Writing Functions

Overview

Questions

• How can I create my own functions?

Objectives

• Explain and identify the difference between function definition and function call.
• Write a function that takes a small, fixed number of arguments and produces a single result.

Break programs down into functions to make them easier to understand.

---

• Human beings can only keep a few items in working memory at a time.
• Understand larger/more complicated ideas by understanding and combining pieces.
  • Components in a machine.
  • Lemmas when proving theorems.
• Functions serve the same purpose in programs.
  • Encapsulate complexity so that we can treat it as a single “thing”.
• Also enables re-use.
  • Write one time, use many times.

Define a function using def with a name, parameters, and a block of code.

---

• Begin the definition of a new function with def.
• Followed by the name of the function.
  • Must obey the same rules as variable names.
• Then parameters in parentheses.
  • Empty parentheses if the function doesn’t take any inputs.
  • We will discuss this in detail in a moment.
• Then a colon.
• Then an indented block of code.

PYTHON

def print_greeting():
    print('Hello!')
    print('The weather is nice today.')
    print('Right?')

Defining a function does not run it.

---

• Defining a function does not run it.
  • Like assigning a value to a variable.
• Must call the function to execute the code it contains.

PYTHON

print_greeting()

OUTPUT

Hello!

Arguments in a function call are matched to its defined parameters.

---

• Functions are most useful when they can operate on different data.
• Specify parameters when defining a function.
  • These become variables when the function is executed.
  • Are assigned the arguments in the call (i.e., the values passed to the function).
  • If you don’t name the arguments when using them in the call, the arguments will be matched to parameters in the order the parameters are defined in the function.

PYTHON

def print_date(year, month, day):
    joined = str(year) + '/' + str(month) + '/' + str(day)
    print(joined)

print_date(1871, 3, 19)

OUTPUT

1871/3/19

Or, we can name the arguments when we call the function, which allows us to specify them in any order and adds clarity to the call site; otherwise as one is reading the code they might forget if the second argument is the month or the day for example.

PYTHON

print_date(month=3, day=19, year=1871)

OUTPUT

1871/3/19

• Via Twitter: () contains the ingredients for the function while the body contains the recipe.

Functions may return a result to their caller using return.

---

• Use return ... to give a value back to the caller.
• May occur anywhere in the function.
• But functions are easier to understand if return occurs:
  • At the start to handle special cases.
  • At the very end, with a final result.

PYTHON

def average(values):
    if len(values) == 0:
        return None
    return sum(values) / len(values)

PYTHON

a = average([1, 3, 4])
print('average of actual values:', a)

OUTPUT

average of actual values: 2.6666666666666665

PYTHON

print('average of empty list:', average([]))

OUTPUT

average of empty list: None

• Remember: every function returns something.
• A function that doesn’t explicitly return a value automatically returns None.

PYTHON

result = print_date(1871, 3, 19)
print('result of call is:', result)

OUTPUT

1871/3/19
result of call is: None

Identifying Syntax Errors

1. Read the code below and try to identify what the errors are without running it.
2. Run the code and read the error message. Is it a SyntaxError or an IndentationError?
3. Fix the error.
4. Repeat steps 2 and 3 until you have fixed all the errors.

PYTHON

def another_function
  print("Syntax errors are annoying.")
   print("But at least python tells us about them!")
  print("So they are usually not too hard to fix.")

Show me the solution

PYTHON

def another_function():
  print("Syntax errors are annoying.")
  print("But at least Python tells us about them!")
  print("So they are usually not too hard to fix.")

Definition and Use

What does the following program print?

PYTHON

def report(pressure):
    print('pressure is', pressure)

print('calling', report, 22.5)

Show me the solution

OUTPUT

calling <function report at 0x7fd128ff1bf8> 22.5

A function call always needs parenthesis, otherwise you get memory address of the function object. So, if we wanted to call the function named report, and give it the value 22.5 to report on, we could have our function call as follows

PYTHON

print("calling")
report(22.5)

OUTPUT

calling
pressure is 22.5

Order of Operations

1. What’s wrong in this example?

PYTHON

result = print_time(11, 37, 59)

def print_time(hour, minute, second):
   time_string = str(hour) + ':' + str(minute) + ':' + str(second)
   print(time_string)

2. After fixing the problem above, explain why running this example code:

PYTHON

result = print_time(11, 37, 59)
print('result of call is:', result)

gives this output:

OUTPUT

11:37:59
result of call is: None

3. Why is the result of the call None?

Show me the solution

1. The problem with the example is that the function print_time() is defined after the call to the function is made. Python doesn’t know how to resolve the name print_time since it hasn’t been defined yet and will raise a NameError e.g., NameError: name 'print_time' is not defined

2. The first line of output 11:37:59 is printed by the first line of code, result = print_time(11, 37, 59) that binds the value returned by invoking print_time to the variable result. The second line is from the second print call to print the contents of the result variable.

