Massimo Nocentini, PhD.

February 7, 2020: init



Abstract
A (very concise) introduction to matplotlib.

In [1]:
__AUTHORS__ = {'am': ("Andrea Marino", 
                      "andrea.marino@unifi.it",),
               'mn': ("Massimo Nocentini", 
                      "massimo.nocentini@unifi.it", 
                      "https://github.com/massimo-nocentini/",)}

__KEYWORDS__ = ['Python', 'Jupyter', 'matplotlib', 'keynote',]

Visualization with Matplotlib

We'll now take an in-depth look at the Matplotlib package for visualization in Python. Matplotlib is a multi-platform data visualization library built on NumPy arrays, and designed to work with the broader SciPy stack. It was conceived by John Hunter in 2002, originally as a patch to IPython for enabling interactive MATLAB-style plotting via gnuplot from the IPython command line. IPython's creator, Fernando Perez, was at the time scrambling to finish his PhD, and let John know he wouldn’t have time to review the patch for several months. John took this as a cue to set out on his own, and the Matplotlib package was born, with version 0.1 released in 2003. It received an early boost when it was adopted as the plotting package of choice of the Space Telescope Science Institute (the folks behind the Hubble Telescope), which financially supported Matplotlib’s development and greatly expanded its capabilities.

One of Matplotlib’s most important features is its ability to play well with many operating systems and graphics backends. Matplotlib supports dozens of backends and output types, which means you can count on it to work regardless of which operating system you are using or which output format you wish. This cross-platform, everything-to-everyone approach has been one of the great strengths of Matplotlib. It has led to a large user base, which in turn has led to an active developer base and Matplotlib’s powerful tools and ubiquity within the scientific Python world.

In recent years, however, the interface and style of Matplotlib have begun to show their age. Newer tools like ggplot and ggvis in the R language, along with web visualization toolkits based on D3js and HTML5 canvas, often make Matplotlib feel clunky and old-fashioned. Still, I'm of the opinion that we cannot ignore Matplotlib's strength as a well-tested, cross-platform graphics engine. Recent Matplotlib versions make it relatively easy to set new global plotting styles (see Customizing Matplotlib: Configurations and Style Sheets), and people have been developing new packages that build on its powerful internals to drive Matplotlib via cleaner, more modern APIs—for example, Seaborn (discussed in Visualization With Seaborn), ggpy, HoloViews, Altair, and even Pandas itself can be used as wrappers around Matplotlib's API. Even with wrappers like these, it is still often useful to dive into Matplotlib's syntax to adjust the final plot output. For this reason, I believe that Matplotlib itself will remain a vital piece of the data visualization stack, even if new tools mean the community gradually moves away from using the Matplotlib API directly.

Importing Matplotlib

Just as we use the np shorthand for NumPy and the pd shorthand for Pandas, we will use some standard shorthands for Matplotlib imports:


In [1]:
import matplotlib as mpl
import matplotlib.pyplot as plt

Setting Styles

We will use the plt.style directive to choose appropriate aesthetic styles for our figures. Here we will set the classic style, which ensures that the plots we create use the classic Matplotlib style:


In [2]:
plt.style.use('classic')

Throughout this section, we will adjust this style as needed. Note that the stylesheets used here are supported as of Matplotlib version 1.5; if you are using an earlier version of Matplotlib, only the default style is available. For more information on stylesheets, see Customizing Matplotlib: Configurations and Style Sheets.

General Matplotlib Tips

Before we dive into the details of creating visualizations with Matplotlib, there are a few useful things you should know about using the package.

Plotting from an IPython notebook

The IPython notebook is a browser-based interactive data analysis tool that can combine narrative, code, graphics, HTML elements.

Plotting interactively within an IPython notebook can be done with the %matplotlib command, and works in a similar way to the IPython shell. In the IPython notebook, you also have the option of embedding graphics directly in the notebook, with two possible options:

  • %matplotlib notebook will lead to interactive plots embedded within the notebook
  • %matplotlib inline will lead to static images of your plot embedded in the notebook

For this book, we will generally opt for %matplotlib inline:


In [5]:
%matplotlib inline

After running this command (it needs to be done only once per kernel/session), any cell within the notebook that creates a plot will embed a PNG image of the resulting graphic:


In [6]:
import numpy as np
x = np.linspace(0, 10, 100)

fig = plt.figure()
plt.plot(x, np.sin(x), '-')
plt.plot(x, np.cos(x), '--');


