python - calculate distance of 2 list of points in numpy

Question

I have 2 lists of points as numpy.ndarray, each row is the coordinate of a point, like:

a = np.array([[1,0,0],[0,1,0],[0,0,1]])
b = np.array([[1,1,0],[0,1,1],[1,0,1]])

Here I want to calculate the euclidean distance between all pairs of points in the 2 lists, for each point p_a in a, I want to calculate the distance between it and every point p_b in b. So the result is

d = np.array([[1,sqrt(3),1],[1,1,sqrt(3)],[sqrt(3),1,1]])

How to use matrix multiplication in numpy to compute the distance matrix?

Answer 1

Using direct numpy broadcasting, you can do this:

dist = np.sqrt(((a[:, None] - b[:, :, None]) ** 2).sum(0))

Alternatively, scipy has a routine that will compute this slightly more efficiently (particularly for large matrices)

from scipy.spatial.distance import cdist
dist = cdist(a, b)

I would avoid solutions that depend on factoring-out matrix products (of the form A^2 + B^2 - 2AB), because they can be numerically unstable due to floating point roundoff errors.