Create a matrix with multiple values at each element and apply a function to all?

This is for optimization purposes - I have 2 linspaces of parameters, and a 2 parameter function f (random values/function):

Xs = linspace(0, 1000, 1000)
Ys = linspace(0, 10000, 10000)
f = @(x, y) cos(x) + sin(y)

I want to populate a matrix M which has size [length(Xs), length(Ys)], where each element of M is f(x, y) for each x in Xs and y in Ys.

I can do this slowly with a for/parfor loop - how can I use direct vectorisation to achieve this?

Thanks

Answer 1

[Steven Lord]

If all the binary operations in your f function support implicit expansion (which is the case for your sample f, as plus supports implicit expansion) call it with vectors of different orientations.

Xs = linspace(0, 1000, 1000);
Ys = linspace(0, 10000, 10000);
f = @(x, y) cos(x) + sin(y);
M = f(Xs.', Ys);

Let's ensure M is the correct size.

isequal(size(M), [length(Xs), length(Ys)]) % true

We can spot-check an element or two of M to ensure it's the same as if we'd called your function with scalar inputs.

check = M(457, 9284) - f(Xs(457), Ys(9284)) % 0 difference

Answer 2

[the cyclist]

Here is one way:

[XXs,YYs] = meshgrid(Xs,Ys);
fxy = f(XXs,YYs);