Finding distance between elements of two different list

Question

The code below finds the Euclidean distance between each element of list a and each element of list b.

from scipy.spatial import distance
a = [[1, 2, 3], [4, 5, 6]]
b = [[10, 20]]

Final_distance = []
for i in [j for sub in a for j in sub]:
    for k in [m for t in b for m in t]:
        dist = distance.euclidean(i, k)
        Final_distance.append(dist)
print(Final_distance)

The output is

[9.0, 19.0, 8.0, 18.0, 7.0, 17.0, 6.0, 16.0, 5.0, 15.0, 4.0, 14.0]

But for very large list it is taking very long time. Is there a way to reduce the time complexity of the above code?

Answer 1

Since your euclidian distances are on scalars, it's equivalent to the absolute value between each point. So you can repeat your arrays in the appropriate order using np.repeat and np.tile , and just subtract your arrays from one another:

import numpy as np

a = [[1, 2, 3], [4, 5, 6]]
b = [[10, 20]]

a1 = np.array(a).flatten()
b1 = np.array(b).flatten()

Final_distance = np.abs(np.subtract(np.repeat(a1, len(b1)), np.tile(b1, len(a1))))

Which returns:

array([ 9, 19,  8, 18,  7, 17,  6, 16,  5, 15,  4, 14])