Re: [eigen] Plans for EigenSolver

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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.


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