1.4. Matplotlib: plotting

Thanks

Many thanks to Bill Wing and Christoph Deil for review and corrections.

Authors: Nicolas Rougier, Mike Müller, Gaël Varoquaux

1.4.1. Introduction

Tip

Matplotlib is probably the single most used Python package for 2D-graphics. It provides both a very quick way to visualize data from Python and publication-quality figures in many formats. We are going to explore matplotlib in interactive mode covering most common cases.

1.4.1.1. IPython and the matplotlib mode

Tip

IPython is an enhanced interactive Python shell that has lots of interesting features including named inputs and outputs, access to shell commands, improved debugging and many more. It is central to the scientific-computing workflow in Python for its use in combination with Matplotlib:

For interactive matplotlib sessions with Matlab/Mathematica-like functionality, we use IPython with it’s special Matplotlib mode that enables non-blocking plotting.

IPython console:  

When using the IPython console, we start it with the command line argument --matplotlib (-pylab in very old versions).

IPython notebook:  

In the IPython notebook, we insert, at the beginning of the notebook the following magic:

%matplotlib inline

1.4.1.2. pyplot

import matplotlit.pyplot as plt

1.4.2. Simple plot

Tip

In this section, we want to draw the cosine and sine functions on the same plot. Starting from the default settings, we’ll enrich the figure step by step to make it nicer.

First step is to get the data for the sine and cosine functions:

import numpy as np

X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)

X is now a numpy array with 256 values ranging from -π to +π (included). C is the cosine (256 values) and S is the sine (256 values).

To run the example, you can type them in an IPython interactive session:

$ ipython --pylab

This brings us to the IPython prompt:

IPython 0.13 -- An enhanced Interactive Python.
?       -> Introduction to IPython's features.
%magic  -> Information about IPython's 'magic' % functions.
help    -> Python's own help system.
object? -> Details about 'object'. ?object also works, ?? prints more.

Welcome to pylab, a matplotlib-based Python environment.
For more information, type 'help(pylab)'.

Tip

You can also download each of the examples and run it using regular python, but you will loose interactive data manipulation:

$ python exercice_1.py

You can get source for each step by clicking on the corresponding figure.

1.4.2.1. Plotting with default settings

Hint

Documentation

• plot tutorial
• plot() command

Tip

Matplotlib comes with a set of default settings that allow customizing all kinds of properties. You can control the defaults of almost every property in matplotlib: figure size and dpi, line width, color and style, axes, axis and grid properties, text and font properties and so on.

import numpy as np
import matplotlib.pyplot as plt

X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)

plt.plot(X, C)
plt.plot(X, S)

plt.show()

1.4.2.2. Instantiating defaults

Hint

Documentation

• Customizing matplotlib

In the script below, we’ve instantiated (and commented) all the figure settings that influence the appearance of the plot.

Tip

The settings have been explicitly set to their default values, but now you can interactively play with the values to explore their affect (see Line properties and Line styles below).

import numpy as np
import matplotlib.pyplot as plt

# Create a figure of size 8x6 inches, 80 dots per inch
plt.figure(figsize=(8, 6), dpi=80)

# Create a new subplot from a grid of 1x1
ax = plt.subplot(1, 1, 1)

X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)

# Plot cosine with a blue continuous line of width 1 (pixels)
ax.plot(X, C, color="blue", linewidth=1.0, linestyle="-")

# Plot sine with a green continuous line of width 1 (pixels)
ax.plot(X, S, color="green", linewidth=1.0, linestyle="-")

# Set x limits
ax.set_xlim(-4.0, 4.0)

# Set x ticks
ax.set_xticks(np.linspace(-4, 4, 9, endpoint=True))

# Set y limits
ax.set_ylim(-1.0, 1.0)

# Set y ticks
ax.set_yticks(np.linspace(-1, 1, 5, endpoint=True))

# Save figure using 72 dots per inch
# ax.savefig("exercice_2.png", dpi=72)

# Show result on screen
plt.show()

1.4.2.3. Changing colors and line widths

Hint

Documentation

• Controlling line properties
• Line API

Tip

First step, we want to have the cosine in blue and the sine in red and a slighty thicker line for both of them. We’ll also slightly alter the figure size to make it more horizontal.

