GRADIENT_OP3D - 3 Dimentional gradient operator

function [dx, dy, dz] = gradient_op3d(I, wx, wy, wz)
%GRADIENT_OP3D 3 Dimentional gradient operator
%   Usage:  [dx, dy, dz] = gradient_op3d(I)
%           [dx, dy, dz] = gradient_op3d(I, wx, wy, wz)
%
%   Input parameters:
%         I     : Input data 
%         wx    : Weights along x
%         wy    : Weights along y
%         wz    : Weights along z
%
%   Output parameters:
%         dx    : Gradient along x
%         dy    : Gradient along y
%         dz    : Gradient along z
%
%   Compute the 3-dimentional gradient of I. If the input I has 4
%   dimentions. This function will compute the gradient of all cubes and
%   return 3 4-dimentionals signals
%
%   See also: gradient_op gradient_op1d div_op laplacian_op
%
%   Url: https://epfl-lts2.github.io/unlocbox-html/doc/utils/gradient_op3d.html

% Copyright (C) 2012-2016 Nathanael Perraudin.
% This file is part of UNLOCBOX version 1.7.4
%
% 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 of the License, 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 program.  If not, see <http://www.gnu.org/licenses/>.

% Author: Nathanael Perraudin
% Date:   1 February 2014

dx = [I(2:end, :, :,:)-I(1:end-1, :, :,:) ;...
      zeros(1, size(I, 2), size(I, 3),size(I, 4))];
dy = [I(:, 2:end, :,:)-I(:, 1:end-1, :,:) , ...
    zeros(size(I, 1), 1, size(I, 3),size(I, 4))];
dz = cat(3, I(:, :, 2:end,:)-I(:, :, 1:end-1,:) , ...
    zeros(size(I, 1),size(I, 2), 1,size(I, 4)));

if nargin>1
    dx = dx .* wx;
    dy = dy .* wy;
    dz = dz .* wz;
end

end