Lesson_1: Linear Algebra Python Control Flow

Practice Goals

• Build some basic linear algebra functions
• Improve comfort with flow patterns
• Explore list comprehensions

Practice: Python Control flow

Here is the common if/else example from lecture. Notice each x and y are False, and the lone "if x/y" statements check to see if they are true.

x,y = False, False
if x:
    print 'apple'
elif y:
	print 'banana'
else:
	print 'sandwich'

While loops allow iteration until some event happens:

x = 0
while True:
	print 'HELLO!'
	x += 1
	if x >= 3:
		break

For loops are more useful going through a predetermined range of things, particularly lists:

for k in range(4):
	print k

These are all most useful as we combine these things to help filter out information.

a = [10, 20, 25, 35, 45]
for value in a:
	if value >= 30:
		print value

(This should all be relatively familiar already given some of the extra work we had done last class)

Practice: Linear Algebra

Primarily let's focus on some of the concrete components we talked about in class

Matrices and Vectors

For the most part, we can consider using lists to create matrices and vectors (especially given that a Python list is, essentially, a vector)

vector = [1, 2, 3]
matrix = [ [1, 2, 3, 4], 
  [5, 6, 7, 8],
  [9, 10, 11, 12] ]

We'll learn more about numpy next week, but numpy makes it incredibly easy to auto generate both of these!

import numpy as np
npMatrix = np.matrix('1 2 3; 4 5 6; 7 8 9')

Math

vector * 3

Note that "common sense" here won't work: we're looking for a way to multiply each value within a vector by a value, not no repeat the vector 3 times. Here, we can use list comprehensions instead:

[x*3 for x in vector]

Can also use list comprehensions to transpose a matrix, which should turn the matrix, essentially, "90 degrees."

def matrix_transpose(matrix):
     return [ [row[i] for row in matrix] for i in range(len(matrix[0]))]

Classwork

1. Write two more functions: vector_matrix_multiplication and matrix_matrix_multiplication. No numpy/scipy! Do this with pure python. Check your answers using the logic we went over from lecture. Output the file to hw2/student/output/hw_mult.csv.

• PROGRAMMER ONLY GOAL: Customize this matrix.py and create multiplication functions to the class.

2. Write a function that creates an identity matrix. An identity matrix is a matrix where value = 1 if the row and column index are the same, and 0 otherwise. It should build any size identity matrix you want. Multiply a 4x4 identity matrix by matrix1 in the input file, and save the result as hw_inv_mult.csv in your output Dropbox folder.

    Example: identity_matrix(4) should be:
    [ [1, 0, 0, 0],
    [0, 1, 0, 0],
    [0, 0, 1, 0],
    [0, 0, 0, 1] ]
   

Homework

Let's revise the original script we wrote on Class01 to now return a new csv file that summarizes the data in such a way:

HEADERS:

"age", "gender", "signed_in", "avg_click", "avg_impressions", "max_click", "max_impressions"

This means that we are now aggregating data by age, gender, and signed_in to get these new data features: avg_click, avg_impressions, max_click, max_impressions. Let's include Age = 0 (null age) as a possible groupable. Look at the results to see if you could find any trends that stand out to you.

Extra Links

Great review on Linear Algebra

Early learning on its application to linear models