Reading: NumPy Library

Pre-Class Reading Assignment

On the O'Reilly's website read part II: Intro to NumPy and chapters 4, 5, 6, 7, and 11 in Python Data Science Handbook, 2nd Edition.
Here is a direct link to the readings:

Part II: Introduction to NumPy
Chapter 4: Understanding Data Types in Python
Chapter 5: The Basics of NumPy Arrays
Chapter 6: Computation on NumPy Arrays: Universal Functions
Note: For chapter 6, read up to but not including the section Specialized Ufuncs. Skip the rest.
Chapter 7: Aggregations — min, max, and everything in between
Chapter 11: Sorting Arrays

The chapters we skip are about indexing and broadcasting, which we will not cover in this class. We will typically use NumPy arrays like a spreadsheet, where we just want to access the entire row or column of data. We will not be using the more advanced indexing features of NumPy.

You may want to skim through Chapter 9. Comparisons, Masks, and Boolean Logic, while the topics aren't required for this class - they are useful.

Chapter 9: Comparisons, Masks, and Boolean Logic

Remember that you will have to sign in to your free account that you created earlier.

Things to look out for

What is the difference between a list and a NumPy array?
How to turn a list into a NumPy array?
How to append 2 NumPy arrays together?
The different functions you can do with a NumPy array

NumPy Vectorization

Vectorization is a powerful feature of NumPy that allows you to perform operations on entire arrays without the need for explicit loops. This can lead to more concise and efficient code.

import numpy as np
# Create two NumPy arrays
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
# Perform element-wise addition
c = a + b
print(c)  # Output: [5 7 9]

In python, you would need to loop through the arrays to add them together. With NumPy, you can add the arrays together without a loop.

It also works with other math operations like multiplication, division, and subtraction.

# Perform element-wise multiplication
d = a * b
print(d)  # Output: [ 4 10 18]
# Perform element-wise division
e = a / b
print(e)  # Output: [0.25 0.4  0.5 ]

NumPy Functions

NumPy also has a lot of built-in functions that you can use to perform operations on arrays. For example, you can find the mean of an array using the np.mean() function or more advanced things like taking the sin or cos of the numbers in an array using np.sin().

Normally you would need a loop to do this, but with NumPy, you can do it in one line of code.

# Find the mean of an array
mean_a = np.mean(a)
print(mean_a)  # Output: 2.0
# Find the sin of an array
sin_a = np.sin(a)
print(sin_a)  # Output: [0.84147098 0.90929743 0.14112001]

Here is a link to the NumPy website that lists all the mathematical functions you can use with NumPy arrays: NumPy Mathematical Functions

Here is a link to the NumPy website that lists all the statistical functions you can use with NumPy arrays: NumPy Statistical Functions
Here is a link to the NumPy website that lists all the linear algebra functions you can use with NumPy arrays: NumPy Linear Algebra Functions

Create NumPy Sequences

You often need a list of numbers, such as a list of numbers from 0 to 10. You can use the np.arange() function to create a NumPy array with a sequence of numbers.

# Create a NumPy array with a sequence of numbers from 0 to 10
sequence = np.arange(0, 10, 2)
print(sequence)  # Output: [0 2 4 6 8]

In the code above you give the starting value, stopping value, and step size. The function will then create an array with that many values between the starting and stopping values. If the step size doesn't fit, you may not get the last number.

You can also use the np.linspace() function to create a NumPy array with a specific number of numbers between two values.

# Create a NumPy array with a sequence of numbers between 0 and 1
sequence = np.linspace(0, 1, 5)
print(sequence)  # Output: [0.   0.25 0.5  0.75 1.  ]

In the code above you give the starting and stopping values and the number of values you want in the array. The function will then create an array with that many values between the starting and stopping values.

Here is a link to the NumPy website that lists all the functions you can use to create NumPy arrays: NumPy Array Creation Functions.

The section on Numeric Ranges is particularly useful for creating sequences of numbers.

Generate random numbers

You can also use the np.random.rand() function to create a NumPy array with random numbers.

# Create a NumPy array with random numbers
random_numbers = np.random.rand(5)
print(random_numbers)  # Output: [0.5488135  0.71518937 0.60276338 0.54488318 0.4236548 ]

You can also use the np.random.randint() function to create a NumPy array with random integers. If you run it again, you will get different numbers.

# Create a NumPy array with random integers
random_integers = np.random.randint(0, 10, 5)
print(random_integers)  # Output: [5 0 3 3 7]

And there are other functions you can use to create NumPy arrays with random numbers. Here is a link to the NumPy website that lists all the functions you can use to create NumPy arrays: NumPy Random Functions

NumPy with Matplotlib

We can use NumPy with Matplotlib to create plots. For example, we can use NumPy to create a list of numbers and then use Matplotlib to plot those numbers. We can use the numpy routines to easily create the data we want to plot. For example if we want to plot the sin, cos, and tan of a list of numbers, we can use NumPy to create the list of numbers and then use Matplotlib to plot the data. Say we want a list of number from 0 to 3*360 degrees every 0.5 degrees. We can use the np.linspace() function to create the list of numbers. Then we can use the np.sin() and np.cos() functions to create the data we want to plot. Finally, we can use Matplotlib to plot the data.

import numpy as np
import matplotlib.pyplot as plt
# Create a list of numbers from 0 to 3*360 degrees with 1000 points.
x = np.linspace(0, 3*360, 1000)
# Or use arange to create a list with steps every 1/2 degree
x = np.arange(0, 3*360, 0.5)  # This will overwrite the previous x variable. Comment it out if you want to use the linspace version.

# Create the data we want to plot
y1 = np.sin(np.radians(x))
y2 = np.cos(np.radians(x))

# Plot the data
plt.plot(x, y1, label='sin')
plt.plot(x, y2, label='cos')

plt.xlabel('Degrees')
plt.ylabel('Value')
plt.title('Sin and Cos')
plt.legend()
plt.show()

In the code above we use the np.radians() function to convert the degrees to radians. This is because the np.sin() and np.cos() functions expect the input to be in radians. We then use Matplotlib to plot the data.

Here is a link to the Matplotlib website that lists all the functions you can use to create plots: Matplotlib Pyplot

Pre-Class Quiz Challenge

Open the following notebook and complete the instructions in the comments:

Rename it something like "(Your_Name)_Pre_Numpy.ipynb"

Save changes to your Google Drive and submit the link to the notebook in your Pre-Class Quiz.

Turning in/Rubric

REMINDER - For this class, you will only turn in the links to your colab notebooks. You will get a 0 for this assignment if you turn in a python file or a link that is not correct, wrong assignment, or does not give editor permission.

Rubric:

Item	Points Possible
Total	3

The following is not a part of the rubric, but specifies how you can lose points. For example: if you fail to share your link correctly.

Reasons for Points Lost	Amount
Link shared incorrectly	-10%