discrete deriviative has wrong sign

I have the following MWE that calculates the derivative of a function along the y-direction:

x=1:50;
y=x;

phi = sin((x-10)/10);

dyPhi = (4.0*(circshift(phi(:,:), [+0, +1]) - circshift(phi(:,:), [+0, -1])) + ...
         1.0*(circshift(phi(:,:), [+1, +1]) - circshift(phi(:,:), [-1, -1])) + ...
         1.0*(circshift(phi(:,:), [-1, +1]) - circshift(phi(:,:), [+1, -1])))/12.0;

figure(1)
imagesc(phi)
colorbar

figure(2)
imagesc(dyPhi)
colorbar

However, please take a look at the two plots: On the plot for dyPhi, it seems that the derivative has a wrong sign.

Why is that? If I swap the sign, then I get what I would expect.

Answer 1

[Adam]

At a guess I would say it is because circshift shifts in the opposite direction to what you would expect. Certainly that catches me quite often when I have to shift by -1 when I intuitively thought it should be +1