angular_distance_example.py

from math import pi
import numpy as np

x = np.array([1, 0, 0])
y = np.array([1, 0, 0.001])  # very similar to 
z = np.array([0, 1, 0])      # orthogonal to x
q = np.array([-1, 0, 0])     # looks in the opposite direction to x

def angular_distance(v1, v2):
    cos_of_angle = np.dot(v1, v2) / np.linalg.norm(v1) / np.linalg.norm(v2)
    # We can divide by pi to make the distance range from 0 to 1
    return np.acos(cos_of_angle) / pi

print(f'{angular_distance(x, y)=}')
print(f'{angular_distance(x, z)=}')
print(f'{angular_distance(x, q)=}')