Is Matlabs function gradient necessary?

Question

I stumbled over this by visualizing changes in data. In my opinion the gradient function in Matlab has a weakness for certain inputs. Let's say I have a matrix like a chessfield and compute the gradient:

matrix = repmat([1 5;5 1], 10, 10)
[Fx,Fy] = gradient(matrix);

In matrix we have a lot of changes in both direction. But because of the behaviour of gradient, Fx and Fy will only contain zeros except for the borders.
Is this behaviour wanted? Is it then not always better to use diff() and then achieving equal size of in- and output matrix with padding? Or in other words, when is it useful to use gradient() instead of diff()?

Answer 1

The documentation tells use that gradient uses central differences to compute the gradient at interior points, which explains the behaviour with your chessboard-pattern.

This function is intended for computing the gradient of a function that was evaluated on a regular grid. For the gradient to make sense, we assume that the function is differentiable. But a central difference (or any finite difference scheme) only makes sense if the function is sampled sufficiently densely, otherwise you will have issues like these.