Saving Figures to File

One nice feature of Matplotlib is the ability to save figures in a wide variety of formats. Saving a figure can be done using the savefig() command. For example, to save the previous figure as a PNG file, you can run this:


In [7]:
fig.savefig('my_figure.png')

We now have a file called my_figure.png in the current working directory:


In [8]:
!ls -lh my_figure.png


-rw-r--r-- 1 mn mn 26K Apr  5 22:51 my_figure.png

In savefig(), the file format is inferred from the extension of the given filename. Depending on what backends you have installed, many different file formats are available. The list of supported file types can be found for your system by using the following method of the figure canvas object:


In [9]:
fig.canvas.get_supported_filetypes()


Out[9]:
{'ps': 'Postscript',
 'eps': 'Encapsulated Postscript',
 'pdf': 'Portable Document Format',
 'pgf': 'PGF code for LaTeX',
 'png': 'Portable Network Graphics',
 'raw': 'Raw RGBA bitmap',
 'rgba': 'Raw RGBA bitmap',
 'svg': 'Scalable Vector Graphics',
 'svgz': 'Scalable Vector Graphics'}

Two Interfaces for the Price of One

A potentially confusing feature of Matplotlib is its dual interfaces: a convenient MATLAB-style state-based interface, and a more powerful object-oriented interface. We'll quickly highlight the differences between the two here.

MATLAB-style Interface

Matplotlib was originally written as a Python alternative for MATLAB users, and much of its syntax reflects that fact. The MATLAB-style tools are contained in the pyplot (plt) interface. For example, the following code will probably look quite familiar to MATLAB users:


In [10]:
plt.figure()  # create a plot figure

# create the first of two panels and set current axis
plt.subplot(2, 1, 1) # (rows, columns, panel number)
plt.plot(x, np.sin(x))

# create the second panel and set current axis
plt.subplot(2, 1, 2)
plt.plot(x, np.cos(x));


Object-oriented interface

The object-oriented interface is available for these more complicated situations, and for when you want more control over your figure. Rather than depending on some notion of an "active" figure or axes, in the object-oriented interface the plotting functions are methods of explicit Figure and Axes objects. To re-create the previous plot using this style of plotting, you might do the following:


In [11]:
# First create a grid of plots
# ax will be an array of two Axes objects
fig, ax = plt.subplots(2)

# Call plot() method on the appropriate object
ax[0].plot(x, np.sin(x))
ax[1].plot(x, np.cos(x));


Simple Line Plots

Perhaps the simplest of all plots is the visualization of a single function $y = f(x)$. Here we will take a first look at creating a simple plot of this type. As with all the following sections, we'll start by setting up the notebook for plotting and importing the packages we will use:


In [3]:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')
import numpy as np

For all Matplotlib plots, we start by creating a figure and an axes. In their simplest form, a figure and axes can be created as follows:


In [13]:
fig = plt.figure()
ax = plt.axes()


In Matplotlib, the figure (an instance of the class plt.Figure) can be thought of as a single container that contains all the objects representing axes, graphics, text, and labels. The axes (an instance of the class plt.Axes) is what we see above: a bounding box with ticks and labels, which will eventually contain the plot elements that make up our visualization. Throughout this book, we'll commonly use the variable name fig to refer to a figure instance, and ax to refer to an axes instance or group of axes instances.

Once we have created an axes, we can use the ax.plot function to plot some data. Let's start with a simple sinusoid:


In [14]:
fig = plt.figure()
ax = plt.axes()

x = np.linspace(0, 10, 1000)
ax.plot(x, np.sin(x));


Alternatively, we can use the pylab interface and let the figure and axes be created for us in the background:


In [15]:
plt.plot(x, np.sin(x));


If we want to create a single figure with multiple lines, we can simply call the plot function multiple times:


In [16]:
plt.plot(x, np.sin(x))
plt.plot(x, np.cos(x));


Adjusting the Plot: Line Colors and Styles

The first adjustment you might wish to make to a plot is to control the line colors and styles. The plt.plot() function takes additional arguments that can be used to specify these. To adjust the color, you can use the color keyword, which accepts a string argument representing virtually any imaginable color.

