I need to determine the angle(s) between two n-dimensional vectors in Python. For example, the input can be two lists like the following: [1,2,3,4]
and [6,7,8,9]
.
Note: all of the other answers here will fail if the two vectors have either the same direction (ex, (1, 0, 0)
, (1, 0, 0)
) or opposite directions (ex, (-1, 0, 0)
, (1, 0, 0)
).
Here is a function which will correctly handle these cases:
import numpy as np
def unit_vector(vector):
""" Returns the unit vector of the vector. """
return vector / np.linalg.norm(vector)
def angle_between(v1, v2):
""" Returns the angle in radians between vectors 'v1' and 'v2'::
>>> angle_between((1, 0, 0), (0, 1, 0))
1.5707963267948966
>>> angle_between((1, 0, 0), (1, 0, 0))
0.0
>>> angle_between((1, 0, 0), (-1, 0, 0))
3.141592653589793
"""
v1_u = unit_vector(v1)
v2_u = unit_vector(v2)
return np.arccos(np.clip(np.dot(v1_u, v2_u), -1.0, 1.0))