Contents

Introduction to functions

This is a very short introduction to functions.

Functions are recipes with names 1.

Let’s start with an example where you have seen functions - mathematics.

cosine

You have used functions in mathematics. For example, cosine is a function in mathematics. We often write the cosine function as cos

We might write something like this, in mathematics:

\[ y = cos(0) \]

You can read \(cos(0)\) as:

Call the function “cos” with the value 0, and return the result.

Then \(y = cos(0)\) means:

Call the function “cos” with the value 0, and return the result, storing the result in “y”.

We pass a value to the function. In our case we pass the value \(0\). The value that we pass is called the argument.

The function returns a value. In our case it returns the calculation of the cosine of \(0\).

You may remember that the cosine of 0 is 1. So, after \(y = cos(0)\), we expect \(y\) to equal 1.

Functions in Python work in a similar way.

Functions in Python

First we load up the cos function from a library called numpy.

Don’t worry about the command to load the function, for now. We will come back to that later. Here is the command you need. Just run it in the notebook.

# Get the cos function from the numpy library.
from numpy import cos

Now we call the cos function, passing the value 0, and see what we get:

cos(0)

1.0

  • cos is the name of the function;

  • 0 is the value we pass to the function.

  • The value we pass to the function goes between the parentheses ( and ) 2.

  • 1.0 is the value that the function returns. It is the return value of the function.

The value we pass to the function is also called the function argument.

In our case we pass 0 as the argument to the cos function.

We can also store the return value in a variable, like this:

y = cos(0)

y

1.0

As you will see, it’s a very common pattern in Jupyter notebooks to store the value, and then show the value, in the same cell, like this:

y = cos(0)
y

1.0

Read this code as:

Pass the value 0 to the cos function. Put the result into the variable y. Show the contents of variable y.

Again with the recipe metaphor

A recipe is the procedure to go from ingredients to a meal.

A function is the procedure to go from the arguments to the return value.

The arguments are the things that I send to the function. The return value is the thing that the function sends back.

It is the job of the function to do some work on the arguments, and return the correct return value.

For example, I might have a recipe with the procedure to go from the ingredients: two eggs; butter; and cheese - to the meal - a cheese omelette.

The function cos has the procedure to go from the input argument - a number - to the return value, which is the calculation of the cosine of the value of the input argument.

I could call my recipe “two egg cheese omelette”, or “recipe number 4”. Whatever I called it, it would be the same recipe. I might prefer a name that describes what the recipe makes, to help me remember.

Likewise, the name cos refers to a procedure above. The folks who wrote the Numpy library could have give it another name, like some_function, but cos is a good name, because it helps us remember what the procedure does.

Practice with functions

So far we have used the cos function from Numpy. Let’s try doing the same thing with the sin function:

# Get the sin function from the numpy library.
from numpy import sin

sin(0)

0.0

  • sin - the function name;

  • 0 - the value we pass to the function;

  • The value goes after the function name, and between parentheses;

  • 0.0 - the value that the function returns.

We pass 0 as the argument to the sin function.

Now your turn.

Try importing the sqrt function. Yes, you guessed it, sqrt is the procedure to go from a number (the argument) to the square root of that number (the return value).

# Get the sqrt function from the numpy library.
# Your code here.

Call the sqrt function with the value 9; you should see this returns the value 3.0.

# Your code here.

Use Python to show that \(3^2\) is indeed 9:

# Your code to show the value of 3 squared.

We will see more about functions in the section on call expressions.

1

Thanks to the Berkeley team for this metaphor.

2

Please be very careful to distinguish between different types of brackets in Python (and other languages). The different types of brackets are: parentheses (round brackets), as in (); square brackets as in []; and curly brackets as in {}. These brackets have different meanings to Python; if you use the wrong type of brackets, you will either get an error, or you will get a result you didn’t expect. Calling functions uses parentheses.