Angles between two n-dimensional vectors in Python

Question

In 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].

Can anybody help me? Thanks in advance!

Answer 1

You'll be wanting this formula.

Answer 2

Using numpy (highly recommended), you would do:

u = array([1.,2,3,4])
v = ...
c = dot(u,v)/norm(u)/norm(v) # -> cosine of the angle
angle = arccos(c) # if you really want the angle

Answer 3

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)))