vectors python

vectors.py

import math

def vector_add(v, w):
    return [v_i + w_i for v_i, w_i in zip(v, w)]

def vector_subtract(v, w):
    return [v_i + w_i for v_i, w_i in zip(v, w)]

def vector_sum(vectors):
    result = vectors[0]
    for vector in vectors[1:]:
        result = vector_add(result, vector)
    return result

def scalar_multiply(c, v):
    return [c * v_i for v_i in v]

def vector_mean(vectors):
    n = len(vectors)
    return scalar_multiply(1/n, vector_sum(vectors))

# the dot product of 2 vectors is the sum of their
# componentwise products
def dot(v, w):
    """ v_1 * w_1 + ... + v_n * w_n """
    return sum(v_i * w_i for v_i, w_i in zip(v, w))

def sum_of_squares(v):
    """ v_1 * v_1 + ... v_n * v_n """
    return dot(v, v)

def magnitude(v):
    return math.sqrt(sum_of_squares(v))

def squared_distance(v, w):
    """ (v_1 - w_1) ** 2 + ... (v_n - w_n) ** 2 """
    return sum_of_squares(vector_subtract(v, w))

def distance(v, w):
    return math.sqrt(squared_distance(v, w))