Exercises

Last updated on 2026-03-31 | Edit this page

Overview

Questions

  • How much did I learn over the past two days?

Objectives

  • Test your knowledge on these tasks
Challenge

Sorting Out References

Python allows you to assign multiple values to multiple variables in one line by separating the variables and values with commas. What does the following program display to the console?

PYTHON 

first, second = 'Grace', 'Hopper'
third, fourth = second, first
print(third, fourth)

OUTPUT 

Hopper Grace
Challenge

Seeing Data Types

What are the data types of the following variables?

PYTHON 

planet = 'Earth'
apples = 5
distance = 10.5

PYTHON 

print(type(planet))
print(type(apples))
print(type(distance))

OUTPUT 

<class 'str'>
<class 'int'>
<class 'float'>
Challenge

Slicing Strings

A section of an array is called a slice. We can take slices of character strings as well:

PYTHON 

element = 'oxygen'
print('first three characters:', element[0:3])
print('last three characters:', element[3:6])

OUTPUT 

first three characters: oxy
last three characters: gen

What is the value of element[:4]? What about element[4:]? Or element[:]?

OUTPUT 

oxyg
en
oxygen
Challenge

Slicing Strings (continued)

What is element[-1]? What is element[-2]?

OUTPUT 

n
e
Challenge

Slicing Strings (continued)

Given those answers, explain what element[1:-1] does.

Creates a substring from index 1 up to (not including) the final index, effectively removing the first and last letters from ‘oxygen’

Challenge

Slicing Strings (continued)

How can we rewrite the slice for getting the last three characters of element, so that it works even if we assign a different string to element? Test your solution with the following strings: carpentry, clone, hi.

PYTHON 

element = 'oxygen'
print('last three characters:', element[-3:])
element = 'carpentry'
print('last three characters:', element[-3:])
element = 'clone'
print('last three characters:', element[-3:])
element = 'hi'
print('last three characters:', element[-3:])

OUTPUT 

last three characters: gen
last three characters: try
last three characters: one
last three characters: hi
Challenge

Overloading

+ usually means addition, but when used on strings or lists, it means “concatenate”. Given that, what do you think the multiplication operator * does on lists? In particular, what will be the output of the following code?

PYTHON 

counts = [2, 4, 6, 8, 10]
repeats = counts * 2
print(repeats)
  1. [2, 4, 6, 8, 10, 2, 4, 6, 8, 10]
  2. [4, 8, 12, 16, 20]
  3. [[2, 4, 6, 8, 10], [2, 4, 6, 8, 10]]
  4. [2, 4, 6, 8, 10, 4, 8, 12, 16, 20]

The technical term for this is operator overloading: a single operator, like + or *, can do different things depending on what it’s applied to.

The multiplication operator * used on a list replicates elements of the list and concatenates them together:

OUTPUT 

[2, 4, 6, 8, 10, 2, 4, 6, 8, 10]

It’s equivalent to:

PYTHON 

counts + counts
Challenge

Thin Slices

The expression element[3:3] produces an empty string, i.e., a string that contains no characters. If data holds our array of patient data, what does data[3:3, 4:4] produce? What about data[3:3, :]?

OUTPUT 

array([], shape=(0, 0), dtype=float64)
array([], shape=(0, 40), dtype=float64)
Challenge

Stacking Arrays

Arrays can be concatenated and stacked on top of one another, using NumPy’s vstack and hstack functions for vertical and horizontal stacking, respectively.

PYTHON 

import numpy

A = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print('A = ')
print(A)

B = numpy.hstack([A, A])
print('B = ')
print(B)

C = numpy.vstack([A, A])
print('C = ')
print(C)

OUTPUT 

A =
[[1 2 3]
 [4 5 6]
 [7 8 9]]
B =
[[1 2 3 1 2 3]
 [4 5 6 4 5 6]
 [7 8 9 7 8 9]]
C =
[[1 2 3]
 [4 5 6]
 [7 8 9]
 [1 2 3]
 [4 5 6]
 [7 8 9]]

Write some additional code that slices the first and last columns of A, and stacks them into a 3x2 array. Make sure to print the results to verify your solution.

