Graphics for plotting data is built into standard Python with the matplotlib module, providing tools for interactive 2-D and 3-D graphics to our very short course in Python for scientific research. Matplotlib may be used to generate and save plots in file formats you can display on the web or in other programs, print, and incorporate in documents. It is, however, designed to emulate Matlab, a popular commercial computing environment. The graphics it produces are functional, can be of publication quality, but lack many of the features now appearing in web-based graphical tools. For those dynamic options we will turn to Bokeh, data visualization code that utilizes the browser, e.g. Chrome or Firefox. Bokeh is a bridge between the power of Python for analysis, and the power of the browser engine and the web for display and acquisition, and it is at the current (2018) cuttiing edge of interactive visualization. Matplotlib is a solid foundation that remains very useful, especially for simple applications. Let's start there.

On Linux the operating system may not by default include matplotlib. If it is not present, then install numpy first because it is a requirement for matplotlib. Try the package that comes with your operating system for both. For example, under Ubuntu you would use

sudo apt-get install python-matplotlib

to get the most recent version available for your system and resolve missing components. Under Opensuse you would use yast2, and look for python3-matplotlib packages.

Unfortunately this is a weak link in using the distribution versions because the compiled packages may not include the features you need. At this time (March 2018), Opensuse's matplotlib is outdated and does not support Tk which is needed for graphical user interfaces.

Therefore if you do get messages indicating something is missing or out of date, remove the system package using apt or yast or zypper as appropriate, and install directly as superuser or root user with "pip" after you read the documentation on pip first if you are not familiar with it. Also check on your system that the "pip" command is actually running it for Python3.

pip --version # will return a line which well tell you what it is for pip install matplotlib # will install matplotlib without options

Your option to use pip is always there for any Python module. Just remove the system version before installing your own so that later updates will not overwrite your additions.

If you find errors with missing components, probably there is something in the installation that is out of date. This is a likely cure:

pip uninstall -y matplotlib # will remove matplotlib without asking questions pip --no-cache-dir install --upgrade matplotlib # will install fresh version

Alternatively, an increasingly popular solution is to let the system version stay as is, even on Linux or MacOS, and install your own copy of Canopy or Anaconda Python. Canopy can coexist with your operating system without issues, as can Anaconda. If you install them as an unprivileged user, then the entire package is under your control and for your use only.

Whether with Linux, Windows and MacOS, users Enthought Canopy and Anaconda Python will have everything they need working together, "out of the box". For others, those who maintain servers and operating systems on a larger scale, look at the matplotlib installation website for directions on how to install it.

Once installed, programs that use this library will have to import it with lines such as

import numpy as np import matplotlib as plt

to make the functions available. With these, numpy functions will start with np. and mathplotlib functions will have plt. in front of the function name, which shortens the code you would write. You can check that your computer has numpy and matplotlib by trying these commands in interactive Python or Idle. The version numbers will be available too with

print (np.__version__) print (plt.__version__)

Matplotlib is configured by a file matplotlibrc that is kept on your computer to set its defaults. On Linux there will be a version saved with your Python installation, typically in a location such as

/usr/lib64/python3.4/site-packages/matplotlib/mpl-data/matplotlibrc

and another copy if it that is personalized, probably in a hidden directory

/home/username/.config/matplotlib/matplotlibrc

With these files there will be a line setting how matplotlib is to render its graphics for you:

backend : TkAgg

in which choices depend on what libraries are installed, and may include Tkagg, GTK3Agg, qt5Agg and others. You can try them out with your own programs below and pick one you like. However "Tkagg" will tie matplotlib to the preferred GUI interface and allow you to build applications that have a graphical user interface surrounding the plotting. Because Tk has improved recently and is the easiest of the GUI systems to use, this is the recommended setting. You can override your personal and the system defaults by specifying the backend in your program with a line such as this one:

matplotlib.use("TkAgg")

The matplotlib on-line user's guide offers a tutorial with many examples, some of which we will look at here. The guide may also be downloaded as a handy readable pdf for off-line reference. There is also a helpful but unfinished quick start guide written by an astrophysics graduate student. Attention to size, fonts, color and detail in matplotlib will yield plots suitable for scientific publications, and a helpful guide is available from Python 4 Astronomers.

