vectors.md

Vectors

Goals

• represent vectors as lists of numbers
• iterate with counter variable and while
• iterate with for loop
• use print variations

The end result is file vectors.py.

Description

A vector from linear algebra is really just a list of numbers, which is how we can represent them in Python.

v = [1, 2, 3]
w = [90,50,10]

Python doesn't inherently know how to do linear algebra. We can either pull in some libraries such as numpy, which we will do eventually, or we can build our own library functions such as for:

def dot(v,w):
    "Return dot product of v and w or None if lengths are different"
    i = 0 # lists are 0-indexed
    if len(v)!=len(w):
        return None
    n = len(v)
    sum = 0
    while i < n:
        sum += v[i] * w[i]
        i += 1
    return sum

We can try that out with a simple statement:

print dot(v,w) # gives 220

The idea of iterating a variable, i, from 0 to the length of a list - 1 is such a common pattern that almost all languages have something to automate this boilerplate code for us: for loops.

n = 5
print range(0,5) # gives [0, 1, 2, 3, 4]
for i in range(5): # range(5) == range(0,5)
    print i, # comma on the end of a print means no \n
print # print with no arguments simply gives a \n

That prints 0 1 2 3 4.

Student exercise

Alter the dot function so that it uses a for loop instead of a while loop.

def dot2(v,w):
    """
    Return dot product of v and w or None if lengths are different.
    Use for not while loop.
    Note:  triple quote allows newlines within comments
    """
    i = 0 # lists are 0-indexed
    if len(v)!=len(w):
        return None
    n = len(v)
    sum = 0
    ...
    return sum

Test it with a print statement to make sure you get 220 for the two vectors defined above.