A ‘gotcha’ with array indexing is that singleton dimensions are dropped by default. That means A[:, 0] is a one dimensional array, which won’t stack as desired. To preserve singleton dimensions, the index itself can be a slice or array. For example, A[:, :1] returns a two dimensional array with one singleton dimension (i.e. a column vector).

PYTHON 

D = numpy.hstack((A[:, :1], A[:, -1:]))
print('D = ')
print(D)

OUTPUT 

D =
[[1 3]
 [4 6]
 [7 9]]

An alternative way to achieve the same result is to use Numpy’s delete function to remove the second column of A. If you’re not sure what the parameters of numpy.delete mean, use the help files.

PYTHON 

D = numpy.delete(arr=A, obj=1, axis=1)
print('D = ')
print(D)

OUTPUT 

D =
[[1 3]
 [4 6]
 [7 9]]
Challenge

Change In Inflammation

The patient data is longitudinal in the sense that each row represents a series of observations relating to one individual. This means that the change in inflammation over time is a meaningful concept. Let’s find out how to calculate changes in the data contained in an array with NumPy.

The numpy.diff() function takes an array and returns the differences between two successive values. Let’s use it to examine the changes each day across the first week of patient 3 from our inflammation dataset.

PYTHON 

patient3_week1 = data[3, :7]
print(patient3_week1)

OUTPUT 

 [0. 0. 2. 0. 4. 2. 2.]

Calling numpy.diff(patient3_week1) would do the following calculations

PYTHON 

[ 0 - 0, 2 - 0, 0 - 2, 4 - 0, 2 - 4, 2 - 2 ]

and return the 6 difference values in a new array.

PYTHON 

numpy.diff(patient3_week1)

OUTPUT 

array([ 0.,  2., -2.,  4., -2.,  0.])

Note that the array of differences is shorter by one element (length 6).

When calling numpy.diff with a multi-dimensional array, an axis argument may be passed to the function to specify which axis to process. When applying numpy.diff to our 2D inflammation array data, which axis would we specify?

Since the row axis (0) is patients, it does not make sense to get the difference between two arbitrary patients. The column axis (1) is in days, so the difference is the change in inflammation – a meaningful concept.

PYTHON 

numpy.diff(data, axis=1)
Challenge

Change In Inflammation (continued)

If the shape of an individual data file is (60, 40) (60 rows and 40 columns), what would the shape of the array be after you run the diff() function and why?

The shape will be (60, 39) because there is one fewer difference between columns than there are columns in the data.

Challenge

Change In Inflammation (continued)

How would you find the largest change in inflammation for each patient? Does it matter if the change in inflammation is an increase or a decrease?

By using the numpy.amax() function after you apply the numpy.diff() function, you will get the largest difference between days.

PYTHON 

numpy.amax(numpy.diff(data, axis=1), axis=1)

PYTHON 

array([  7.,  12.,  11.,  10.,  11.,  13.,  10.,   8.,  10.,  10.,   7.,
         7.,  13.,   7.,  10.,  10.,   8.,  10.,   9.,  10.,  13.,   7.,
        12.,   9.,  12.,  11.,  10.,  10.,   7.,  10.,  11.,  10.,   8.,
        11.,  12.,  10.,   9.,  10.,  13.,  10.,   7.,   7.,  10.,  13.,
        12.,   8.,   8.,  10.,  10.,   9.,   8.,  13.,  10.,   7.,  10.,
         8.,  12.,  10.,   7.,  12.])

If inflammation values decrease along an axis, then the difference from one element to the next will be negative. If you are interested in the magnitude of the change and not the direction, the numpy.absolute() function will provide that.

Notice the difference if you get the largest absolute difference between readings.

