Creating Functions

Overview

Teaching: 30 min
Exercises: 0 min

Questions

How can I define new functions?

What’s the difference between defining and calling a function?

What happens when I call a function?

Objectives

Define a function that takes parameters.

Return a value from a function.

Test and debug a function.

Set default values for function parameters.

Explain why we should divide programs into small, single-purpose functions.

At this point, we’ve written code to draw some interesting features in our supernova data, loop over all our data files to quickly draw these plots for each of them, and have Python make decisions based on what it sees in our data. But, our code is getting pretty long and complicated; what if we had thousands of datasets, and didn’t want to generate a figure for every single one? Commenting out the figure-drawing code is a nuisance. Also, what if we want to use that code again, on a different dataset or at a different point in our program? Cutting and pasting it is going to make our code get very long and very repetitive, very quickly. We’d like a way to package our code so that it is easier to reuse, and Python provides for this by letting us define things called ‘functions’ — a shorthand way of re-executing longer pieces of code. Let’s start by defining a function fahr_to_celsius that converts temperatures from Fahrenheit to Celsius:

def fahr_to_celsius(temp):
    return ((temp - 32) * (5/9))

The Blueprint for a Python Function

The function definition opens with the keyword def followed by the name of the function (fahr_to_celsius) and a parenthesized list of parameter names (temp). The body of the function — the statements that are executed when it runs — is indented below the definition line. The body concludes with a return keyword followed by the return value.

When we call the function, the values we pass to it are assigned to those variables so that we can use them inside the function. Inside the function, we use a return statement to send a result back to whoever asked for it.

Let’s try running our function.

fahr_to_celsius(32)

This command should call our function, using “32” as the input and return the function value.

In fact, calling our own function is no different from calling any other function:

print('freezing point of water:', fahr_to_celsius(32), 'C')
print('boiling point of water:', fahr_to_celsius(212), 'C')

freezing point of water: 0.0 C
boiling point of water: 100.0 C

We’ve successfully called the function that we defined, and we have access to the value that we returned.

Composing Functions

Now that we’ve seen how to turn Fahrenheit into Celsius, we can also write the function to turn Celsius into Kelvin:

def celsius_to_kelvin(temp_c):
    return temp_c + 273.15

print('freezing point of water in Kelvin:', celsius_to_kelvin(0.))

freezing point of water in Kelvin: 273.15

What about converting Fahrenheit to Kelvin? We could write out the formula, but we don’t need to. Instead, we can compose the two functions we have already created:

def fahr_to_kelvin(temp_f):
    temp_c = fahr_to_celsius(temp_f)
    temp_k = celsius_to_kelvin(temp_c)
    return temp_k

print('boiling point of water in Kelvin:', fahr_to_kelvin(212.0))

boiling point of water in Kelvin: 373.15

This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-large chunks to get the effect we want. Real-life functions will usually be larger than the ones shown here — typically half a dozen to a few dozen lines — but they shouldn’t ever be much longer than that, or the next person who reads it won’t be able to understand what’s going on.

Tidying up

Now that we know how to wrap bits of code up in functions, we can make our supernova analysis easier to read and easier to reuse.

Let’s make a function called detect_problems that checks for those systematics we noticed:

def detect_problems(filename):

    data = np.loadtxt(fname=filename, delimiter=',', skiprows=1)

    for i in [1,3,5,7]:
        if np.nanmin(data[:,i]) < 0.:
            print(filename + ': A negative flux.')
        elif np.sum(np.isnan(data[:,i])) == data.shape[0]:
            print(filename + ': A NaN column')
        else:
            print('Seems OK!')

Notice that rather than jumbling this code together in one giant for loop, we can now read and reuse both ideas separately. We can reproduce the previous analysis with a much simpler for loop:

import glob
import numpy as np
filenames = sorted(glob.glob('data/*.csv'))

for f in filenames[:3]:
    print(f)
    detect_problems(f)

By giving our functions human-readable names, we can more easily read and understand what is happening in the for loop. Even better, if at some later date we want to use either of those pieces of code again, we can do so in a single line.

Documenting

Once we start putting things in functions so that we can re-use them, it is useful to add some documentation so that we remember what the function does.

The usual way to put documentation in software is to add comments like this:

#fahr_to_celsius(temp):
#converts fahrenheit degrees to celsius degrees
def fahr_to_celsius(temp):
    return ((temp - 32) * (5/9))

There’s a better way, though. If the first thing in a function is a string that isn’t assigned to a variable, that string is attached to the function as its documentation:

def fahr_to_celsius(temp):
    """Converts fahrenheit degrees to celsius degrees."""
    return ((temp - 32) * (5/9))

This is better because we can now ask Python’s built-in help system to show us the documentation for the function:

help(fahr_to_celsius)

Help on function fahr_to_celsius in module __main__:

fahr_to_celsius(temp)
   Converts fahrenheit degrees to celsius degrees.

