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Re: eigensystem


From: Alan Mead
Subject: Re: eigensystem
Date: Tue, 19 Jan 2021 12:22:45 -0600
User-agent: Mozilla/5.0 (Windows NT 6.1; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.6.1

Despite being on this mailing list, I'm not very familiar with GSL, but
I have experience solving eigenvalue problems as an end-user.

I'm going to assume that your matrix is singular, because that's common.
If your problem is something else (e.g., you're running out of memory)
then you should probably reply to the list with more details.

Usually you have to resort to removing variables or units of analysis.
If any of your variables have a perfect (or near perfect) correlation,
you should combine them (or drop one, they're not providing usefully
independent information in your sample if they're perfectly correlated).
You could also add or remove units of analysis or even add in some units
with some random noise. You might find one of these helpful:

  * Wothke, W. (1993). Testing structural equation models. In K. A.
    Bollen & J. S. Long (Eds.), Nonpositive definite matrices in
    structural modeling (pp. 256–293). Newbury Park, CA: Sage.
    doi:10.1093/sf/73.3.1161.
  * https://doi.org/10.1080/10705511.2020.1735393
  * https://www.johndcook.com/blog/2012/06/13/matrix-condition-number/
  * http://www.netlib.org/lapack/lug/node70.html (this from the LAPACK
    manual, not GSL, but it discusses solving Eigenvalue problems)

-Alan


On 1/19/2021 11:33 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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