Creating Functions
Last updated on 2023-04-20 | Edit this page
Overview
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 seen that code can have Python make decisions about what it sees in our data. What if we want to convert some of our data, like taking a temperature in Fahrenheit and converting it to Celsius. We could write something like this for converting a single number
and for a second number we could just copy the line and rename the variables
PYTHON
fahrenheit_val = 99
celsius_val = ((fahrenheit_val - 32) * (5/9))
fahrenheit_val2 = 43
celsius_val2 = ((fahrenheit_val2 - 32) * (5/9))But we would be in trouble as soon as we had to do this more than a
couple times. 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, a shorthand way of re-executing
longer pieces of code. In Python we can use ‘functions’. Let’s start by
defining a function fahr_to_celsius that converts
temperatures from Fahrenheit to Celsius:
PYTHON
def explicit_fahr_to_celsius(temp):
# Assign the converted value to a variable
converted = ((temp - 32) * (5/9))
# Return the value of the new variable
return converted
def fahr_to_celsius(temp):
# Return converted value more efficiently using the return
# function without creating a new variable. This code does
# the same thing as the previous function but it is more explicit
# in explaining how the return command works.
return ((temp - 32) * (5/9))
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.
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:
PYTHON
print('freezing point of water:', fahr_to_celsius(32), 'C')
print('boiling point of water:', fahr_to_celsius(212), 'C')OUTPUT
freezing point of water: 0.0 C
boiling point of water: 100.0 CWe’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:
PYTHON
def celsius_to_kelvin(temp_c):
return temp_c + 273.15
print('freezing point of water in Kelvin:', celsius_to_kelvin(0.))OUTPUT
freezing point of water in Kelvin: 273.15What 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:
PYTHON
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))OUTPUT
boiling point of water in Kelvin: 373.15This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-larger 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.
Variable Scope
In composing our temperature conversion functions, we created
variables inside of those functions, temp,
temp_c, temp_f, and temp_k. We
refer to these variables as local variables because they no
longer exist once the function is done executing. If we try to access
their values outside of the function, we will encounter an error:
ERROR
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-1-eed2471d229b> in <module>
----> 1 print('Again, temperature in Kelvin was:', temp_k)
NameError: name 'temp_k' is not definedIf you want to reuse the temperature in Kelvin after you have
calculated it with fahr_to_kelvin, you can store the result
of the function call in a variable:
OUTPUT
temperature in Kelvin was: 373.15The variable temp_kelvin, being defined outside any
function, is said to be global.
Inside a function, one can read the value of such global variables:
PYTHON
def print_temperatures():
print('temperature in Fahrenheit was:', temp_fahr)
print('temperature in Kelvin was:', temp_kelvin)
temp_fahr = 212.0
temp_kelvin = fahr_to_kelvin(temp_fahr)
print_temperatures()OUTPUT
temperature in Fahrenheit was: 212.0
temperature in Kelvin was: 373.15Tidying up
Now that we know how to wrap bits of code up in functions, we can
make our inflammation analysis easier to read and easier to reuse.
First, let’s make a visualize function that generates our
plots:
PYTHON
def visualize(filename):
data = numpy.loadtxt(fname=filename, delimiter=',')
fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))
axes1 = fig.add_subplot(1, 3, 1)
axes2 = fig.add_subplot(1, 3, 2)
axes3 = fig.add_subplot(1, 3, 3)
axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0))
axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0))
axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))
fig.tight_layout()
matplotlib.pyplot.show()and another function called detect_problems that checks
for those systematics we noticed:
PYTHON
def detect_problems(filename):
data = numpy.loadtxt(fname=filename, delimiter=',')
if numpy.amax(data, axis=0)[0] == 0 and numpy.amax(data, axis=0)[20] == 20:
print('Suspicious looking maxima!')
elif numpy.sum(numpy.amin(data, axis=0)) == 0:
print('Minima add up to zero!')
else:
print('Seems OK!')Wait! Didn’t we forget to specify what both of these functions should
return? Well, we didn’t. In Python, functions are not required to
include a return statement and can be used for the sole
purpose of grouping together pieces of code that conceptually do one
thing. In such cases, function names usually describe what they do,
e.g. visualize, detect_problems.
