[R] positive semi-definite matrix
Martin Maechler
maechler at stat.math.ethz.ch
Fri Jul 21 19:13:39 CEST 2006
>>>>> "Ravi" == Ravi Varadhan <rvaradhan at 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 at jhmi.edu
Ravi> Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
Ravi> --------------------------------------------------------------------------
>> -----Original Message-----
>> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
>> bounces at 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
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