Hi,
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.
Baptiste
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.
Regards,
Moshe.
--- On Thu, 19/6/08, baptiste Auguié <[EMAIL PROTECTED]> wrote:
From: baptiste Auguié <[EMAIL PROTECTED]>
Subject: [R] highest eigenvalues of a matrix
To: "R Help" <[EMAIL PROTECTED]>
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
eigenvalues
and corresponding orthogonal eigenvectors, which would
provide a nice
alternative (once I have the first 3, say, I stop the
search).
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
Fortran
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,
Sincerely,
Baptiste
dummy example if needed:
test <- matrix(c(1, 2, 0, 4, 5, 6, 1.00001, 2, 0),
ncol=3)
eigen(test)
_____________________________
Baptiste Auguié
Physics Department
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK
Phone: +44 1392 264187
http://newton.ex.ac.uk/research/emag
http://projects.ex.ac.uk/atto
______________________________________________
[email protected] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained,
reproducible code.
_____________________________
Baptiste Auguié
Physics Department
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK
Phone: +44 1392 264187
http://newton.ex.ac.uk/research/emag
http://projects.ex.ac.uk/atto
______________________________________________
[email protected] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
