On Sun, 10 Sep 2006, w wrote:
Dear R-list members,
Just wondering if there is any way to compute the duplication matrix in R.
I tried to search for it but only found functions "xpnd" and "vech".
Something like this:
Dn <- function(x){
mat <- diag(x)
index <- seq(x*(x+1)/2)
mat[ lower.tri( mat , TRUE ) ] <- index
mat[ upper.tri( mat ) ] <- t( mat )[ upper.tri( mat ) ]
outer(c(mat), index , function( x , y ) ifelse(x==y, 1, 0 ) )
}
Dn(4) returns what you describe for a 4 x 4 matrix
Basically for a symmetric n by n matrix A, the duplication matrix D_n is
a matrix of dimension n^2 by n(n+1)/2 such that
D_n vech(A)= c(A), where c(A) just vectorizes A.
The duplication matrix is defined on page 49 of the book "Matrix
differential calculus with applications in statistics and econometrics"
by Magnus and Neudecker (1988 )
Thanks a lot!
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:[EMAIL PROTECTED] UC San Diego
http://biostat.ucsd.edu/~cberry/ La Jolla, San Diego 92093-0717
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