3. An Introductory Example

3.1. Overview

We are now ready to begin learning the Python language.

In this lecture, we will create and analyze small Python programs.

Our goal is to introduce you to fundamental Python syntax and data structures.

More advanced topics will be covered in future lectures.

Make sure you have read the lecture lecture before starting this one.

3.2. The Task: Plotting a Sine Function

Here our goal is to plot Sin(x) where x get the values in the range [0,\(2\pi\)]

Here are a few lines of code that perform the task we set

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 2 * np.pi, 1000) # Generate a range of values from 0 to 2π (approximately 6.28)

y = np.sin(x) # Calculate the sine of each value in x

plt.plot(x, y) # Create a plot
plt.show()  # Display the plot

Let’s break this program down and see how it works.

3.2.1. Imports

The first two lines of the program import functionality from external code libraries.

The first line imports NumPy, a favorite Python package for tasks like

• working with arrays (vectors and matrices)

• common mathematical functions like cos and sqrt

• generating random numbers

• linear algebra, etc.

After import numpy as np we have access to these attributes via the syntax np.attribute.

Here’s two more examples

np.sqrt(4)

2.0

np.log(4)

1.3862943611198906

3.2.1.1. Why So Many Imports?

Python programs typically require multiple import statements.

The reason is that the core language is deliberately kept small, so that it’s easy to learn, maintain and improve.

When you want to do something interesting with Python, you almost always need to import additional functionality.

3.2.1.2. Packages

As stated above, NumPy is a Python package.

Packages are used by developers to organize code they wish to share.

In fact, a package is just a directory containing

1. files with Python code — called modules in Python speak

2. possibly some compiled code that can be accessed by Python (e.g., functions compiled from C or FORTRAN code)

3. a file called __init__.py that specifies what will be executed when we type import package_name

You can check the location of your __init__.py for NumPy in python by running the code:

import numpy as np

print(np.__file__)

3.2.1.3. Subpackages

Consider the line x = np.linspace(0, 2 * np.pi, 1000).

Here np refers to the package NumPy, while linspace is a subpackage of NumPy.

Subpackages are just packages that are subdirectories of another package.

For instance, you can find folder linspace under the directory of NumPy.

3.2.2. Importing Names Directly

Recall this code that we saw above

import numpy as np

np.sqrt(4)

2.0

Here’s another way to access NumPy’s square root function

from numpy import sqrt

sqrt(4)

2.0

This is also fine.

The advantage is less typing if we use sqrt often in our code.

The disadvantage is that, in a long program, these two lines might be separated by many other lines.

Then it’s harder for readers to know where sqrt came from, should they wish to.

3.2.3. Evenly spaced numbers over a specified interval and evaluate output at these generated numbers

Returning to our program that plots Sine function, the remaining lines after the import statements are

x = np.linspace(0, 2 * np.pi, 1000)
y = np.sin(x)
plt.plot(x, y)
plt.show()

The first line return 1000 evenly spaced numbers over [0,\(2\pi\)] interval.

The next line compute the value of Sine function over each of the 1000 numbers in the interval

The next two lines genererate the plot.