Angles between two n-dimensional vectors in Python

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

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))