Hi Guillermo, https://metacpan.org/pod/PDL::LinearAlgebra#meigen says it uses https://metacpan.org/pod/PDL::LinearAlgebra::Real#geev. That obviously uses the relevant LAPACK function. The double-precision version, dgeev, is documented at https://www.netlib.org/lapack/explore-html/d9/d8e/group__double_g_eeigen_ga66e19253344358f5dee1e60502b9e96f.html and says it does indeed normalise the eigenvectors. If that is not the final result, then it looks like my _eigen_extract function isn’t working right (which is unfortunate but fixable).
Could you please make a smaller (ideally 2x2 or 3x3) example data with expected results, so I can use that to fix this? None of the docs linked above mention sorting the eigenvalues, and I don’t believe the wrappers change that, so I believe if you want them sorted then you’d have to do that yourself. As usual, I have to caveat I am not either a linear-algebra nor LAPACK expert, so if you or anyone know better concerning these points, please speak up :-) Best regards, Ed From: Guillermo P. Ortiz<mailto:gor...@exa.unne.edu.ar> Sent: 05 July 2022 19:34 To: pdl-general@lists.sourceforge.net<mailto:pdl-general@lists.sourceforge.net>; pdl-de...@lists.sourceforge.net<mailto:pdl-de...@lists.sourceforge.net> Subject: [Pdl-devel] meigen sort criteria for eigenvalue and eigenvectors. Dear PDL developers, Trying to use meigen() for eigenvalue problem with matrix 4x4 without threading for now, I realize that eigenvalues seems did not have any ordered output, is not it? In the first example below the second eigenvalue is larger than the first =========== Matrix: [ [ 0 1 0 0] [ 1.19256986494742 0 -0.00449505340171719 0] [ 0 0 0 -1] [ 0.00449505340171719 0 -1.20412391559198 0] ] Eigenvalue: [1.09134187427168 1.09802854880944 -1.09134187427168 -1.09802854880944] Right Eigenvector (tranposed matrix) [ [ 0.638990630564561 0.697357232402369 0.219312399660024 -0.23934480529599] [ 0.218583370045276 0.240010780604692 -0.636866523154502 0.699297624204653] [-0.638990630564568 0.697357232402378 -0.219312399660001 -0.239344805295965] [-0.218583370045231 0.240010780604642 0.636866523154517 0.69929762420467] ] In the second example, neither, and also the eigenvectors seem not be normalized Matrix: [ [ 0 1 0 0] [ 1.18623905553229 0 -3.55105833627078e-10 0] [ 0 0 0 -1] [ 3.55105833627078e-10 0 -1.21150887543497 0] ] [1.08914602121676 -1.08914602121676 1.10068563878838 -1.10068563878838] [ [ 0.676318357570712 0.736609448223992 9.50400893585054e-09 -1.03512535180901e-08] [ -0.676318357570712 0.736609448223992 -9.50400893585071e-09 -1.03512535180903e-08] [ 9.44955412328998e-09 1.04009885164588e-08 -0.672443278155145 0.740148659165145] [-9.44955412328967e-09 1.04009885164584e-08 0.672443278155145 0.740148659165145] ] Thank you in advance. Regards -- Dr. Guillermo P. Ortiz Electromagnetismo Aplicado Dto. Física, Facultad de Ciencias Exactas Universidad Nacional del Nordeste Avda Libertad 5460, W3404AAS Corrientes, Argentina. (+54) 379-4424678 interno 4613 gortiz at unne edu ar
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