Re: [eigen] Plans for EigenSolver

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to update the list:

- I've split the QR module into a pure QR one and an Eigenvalues
module for all eigen values related stuff
- I've recently merged this patch into the main devel branch: it
provides a ComplexSchur decomposition and a ComplexEigenSolver for
general matrices
- Actually the real and complex Schur decompositions are too different
to factorize them, and the way you use them is also very different. So
I plan to have a RealSchur decomposition but no generic Schur
decomposition class.
- On the other hand once we'll have a clean RealSchur class, I plane
to have a unique EigenSolver and remove the ComplexEigenSolver class.

if anybody have some idea to build tricky matrices for our eigen solvers...


On Sun, Aug 23, 2009 at 6:29 PM, Gael
Guennebaud<gael.guennebaud@xxxxxxxxx> wrote:
> hi,
> here is a general eigen solver working for complexes:
> this a very rough implementation ported from JAMAPACK, but at least it
> passes all the unit tests and unlike the current EigenSolver the
> algorithm is easy to follow.
> Any help to make it better is more than welcome, some ideas:
> - make it suitable for real (it is currently specialized for complexes)
> - more unit tests to check the accuracy, etc.
> these 2 todo are mandatory to include it in Eigen, and then:
> - offer the possibility not to compute the eigenvectors
> - make the internal Shur decomposition available
> - more cleaning
> - improve speed,
> - improve accuracy,
> gael
> On Tue, Aug 18, 2009 at 4:40 PM, Gael
> Guennebaud<gael.guennebaud@xxxxxxxxx> wrote:
>> actually someone told me yesterday she managed to hack an EigenSolver
>> for complexes on top of our HessenbergDecomposition and mimicking the
>> implementation of the Shur decomposition of JAMPACK. I waiting for her
>> reply about its integration in Eigen... She acknowledged her
>> implementation was certainly not perfect, but I'm sure this is already
>> a good step in the right direction and that would be a very nice
>> contribution. I'll let you now as soon as I have more info.
>> gael.
>> On Tue, Aug 18, 2009 at 3:22 PM, Benoit Jacob<jacob.benoit.1@xxxxxxxxx> wrote:
>>> 2009/8/18 Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>:
>>>> 2. I rewrite EigenSolver along the lines of SelfAdjointEigenSolver, possibly
>>>> working with Benoit (and others) to achieve this. This may be more useful
>>>> (there is more interest in eigenvalue problem solvers than matrix function),
>>>> but I'm not sure it's efficient because Benoit works much faster than me.
>>> .... BUT if you want to rewrite EigenSolver on your own, by all means
>>> do it ! ;) it's just that i'm not able to help at the moment.
>>> I think that Gael just made Hessenberg use the new Householder
>>> transformations, which is a good first step, you'll have to do on your
>>> own the rest.
>>> Benoit

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