Re: [R] positive semi-definite matrix
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
--
> -Original Message-
> From: Martin Maechler [mailto:[EMAIL PROTECTED]
> Sent: Friday, July 21, 2006 1:14 PM
> To: Ravi Varadhan
> Cc: 'Duncan Murdoch'; 'roger bos'; 'RHelp'; [EMAIL PROTECTED]
> Subject: Re: [R] positive semi-definite matrix
>
> >>>>> "Ravi" == Ravi Varadhan <[EMAIL PROTECTED]>
> >>>>> 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.
>
> O... ! 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: [EMAIL PROTECTED]
> Ravi> Webpage:
> http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
> Ravi>
> --
>
> >> -Original Message-
> >> From: [EMAIL PROTECTED] [mailto:r-help-
> >> [EMAIL PROTECTED] 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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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.
Re: [R] positive semi-definite matrix
>>>>> "Ravi" == Ravi Varadhan <[EMAIL PROTECTED]>
>>>>> 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.
O... ! 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: [EMAIL PROTECTED]
Ravi> Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
Ravi>
--
>> -Original Message-----
>> From: [EMAIL PROTECTED] [mailto:r-help-
>> [EMAIL PROTECTED] 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.
Re: [R] positive semi-definite matrix
There is a paper by N.J. Higham (SIAM J Matrix Anal, 1998) on a modified
cholesky decomposition of symmetric and not necessarily positive definite
matrix (say, A), with an important goal of producing a "small-normed"
perturbation of A (say, delA), that makes (A + delA) positive definite.
http://epubs.siam.org/sam-bin/dbq/article/30289
There is also an algorithm in Gill, Murray and Wright's text - Practical
Optimization (section 4.4.2).
These may be relevant to your problem. I am not sure if these algorithms
have been implemented in R, for example, in the "matrix" library.
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
--
> -Original Message-
> From: [EMAIL PROTECTED] [mailto:r-help-
> [EMAIL PROTECTED] 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$vectors))
> }
>
> Rounding error means this is not guaranteed to be positive
> semi-definite, but it will be very close.
>
> Duncan Murdoch
>
> __
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] positive semi-definite matrix
Take a look at make.positive.definite in the corpcor package. The
implementation is very similar to what Duncan suggested.
Regards,
Francisco
Dr. Francisco J. Zagmutt
College of Veterinary Medicine and Biomedical Sciences
Colorado State University
>From: Duncan Murdoch <[EMAIL PROTECTED]>
>To: roger bos <[EMAIL PROTECTED]>
>CC: RHelp
>Subject: Re: [R] positive semi-definite matrix
>Date: Fri, 21 Jul 2006 09:44:42 -0400
>
>On 7/21/2006 8:59 AM, roger bos wrote:
> > I have a covariance matrix that is not positive semi-definite matrix and
>I
> > need it to be via some sort of adjustment. Is there any R routine or
> > package to help me do this?
>
>I think you need to be more specific about what have and what you want,
>but if the matrix is symmetric and nearly positive semi-definite (but
>not exactly because of rounding error), you might try something like
>
>fixit <- function(A) {
>eig <- eigen(A, symmetric = TRUE)
>eig$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.
__
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.
Re: [R] positive semi-definite matrix
> "Duncan" == Duncan Murdoch <[EMAIL PROTECTED]>
> on Fri, 21 Jul 2006 09:44:42 -0400 writes:
Duncan> 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?
Duncan> I think you need to be more specific about what have and what you
want,
Duncan> but if the matrix is symmetric and nearly positive semi-definite
(but
Duncan> not exactly because of rounding error), you might try something like
Duncan> fixit <- function(A) {
Duncan> eig <- eigen(A, symmetric = TRUE)
Duncan> eig$values <- pmax(0, eig$values)
Duncan> return(eig$vectors %*% diag(eig$values) %*% t(eig$vectors))
Duncan> }
Duncan> Rounding error means this is not guaranteed to be positive
Duncan> semi-definite, but it will be very close.
A slightly more general and stable version of the above
is available via sfsmisc::posdefify(.) :
install.packages("sfsmisc")
?posdefify
Martin Maechler, ETH Zurich
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] positive semi-definite matrix
On 7/21/2006 8:59 AM, roger bos wrote:
> I have a covariance matrix that is not positive semi-definite matrix and I
> need it to be via some sort of adjustment. Is there any R routine or
> package to help me do this?
I think you need to be more specific about what have and what you want,
but if the matrix is symmetric and nearly positive semi-definite (but
not exactly because of rounding error), you might try something like
fixit <- function(A) {
eig <- eigen(A, symmetric = TRUE)
eig$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.
[R] positive semi-definite matrix
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? Thanks, Roger [[alternative HTML version deleted]] __ 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.
