Joseph Kliegman / Nov 15 2018

Python Crash Course

Hello! This is a quick intro to programming in Python to help you hit the ground running with the 12 Steps to Navier–Stokes.

There are two ways to enjoy these lessons with Python:

  • You can download and install a Python distribution on your computer. One option is the free Anaconda Scientific Python distribution. Another is Canopy, which is free for academic use. Our recommendation is Anaconda.

  • You can run Python in the cloud using Wakari web-based data analysis, for which you need to create a free account. (No software installation required!)

In either case, you will probably want to download a copy of this notebook, or the whole AeroPython collection. We recommend that you then follow along each lesson, experimenting with the code in the notebooks, or typing the code into a separate Python interactive session.

If you decided to work on your local Python installation, you will have to navigate in the terminal to the folder that contains the .ipynb files. Then, to launch the notebook server, just type: ipython notebook

You will get a new browser window or tab with a list of the notebooks available in that folder. Click on one and start working!


Python is a high-level open-source language. But the Python world is inhabited by many packages or libraries that provide useful things like array operations, plotting functions, and much more. We can import libraries of functions to expand the capabilities of Python in our programs.

OK! We'll start by importing a few libraries to help us out. First: our favorite library is NumPy, providing a bunch of useful array operations (similar to MATLAB). We will use it a lot! The second library we need is Matplotlib, a 2D plotting library which we will use to plot our results. The following code will be at the top of most of your programs, so execute this cell first:

# <-- comments in python are denoted by the pound sign, like this one

import numpy                 # we import the array library
from matplotlib import pyplot    # import plotting library

We are importing one library named numpy and we are importing a module called pyplot of a big library called matplotlib. To use a function belonging to one of these libraries, we have to tell Python where to look for it. For that, each function name is written following the library name, with a dot in between. So if we want to use the NumPy function linspace(), which creates an array with equally spaced numbers between a start and end, we call it by writing:

myarray = numpy.linspace(0, 5, 10)

If we don't preface the linspace() function with numpy, Python will throw an error.

#myarray = linspace(0, 5, 10)

The function linspace() is very useful. Try it changing the input parameters!

Import style:

You will often see code snippets that use the following lines

import numpy as np import matplotlib.pyplot as plt

What's all of this import-as business? It's a way of creating a 'shortcut' to the NumPy library and the pyplot module. You will see it frequently as it is in common usage, but we prefer to keep out imports explicit. We think it helps with code readability.

Pro tip:

Sometimes, you'll see people importing a whole library without assigning a shortcut for it (like from numpy import *). This saves typing but is sloppy and can get you in trouble. Best to get into good habits from the beginning!

To learn new functions available to you, visit the NumPy Reference page. If you are a proficient Matlab user, there is a wiki page that should prove helpful to you: NumPy for Matlab Users


Python doesn't require explicitly declared variable types like C and other languages.

a = 5        #a is an integer 5
b = 'five'   #b is a string of the word 'five'
c = 5.0      #c is a floating point 5  

Note that if you divide an integer by an integer that yields a remainder, the result will be converted to a float. (This is different from the behavior in Python 2.7, beware!)

Whitespace in Python

Python uses indents and whitespace to group statements together. To write a short loop in C, you might use:

for (i = 0, i < 5, i++){ printf("Hi! \n"); }

Python does not use curly braces like C, so the same program as above is written in Python as follows:

for i in range(5):
    print("Hi \n")

If you have nested for-loops, there is a further indent for the inner loop.

for i in range(3):
    for j in range(3):
        print(i, j)
    print("This statement is within the i-loop, but not the j-loop")

Slicing Arrays

In NumPy, you can look at portions of arrays in the same way as in Matlab, with a few extra tricks thrown in. Let's take an array of values from 1 to 5.

myvals = numpy.array([1, 2, 3, 4, 5])

Python uses a zero-based index, so let's look at the first and last element in the array myvals

myvals[0], myvals[4]

There are 5 elements in the array myvals, but if we try to look at myvals[5], Python will be unhappy, as myvals[5] is actually calling the non-existant 6th element of that array.


Arrays can also be 'sliced', grabbing a range of values. Let's look at the first three elements


Note here, the slice is inclusive on the front end and exclusive on the back, so the above command gives us the values of myvals[0], myvals[1] and myvals[2], but not myvals[3].

Assigning Array Variables

One of the strange little quirks/features in Python that often confuses people comes up when assigning and comparing arrays of values. Here is a quick example. Let's start by defining a 1-D array called aa:

a = numpy.linspace(1,5,5)

OK, so we have an array aa, with the values 1 through 5. I want to make a copy of that array, called bb, so I'll try the following:

Great. So aa has the values 1 through 5 and now so does bb. Now that I have a backup of aa, I can change its values without worrying about losing data (or so I may think!).

a[2] = 17

Here, the 3rd element of aa has been changed to 17. Now let's check on bb.

And that's how things go wrong! When you use a statement like a=ba = b, rather than copying all the values of aa into a new array called bb, Python just creates an alias (or a pointer) called bb and tells it to route us to aa. So if we change a value in aa then bb will reflect that change (technically, this is called assignment by reference). If you want to make a true copy of the array, you have to tell Python to copy every element of aa into a new array. Let's call it cc.

c = a.copy()

Now, we can try again to change a value in aa and see if the changes are also seen in cc.

a[2] = 3

OK, it worked! If the difference between a = b and a = b.copy() is unclear, you should read through this again. This issue will come back to haunt you otherwise.

Learn More

There are a lot of resources online to learn more about using NumPy and other libraries. Just for kicks, here we use Jupyter's feature for embedding videos to point you to a short video on YouTube on using NumPy arrays.

from IPython.display import YouTubeVideo
# a short video about using NumPy arrays, from Enthought
#from IPython.core.display import HTML
#def css_styling():
#    styles = open("../styles/custom.css", "r").read()
#    return HTML(styles)