...
fig, ax = plt.subplots(figsize=(10, 6), dpi=80)
ax.plot(X, C, color="blue", linewidth=2.5, linestyle="-")
ax.plot(X, S, color="red",  linewidth=2.5, linestyle="-")
...

1.4.2.4. Setting limits

Tip

Current limits of the figure are a bit too tight and we want to make some space in order to clearly see all data points.

...
ax.set_xlim(X.min() * 1.1, X.max() * 1.1)
ax.set_ylim(C.min() * 1.1, C.max() * 1.1)
...

1.4.2.5. Setting ticks

Hint

Documentation

• Tick container
• Tick locating and formatting

Tip

Current ticks are not ideal because they do not show the interesting values (+/-π,+/-π/2) for sine and cosine. We’ll change them such that they show only these values.

...
ax.set_xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi])
ax.set_yticks([-1, 0, +1])
...

1.4.2.6. Setting tick labels

Hint

Documentation

• Working with text
• set_xticklabels()
• set_yticklabels()

Tip

Ticks are now properly placed but their label is not very explicit. We could guess that 3.142 is π but it would be better to make it explicit. When we set tick values, we can also provide a corresponding label in the second argument list. Note that we’ll use latex to allow for nice rendering of the label.

...
ax.set_xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi],
              [r'$-\pi$', r'$-\pi/2$', r'$0$', r'$+\pi/2$', r'$+\pi$'])

ax.set_yticks([-1, 0, +1],
              [r'$-1$', r'$0$', r'$+1$'])
...

1.4.2.7. Moving spines

Hint

Documentation

• Spines
• Axis container
• Transformations tutorial

Tip

Spines are the lines connecting the axis tick marks and noting the boundaries of the data area. They can be placed at arbitrary positions and until now, they were on the border of the axis. We’ll change that since we want to have them in the middle. Since there are four of them (top/bottom/left/right), we’ll discard the top and right by setting their color to none and we’ll move the bottom and left ones to coordinate 0 in data space coordinates.

...
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))
...

1.4.2.8. Adding a legend

Hint

Documentation

• Legend guide
• legend() command
• Legend API

Tip

Let’s add a legend in the upper left corner. This only requires adding the keyword argument label (that will be used in the legend box) to the plot commands.

...
ax.plot(X, C, color="blue", linewidth=2.5, linestyle="-", label="cosine")
ax.plot(X, S, color="red",  linewidth=2.5, linestyle="-", label="sine")

ax.legend(loc='upper left')
...

1.4.2.9. Annotate some points

Hint

Documentation

• Annotating axis
• annotate() command

Tip

Let’s annotate some interesting points using the annotate command. We chose the 2π/3 value and we want to annotate both the sine and the cosine. We’ll first draw a marker on the curve as well as a straight dotted line. Then, we’ll use the annotate command to display some text with an arrow.

...

t = 2 * np.pi / 3
ax.plot([t, t], [0, np.cos(t)], color='blue', linewidth=2.5, linestyle="--")
ax.scatter([t, ], [np.cos(t), ], 50, color='blue')

ax.annotate(r'$sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$',
             xy=(t, np.sin(t)), xycoords='data',
             xytext=(+10, +30), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

ax.plot([t, t],[0, np.sin(t)], color='red', linewidth=2.5, linestyle="--")
ax.scatter([t, ],[np.sin(t), ], 50, color='red')

ax.annotate(r'$cos(\frac{2\pi}{3})=-\frac{1}{2}$',
             xy=(t, np.cos(t)), xycoords='data',
             xytext=(-90, -50), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))
...

1.4.2.10. Devil is in the details

Hint

Documentation

• Artists
• BBox

Tip

The tick labels are now hardly visible because of the blue and red lines. We can make them bigger and we can also adjust their properties such that they’ll be rendered on a semi-transparent white background. This will allow us to see both the data and the labels.

