Introduction to functions

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A function is a key element in writing programs. You can think of a function in a computing language much the same way you think of a mathematical function. The function takes in arguments, performs some operation based on the identities of the arguments, and then returns a result. For example, the mathematical function

\begin{align} f(x, y) = \frac{x}{y} \end{align}

takes arguments \(x\) and \(y\) and then returns the ratio between the two, \(x/y\). In this lesson, we will learn how to construct functions in Python.

Basic function syntax

For our first example, we will translate the above function into Python. A function is defined using the def keyword. This is best seen by example.

def ratio(x, y):
    """The ratio of `x` to `y`."""
    return x / y

Following the def keyword is a function signature which indicates the function’s name and its arguments. Just like in mathematics, the arguments are separated by commas and enclosed in parentheses. The indentation following the def line specifies what is part of the function. As soon as the indentation goes to the left again, aligned with def, the contents of the functions are complete.

Immediately following the function definition is the doc string (short for documentation string), a brief description of the function. The first string after the function definition is always defined as the doc string. Usually, it is in triple quotes, as doc strings often span multiple lines.

Doc strings are more than just comments for your code, the doc string is what is returned by the native python function help() when someone is looking to learn more about your function. For example:

help(ratio)

Help on function ratio in module __main__:

ratio(x, y)
    The ratio of `x` to `y`.

They are also printed out when you use the ? in a Jupyter notebook or JupyterLab console.

ratio?

Signature: ratio(x, y)
Docstring: The ratio of `x` to `y`.
File:      /var/folders/j_/c5r9ch0913v3h1w4bdwzm0lh0000gn/T/ipykernel_21013/1007532851.py
Type:      function

You are free to type whatever you like in doc strings, or even omit them, but you should always have a doc string with some information about what your function is doing. True, this example of a function is kind of silly, since it is easier to type x / y than ratio(x, y), but it is still good form to have a doc string. This is worth saying explicitly.

All functions should have doc strings.

In the next line of the function, we see a return keyword. Whatever is after the return statement is, you guessed it, returned by the function. Any code after the return is not executed because the function has already returned!

Calling a function

Now that we have defined our function, we can call it with the arguments in parentheses.

ratio(5, 4)

1.25

ratio(4, 2)

2.0

ratio(90.0, 8.4)

10.714285714285714

In each case, the function returns a float with the ratio of its arguments.

Functions need not have arguments

A function does not need arguments. As a silly example, let’s consider a function that just returns 42 every time. Of course, it does not matter what its arguments are, so we can define a function without arguments.

def answer_to_the_ultimate_question_of_life_the_universe_and_everything():
    """Simpler program than Deep Thought's, I bet."""
    return 42

We still needed the open and closed parentheses at the end of the function name. Similarly, even though it has no arguments, we still have to call it with parentheses.

answer_to_the_ultimate_question_of_life_the_universe_and_everything()

42

Functions need not return anything

Just like they do not necessarily need arguments, functions also do not need to return anything. If a function does not have a return statement (or it is never encountered in the execution of the function), the function runs to completion and returns None by default. None is a special Python keyword which basically means “nothing.” For example, a function could simply print something to the screen.

def think_too_much():
    """Express Caesar's skepticism about Cassius"""
    print("""Yond Cassius has a lean and hungry look,
He thinks too much; such men are dangerous.""")

We call this function as all others, but we can show that the result it returns is None.

return_val = think_too_much()

# Print a blank line
print()

# Print the return value
print(return_val)

Yond Cassius has a lean and hungry look,
He thinks too much; such men are dangerous.

None

Built-in functions in Python

The Python programming language has several built-in functions. We have already encountered print(), id(), ord(), len(), range(), enumerate(), zip(), and reversed(), in addition to type conversions such as list(). The complete set of built-in functions can be found here. A word of warning about these functions and naming your own.

Never define a function or variable with the same name as a built-in function.

Additionally, Python has keywords (such as def, for, in, if, True, None, etc.), many of which we have already encountered. A complete list of them is here. The interpreter will throw an error if you try to define a function or variable with the same name as a keyword.

An example function: reverse complement

Let’s write a function that does not do something so trivial as computing ratios or giving us the Answer to the Ultimate Question of Life, the Universe, and Everything. We’ll write a function to compute the reverse complement of a sequence of DNA. Within the function, we’ll use some of our newly acquired iteration skills.

def complement_base(base):
    """Returns the Watson-Crick complement of a base."""
    if base in 'Aa':
        return 'T'
    elif base in 'Tt':
        return 'A'
    elif base in 'Gg':
        return 'C'
    else:
        return 'G'


def reverse_complement(seq):
    """Compute reverse complement of a sequence."""
    # Initialize reverse complement
    rev_seq = ''

    # Loop through and populate list with reverse complement
    for base in reversed(seq):
        rev_seq += complement_base(base)

    return rev_seq

Note that we do not have error checking here, which we should definitely do, but we’ll cover that in a future lesson. For now, let’s test it to see if it works.

