Re: eigensystem

[Alan Mead]

Your matrix is singular (the first two columns are perfectly correlated,
so your matrix does not have full rank).

The standard test of singularity is that the determinant cannot be
computed (you try to calculate it, and you get zero or a numerical
error). This post describes the problem and a shortcut:

https://stackoverflow.com/questions/13145948/how-to-find-out-if-a-matrix-is-singular

-Alan


On 1/19/2021 2:51 PM, Patrick Dupre wrote:
> gsl_eigen_nonsymmv_workspace
> has no member n_evals
>
> issue:
>
> Diagonalizing
> double data_3 [] = { 0.0, 0.0, 1.0,
>               0.0, 0.0, 0.0,
>               0.0, 0.0, 0.0 } ;
>
> I get
> eigenvalue = 0 +0i
> eigenvector = 
> 1 +0i
> 0 +0i
> 0 +0i
> eigenvalue = 0 +0i
> eigenvector = 
> 0 +0i
> 1 +0i
> 0 +0i
> eigenvalue = 0 +0i
> eigenvector = 
> -1 +0i
> 0 +0i
> 3.00625e-292 +0i
>
>
> which is wrong.
> The last eigenvector is not correct because this matrix is not diagonalizable.
>
> I need to identify such matrices.
>
>
> ===========================================================================
>  Patrick DUPRÉ                                 | | email: pdupre@gmx.com
>  Laboratoire interdisciplinaire Carnot de Bourgogne
>  9 Avenue Alain Savary, BP 47870, 21078 DIJON Cedex FRANCE
>  Tel: +33 (0)380395988
> ===========================================================================
>
>
>> Sent: Tuesday, January 19, 2021 at 6:56 PM
>> From: "Patrick Alken" <patrick.alken@Colorado.EDU>
>> To: help-gsl@gnu.org
>> Subject: Re: eigensystem
>>
>> What do you mean by handle it? According to the documentation, if the
>> function cannot compute all eigenvalues, an error code is returned. In
>> the case of gsl_eigen_nonsymm, the number of converged eigenvalues is
>> stored in w->n_evals.
>>
>> Patrick
>>
>> On 1/19/21 10:33 AM, Patrick Dupre wrote:
>>> Hello,
>>>
>>> Is there a way to handle the possible error of gsl_eigen_nonsymmv ?
>>>
>>> For example, when the matrix is not diagonalizable.
>>>
>>> Thanks
>>>
>>> ===========================================================================
>>>  Patrick DUPRÉ                                 | | email: pdupre@gmx.com
>>>  Laboratoire interdisciplinaire Carnot de Bourgogne
>>>  9 Avenue Alain Savary, BP 47870, 21078 DIJON Cedex FRANCE
>>>  Tel: +33 (0)380395988
>>> ===========================================================================
>>>
>>>
>>
>>

-- 

Alan D. Mead, Ph.D.
President, Talent Algorithms Inc.

science + technology = better workers

http://www.alanmead.org

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