Calculating euclidean distances in a matrix

I have to a matrix n x 2 in which each row represent a point in a Cartesian space in X and Y. The distance I have to calculate is between a row and its follower so at the end I have an array (n-1) x 1. I ve coded a simply function but since n = 50 000 it takes a lot of time to compute. How to speed up the entire process?

That s my function:

function [Dist] = Distances(A)

n = length(A)
Dist = (n -1);
for i=1:n 
        if i == n
            break
        end
    Dist(i,1)= sqrt((A(i+1,1)- A(i,1))^2 + (A(i+1,2)- A(i,2))^2)
    i= i+1
    
end 

Answer 1

[KSSV]

% demo data 
n = 100 ; 
A = rand(n,2) ; 
dA = diff(A) ;
d = sqrt(sum(dA.^2,2)) ;

[Image Analyst]

This is what I'd do too. It's fast:

tic
n = 50000; % fifty thousand
xy = rand(n,2);
dxy = diff(xy);
d = sqrt(sum(dxy.^2,2));
toc

On my computer it takes 0.003 seconds for 50,000 rows.

Answer 2

[Star Strider]

Use the pdist function, then squareform.

Example —

x = randi(99, 5, 2);                                    % Create Matrix
d = pdist(x);
m = squareform(d);

The information you want are in the upper and lower diagonals of ‘m’, so:

Result = diag(m,1);

equivalently:

Result = diag(m,-1);

This is likely faster than an explicit loop, however I did not time it with a large matrix.