Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / linear-algebra-2.2.0 / @kronprod / det.m

diff --git a/octave_packages/linear-algebra-2.2.0/@kronprod/det.m b/octave_packages/linear-algebra-2.2.0/@kronprod/det.m
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+## Copyright (C) 2010  Soren Hauberg
+## 
+## 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 3, 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, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} det (@var{KP})
+## Compute the determinant of a Kronecker product.
+##
+## If @var{KP} is the Kronecker product of the @var{n}-by-@var{n} matrix @var{A}
+## and the @var{q}-by-@var{q} matrix @var{B}, then the determinant is computed
+## as
+##
+## @example
+## det (@var{A})^q * det (@var{B})^n
+## @end example
+##
+## If @var{KP} is not a Kronecker product of square matrices the determinant is
+## computed by forming the full matrix and then computing the determinant.
+## @seealso{det, @@kronprod/trace, @@kronprod/rank, @@kronprod/full}
+## @end deftypefn
+
+function retval = det (KP)
+  ## Check input
+  if (nargin != 1)
+    print_usage ();
+  endif
+  
+  if (!isa (KP, "kronprod"))
+    error ("det: input argument must be of class 'kronprod'");
+  endif
+
+  if (!issquare (KP))
+    error ("det: argument must be a square matrix");
+  endif
+
+  ## Take action
+  [n, m] = size (KP.A);
+  [q, r] = size (KP.B);
+  if (n == m && q == r) # A and B are both square
+    retval = (det (KP.A)^q) * (det (KP.B)^n);
+  elseif (n*q == m*r) # kron (A, B) is square
+    ## XXX: Can we do something smarter here? We should be able to use the SVD...
+    retval = det (full (KP));
+  endif
+endfunction