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comm_mat.m
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Text File
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1999-12-24
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3KB
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108 lines
## Copyright (C) 1995, 1996 Kurt Hornik
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## -*- texinfo -*-
## @deftypefn {Function File} {} comm_mat (@var{m}, @var{n})
## Return the commutation matrix
## @iftex
## @tex
## $K_{m,n}$
## @end tex
## @end iftex
## @ifinfo
## K(m,n)
## @end ifinfo
## which is the unique
## @iftex
## @tex
## $m n \times m n$
## @end tex
## @end iftex
## @ifinfo
## @var{m}*@var{n} by @var{m}*@var{n}
## @end ifinfo
## matrix such that
## @iftex
## @tex
## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$
## @end tex
## @end iftex
## @ifinfo
## @var{K}(@var{m},@var{n}) * vec (@var{A}) = vec (@var{A}')
## @end ifinfo
## for all
## @iftex
## @tex
## $m\times n$
## @end tex
## @end iftex
## @ifinfo
## @var{m} by @var{n}
## @end ifinfo
## matrices
## @iftex
## @tex
## $A$.
## @end tex
## @end iftex
## @ifinfo
## @var{A}.
## @end ifinfo
##
## If only one argument @var{m} is given,
## @iftex
## @tex
## $K_{m,m}$
## @end tex
## @end iftex
## @ifinfo
## K(m,m)
## @end ifinfo
## is returned.
##
## See Magnus and Neudecker (1988), Matrix differential calculus with
## applications in stat and econometrics.
## @end deftypefn
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 8 May 1995
## Adapted-By: jwe
function k = comm_mat (m, n)
if (nargin < 1 || nargin > 2)
usage ("comm_mat (m [, n])");
else
if (! (is_scal (m) && m == round (m) && m > 0))
error ("comm_mat: m must be a positive integer");
endif
if (nargin == 1)
n = m;
elseif (! (is_scal (n) && n == round (n) && n > 0))
error ("comm_mat: n must be a positive integer");
endif
endif
## It is clearly possible to make this a LOT faster!
k = zeros (m * n, m * n);
for i = 1 : m
for j = 1 : n
k ((i - 1) * n + j, (j - 1) * m + i) = 1;
endfor
endfor
endfunction