Nested for loop vectorization

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);

Answer 1

[Marco Riani]

% 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'))

[Gabriele Dessena]

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