Re: [R] positive semi-definite matrix

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Sat 22 Jul 2006 - 03:34:30 EST


Martin,

You are most welcome. I apologize for my faux pas. I really did mean to say "Matrix" package, but got sloppy!

There is also another (more recent) article by Higham: http://www.maths.man.ac.uk/~nareports/narep369.pdf  

Best,
Ravi.



Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan@jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

> -----Original Message-----
> From: Martin Maechler [mailto:maechler@stat.math.ethz.ch]
> Sent: Friday, July 21, 2006 1:14 PM
> To: Ravi Varadhan
> Cc: 'Duncan Murdoch'; 'roger bos'; 'RHelp'; bates@r-project.org
> Subject: Re: [R] positive semi-definite matrix
>
> >>>>> "Ravi" == Ravi Varadhan <rvaradhan@jhmi.edu>
> >>>>> on Fri, 21 Jul 2006 11:33:23 -0400 writes:
>
> Ravi> There is a paper by N.J. Higham (SIAM J Matrix Anal,
> Ravi> 1998) on a modified cholesky decomposition of
> Ravi> symmetric and not necessarily positive definite matrix
> Ravi> (say, A), with an important goal of producing a
> Ravi> "small-normed" perturbation of A (say, delA), that
> Ravi> makes (A + delA) positive definite.
>
> Ravi> http://epubs.siam.org/sam-bin/dbq/article/30289
>
> Ravi> There is also an algorithm in Gill, Murray and
> Ravi> Wright's text - Practical Optimization (section
> Ravi> 4.4.2).
>
> Thanks a lot, Ravi,
> for the interesting references, in the past I once had looked
> for such things but did not find any --- most probably because I
> used wrong keywords.
>
> Ravi> These may be relevant to your problem. I am not sure
> Ravi> if these algorithms have been implemented in R, for
> Ravi> example, in the "matrix" library.
>
> Ooooo... ! It's "Matrix" and `package', yes `package', yes `package' ..
>
> but no, it hasn't been implemented there yet, AFAIK.
> OTOH, it's not a bad idea to do there, since it's building on
> the LDL' cholesky factorization which we are using
> in "Matrix" in other places anyway.
>
> Thanks again for your help!
> Martin Maechler, ETH Zurich
>
> Ravi> ----------------------------------------------------------------
> ----------
> Ravi> Ravi Varadhan, Ph.D.
> Ravi> Assistant Professor, The Center on Aging and Health
> Ravi> Division of Geriatric Medicine and Gerontology
> Ravi> Johns Hopkins University
> Ravi> Ph: (410) 502-2619
> Ravi> Fax: (410) 614-9625
> Ravi> Email: rvaradhan@jhmi.edu
> Ravi> Webpage:
> http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
> Ravi> ----------------------------------------------------------------
> ----------
>
> >> -----Original Message-----
> >> From: r-help-bounces@stat.math.ethz.ch [mailto:r-help-
> >> bounces@stat.math.ethz.ch] On Behalf Of Duncan Murdoch
> >> Sent: Friday, July 21, 2006 9:45 AM
> >> To: roger bos
> >> Cc: RHelp
> >> Subject: Re: [R] positive semi-definite matrix
> >>
> >> On 7/21/2006 8:59 AM, roger bos wrote:
> >> > I have a covariance matrix that is not positive semi-definite
> matrix and
> >> I
> >> > need it to be via some sort of adjustment. Is there any R
> routine or
> >> > package to help me do this?
> >>
> >> I think you need to be more specific about what have and what you
> want,
> >> but if the matrix is symmetric and nearly positive semi-definite
> (but
> >> not exactly because of rounding error), you might try something
> like
> >>
> >> fixit <- function(A) {
> >> eig <- eigen(A, symmetric = TRUE)
> >> eig$values <- pmax(0, eig$values)
> >> return(eig$vectors %*% diag(eig$values) %*% t(eig$vectors))
> >> }
> >>
> >> Rounding error means this is not guaranteed to be positive
> >> semi-definite, but it will be very close.
> >>
> >> Duncan Murdoch
>

R-help@stat.math.ethz.ch 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. Received on Sat Jul 22 05:53:17 2006

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.1.8, at Sat 22 Jul 2006 - 06:15:35 EST.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.