need help vectorizing a complicated loop

Hi,

I need to evaluate a vector of a function on a mesh then sum that vector at each point on the mesh. Let me elaborate:

I have a mesh:

    a = -0.5:0.001:0.5;
    b = a;
    [A,B]=meshgrid(a,b);

At each point on that mesh, I want to evaluate a function over a vector (here, instead of giving the vector values I'm just trying to indicate that I have some vectors with some length):

   % I have 3 vectors of length 2000 with some data in them
    s = 2000x1 double, c = 2000x1 double, y = 2000x1 double
   %at each point A,B on grid evaluate:
   fake_function_vec = (c.*A+s.*B-y).^2
   %result is some vector of length 2000. Now sum that vector
   fake_function = sen(fake_function_vec,1)
   %repeat for every other point on the mesh

I can't figure out how to do this efficiently. I'm currently using two for loops to evaluate the function (which returns a vector) and summing that vector at each point in the grid. Surely there must be a better way!

[supernoob]

Another option is to use one for loop to evaluate each matrix element on the mesh then sum the stacked matrices. This is also slow.

Answer 1

[Stephen23]

If you change the size of the s, c and y vectors to 1x1x2000 then this is easy. For MATLAB version R2016b or later:

s = rand(1,1,2000);
c = rand(1,1,2000);
y = rand(1,1,2000);
M = sum((c.*A+s.*B-y).^2,3)

For MATLAB versions prior to R2016b use bsxfun to replace the arithmetic operators.

[supernoob]

Thanks so much! Unfortunately this took it from 30s per evaluation to 70s, which really surprised me.