},
{ 8.95, -6.53}, {-3.50, -4.26}, {-3.36, -0.40}, { 2.58,  3.60},
{-9.87,  4.82}, {-3.15,  7.36}, {-0.75,  5.23}, { 4.59,  5.41}
};
/* Executable statements */
printf( " ZGEEV Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
zgeev( "Vectors", "Vectors", &n, a, &lda, w, vl, &ldvl, vr, &ldvr,
&wkopt, &lwork, rwork, &info );
lwork = (int)wkopt.re;
work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
/* Solve eigenproblem */
zgeev( "Vectors", "Vectors", &n, a, &lda, w, vl, &ldvl, vr, &ldvr,
work, &lwork, rwork, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm failed to compute eigenvalues.\n" );
exit( 1 );
}
/* Print eigenvalues */
print_matrix( "Eigenvalues", 1, n, w, 1 );
/* Print left eigenvectors */
print_matrix( "Left eigenvectors", n, n, vl, ldvl );
/* Print right eigenvectors */
print_matrix( "Right eigenvectors", n, n, vr, ldvr );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of ZGEEV 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" );
}
}

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