Nested for loop vectorization

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Hello everyone,
I am trying to vectorize the creation of this symmetric matrix.
I have tried with meshgrid and ngrid, but I could not find a way to make them work with the way I use X.
Any advice?
Thank you!
X = [1:10; 2:11]';
n = length(X);
theta = .1;
Mat = zeros(n,n);
for i=1:n
for j=i+1:n
Mat(i,j)=exp(-sum(theta.*abs(X(i,:)-X(j,:)).^p));
end
end
Mat = Mat+Mat'+eye(n);

Accepted Answer

Marco Riani
Marco Riani on 1 Apr 2021
% Hi, in your code p is not defined. I assume it is a scalar
% If you want to avoid the loop the answer is
% Mat=exp(-theta*(squareform(pdist(X,'minkowski',p))).^p);
% The code below checks that my implementation gives the same answer as
% your implementation
% Best
% Marco
X = [1:10; 2:11]';
p=3;
n = length(X);
theta = 0.1;
Mat = zeros(n,n);
for i=1:n
for j=i+1:n
Mat(i,j)=exp(-sum(theta.*abs(X(i,:)-X(j,:)).^p));
end
end
Mat = Mat+Mat'+eye(n);
Matchk=exp(-theta*(squareform(pdist(X,'minkowski',p))).^p);
disp(max(abs(Mat-Matchk),[],'all'))
  1 Comment
Gabriele Dessena
Gabriele Dessena on 1 Apr 2021
Edited: Gabriele Dessena on 1 Apr 2021
It works flawlessly, just a note on performance for future readers. The code is more efficient than the nested loop for n>100.
Grazie Mille Marco

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