matlab 中gradient（）函数的用法

1.官方给出的解释：（看不懂就直接略过看下面实例）

%GRADIENT Approximate gradient.
%   [FX,FY] = GRADIENT(F) returns the numerical gradient of the
%   matrix F. FX corresponds to dF/dx, the differences in x (horizontal) 
%   direction. FY corresponds to dF/dy, the differences in y (vertical) 
%   direction. The spacing between points in each direction is assumed to 
%   be one. When F is a vector, DF = GRADIENT(F) is the 1-D gradient.
%
%   [FX,FY] = GRADIENT(F,H), where H is a scalar, uses H as the
%   spacing between points in each direction.
%
%   [FX,FY] = GRADIENT(F,HX,HY), when F is 2-D, uses the spacing
%   specified by HX and HY. HX and HY can either be scalars to specify
%   the spacing between coordinates or vectors to specify the
%   coordinates of the points.  If HX and HY are vectors, their length
%   must match the corresponding dimension of F.
%
%   [FX,FY,FZ] = GRADIENT(F), when F is a 3-D array, returns the
%   numerical gradient of F. FZ corresponds to dF/dz, the differences
%   in the z direction. GRADIENT(F,H), where H is a scalar, 
%   uses H as the spacing between points in each direction.
%
%   [FX,FY,FZ] = GRADIENT(F,HX,HY,HZ) uses the spacing given by
%   HX, HY, HZ. 
%
%   [FX,FY,FZ,...] = GRADIENT(F,...) extends similarly when F is N-D
%   and must be invoked with N outputs and either 2 or N+1 inputs.
%
%   Note: The first output FX is always the gradient along the 2nd
%   dimension of F, going across columns.  The second output FY is always
%   the gradient along the 1st dimension of F, going across rows.  For the
%   third output FZ and the outputs that follow, the Nth output is the
%   gradient along the Nth dimension of F.

2.举个栗子

定义一个二维矩阵x，求其梯度：

由上图可知，梯度值Fx(i,j)可分为三个部分：

左边界梯度： Fx(:,j) = Fx(:,j+1) - Fx(:,j) ；

右边界梯度： Fx(:,j) = Fx(:,j) - Fx(:,j-1);

中间区域梯度： Fx(:,j) = (Fx(:,j+1) - Fx(:,j-1)) / 2.

同理，可以得出Fy，此处不再赘述。