R help - Aug 2006 - horizontal direct product

II am translating some gauss code into R, and gauss has a matrix  
product function called the horizontal direct product (*~), which is  
some sort of variant on the Kronecker product.

For example if x is 2x2 and y is 2x2

the horizontal direct product, z, of x and y is defined (in the Gauss  
manual) as:

row 1 = x11*y11 x11*y12 x12*y11 x12*y12
row 2 = x21*y21 x21*y22 x22*y21 x22*y22

Or in R code if:

x <- matrix(seq(1,4,by=1),2,2, byrow=TRUE)
y <- matrix(seq(5,8,by=1),2,2, byrow=TRUE)

The resulting matrix, if I had an operator, would be the following  
matrix z, here formed in a contrived manner:

z.1 <- c(5, 6, 10, 12)
z.2 <- c(21,24,28,32)
z <- rbind(z.1,z.2)

I realize that this is just the first and last row of x%*%y when x  
and y are two by two but this  won't generalize with larger  
matrices.  Any ideas about whether this can be done with existing R  
functions in a general way short of writing my own function?

   Thanks

Luke




Luke Keele
Department of Political Science
Ohio State University
keele.4@polisci.osu.edu




	[[alternative HTML version deleted]]

maybe something like:

"%*~%" <- function(x, y){
     n <- nrow(x)
     out <- matrix(0, n, ncol(x) * ncol(y))
     for(i in 1:n)
         out[i, ] <- c(y[i, ] %o% x[i, ])
     out
}

x <- matrix(1:4, 2, 2, TRUE)
y <- matrix(5:8, 2, 2, TRUE)

x %*~% y


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
      http://www.student.kuleuven.be/~m0390867/dimitris.htm


Quoting Luke Keele <keele.4 at polisci.osu.edu>:
> II am translating some gauss code into R, and gauss has a matrix
> product function called the horizontal direct product (*~), which is
> some sort of variant on the Kronecker product.
>
> For example if x is 2x2 and y is 2x2
>
> the horizontal direct product, z, of x and y is defined (in the Gauss
> manual) as:
>
> row 1 = x11*y11 x11*y12 x12*y11 x12*y12
> row 2 = x21*y21 x21*y22 x22*y21 x22*y22
>
> Or in R code if:
>
> x <- matrix(seq(1,4,by=1),2,2, byrow=TRUE)
> y <- matrix(seq(5,8,by=1),2,2, byrow=TRUE)
>
> The resulting matrix, if I had an operator, would be the following
> matrix z, here formed in a contrived manner:
>
> z.1 <- c(5, 6, 10, 12)
> z.2 <- c(21,24,28,32)
> z <- rbind(z.1,z.2)
>
> I realize that this is just the first and last row of x%*%y when x
> and y are two by two but this  won't generalize with larger
> matrices.  Any ideas about whether this can be done with existing R
> functions in a general way short of writing my own function?
>
>    Thanks
>
> Luke
>
>
>
>
> Luke Keele
> Department of Political Science
> Ohio State University
> keele.4 at polisci.osu.edu
>
>
>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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.
>
>


Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm

On Fri, 25 Aug 2006, Luke Keele wrote:
> II am translating some gauss code into R, and gauss has a matrix
> product function called the horizontal direct product (*~), which is
> some sort of variant on the Kronecker product.
>
> For example if x is 2x2 and y is 2x2
>
> the horizontal direct product, z, of x and y is defined (in the Gauss
> manual) as:
>
> row 1 = x11*y11 x11*y12 x12*y11 x12*y12
> row 2 = x21*y21 x21*y22 x22*y21 x22*y22
>
It looks as though
"%~%" <- function (A, B)
{
     m <- ncol(A)
     n <- ncol(B)
     A[, rep(1:m, each = n)] * B[, rep(1:n, m)]
}

would do it.


 	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle