[R] duplication matrix

[Charles C. Berry]

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:cberry at tajo.ucsd.edu	         UC San Diego
http://biostat.ucsd.edu/~cberry/         La Jolla, San Diego 92093-0717