In [1]:
# Set up packages for lecture. Don't worry about understanding this code, but
# make sure to run it if you're following along.
import numpy as np
import babypandas as bpd
import pandas as pd
from matplotlib_inline.backend_inline import set_matplotlib_formats
import matplotlib.pyplot as plt
set_matplotlib_formats("svg")
plt.style.use('ggplot')
plt.rcParams['figure.figsize'] = (10, 5)

np.set_printoptions(threshold=20, precision=2, suppress=True)
pd.set_option("display.max_rows", 7)
pd.set_option("display.max_columns", 8)
pd.set_option("display.precision", 2)

from IPython.display import display, IFrame
def show_def():
    src = "https://docs.google.com/presentation/d/e/2PACX-1vRKMMwGtrQOeLefj31fCtmbNOaJuKY32eBz1VwHi_5ui0AGYV3MoCjPUtQ_4SB1f9x4Iu6gbH0vFvmB/embed?start=false&loop=false&delayms=60000"
    width = 960 
    height = 569
    display(IFrame(src, width, height))

Lecture 8 – Functions and Apply¶

DSC 10, Winter 2023¶

Announcements¶

  • Lab 2 is due tomorrow at 11:59PM.
  • Homework 2 is due Tuesday 1/31 at 11:59PM.
  • The Midterm Project will be released in the middle of next week – start thinking about who you may want to partner up with!
    • You don't have to work with a partner, but it is highly recommended.
    • If you do, your partner doesn't have to be from your lecture section.

Agenda¶

  • Functions.
  • Applying functions to DataFrames.
  • Example: Student names.

Reminder: Use the DSC 10 Reference Sheet. You can also use it on exams!

Functions¶

Defining functions¶

  • We've learned how to do quite a bit in Python:
    • Manipulate arrays, Series, and DataFrames.
    • Perform operations on strings.
    • Create visualizations.
  • But so far, we've been restricted to using existing functions (e.g. max, np.sqrt, len) and methods (e.g. .groupby, .assign, .plot).

Motivation¶

Suppose you drive to a restaurant 🥘 in LA, located exactly 100 miles away.

  • For the first 50 miles, you drive at 80 miles per hour.
  • For the last 50 miles, you drive at 60 miles per hour.
  • Question: What is your average speed throughout the journey?
  • 🚨 The answer is not 70 miles per hour! Remember, from Homework 1, you need to use the fact that $\text{speed} = \frac{\text{distance}}{\text{time}}$.
$$\text{average speed} = \frac{\text{distance}}{\text{time}} = \frac{50 + 50}{\text{time}_1 + \text{time}_2} \text{ miles per hour}$$

In segment 1, when you drove 50 miles at 80 miles per hour, you drove for $\frac{50}{80}$ hours:

$$\text{speed}_1 = \frac{\text{distance}_1}{\text{time}_1}$$
$$80 \text{ miles per hour} = \frac{50 \text{ miles}}{\text{time}_1} \implies \text{time}_1 = \frac{50}{80} \text{ hours}$$

Similarly, in segment 2, when you drove 50 miles at 60 miles per hour, you drove for $\text{time}_2 = \frac{50}{60} \text{ hours}$.

Then,

$$\text{average speed} = \frac{50 + 50}{\frac{50}{80} + \frac{50}{60}} \text{ miles per hour} $$
$$\begin{align*}\text{average speed} &= \frac{50}{50} \cdot \frac{1 + 1}{\frac{1}{80} + \frac{1}{60}} \text{ miles per hour} \\ &= \frac{2}{\frac{1}{80} + \frac{1}{60}} \text{ miles per hour} \end{align*}$$

Example: Harmonic mean¶

The harmonic mean ($\text{HM}$) of two positive numbers, $a$ and $b$, is defined as

$$\text{HM} = \frac{2}{\frac{1}{a} + \frac{1}{b}}$$

It is often used to find the average of multiple rates.

Finding the harmonic mean of 80 and 60 is not hard:

In [2]:
2 / (1 / 80 + 1 / 60)
Out[2]:
68.57142857142857

But what if we want to find the harmonic mean of 80 and 70? 80 and 90? 20 and 40? This would require a lot of copy-pasting, which is prone to error.

