Wrong results while solving for eign vectors!

psing51 — Tue, 01 Sep 2015 06:29:27 GMT

i am trying to use the dsyev routine. Now i modified your default example slightly by solving for matrix:

2,1,3,
1,2,3,
3,3,20

i am getting :
Eigenvalues
   1.00   2.00 21.00
Eigenvectors (stored columnwise)
   0.71   0.69   0.16
-0.71   0.69   0.16
   0.00 -0.23   0.97

i again tried with vector:
1,2
2,1

Eigenvalues
-1.00   3.00
Eigenvectors (stored columnwise)
-0.71   0.71
   0.71   0.71

eign values are fine , but why eign vectors are wrong !
according to this and this the eign vectors should have been :
[-1 , 1 , 0] , [-3,-3,1] , [1,1,6]
and [1,-1] , [1,1]

  
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/*
   LAPACKE_dsyev Example.
   ======================

   Program computes all eigenvalues and eigenvectors of a real symmetric
   matrix A:

     1.96  -6.49  -0.47  -7.20  -0.65
    -6.49   3.80  -6.39   1.50  -6.34
    -0.47  -6.39   4.17  -1.51   2.67
    -7.20   1.50  -1.51   5.70   1.80
    -0.65  -6.34   2.67   1.80  -7.10

   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.

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

 LAPACKE_dsyev (row-major, high-level) Example Program Results

 Eigenvalues
 -11.07  -6.23   0.86   8.87  16.09

 Eigenvectors (stored columnwise)
  -0.30  -0.61   0.40  -0.37   0.49
  -0.51  -0.29  -0.41  -0.36  -0.61
  -0.08  -0.38  -0.66   0.50   0.40
   0.00  -0.45   0.46   0.62  -0.46
  -0.80   0.45   0.17   0.31   0.16
*/
#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, double* a, MKL_INT lda );

/* Parameters */
#define N 2
#define LDA N

/* Main program */
int main() {
        /* Locals */
        MKL_INT n = N, lda = LDA, info;
        /* Local arrays */
        double w;
        double a[LDA*N] = {
		1,2,
		2,1		
        };
        /* Executable statements */
        printf( "LAPACKE_dsyev (row-major, high-level) Example Program Results\n" );
        /* Solve eigenproblem */
        info = LAPACKE_dsyev( LAPACK_ROW_MAJOR, 'V', 'U', n, a, lda, w );
        /* 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 );
        exit( 0 );
} /* End of LAPACKE_dsyev Example */

/* Auxiliary routine: printing a matrix */
void print_matrix( 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*lda+j] );
                printf( "\n" );
        }
}

Please define "wrong

mecej4 — Tue, 01 Sep 2015 11:42:00 GMT

Please define "wrong eigenvector". Did you forget that if A.x = λx, it is also true that A.y = λy, where y = c.x, with c a scalar multiplier? The eigenvectors (that you reported as those that were given by Lapack) happen to be scaled so that they have norm = 1, but other choices are equally valid.

topic Wrong results while solving for eign vectors! in Intel® oneAPI Math Kernel Library

Wrong results while solving for eign vectors!

Please define "wrong