Angles between two n-dimensional vectors in Python

Question

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].

Answer 1

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)) 

Answer 2

import math  def dotproduct(v1, v2):   return sum((a*b) for a, b in zip(v1, v2))  def length(v):   return math.sqrt(dotproduct(v, v))  def angle(v1, v2):   return math.acos(dotproduct(v1, v2) / (length(v1) * length(v2))) 

Note: this will fail when the vectors have either the same or the opposite direction. The correct implementation is here: https://stackoverflow.com/a/13849249/71522