Lectures on Computational Economics

John Stachurski

Modules

A module is just a file containing code that can be understood by Python

• Any script we write is a module
• Other modules come with the Python distribution
• And others are third party (see, for example, PyPi)

In this lecture we will focus on modules in the Standard library

• Bundled with every Python distribution
• Very comprehensive and high quality

Python philosophy:

• Keep the core language small
  • Makes it clean and consistent
• And put most functionality in the standard library

The import Statement

The Python keyword import is used to access code in modules

Let's look at some examples, using the math module from the standard library

Importing the Module

One way to load the math module is as follows

>>> import math

Now we can use the objects defined in the module:

>>> math.e                # A float (Euler's number e)
2.7182818284590451
>>> math.exp(10)          # exp() is a function (the exponential function)
22026.465794806718
>>> math.pi               # A float
3.1415926535897931
>>> math.sqrt(100)        # Another function
10.0
>>> math.exp(math.log(10))
10.000000000000002
>>> math.cos(math.pi)
-1.0

Notice the syntax

• To access 'pi' we type 'math.pi'
• To access 'sqrt()' we type 'math.sqrt()', etc.

Collectively, pi, sqrt(), etc. are called attributes of math

To access attribute, type 'moduleName.attributeName'

• E.g., math.pi

In IDLE and IPython, typing 'math.' and then TAB lists attributes

• Very useful
• You can also try 'help(math)'

Importing Attributes Directly

If I start with

>>> import math

then to access pi I need to type math.pi

An alternative is to import pi directly

>>> from math import pi
>>> pi
3.1415926535897931

We can import multiple attributes as follows

>>> from math import pi, e
>>> pi
3.1415926535897931
>>> e
2.7182818284590451

This is convenient if you want to use just one or two attributes of a library

In fact we can directly import all the attributes in math as follows

>>> from math import * 
>>> pi
3.1415926535897931
>>> sqrt(4)
2.0

This method is not used so much by good programmers

• Suddenly there are lots of variables defined, and it's hard to keep track

Other Modules

Let's look at some more modules in the standard library

The Random Module

Examples

>>> import random
>>> random.uniform(0, 1)     # Uniform r.v. on (0,1)
0.91175197121395068
>>> random.uniform(0, 1)     # Another one, independent of first
0.86542825268640777
>>> [random.uniform(0, 1) for i in range(3)]
[0.83426715541997887, 0.067833169185644748, 0.22589302179038462]
>>> random.normalvariate(0, 1)  # Standard normal
-1.0375932163018793
>>> X = ['a', 'b', 'c', 'd']
>>> random.choice(X)
'b'
>>> random.choice(X)
'b'
>>> random.choice(X)
'c'
>>> X
['a', 'b', 'c', 'd']
>>> random.shuffle(X)
>>> X
['a', 'd', 'b', 'c']

Others

The os module is for interacting with operating system

>>> import os    
>>> os.getcwd()   # Returns the current working directory
'/home/john/sync_dir/teaching/kyoto_08'
>>> os.listdir('.')   # List files in current directory
['index.txt',
...

See also sys, datetime, email, etc.

Problems

Write the following as programs

• Using IDLE?

Problem 1:

• Simulate a draw from Y = max{|X_1|,...,|X_10|}, where X_i ~ N(0, 1)
• And print out the result
  • Hint: Use list comprehensions

Problem 2:

• Simulate a draw from Y ~ Bin(n, 0.5) using random.choice()
  • num of successes in n indep trials with success prob 0.5
  • E.g., num of heads in n flips of fair coin
  • The value of n is read in from the user at run time

Solutions

Solution to Problem 1

import random

N = [random.normalvariate(0, 1) for i in range(10)]
M = [abs(x) for x in N]
Y = max(M)
print Y

Solution to Problem 2

import random

n = int(raw_input("What is the value of n? "))
C = 0, 1
M = [random.choice(C) for i in range(n)]
Y = sum(M)
print Y

Alternatively,

import random

n = int(raw_input("What is the value of n? "))
C = 'heads', 'tails'
M = [random.choice(C) for i in range(n)]
Y = M.count('heads')
print Y

Copyright John Stachurski 2010