reverse_complement('GCAGTTGCA')

'TGCAACTGC'

It looks good, but we might want to write yet another function to display the template strand (from 5′ to 3′) above its reverse complement (from 3′ to 5′). This make it easier to verify.

def display_complements(seq):
    """Print sequence above its reverse complement."""
    # Compute the reverse complement
    rev_comp = reverse_complement(seq)

    # Print template
    print(seq)

    # Print "base pairs"
    for base in seq:
        print('|', end='')

    # Print final newline character after base pairs
    print()

    # Print reverse complement
    for base in reversed(rev_comp):
        print(base, end='')

    # Print final newline character
    print()

Let’s call this function and display the input sequence and the reverse complement returned by the function.

seq = 'GCAGTTGCA'
display_complements(seq)

GCAGTTGCA
|||||||||
CGTCAACGT

Ok, now it’s clear that the result looks good! This example demonstrates an important programming principle regarding functions. We used three functions to compute and display the reverse complement.

1. complement_base() gives the Watson-Crick complement of a given base.

2. reverse_complement() computes the reverse complement.

3. display_complements() displays the sequence and the reverse complement.

We could very well have written a single function to compute the reverse complement with the if statements included within the for loop. Instead, we split this larger operation up into smaller functions. This is an example of modular programming, in which the desired functionality is split up into small, independent, interchangeable modules. This is a very, very important concept.

Write small functions that do single, simple tasks.

Pause and think about testing

Let’s pause for a moment and think about what the complement_base() and reverse_complement() functions do. They do a well-defined operation on string inputs. If we’re doing some bioinformatics, we might use these functions over and over again. We should therefore thoroughly test the functions. For example, we should test that reverse_complement('GCAGTTGCA') returns 'TGCAACTGC'. For now, we will proceed without writing tests, but we will soon cover test-driven development, in which your functions are built around tests. For now, I will tell you this: If your functions are not thoroughly tested, you are entering a world of pain. Test your functions, at least for code used in real research.

Keyword arguments

Now let’s say that instead of the reverse DNA complement, we want the reverse RNA complement. We could re-write the complement_base() function to do this. Better yet, let’s modify it.

def complement_base(base, material='DNA'):
    """Returns the Watson-Crick complement of a base."""
    if base in 'Aa':
        if material == 'DNA':
            return 'T'
        elif material == 'RNA':
            return 'U'
    elif base in 'TtUu':
        return 'A'
    elif base in 'Gg':
        return 'C'
    else:
        return 'G'

def reverse_complement(seq, material='DNA'):
    """Compute reverse complement of a sequence."""
    # Initialize reverse complement
    rev_seq = ''

    # Loop through and populate list with reverse complement
    for base in reversed(seq):
        rev_seq += complement_base(base, material=material)

    return rev_seq

We have added a named keyword argument, also known as a named kwarg. The syntax for a named kwarg is

kwarg_name=default_value

in the def clause of the function definition. In this case, we say that the default material is DNA, but we could call the function with another material (RNA). Conveniently, when you call the function and omit the kwargs, they take on the default value within the function. So, if we wanted to use the default material of DNA, we don’t have to do anything different in the function call.

reverse_complement('GCAGTTGCA')

'TGCAACTGC'

But, if we want RNA, we can use the kwarg. We use the same syntax to call it that we did when defining it.

reverse_complement('GCAGTTGCA', material='RNA')

'UGCAACUGC'

Calling a function with a splat

Python offers another convenient way to call functions. Say a function takes three arguments, a, b, and c, taken to be the sides of a triangle, and determines whether or not the triangle is a right triangle. I.e., it checks to see if \(a^2 + b^2 = c^2\).

def is_almost_right(a, b, c):
    """
    Checks to see if a triangle with side lengths
    `a`, `b`, and `c` is right.
    """

    # Use sorted(), which gives a sorted list
    a, b, c = sorted([a, b, c])

    # Check to see if it is almost a right triangle
    if abs(a**2 + b**2 - c**2) < 1e-12:
        return True
    else:
        return False

Remember our warning from before: never use equality checks with floats. We therefore just check to see if the Pythagorean theorem almost holds. The function works as expected.

is_almost_right(13, 5, 12)

True

is_almost_right(1, 1, 1.4)

False

Now, let’s say we had a tuple with the triangle side lengths in it.

side_lengths = (13, 5, 12)

We can pass these all in separately by splitting the tuple but putting a * in front of it. A * before a tuple used in this way is referred an unpacking operator, and is referred to by some programmers as a “splat.”

is_almost_right(*side_lengths)

True

This can be very convenient, and we will definitely use this in the course.

