[R] highest eigenvalues of a matrix
ba208 at exeter.ac.uk
Thu Jun 19 09:29:43 CEST 2008
On 18 Jun 2008, at 23:52, Moshe Olshansky wrote:
> Hi Baptiste,
> If the rank of your matrix is 3 than all the eigenvalues, except
> for 3, are 0.
Good point! I obviously mixed up the rank of the matrix with the
degeneracy (multiplicity) of its eigenvalues. What I meant is that
out of 200 eigenvalues returned by eigen(), only 2 or 3 are
noticeably different and these are the ones I am looking for. None
are 0, which means the rank is 200. The high degeneracy comes from a
very high symmetry in the particular problem, so most eigenvectors
will describe the same state, I think.
Sorry for the confusion, I hope this makes sense now.
> How do you know that the rank is so low?
> If your matrix is A and it is of order N (NxN) and it's rank is 3
> then there exist matrices B and C such that B is Nx3 and C is 3xN
> and A = B*C (if A is symmetric then C = t(B)).
> Can you get that representation? If yes then any non-zero
> eigenvector of A is a linear combination of columns of B and your
> problem can be reduced to finding eigenvalues and eigenvectors of a
> 3x3 matrix, which is trivial.
> --- On Thu, 19/6/08, baptiste Auguié <ba208 at exeter.ac.uk> wrote:
>> From: baptiste Auguié <ba208 at exeter.ac.uk>
>> Subject: [R] highest eigenvalues of a matrix
>> To: "R Help" <r-help at stat.math.ethz.ch>
>> Received: Thursday, 19 June, 2008, 6:56 AM
>> DeaR list,
>> I happily use eigen() to compute the eigenvalues and
>> eigenvectors of
>> a fairly large matrix (200x200, say), but it seems
>> over-killed as its
>> rank is limited to typically 2 or 3. I sort of remember
>> being taught
>> that numerical techniques can find iteratively decreasing
>> and corresponding orthogonal eigenvectors, which would
>> provide a nice
>> alternative (once I have the first 3, say, I stop the
>> Looking at the R source code for eigen and some posts on
>> this list,
>> it seems that the function uses a LAPACK routine, but
>> obviously all
>> the options are not available through the R wrapper.
>> I'm not
>> experienced enough to try and make my own interface with
>> code, so here are two questions:
>> - is this option (choosing a desired number of
>> eigenvectors) already
>> implemented in some function / package that I missed?
>> - is the "range of indices" option in DSYEVR.f
>> < http://
>> www.netlib.org/lapack/double/dsyevr.f > what I think,
>> the indices of
>> the desired eigenvalues ordered from the highest to lowest?
>> Many thanks in advance for any piece of advice,
>> dummy example if needed:
>> test <- matrix(c(1, 2, 0, 4, 5, 6, 1.00001, 2, 0),
>> Baptiste Auguié
>> Physics Department
>> University of Exeter
>> Stocker Road,
>> Exeter, Devon,
>> EX4 4QL, UK
>> Phone: +44 1392 264187
>> R-help at r-project.org mailing list
>> PLEASE do read the posting guide
>> and provide commented, minimal, self-contained,
>> reproducible code.
University of Exeter
EX4 4QL, UK
Phone: +44 1392 264187
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