Egenvalues/Eigenvectors for Non-Symmetric Arrays?

ack has asked for the wisdom of the Perl Monks concerning the following question:

Brother and sister monks; I have an application that needs to compute the eigenvalues and eigenvectors for square, non-symmetric matrices.

I have looked all over CPAN and have found several nice pacages (e.g., in the Math:: section, Statistics:: section, etc.). But all require symmetric matrices (which mine are not).

I have found a couple of nice applets out on the net that can do the job and I can do the calculations in the R language. But I need to be able to do it in Perl so that I can fold it into a larger Perl application that I'm developing for use at work.

Does anyone in the Monestary know of a Perl package that can compute eigenvalues and eigenvectors for non-symmetric square matrices?

ack Albuquerque, NM

Comment on Egenvalues/Eigenvectors for Non-Symmetric Arrays?

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Re: Egenvalues/Eigenvectors for Non-Symmetric Arrays? by Corion (Patriarch) on Jun 16, 2009 at 14:50 UTC
Eigen returns at least Math::GSL::Eigen, which has functions for eigenvalues of both symmetric and nonsymmetric matrices. I'm not sure where you've looked or why GSL was inappropriate. PDL::MatrixOps also discusses an `eigens` function which computes the eigenvalues and vectors using PDL (I guess).	[reply] [d/l]
Re^2: Egenvalues/Eigenvectors for Non-Symmetric Arrays? by ack (Deacon) on Jun 16, 2009 at 15:27 UTC
I just took a look at Math::GSL::Eigen, installed it and tested it; looks like it'll do the job. I don't know why I missed it either. I had done several searches on CPAN and Super Searches here in the Monestary but came up empty except for 2 or 3 packages that all, according to their documentation, only worked with symmetric matrices. I actually tried several using known test matrices and they all failed on all but the symmetric matrices. But I never came up with Math::GSL::Eigen...don't know why. Maybe I didn't phrase my search question quite right. When I just went out a couple of minutes ago and checked it out with Perl Package Manager I realized that I probably was scared off thinking I need to install the GNU package, too. I think perhaps I didn't overlook Math::GSL::Eigen; just thought I didn't have all that was required to use it. I should've known better. Anyway, thank you so much for the pointer. Somehow I just knew that someone had to have done this. Your pointer is so very much appreciated. ack Albuquerque, NM	[reply]
Re^3: Egenvalues/Eigenvectors for Non-Symmetric Arrays? by downer (Monk) on Jun 16, 2009 at 15:50 UTC
If the matricies are very large and sparse, you may be better off using a sparse format and using something like power method. This may also be a good job for a little inline C.	[reply]
Re^2: Egenvalues/Eigenvectors for Non-Symmetric Arrays? by etj (Priest) on May 31, 2022 at 23:07 UTC
You'd want to also check out PDL::LinearAlgebra, particularly the `meigen*` routines.	[reply] [d/l]
Re: Egenvalues/Eigenvectors for Non-Symmetric Arrays? by tmaly (Monk) on Jun 16, 2009 at 22:23 UTC
If you wanted to keep that part in R, you could use the R to perl bridge RSPerl http://www.omegahat.org/RSPerl/ I have used it before to do kernel density estimations and it works quite well	[reply]