[HELP] Vector loops :'(

Anybody knows how can i optimize this? Thanks <3!

 function filter() 
 r=[cos(c) -sin(c);
   sin(c)  cos(c)];
 for i = 1 : n2 
    for j = 1 : n1
        h(i,j) = magic(r(1),std)*magic(r(2),std);
    end
end 
 function y = magic(r,s)
  y = exp(-r^2));

Answer 1

[Roger Stafford]

You have set std1 and std2 to equal values. Provided you do that, the result in 'h' is independent of the value 'c' and can be vectorized as:

   n1 = 10;
   n2 = 3;
   s = 2
   h = exp(-(((1-n2)/2:(n2-1)/2)').^2/(2*s^2))*...
       exp(-(((1-n1)/2:(n1-1)/2)).^2/(2*s^2))/s^2/(2*pi);

The code can also be vectorized with unequal values of std1 and std2, but is somewhat more complicated. Do you wish to see that?

Answer 2

[amelia_3]

Thank you!! :) Actually, I'm trying to make it with different values too. However, I don't understand your solution neither :/

[Roger Stafford]

For unequal std1 and std2 a vectorized form would be:

   [J,I] = meshgrid((1-n1)/2:(n1-1)/2,(1-n2)/2:(n2-1)/2);
   cc = cos(c); sc = sin(c);
   h = exp(-(cc*J-sc*I).^2/(2*std1^2)-(sc*J+cc*I).^2/(2*std2^2))...
           /(std1*std2*2*pi);

To show that if std1 = std2, then the result is independent of c, the argument of exp above becomes:

   -(cc*J-sc*I).^2/(2*std^2)-(sc*J+cc*I).^2/(2*std^2) =
   (-(cc^2+sc^2)*J^2+(2*cc*sc-2*sc*cc)*I*J-(sc^2+cc^2)*I^2)/(2*std^2) =
   -(J^2+I^2)/(2*std^2)

which is indeed independent of c.