Homework Assignment 2

Problem 1: Debugging (Weight 2). Debugging is the process of identifying and resolving issues ('bugs') that prevent your code from running correctly. In this problem, you are asked to find and fix the bugs in the class SumRatio (in the file \Debugging\SumRatio.py). The class SumRatio has a very simple task. It gets two arrays (x1, x2, ..., xn) and (y1, y2, ..., yn), and returns the sum of element-wise ratios (x1/y1 + x2/y2 + ... + xn/yn).

1. Find and fix the bugs in the current implementation of SumRatio class such that you can run Test1.py script without any error. Hint: Watch this video to learn about the debugging features of PyCharm and read this post for some debugging tips.

2. After fixing bugs in the SumRatio class, run Test2.py script. Note that while SumRatio class implicitly assumes the x and y have the same number of elements, the x and y used in Test2.py have different sizes. But when you run Test2.py it runs without any issues and prints 1.0 for the sum of element-wise ratios. This is clearly an error since the sum of element-wise ratios of two arrays that have different length is not defined. These types of errors are often hard to catch because Python won't complain about them at run time. One way to safe-guard your code against these such errors is to have Python explicitly check the assumptions held by classes. Read this post to learn how to use assert for this purpose. Use assert in the implementation of SumRatio to ensure that x and y have the same size. If not, we want assert to display x and y should have the same number of elements.

Problem 2: Exception Handling (Weight 2). Open Test3.py. Note that the second element of y is 0. So as expected, when we run Test3.py, Python will generate a ZeroDivisionError and terminates the execution of Test3.py with minimal information about what caused the error (it tells us that ZeroDivisionError occurred in line sum += self.x[i]/self.y[i] but it doesn't specify calculating which ratio caused the error). Also, in many cases, we would like to handle errors in a specific way. For example in this exercise, we are going to assume that division by zero is accepted (and hence should not terminate the execution) but then we want to return 'Not a number' if the denominator of one of the ratios is 0. The simplest way to handle exceptions is with a "try-except" block. Here is an example:

    x = 10
    y = 0
    try:
        ratio = x/y
    except ZeroDivisionError:
        print('Division by 0 in calculating the ratio x/y')

Watch Lecture 7 of the MIT Open Course Introduction to Computer Science and Programming in Python to learn how to use "try-except" blocks to handle errors.

Modify the class SumRatio such that if ZeroDivisionError occurred in line sum += self.x[i]/self.y[i] your code:

1. prints Warning: Division by zero occurred in calculating the ratio in position x., where x takes the value of index i.
2. returns math.nan as the results of calculating the sum of ratios (not that to use math.nan you need to add import math at the top of SumRatio.py).

Problem 3: Expected Health Utility (Weight 3). Modify the decision tree classes we implemented in class (DecisionTree.py in this repository) such that you can also get the expected health utility of alternatives in addition to the expected cost. Test your code on the decision tree below and print the expected cost and expected health utility of nodes C1 and C3.

Problem 4: Economic Evaluation (Weight 1). For the decision tree you created in Problem 3, calculate the incremental cost-effectiveness ratio (ICER) of Arm 2 with respect to Arm 1.