How can I convert the following loop operation into vectorization?

S is the 3-dimensional array of size 64X36X36

d_E1=[];
  for d=1:length(th_2)%Page selection
    for c=1:length(th_3)%column celection
        for i=1:size(S,1)-1%row selection
            for j=i+1:size(S,1)
                d_E=norm(S(i,c,d)-S(j,c,d));
               d_E1=[d_E1 d_E];
            end
        end
    end
 end
    %creating 3-dimensional PEP arra
d_E_new=reshape(d_E1,nchoosek(size(S_sum1,1),2),length(th_3),length(th_2));

[vinjamoori vikas]

Sorry, I have not mentioned about lengths.

take

length(th_2)=36(3rd dimension of the matrix)

length(th_3)=36(2nd dimension of the matrix)

[darova]

I think vectorization version can be too complicated. I suggest you to preallocate d_E1 variable (calculate the size)

I also don't understand why do you norm function if oyu just substracting numbers

norm(2-1)

ans = 1

norm(5-3)

ans = 2

Answer 1

[DGM]

I'm not sure why you're using norm() on scalars. Abs() has the same effect.

% test array/size
N = 4; % rows/cols
D = 4; % pages
S = repmat(magic(N),[1 1 1 D]);

% original structure
E1=[];
for d=1:D%Page selection
	for c=1:N%column celection
		for i=1:N-1%row selection
			for j=i+1:N
				E=norm(S(i,c,d)-S(j,c,d));
				E1=[E1 E];
			end
		end
	end
end

% somewhat simplified
E3=[];
for i=1:N-1 % row selection
	E = abs(S(i,:,:)-S(i+1:N,:,:));
	E3 = [E3; E];
end
E3 = reshape(E3,1,[]);

immse(E1,E3) % they should be identical

ans = 0

I didn't really think it would be that much faster, but for a 20x20x20 array, the revised code executes in less than 1/1000th the time (on my hardware/version/environment).