Distance Between a Set of Points

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Suyapa Gonzalez
Suyapa Gonzalez on 18 Jun 2015
Commented: Walter Roberson on 17 Nov 2018
I have a list of X and Y values and I need to get the distance between each point. So basically, the distance between point 1 to the other 14 points, point 2 to the other 14 points, point 3 to the other 14 points, for example. How do I do this without manually plotting in every pair of coordinates???

Answers (3)

Joseph Cheng
Joseph Cheng on 18 Jun 2015
Edited: Joseph Cheng on 18 Jun 2015
you can use the function nchoosek to generate the pairs:
xy= randi(10,15,2)
pairs = nchoosek(1:5,2)
p1 = xy(pairs(:,1),:);
p2 = xy(pairs(:,2),:);
distance = sqrt(sum((p1-p2).^2,2));
  2 Comments
Suyapa Gonzalez
Suyapa Gonzalez on 18 Jun 2015
Where do I plug in my data points? I have 15 different pair of coordinates.
Joseph Cheng
Joseph Cheng on 18 Jun 2015
it would be the xy points, since i do not have your data i created my own list of X and Y values.

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Jacob Strang
Jacob Strang on 17 Nov 2018
I believe that pdist does this automatically if you provide more than 2 points, as seen in the first example on the linked page:
% Compute the Euclidean distance between pairs of observations, and convert the distance vector to a matrix using squareform.
% Create a matrix with three observations and two variables.
rng('default') % For reproducibility
X = rand(3,2);
% Compute the Euclidean distance.
D = pdist(X)
% D = 1×3
% 0.2954 1.0670 0.9448
% The pairwise distances are arranged in the order (2,1), (3,1), (3,2). You can easily locate the distance between observations i and j by using squareform.
  1 Comment
Walter Roberson
Walter Roberson on 17 Nov 2018
You can use squareform() to convert the pdist() triangular matrix result to a symmetric square matrix.

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Chad Greene
Chad Greene on 18 Jun 2015
Or there's John D'Errico's ipdm function.

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