Hi Jonathan,
you probably mixed up positive matrices and positive definite matrices.
To have only positive eigen values a matrix must be positive definite.
Covariance matrices are for example are always positive semi-definite,
even though they can contain negative entries.
D is symmetric therefore all eigen values are reel and positive
therefore the largest eigen value is positive (Perron–Frobenius
theorem).
Regards
Klaus
On 9/27/11, Jonathan Mitchell jonsmit...@gmail.com wrote:
Hello!
I tried on some simulated trees last night and they weren't working, but
after your message I started a fresh R session and now solve() works fine
for both my ultrametric tree, and my simulated trees. No idea what happened
there, but thanks!
Unfortunately, I still am getting almost all negative eigenvalues for the
decomposition of the distance matrix, which doesn't make sense to me. I was
under the impression that the distance matrix from an ultrametric tree
should be Euclidean. Further, I can confirm that the distance matrix is
supposed to be euclidean by using the is.euclid() function from ade4
[is.euclid(as.dist(D)) returns TRUE], which means I have no idea why
eigen(D) is giving me negative eigenvalues...
Any thoughts?
--Jon
On Tue, Sep 27, 2011 at 12:23 AM, Emmanuel Paradis
emmanuel.para...@ird.frwrote:
Hi John,
I tried with a couple of simulated trees (ultrametric or not) and got no
error. Have you tried using the 'tol' argument of solve()?
Emmanuel
-Original Message-
From: Jonathan Mitchell mitchel...@uchicago.edu
Sender: r-sig-phylo-boun...@r-project.org
Date: Mon, 26 Sep 2011 17:42:49
To: r-sig-phylo@r-project.org
Reply-To: jonsmit...@gmail.com
Subject: [R-sig-phylo] Negative Eigenvalues from Phylo Distance Matrix
Hello all,
I've run into a problem trying to find the eigen vectors for a
phylogenetic
distance matrix. Namely, the transposed vector matrix crossed with the
matrix itself is singular. Also, the eigenvalues for the distance matrix
proper are almost all negative, which I don't understand whatsoever.
#Given a tree with branch lengths (in my case, it's ultrametric)
D - cophenetic(tree)
eD - eigen(D, symmetric=TRUE)$vectors #note that all elements except the
first in eD$values are negative for me
inv - solve(t(eD)%*%eD) #this is what I really want, the inverse of the
transposed matrix of vectors multiplied by itself
Error in solve.default(t(eD) %*% eD) :
system is computationally singular: reciprocal condition number =
2.46807e-29
Any help would be greatly appreciated!
-- Jon
_
Jonathan S. Mitchell
http://home.uchicago.edu/~mitchelljs/
PhD Student
Committee on Evolutionary Biology
The University of Chicago
1025 57th Str, Culver Hall 402
Chicago, IL 60637
Geology Department
The Field Museum of Natural History
1400 S. Lake Shore Dr.
Chicago, IL 60605
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--
Klaus Schliep
Université Paris 6 (Pierre et Marie Curie)
9, Quai Saint-Bernard, 75005 Paris
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