Evaluate function over a mesh grid (without for loops)

Is there a way to evaluate a function that takes an [x, y] vector as input over a grid of points?

Here is the function I want to evaluate:

Jfun = @(u) (17*u(1)^2)/2 - 14*u(1)*u(2) - 40*u(1) + 19*u(2)^2 - 20*u(2)

The reason I defined the function this way is so that I can find the minimum thus:

umin = fminsearch(Jfun,[0,0])

Now I want to make the contour plot.

Something like this perhaps:

x = linspace(-1,6);
y = linspace(-3,5);
[X,Y] = meshgrid(x,y);
for i=1:numel(x)
  for j=1:numel(y)
    Z(i,j)=Jfun([X(j,i) Y(j,i)]);
  end
end
contourf(X,Y,Z,10)

But is there a way to compute Z without having to use nested for loops?

I tried this:

Z = Jfun(cat(3,X,Y));

but it doesn't work. It simply returns 173.5000 which is Jfun([-1 -1]).

Answer 1

[Rik]

You have to vectorize the function and split it into two steps:

Jfun = @(x,y) (17*x.^2)/2 - 14*x.*y - 40*x + 19*y.^2 - 20*y;
umin = fminsearch(@(u) Jfun(u(1),u(2)),[0,0])

x = linspace(-1,6);
y = linspace(-3,5);
[X,Y]=ndgrid(x,y);
Z=Jfun(X,Y);

[Bill Tubbs]

Thanks, this works.

[Bill Tubbs]

Unfortunately the execution of the fminsearch is about 40% slower with this approach but the computation of Z is very fast.

[Rik]

You can remove the overhead of the outer layer of anonymous function if that 40% is important for you. That does mean you will have two copies of virtually the same function, but that is a small price to pay.

Answer 2

[madhan ravi]

 v = num2cell([X(:), Y(:)], 2);
 Z = reshape(cellfun(Jfun, v), size(X));

[Bill Tubbs]

Thanks. This works but is not very efficient according to timeit().