A string like this is called a docstring. We don’t need to use triple quotes when we write one, but if we do, we can break the string across multiple lines.

def fahr_to_celsius(temp):
    """
    Converts fahrenheit degrees to celsius degrees.
    Example:
    >fahr_to_celsius(125)
    37.77777777777778
    """
    return ((temp - 32) * (5/9))

help(fahr_to_celsius)

Help on function fahr_to_celsius in module __main__:

fahr_to_celsius(temp)
    Converts fahrenheit degrees to celsius degrees.
    Example:
    >fahr_to_celsius(125)
    37.77777777777778

Defining Defaults

We have passed parameters to functions in two ways: directly, as in type(data), and by name, as in numpy.loadtxt(fname='something.csv', delimiter=','). In fact, we can pass the filename to loadtxt without the fname=:

np.loadtxt('data/03D1ar.csv', delimiter=',',skiprows=1)

array([[ 0.,  0.,  1., ...,  3.,  0.,  0.],
       [ 0.,  1.,  2., ...,  1.,  0.,  1.],
       [ 0.,  1.,  1., ...,  2.,  1.,  1.],
       ...,
       [ 0.,  1.,  1., ...,  1.,  1.,  1.],
       [ 0.,  0.,  0., ...,  0.,  2.,  0.],
       [ 0.,  0.,  1., ...,  1.,  1.,  0.]])

but we still need to say delimiter=:

np.loadtxt('data/03D1ar.csv', ',',1)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/username/anaconda3/lib/python3.6/site-packages/numpy/lib/npyio.py", line 1041, in loa
dtxt
    dtype = np.dtype(dtype)
  File "/Users/username/anaconda3/lib/python3.6/site-packages/numpy/core/_internal.py", line 199, in
_commastring
    newitem = (dtype, eval(repeats))
  File "<string>", line 1
    ,
    ^
SyntaxError: unexpected EOF while parsing

With that in hand, let’s look at the help for np.loadtxt:

help(np.loadtxt)

Help on function loadtxt in module np.lib.npyio:

loadtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, converters=None, skiprows=0, use
cols=None, unpack=False, ndmin=0, encoding='bytes')
    Load data from a text file.

    Each row in the text file must have the same number of values.

    Parameters
    ----------
...

There’s a lot of information here, but the most important part is the first couple of lines:

loadtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, converters=None, skiprows=0, use
cols=None, unpack=False, ndmin=0, encoding='bytes')

This tells us that loadtxt has one parameter called fname that doesn’t have a default value, and eight others that do. If we call the function like this:

np.loadtxt('data/03D1ar.csv', ',',1)

then the filename is assigned to fname (which is what we want), but the delimiter string ',' is assigned to dtype rather than delimiter, because dtype is the second parameter in the list. However ',' isn’t a known dtype so our code produced an error message when we tried to run it. When we call loadtxt we don’t have to provide fname= for the filename because it’s the first item in the list, but if we want the ',' to be assigned to the variable delimiter, we do have to provide delimiter= for the second parameter since delimiter is not the second parameter in the list.

Readable functions

Consider these two functions:

def s(p):
    a = 0
    for v in p:
        a += v
    m = a / len(p)
    d = 0
    for v in p:
        d += (v - m) * (v - m)
    return np.sqrt(d / (len(p) - 1))

def std_dev(sample):
    sample_sum = 0
    for value in sample:
        sample_sum += value

    sample_mean = sample_sum / len(sample)

    sum_squared_devs = 0
    for value in sample:
        sum_squared_devs += (value - sample_mean) * (value - sample_mean)

    return np.sqrt(sum_squared_devs / (len(sample) - 1))

The functions s and std_dev are computationally equivalent (they both calculate the sample standard deviation), but to a human reader, they look very different. You probably found std_dev much easier to read and understand than s.

As this example illustrates, both documentation and a programmer’s coding style combine to determine how easy it is for others to read and understand the programmer’s code. Choosing meaningful variable names and using blank spaces to break the code into logical “chunks” are helpful techniques for producing readable code. This is useful not only for sharing code with others, but also for the original programmer. If you need to revisit code that you wrote months ago and haven’t thought about since then, you will appreciate the value of readable code!

Combining Strings

“Adding” two strings produces their concatenation: 'a' + 'b' is 'ab'. Write a function called fence that takes two parameters called original and wrapper and returns a new string that has the wrapper character at the beginning and end of the original. A call to your function should look like this:
print(fence('name', '*'))
*name*
Solution
def fence(original, wrapper):
    return wrapper + original + wrapper

Return versus print

Note that return and print are not interchangeable. print is a Python function that prints data to the screen. It enables us, users, see the data. return statement, on the other hand, makes data visible to the program. Let’s have a look at the following function:
def add(a, b):
    print(a + b)
Question: What will we see if we execute the following commands?
A = add(7, 3)
print(A)
Solution

Python will first execute the function add with a = 7 and b = 3, and, therefore, print 10. However, because function add does not have a line that starts with return (no return “statement”), it will, by default, return nothing which, in Python world, is called None. Therefore, A will be assigned to None and the last line (print(A)) will print None. As a result, we will see:
10
None

