--- /dev/null
+## Copyright (C) 2000-2012 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 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} {@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{})
+##
+## Calculate the discrete Laplace
+## @tex
+## operator $( \nabla^2 )$.
+## @end tex
+## @ifnottex
+## operator.
+## @end ifnottex
+## For a 2-dimensional matrix @var{M} this is defined as
+## @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
+## @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
+## For N-dimensional arrays the sum in parentheses is expanded to include second
+## derivatives over the additional higher dimensions.
+##
+## The spacing between evaluation points may be defined by @var{h}, which is a
+## scalar defining the equidistant spacing in all dimensions. Alternatively,
+## the spacing in each dimension may be defined separately by @var{dx},
+## @var{dy}, etc. A scalar spacing argument defines equidistant spacing,
+## whereas a vector argument can be used to specify variable spacing. The
+## length of the spacing vectors must match the respective dimension of
+## @var{M}. The default spacing value is 1.
+##
+## At least 3 data points are needed for each dimension. Boundary points are
+## calculated from the linear extrapolation of 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 ("del2: 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 ("del2: 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
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff