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Re: Re: st: re: interaction of column matrix


From   n j cox <n.j.cox@durham.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: re: interaction of column matrix
Date   Fri, 19 Oct 2007 16:42:14 +0100

My reaction was like Kit's: in my ignorance
I had not heard of horizontal direct products,
and wondered about any connection to Kronecker.

No matter. Abdel has working code, and his
approach is likely to be as direct as any other.
I think his code can be tweaked, although the
changes are essentially cosmetic. I would write:

real matrix hdp(real matrix A, real matrix B)
{
assert(rows(A) == rows(B))
real matrix C
C = J(rows(A), 0, .)
for (i = 1; i <= cols(A); i++) {
C = C, (A[, i] :* B)
}
return(C)
}

What's different? Not much.

0. Style. I like to put spaces around most binary operators
and after commas, if there is space to spare. 100% of the publications
on Stata style agree. However, no spaces around * and / can be
good style, to indicate binding.

1. You don't need to declare n, which is used only once.

2. The cutest, and this is due to Bill Gould, not me, is
to initialise with a matrix of 0 columns. That way, you
need take away nothing (or, more precisely, need not take away
anything) at the end.

I can't see a reason why this could not be generalised to
complex matrices. An official program would be more informative
if the -assert- failed.

I presume there is a vertical direct product, and I guess
that in practice it is even less used.

Abdel replied to Kit Baum who replied to Abdel Rahmen El Lahga

> 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...

the term "horizontal direct product" is used in Gauss manual ( and R i
think) and denoted by the operator
" *~ " and is different from the kronecker product in Gauss denoted by " .*. "
You are right when tou say that "it appears that whatever this
construction might be it
> could be generated from a Kronecker" but the question is how to automate such task in Mata. You know that with matrix A(k,l), B(m,n) ; A#B =C(k*m,l*n) but here we want a new matrix C(k,l*n) asumming that k=m. Hence my motivation to write my hdp() function
AbdelRahmen

2007/10/19, Kit Baum <kitbaum@mac.com>:
> 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.


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