[eigen] Eigenvalue solving and balancing
• To: eigen@xxxxxxxxxxxxxxxxxxx
• Subject: [eigen] Eigenvalue solving and balancing
• From: Ian Bell <ian.h.bell@xxxxxxxxx>
• Date: Sun, 2 Apr 2017 21:57:15 -0600
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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

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