Developer Reference

ID 766877
Date 3/22/2024
Public

DSYEVD Example Program in C

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/*
DSYEVD Example.
==============

Program computes all eigenvalues and eigenvectors of a real symmetric
matrix A using divide and conquer algorithm, where A is:

6.39   0.13  -8.23   5.71  -3.18
0.13   8.37  -4.46  -6.10   7.21
-8.23  -4.46  -9.58  -9.25  -7.42
5.71  -6.10  -9.25   3.72   8.54
-3.18   7.21  -7.42   8.54   2.51

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

The routine computes all eigenvalues and, optionally, eigenvectors of an
n-by-n real symmetric 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.
If the eigenvectors are requested, then this routine uses a divide and
conquer algorithm to compute eigenvalues and eigenvectors.

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

DSYEVD Example Program Results

Eigenvalues
-17.44 -11.96   6.72  14.25  19.84

Eigenvectors (stored columnwise)
-0.26   0.31  -0.74   0.33   0.42
-0.17  -0.39  -0.38  -0.80   0.16
-0.89   0.04   0.09   0.03  -0.45
-0.29  -0.59   0.34   0.31   0.60
-0.19   0.63   0.44  -0.38   0.48
*/
#include <stdlib.h>
#include <stdio.h>

/* DSYEVD prototype */
extern void dsyevd( char* jobz, char* uplo, int* n, double* a, int* lda,
double* w, double* work, int* lwork, int* iwork, int* liwork, int* info );
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, int m, int n, double* a, int lda );

/* Parameters */
#define N 5
#define LDA N

/* Main program */
int main() {
/* Locals */
int n = N, lda = LDA, info, lwork, liwork;
int iwkopt;
int* iwork;
double wkopt;
double* work;
/* Local arrays */
double w[N];
double a[LDA*N] = {
6.39,  0.00,  0.00,  0.00,  0.00,
0.13,  8.37,  0.00,  0.00,  0.00,
-8.23, -4.46, -9.58,  0.00,  0.00,
5.71, -6.10, -9.25,  3.72,  0.00,
-3.18,  7.21, -7.42,  8.54,  2.51
};
/* Executable statements */
printf( " DSYEVD Example Program Results\n" );
/* Query and allocate the optimal workspace */
lwork = -1;
liwork = -1;
dsyevd( "Vectors", "Upper", &n, a, &lda, w, &wkopt, &lwork, &iwkopt,
&liwork, &info );
lwork = (int)wkopt;
work = (double*)malloc( lwork*sizeof(double) );
liwork = iwkopt;
iwork = (int*)malloc( liwork*sizeof(int) );
/* Solve eigenproblem */
dsyevd( "Vectors", "Upper", &n, a, &lda, w, work, &lwork, iwork,
&liwork, &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 eigenvectors */
print_matrix( "Eigenvectors (stored columnwise)", n, n, a, lda );
/* Free workspace */
free( (void*)iwork );
free( (void*)work );
exit( 0 );
} /* End of DSYEVD Example */

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