Re: [eigen] ordering of eigenvalues of EigenSolver |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] ordering of eigenvalues of EigenSolver*From*: Susanne Suter <susanne.suter@xxxxxxxxx>*Date*: Mon, 21 Feb 2011 15:12:53 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:in-reply-to:references:date :message-id:subject:from:to:content-type:content-transfer-encoding; bh=doyojx2S44cPO5pyG8TPD/7e+8GUTmiD4DZ4D02Q4sc=; b=KPbRg/zTuWUQHLNjvlTLL/zMN7heMWPoiXIZjj9hm/45bigQxaMyDYRBVI0FAHxX5n aktVwGy0Q3QRltKBfl9X9SUrOfFeF9uBvthLr+piVPVI4LdBUNak77RuQEGN2kw4ebXM BIevRRVjCA1TWY/G9h282eezODNfxxiKpAw5Y=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=JVBWQfCmy4oXRoqiIAg9xsnBs/Ln9CTnPcOhE80BITHfs9JcSU9zxIAk+nEIQVLach vWs6EZlCqGdWTaclZ+DxEF478bWXLkE9moyTMreqsT20P17gOcg5JCl+9fULbJ1DkQ4R cmd28cAN1R8lRqRnN0q4rBzwifWcdnTDB99L8=

Hi Thanks Robert for pointing out my question, which was about sorting according to absolute value or signed value. Because in the current implementation the eigenvalues are ordered taking into account the sign (my example: -2.77687, -1.50582, -0.0370092, 0.848378 (last two values should be switched or if ascending order, the whole ordering should be reversed). I'm actually using LAPACK SVD now, but I was considering to use eigen library for SVD and/or Eigenvalue decomposition. So, I'm verifying if eigen produces the results I expect. I think we should draw a differentiation between SVD and eigenvalue decomposition: For SVD, the solution is unique except for the sign and the singular values are always ordered descending. I.e., the singular values are ordered according to their absolute value. To my understanding, for eigenvalue decomposition the values don't necessarily have to be ordered. But I can only think of applications, which use them ordered and when ordering them, I would use it according to absolute value (for real value problems). I.e., use the x largest magnitude values. Furthermore, other eigenvalue decomposition libraries seem to order eigenvalues, too. E.g., MatLab (based on ARPACK) orders the eigenvalue according to absolute value and it seems that LAPACK SSYEV does the same but in reverse order. So, is there a bug in the eigen library or are the values intended to be sorted like that (according to weight and direction/sign)? Thank you and best, Susanne On Mon, Feb 21, 2011 at 10:20 AM, Robert Bocquier <robert.bocquier@xxxxxxxxxxx> wrote: > Hi Benoit, > > I am interested in your answer to Susanne question, but I think you > didn't fully address it. > Her question wasn't about ascending versus descending ordering, but was > about the basis for the sort. Is it (and should it be) the eingenvalues > directly, or the absolute values of the eigenvalues ? > > Thx > Robert > > Le 18/02/2011 16:59, Benoit Jacob a écrit : >> Hi, >> >> Sorry for the belated answer, I hadn't actually checked carefully what >> both Eigen and others (LAPACK) were doing until today. >> >> As it turns out, we are doing exactly the same thing as LAPACK: >> >> * for self-adjoint eigensolver, we sort eigenvalues in ascending >> order. For LAPACK, see: >> http://www.netlib.org/lapack/single/ssyev.f >> >> * for SVD, we sort singular values in descending order. For SVD, see: >> http://www.netlib.org/lapack/single/sgesvd.f >> >> I agree that it's pretty weird to be using sometimes ascending and >> sometimes descending order. But since that's what both LAPACK and >> ourselves have been doing, we shouldn't change that now. >> >> Benoit >> >> 2011/2/8 Susanne Suter <susanne.suter@xxxxxxxxx>: >>> Hi >>> >>> Sorry, I accidently hit the "send button" too early. Here my complete >>> messge again. >>> >>> I'm testing the Eigen library in order to use it for eigenvalue >>> decomposition or SVD. In the end I need the eigenvectors (left >>> singular vectors) and the eigenvalues (singular values). >>> >>> I noticed that when using the EigenSolver classes, the ordering of the >>> eigenvalues is not as I expected. Normally, I would expect that I get >>> an ordering analogous to the singular values, i.e., an ordering with >>> the maximum absolute value first and then decreasing values ordered by >>> their absolute value (sometimes also called "largest magnitude >>> eigenvalues"). What I get now, looks a bit like an ordering >>> considering the sign (SelfAdjointEigenSolver). I had similar issues >>> with EigenSolver and ComplexEigenSolver (however, I found the ordering >>> not consistent in all methods). >>> >>> ### SelfAdjointEigenSolver: eigenvalues of A are: -2.77687 >>> -1.50582 -0.0370092 0.848378 >>> ### ComplexEigenSolver: eigenvalues are: (-0.0370093,0) (0.848378,0) >>> (-1.50582,0) (-2.77687,0) >>> ### EigenSolver: eigenvalues are : (-2.77687,0) (-0.0370092,0) >>> (0.848379,0) (-1.50582,0) >>> >>> However, I would expect >>> ### eigenvalues of A are: -2.77687 -1.50582 0.848378 -0.0370092 >>> >>> Until now, I only was using eigenvalue decompositions, which used the >>> same ordering for eigenvalues as the SVD for the singular values (e.g. >>> Matlab). Is there any reason why the implementation of Eigen is >>> different? Or is there any option to change the ordering? >>> >>> I'm using the following test matrix: >>> >>> A = >>> >>> -2.0000 -0.6714 0.8698 0.5792 >>> -0.6714 -1.1242 -0.0365 -0.5731 >>> 0.8698 -0.0365 -0.4660 -0.8542 >>> 0.5792 -0.5731 -0.8542 0.1188 >>> >>> and I test it with the following code (using the Eigen3 version). >>> >>> Eigen::SelfAdjointEigenSolver<Eigen::Matrix4f> es; >>> es.compute(A); >>> std::cout << "### SELFADJOINT EIGENVALUE DECOMPOSITION ### " << std::endl; >>> std::cout << "** eigenvalues of A are: " << >>> es.eigenvalues().transpose() << std::endl; >>> std::cout << "** eigenvectors of A are: " << std::endl << >>> es.eigenvectors() << std::endl; >>> >>> Thank you for any hints or advice on that topic. >>> >>> Best, >>> Susanne >>> >>> >>> >> >> > > > >

**Follow-Ups**:**Re: [eigen] ordering of eigenvalues of EigenSolver***From:*Susanne Suter

**Re: [eigen] ordering of eigenvalues of EigenSolver***From:*Benoit Jacob

**References**:**[eigen] ordering of eigenvalues of EigenSolver***From:*Susanne Suter

**Re: [eigen] ordering of eigenvalues of EigenSolver***From:*Benoit Jacob

**Re: [eigen] ordering of eigenvalues of EigenSolver***From:*Robert Bocquier

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