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Pair-wise Euclidean Distance Matrix

version (2.62 KB) by Quan Wang
Computing the distance matrix without loops


Updated 20 May 2014

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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).

Comments and Ratings (1)

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;
D = sqrt(D);


Changed the description.

Added distance matrix from X to Y.

MATLAB Release Compatibility
Created with R2013b
Compatible with any release
Platform Compatibility
Windows macOS Linux