Re: [ESA-SoC] Generalized eigenvalue

Andras,

It's a little more complicated than that; balancing is always done in octave for the

standard (one matrix) nonsymmetric eigenvalue problem because dgeev always

does balancing. The generalized eigenvalue problem on the other hand never does

balancing because dggev does not balance.

In order to add the 'nobalance' option to octave to make it more compatible

with ML it would be necessary to use dgeevx in place of dgeev which does not

have the option to turn off balancing. Likewise to add balancing to the generalized

problem it would be necessary to change dggev to dggevx. These are in

liboctave/numeric/EIG.cc

The example shown in the ML doc

http://www.mathworks.com/help/matlab/ref/eig.html

in which 'nobalance' is necessary gives incorrect results in octave when

octave is built with lapack versions prior to 3.5, but gives correct results

when octave is built with 3.5, so it appears the new balancing algorithm works

for this example. It would be interesting to try it with larger examples, say from

http://www.math.wsu.edu/faculty/watkins/pdfiles/balbad.pdf

and difficult balancing cases should be added to the test cases for the

standard and generalized eigenvalue problems.

On Thu, Apr 23, 2015 at 2:51 AM, András Mihálykó [via Octave] <[hidden email]> wrote:

Hi,

so far I have understood, the problem is that balancing is usually beneficial, but there are some matrices, when without balancing the dgeevx (Lapack) function gives more accurate vectors. The octave code never includes the balancing step, and if we want to include it (if one knows that this is an option), we should do it previously manually. Although, it would be even better, if we would include the balancing step to the eig.cc, with optionally turn off. The dgeevx function has this option.
On the other side, the best option would be, if octave could decide if to use the balancing step or not, or have such a balancing step, that doesn't worsen the accuracy of the eigenvectors any times. Here http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=13&t=4270&p=10278&hilit=geev#p10278 they claim that they have a better balancing algorithm. It should be examined, if it really gives proper result for every matrix.
There are also other ways to call eig from ML, the same could be developed, as well.

András

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Ed Meyer

From:	eem2314
Subject:	Re: [ESA-SoC] Generalized eigenvalue
Date:	Thu, 23 Apr 2015 10:18:54 -0700 (PDT)