Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/linear-algebra-2.2.0/@kronprod/inv.m b/octave_packages/linear-algebra-2.2.0/@kronprod/inv.m
new file mode 100644 (file)
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+++ b/octave_packages/linear-algebra-2.2.0/@kronprod/inv.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} inv (@var{KP})
+## Return the inverse of the Kronecker product @var{KP}.
+##
+## If @var{KP} is the Kronecker product of two square matrices @var{A} and @var{B},
+## the inverse will be computed as the Kronecker product of the inverse of
+## @var{A} and @var{B}.
+##
+## If @var{KP} is square but not a Kronecker product of square matrices, the
+## inverse will be computed using the SVD
+## @seealso{@@kronprod/sparse}
+## @end deftypefn
+
+function retval = inv (KP)
+  ## Check input
+  if (nargin != 1)
+    print_usage ();
+  endif
+  
+  if (!isa (KP, "kronprod"))
+    error ("inv: input argument must be of class 'kronprod'");
+  endif
+  
+  ## Do the computations
+  [n, m] = size (KP.A);
+  [q, r] = size (KP.B);
+  if (n == m && q == r) # A and B are both square
+    retval = kronprod (inv (KP.A), inv (KP.B));
+  elseif (n*q == m*r) # kron (A, B) is square
+    ## We use the SVD to compute the inverse.
+    ## XXX: Should we use 'eig' instead?
+    [U, S, V] = svd (KP);
+    retval = U * (1./S) * V';
+  else
+    error ("inv: argument must be a square matrix");
+  endif
+endfunction