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psing51

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08-31-2015
11:29 PM

36 Views

Wrong results while solving for eign vectors!

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]

/******************************************************************************* * Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* 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" ); } }

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mecej4

Black Belt

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09-01-2015
04:42 AM

36 Views

*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.

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