Functions and modules


Functions allow us to group a number of statements into a logical block. We communicate with a function through a clearly defined interface, providing certain parameters to the function, and receiving some information back. Apart from this interface, we generally do not how exactly a function does the work to obtain the value it returns

For example the function math.sqrt: we do not know how exactly it computes the square root, but we know about the interface: if we pass x into the function, it will return (an approximation of) $\\sqrt{x}$.

This abstraction is a useful thing: it is a common technique in engineering to break down a system into smaller (black-box) components that all work together through well defined interfaces, but which do not need to know about the internal realisations of each other’s functionality. In fact, not having to care about these implementation details can help to have a clearer view of the system composed of many of these components.

Functions provide the basic building blocks of functionality in larger programs (and computer simulations), and help to control the inherent complexity of the process.

We can group functions together into a Python module (see modules), and in this way create our own libraries of functionality.

Using functions

The word “function” has different meanings in mathematics and programming. In programming it refers to a named sequence of operations that perform a computation. For example, the function sqrt() which is defined in the math module computes the square root of a given value:

In [1]:
from math import sqrt

The value we pass to the function sqrt is 4 in this example. This value is called the argument of the function. A function may have more than one argument.

The function returns the value 2.0 (the result of its computation) to the “calling context”. This value is called the return value of the function.

It is common to say that a function takes an argument and returns a result or return value.

Common confusion about printing and returning values

It is a common beginner’s mistake to confuse the printing of values with returning values. In the following example it is hard to see whether the function math.sin returns a value or whether it prints the value:

In [2]:
import math

We import the math module, and call the math.sin function with an argument of 2. The math.sin(2) call will actually return the value 0.909... not print it. However, because we have not assigned the return value to a variable, the Python prompt will print the returned object.

The following alternative sequence works only if the value is returned:

In [3]:
x = math.sin(2)

The return value of the function call math.sin(2) is assigned to the variable x, and x is printed in the next line.

Generally, functions should execute “silently” (i.e. not print anything) and report the result of their computation through the return value.

Part of the confusion about printed versus return values at the Python prompt comes from the Python prompt printing (a representation) of returned objects if the returned objects are not assigned. Generally, seeing the returned objects is exactly what we want (as we normally care about the returned object), just when learning Python this may cause mild confusion about functions returning values or printing values.

Further information

Defining functions

The generic format of a function definitions:

def my_function(arg1, arg2, ..., argn):
    """Optional docstring."""

    # Implementation of the function

    return result  # optional

#this is not part of the function

Allen Downey’s terminology (in his book Think Python) of fruitful and fruitless functions distinguishes between functions that return a value, and those that do not return a value. The distinction refers to whether a function provides a return value (=fruitful) or whether the function does not explicitly return a value (=fruitless). If a functions does not make use of the return statement, we tend to say that the function returns nothing (whereas in reality in will always return the None object when it terminates – even if the return statement is missing).

For example, the function greeting will print “Hello World” when called (and is fruitless as it does not return a value).

In [4]:
def greeting():
    print("Hello World!")

If we call that function:

In [5]:
Hello World!

it prints “Hello World” to stdout, as we would expect. If we assign the return value of the function to a variable x, we can inspect it subsequently:

In [6]:
x = greeting()
Hello World!
In [7]:

and find that the greeting function has indeed returned the None object.

Another example for a function that does not return any value (that means there is no return keyword in the function) would be:

In [8]:
def printpluses(n): 
    print(n * "+")

Generally, functions that return values are more useful as these can be used to assemble code (maybe as another function) by combining them cleverly. Let’s look at some examples of functions that do return a value.

Suppose we need to define a function that computes the square of a given variable. The function source could be:

In [9]:
def square(x):
    return x * x

The keyword def tells Python that we are defining a function at that point. The function takes one argument (x). The function returns x*x which is of course $x^2$. Here is the listing of a file that shows how the function can be defined and used: (note that the numbers on the left are line numbers and are not part of the program)

In [10]:
def square(x):
    return x * x

for i in range(5):
    i_squared = square(i)
    print(i, '*', i, '=', i_squared)
0 * 0 = 0
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16

It is worth mentioning that lines 1 and 2 define the square function whereas lines 4 to 6 are the main program.

We can define functions that take more than one argument:

In [11]:
import math

def hypot(x, y):
    return math.sqrt(x * x + y * y)

It is also possible to return more than one argument. Here is an example of a function that converts a given string into all characters uppercase and all characters lowercase and returns the two versions. We have included the main program to show how this function can be called:

In [12]:
def upperAndLower(string):
    return string.upper(), string.lower()

testword = 'Banana'

uppercase, lowercase = upperAndLower(testword)

print(testword, 'in lowercase:', lowercase,
      'and in uppercase', uppercase)
Banana in lowercase: banana and in uppercase BANANA

We can define multiple Python functions in one file. Here is an example with two functions:

In [13]:
def returnstars( n ):
    return n * '*'

def print_centred_in_stars( string ):
    linelength = 46 
    starstring = returnstars((linelength - len(string)) // 2)

    print(starstring + string + starstring)

print_centred_in_stars('Hello world!')
*****************Hello world!*****************
Further reading

Default values and optional parameters

Python allows to define default values for function parameters. Here is an example: This program will print the following output when executed: So how does it work? The function print_mult_table takes two arguments: n and upto. The first argument n is a “normal” variable. The second argument upto has a default value of 10. In other words: should the user of this function only provide one argument, then this provides the value for n and upto will default to 10. If two arguments are provided, the first one will be for n and the second for upto (as shown in the code example above).



  • Group together functionality

  • Provide namespaces

  • Python’s standard library contains a vast collection of modules - “Batteries Included”

    • Try help(’modules’)
  • Means of extending Python

Importing modules

In [14]:
import math

This will introduce the name math into the namespace in which the import command was issued. The names within the math module will not appear in the enclosing namespace: they must be accessed through the name math. For example: math.sin.

In [15]:
import math, cmath

More than one module can be imported in the same statement, although the Python Style Guide recommends not to do this. Instead, we should write

In [16]:
import math
import cmath

import math as mathematics

The name by which the module is known locally can be different from its “official” name. Typical uses of this are

  • To avoid name clashes with existing names

  • To change the name to something more manageable. For example import SimpleHTTPServer as shs. This is discouraged for production code (as longer meaningful names make programs far more understandable than short cryptic ones), but for interactively testing out ideas, being able to use a short synonym can make your life much easier. Given that (imported) modules are first class objects, you can, of course, simply do shs = SimpleHTTPServer in order to obtain the more easily typable handle on the module.

In [17]:
from math import sin

This will import the sin function from the math module, but it will not introduce the name math into the current namespace. It will only introduce the name sin into the current namespace. It is possible to pull in more than one name from the module in one go:

In [18]:
from math import sin, cos

Finally, let’s look at this notation:

In [19]:
from math import *

Once again, this does not introduce the name math into the current namespace. It does however introduce all public names of the math module into the current namespace. Broadly speaking, it is a bad idea to do this:

  • Lots of new names will be dumped into the current namespace.

  • Are you sure they will not clobber any names already present?

  • It will be very difficult to trace where these names came from

  • Having said that, some modules (including ones in the standard library, recommend that they be imported in this way). Use with caution!

  • This is fine for interactive quick and dirty testing or small calculations.

Creating modules

A module is in principle nothing else than a python file. Here is an example of a module file which is saved in

def someusefulfunction():

print("My name is", __name__)

We can execute this (module) file as a normal python program (for example python

In [20]:
cd code/
In [21]:
My name is __main__

We note that the Python magic variable __name__ takes the value __main__ if the program file is executed.

On the other hand, we can import in another file (which could have the name, for example like this:

In [22]:
import module1            #in file
My name is module1

When Python comes across the import module1 statement in, it looks for the file in the current working directory (and if it can’t find it there in all the directories in sys.path) and opens the file While parsing the file from top to bottom, it will add any function definitions in this file into the module1 name space in the calling context (that is the main program in It this example, there is only the function someusefulfunction. Once the import process is completed, we can make use of module1.someusefulfunction in If Python comes across statements other than function (and class) definitions while importing, it carries those out immediately. In this case, it will thus come across the statement print(My name is, __name__).

Note the difference to the output if we import rather than executing it on its own: __name__ inside a module takes the value of the module name if the file is imported.

Use of __name__

In summary,

  • __name__ is __main__ if the module file is run on its own

  • __name__ is the name of the module (i.e. the module filename without the .py suffix) if the module file is imported.

We can therefor use the following if statement in to write code that is only run when the module is executed on its own: This is useful to keep test programs or demonstrations of the abilities of a module in this “conditional” main program. It is common practice for any module files to have such a conditional main program which demonstrates its capabilities.

Example 1

The next example shows a main program for the another file that is used to demonstrate the capabilities of the functions defined in that file:

from __future__ import division
import math

import numpy as N

def norm(x):
    """returns the magnitude of a vector x"""
    return math.sqrt(sum(x ** 2))

def unitvector(x):
    """returns a unit vector x/|x|. x needs to be a numpy array."""
    xnorm = norm(x)
    if xnorm == 0:
        raise ValueError("Can't normalise vector with length 0")
    return x / norm(x)

if __name__ == "__main__":
    #a little demo of how the functions in this module can be used:
    x1 = N.array([0, 1, 2])
    print("The norm of " + str(x1) + " is " + str(norm(x1)) + ".")
    print("The unitvector in direction of " + str(x1) + " is " \
        + str(unitvector(x1)) + ".")

If this file is executed using python, then __name__==__main__ is true, and the output reads

In [23]:
The norm of [0 1 2] is 2.23606797749979.
The unitvector in direction of [0 1 2] is [ 0.          0.4472136   0.89442719].

If this file is imported (i.e. used as a module) into another python file, then __name__==__main__ is false, and that statement block will not be executed (and no output produced).

This is quite a common way to conditionally execute code in files providing library-like functions. The code that is executed if the file is run on its own, often consists of a series of tests (to check that the file’s functions carry out the right operations – regression tests or unit tests ), or some examples of how the library functions in the file can be used.

Example 2

Even if a Python program is not intended to be used as a module file, it is good practice to always use a conditional main program:

  • often, it turns out later that functions in the file can be reused (and saves work then)

  • this is convenient for regression testing.

Suppose an exercise is given to write a function that returns the first 5 prime numbers, and in addition to print them. (There is of course a trivial solution to this as we know the prime numbers, and we should imagine that the required calculation is more complex). One might be tempted to write

In [24]:
def primes5():
    return (2, 3, 5, 7, 11)

for p in primes5():
    print("%d" % p, end=' ')
2 3 5 7 11 

It is better style to use a conditional main function, i.e.:

In [25]:
def primes5():
    return (2, 3, 5, 7, 11)

if __name__=="__main__":
    for p in primes5():
        print("%d" % p, end=' ')
2 3 5 7 11 

A purist might argue that the following is even cleaner:

In [26]:
def primes5():
    return (2, 3, 5, 7, 11)

def main():
    for p in primes5():
        print("%d" % p, end=' ')

if __name__=="__main__":
2 3 5 7 11 

but either of the last two options is good.

The example in Many ways to compute a series demonstrates this technique. Including functions with names starting with test_ is compatible with the very useful py.test regression testing framework (see

Further Reading