Help vectorizing 2 For loops with meshgrid and subscripts

Hello,

I have been thinking on vectorizing this code:

mat=zeros(a^2,a^2);

x=[1:a];
y=[1:a];
[Xm,Ym]=meshgrid(x,y)

for i=1:a^2
    for j=1:a^2
        [x1,y1]=ind2sub([a a],i);
        [x2,y2]=ind2sub([a a],j);
        mat(i,j)=(Xm(x1,y1)-Xm(x2,y2))^2+(Ym(x1,y1)-Ym(x2,y2))^2);
    end
end

This takes too long as

a^2 is about 20k.

I still haven't been able to come with a nice solution, and not sure if it's even possible. If anyone can give me a hand I really appreciate it.

Thank you in advance.

Answer 1

[Yu Jiang]

Hi Carlos

Here is what I would do:

mat1=zeros(a^2,a^2);
x=[1:a];
y=[1:a];
[Xm,Ym]=meshgrid(x,y);

Xm1 = kron(ones(a^2,1), Xm(:));
Xm2 = kron(Xm(:), ones(a^2,1));
Ym1 = kron(ones(a^2,1), Ym(:));
Ym2 = kron(Ym(:), ones(a^2,1));

mat1=(Xm1-Xm2).^2+(Ym1-Ym2).^2;
mat1=reshape(mat1,a^2,a^2);

-Yu

Answer 2

[Roger Stafford]

 [Xm,Ym] = meshgrid(1:a,1:a);
 [X1,X2] = meshgrid(Xm(:),Xm(:));
 [Y1,Y2] = meshgrid(Ym(:),Ym(:));
 mat = (X1-X2).^2+(Y1-Y2).^2;