Datascience

matrixandvectors.py

import math
# coding=utf-8
def vector_add(v,w):
    """adds corresponding elements"""
    return [v_i + w_i
            for v_i, w_i in zip(v,w)]


def vector_subtract(v, w):
    """subtracts corresponding elements"""
    return [v_i - w_i
            for v_i, w_i in zip(v,w)]

"""We’ll also sometimes want to componentwise sum a list of vectors. """

def vector_sum(vectors):
    """ vectors: sum all corresponding elements"""
    result = vectors[0]
    for vector in vectors[1:]:
        result = vector_add(result, vector)
    return result


# multiple a vector by a scalar

def scalar_multiple(c,v):
    """c is a number , v is a vector"""
    return [c * v_i for v_i in v]


# This allows us to compute the componentwise means of a list of (same-sized) vectors:

def vector_mean(vectors):
    """compute the vector whose ith element is the mean of the
    ith elements of the input vectors"""
    n = len(vectors)
    return scalar_multiple(1/n, vector_sum(vectors))

# The dot product measures how far the vector v extends in the w direction.

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))

## Now it is easy to compute vector sum of squares

def sum_of_squares(v):
    """V_1 * v_1 + ... + v_n + v_n"""
    return dot(v,v)


# Which we can use to compute its magnitude (or length):
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))