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## Pair-wise Euclidean Distance Matrix

version 1.2.0.0 (2.62 KB) by Quan Wang

### Quan Wang (view profile)

Computing the distance matrix without loops

Updated 20 May 2014

This is a very simple function to compute pair-wise Euclidean distances within a vector set, from between two vector sets. Although simple, it is very useful. Using loops will be too slow.
D=distanceMatrix(X), where X is N*d data, and D is N*N distance matrix.

or D=distanceMatrix2(X,Y).

Jonas Lundgren

### Jonas Lundgren (view profile)

Dear Quan Wang,

It is a widespread misunderstanding that MATLAB loops are slow in general. Loops with simple math operations can be very fast. Waste of memory is always slow and so is the function repmat.

Compare distanceMatrix(X) with distmat(X) below. X = rand(1000,3).

I am sure you will reply with something even faster. I look forward to update the rating.

Kind regards
Jonas Lundgren

%------------------
function D = distmat(X)
%DISTMAT Compute euclidian distance matrix from coordinates

[n,dim] = size(X);
D = zeros(n);
for j = 1:n
for k = 1:dim
v = X(:,k) - X(j,k);
D(:,j) = D(:,j) + v.*v;
end
end
D = sqrt(D);