Re: eigensystem

[Patrick Dupre]

This is perfectly correct.

My question is how do I detect singular matrix since
gsl_eigen_nonsymmv
does not do it?


>
> 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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