It turns out that we can define our own "harmonic mean" function just once, and re-use it multiple times.

In [3]:
def harmonic_mean(a, b):
    return 2 / (1 / a + 1 / b)
In [4]:
harmonic_mean(80, 60)
Out[4]:
68.57142857142857
In [5]:
harmonic_mean(20, 40)
Out[5]:
26.666666666666664

Note that we only had to specify how to calculate the harmonic mean once!

Functions¶

Functions are a way to divide our code into small subparts to prevent us from writing repetitive code. Each time we define our own function in Python, we will use the following pattern.

In [6]:
show_def()

Functions are "recipes"¶

  • Functions take in inputs, known as arguments, do something, and produce some outputs.
  • The beauty of functions is that you don't need to know how they are implemented in order to use them!
    • This is the premise of the idea of abstraction in computer science – you'll hear a lot about this in DSC 20.
In [7]:
harmonic_mean(20, 40)
Out[7]:
26.666666666666664
In [8]:
harmonic_mean(79, 894)
Out[8]:
145.17163412127442
In [9]:
harmonic_mean(-2, 4)
Out[9]:
-8.0

Parameters and arguments¶

triple has one parameter, x.

In [10]:
def triple(x):
    return x * 3

When we call triple with the argument 5, you can pretend that there's an invisible first line in the body of triple that says x = 5.

In [11]:
triple(5)
Out[11]:
15

Note that arguments can be of any type!

In [12]:
triple('triton')
Out[12]:
'tritontritontriton'

Functions can take 0 or more arguments¶

Functions can have any number of arguments. So far, we've created a function that takes two arguments – harmonic_mean – and a function that takes one argument – triple.

greeting takes no arguments!

In [13]:
def greeting():
    return 'Hi! 👋'
In [14]:
greeting()
Out[14]:
'Hi! 👋'

Functions don't run until you call them!¶

The body of a function is not run until you use (call) the function.

Here, we can define where_is_the_error without seeing an error message.

In [15]:
def where_is_the_error(something):
    '''You can describe your function within triple quotes. For example, this function 
    illustrates that errors don't occur until functions are executed (called).'''
    return (1 / 0) + something

It is only when we call where_is_the_error that Python gives us an error message.

In [16]:
where_is_the_error(5)

---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
/var/folders/ch/hyjw6whx3g9gshnp58738jc80000gp/T/ipykernel_91980/3423408763.py in <module>
----> 1 where_is_the_error(5)

/var/folders/ch/hyjw6whx3g9gshnp58738jc80000gp/T/ipykernel_91980/1703529954.py in where_is_the_error(something)
      2     '''You can describe your function within triple quotes. For example, this function 
      3     illustrates that errors don't occur until functions are executed (called).'''
----> 4     return (1 / 0) + something

ZeroDivisionError: division by zero

Example: first_name¶

Let's create a function called first_name that takes in someone's full name and returns their first name. Example behavior is shown below.

>>> first_name('Pradeep Khosla')
'Pradeep'

Hint: Use the string method .split.

General strategy for writing functions:

  1. First, try and get the behavior to work on a single example.
  2. Then, encapsulate that behavior inside a function.
In [17]:
'Pradeep Khosla'.split(' ')[0]
Out[17]:
'Pradeep'
In [18]:
def first_name(full_name):
    '''Returns the first name given a full name.'''
    return full_name.split(' ')[0]
In [19]:
first_name('Pradeep Khosla')
Out[19]:
'Pradeep'
In [20]:
# What if there are three names?
first_name('Chancellor Pradeep Khosla')
Out[20]:
'Chancellor'

Returning¶

  • The return keyword specifies what the output of your function should be, i.e. what a call to your function will evaluate to.
  • Most functions we write will use return, but using return is not required.
  • Be careful: print and return work differently!
In [21]:
def pythagorean(a, b):
    '''Computes the hypotenuse length of a triangle with legs a and b.'''
    c = (a ** 2 + b ** 2) ** 0.5
    print(c)
In [22]:
x = pythagorean(3, 4)

5.0
In [23]:
# No output – why?
x
In [24]:
# Errors – why?
x + 10

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/ch/hyjw6whx3g9gshnp58738jc80000gp/T/ipykernel_91980/3305400239.py in <module>
      1 # Errors – why?
----> 2 x + 10

TypeError: unsupported operand type(s) for +: 'NoneType' and 'int'
In [25]:
def better_pythagorean(a, b):
    '''Computes the hypotenuse length of a triangle with legs a and b, and actually returns the result.'''
    c = (a ** 2 + b ** 2) ** 0.5
    return c
In [26]:
x = better_pythagorean(3, 4)
x
Out[26]:
5.0
In [27]:
x + 10
Out[27]:
15.0

Returning¶

Once a function executes a return statement, it stops running.

