“Python has gotten sufficiently weapons grade that we don’t descend into R anymore. Sorry, R people. I used to be one of you but we no longer descend into R.” – Chris Wiggins
In this lecture we will
At this stage, it’s not our intention that you try to replicate all you see.
We will work through what follows at a slow pace later in the lecture series.
Our only objective for this lecture is to give you some feel of what Python is, and what it can do.
Python is free and open source, with development coordinated through the Python Software Foundation.
Python has experienced rapid adoption in the last decade and is now one of the most popular programming languages.
Python is a general-purpose language used in almost all application domains such as
Used extensively by Internet services and high tech companies including
Python is very beginner-friendly and is often used to teach computer science and programming.
For reasons we will discuss, Python is particularly popular within the scientific community with users including NASA, CERN and practically all branches of academia.
It is also replacing familiar tools like Excel in the fields of finance and banking.
The following chart, produced using Stack Overflow Trends, shows one measure of the relative popularity of Python
The figure indicates not only that Python is widely used but also that adoption of Python has accelerated significantly since 2012.
We suspect this is driven at least in part by uptake in the scientific domain, particularly in rapidly growing fields like data science.
For example, the popularity of pandas, a library for data analysis with Python has exploded, as seen here.
(The corresponding time path for MATLAB is shown for comparison)
Note that pandas takes off in 2012, which is the same year that we see Python’s popularity begin to spike in the first figure.
Overall, it’s clear that
Elegant code might sound superfluous but in fact it’s highly beneficial because it makes the syntax easy to read and easy to remember.
Remembering how to read from files, sort dictionaries and other such routine tasks means that you don’t need to break your flow in order to hunt down correct syntax.
Closely related to elegant syntax is an elegant design.
Features like iterators, generators, decorators and list comprehensions make Python highly expressive, allowing you to get more done with less code.
Namespaces improve productivity by cutting down on bugs and syntax errors.
It’s either the dominant player or a major player in
Its popularity in economics is also beginning to rise.
This section briefly showcases some examples of Python for scientific programming.
import numpy as np # Load the library a = np.linspace(-np.pi, np.pi, 100) # Create even grid from -π to π b = np.cos(a) # Apply cosine to each element of a c = np.sin(a) # Apply sin to each element of a
Now let’s take the inner product
b @ c
The number you see here might vary slightly but it’s essentially zero.
(For older versions of Python and NumPy you need to use the np.dot function)
The SciPy library is built on top of NumPy and provides additional functionality.
from scipy.stats import norm from scipy.integrate import quad ϕ = norm() value, error = quad(ϕ.pdf, -2, 2) # Integrate using Gaussian quadrature value
The most popular and comprehensive Python library for creating figures and graphs is Matplotlib, with functionality including
Example 2D plot with embedded LaTeX annotations
Example contour plot
Example 3D plot
More examples can be found in the Matplotlib thumbnail gallery.
Other graphics libraries include
from sympy import Symbol x, y = Symbol('x'), Symbol('y') # Treat 'x' and 'y' as algebraic symbols x + x + x + y
We can manipulate expressions
expression = (x + y)**2 expression.expand()
from sympy import solve solve(x**2 + x + 2)
and calculate limits, derivatives and integrals
from sympy import limit, sin, diff limit(1 / x, x, 0)
limit(sin(x) / x, x, 0)
The beauty of importing this functionality into Python is that we are working within a fully fledged programming language.
We can easily create tables of derivatives, generate LaTeX output, add that output to figures and so on.
Python’s data manipulation and statistics libraries have improved rapidly over the last few years.
import pandas as pd np.random.seed(1234) data = np.random.randn(5, 2) # 5x2 matrix of N(0, 1) random draws dates = pd.date_range('28/12/2010', periods=5) df = pd.DataFrame(data, columns=('price', 'weight'), index=dates) print(df)
Python has many libraries for studying graphs.
One well-known example is NetworkX. Its features include, among many other things:
Here’s some example code that generates and plots a random graph, with node color determined by shortest path length from a central node.
%matplotlib inline import networkx as nx import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (10,6) np.random.seed(1234) # Generate a random graph p = dict((i, (np.random.uniform(0, 1), np.random.uniform(0, 1))) for i in range(200)) g = nx.random_geometric_graph(200, 0.12, pos=p) pos = nx.get_node_attributes(g, 'pos') # Find node nearest the center point (0.5, 0.5) dists = [(x - 0.5)**2 + (y - 0.5)**2 for x, y in list(pos.values())] ncenter = np.argmin(dists) # Plot graph, coloring by path length from central node p = nx.single_source_shortest_path_length(g, ncenter) plt.figure() nx.draw_networkx_edges(g, pos, alpha=0.4) nx.draw_networkx_nodes(g, pos, nodelist=list(p.keys()), node_size=120, alpha=0.5, node_color=list(p.values()), cmap=plt.cm.jet_r) plt.show()
There are many other interesting developments with scientific programming in Python.
Some representative examples include