How to get distances between 2 xyz numpy arrays without loop?

February 20, 2022

Suppose I have 2 numpy arrays containing xyz coordinates of points. Each point’s coordinates is a row.

a
[0 1 0]
[3 1 0]
[0 0 3]
[3 4 0]
[0 2 0]
[2 3 4]
[0 1 2]
[0 3 2]
b
[1 1 2]
[1 1 2]
[0 2 2]
[4 2 1]
[4 4 4]

Is it possible to calculate the distance (sqrt((x1-x2)**2+(y1-y2)**2+(z1-z2)**2)) from each point of a to each point of b without a double for loop?

>Solution :

You can use scipy.distance.spatial.cdist:

from scipy.spatial.distance import cdist

out = cdist(a, b)

NB. by default, the distance is euclidean but you have other metrics (see the doc)

output (a.shape[0] x b.shape[0]):

array([[2.23606798, 2.23606798, 2.23606798, 4.24264069, 6.40312424],
       [2.82842712, 2.82842712, 3.74165739, 1.73205081, 5.09901951],
       [1.73205081, 1.73205081, 2.23606798, 4.89897949, 5.74456265],
       [4.12310563, 4.12310563, 4.12310563, 2.44948974, 4.12310563],
       [2.44948974, 2.44948974, 2.        , 4.12310563, 6.        ],
       [3.        , 3.        , 3.        , 3.74165739, 2.23606798],
       [1.        , 1.        , 1.        , 4.24264069, 5.38516481],
       [2.23606798, 2.23606798, 1.        , 4.24264069, 4.58257569]])

used input:

a = np.array([[0, 1, 0], [3, 1, 0], [0, 0, 3], [3, 4, 0], [0, 2, 0], [2, 3, 4], [0, 1, 2], [0, 3, 2]])
b = np.array([[1, 1, 2], [1, 1, 2], [0, 2, 2], [4, 2, 1], [4, 4, 4]])