Re: [eigen] generalized eigenvector solver bug |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] generalized eigenvector solver bug*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Mon, 9 Mar 2015 09:23:49 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; bh=H5FcPDM0AejQCRqHjyNMY0TdlwB8BUO3Pd7gMQRbCZo=; b=gyPhEV+V9S5e+mFuCrOZdPUkHAW9iFvJavuFK6AX4rohTFCbNygbW+/kpKpwiKH1/0 1gejxWFC5fpX5Drs5v7YWm1oku7qeMiYm8Omrj9zGeJ2gga5OdXEZ7+buIT7NTBj3/1n CGGP7WrBkWW7+ceaNanLfRKZUer9yd1KSQl86yJT+G9/jJ/HdVtl2XvrSqM3riX+G7HD 3KBJD0KctiOQEp+AGzm1Y+AAxhCc5+EisdvNLaO8D6NFGKzii2xreHKHDB3ry2dCa3ep mykOI1r2vIwLJKU0+Lie5v2xUVWIHlAzjHtHk/7NfpZoHxCABQUdDybUxoW1U0x1eVIq uP6A==

For the self-adjoint case, if one of the matrices is positive-definite, then the class GeneralizedSelfAdjointEigenSolver is already pretty good. It is based on a LL^T factorizarion of the positive-definite one, and on the SelfAdjointEigenSolver class to carry out the actual eigen-problem.

For the non-symmetric but real case, the class GeneralizedEigenSolver is based on the quite standard QZ algorithm (mostly from Golub's Matrix Computations book), but only the eigenvalues are returned and we're only missing the bits to extract the eigenvectors from QZ and eigenvalues. Improving the QZ implementation as suggested by Pavel won't change the fact that the aforementioned part of the puzzle (aka bug 645) will be missing and should probably be worked out first.

gael

On Sun, Mar 8, 2015 at 4:09 PM, Gareth Owen <gareth.w.owen@xxxxxxxxx> wrote:

GareththanksHi,I've been looking over solvers for the generalized eigenvalue problem a bit this week, and I was wondering which implementation would be meant for the generalized eigensolver within Eigen - generalized symmetric definite or generalized nonsymmetric? Which might be best to try and implement first?On Fri, Mar 6, 2015 at 3:18 PM, Gael Guennebaud <gael.guennebaud@xxxxxxxxx> wrote:As far as I known, nothing has been started yet.gaelOn Fri, Mar 6, 2015 at 12:48 PM, Gareth Owen <gareth.w.owen@xxxxxxxxx> wrote:GareththanksHi,I've noticed that the generalized eigensolver bug (645) is still open - is there any work being done on this?

**Follow-Ups**:**Re: [eigen] generalized eigenvector solver bug***From:*Gareth Owen

**References**:**[eigen] generalized eigenvector solver bug***From:*Gareth Owen

**Re: [eigen] generalized eigenvector solver bug***From:*Gael Guennebaud

**Re: [eigen] generalized eigenvector solver bug***From:*Gareth Owen

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