Re: [Help-gsl] Newbie eigenvalue issues

[Yu Liu]

It looks like the source of gsl_eigen_symmv doesn't check if the input
matrix is indeed symmetric. Is it a good idea to do that? Does it add too
much overhead when the matrix is big?

On Fri, Sep 23, 2016 at 4:23 AM, Dimitrova, Maria <
address@hidden> wrote:

> Hello,
>
> I am getting started with the GSL libraries and tested how finding the
> eigenvalues and eigenvectors of matrices works. I spotted some weird
> results, so I must have made a mistake. The output from my program looks
> like this:
>
> Matrix S
>
>  2.000000   2.000000
>  3.000000   0.000000
>
> View matrix S
> 2.000000
> 2.000000
> 3.000000
> 0.000000
>
> Eigenvalues of S:
> -2.162278  4.162278
>
> However, online calculators do not agree. The eigenvalues are given as
> 3.65 and -1.64. Here are the references to them
>
> http://www.wolframalpha.com/input/?i=eigenvalues+%7B%7B2,2%7D,%7B3,0%7D%7D
>
> www.mathportal.org/calculators/matrices-calculators/matrix-calculator.
> php?formId=1&val1=2%3A2%3Anull%3Anull%3Anull%3Anull%
> 3B3%3A0%3Anull%3Anull%3Anull%3Anull%3Bnull%3Anull%3Anull%
> 3Anull%3Anull%3Anull%3Bnull%3Anull%3Anull%3Anull%3Anull%
> 3Anull%3Bnull%3Anull%3Anull%3Anull%3Anull%3Anull%3Bnull%
> 3Anull%3Anull%3Anull%3Anull%3Anull&val2=2&val3=2&rb1=evec
>
>
> My code is below. Thank you for the help.
>
>
> Best regards,
>
> Maria
>
>
> address@hidden
>
>
>
>
> /***********************************************************
> *************************************
>  *
>                       *
>  *   COMPILED WITH THE LINE:
>                       *
>  *   gcc -Wall -Wextra eigenval-vect.c -lm -lgsl -lgslcblas && ./a.out
>                     *
>  *
>                       *
>  *
>                       *
>  ************************************************************
> ************************************/
> #include <stdio.h>
> #include <stdlib.h>
> #include <math.h>
> #include <gsl/gsl_math.h>
> #include <gsl/gsl_blas.h>
> #include <gsl/gsl_vector.h>
> #include <gsl/gsl_matrix.h>
> #include <gsl/gsl_eigen.h>
> #define MatrixOrder 2
> #define MSG(msg) printf( "\n" #msg "\n")
> #define DIV printf("\n==================================================
> =====================================\n\n")
> #define DEBUG(msg, var, fmt) printf( #msg "\n" #var "=%" #fmt "\n", var)
> #define PRINTF(var, fmt) printf("\n**DEBUG: " #var "=%" #fmt "\n", var)
> void printArr(gsl_matrix *array, int nrows, int ncols)
> {
>     int i,j;
>     printf("\n");
>     for (i=0;i<nrows;i++)
>     {
>         printf("\n");
>         for (j=0;j<ncols;j++)
>         {
>             printf("% f  ",gsl_matrix_get(array,i,j));
>         }
>     }
>     printf("\n\n");
> }
> int main()
> {
>     int i=0;
>     double data[] = { 2.0, 2.0,
>                       3.0, 0.0 };
>     gsl_matrix *S, *C;
>     gsl_vector *E;
>     gsl_eigen_symmv_workspace *wrkDiag; // for diagonalization
>
>
>     S = gsl_matrix_calloc(MatrixOrder,MatrixOrder);
>     C = gsl_matrix_calloc(MatrixOrder,MatrixOrder);
>     E = gsl_vector_calloc(MatrixOrder);
>     wrkDiag = gsl_eigen_symmv_alloc(MatrixOrder); // for NxN matrix wrk
> is O(4N)
> /***********************************************************
> ******************************/
>     gsl_matrix_view m = gsl_matrix_view_array (data, 2, 2);
>     MSG(Matrix S);
>     printArr(&m.matrix,2,2);
>     MSG(View matrix S);
>     gsl_matrix_fprintf(stdout,&m.matrix,"%f");
> /***********************************************************
> ******************************/
>     DIV;
>     gsl_eigen_symmv (&m.matrix,E,C,wrkDiag);
>     gsl_eigen_symmv_sort(E,C,GSL_EIGEN_SORT_VAL_ASC);
>     MSG(Eigenvalues of S:);
>     for (i=0;i<2;i++)
>     {
>         printf("% f\t",gsl_vector_get(E,i));
>     }
>     printf("\n\n");
>     MSG(Eigenvectors of S:);
>     printArr(C,2,2);
>
>     DIV;
> /***********************************************************
> ******************************/
>     gsl_matrix_free(S);
>     gsl_vector_free(E);
>     gsl_matrix_free(C);
>     gsl_eigen_symmv_free(wrkDiag);
>     return 0;
> }
>
>
>
>