Why gradient and diff give different results

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?

Answer 1

[the cyclist]

The exact algorithm that gradient uses is given at the bottom of the documentation page for gradient.

It uses the central difference (two-sided difference, divided by 2) for central points, and single-side difference at the edges.