In [28]:
def motivational(quote):
    return 0
    print("Here's a motivational quote:", quote)
In [29]:
motivational('Fall seven times and stand up eight.')
Out[29]:
0

Scope 🩺¶

The names you choose for a function’s parameters are only known to that function (known as local scope). The rest of your notebook is unaffected by parameter names.

In [30]:
def what_is_awesome(s):
    return s + ' is awesome!'
In [31]:
what_is_awesome('data science')
Out[31]:
'data science is awesome!'
In [32]:
s

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
/var/folders/ch/hyjw6whx3g9gshnp58738jc80000gp/T/ipykernel_91980/1028141915.py in <module>
----> 1 s

NameError: name 's' is not defined
In [33]:
s = 'DSC 10'
In [34]:
what_is_awesome('data science')
Out[34]:
'data science is awesome!'

Applying functions to DataFrames¶

DSC 10 student data¶

The DataFrame roster contains the names and lecture sections of all students enrolled in DSC 10 this quarter. The first names are real, while the last names have been anonymized for privacy.

In [35]:
roster = bpd.read_csv('data/roster-anon.csv')
roster
Out[35]:
name section
0 Anya Iatypd 10AM
1 Nathaniel Kcyrfu 11AM
2 Jae Oadpmw 10AM
... ... ...
347 Danny Zsoyxb 10AM
348 Alex Lrmwwt 11AM
349 Giovanni Ibkdsu 11AM

350 rows × 2 columns

Example: Common first names¶

What is the most common first name among DSC 10 students? (Any guesses?)

In [36]:
roster
Out[36]:
name section
0 Anya Iatypd 10AM
1 Nathaniel Kcyrfu 11AM
2 Jae Oadpmw 10AM
... ... ...
347 Danny Zsoyxb 10AM
348 Alex Lrmwwt 11AM
349 Giovanni Ibkdsu 11AM

350 rows × 2 columns

  • Problem: We can't answer that right now, since we don't have a column with first names. If we did, we could group by it.
  • Solution: Use our function that extracts first names on every element of the 'name' column.

Using our first_name function¶

Somehow, we need to call first_name on every student's 'name'.

In [37]:
roster
Out[37]:
name section
0 Anya Iatypd 10AM
1 Nathaniel Kcyrfu 11AM
2 Jae Oadpmw 10AM
... ... ...
347 Danny Zsoyxb 10AM
348 Alex Lrmwwt 11AM
349 Giovanni Ibkdsu 11AM

350 rows × 2 columns

In [38]:
roster.get('name').iloc[0]
Out[38]:
'Anya Iatypd'
In [39]:
first_name(roster.get('name').iloc[0])
Out[39]:
'Anya'
In [40]:
first_name(roster.get('name').iloc[1])
Out[40]:
'Nathaniel'

Ideally, there's a better solution than doing this hundreds of times...

.apply¶

  • To apply a function to every element of column column_name in DataFrame df, use


df.get(column_name).apply(function_name)
  • The .apply method is a Series method.
    • Important: We use .apply on Series, not DataFrames.
    • The output of .apply is also a Series.
  • Pass just the name of the function – don't call it!
    • Good ✅: .apply(first_name).
    • Bad ❌: .apply(first_name()).
In [41]:
roster.get('name').apply(first_name)
Out[41]:
0           Anya
1      Nathaniel
2            Jae
         ...    
347        Danny
348         Alex
349     Giovanni
Name: name, Length: 350, dtype: object

Example: Common first names¶

In [42]:
roster = roster.assign(
    first=roster.get('name').apply(first_name)
)
roster
Out[42]:
name section first
0 Anya Iatypd 10AM Anya
1 Nathaniel Kcyrfu 11AM Nathaniel
2 Jae Oadpmw 10AM Jae
... ... ... ...
347 Danny Zsoyxb 10AM Danny
348 Alex Lrmwwt 11AM Alex
349 Giovanni Ibkdsu 11AM Giovanni