...
for label in ax.get_xticklabels() + ax.get_yticklabels():
    label.set_fontsize(16)
    label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65))
...

1.4.3. Figures, Subplots, Axes and Ticks

A “figure” in matplotlib means the whole window in the user interface. Within this figure there can be “subplots”.

Tip

So far we have used implicit figure and axes creation. This is handy for fast plots. We can have more control over the display using figure, subplot, and axes explicitly. While subplot positions the plots in a regular grid, axes allows free placement within the figure. Both can be useful depending on your intention. We’ve already worked with figures and subplots without explicitly calling them. When we call plot, matplotlib calls gca() to get the current axes and gca in turn calls gcf() to get the current figure. If there is none it calls figure() to make one, strictly speaking, to make a subplot(111). Let’s look at the details.

1.4.3.1. Figures

Tip

A figure is the windows in the GUI that has “Figure #” as title. Figures are numbered starting from 1 as opposed to the normal Python way starting from 0. This is clearly MATLAB-style. There are several parameters that determine what the figure looks like:

Argument	Default	Description
num	1	number of figure
figsize	figure.figsize	figure size in in inches (width, height)
dpi	figure.dpi	resolution in dots per inch
facecolor	figure.facecolor	color of the drawing background
edgecolor	figure.edgecolor	color of edge around the drawing background
frameon	True	draw figure frame or not

Tip

The defaults can be specified in the resource file and will be used most of the time. Only the number of the figure is frequently changed.

As with other objects, you can set figure properties also setp or with the set_something methods.

When you work with the GUI you can close a figure by clicking on the x in the upper right corner. But you can close a figure programmatically by calling close. Depending on the argument it closes (1) the current figure (no argument), (2) a specific figure (figure number or figure instance as argument), or (3) all figures ("all" as argument).

plt.close(1)     # Closes figure 1

1.4.3.2. Subplots and Axes

Tip

With subplot you can arrange plots in a regular grid. You need to specify the number of rows and columns and the number of the plot. Note that the gridspec command is a more powerful alternative.

1.4.3.3. Axes

Axes are very similar to subplots but allow placement of plots at any location in the figure. So if we want to put a smaller plot inside a bigger one we do so with axes.

1.4.4. Other Types of Plots: examples and exercises

1.4.4.1. Imshow

Hint

You need to take care of the origin of the image in the imshow command and use a colorbar

Starting from the code below, try to reproduce the graphic on the right taking care of colormap, image interpolation and origin.

def f(x, y):
    return (1 - x / 2 + x ** 5 + y ** 3) * np.exp(-x ** 2 - y ** 2)

n = 10
x = np.linspace(-3, 3, 4 * n)
y = np.linspace(-3, 3, 3 * n)
X, Y = np.meshgrid(x, y)
fig, ax = plt.subplots()
ax.imshow(f(X, Y))

Click on the figure for the solution.

1.4.4.2. Scatter Plots

Hint

Color is given by angle of (X,Y).

Starting from the code below, try to reproduce the graphic on the right taking care of marker size, color and transparency.

n = 1024
X = np.random.normal(0,1,n)
Y = np.random.normal(0,1,n)

fig, ax = plt.subplots()
ax.scatter(X,Y)

Click on figure for solution.

1.4.4.3. Bar Plots

Hint

You need to take care of text alignment.

Starting from the code below, try to reproduce the graphic on the right by adding labels for red bars.

n = 12
X = np.arange(n)
Y1 = (1 - X / float(n)) * np.random.uniform(0.5, 1.0, n)
Y2 = (1 - X / float(n)) * np.random.uniform(0.5, 1.0, n)

fig, ax = plt.subplots()
ax.bar(X, +Y1, facecolor='#9999ff', edgecolor='white')
ax.bar(X, -Y2, facecolor='#ff9999', edgecolor='white')

for x, y in zip(X, Y1):
    ax.text(x + 0.4, y + 0.05, '%.2f' % y, ha='center', va='bottom')

ax.set_ylim(-1.25, +1.25)

Click on figure for solution.

