Introduction to Python

This set of course notes involves a mixture of theory and numerical examples demonstrated in Python. All examples, tutorials and project code will be provided in Python.

If you have never used Python before, I recommend that you use a Python IDE. This will help with organizing, running, and debugging your code. There are several Python IDEs that are available. I recoomend PyCharm, which can be downloaded here: https://www.jetbrains.com/pycharm/

One of the key advantages of Python is that it has many useful packages that can be easily installed. There are three critical ones that we’ll use a lot in the course: NumPy, SciPy and matplotlib.

  • NumPy is a package for fast, multi-dimensional arrays and matrices

  • SciPy is a package for scientific computing

  • matplotlib is a package for scientific visualization

In PyCharm, you can install and manage the packages in the Python Packages tab at the bottom of the window. Search for the package and install each one if you don’t have it installed already. You can also install packages using a package manager, like pip or conda.

A complete description on how to use PyCharm is located here: https://www.jetbrains.com/help/pycharm/quick-start-guide.html

For more generic information about Python, start here: https://www.python.org/about/gettingstarted/

Python basics

Python is an interpreted language, meaning that it is not compiled in advance. These notes use Python 3 exclusively. What you write in the file, gets interpreted and run on the command line.

  • In Python you don’t need to declare a variable before using it (Python is implicitly typed)

  • The print function is built-in and very useful

>>> a = 2
>>> a += 2
>>> a *= 4
>>> a -= 2
>>> print(a)
14

  • String manipulation is straight forward, you can concatenate strings using +

>>> a = 'Hello'
>>> b = a + ' World!'
>>> print(b)
Hello World!

  • You can format an output string, using the format command. This is helpful for controlling how floating point numbers are printed.

>>> pi = 3.141592653589793
>>> print('{}'.format(pi))
3.141592653589793
>>> print('{:.3f}'.format(pi))
3.142

  • Output can be formatted in very sophisticated ways. See this page for many more details: https://docs.python.org/3/library/string.html

  • Loops can be made using the range keyword. The function range can take one, two or three arguments range(stop) executes a loop terminating at the index stop-1. With two or three arguments, range starts from the provided index, and stops on the next to last index with step taken as the increment to the loop counter.

>>> for i in range(5):
...     print(i)
...
0
1
2
3
4

>>> start = 2
>>> end = 6
>>> for i in range(start, end):
...     print(i)
...
2
3
4
5

>>> for i in range(2, 8, 2):
...     print(i)
...
2
4
6

  • Logical conditions are straightforward in Python.

>>> a = 1
>>> b = 2
>>> c = 3
>>> if a == b:
...     print('a == b')
... elif a == c:
...     print('a == c')
... else:
...     print('a != b and b != c')
...
a != b and b != c

  • Python also has some built-in data types like lists and dictionaries that are helpful.

>>> if a >= b:
...     print('a >= b')
... elif a <= c:
...     print('a <= c')
... else:
...     print('!(a >= b and a <= c)')
...
a <= c

  • Boolean logic in python uses the keywords and and or:

>>> a = False
>>> b = True
>>> print(a and b)
False
>>> print(a and not b)
False
>>> print(not a and b)
True
>>> print(a or b)
True

  • Python also implements some handy data structures that can be useful. Lists of objects take the form

>>> a = [1, 2, 3, 4]
>>> a.append('Nocedal')
>>> a.extend(['Wright', 'Mangasarian'])
>>> print(a)
[1, 2, 3, 4, 'Nocedal', 'Wright', 'Mangasarian']
>>> for obj in a:
...     print(obj)
...
1
2
3
4
Nocedal
Wright
Mangasarian
>>> for index, obj in enumerate(a):
...     print(index, obj)
...
0 1
1 2
2 3
3 4
4 Nocedal
5 Wright
6 Mangasarian

  • Functions can be defined in python as follows

>>> def isThisFletcher(s, default='conjugate'):
...     if s == 'Fletcher':
...             return True
...     return False
...
>>> isThisFletcher('Fletcher')
True
>>> isThisFletcher('Reeves')
False

  • Note that variables that are global or local (including the arguments to the function) can be accessed within the function.

  • I strongly recommend that you do not use global variables. Pass variables as arguments. Do not use global variables!

  • If there is a global variable and a local variable with the same name, the local variable is used. But it can be confusing if you rely on this!

There are a lot of additional things we’ll do with python. There are many examples in these notes.

NumPy basics

NumPy is a powerful package that implements multi-dimensional arrays in Python.

  • To use any NumPy features in Python, you have to first import the package.

>>> import numpy as np

  • NumPy uses arrays that can either be generated directly or be created from Python lists

>>> apy = [0, 1, 2, 5, 10, 10]
>>> a = np.array(apy)
>>> print(a)
[ 0  1  2  5 10 10]
>>> print(a.dtype)
int64

  • Be careful of the data type. Sometimes you might create a NumPy array of integers when you wanted floats!

  • There are two ways around this, either declare the type directly or make sure to initialize the list as a float.

>>> apy = [0, 1, 2, 5, 10, 10]
>>> a = np.array(apy, dtype=float)
>>> print(a)
[ 0.  1.  2.  5. 10. 10.]
>>> print(a.dtype)
float64

  • 2 dimensional (and higher-dimensional) arrays can also be created from lists of lists as long as they’re the right length

>>> apy = [[1, 2, 3], [3, 4, 5]]
>>> a = np.array(apy)
>>> print(a)
array([[1, 2, 3],
      [3, 4, 5]])
>>> print(a.shape)
(2, 3)

  • You can create NumPy arrays directly as well. The default data type is a float.

>>> a = np.zeros(4)
>>> print(a)
[0. 0. 0. 0.]
>>> a = np.zeros((4, 5))
>>> print(a)
[[0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0.]]
>>> print(a.shape)
(4, 5)

  • There are many ways to index into arrays. Indexing is zero-based so you can do the following

>>> a = np.zeros((5, 6))
>>> for i in range(5):
...     for j in range(6):
...             a[i, j] = i + j
...
>>> print(a)
[[0. 1. 2. 3. 4. 5.]
[1. 2. 3. 4. 5. 6.]
[2. 3. 4. 5. 6. 7.]
[3. 4. 5. 6. 7. 8.]
[4. 5. 6. 7. 8. 9.]]

  • You can assign slices of values to arrays

For more details on how to use NumPy, please read this document: https://numpy.org/doc/stable/user/absolute_beginners.html

matplotlib basics

Matplotlib is a package for scientific visualization in Python. For a thorough introduction to matplotlib, see this link: https://matplotlib.org/stable/tutorials/introductory/pyplot.html