UrbanSim Capstone - Warmup Assignment

The following assignment is intended to give you an introduction to the supporting software for UrbanSim.

The undergrad lab machines have Python, Eclipse, and PyDev installed -- if you want to do this assignment on the ugrad machines, you just need to download and install numpy.

Due: Jan 17, 10:30am. By email to Alice, turn in the .py file for your BankAccount class for Question 1, and for the functions defined for Questions 2-5. Also turn in a copy of the transcript showing the results for Questions 3-5.

1. Python -- Objects and Classes

This question is intended to give an introduction to Eclipse and unit testing in Python. Using Eclipse, define a new Python class BankAccount.  BankAccount should have the following methods:

• a constructor, which takes an optional parameter initial_balance (default is 0)
• deposit -- takes the amount to deposit as a parameter
• withdraw -- takes the amount to withdraw as a parameter.  If the balance would be negative, raises an Overdraft exception.
• balance -- takes no parameters; returns the current balance

You'll also need to define a new exception Overdraft.

Also write unit tests for your BankAccount object.  These should test each of the methods, including a case in which there is an overdraft.

2. Higher-Order Functions in Python

Using lambda and functions such as map, define the following functions. Don't use recursion or loops, and use lambda rather than defining named auxiliary helper functions.

• A function scale that takes a number n, and a list of numbers s, and returns a new list with each element in s multiplied by n. For example scale(5, [10,20]) should return [50, 100].
• A function evens that takes a list of numbers as an argument, and returns a list of just the even numbers.

3. numpy arrays

Define a function make_table that takes a parameter n, and returns a 2-d array showing the results of applying different functions to a range of numbers. It is defined as follows:

Set ns to a numpy array consisting of the numbers between 0 and n-1.

Return a 2-d numpy array consisting of the following rows::

• ns
• the square roots of ns (0, 1, 1.414, ...)
• squares of ns (0, 1, 4, 9, ...)
• logs of ns
• exp of ns

You should do this just with numpy operators -- no explicit loops!!

(Hint: you can use 'vstack' to take a tuple of 1-d arrays and turn them into a 2-d array.)

4. Using the numpy 'where' function

Define a function rand_tester that takes an integer n, and returns another integer (which should be around n/2 if numpy's random number generator is working properly). Specifically, first create an array of n floats between 0 and 1 using the random.rand function. Now find how many of these are greater than 0.5, and return that number. For example, when I tried this with n=1000000, I got a result of 500039.

Again, no explicit loops!  Hints: check out the sum and where functions.

5. A simple probability computation using numpy

This last question uses numpy to do some of the kinds of computations we do in the UrbanSim model.

Define a function desirable_apartment_count that takes two arrays: one representing the monthly incomes of a set of households, and the other the monthly rents for a set of apartments.  It should return an array of the same length as the households, where each element is the number of 'desirable' apartments for that household. A 'desirable' apartment is defined as a function of the ratio of apartment rent to household income. In this problem, the desirability threshold is simply set to 1/3, with greater than 1/3 being undesirable. This is to say, a household will only consider moving to an apartment if the household income is at least thrice the rent.

The function desirable_apartment_count should define a m by n array 'cost_to_income' consisting of the ratio of the rents to incomes for each apartment/household pair. Then, using the 'cost_to_income' ratios, compute the number of apartments that each household would be willing to move to and return those values.

For example, we might test the function with these inputs:

apartments = array([800, 1000, 1300, 2000, 650])
households = array([1000, 2500, 5000])

Then within the function you'd define a 3x5 array 'cost_to_income', and compute the result. The cost_to_income array would be:

[[ 0.80, 0.32, 0.16 ],
 [ 1.00, 0.40, 0.20 ],
 [ 1.30, 0.52, 0.26 ],
 [ 2.00, 0.80, 0.40 ],
 [ 0.65, 0.26, 0.13 ]]