The color can be specified in a variety of ways (If no color is specified, Matplotlib will automatically cycle through a set of default colors for multiple lines):


In [17]:
plt.plot(x, np.sin(x - 0), color='blue')        # specify color by name
plt.plot(x, np.sin(x - 1), color='g')           # short color code (rgbcmyk)
plt.plot(x, np.sin(x - 2), color='0.75')        # Grayscale between 0 and 1
plt.plot(x, np.sin(x - 3), color='#FFDD44')     # Hex code (RRGGBB from 00 to FF)
plt.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple, values 0 to 1
plt.plot(x, np.sin(x - 5), color='chartreuse'); # all HTML color names supported


Similarly, the line style can be adjusted using the linestyle keyword:


In [18]:
plt.plot(x, x + 0, linestyle='solid')
plt.plot(x, x + 1, linestyle='dashed')
plt.plot(x, x + 2, linestyle='dashdot')
plt.plot(x, x + 3, linestyle='dotted');

# For short, you can use the following codes:
plt.plot(x, x + 4, linestyle='-')  # solid
plt.plot(x, x + 5, linestyle='--') # dashed
plt.plot(x, x + 6, linestyle='-.') # dashdot
plt.plot(x, x + 7, linestyle=':');  # dotted


If you would like to be extremely terse, these linestyle and color codes can be combined into a single non-keyword argument to the plt.plot() function:


In [19]:
plt.plot(x, x + 0, '-g')  # solid green
plt.plot(x, x + 1, '--c') # dashed cyan
plt.plot(x, x + 2, '-.k') # dashdot black
plt.plot(x, x + 3, ':r');  # dotted red


Adjusting the Plot: Axes Limits

Matplotlib does a decent job of choosing default axes limits for your plot, but sometimes it's nice to have finer control. The most basic way to adjust axis limits is to use the plt.xlim() and plt.ylim() methods:


In [20]:
plt.plot(x, np.sin(x))

plt.xlim(-1, 11)
plt.ylim(-1.5, 1.5);


If for some reason you'd like either axis to be displayed in reverse, you can simply reverse the order of the arguments:


In [21]:
plt.plot(x, np.sin(x))

plt.xlim(10, 0)
plt.ylim(1.2, -1.2);


A useful related method is plt.axis() (note here the potential confusion between axes with an e, and axis with an i). The plt.axis() method allows you to set the x and y limits with a single call, by passing a list which specifies [xmin, xmax, ymin, ymax]:


In [22]:
plt.plot(x, np.sin(x))
plt.axis([-1, 11, -1.5, 1.5]);


The plt.axis() method goes even beyond this, allowing you to do things like automatically tighten the bounds around the current plot:


In [23]:
plt.plot(x, np.sin(x))
plt.axis('tight');


It allows even higher-level specifications, such as ensuring an equal aspect ratio so that on your screen, one unit in x is equal to one unit in y:


In [24]:
plt.plot(x, np.sin(x))
plt.axis('equal');


Labeling Plots

As the last piece of this section, we'll briefly look at the labeling of plots: titles, axis labels, and simple legends.

Titles and axis labels are the simplest such labels—there are methods that can be used to quickly set them:


In [25]:
plt.plot(x, np.sin(x))
plt.title("A Sine Curve")
plt.xlabel("x")
plt.ylabel("sin(x)");


When multiple lines are being shown within a single axes, it can be useful to create a plot legend that labels each line type. Again, Matplotlib has a built-in way of quickly creating such a legend. It is done via the (you guessed it) plt.legend() method. Though there are several valid ways of using this, I find it easiest to specify the label of each line using the label keyword of the plot function:


In [26]:
plt.plot(x, np.sin(x), '-g', label='sin(x)')
plt.plot(x, np.cos(x), ':b', label='cos(x)')
plt.axis('equal')

plt.legend();


Aside: Matplotlib Gotchas

While most plt functions translate directly to ax methods (such as plt.plot()ax.plot(), plt.legend()ax.legend(), etc.), this is not the case for all commands. In particular, functions to set limits, labels, and titles are slightly modified. For transitioning between MATLAB-style functions and object-oriented methods, make the following changes:

  • plt.xlabel()ax.set_xlabel()
  • plt.ylabel()ax.set_ylabel()
  • plt.xlim()ax.set_xlim()
  • plt.ylim()ax.set_ylim()
  • plt.title()ax.set_title()

In the object-oriented interface to plotting, rather than calling these functions individually, it is often more convenient to use the ax.set() method to set all these properties at once:


In [27]:
ax = plt.axes()
ax.plot(x, np.sin(x))
ax.set(xlim=(0, 10), ylim=(-2, 2), xlabel='x', ylabel='sin(x)', title='A Simple Plot');


Simple Scatter Plots

Another commonly used plot type is the simple scatter plot, a close cousin of the line plot. Instead of points being joined by line segments, here the points are represented individually with a dot, circle, or other shape. We’ll start by setting up the notebook for plotting and importing the functions we will use:


In [4]:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')
import numpy as np

