--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/general/del2.m	Mon Jul 23 22:05:30 2007 +0000
@@ -0,0 +1,156 @@
+## Copyright (C) 2000  Kai Habel
+## Copyright (C) 2007  David Bateman
+##
+## 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 2, 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, write to the Free
+## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+## 02110-1301, USA.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{d} =} del2 (@var{m})
+## @deftypefnx {Function File} {@var{d} =} del2 (@var{m}, @var{h})
+## @deftypefnx {Function File} {@var{d} =} del2 (@var{m}, @var{dx}, @var{dy}, @dots{})
+##
+## Calculates the discrete Laplace operator. If @var{m} is a matrix this is
+## defined as
+##
+## @iftex
+## @tex
+## $d = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$
+## @end tex
+## @end iftex
+## @ifnottex
+## @example
+## @group
+##       1    / d^2            d^2         \
+## D  = --- * | ---  M(x,y) +  ---  M(x,y) | 
+##       4    \ dx^2           dy^2        /
+## @end group
+## @end example
+## @end ifnottex
+##
+## The above to continued to N-dimensional arrays calculating the second
+## derivative over the higher dimensions.
+##
+## The spacing between evaluation points may be defined by @var{h}, which is a
+## scalar defining the spacing in all dimensions. Or alternative, the spacing
+## in each dimension may be defined separately by @var{dx}, @var{dy}, etc. 
+## Scalar spacing values give equidistant spacing, whereas vector spacing 
+## values can be used to specify variable spacing. The length of the vectors
+## must match the respective dimension of @var{m}. The default spacing value
+## is 1.
+##
+## You need at least 3 data points for each dimension. Boundary points are
+## calculated as the linear extrapolation of the interior points.
+##
+## @seealso{gradient, diff}
+## @end deftypefn
+
+## Author:  Kai Habel <kai.habel@gmx.de>
+
+function D = del2 (M, varargin)
+  
+  if (nargin < 1)
+    print_usage ();
+  endif
+
+  nd = ndims (M);
+  sz = size (M);
+  dx = cell (1, nd);
+  if (nargin == 2 || nargin == 1)
+    if (nargin == 1)
+      h = 1;
+    else
+      h = varargin{1}
+    endif
+    for i = 1 : nd
+      if (isscalar (h))
+	dx{i} = h * ones (sz (i), 1);
+      else
+	if (length (h) == sz (i))
+	  dx{i} = diff (h)(:);
+	else
+	  error ("dimensionality mismatch in %d-th spacing vector", i);
+	endif
+      endif
+    endfor
+  elseif (nargin - 1 == nd)
+    ## Reverse dx{1} and dx{2} as the X-dim is the 2nd dim of the ND array
+    tmp = varargin{1};
+    varargin{1} = varargin{2};
+    varargin{2} = tmp;
+
+    for i = 1 : nd
+      if (isscalar (varargin{i}))
+	dx{i} = varargin{i} * ones (sz (i), 1);
+      else
+	if (length (varargin{i}) == sz (i))
+	  dx{i} = diff (varargin{i})(:);
+	else
+	  error ("dimensionality mismatch in %d-th spacing vector", i);
+	endif
+      endif
+    endfor
+  else
+    print_usage ();
+  endif
+
+  idx = cell (1, nd);
+  for i = 1: nd
+    idx{i} = ":";
+  endfor
+
+  D = zeros (sz);
+  for i = 1: nd
+    if (sz(i) >= 3)
+      DD = zeros (sz);
+      idx1 = idx2 = idx3 = idx;
+
+      ## interior points
+      idx1{i} = 1 : sz(i) - 2;
+      idx2{i} = 2 : sz(i) - 1;
+      idx3{i} = 3 : sz(i);
+      szi = sz;
+      szi (i) = 1;
+
+      h1 = repmat (shiftdim (dx{i}(1 : sz(i) - 2), 1 - i), szi);
+      h2 = repmat (shiftdim (dx{i}(2 : sz(i) - 1), 1 - i), szi);
+      DD(idx2{:}) = ((M(idx1{:}) - M(idx2{:})) ./ h1 + ...
+		     (M(idx3{:}) - M(idx2{:})) ./ h2) ./ (h1 + h2);
+
+      ## left and right boundary
+      if (sz(i) == 3)
+	DD(idx1{:}) = DD(idx3{:}) = DD(idx2{:});
+      else
+	idx1{i} = 1;
+	idx2{i} = 2;
+	idx3{i} = 3;
+	DD(idx1{:}) = (dx{i}(1) + dx{i}(2)) / dx{i}(2) * DD (idx2{:}) - ...
+	    dx{i}(1) / dx{i}(2) * DD (idx3{:});
+
+	idx1{i} = sz(i);
+	idx2{i} = sz(i) - 1;
+	idx3{i} = sz(i) - 2;
+	DD(idx1{:}) =  (dx{i}(sz(i) - 1) + dx{i}(sz(i) - 2)) / ...
+	    dx{i}(sz(i) - 2) * DD (idx2{:}) - ...
+	    dx{i}(sz(i) - 1) / dx{i}(sz(i) - 2) * DD (idx3{:});
+      endif
+
+      D += DD;
+    endif
+  endfor
+
+  D = D ./ nd;
+endfunction