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From Thomas Neidhart <thomas.neidh...@gmail.com>
Subject Re: [math] eigenvector doubts and issues
Date Tue, 12 Nov 2013 10:48:30 GMT
```Hi Andrea,

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,

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,
> >>
> >>> 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
> >>
> >> 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
> >
> > You can also easily verify if your eigenvector is correct:
> >
> >  A * v = lambda * v
> >
> > Thomas
> >
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> >
>
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>

```
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