PYTHON 

numpy.amax(numpy.absolute(numpy.diff(data, axis=1)), axis=1)

PYTHON 

array([ 12.,  14.,  11.,  13.,  11.,  13.,  10.,  12.,  10.,  10.,  10.,
        12.,  13.,  10.,  11.,  10.,  12.,  13.,   9.,  10.,  13.,   9.,
        12.,   9.,  12.,  11.,  10.,  13.,   9.,  13.,  11.,  11.,   8.,
        11.,  12.,  13.,   9.,  10.,  13.,  11.,  11.,  13.,  11.,  13.,
        13.,  10.,   9.,  10.,  10.,   9.,   9.,  13.,  10.,   9.,  10.,
        11.,  13.,  10.,  10.,  12.])
Challenge

From 1 to N

Python has a built-in function called range that generates a sequence of numbers. range can accept 1, 2, or 3 parameters.

  • If one parameter is given, range generates a sequence of that length, starting at zero and incrementing by 1. For example, range(3) produces the numbers 0, 1, 2.
  • If two parameters are given, range starts at the first and ends just before the second, incrementing by one. For example, range(2, 5) produces 2, 3, 4.
  • If range is given 3 parameters, it starts at the first one, ends just before the second one, and increments by the third one. For example, range(3, 10, 2) produces 3, 5, 7, 9.

Using range, write a loop that prints the first 3 natural numbers:

PYTHON 

1
2
3

PYTHON 

for number in range(1, 4):
    print(number)
Challenge

Understanding the loops

Given the following loop:

PYTHON 

word = 'oxygen'
for letter in word:
    print(letter)

How many times is the body of the loop executed?

  • 3 times
  • 4 times
  • 5 times
  • 6 times

The body of the loop is executed 6 times.

Challenge

Computing Powers With Loops

Exponentiation is built into Python:

PYTHON 

print(5 ** 3)

OUTPUT 

125

Write a loop that calculates the same result as 5 ** 3 using multiplication (and without exponentiation).

PYTHON 

result = 1
for number in range(0, 3):
    result = result * 5
print(result)
Challenge

Summing a list

Write a loop that calculates the sum of elements in a list by adding each element and printing the final value, so [124, 402, 36] prints 562

PYTHON 

numbers = [124, 402, 36]
summed = 0
for num in numbers:
    summed = summed + num
print(summed)
Challenge

Computing the Value of a Polynomial

The built-in function enumerate takes a sequence (e.g. a list) and generates a new sequence of the same length. Each element of the new sequence is a pair composed of the index (0, 1, 2,…) and the value from the original sequence:

PYTHON 

for idx, val in enumerate(a_list):
    # Do something using idx and val

The code above loops through a_list, assigning the index to idx and the value to val.

Suppose you have encoded a polynomial as a list of coefficients in the following way: the first element is the constant term, the second element is the coefficient of the linear term, the third is the coefficient of the quadratic term, where the polynomial is of the form \(ax^0 + bx^1 + cx^2\).

PYTHON 

x = 5
coefs = [2, 4, 3]
y = coefs[0] * x**0 + coefs[1] * x**1 + coefs[2] * x**2
print(y)

OUTPUT 

97

Write a loop using enumerate(coefs) which computes the value y of any polynomial, given x and coefs.

PYTHON 

y = 0
for idx, coef in enumerate(coefs):
    y = y + coef * x**idx
Challenge

Plot Scaling

Why do all of our plots stop just short of the upper end of our graph?

Because matplotlib normally sets x and y axes limits to the min and max of our data (depending on data range)

Challenge

Plot Scaling (continued)

If we want to change this, we can use the set_ylim(min, max) method of each ‘axes’, for example:

PYTHON 

axes3.set_ylim(0, 6)

Update your plotting code to automatically set a more appropriate scale. (Hint: you can make use of the max and min methods to help.)

PYTHON 

# One method
axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))
axes3.set_ylim(0, 6)

PYTHON 

# A more automated approach
min_data = numpy.amin(data, axis=0)
axes3.set_ylabel('min')
axes3.plot(min_data)
axes3.set_ylim(numpy.amin(min_data), numpy.amax(min_data) * 1.1)
Challenge

Drawing Straight Lines

In the center and right subplots above, we expect all lines to look like step functions because non-integer values are not realistic for the minimum and maximum values. However, you can see that the lines are not always vertical or horizontal, and in particular the step function in the subplot on the right looks slanted. Why is this?

