Efficiently Calculating a Euclidean Distance Matrix Using Numpy

Question

I have a set of points in 2-dimensional space and need to calculate the distance from each point to each other point.

I have a relatively small number of points, ma

Answer 1

Here is how you can do it using numpy:

import numpy as np

x = np.array([0,1,2])
y = np.array([2,4,6])

# take advantage of broadcasting, to make a 2dim array of diffs
dx = x[..., np.newaxis] - x[np.newaxis, ...]
dy = y[..., np.newaxis] - y[np.newaxis, ...]
dx
=> array([[ 0, -1, -2],
          [ 1,  0, -1],
          [ 2,  1,  0]])

# stack in one array, to speed up calculations
d = np.array([dx,dy])
d.shape
=> (2, 3, 3)

Now all is left is computing the L2-norm along the 0-axis (as discussed here):

(d**2).sum(axis=0)**0.5
=> array([[ 0.        ,  2.23606798,  4.47213595],
          [ 2.23606798,  0.        ,  2.23606798],
          [ 4.47213595,  2.23606798,  0.        ]])