Re: [eigen] Plans for EigenSolver

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On Mon, Sep 7, 2009 at 11:56 AM, Jitse Niesen<jitse@xxxxxxxxxxxxxxxxx> wrote:
> On Fri, 4 Sep 2009, Gael Guennebaud wrote:
>> - 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
> Good. I'm starting to program general matrix functions but the algorithm is
> rather more complicated than I thought, so it will take a while.
>> - 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.
> I need only the complex Schur decomposition; even for real matrices.
> However, for real matrices, I'd guess it's probably faster to compute the
> real Schur decomposition in real arithmetic and then convert it to the
> complex Schur decomposition, compared to casting the real matrix to a
> complex matrix and then computing the complex Schur decomposition directly.
> I guess that this is what the current EigenSolver is doing now, and what the
> new EigenSolver will do, so it shouldn't be too hard to make the complex
> Schur decomposition available for real matrices.

Yes the plan is to add a conversion ctor from a RealSchur to a
ComplexSchur, and then the new EigenSolver will probably use it. I
also guess that ComplexSchur<real_matrix_type> could call RealSchur
and then do the conversion for you.


> Cheers,
> Jitse

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