lab04 : matplotlib and visualizations

In this lab, you’ll continue practicing writing functions and testing them. You will also see how to visualize data using the matplotlib package.

The tools you’ll be creating will be useful in other courses and applicable to other disciplines, so we hope you have fun.

Get started with Matplotlib.pyplot

Drawing plots is a good way to visualize data, so in this lab, you will get to learn how to use Matplotlib.pyplot. For more in-depth guides for using Matplotlib, take a look at their tutorials page https://matplotlib.org/tutorials/index.html.

Pyplot is a module of Matplotlib which provides simple functions to add plot elements like lines, images, text, etc. to the current axes in the current figure.

Install matplotlib

First, let’s install the module by typing the following command line in the Terminal:

pip3 install --user matplotlib

Create lab04_plot.py

Open a new file in idle3 as before and type the following line to import the module.

import matplotlib.pyplot as plt

Save your file as lab04_plot.py.

Visualize movie data

Let’s look at a table consisting of movie statistics in the last 10 years (Source: The Numbers database).

For each column in the table, we want to create a list:

year_list = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020]
num_movies = [1251, 1287, 1494, 1419, 1514, 3009, 3506, 3607, 3885, 3961, 506]
money_list = [2540, 2742, 3158, 2972, 2995, 3597, 3690, 3789, 3826, 3769, 70]

Now, there are two plots we want to show: one for number of movies vs. year, and the other for money vs. year. Remember that the convention of “vs.” is y axis variable vs. x axis variable. However, when we call the plt.plot function to plot the graph, the first parameter is the data of x axis variable and the second parameter is the data of y axis variable.

Therefore, to plot the number of movies vs. year plot, year should be on the x axis and number of movies should be on the y axis.

Here’s how to do it in code:

plt.plot(year_list, num_movies)

In order to visualize this plot, add the following line:

plt.show()

Similarity, to plot and visualize the graph of money vs. year, add the following two lines:

plt.plot(year_list, money_list)
plt.show()

Note that the second plot will show up after you close the first one.

This is the code you should have for now for showing two plots separately:

import matplotlib.pyplot as plt

year_list = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020]
num_movies = [1251, 1287, 1494, 1419, 1514, 3009, 3506, 3607, 3885, 3961, 506]
money_list = [2540, 2742, 3158, 2972, 2995, 3597, 3690, 3789, 3826, 3769, 70]

plt.plot(year_list, num_movies)
plt.show()

plt.plot(year_list, money_list)
plt.show()

But what if we want to have both plots in the same graph?

We would remove the first plt.show() line, thus changing the code to the following:

import matplotlib.pyplot as plt

year_list = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020]
num_movies = [1251, 1287, 1494, 1419, 1514, 3009, 3506, 3607, 3885, 3961, 506]
money_list = [2540, 2742, 3158, 2972, 2995, 3597, 3690, 3789, 3826, 3769, 70]

plt.plot(year_list, num_movies)

plt.plot(year_list, money_list)
plt.show()

To distinguish which plot represents what data, we need to add a legend that labels the plots. In order to do so, we want to label each plot when calling plt.plot() as follows:

plt.plot(year_list, num_movies, label="number of movies")
plt.plot(year_list, money_list, label="money (in 10^7 dollars)")

In additionally, we need to add the legend which will create a legend on the plot using our labels:

plt.legend()

Therefore, your code after above changes should be the following:

import matplotlib.pyplot as plt

year_list = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020]
num_movies = [1251, 1287, 1494, 1419, 1514, 3009, 3506, 3607, 3885, 3961, 506]
money_list = [2540, 2742, 3158, 2972, 2995, 3597, 3690, 3789, 3826, 3769, 70]

plt.plot(year_list, num_movies, label="number of movies")
plt.plot(year_list, money_list, label="money (in 10^7 dollars)")
plt.legend()
plt.show()

Lastly, to add labels for the x axis, add the following line before plt.show():

plt.xlabel("Year")