350 rows × 3 columns

In [43]:
name_counts = roster.groupby('first').count().sort_values('name', ascending=False).get(['name'])
name_counts
Out[43]:
name
first
Ryan 6
Jason 3
Ethan 3
... ...
Hannah 1
Gwendal 1
Zoe 1

315 rows × 1 columns

Activity¶

Below:

  • Create a bar chart showing the number of students with each first name, but only include first names shared by at least two students.
  • Determine the proportion of students in DSC 10 who have a first name that is shared by at least two students.
In [44]:
...
Out[44]:
Ellipsis
In [45]:
...
Out[45]:
Ellipsis

Note: .apply works with built-in functions, too!¶

For instance, to find the length of each name, we might use the len function:

In [46]:
roster
Out[46]:
name section first
0 Anya Iatypd 10AM Anya
1 Nathaniel Kcyrfu 11AM Nathaniel
2 Jae Oadpmw 10AM Jae
... ... ... ...
347 Danny Zsoyxb 10AM Danny
348 Alex Lrmwwt 11AM Alex
349 Giovanni Ibkdsu 11AM Giovanni

350 rows × 3 columns

In [47]:
roster.get('first').apply(len)
Out[47]:
0      4
1      9
2      3
      ..
347    5
348    4
349    8
Name: first, Length: 350, dtype: int64

Aside: what if names are in the index?¶

We were able to apply first_name to the 'name' column because it's a Series. The .apply method doesn't work on the index, because the index is not a Series.

In [48]:
indexed_by_name = roster.set_index('name')
indexed_by_name
Out[48]:
section first
name
Anya Iatypd 10AM Anya
Nathaniel Kcyrfu 11AM Nathaniel
Jae Oadpmw 10AM Jae
... ... ...
Danny Zsoyxb 10AM Danny
Alex Lrmwwt 11AM Alex
Giovanni Ibkdsu 11AM Giovanni

350 rows × 2 columns

In [49]:
indexed_by_name.index.apply(first_name)

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
/var/folders/ch/hyjw6whx3g9gshnp58738jc80000gp/T/ipykernel_91980/1621495788.py in <module>
----> 1 indexed_by_name.index.apply(first_name)

AttributeError: 'Index' object has no attribute 'apply'

Solution: .reset_index()¶

Use .reset_index() to turn the index of a DataFrame into a column, and to reset the index back to the default of 0, 1, 2, 3, and so on.

In [50]:
indexed_by_name.reset_index()
Out[50]:
name section first
0 Anya Iatypd 10AM Anya
1 Nathaniel Kcyrfu 11AM Nathaniel
2 Jae Oadpmw 10AM Jae
... ... ... ...
347 Danny Zsoyxb 10AM Danny
348 Alex Lrmwwt 11AM Alex
349 Giovanni Ibkdsu 11AM Giovanni

350 rows × 3 columns

In [51]:
indexed_by_name.reset_index().get('name').apply(first_name)
Out[51]:
0           Anya
1      Nathaniel
2            Jae
         ...    
347        Danny
348         Alex
349     Giovanni
Name: name, Length: 350, dtype: object

Example: Shared first names and sections¶

  • Suppose you're one of the $\approx$18\% of students in DSC 10 who has a first name that is shared with at least one other student.
  • Let's try and determine whether someone in your lecture section shares the same first name as you.
In [52]:
roster
Out[52]:
name section first
0 Anya Iatypd 10AM Anya
1 Nathaniel Kcyrfu 11AM Nathaniel
2 Jae Oadpmw 10AM Jae
... ... ... ...
347 Danny Zsoyxb 10AM Danny
348 Alex Lrmwwt 11AM Alex
349 Giovanni Ibkdsu 11AM Giovanni

350 rows × 3 columns

For example, maybe 'Giovanni Ibkdsu' wants to see if there's another 'Giovanni' in their section.

