In the context of programming, a function is a named sequence of statements that performs a computation. When you define a function, you specify the name and the sequence of statements. Later, you can "call" the function by name.

Why functions?

We know the area of a circle is: $A= πr^2$. Suppose we need to calculate the areas of three circles, we can do:

$r_1 = 20.16$

$r_2 = 9.13$

$r_3 = 11.55$

$A_1 = 3.14 * r_1^2$

$A_2 = 3.14 * r_2^2$

$A_3 = 3.14 * r_3^2$

Question: Is there an easier way to do this?

Question: What if we change $π$ to 3.14159 instead of 3.14?

If a function area_of_cicle(x) is defined, then we could reuse it many times, like this

a_1 = area_of_cicle(r_1)
a_2 = area_of_cicle(r_2)
a_3 = area_of_cicle(r_3)

Function calls

Example of a function call:

type(42)

The name of the function is type. The expression in parentheses is called the argument of the function. The result, for this function, is the type of the argument.

It is common to say that a function "takes" an argument and "returns" a result. The result is also called the return value.

To know more about this function, visit the documentation https://docs.python.org/3/library/functions.html#type.

type('42')

int('42')

int('Hello')

int(3.99)

int(-2.3)

float(42)

float('3.14')

str(42)

str(3.14)

abs(-100)

abs(-100, 42)

max(1, 2)

max(43, 5345, -654, 2, 0, 99999)

Exercise 01

Play with functions round(), min(), ord(), chr(). Read documentation https://docs.python.org/3/library/functions.html.

Math functions

Python has a math module that provides most of the familiar mathematical functions. A module is a file that contains a collection of related functions. Before we can use the functions in a module, we have to import it with an import statement:

import math

This statement creates(borrows) a module object named math. If you display the module object, you get some information about it:

math

<module 'math' (built-in)>
help(math)

How to call a function? By using dot.

ratio = 100
math.log10(ratio)

degrees = 45
radians = degrees / 180.0 * math.pi # math.pi is not a function. It is a constant.
math.sin(radians)

Exercise 02

From the documentation of math module https://docs.python.org/3/library/math.html, pick up two functions and play with them.

Add new functions

We can define our own functions.

Example:

def print_lyrics():
    print("Hey Jude. Don't make it bad.")
    print("Take a sad song and make it better.")

type(print_lyrics)

function
print_lyrics()

Hey Jude. Don't make it bad.
Take a sad song and make it better.

We can use a function inside another function.

def repeat_lyrics():
    print_lyrics()
    print('Na - na - na - na - na, na - na - na - na')
    print_lyrics()

repeat_lyrics()

Hey Jude. Don't make it bad.
Take a sad song and make it better.
Na - na - na - na - na, na - na - na - na
Hey Jude. Don't make it bad.
Take a sad song and make it better.

Parameters and arguments

Some of the functions we have seen require arguments. For example, when you call math.sin you pass a number as an argument.

Inside the function, the arguments are assigned to variables called parameters. Here is a definition for a function that takes an argument:

def print_twice(whatever_name):
    print(whatever_name)
    print(whatever_name)

print_twice('Babson')

Babson
Babson

my_name = 'Jack'
print_twice(my_name)

Jack
Jack

Exercise 03

Define a function my_abs to print the absolute value of any number. Note: you are not allowed to use built-in function abs().

Variables and parameters are local

When you create a variable inside a function, it is local, which means that it only exists inside the function. For example:

def cat_twice(part1, part2):
    cat = part1 + part2
    print_twice(cat)

This function takes two arguments, concatenates them, and prints the result twice. Here is an example that uses it:

line1 = 'Bing tiddle '
line2 = 'tiddle bang.'
cat_twice(line1, line2)

Bing tiddle tiddle bang.
Bing tiddle tiddle bang.

However, when cat_twice terminates, the variable cat is destroyed. If we try to print it, we get an exception:

print(cat)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-14-34599fba884e> in <module>
----> 1 print(cat)

NameError: name 'cat' is not defined

Parameters are also local. For example, outside function print_twice, there is no such thing as whatever_name.

Functions with return value(s) and void functions

Return values: 

def give_me_a_break():
    str1 = 'break'
    return str1

print(give_me_a_break())

def give_me_a_break():
    str1 = 'break'
    return str1
    print('another break')
    
print(give_me_a_break())

Void functions:

Void functions might display something on the screen or have some other effect, but they don’t have a return value. If you assign the result to a variable, you get a special value called None.

result = print_twice('Bing')

print(result)

Exercise 04

Modify the function my_abs to return the absolute value of any number.

Empty function

When we have not decided how to write this function, just use pass to make it run.

def nop():
    pass

We can use pass in other statements as well.

age= int(input())
if age >= 18:
    pass # without pass, you will see error.

Argument checking

Let's see an example first:

abs('A')

Exercise 05

Modify the function my_abs to first only allow integers and floating numbers, then return the absolute value of any number. You may need a built-in function isinstance() https://docs.python.org/3/library/functions.html#isinstance.

Return more than one value

Take a game program as an example: a function move is created to return the new coordinates - nx and ny - after moving certain steps.

import math
def move(x, y, step, angle):
    nx = x + step * math.cos(angle)
    ny = y - step * math.sin(angle)
    return nx, ny

x, y = move(100, 100, 60, math.pi / 6)
print(x, y)

Exercise 06

Define a function quadratic(a, b, c) to solve a quadratic equation and return the values of two roots:

$ax^2 + bx + c = 0$

def quadratic(a, b, c):
    pass # please modify it so the function solves the quadratic equation and return two values