Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing

[Victor Liu <victor.liu@xxxxxxxxx>]

Hi, not to hijack the thread, but I think this is related (I haven't 
been on the list long enough to see the original thread).

I would love to use Eigen except for the fact that the complex 
eigensolver is much slower compared to Lapack, which does both blocking 
in the Hessenberg reduction, as well as uses a better shift strategy and 
aggressive early deflation in the QR iteration. Now, I've ported the 
entire dependency chain of Lapack's zgeev to C++, if there is any 
interest in including it into Eigen (the original motivation was to deal 
with Lapack errata 0061). The source tree is at:
https://github.com/victorliu/S4/tree/master/src/RNP
The core QR routines are in Eigensystems.cpp, while the auxiliary 
routines like Hessenberg reduction and balancing is in TLASupport.h. I 
considered contributing to the Eigen code base but it appears to be 
quite complicated and I'm not sure I have the time for it.

-Victor

On 07/20/2012 12:24 AM, Markus Moll wrote:
> Hi
>
> Sorry for reviving an "ancient" thread, but:
> I recently had to extract roots of a fourth order polynomial. Using Eigen to
> find the eigenvalues of the companion matrix, I found that some roots were
> horribly bad (compared to matlab, which gave much more reliable results). I
> soon figured that the difference is that Matlab balances the matrices
> beforehand. In this thread, Manuel said he had written a balancer, but I
> cannot find it among the unsupported modules, nor can I find his bitbucket
> account any more.
>
> Because I wasn't aware of this previous effort, I had already translated
> LAPACK's dgebal (the diagonal scaling part only) to C++. As I feel that
> balancing should be supported in Eigen (via another EigenSolver flag?), I
> wonder if this could be included. The original LAPACK dgebal.f is published
> under the 3-clause BSD license, so the licenses should be compatible according
> to my understanding.
>
> Regards
> Markus