[R] about the Choleski factorization

[Ravi Varadhan]

Very nice, Duncan.

Here is a little function called loch() that implements your idea for the Lochesky factorization:

loch <- function(mat) {
n <- ncol(mat)
rev <- diag(1, n)[, n: 1]
rev %*% chol(rev %*% mat %*% rev) %*% rev
}

x=matrix(c(5,1,2,1,3,1,2,1,4),3,3)

L <- loch(x)
all.equal(x, t(L) %*% L)

A <- matrix(rnorm(36), 6, 6)
A <- A %*% t(A)
L <- loch(x)
all.equal(x, t(L) %*% L)


Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: 93354504 <93354504 at nccu.edu.tw>
Date: Friday, March 27, 2009 11:58 am
Subject: [R] about the Choleski factorization
To: r-help <r-help at r-project.org>


> Hi there, 
>  
>  Given a positive definite symmetric matrix, I can use chol(x) to 
> obtain U where U is upper triangular
>  and x=U'U. For example,
>  
>  x=matrix(c(5,1,2,1,3,1,2,1,4),3,3)
>  U=chol(x)
>  U
>  #         [,1]      [,2]      [,3]
>  #[1,] 2.236068 0.4472136 0.8944272
>  #[2,] 0.000000 1.6733201 0.3585686
>  #[3,] 0.000000 0.0000000 1.7525492
>  t(U)%*%U   # this is exactly x
>  
>  Does anyone know how to obtain L such that L is lower triangular and 
> x=L'L? Thank you.
>  
>  Alex
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.