MATLAB: Simple Question: gradient function Formula

gradient formula

in the following line, x is a 200 element column vector, h is a scalar eg.say 20 or 30

a = gradient(x,h)

can you please tell how 'a' is computed from x and h? Thanks in advance

For 2 <= k <= 199, the computation is a central difference:

   a(k) = (x(k+1)-x(k-1))/(2*h)

However, for the two endpoints it is:

   a(1) = (x(2)-x(1))/h
   a(200) = (x(200)-x(199))/h

In case h is a vector of the same length as x, then it becomes a divided difference:

   a(k) = (x(k+1)-x(k-1))/(h(k+1)-h(k-1))

and

   a(1) = (x(2)-x(1))/(h(2)-h(1))
   a(200) = (x(200)-x(199))/(h(200)-h(199))

You're not updating h and dh within your loop.

Probably the easiest way is to set ‘x0’ appropriately and then bound ‘x(2)’ to be 40:

x0 = [20 40 20];
lb = [0 40 0];
ub = [100 40 100];
fun = @(x) x(1)+x(2)+x(3);
x_min = fmincon(fun,x0,[],[],[],[],lb,ub)