Code should execute sequentially if run in a Jupyter notebook

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
• animation, etc., etc.

Sure, you will find the odd disgruntled individual who complains about Matplotlib

Typically, this is because they don’t know how to use it properly

Once you do, Matplotlib is a joy to use — powerful, elegant and intuitive

Matplotlib’s Split Personality¶

There’s one thing you need to know before we get started

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

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

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

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

But first, let’s discuss the difference

The MATLAB-Style API¶

Let’s cover the MATLAB-style API first

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

from pylab import *  # Deprecated
x = linspace(0, 10, 200)
y = sin(x)
plot(x, y, 'b-', linewidth=2)
show()


Typically this will appear as a separate window, like so

The buttons at the bottom of the window allow you to manipulate the figure and then save it if you wish

If you’re using Jupyter notebook you can also have it appear inline, as described here

The pylab module is actually just a few lines of code instructing the interpreter to pull in some key functionality from matplotlib and numpy

It is in fact deprecated, although still in common use

Also, from pylab import * pulls lots of names into the global namespace, which is a potential source of name conflicts

A better syntax would be

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0, 10, 200)
y = np.sin(x)
plt.plot(x, y, 'b-', linewidth=2)
plt.show()


The Object-Oriented API¶

The API described above 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 (type import this in the IPython (or Python) shell and look at the second line)

This leads us to the alternative, object oriented Matplotlib API

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

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.linspace(0, 10, 200)
y = np.sin(x)
ax.plot(x, y, 'b-', linewidth=2)
plt.show()


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

This will become more clear as we go along

Incidentally, regarding the above lines of code,

• the form of the import statement import matplotlib.pyplot as plt is standard

• 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

Tweaks¶

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

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.linspace(0, 10, 200)
y = np.sin(x)
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')

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.linspace(0, 10, 200)
y = np.sin(x)
ax.plot(x, y, 'r-', linewidth=2, label='sine function', alpha=0.6)
ax.legend(loc='upper center')
plt.show()


If everthing is properly configured, then adding LaTeX is trivial

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.linspace(0, 10, 200)
y = np.sin(x)
ax.plot(x, y, 'r-', linewidth=2, label=r'$y=\sin(x)$', alpha=0.6)
ax.legend(loc='upper center')
plt.show()


The r in front of the label string tells Python that this is a raw string

The figure now looks as follows

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

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
x = np.linspace(0, 10, 200)
y = np.sin(x)
ax.plot(x, y, 'r-', linewidth=2, label=r'$y=\sin(x)$', alpha=0.6)
ax.legend(loc='upper center')
ax.set_yticks([-1, 0, 1])
ax.set_title('Test plot')
plt.show()


Here’s the figure

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 mutiple plots on the same axes

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

import matplotlib.pyplot as plt
import numpy as np
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 = r'$\mu = {0:.2f}$'.format(m)
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

import matplotlib.pyplot as plt
from scipy.stats import norm
from random import uniform
num_rows, num_cols = 3, 2
fig, axes = plt.subplots(num_rows, num_cols, figsize=(8, 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 = r'$\mu = {0:.1f}, \quad \sigma = {1:.1f}$'.format(m, s)
axes[i, j].set_title(t)
axes[i, j].set_xticks([-4, 0, 4])
axes[i, j].set_yticks([])
plt.show()


The output looks as follows

In fact the preceding figure was generated by the code above preceded by the following three lines

from matplotlib import rc
rc('font',**{'family':'serif','serif':['Palatino']})
rc('text', usetex=True)


Depending on your LaTeX installation, this may or may not work for you — try experimenting and see how you go

3D Plots¶

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

The source code is

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np
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.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 this blog 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

import matplotlib.pyplot as plt
import numpy as np

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()


Here’s the figure it produces (note axes through the origin and the grid)

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