Because matplotlib interpolates (draws a straight line) between the points. One way to do avoid this is to use the Matplotlib drawstyle option:

PYTHON 

import numpy
import matplotlib.pyplot

data = numpy.loadtxt(fname='inflammation-01.csv', 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), drawstyle='steps-mid')

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0), drawstyle='steps-mid')

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0), drawstyle='steps-mid')

fig.tight_layout()

matplotlib.pyplot.show()
Three line graphs, with step lines connecting the points, showing the daily average, maximumand minimum inflammation over a 40-day period.
Challenge

Make Your Own Plot

Create a plot showing the standard deviation (numpy.std) of the inflammation data for each day across all patients.

PYTHON 

std_plot = matplotlib.pyplot.plot(numpy.std(data, axis=0))
matplotlib.pyplot.show()
Challenge

Moving Plots Around

Modify the program to display the three plots on top of one another instead of side by side.

PYTHON 

import numpy
import matplotlib.pyplot

data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')

# change figsize (swap width and height)
fig = matplotlib.pyplot.figure(figsize=(3.0, 10.0))

# change add_subplot (swap first two parameters)
axes1 = fig.add_subplot(3, 1, 1)
axes2 = fig.add_subplot(3, 1, 2)
axes3 = fig.add_subplot(3, 1, 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()
Challenge

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?

  1. 1234
  2. one2three4
  3. 1239
  4. SyntaxError

Given that, what does the following piece of code display when run?

PYTHON 

def func(a, b=3, c=6):
    print('a: ', a, 'b: ', b, 'c:', c)

func(-1, 2)
  1. a: b: 3 c: 6
  2. a: -1 b: 3 c: 6
  3. a: -1 b: 2 c: 6
  4. a: 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.

Discussion

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.

Challenge

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, as 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:

PYTHON 

def add(a, b):
    print(a + b)

Question: What will we see if we execute the following commands?

PYTHON 

A = add(7, 3)
print(A)

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 represented as 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
None
Challenge

Selecting 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:

PYTHON 

print(outer('helium'))

OUTPUT 

hm

PYTHON 

def outer(input_string):
    return input_string[0] + input_string[-1]
Challenge

Rescaling 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).)

PYTHON 

def rescale(input_array):
    L = numpy.amin(input_array)
    H = numpy.amax(input_array)
    output_array = (input_array - L) / (H - L)
    return output_array
Challenge

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.  ])
"""
Challenge

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_array
Challenge

Identifying Syntax Errors

  1. Read the code below, and (without running it) try to identify what the errors are.
  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.')

SyntaxError for missing (): at end of first line, IndentationError for mismatch between second and third lines. A fixed version is:

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.')
Challenge

Identifying Variable Name Errors

  1. Read the code below, and (without running it) try to identify what the errors are.
  2. Run the code, and read the error message. What type of NameError do you think this is? In other words, is it a string with no quotes, a misspelled variable, or a variable that should have been defined but was not?
  3. Fix the error.
  4. Repeat steps 2 and 3, until you have fixed all the errors.

PYTHON 

for number in range(10):
    # use a if the number is a multiple of 3, otherwise use b
    if (Number % 3) == 0:
        message = message + a
    else:
        message = message + 'b'
print(message)

3 NameErrors for number being misspelled, for message not defined, and for a not being in quotes.

Fixed version:

PYTHON 

message = ''
for number in range(10):
    # use a if the number is a multiple of 3, otherwise use b
    if (number % 3) == 0:
        message = message + 'a'
    else:
        message = message + 'b'
print(message)
Challenge

Identifying Index Errors

  1. Read the code below, and (without running it) try to identify what the errors are.
  2. Run the code, and read the error message. What type of error is it?
  3. Fix the error.

PYTHON 

seasons = ['Spring', 'Summer', 'Fall', 'Winter']
print('My favorite season is ', seasons[4])

IndexError; the last entry is seasons[3], so seasons[4] doesn’t make sense. A fixed version is:

PYTHON 

seasons = ['Spring', 'Summer', 'Fall', 'Winter']
print('My favorite season is ', seasons[-1])
Key Points
  • Practice makes perfect.