Re: [Help-gsl] Newbie eigenvalue issues

[Patrick Alken]

This is for the user to verify. The symm/symmv routines reference only
the lower triangle of the matrix, ignoring the upper part.

On 09/23/2016 08:18 PM, Yu Liu wrote:
> 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;
>> }
>>
>>
>>
>>