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Matplotlib

Overview

We’ve already generated quite a few figures in these lectures using Matplotlib

Matplotlib is an outstanding graphics library, designed for scientific computing, with

  • high quality 2D and 3D plots
  • output in all the usual formats (PDF, PNG, etc.)
  • LaTeX integration
  • fine grained control over all aspects of presentation
  • animation, etc.

Matplotlib’s Split Personality

Matplotlib is unusual in that it offers two different interfaces to plotting

One is a simple MATLAB-style API (Application Programming Interface) that was written to help MATLAB refugees find a ready home

The other is a more “Pythonic” object-oriented API

For reasons described below, we recommend that you use the second API

But first, let’s discuss the difference

The APIs

The MATLAB-style API

Here’s the kind of easy example you might find in introductory treatments

In [1]:
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np

x = np.linspace(0, 10, 200)
y = np.sin(x)

plt.plot(x, y, 'b-', linewidth=2)
plt.show()

This is simple and convenient, but also somewhat limited and un-Pythonic

For example, in the function calls, a lot of objects get created and passed around without making themselves known to the programmer

Python programmers tend to prefer a more explicit style of programming (run import this in a code block and look at the second line)

This leads us to the alternative, object oriented Matplotlib API

The Object Oriented API

Here’s the code corresponding to the preceding figure using the object-oriented API

In [2]:
fig, ax = plt.subplots()
ax.plot(x, y, 'b-', linewidth=2)
plt.show()

Here the call fig, ax = plt.subplots() returns a pair, where

  • fig is a Figure instance—like a blank canvas
  • ax is an AxesSubplot instance—think of a frame for plotting in

The plot() function is actually a method of ax

While there’s a bit more typing, the more explicit use of objects gives us better control

This will become more clear as we go along

Tweaks

Here we’ve changed the line to red and added a legend

In [3]:
fig, ax = plt.subplots()
ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6)
ax.legend()
plt.show()

We’ve also used alpha to make the line slightly transparent—which makes it look smoother

The location of the legend can be changed by replacing ax.legend() with ax.legend(loc='upper center')

In [4]:
fig, ax = plt.subplots()
ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6)
ax.legend(loc='upper center')
plt.show()

If everything is properly configured, then adding LaTeX is trivial

In [5]:
fig, ax = plt.subplots()
ax.plot(x, y, 'r-', linewidth=2, label='$y=\sin(x)$', alpha=0.6)
ax.legend(loc='upper center')
plt.show()

Controlling the ticks, adding titles and so on is also straightforward

In [6]:
fig, ax = plt.subplots()
ax.plot(x, y, 'r-', linewidth=2, label='$y=\sin(x)$', alpha=0.6)
ax.legend(loc='upper center')
ax.set_yticks([-1, 0, 1])
ax.set_title('Test plot')
plt.show()

More Features

Matplotlib has a huge array of functions and features, which you can discover over time as you have need for them

We mention just a few

Multiple Plots on One Axis

It’s straightforward to generate multiple plots on the same axes

Here’s an example that randomly generates three normal densities and adds a label with their mean

In [7]:
from scipy.stats import norm
from random import uniform

fig, ax = plt.subplots()
x = np.linspace(-4, 4, 150)
for i in range(3):
    m, s = uniform(-1, 1), uniform(1, 2)
    y = norm.pdf(x, loc=m, scale=s)
    current_label = f'$\mu = {m:.2}$'
    ax.plot(x, y, linewidth=2, alpha=0.6, label=current_label)
ax.legend()
plt.show()

Multiple Subplots

Sometimes we want multiple subplots in one figure

Here’s an example that generates 6 histograms

In [8]:
num_rows, num_cols = 3, 2
fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 12))
for i in range(num_rows):
    for j in range(num_cols):
        m, s = uniform(-1, 1), uniform(1, 2)
        x = norm.rvs(loc=m, scale=s, size=100)
        axes[i, j].hist(x, alpha=0.6, bins=20)
        t = f'$\mu = {m:.2}, \quad \sigma = {s:.2}$'
        axes[i, j].set(title=t, xticks=[-4, 0, 4], yticks=[])
plt.show()

3D Plots

Matplotlib does a nice job of 3D plots — here is one example

In [9]:
from mpl_toolkits.mplot3d.axes3d import Axes3D
from matplotlib import cm


def f(x, y):
    return np.cos(x**2 + y**2) / (1 + x**2 + y**2)

xgrid = np.linspace(-3, 3, 50)
ygrid = xgrid
x, y = np.meshgrid(xgrid, ygrid)

fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x,
                y,
                f(x, y),
                rstride=2, cstride=2,
                cmap=cm.jet,
                alpha=0.7,
                linewidth=0.25)
ax.set_zlim(-0.5, 1.0)
plt.show()

A Customizing Function

Perhaps you will find a set of customizations that you regularly use

Suppose we usually prefer our axes to go through the origin, and to have a grid

Here’s a nice example from Matthew Doty of how the object-oriented API can be used to build a custom subplots function that implements these changes

Read carefully through the code and see if you can follow what’s going on

In [10]:
def subplots():
    "Custom subplots with axes throught the origin"
    fig, ax = plt.subplots()

    # Set the axes through the origin
    for spine in ['left', 'bottom']:
        ax.spines[spine].set_position('zero')
    for spine in ['right', 'top']:
        ax.spines[spine].set_color('none')

    ax.grid()
    return fig, ax


fig, ax = subplots()  # Call the local version, not plt.subplots()
x = np.linspace(-2, 10, 200)
y = np.sin(x)
ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6)
ax.legend(loc='lower right')
plt.show()

The custom subplots function

  1. calls the standard plt.subplots function internally to generate the fig, ax pair,
  2. makes the desired customizations to ax, and
  3. passes the fig, ax pair back to the calling code

Further Reading

Exercises

Exercise 1

Plot the function

$$ f(x) = \cos(\pi \theta x) \exp(-x) $$

over the interval $ [0, 5] $ for each $ \theta $ in np.linspace(0, 2, 10)

Place all the curves in the same figure

The output should look like this

Solutions

Exercise 1

Here’s one solution

In [11]:
θ_vals = np.linspace(0, 2, 10)
x = np.linspace(0, 5, 200)
fig, ax = plt.subplots()

for θ in θ_vals:
    ax.plot(x, np.cos(np.pi * θ * x) * np.exp(- x))

plt.show()