MATLAB: Help vectorizing 2 For loops with meshgrid and subscripts

for loopind2subMATLABmeshgridvectorization

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.

Best Answer

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
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