# Functions¶

## Introduction¶

In the previous lab, you were exposed to functions. You called functions that were provided, but you did not write any functions yourself. In this lab, you will write your own functions.

By the end of this lab, you should be able to:

1. write simple functions and
2. call them from the interpreter and from other functions.

The concepts required for this lab are discussed here. We encourage you to try the exercises before you look at the explanation.

## Getting started¶

Open up a terminal and navigate (cd) to your cmsc12100-aut-17-username directory, where username is your CNetID. Run git pull upstream master to collect the lab materials and git pull to sync with your personal repository.

## Revisit Real Valued Functions and Plots¶

The lab3 folder contains an enhanced solution to the plotting question from the previous lab. You will now write some new functions to plot different mathematical functions.

1. Open ipython3 in one window and the file plot_lab.py in your editor in another window.
2. Load the code in the interpreter (that is, in ipython3) using run plot_lab.py:
3. Look at the functions sinc and plot_sinc in your editor and then try calling these functions in the interpreter:
In [2]: sinc(1.0)
Out[2]: 0.8414709848078965

In [3]: sinc(5.3)
Out[3]: -0.1570315928724342

In [4]: plot_sinc(-10.0, 10.0, 0.01)

1. Write a function square that takes a floating point value x and returns x * x. Run plot_lab.py in the interpreter again, and give your new function a try.

2. Write a function plot_square that plots the new square function. You do not need to write this function from scratch; you can simply make a copy of the plot_sinc function, change the name to plot_square, update the docstring, replace the call to sinc and update the arguments to pylab.title and pylab.ylabel. Then call plot_square in the interpreter. How does the plot differ from the plot of the sinc function? (Remember to save the changes to your file and to re-run it in ipython3 before your try out your new code.)

3. You will notice that the code for plot_square and plot_sinc have a lot in common. Keeping multiple copies of the same code almost always creates trouble. You may fix a bug in one copy but forget to fix it in the other, or find you need a third or fourth version of it. When you find yourself repeating code you should move the common code into a function.

Pull out the code that plots the figure into a new function. What arguments and how many of them should this function take?

You need to write one new line of code for the new function: a function header. The rest of the body of the function can be copied directly from plot_sinc and then modified to replace the constants with parameters.

4. Rewrite plot_sinc and plot_square to use this new function. plot_sinc and plot_square should now be much smaller and simpler. Creating more plot_whatever functions should now be much easier too.

You’ll notice that there is still a fair amount of code that is repeated in plot_sinc and plot_square. In fact, the only difference between the two functions is the call to sinc versus square. Later in the course you’ll see that we can write functions that take other functions as parameters, which will allow us to abstract more and further alleviate the need for repeated code.

## Geometry¶

In this section you will be asked to write several functions from scratch. You will need to decide what each function requires as input and what it produces as an output.

A point in the real plane can be described by an x and y coordinate, written mathematically as the point (x, y). A line segment can be described by two points (x1, y1) and (x2, y2). The length of a line segment can be found by computing the following mathematical formula:

$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

In this section you will create functions to compute the distance between two points and a function to compute the perimeter of a triangle. You will see how one function can be used by another.

Open the file geometry.py in an editor.

1. What types can we use to describe a point in Python? What effect does the choice of type have on the number of variables we need to represent a point?

2. Consider a function dist that takes in arguments that describe two points and returns one value that is the distance between those two points. Write the function header for the function dist. If you’re not sure how to write the header then ask for help. It is important to get this code right before you move on.

3. After you have written the function header, write the body of the function. Be sure to return the correct value. You will need to use the function math.sqrt, which takes a float as an argument and returns its square root as a float.

4. Verify that your code works by using dist in the interpreter with a simple example. For example, compute the distance between the points (0, 1) and (1, 0). You should get a number very close to 1.414.

You may also add code to print the output of dist, along with its expected output, in the go function, so that you can check it anytime geometry.py is run.

5. Repeat steps 2, 3, 4 with a new function named perimeter that takes in enough information to describe three points that define a triangle and returns the perimeter of that triangle. Do not call math.sqrt within the body of the perimeter function.

## Useful List Functions¶

Open the file list_exercises.py in an editor.

1. Write a function are_any_true that takes a list of booleans as arguments and returns True if at least one of the entries in the list is True, and False otherwise. Add code to the function named go to test your function on a few different lists. Recall that you can initialize lists directly to generate test cases. For example:

test_list = [True, True, False, True, True]

2. Write a function add_lists that takes two lists of the same length as arguments and adds corresponding values together [a[0] + b[0], a[1] + b[1], ...]. The function should return a new list with the result of the addition. (Your code may assume that the lists are of the same length.)

Add calls to your function to go(). Try out different types for the elements. What happens if the elements are integers? What happens when they are strings? What happens if the lists are of mixed types (for example, [5, "a", 3.4])

3. Write a function add_one that takes a list and adds 1 to each element in the list. This function should update the input list, not create a new one. What value is printed by the following code?

a = [1, 2, 3, 4, 5]
print(a)


## When Finished¶

When finished with the lab please check in your work. Assuming you are inside the lab directory, run the following commands from the Linux command-line:

git add plot_lab.py