Scatter Plots with plt.plot

In the previous section we looked at plt.plot/ax.plot to produce line plots. It turns out that this same function can produce scatter plots as well:


In [5]:
x = np.linspace(0, 10, 30)
y = np.sin(x)

plt.plot(x, y, 'o', color='black');


The third argument in the function call is a character that represents the type of symbol used for the plotting. Just as you can specify options such as '-', '--' to control the line style, the marker style has its own set of short string codes. The full list of available symbols can be seen in the documentation of plt.plot, or in Matplotlib's online documentation. Most of the possibilities are fairly intuitive, and we'll show a number of the more common ones here:


In [6]:
rng = np.random.RandomState(0)
for marker in ['o', '.', ',', 'x', '+', 'v', '^', '<', '>', 's', 'd']:
    plt.plot(rng.rand(5), rng.rand(5), marker, label="marker='{0}'".format(marker))
plt.legend(numpoints=1)
plt.xlim(0, 1.8);


For even more possibilities, these character codes can be used together with line and color codes to plot points along with a line connecting them:


In [7]:
plt.plot(x, y, '-ok');


Additional keyword arguments to plt.plot specify a wide range of properties of the lines and markers:


In [8]:
plt.plot(x, y, '-p', color='gray',
         markersize=15, linewidth=4,
         markerfacecolor='white',
         markeredgecolor='gray',
         markeredgewidth=2)
plt.ylim(-1.2, 1.2);


Scatter Plots with plt.scatter

A second, more powerful method of creating scatter plots is the plt.scatter function, which can be used very similarly to the plt.plot function:


In [9]:
plt.scatter(x, y, marker='o');


The primary difference of plt.scatter from plt.plot is that it can be used to create scatter plots where the properties of each individual point (size, face color, edge color, etc.) can be individually controlled or mapped to data.

Let's show this by creating a random scatter plot with points of many colors and sizes. In order to better see the overlapping results, we'll also use the alpha keyword to adjust the transparency level:


In [10]:
rng = np.random.RandomState(0)
x = rng.randn(100)
y = rng.randn(100)
colors = rng.rand(100)
sizes = 1000 * rng.rand(100)

plt.scatter(x, y, c=colors, s=sizes, alpha=0.3, cmap='viridis')
plt.colorbar();  # show color scale


Notice that the color argument is automatically mapped to a color scale (shown here by the colorbar() command), and that the size argument is given in pixels. In this way, the color and size of points can be used to convey information in the visualization, in order to visualize multidimensional data.

For example, we might use the Iris data from Scikit-Learn, where each sample is one of three types of flowers that has had the size of its petals and sepals carefully measured:


In [11]:
from sklearn.datasets import load_iris
iris = load_iris()
features = iris.data.T

plt.scatter(features[0], features[1], alpha=0.2, s=100*features[3], c=iris.target, cmap='viridis')
plt.xlabel(iris.feature_names[0])
plt.ylabel(iris.feature_names[1]);


plot Versus scatter: A Note on Efficiency

Aside from the different features available in plt.plot and plt.scatter, why might you choose to use one over the other? While it doesn't matter as much for small amounts of data, as datasets get larger than a few thousand points, plt.plot can be noticeably more efficient than plt.scatter. The reason is that plt.scatter has the capability to render a different size and/or color for each point, so the renderer must do the extra work of constructing each point individually. In plt.plot, on the other hand, the points are always essentially clones of each other, so the work of determining the appearance of the points is done only once for the entire set of data. For large datasets, the difference between these two can lead to vastly different performance, and for this reason, plt.plot should be preferred over plt.scatter for large datasets.

Visualizing Errors

For any scientific measurement, accurate accounting for errors is nearly as important, if not more important, than accurate reporting of the number itself. For example, imagine that I am using some astrophysical observations to estimate the Hubble Constant, the local measurement of the expansion rate of the Universe. I know that the current literature suggests a value of around 71 (km/s)/Mpc, and I measure a value of 74 (km/s)/Mpc with my method. Are the values consistent? The only correct answer, given this information, is this: there is no way to know.

Suppose I augment this information with reported uncertainties: the current literature suggests a value of around 71 $\pm$ 2.5 (km/s)/Mpc, and my method has measured a value of 74 $\pm$ 5 (km/s)/Mpc. Now are the values consistent? That is a question that can be quantitatively answered.

In visualization of data and results, showing these errors effectively can make a plot convey much more complete information.

Basic Errorbars

A basic errorbar can be created with a single Matplotlib function call:


In [12]:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')
import numpy as np

Here the fmt is a format code controlling the appearance of lines and points, and has the same syntax as the shorthand used in plt.plot.


