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st: re: interaction of column matrix


From   Kit Baum <kitbaum@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: interaction of column matrix
Date   Fri, 19 Oct 2007 06:58:26 -0400

Abdel wrote

I've written this mata function as a solution to my own question yesterday.
horizontal direct product (hdp).
--------begin code------------
version 9.2
local mydir "."
mata:
mata clear
real matrix hdp(real matrix A, real matrix B)
{
assert(rows(A)==rows(B))
real scalar n
real matrix C
n=rows(A)
C=J(n,1,.)
for (i=1; i<=cols(A); i++) {
C=C,(A[.,i]:*B)
}
C=C[.,2..cols(C)]
return(C)
}


I've never heard of a 'horizontal direct product' but in a 2x2 example it seems to be the first and last rows of a conventional Kronecker product:

: a
1 2
+---------+
1 | 1 2 |
2 | 3 4 |
+---------+

: b
1 2
+---------+
1 | 5 6 |
2 | 0 1 |
+---------+

: c
1 2 3 4
+---------------------+
1 | 5 6 10 12 |
2 | 0 3 0 4 |
+---------------------+

: a#b
1 2 3 4
+---------------------+
1 | 5 6 10 12 |
2 | 0 1 0 2 |
3 | 15 18 20 24 |
4 | 0 3 0 4 |
+---------------------+


For a 3x3 example, it is the 1st, 5th and 9th rows of the Kronecker product. Thus it appears that whatever this construction might be it could be generated from a Kronecker.




Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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