Last but not least, let’s add a simple title to our plot:

plt.title("Movie Statistics")

Therefore, our final code is

import matplotlib.pyplot as plt

year_list = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020]
num_movies = [1251, 1287, 1494, 1419, 1514, 3009, 3506, 3607, 3885, 3961, 506]
money_list = [2540, 2742, 3158, 2972, 2995, 3597, 3690, 3789, 3826, 3769, 70]

plt.plot(year_list, num_movies, label="number of movies")
plt.plot(year_list, money_list, label="money (in 10^7 dollars)")
plt.legend()
plt.xlabel("Year")
plt.title("Movie Statistics")
plt.show()

That’s it for plotting! Feel free to include additional data to visualize.

Please save your code in a file named lab04_plot.py and submit it in gradescope along with other files you complete in this lab.

Applications

Let us now switch gears and look at the financial application of what we are learning. Note that when you compute the savings and earnings using the functions below, you can use matplotlib to visualize the amounts per month and per year. We will leave it up to you to play around with those in your lab04_plot.py file.

The following functions should be in a separate file called lab04.py.

Applications : Continuously Compounded Interest

Suppose we decide to invest some money in an account that continously compounds interest. In other words, the amount that we initially invested is constantly earning interest and any interest that we earned also keeps acquiring interest.

Update 3/9/2020: The interest rate that you are given is an annual rate, e.g., 5% or 7.5%. Before the first month, you only have the initial amount that you contributed in your account (e.g., 100 dollars).

At first, let’s compute our earnings in the short term. Suppose you save $100 each month into a savings account that has an annual interest rate of 5%. So, the monthly interest rate is $0.05 / 12 = 0.00417$. After the first month, the value in the account becomes

After the second month, the value in the account becomes

After the third month, the value in the account becomes

and so on.

Before you begin writing any code, try writing out the pseudocode for your function. Think about how you would calculate the compound interest if you did the math by hand and use this to help you in the implementation.

Write a function savings that computes and returns the savings amount after the given month, given a monthly contribution amount (e.g., 100), the annual interest rate (e.g., 5), and the number of months (e.g., 6), .

Use the while loop to implement this function.

def savings(amount, interest_rate, months):
        '''
        Given a monthly contribution amount (e.g., 100), 
        the annual interest rate (e.g., 5), 
        and the number of months (e.g., 6), 
        returns the savings amount after 
        the given month.
        '''

        return "stub"   # TODO: replace return "stub" with a correct return statement

Now, write a new function savingsByMonth() that will save each month’s savings as a new element in the list, which gets returned from the function. So, in the example above, the list would have the initial amount stored as the first element, 100.417 as the second element, etc.

def savingsByMonth(amount, interest_rate, months):
        '''
        Given a monthly contribution amount (e.g., 100), 
        the annual interest rate (e.g., 5), 
        and the number of months (e.g., 6), 
        returns a list with the savings amount 
        for each month, including the initial amount
        as the first element, and the savings in
        the given month as the last element.
        '''

        return "stub"   # TODO: replace return "stub" with a correct return statement

Now that you have the list, you can switch to your lab04_plot.py and use the matplotlib package to visualize the earnings.

Continuously Compounded Interest

The formula for continously compounded interest is modeled by $A = Pe^{Rt}$, where $A$ is the amount earned, $P$ is the principal, which is our initial investment, $e$ is the Euler’s constant, $R$ is the annual rate of interest, and $t$ is time in years.

def compound_interest(principal, interest_rate, time):
        '''
        - Given an initial investment (principal),
        return the amount earned using the formula
        for continously compounded interest:
        A = P*e**(R*t), where 
        A = the amount earned,
        P = the principal (initial investment), 
        e = the Euler's constant, 
        R = the annual rate of interest, and
        t = time in years
        '''

        return "stub"   # TODO: replace return "stub" with a correct return statement

Suppose we decide to invest 50,000 dollars at the bank of CS8. The bank offers an interest rate of 8.0%. Assuming that our investment continously compounds interest, compute the amount of money earned after 10 years (use import math to be able to use math.e).

