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Homework 1

Instructions

Obtain the GitHub repository you will use to complete the homework assignment, which contains the starter Jupyter notebook file homework1.ipynb. The notebook template provides space for you to answer each question. Your notebook should run without error when you select Restart Kernel and Run All Cells:

When you’re done, save your file, then stage, commit, and push (upload) it to GitHub, and then follow the instructions in the How to submit section.

Questions

  1. Create variables that are assigned the following values:

    1. A list called ages with values 19, 21, 21, and 20.

    2. A list called names with three values “Ruth,” “Callixte,” and “Talishia.”

  2. Define a function named sine_compute that takes x as input and returns the value of the mathematical expression 3\sin(x-1)+2. Evaluate sine_compute when x=5.

  3. Assign 1 to a variable named d. Then, in a loop that executes 10 times, update the value of d to be double what it was before the previous iteration. Before executing the loop, determine the final value by hand so you can check your work (write this out in a Markdown block). Then test your code, and type print(d) to display d’s final value to check your work.

  4. The following code computes a distance and a time for several steps in a loop and prints the results:

    import math  # only needed if math hasn't been imported yet

dist = 0
for i in range(1, 8):
    dist += 2.25
    time = (24.5 - math.sqrt(600.25 - 19.6 * dist)) / 9.8
    print("For distance {0}, time = {1}".format(dist, time))

    Copy this code into your notebook and run it to see the output. Next, modify the code so that you do not need to initialize dist with dist = 0, but will still get the same results.

  5. Define a function called ln_compute that returns the value of the mathematical expression \ln(3x+2). Then, write a loop that creates a variable k that takes on integer values from 1 through 8. Inside the loop, print the value of k and ln_compute(k) in the style of the print() statement used in question 4.

  6. Create the following numpy arrays and assign them each to a unique variable. Only the first exercise can be created manually, the rest must use function(s) to generate the sequence (in some instances, you may need to generate sequences individually and join them afterwards).

    1. Manually create a numpy array with the numbers 47, 35, 22, and 10.

    2. Generate a numpy array with the numbers 1 through 12.

    3. Generate a numpy array with the numbers 4, 8, 12, 16, …, 84.

    4. Generate a numpy array with eleven 3’s followed by eleven 4’s followed by twelve 5’s.

    5. Generate a numpy array with the numbers 7, 6, 5, …, 1, 19, 2, 4, 6, 8, …, 30.

  7. The code snippet below generates the temperatures matrix:

    import numpy as np  # only if numpy hasn't been imported

t = [57, 64, 88, 81, 61, 88, 86, 76, 63, 89, 70, 76]
temperatures = np.reshape(t, newshape=(3, 4))

    Slice the numpy array to return each of the following. Remember, Python starts indexing from 0, meaning row 1 is index 0!

    1. The element at row 3, column 3.

    2. The element at row 2, column 1.

    3. The entire 3rd row.

    4. The entire 2nd column.

    5. Columns 2 through 4 of rows 1 and 3.

  8. The code snippet below generates the air_pressure matrix:

    import numpy as np  # only if numpy hasn't been imported

air_pressure = np.ones((5, 5, 3))
air_pressure[:, :, 1] = 0.99
air_pressure[:, :, 2] = 0.98

    “Height” is what we call the third index. Slice the numpy array to return each of the following. Remember, Python starts indexing from 0, meaning row 1 is index 0!

    1. The element at row 3, column 3 at height 3.

    2. The element at row 4, column 2 at height 1.

    3. The entire 3rd row for all columns and heights.

    4. All rows and columns for the lowest height.

    5. All heights for row 4, columns 2 through 5.

  9. Perform the following vector operations

    1. With one assignment statement, make my_matrix be a 2-by-4 matrix of all zeros.

    2. With one assignment statement, make the first row of my_matrix be the sequence of positive integers 1, 3, 5, 7.

    3. Return the product of 3 by every element of my_matrix without changing my_matrix.

    4. Return the square root of every element of my_matrix without changing my_matrix (hint, numpy has its own version of square root).

    5. Add 2 to every element of my_matrix, changing the value of my_matrix to hold those increased numbers.

  10. Use list comprehensions to a “list of lists” named pairs_list containing a column of x-values, which are positive integers from 1 through 9, and a second column with values of 3\sqrt{x}, where the x is taken from the first column.

  11. Create a new file named rectangle.py in the same directory as your Jupyter notebook. In this file, define a function called circumference that returns the circumference of a rectangle with parameters for length and width, l and w, respectively. Save the file. Then, in your Jupyter notebook, import the file you created and test the function you just defined by having it return the circumference of a rectangle with dimensions 3 and 4.2, respectively.

  12. Compute the following matrix-vector exercises using numpy:

    1. Generate a 4-by-2 matrix mA, where the i - j element is the sum of i and j. For example, after forming mA, mA[3, 2] should be 5, which is 3 + 2.

    2. Generate a 4-by-2 matrix mO of all ones.

    3. Give matrix sum of mA and mO.

    4. Define a one-dimensional array u with elements 2 and 7.

    5. Define a one-dimensional array v with elements 5 and 3.

    6. Compute the dot product of u and v.

    7. Generate a 2-by-3 matrix mB, where the i - j element is the difference of i and j, i - j.

    8. Give the matrix product of mA and mB.

  13. Use matplotlib to plot the function e^{\sin(x)} from -3 to 3, where x is stepped through in increments of 0.1. Label the x axis as t and the y axis as e^{\sin(x)}.

  14. Load the provided iris.csv file into Pandas and write code that reproduces the following plot:

    Hint: For some relevant examples, take a look at https://scipython.com/book/chapter-7-matplotlib/examples/.

  15. Load the provided gapminder_all.csv file into Pandas. Determine which countries saw the largest increase and the largest decrease in life expectancy between 1987 and 1992.

How to submit

To lock in your submission time, export your notebook to PDF and upload the PDF file to the assignment posting on Blackboard.

In addition, be sure to save, commit, and push your final result so that everything is synchronized to GitHub. I may want to inspect your source files directly and run your notebook, so it’s very important that the files in your homework repository match what I see in the PDF export uploaded to Blackboard.