Selecting Characters From Strings

If the variable s refers to a string, then s[0] is the string’s first character and s[-1] is its last. Write a function called outer that returns a string made up of just the first and last characters of its input. A call to your function should look like this:
print(outer('helium'))
hm
Solution
def outer(input_string):
    return input_string[0] + input_string[-1]

Rescaling an Array

Write a function rescale that takes an array as input and returns a corresponding array of values scaled to lie in the range 0.0 to 1.0. (Hint: If L and H are the lowest and highest values in the original array, then the replacement for a value v should be (v-L) / (H-L).)
Solution
def rescale(input_array):
    L = np.min(input_array)
    H = np.max(input_array)
    output_array = (input_array - L) / (H - L)
    return output_array

Testing and Documenting Your Function

Run the commands help(np.arange) and help(np.linspace) to see how to use these functions to generate regularly-spaced values, then use those values to test your rescale function. Once you’ve successfully tested your function, add a docstring that explains what it does.
Solution
'''Takes an array as input, and returns a corresponding array scaled so
that 0 corresponds to the minimum and 1 to the maximum value of the input array.

Examples:
>>> rescale(np.arange(10.0))
array([ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,
       0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ])
>>> rescale(np.linspace(0, 100, 5))
array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ])
'''

Defining Defaults

Rewrite the rescale function so that it scales data to lie between 0.0 and 1.0 by default, but will allow the caller to specify lower and upper bounds if they want. Compare your implementation to your neighbor’s: do the two functions always behave the same way?
Solution
def rescale(input_array, low_val=0.0, high_val=1.0):
    '''rescales input array values to lie between low_val and high_val'''
    L = np.min(input_array)
    H = np.max(input_array)
    intermed_array = (input_array - L) / (H - L)
    output_array = intermed_array * (high_val - low_val) + low_val
    return output_array

Variables Inside and Outside Functions

What does the following piece of code display when run — and why?
f = 0
k = 0

def f2k(f):
    k = ((f-32)*(5.0/9.0)) + 273.15
    return k

f2k(8)
f2k(41)
f2k(32)

print(k)
Solution
259.81666666666666
287.15
273.15
0
k is 0 because the k inside the function f2k doesn’t know about the k defined outside the function.

Mixing Default and Non-Default Parameters

Given the following code:
def numbers(one, two=2, three, four=4):
    n = str(one) + str(two) + str(three) + str(four)
    return n

print(numbers(1, three=3))
what do you expect will be printed? What is actually printed? What rule do you think Python is following?

1234

one2three4

1239

SyntaxError

Given that, what does the following piece of code display when run?
def func(a, b=3, c=6):
    print('a: ', a, 'b: ', b, 'c:', c)

func(-1, 2)
a: b: 3 c: 6

a: -1 b: 3 c: 6

a: -1 b: 2 c: 6

a: b: -1 c: 2

Solution

Attempting to define the numbers function results in 4. SyntaxError. The defined parameters two and four are given default values. Because one and three are not given default values, they are required to be included as arguments when the function is called and must be placed before any parameters that have default values in the function definition.

The given call to func displays a: -1 b: 2 c: 6. -1 is assigned to the first parameter a, 2 is assigned to the next parameter b, and c is not passed a value, so it uses its default value 6.

The Old Switcheroo

Consider this code:
a = 3
b = 7

def swap(a, b):
    temp = a
    a = b
    b = temp

swap(a, b)

print(a, b)
Which of the following would be printed if you were to run this code? Why did you pick this answer?

7 3

3 7

3 3

7 7

Solution

3 7 is the correct answer. Initially, a has a value of 3 and b has a value of 7. When the swap function is called, it creates local variables (also called a and b in this case) and trades their values. The function does not return any values and does not alter a or b outside of its local copy. Therefore the original values of a and b remain unchanged.

Readable Code

Revise a function you wrote for one of the previous exercises to try to make the code more readable. Then, collaborate with one of your neighbors to critique each other’s functions and discuss how your function implementations could be further improved to make them more readable.

Key Points

Define a function using def function_name(parameter).

The body of a function must be indented.

Call a function using function_name(value).

Numbers are stored as integers or floating-point numbers.

Variables defined within a function can only be seen and used within the body of the function.

If a variable is not defined within the function it is used, Python looks for a definition before the function call

Use help(thing) to view help for something.

Put docstrings in functions to provide help for that function.

Specify default values for parameters when defining a function using name=value in the parameter list.

Parameters can be passed by matching based on name, by position, or by omitting them (in which case the default value is used).

Put code whose parameters change frequently in a function, then call it with different parameter values to customize its behavior.

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Programming with Python

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Creating Functions

Overview

Composing Functions

Tidying up

Documenting

Defining Defaults

Readable functions

Combining Strings

Solution

Return versus print

Solution

Selecting Characters From Strings

Solution

Rescaling an Array

Solution

Testing and Documenting Your Function

Solution

Defining Defaults

Solution

Variables Inside and Outside Functions

Solution

Mixing Default and Non-Default Parameters

Solution

The Old Switcheroo

Solution

Readable Code

Key Points

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