No Sorting

[GreenPatriot]

Hi everyone. I'm looking for a diagonalization subroutine that does not sort the outputted eigenvectors. All of the LAPACK programs automatically sort the eigenvalues and eigenvectors, with no obvious way of changing this option. Does anyone know of 1) a subroutine that will not sort or 2) a way to alter the LAPACK program so that it will not automatically sort the eigenvectors? Thanks!!

[tjcarroll]

Hi,
First, this is not an answer to your question...but I'm looking for basically the same thing. The way I understand it, the original order of the eigenvalues/eigenvectors is not preserved since the LAPACK algorithms will, in general, swap rows/columns in the process of diagonalization. Having the routing NOT sort the values would not give you your original ordering back.

I'm wondering if there is a way to at least record the re-ordering that took place so that one could determine what the original ordering was...maybe just a vector that stored the original positions?

Anyway, if I figure out how to do what you're asking, I will be sure to post it.

-tom

[Julien Langou]

Hello both of you,

The eigenvalue decomposition of a real symmetric matrix is: "given A, find A = V * D * V^T" and, since A is real symmetric, we additional impose V^TV=I.

If you perform column permutation in V (permutation of the eigenvectors) and symmetric permutation in D (permutation of the eigenvalues) you obtain "another" eigenvalue decomposition.

There is not one better than another.

The concept of "original order" in the sentence:

the original order of the eigenvalues/eigenvectors is not preserved [ in LAPACK ]

makes no sense. There is nothing as an "original order".

Julien.