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From andrea antonello <andrea.antone...@gmail.com>
Subject Re: [math] eigenvector doubts and issues
Date Tue, 12 Nov 2013 10:54:25 GMT
Hi Thomas,

> good to hear.
> Sounds like an interesting problem you are working on.
> If you have found a good solution feel free to come back to use, we might
> want to include it in our user guide how an EigenDecomposition could be
> used.

thanks for pointing this out, I was a bit afraid to go offtopic.
But I would be happy to share a small eigenvector real world example
if there is interest. I will try to put together something on an
accessible wiki page, but I might need some help to finish it for
proper use in documentation :)

I'll keep you posted.
Thanks,
Andrea

>
> Thanks,
>
> Thomas
>
>
>
> On Tue, Nov 12, 2013 at 11:31 AM, andrea antonello <
> andrea.antonello@gmail.com> wrote:
>
>> Hi Thomas,
>> you are definitely right. I was fooled by the "nice" result of the
>> JAMA calculation, not noticing that it is there that I was extracting
>> values in a strange order.
>>
>> I now made some 3x3 tests on known results and also with the A * v =
>> lambda * v constraint and everything is alright.
>>
>> I still have to figure out how to properly use the results to split
>> higher elevation parts from lower z parts in a x,y,z dataset, but the
>> eigenvectors and values are in the right place now.
>>
>> Thanks,
>> Andrea
>>
>>
>>
>>
>> On Mon, Nov 11, 2013 at 1:21 PM, Thomas Neidhart
>> <thomas.neidhart@gmail.com> wrote:
>> > On 11/11/2013 11:40 AM, andrea antonello wrote:
>> >> Hi Thomas,
>> >> thanks for your reply.
>> >>
>> >>> the result of CM and jama are identical, the difference is just in the
>> >>> way how the data is stored.
>> >>>
>> >>> Afaik in jama calling getV() returns a vector in row format whereas
in
>> >>> CM the are stored in column format.
>> >>>
>> >>> If you transpose the matrix (or call getVT()) you will see that the
>> >>> vectors are identical, except for the signs and order. The reason for
>> >>> this is that for CM the eigenvalues/eigenvectors are sorted in
>> >>> descending order in case of a symmetric matrix, which is the case for
>> >>> your matrix.
>> >>
>> >> the problems is that the result is not just different in the
>> >> transposed way. And in fact if I pick the getVT,results are still not
>> >> the same.
>> >> The result seems to be reflected on the secondary diagonal, not the
>> >> primary diagonal.
>> >>
>> >> Furthermore, if I use the API, I do not expect to be problems of rows
>> >> and columns, so if I use:
>> >>
>> >> double eigenValue = eigenDecomposition.getRealEigenvalue(i);
>> >> RealVector eigenVector = eigenDecomposition.getEigenvector(i);
>> >>
>> >> I expect the eigenvector and eigenvalue to be the right ones for the
>> >> given index, no matter how the results are given in the matrixes.
>> >>
>> >> But the results I get are, for the same eigenvalue:
>> >> CM: eigenVal: 0.8056498828134406, eigenVect: [0.9015723557614027,
>> >> 0.19005937823202243, 0.38864472217295326
>> >> JAMA: eigenVal: 0.8056498828134406, eigenVect: [-0.7731388420716028,
>> >> 0.5012101463530931, -0.38864472217295326]
>> >>
>> >> I am still quite puzzled about what I am missing.
>> >
>> > I do not know how you get the eigenvector from jama, as there is no
>> > getEigenVector method.
>> >
>> > The class javadoc of their EigenvalueDecomposition states:
>> >
>> >     columns of V represent the eigenvectors in the sense that A*V = V*D,
>> >     i.e. A.times(V) equals V.times(D).  The matrix V may be badly
>> >     conditioned, or even singular, so the validity of the equation
>> >     A = V*D*inverse(V) depends upon V.cond().
>> >
>> > Looking at your example it looks like you took the rows of V to extract
>> > your eigenvector.
>> >
>> > You can also easily verify if your eigenvector is correct:
>> >
>> >  A * v = lambda * v
>> >
>> > Thomas
>> >
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>>
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