You may be interested:
function [T1, T2, T3, T4] = test
A = rand(10000,2);
T1 = timeit(@method1);
T2 = timeit(@method2);
T3 = timeit(@method3);
T4 = timeit(@method4);
function dist = method1
dist = squeeze(sqrt(sum((A - reshape(A',1,2,[])).^2,2)));
end
function dist = method2
dist = sqrt(triu((A(:,1)-A(:,1)')).^2+triu((A(:,2)-A(:,2)')).^2);
dist = dist+dist';
end
function dist = method3
dist = sqrt(((A(:,1)-A(:,1)')).^2+((A(:,2)-A(:,2)')).^2);
end
function dist = method4
dist = squareform(pdist(A));
end
end
Output:
>> [T1, T2, T3, T4] = test
T1 =
0.6294 % sec
T2 =
1.0634 % sec
T3 =
0.3852 % sec
T4 =
1.0522 % sec
Using triu (or similarly tril) seems a bit pointless as long as every operation (subtraction, raise to 2nd power, addition, sqrt) is applied to every element in the matrix, even if half of those elements are 0. Using two loops or linearizing half of the matrix and then reshaping are two ways I can think of to really avoid half of the triangle, but I'm not sure you'd gain anything.
But maybe the behavior would change with larger matrices and you're thinking higher than 10,000.