Strategy:

  1. What section is 'Giovanni Ibkdsu' in?
  2. How many people are in that section and named 'Giovanni'?
In [53]:
what_section = roster[roster.get('name') == 'Giovanni Ibkdsu'].get('section').iloc[0]
what_section
Out[53]:
'11AM'
In [54]:
how_many = roster[(roster.get('section') == what_section) & (roster.get('first') == 'Giovanni')].shape[0]
how_many
Out[54]:
2

Another function: shared_first_and_section¶

Let's create a function named shared_first_and_section. It will take in the full name of a student and return the number of students in their section with the same first name and section (including them).

Note: This is the first function we're writing that involves using a DataFrame within the function – this is fine!

In [55]:
def shared_first_and_section(name):
    # First, find the row corresponding to that full name in roster.
    # We're assuming that full names are unique.
    row = roster[roster.get('name') == name]
    
    # Then, get that student's first name and section.
    first = row.get('first').iloc[0]
    section = row.get('section').iloc[0]
    
    # Now, find all the students with the same first name and section.
    shared_info = roster[(roster.get('first') == first) & (roster.get('section') == section)]
    
    # Return the number of such students.
    return shared_info.shape[0]
In [56]:
shared_first_and_section('Giovanni Ibkdsu')
Out[56]:
2
In [57]:
shared_first_and_section('Danny Zsoyxb')
Out[57]:
1

Now, let's add a column to roster that contains the values returned by shared_first_and_section.

In [58]:
roster = roster.assign(shared=roster.get('name').apply(shared_first_and_section))
roster
Out[58]:
name section first shared
0 Anya Iatypd 10AM Anya 1
1 Nathaniel Kcyrfu 11AM Nathaniel 1
2 Jae Oadpmw 10AM Jae 1
... ... ... ... ...
347 Danny Zsoyxb 10AM Danny 1
348 Alex Lrmwwt 11AM Alex 1
349 Giovanni Ibkdsu 11AM Giovanni 2

350 rows × 4 columns

Let's look at all the students who are in a section with someone that has the same first name as them.

In [59]:
roster[(roster.get('shared') > 1)].sort_values('shared', ascending=False)
Out[59]:
name section first shared
300 Ryan Siubvw 9AM Ryan 3
140 Ryan Pxydjz 9AM Ryan 3
167 Ryan Nwivbq 9AM Ryan 3
... ... ... ... ...
37 Jasmine Nztgqf 9AM Jasmine 2
35 Ruby Lopqun 9AM Ruby 2
349 Giovanni Ibkdsu 11AM Giovanni 2

25 rows × 4 columns

We can narrow this down to a particular lecture section if we'd like.

In [60]:
one_section_only = roster[(roster.get('shared') > 1) & 
                              (roster.get('section') == '9AM')].sort_values('shared', ascending=False)
one_section_only
Out[60]:
name section first shared
140 Ryan Pxydjz 9AM Ryan 3
167 Ryan Nwivbq 9AM Ryan 3
300 Ryan Siubvw 9AM Ryan 3
... ... ... ... ...
212 Jonathan Jgchdp 9AM Jonathan 2
316 Bruce Rinuux 9AM Bruce 2
339 Jonathan Lspjmb 9AM Jonathan 2

13 rows × 4 columns

In [61]:
one_section_only.get('first').unique()
Out[61]:
array(['Ryan', 'Bruce', 'Eddie', 'Ruby', 'Jasmine', 'Jonathan'],
      dtype=object)

Sneak peek¶

While the DataFrames on the previous slide contain the info we were looking for, they're not organized very conveniently. For instance, there are three rows containing the fact that there are 3 'Ryan's in the 9AM lecture section.

Wouldn't it be great if we could create a DataFrame like the one below? We'll see how on Monday!

section first count
0 9AM Ryan 3
1 10AM Ryan 2
2 9AM Ruby 2
3 10AM Jason 2
4 11AM Giovanni 2

Activity¶

Find the shortest first name in the class that is shared by at least two students in the same section.

Hint: You'll have to use both .assign and .apply.

In [62]:
...
Out[62]:
Ellipsis

Summary, next time¶

Summary¶

  • Functions are a way to divide our code into small subparts to prevent us from writing repetitive code.
  • The .apply method allows us to call a function on every single element of a Series, which usually comes from .getting a column of a DataFrame.

Next time¶

More advanced DataFrame manipulations!