Re: [eigen] Eigenvalue solving and balancing

[Ian Bell <ian.h.bell@xxxxxxxxx>]

This is quite crucial to getting reasonable eigenvalues - I would recommend that at the very least some information is added to the docs.  If something is already available in Eigen, all the better

Ian

On Mon, Apr 3, 2017 at 7:35 AM, Julian Kent <jkflying@xxxxxxxxx> wrote:

Hi Ian

There is something similar available in the unsupported modules, in unsupported/Eigen/src/IterativeSolvers/Scaling.h, called IterScaling.

However, it doesn't support the lossless radix-only scaling that you've implemented.

Cheers

Julian

On 3 April 2017 at 05:57, Ian Bell <ian.h.bell@xxxxxxxxx> wrote:

So it turns out that balancing the matrix prior to taking the eigenvalues is absolutely crucial (for my problem at the very least).  

I rapidly came to this conclusion after giving up on Eigen's eigenvalue solver due to the terrible eigenvalues that I was obtaining due to the ill-conditioning of the matrix.  Numpy crucially does balance the matrix prior to eigenvalue solving.  I would recommend that a method like the attached in my stack overflow question be made available : http://stackoverflow.com/a/43169781/1360263 .  I'm not sure what the protocol is for PR (I don't use mercurial), and I am sure my solution needs a bit more templating magic, but without this, the eigenvalues from Eigen are useless for some challenging eigenvalue solving problems.

Best,

Ian