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:
PYTHON
filenames = sorted(glob.glob('inflammation*.csv'))
for filename in filenames[:3]:
print(filename)
visualize(filename)
detect_problems(filename)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.
Testing and Documenting
Once we start putting things in functions so that we can re-use them, we need to start testing that those functions are working correctly. To see how to do this, let’s write a function to offset a dataset so that it’s mean value shifts to a user-defined value:
PYTHON
def offset_mean(data, target_mean_value):
return (data - numpy.mean(data)) + target_mean_valueWe could test this on our actual data, but since we don’t know what the values ought to be, it will be hard to tell if the result was correct. Instead, let’s use NumPy to create a matrix of 0’s and then offset its values to have a mean value of 3:
OUTPUT
[[ 3. 3.]
[ 3. 3.]]That looks right, so let’s try offset_mean on our real
data:
OUTPUT
[[-6.14875 -6.14875 -5.14875 ... -3.14875 -6.14875 -6.14875]
[-6.14875 -5.14875 -4.14875 ... -5.14875 -6.14875 -5.14875]
[-6.14875 -5.14875 -5.14875 ... -4.14875 -5.14875 -5.14875]
...
[-6.14875 -5.14875 -5.14875 ... -5.14875 -5.14875 -5.14875]
[-6.14875 -6.14875 -6.14875 ... -6.14875 -4.14875 -6.14875]
[-6.14875 -6.14875 -5.14875 ... -5.14875 -5.14875 -6.14875]]It’s hard to tell from the default output whether the result is correct, but there are a few tests that we can run to reassure us:
PYTHON
print('original min, mean, and max are:', numpy.amin(data), numpy.mean(data), numpy.amax(data))
offset_data = offset_mean(data, 0)
print('min, mean, and max of offset data are:',
numpy.amin(offset_data),
numpy.mean(offset_data),
numpy.amax(offset_data))OUTPUT
original min, mean, and max are: 0.0 6.14875 20.0
min, mean, and and max of offset data are: -6.14875 2.84217094304e-16 13.85125That seems almost right: the original mean was about 6.1, so the lower bound from zero is now about -6.1. The mean of the offset data isn’t quite zero — we’ll explore why not in the challenges — but it’s pretty close. We can even go further and check that the standard deviation hasn’t changed:
OUTPUT
std dev before and after: 4.61383319712 4.61383319712Those values look the same, but we probably wouldn’t notice if they were different in the sixth decimal place. Let’s do this instead:
PYTHON
print('difference in standard deviations before and after:',
numpy.std(data) - numpy.std(offset_data))OUTPUT
difference in standard deviations before and after: -3.5527136788e-15Again, the difference is very small. It’s still possible that our function is wrong, but it seems unlikely enough that we should probably get back to doing our analysis. We have one more task first, though: we should write some documentation for our function to remind ourselves later what it’s for and how to use it.
The usual way to put documentation in software is to add comments like this:
PYTHON
# offset_mean(data, target_mean_value):
# return a new array containing the original data with its mean offset to match the desired value.
def offset_mean(data, target_mean_value):
return (data - numpy.mean(data)) + target_mean_valueThere’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:
PYTHON
def offset_mean(data, target_mean_value):
"""Return a new array containing the original data
with its mean offset to match the desired value."""
return (data - numpy.mean(data)) + target_mean_valueThis is better because we can now ask Python’s built-in help system to show us the documentation for the function:
OUTPUT
Help on function offset_mean in module __main__:
offset_mean(data, target_mean_value)
Return a new array containing the original data with its mean offset to match the desired value.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:
PYTHON
def offset_mean(data, target_mean_value):
"""Return a new array containing the original data
with its mean offset to match the desired value.
Examples
--------
>>> offset_mean([1, 2, 3], 0)
array([-1., 0., 1.])