3. print_time() does not explicitly return a value, so it automatically returns None.

Encapsulation

Fill in the blanks to create a function that takes a single filename as an argument, loads the data in the file named by the argument, and returns the minimum value in that data.

PYTHON

import pandas as pd

def min_in_data(____):
    data = ____
    return ____

Show me the solution

PYTHON

import pandas as pd

def min_in_data(filename):
    data = pd.read_csv(filename)
    return data.min()

Find the First

Fill in the blanks to create a function that takes a list of numbers as an argument and returns the first negative value in the list. What does your function do if the list is empty? What if the list has no negative numbers?

PYTHON

def first_negative(values):
    for v in ____:
        if ____:
            return ____

Show me the solution

PYTHON

def first_negative(values):
    for v in values:
        if v < 0:
            return v

If an empty list or a list with all positive values is passed to this function, it returns None:

PYTHON

my_list = []
print(first_negative(my_list))

OUTPUT

None

Calling by Name

Earlier we saw this function:

PYTHON

def print_date(year, month, day):
    joined = str(year) + '/' + str(month) + '/' + str(day)
    print(joined)

We saw that we can call the function using named arguments, like this:

PYTHON

print_date(day=1, month=2, year=2003)

1. What does print_date(day=1, month=2, year=2003) print?
2. When have you seen a function call like this before?
3. When and why is it useful to call functions this way?

Show me the solution

1. 2003/2/1
2. We saw examples of using named arguments when working with the pandas library. For example, when reading in a dataset using data = pd.read_csv('data/gapminder_gdp_europe.csv', index_col='country'), the last argument index_col is a named argument.
3. Using named arguments can make code more readable since one can see from the function call what name the different arguments have inside the function. It can also reduce the chances of passing arguments in the wrong order, since by using named arguments the order doesn’t matter.

Encapsulation of an If/Print Block

The code below will run on a label-printer for chicken eggs. A digital scale will report a chicken egg mass (in grams) to the computer and then the computer will print a label.

PYTHON

import random
for i in range(10):

    # simulating the mass of a chicken egg
    # the (random) mass will be 70 +/- 20 grams
    mass = 70 + 20.0 * (2.0 * random.random() - 1.0)

    print(mass)

    # egg sizing machinery prints a label
    if mass >= 85:
        print("jumbo")
    elif mass >= 70:
        print("large")
    elif mass < 70 and mass >= 55:
        print("medium")
    else:
        print("small")

The if-block that classifies the eggs might be useful in other situations, so to avoid repeating it, we could fold it into a function, get_egg_label(). Revising the program to use the function would give us this:

PYTHON

# revised version
import random
for i in range(10):

    # simulating the mass of a chicken egg
    # the (random) mass will be 70 +/- 20 grams
    mass = 70 + 20.0 * (2.0 * random.random() - 1.0)

    print(mass, get_egg_label(mass))

1. Create a function definition for get_egg_label() that will work with the revised program above. Note that the get_egg_label() function’s return value will be important. Sample output from the above program would be 71.23 large.
2. A dirty egg might have a mass of more than 90 grams, and a spoiled or broken egg will probably have a mass that’s less than 50 grams. Modify your get_egg_label() function to account for these error conditions. Sample output could be 25 too light, probably spoiled.

Show me the solution

PYTHON

def get_egg_label(mass):
    # egg sizing machinery prints a label
    egg_label = "Unlabelled"
    if mass >= 90:
        egg_label = "warning: egg might be dirty"
    elif mass >= 85:
        egg_label = "jumbo"
    elif mass >= 70:
        egg_label = "large"
    elif mass < 70 and mass >= 55:
        egg_label = "medium"
    elif mass < 50:
        egg_label = "too light, probably spoiled"
    else:
        egg_label = "small"
    return egg_label

Encapsulating Data Analysis

Assume that the following code has been executed:

PYTHON

import pandas as pd

data_asia = pd.read_csv('data/gapminder_gdp_asia.csv', index_col=0)
japan = data_asia.loc['Japan']

1. Complete the statements below to obtain the average GDP for Japan across the years reported for the 1980s.

PYTHON

year = 1983
gdp_decade = 'gdpPercap_' + str(year // ____)
avg = (japan.loc[gdp_decade + ___] + japan.loc[gdp_decade + ___]) / 2

2. Abstract the code above into a single function.

PYTHON

def avg_gdp_in_decade(country, continent, year):
    data_countries = pd.read_csv('data/gapminder_gdp_'+___+'.csv',delimiter=',',index_col=0)
    ____
    ____
    ____
    return avg

3. How would you generalize this function if you did not know beforehand which specific years occurred as columns in the data? For instance, what if we also had data from years ending in 1 and 9 for each decade? (Hint: use the columns to filter out the ones that correspond to the decade, instead of enumerating them in the code.)