Anonymous (a.k.a. lambda) functions

So far, we have written functions using a def statement, followed by an indented block of code defining what will be executed when the function is called. Sometimes the functions are very short, like the ratio() function at the beginning of this lesson. We might wish to more succinctly define a function like this. Python’s lambda keyword enables this. As an example, let’s look at how we could define the ratio() function from before.

f = lambda x, y: x / y

f(3, 5)

0.6

The syntax for defining an anonymous function, which must be on one line, is as follows.

1. The keyword lambda.

2. The arguments of the anonymous function, separated by commas.

3. An expression that is the return value of the function.

You may be thinking that anonymous functions run contrary to the idea that all functions should have doc strings. You’re right. Anonymous functions are typically only used when another function requires a function as an argument. As we have seen, the sorted() function is used to sort a list, as demonstrated below on the Nobel laureates of 2018. First, we’ll construct our list again, like we did in the previous lesson.

names = (
    'Frances Arnold', 'George Smith', 'Gregory Winter',
    'postponed',
    'Denis Mukwege', 'Nadia Murad',
    'Arthur Ashkin', 'Gérard Mourou', 'Donna Strickland',
    'James Allison', 'Tasuku Honjo',
    'William Nordhaus', 'Paul Romer'
)

nationalities = (
    'USA', 'USA', 'UK',
    '---',
    'DRC', 'Iraq',
    'USA', 'France', 'Canada',
    'USA', 'Japan',
    'USA', 'USA'
)

categories = (
    'Chemistry', 'Chemistry', 'Chemistry',
    'Literature',
    'Peace', 'Peace',
    'Physics', 'Physics', 'Physics',
    'Physiology or Medicine', 'Physiology or Medicine',
    'Economics', 'Economics'
)

laureates = [(cat, name, nat) for name, nat, cat in zip(names, nationalities, categories)]

# Take a look
laureates

[('Chemistry', 'Frances Arnold', 'USA'),
 ('Chemistry', 'George Smith', 'USA'),
 ('Chemistry', 'Gregory Winter', 'UK'),
 ('Literature', 'postponed', '---'),
 ('Peace', 'Denis Mukwege', 'DRC'),
 ('Peace', 'Nadia Murad', 'Iraq'),
 ('Physics', 'Arthur Ashkin', 'USA'),
 ('Physics', 'Gérard Mourou', 'France'),
 ('Physics', 'Donna Strickland', 'Canada'),
 ('Physiology or Medicine', 'James Allison', 'USA'),
 ('Physiology or Medicine', 'Tasuku Honjo', 'Japan'),
 ('Economics', 'William Nordhaus', 'USA'),
 ('Economics', 'Paul Romer', 'USA')]

We can sort the list, which will result in the list being sorted by the first entry in the tuples, which is the category.

sorted(laureates)

[('Chemistry', 'Frances Arnold', 'USA'),
 ('Chemistry', 'George Smith', 'USA'),
 ('Chemistry', 'Gregory Winter', 'UK'),
 ('Economics', 'Paul Romer', 'USA'),
 ('Economics', 'William Nordhaus', 'USA'),
 ('Literature', 'postponed', '---'),
 ('Peace', 'Denis Mukwege', 'DRC'),
 ('Peace', 'Nadia Murad', 'Iraq'),
 ('Physics', 'Arthur Ashkin', 'USA'),
 ('Physics', 'Donna Strickland', 'Canada'),
 ('Physics', 'Gérard Mourou', 'France'),
 ('Physiology or Medicine', 'James Allison', 'USA'),
 ('Physiology or Medicine', 'Tasuku Honjo', 'Japan')]

Now, say we wish to sort them by nationality first. The sorted() function allows sorting according to the value returned by a function that takes the list element as an argument. This is accomplished with the key keyword argument. We can use an anonymous function for this kwarg. We simply want to return the last entry in each tuple, which is the nationality of the laureate.

sorted(laureates, key=lambda x: x[-1])

[('Literature', 'postponed', '---'),
 ('Physics', 'Donna Strickland', 'Canada'),
 ('Peace', 'Denis Mukwege', 'DRC'),
 ('Physics', 'Gérard Mourou', 'France'),
 ('Peace', 'Nadia Murad', 'Iraq'),
 ('Physiology or Medicine', 'Tasuku Honjo', 'Japan'),
 ('Chemistry', 'Gregory Winter', 'UK'),
 ('Chemistry', 'Frances Arnold', 'USA'),
 ('Chemistry', 'George Smith', 'USA'),
 ('Physics', 'Arthur Ashkin', 'USA'),
 ('Physiology or Medicine', 'James Allison', 'USA'),
 ('Economics', 'William Nordhaus', 'USA'),
 ('Economics', 'Paul Romer', 'USA')]

We will use anonymous functions when doing sorting and filtering of data sets using Pandas, so they are good to have in your toolbox.

Computing environment

%load_ext watermark
%watermark -v -p jupyterlab

Python implementation: CPython
Python version       : 3.9.12
IPython version      : 8.4.0

jupyterlab: 3.4.4