"""
return (data - numpy.mean(data)) + target_mean_value
help(offset_mean)OUTPUT
Help on function offset_mean in module __main__:
offset_mean(data, target_mean_value)
Return a new array containing the original data
with its mean offset to match the desired value.
Examples
--------
>>> offset_mean([1, 2, 3], 0)
array([-1., 0., 1.])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=:
OUTPUT
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=:
ERROR
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 parsingTo understand what’s going on, and make our own functions easier to
use, let’s re-define our offset_mean function like
this:
PYTHON
def offset_mean(data, target_mean_value=0.0):
"""Return a new array containing the original data
with its mean offset to match the desired value, (0 by default).
Examples
--------
>>> offset_mean([1, 2, 3])
array([-1., 0., 1.])
"""
return (data - numpy.mean(data)) + target_mean_valueThe key change is that the second parameter is now written
target_mean_value=0.0 instead of just
target_mean_value. If we call the function with two
arguments, it works as it did before:
OUTPUT
[[ 3. 3.]
[ 3. 3.]]But we can also now call it with just one parameter, in which case
target_mean_value is automatically assigned the default value of 0.0:
PYTHON
more_data = 5 + numpy.zeros((2, 2))
print('data before mean offset:')
print(more_data)
print('offset data:')
print(offset_mean(more_data))OUTPUT
data before mean offset:
[[ 5. 5.]
[ 5. 5.]]
offset data:
[[ 0. 0.]
[ 0. 0.]]This is handy: if we usually want a function to work one way, but occasionally need it to do something else, we can allow people to pass a parameter when they need to but provide a default to make the normal case easier. The example below shows how Python matches values to parameters:
PYTHON
def display(a=1, b=2, c=3):
print('a:', a, 'b:', b, 'c:', c)
print('no parameters:')
display()
print('one parameter:')
display(55)
print('two parameters:')
display(55, 66)OUTPUT
no parameters:
a: 1 b: 2 c: 3
one parameter:
a: 55 b: 2 c: 3
two parameters:
a: 55 b: 66 c: 3As this example shows, parameters are matched up from left to right, and any that haven’t been given a value explicitly get their default value. We can override this behavior by naming the value as we pass it in:
OUTPUT
only setting the value of c
a: 1 b: 2 c: 77With that in hand, let’s look at the help for
numpy.loadtxt:
OUTPUT
Help on function loadtxt in module numpy.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:
OUTPUT
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:
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:
PYTHON
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 numpy.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 numpy.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:
OUTPUT
*name*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:
Question: What will we see if we execute the following commands?
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:
OUTPUT
10
NoneSelecting 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:
OUTPUT
hmRescaling 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).)
Testing and Documenting Your Function
Run the commands help(numpy.arange) and
help(numpy.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.
PYTHON
"""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(numpy.arange(10.0))
array([ 0. , 0.11111111, 0.22222222, 0.33333333, 0.44444444,
0.55555556, 0.66666667, 0.77777778, 0.88888889, 1. ])
>>> rescale(numpy.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?
PYTHON
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 = numpy.amin(input_array)
H = numpy.amax(input_array)
intermed_array = (input_array - L) / (H - L)
output_array = intermed_array * (high_val - low_val) + low_val
return output_arrayOUTPUT
259.81666666666666
278.15
273.15
0k is 0 because the k inside the function
f2k doesn’t know about the k defined outside
the function. When the f2k function is called, it creates a
local variable
k. The function does not return any values and does not
alter k outside of its local copy. Therefore the original
value of k remains unchanged. Beware that a local
k is created because f2k internal statements
affect a new value to it. If k was only
read, it would simply retrieve the global k
value.
Mixing Default and Non-Default Parameters
Given the following code:
PYTHON
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?
1234one2three41239SyntaxError
Given that, what does the following piece of code display when run?
a: b: 3 c: 6a: -1 b: 3 c: 6a: -1 b: 2 c: 6a: b: -1 c: 2
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.
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.
- Variables created outside of any function are called global variables.
- Within a function, we can access global variables.
- Variables created within a function override global variables if their names match.
- 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=valuein 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.