As always, write pytest functions to verify that your function produces correct values.

Progressive Taxation

Now that we’ve made so much money with our investment, it’s time to pay taxes on it.

Write a function with a parameter income that calculates the amount of income tax owed according to the specified tax brackets below:

How Tax Brackets Work

A tax bracket is a range of income based on an income cap. Each bracket is taxed at a different marginal tax rate, meaning that only the part of your income that falls within a specific tax bracket gets taxed by the corresponding marginal tax rate for that tax bracket.

For example,

• if income = $150,000, the first $10,000 that fall in the tax bracket [0, 10000] would be taxed at 0%,
• the next $30,000 that fall in the tax bracket (10000, 40000] would be taxed at 12%,
• the next $45,000 that fall in the tax bracket (40000, 85000) would be taxed at 22%, and

• the remaining $65,000 that fall in the tax bracket (85000, 163000] would be taxed at 24%.

  Your total tax owed would be the sum of the tax amounts at each tax bracket. So if income = $150,000, then tax owed = (30,000 * 0.12) + (45,000 * 0.22) + (65,000 * 0.24) = $29100.

For more information on how tax brackets work, read more here.

• This function could be implemented with a while loop or with a series of if or if/elif/else statements. You can decide how you want to implement the function. (Note: you might find that this function is much more straight forward if you implement it using if statesments (or if/elif/else).)
• Before you begin writing any code, try writing out the pseudocode for your function. Think about how you would calculate the taxed owed if you did the math by hand and use this to help you in the implementation.

#income cap         marginal tax rate
# [0, 10000]           0.00 (0%)
# (10000, 40000]        0.12 (12%)
# (40000, 85000]        0.22 (22%)
# (85000, 163000]       0.24 (24%)
# (163000, 200000]      0.32 (32%)
# (200000, 500000]      0.35 (35%)
# (500000, 100000000]   0.37 (37%)

def tax(income):
        '''
        - Given an income amount as a whole number 
        where 0 <= income <= 100,000,000 , calculate 
        the amount of tax owed according to the tax brackets above.
        Return the total tax owed.
        - Example: if income = 70000, then 
        tax owed = 30000 * 0.12 + (income - 40000) * 0.22
        '''

        return "stub"   # TODO: replace return "stub" with a correct return statement

Starter code for the practice function

This is the end of the required/graded portion of the lab.

The functions below are designed to get you practicing using the concepts of while loops, conditionals, accumulator pattern, writing functions.

def volleyballset():
        '''
        -This function roughly stimulates a volleyball game 
         between two teams. 
        -The team that reaches 25 points first wins.
        -The score is updated randomly through the use of the
         random number generator.
        -If the number generated is even, add one point to the first team.
        -If the number is odd, add one point to the second team.
        -Whichever team reaches 25 points first win.s
         print("team ___ wins with a score of " + score) 
         along with their score (which should be 25) 
         Also print the score of the losing team
        print("team ___ loses with a score of " + score) 
         along with their score.
        Hint: you need two different scores
        Hint: use a while loop to keep going until a team reaches 25
        Hint: use random number generator to generate a number 
        '''
        
def guessinggame():
        '''
        -This function stimulates a guessing game.
        -First, generate a random number between 0 and 100
        -Then prompt the user to enter a number 
         input("Enter a number between 0 and 100: ")
        -The user will keep guessing a number until 
         they correctly guess the one generated
        by the random number generator
        -If the number they guess is too low print 
         "Your number was too low. Try again!"
        -If the number they guess is too high print 
         "Your number was too high. Try again!"
        -Once they guess the right number print 
         "Good Job! You guessed the right number!"
        Hint: make sure you store the value that the user inputs 
        '''     

Final Step: Log Out

Acknowledgments: Special thanks to Sara Mandic, April Sanchez, Radha Kumaran, and Sherry Chen who helped create this lab.