Re: eigs compatibility

[Rik]

On 07/03/2013 12:08 PM, address@hidden wrote:
> Message: 7
> Date: Wed, 03 Jul 2013 15:08:04 -0400
> From: "John W. Eaton" <address@hidden>
> To: Jordi Guti?rrez Hermoso <address@hidden>
> Cc: David Bateman <address@hidden>,   octave maintainers mailing list
>       <address@hidden>
> Subject: Re: eigs fails for scalars and 2x2 matrices
> Message-ID: <address@hidden>
> Content-Type: text/plain; charset=UTF-8; format=flowed
>
> On 06/26/2013 09:59 AM, Jordi Guti?rrez Hermoso wrote:
>> > On 26 June 2013 04:28, John W. Eaton<address@hidden>  wrote:
>>> >> eigs fails for scalars and 2x2 matrices, apparently intentionally
>>> >> given the error message.  Is this a limitation of ARPACK?  Should we
>>> >> work around this problem by calling eig for these cases?
>> >
>> > This was Bateman's response:
>> >
>> >      
>> > https://mailman.cae.wisc.edu/pipermail/octave-maintainers/2011-July/024272.html
> OK, to make the discussion easier to follow, I'm reproducing that
> message here and I'm adding David to the Cc: line since he wrote
> the eigs function in Octave.
>
>    On 07/24/2011 09:10 PM, Jordi Guti?rrez Hermoso wrote:
>    > While porting Matlab code, I noticed that someone had used eigs for a
>    > 2x2 matrix, which produces an error to use eig instead. I patched the
>    > code to do that, but I inadverently introduced a bug because I forgot
>    > that eigs sorts its eigenvalues but eig does not.
>    >
>    > Should eigs be patched to call eig for small matrices and just sort
>    > them? Also, for the case of when you need all eigenvalues, should eigs
>    > just silently call eig instead of warning about it?
>    >
>    > - Jordi G. H.
>    >
>
>    The sorting rules aren't that obvious as the order of the values
>    returned might be largest eignevalue first, smallest first or even
>    sorted relative to a distance from a particular eigenvalue. So if matlab
>    does this it might be better to relax the error in eigs-base.cc to a
>    warning and letter ARPACK do the work.
>
>    David
>
> It does seem that eigs in Matlab works for small matrices.
>
> I'm not sure that it will work to change the error to a warning and
> ask ARPACK to do the job because ARPACK doesn't seem to be able to
> return all eigenvalues, and in Matlab, eigs (rand (2)) returns 2
> eigenvalues.  It also seems that it only starts warning when the size
> of the matrix is greater than 8.
>
> I agree that getting all the sorting options right will take some
> effort.  It seems like the easiest way to deal with this would be to
> write a wrapper eigs.m function that checks the size of the input
> matrix (or matrices) and the number of requested eigenvalues and then
> calls the current eigs function if possible, otherwise issues a
> warning (if appropriate) and calls eig + sort as directed by the
> options.
>
> Does that seem like a reasonable solution?  If so, I'll take a shot at
> doing it.  If not, do you see a better way?
Seems like a low value compatibility item.  'eigs' is supposed to be for
determining a few eigenvectors of a very large, sparse matrix.  Asking it
for the eigenvalues of a 2x2 matrix is attempting to use a sledge hammer to
swat a fly.  I would be more inclined to just check the dimensions of the
input and if it is less than 10 print a warning suggesting that the user
consider 'eig' for their problem.  However, if someone is paying for this
compatibility fix then your method seems reasonable.

--Rik