In [13]:
x = np.linspace(0, 10, 50)
dy = 0.8
y = np.sin(x) + dy * np.random.randn(50)

plt.errorbar(x, y, yerr=dy, fmt='.k');


In addition to these basic options, the errorbar function has many options to fine-tune the outputs. Using these additional options you can easily customize the aesthetics of your errorbar plot. I often find it helpful, especially in crowded plots, to make the errorbars lighter than the points themselves:


In [14]:
plt.errorbar(x, y, yerr=dy, fmt='o', color='black', ecolor='lightgray', elinewidth=3, capsize=0);


Density and Contour Plots

Sometimes it is useful to display three-dimensional data in two dimensions using contours or color-coded regions. There are three Matplotlib functions that can be helpful for this task: plt.contour for contour plots, plt.contourf for filled contour plots, and plt.imshow for showing images. This section looks at several examples of using these. We'll start by setting up the notebook for plotting and importing the functions we will use:


In [23]:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn-white')
import numpy as np

Visualizing a Three-Dimensional Function

We'll start by demonstrating a contour plot using a function $z = f(x, y)$, using the following particular choice for $f$ (we've seen this before in Computation on Arrays: Broadcasting, when we used it as a motivating example for array broadcasting):


In [24]:
def f(x, y):
    return np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)

A contour plot can be created with the plt.contour function. It takes three arguments: a grid of x values, a grid of y values, and a grid of z values. The x and y values represent positions on the plot, and the z values will be represented by the contour levels. Perhaps the most straightforward way to prepare such data is to use the np.meshgrid function, which builds two-dimensional grids from one-dimensional arrays:


In [25]:
x = np.linspace(0, 5, 50)
y = np.linspace(0, 5, 40)

X, Y = np.meshgrid(x, y)
Z = f(X, Y)

Now let's look at this with a standard line-only contour plot:


In [26]:
plt.contour(X, Y, Z, colors='black');


Notice that by default when a single color is used, negative values are represented by dashed lines, and positive values by solid lines.

Alternatively, the lines can be color-coded by specifying a colormap with the cmap argument. Here, we'll also specify that we want more lines to be drawn—20 equally spaced intervals within the data range:


In [29]:
plt.contour(X, Y, Z, 20, cmap='RdGy');


Here we chose the RdGy (short for Red-Gray) colormap, which is a good choice for centered data. Matplotlib has a wide range of colormaps available, which you can easily browse in IPython by doing a tab completion on the plt.cm module:

plt.cm.<TAB>

Our plot is looking nicer, but the spaces between the lines may be a bit distracting. We can change this by switching to a filled contour plot using the plt.contourf() function (notice the f at the end), which uses largely the same syntax as plt.contour().

Additionally, we'll add a plt.colorbar() command, which automatically creates an additional axis with labeled color information for the plot:


In [31]:
plt.contourf(X, Y, Z, 20, cmap='RdGy')
plt.colorbar(); # The colorbar makes it clear that the black regions 
                # are "peaks," while the red regions are "valleys."


One potential issue with this plot is that it is a bit "splotchy." That is, the color steps are discrete rather than continuous, which is not always what is desired. This could be remedied by setting the number of contours to a very high number, but this results in a rather inefficient plot: Matplotlib must render a new polygon for each step in the level. A better way to handle this is to use the plt.imshow() function, which interprets a two-dimensional grid of data as an image. The following code shows this:


In [32]:
plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower', cmap='RdGy')
plt.colorbar()
plt.axis(aspect='image');


There are a few potential gotchas with imshow(), however:

  • plt.imshow() doesn't accept an x and y grid, so you must manually specify the extent [xmin, xmax, ymin, ymax] of the image on the plot.
  • plt.imshow() by default follows the standard image array definition where the origin is in the upper left, not in the lower left as in most contour plots. This must be changed when showing gridded data.
  • plt.imshow() will automatically adjust the axis aspect ratio to match the input data; this can be changed by setting, for example, plt.axis(aspect='image') to make x and y units match.

Finally, it can sometimes be useful to combine contour plots and image plots. For example, here we'll use a partially transparent background image (with transparency set via the alpha parameter) and overplot contours with labels on the contours themselves (using the plt.clabel() function):


In [33]:
contours = plt.contour(X, Y, Z, 3, colors='black')
plt.clabel(contours, inline=True, fontsize=8)

plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower', cmap='RdGy', alpha=0.5)
plt.colorbar();