Why gradient and diff give different results

Question

Ki 2016-2-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/267179-why-gradient-and-diff-give-different-results

回答： the cyclist 2016-2-8

Hi there, I am trying to derive a force from given potential, that F = - gradient of potential if mass is one. To test it, I try to set up a very simple 2D case with potential is

A=[1 2 3; 3 2 6; -2 -7 2];
dx=1;
dy=1;
[fx, fy]=gradient(A, dx, dy);

Now I am thinking to use diff instead. ax=diff(A')/dx; ay=diff(A)/dy;

Ignore the fact that diff will lose 1 row or column, the numbers of results for those two methods are not in agreement as well. So why is that? Besides differentiation, what else gradient calculate?