1.4.4.4. Grids

Starting from the code below, try to reproduce the graphic on the right taking care of line styles.

ax.set_xlim(0, 4)
ax.set_ylim(0, 3)
ax.set_xticklabels([])
ax.set_yticklabels([])

Click on figure for solution.

1.4.4.5. Multi Plots

Hint

You can use several subplots with different partition.

Starting from the code below, try to reproduce the graphic on the right.

plt.subplot(2, 2, 1)
plt.subplot(2, 2, 3)
plt.subplot(2, 2, 4)

Click on figure for solution.

---

Quick read

If you want to do a first quick pass through the Scipy lectures to learn the ecosystem, you can directly skip to the next chapter: Scipy : high-level scientific computing.

The remainder of this chapter is not necessary to follow the rest of the intro part. But be sure to come back and finish this chapter later.

1.4.5. Beyond this tutorial

Matplotlib benefits from extensive documentation as well as a large community of users and developers. Here are some links of interest:

1.4.5.1. Tutorials

Pyplot tutorial Introduction Controlling line properties Working with multiple figures and axes Working with text Image tutorial Startup commands Importing image data into Numpy arrays Plotting numpy arrays as images Text tutorial Text introduction Basic text commands Text properties and layout Writing mathematical expressions Text rendering With LaTeX Annotating text

Artist tutorial Introduction Customizing your objects Object containers Figure container Axes container Axis containers Tick containers Path tutorial Introduction Bézier example Compound paths Transforms tutorial Introduction Data coordinates Axes coordinates Blended transformations Using offset transforms to create a shadow effect The transformation pipeline

1.4.5.2. Matplotlib documentation

• User guide
• FAQ
  • Installation
  • Usage
  • How-To
  • Troubleshooting
  • Environment Variables
• Screenshots

1.4.5.3. Code documentation

The code is well documented and you can quickly access a specific command from within a python session:

>>> import matplotlib.pyplot as plt
>>> help(plt.plot)    
Help on function plot in module matplotlib.pyplot:

plot(*args, **kwargs)
   Plot lines and/or markers to the
   :class:`~matplotlib.axes.Axes`.  *args* is a variable length
   argument, allowing for multiple *x*, *y* pairs with an
   optional format string.  For example, each of the following is
   legal::

       plot(x, y)         # plot x and y using default line style and color
       plot(x, y, 'bo')   # plot x and y using blue circle markers
       plot(y)            # plot y using x as index array 0..N-1
       plot(y, 'r+')      # ditto, but with red plusses

   If *x* and/or *y* is 2-dimensional, then the corresponding columns
   will be plotted.
...

1.4.5.4. Galleries

The matplotlib gallery is also incredibly useful when you search how to render a given graphic. Each example comes with its source.

1.4.5.5. Mailing lists

Finally, there is a user mailing list where you can ask for help and a developers mailing list that is more technical.

1.4.6. Quick references

Here is a set of tables that show main properties and styles.

1.4.6.1. Line properties

Property	Description	Appearance
alpha (or a)	alpha transparency on 0-1 scale
antialiased	True or False - use antialised rendering
color (or c)	matplotlib color arg
linestyle (or ls)	see Line properties
linewidth (or lw)	float, the line width in points
solid_capstyle	Cap style for solid lines
solid_joinstyle	Join style for solid lines
dash_capstyle	Cap style for dashes
dash_joinstyle	Join style for dashes
marker	see Markers
markeredgewidth (mew)	line width around the marker symbol
markeredgecolor (mec)	edge color if a marker is used
markerfacecolor (mfc)	face color if a marker is used
markersize (ms)	size of the marker in points

1.4.6.2. Line styles

1.4.6.3. Markers

1.4.6.4. Colormaps

All colormaps can be reversed by appending _r. For instance, gray_r is the reverse of gray.

If you want to know more about colormaps, checks Documenting the matplotlib colormaps.