How do I the minimum points on a 3D surface diagram (x,y,z) as a function of the x and y variables?

Here I have plotted an energy surface diagram:

clc, clear;

%x=phi, y=theta, z=h
K=1;
hval = 2*pi;
y=pi/3;

[ x, z] = meshgrid(0:0.1:hval, -2:0.1:2);
E= (K*sin(x-y).^2)-K*z.*cos(x);
figure 
surf(x, z, E)
xlabel('phi')
ylabel('h')
zlabel('E')

rotate3d on
cos(0)
sin(-y)
F= (K*sin(0-y).^2)-K*z.*cos(0);

I need to obtain the minimum energy points on this diagram as a function of phi and h to plot another graph. My thought was to create for loops which go through each value of phi to find the minimum energy and return the value of h, but I haven't been able to do this.

Answer 1

[Ridwan Alam]

I am assuming your x-axis is phi and y-axis is h:

min_phi = min(E,[],1);
min_h = min(E,[],2);

[Alex Bregazzi]

Thanks, if there are two minimums at the same point how do I return both values?