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Re: [ESA-SoC] Generalized eigenvalue


From: eem2314
Subject: Re: [ESA-SoC] Generalized eigenvalue
Date: Mon, 27 Apr 2015 09:56:07 -0700 (PDT)



On Mon, Apr 27, 2015 at 4:50 AM, András Mihálykó [via Octave] <[hidden email]> wrote:
Thanks,

I think it's clear now. I have also seen, that in ML there are two algorithms, that can be chosen for the generalized eigenvalue problem, these could be implemented, too, if there exist such a Lapack routine, that uses Cholesky decompozition. So far I've seen, the dggevx does the qz iteration. I see it's not too important, while usually qz does it better. I can examine the dggeevx routine for other matrices, too.
I can do the things above, or what else should I pay attention to?
Regards:

András


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Andras,
The symmetric generalized problem is treated in octave using dsygv.
Balancing is not done for symmetric problems -  it is unnecessary because
they are well-conditioned. So it seems the important tasks are
1) change calls to dggev to dggevx so that balancing can be done
2) add the 'nobalance' option to the eig command
3) change calls to dgeev to dgeevx so that balancing can be turned off with
    the 'nobalance' option (dgeev always balances)
4) add an argument to eig that determines the algorithm used: 'qz' is the
    default for non-symmetric, 'chol' is the default for symmetric-generalized.
    The 'qz' option would be necessary if eig is called with symmetric matrices
    but the B matrix is not positive-definite

Additionally to make octave more compatible with ML you could
4) add an optional output W to get the left eigenvectors for non-symmetric problems:
     [V,D,W] =  eig(...)
    left and right eigenvectors are the same for symmetric.
5) add an optional argument to eig to return the eigenvalues as a vector instead of
    a diagonal matrix - ML uses 'vector' and 'matrix'

--
Ed Meyer


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