Show me the solution

1. The average GDP for Japan across the years reported for the 1980s is computed with:

PYTHON

year = 1983
gdp_decade = 'gdpPercap_' + str(year // 10)
avg = (japan.loc[gdp_decade + '2'] + japan.loc[gdp_decade + '7']) / 2

2. That code as a function is:

PYTHON

def avg_gdp_in_decade(country, continent, year):
    data_countries = pd.read_csv('data/gapminder_gdp_' + continent + '.csv', index_col=0)
    c = data_countries.loc[country]
    gdp_decade = 'gdpPercap_' + str(year // 10)
    avg = (c.loc[gdp_decade + '2'] + c.loc[gdp_decade + '7'])/2
    return avg

3. To obtain the average for the relevant years, we need to loop over them:

PYTHON

def avg_gdp_in_decade(country, continent, year):
    data_countries = pd.read_csv('data/gapminder_gdp_' + continent + '.csv', index_col=0)
    c = data_countries.loc[country]
    gdp_decade = 'gdpPercap_' + str(year // 10)
    total = 0.0
    num_years = 0
    for yr_header in c.index: # c's index contains reported years
        if yr_header.startswith(gdp_decade):
            total = total + c.loc[yr_header]
            num_years = num_years + 1
    return total/num_years

The function can now be called by:

PYTHON

avg_gdp_in_decade('Japan','asia',1983)

OUTPUT

20880.023800000003

Simulating a dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. A canonical example of a dynamical system is the logistic map, a growth model that computes a new population density (between 0 and 1) based on the current density. In the model, time takes discrete values 0, 1, 2, …

1. Define a function called logistic_map that takes two inputs: x, representing the current population (at time t), and a parameter r = 1. This function should return a value representing the state of the system (population) at time t + 1, using the mapping function:

f(t+1) = r * f(t) * [1 - f(t)]

2. Using a for or while loop, iterate the logistic_map function defined in part 1, starting from an initial population of 0.5, for a period of time t_final = 10. Store the intermediate results in a list so that after the loop terminates you have accumulated a sequence of values representing the state of the logistic map at times t = [0,1,...,t_final] (11 values in total). Print this list to see the evolution of the population.

3. Encapsulate the logic of your loop into a function called iterate that takes the initial population as its first input, the parameter t_final as its second input and the parameter r as its third input. The function should return the list of values representing the state of the logistic map at times t = [0,1,...,t_final]. Run this function for periods t_final = 100 and 1000 and print some of the values. Is the population trending toward a steady state?

Show me the solution

1. PYTHON

   def logistic_map(x, r):
       return r * x * (1 - x)

2. PYTHON

   initial_population = 0.5
   t_final = 10
   r = 1.0
   population = [initial_population]
   
   for t in range(t_final):
       population.append( logistic_map(population[t], r) )

3. PYTHON

   def iterate(initial_population, t_final, r):
       population = [initial_population]
       for t in range(t_final):
           population.append( logistic_map(population[t], r) )
       return population
   
   for period in (10, 100, 1000):
       population = iterate(0.5, period, 1)
       print(population[-1])

   OUTPUT

   0.06945089389714401
   0.009395779870614648
   0.0009913908614406382

   The population seems to be approaching zero.

Using Functions With Conditionals in Pandas

Functions will often contain conditionals. Here is a short example that will indicate which quartile the argument is in based on hand-coded values for the quartile cut points.

PYTHON

def calculate_life_quartile(exp):
    if exp < 58.41:
        # This observation is in the first quartile
        return 1
    elif exp >= 58.41 and exp < 67.05:
        # This observation is in the second quartile
       return 2
    elif exp >= 67.05 and exp < 71.70:
        # This observation is in the third quartile
       return 3
    elif exp >= 71.70:
        # This observation is in the fourth quartile
       return 4
    else:
        # This observation has bad data
       return None

calculate_life_quartile(62.5)

OUTPUT

2

That function would typically be used within a for loop, but Pandas has a different, more efficient way of doing the same thing, and that is by applying a function to a dataframe or a portion of a dataframe. Here is an example, using the definition above.

PYTHON

data = pd.read_csv('data/gapminder_all.csv')
data['life_qrtl'] = data['lifeExp_1952'].apply(calculate_life_quartile)

There is a lot in that second line, so let’s take it piece by piece. On the right side of the = we start with data['lifeExp'], which is the column in the dataframe called data labeled lifExp. We use the apply() to do what it says, apply the calculate_life_quartile to the value of this column for every row in the dataframe.

Key Points

• Break programs down into functions to make them easier to understand.
• Define a function using def with a name, parameters, and a block of code.
• Defining a function does not run it.
• Arguments in a function call are matched to its defined parameters.
• Functions may return a result to their caller using return.