update packages

[CreaPhase.git] / octave_packages / m / linear-algebra / duplication_matrix.m

diff --git a/octave_packages/m/linear-algebra/duplication_matrix.m b/octave_packages/m/linear-algebra/duplication_matrix.m
new file mode 100644 (file)
index 0000000..20d373d
--- /dev/null
+++ b/octave_packages/m/linear-algebra/duplication_matrix.m
@@ -0,0 +1,120 @@
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## This file is part of Octave.
+##
+## Octave 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 3 of the License, or (at
+## your option) any later version.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} duplication_matrix (@var{n})
+## Return the duplication matrix
+## @tex
+##  $D_n$
+## @end tex
+## @ifnottex
+##  @math{Dn}
+## @end ifnottex
+##  which is the unique
+## @tex
+##  $n^2 \times n(n+1)/2$
+## @end tex
+## @ifnottex
+##  @math{n^2} by @math{n*(n+1)/2}
+## @end ifnottex
+##  matrix such that
+## @tex
+##  $D_n * {\rm vech} (A) = {\rm vec} (A)$
+## @end tex
+## @ifnottex
+##  @math{Dn vech (A) = vec (A)}
+## @end ifnottex
+##  for all symmetric
+## @tex
+##  $n \times n$
+## @end tex
+## @ifnottex
+##  @math{n} by @math{n}
+## @end ifnottex
+##  matrices
+## @tex
+##  $A$.
+## @end tex
+## @ifnottex
+##  @math{A}.
+## @end ifnottex
+##
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 8 May 1995
+## Adapged-By: jwe
+
+function d = duplication_matrix (n)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (! (isscalar (n) && n > 0 && n == fix (n)))
+    error ("duplication_matrix: N must be a positive integer");
+  endif
+
+  d = zeros (n * n, n * (n + 1) / 2);
+
+  ## It is clearly possible to make this a LOT faster!
+  count = 0;
+  for j = 1 : n
+    d ((j - 1) * n + j, count + j) = 1;
+    for i = (j + 1) : n
+      d ((j - 1) * n + i, count + i) = 1;
+      d ((i - 1) * n + j, count + i) = 1;
+    endfor
+    count = count + n - j;
+  endfor
+
+endfunction
+
+%!test
+%! N = 2;
+%! A = rand(N);
+%! B = A * A';
+%! C = A + A';
+%! D = duplication_matrix (N);
+%! assert (D * vech (B), vec (B), 1e-6);
+%! assert (D * vech (C), vec (C), 1e-6);
+
+%!test
+%! N = 3;
+%! A = rand(N);
+%! B = A * A';
+%! C = A + A';
+%! D = duplication_matrix (N);
+%! assert (D * vech (B), vec (B), 1e-6);
+%! assert (D * vech (C), vec (C), 1e-6);
+
+%!test
+%! N = 4;
+%! A = rand(N);
+%! B = A * A';
+%! C = A + A';
+%! D = duplication_matrix (N);
+%! assert (D * vech (B), vec (B), 1e-6);
+%! assert (D * vech (C), vec (C), 1e-6);
+
+%!error duplication_matrix ();
+%!error duplication_matrix (0.5);
+%!error duplication_matrix (-1);
+%!error duplication_matrix (ones(1,4));