Let's look at a simple program that generates its own data and creates one plot you can view on the screen using pyplot, a MATLAB-like interface:

# Import the plotting and math packages import matplotlib.pyplot as plt import math

# Define initial constants f0 = 5. a0 = 100. tdecay = 2.

# Create lists for the (x,y) data time = [] amplitude = []

# Calculate the data and append to the lists for i in range(0, 10000, 1): t = 0.001 * float(i) a = a0 * math.exp(-t/tdecay)*math.cos(2. * math.pi * f0 * t) time.append(t) amplitude.append(a)

# Create an x-y plot of the data with labeled axes plt.figure().canvas.set_window_title('Oscillator') plt.plot(time, amplitude) plt.xlabel('Time') plt.ylabel('Amplitude') plt.title('A Damped Oscillator') # Show the data plt.show()

Most of this program is used to create and prepare the data lists. The plotting is done in one line! We add labels to the canvas so the new window is labeled on the screen, to the axes, a title to the plot, and show the work. The way in which it appears will depend on our installation, but the default is a Tkl interface that offers control for panning, zooming, and saving as png file. The data go into the plot as lists, and appear by default as a drawn line connecting the points. However, if you prefer red circles to a "pen down" line, then change the plt.plot to

plt.plot(time,amplitude,'ro')

or to

'r--' # red dashes 'bs' # blue stars 'g^' # green triangles

The properties of the line would be controlled by variables in the plot function using MATLAB-style string/value pairs.

plt.plot(time,amplitude, color='g', linewidth='2.0')

or alternatively a plot control function

lines = plt.plot(time,amplitude) plt.setp(lines, color='r', linewidth=2.0)

This has the useful feature that interactively plt.setp(lines) will show you all the parameters and their values.

The data in this example are input as lists, but they could be tuples instead:

# Import the plotting and math packages import matplotlib.pyplot as plt import math

# Define initial constants f0 = 5. a0 = 100. tdecay = 2.

# Create lists for the (x,y) data time = [] amplitude = []

# Calculate the data and append to the lists for i in range(0, 10000, 1): t = 0.001 * float(i) a = a0 * math.exp(-t/tdecay)*math.cos(2. * math.pi * f0 * t) time.append(t) amplitude.append(a)

x = tuple(time) y = tuple(amplitude)

# Create an x-y plot of the data with labeled axes plt.xlabel('Time') plt.ylabel('Amplitude') plt.title('A Damped Oscillator') oscillator = plt.plot(time,amplitude) plt.setp(oscillator, color='m', linewidth=1.5) # Show the data plt.show()

This is what it looks like on the screen:

You may include a command to save a figure as a png file by adding

fname = 'oscillator.png' plt.savefig(fname)

The savefig function is sensitive to the file type in the extension, and

fname = 'oscillator.ps' plt.savefig(fname,dpi=600)

would be an example of a PostScript figure set to 600 dots per inch resolution. Supported formats are intended for high quality reproduction and include eps, ps, pdf, png, and svg, among others. The resolution may be controlled within the program, or in defaults for the user's custom startup file.

Matplotlib's *pyplot.plot* takes two arrays as arguments and is aware of several modifiers that determine how the data are plotted. When you use plot, you should be aware that implicitly it creates
a figure and a subplot, and then uses these with the data you have provided. The subplot(nrows, ncols, plot_number) function allows you to make arrays of 9 or fewer plots on the same page. When you only have one plot, it is subplot(1,1,1). You are allowed to leave out the commas if the result is unambiguous, and you will sometimes see this written (lazily) as subplot(111). A second subplot on row 2 would be subplot(212) and so on.

If the pyplot.plot function is repeated, it loads another set of x-y data into the one plot, each set with its own properties. The sets can be labeled, and the labels can be turned into legends in the plot. Here's a simple example:

# Import the plotting and math packages import matplotlib.pyplot as plt import math

# Define initial constants f0 = 5. tdecay = 2.

# Create lists for the (x,y) data time = [] sine_amplitude = [] exp_amplitude = [] product_amplitude = []

# Calculate the data and append to the lists for i in range(0, 10000, 1): t = 0.001 * float(i) a1 = math.cos(2. * math.pi * f0 * t) a2 = math.exp(-t/tdecay) a = a1*a2 time.append(t) sine_amplitude.append(a1) exp_amplitude.append(a2) product_amplitude.append(a)

# Create an x-y plot with labels plt.xlabel('Time') plt.ylabel('Amplitude') plt.title('A Damped Oscillator') plt.plot(time,exp_amplitude,'r.', label='Exponential') plt.plot(time, product_amplitude,'b-', label='Sine', linewidth=1.5) plt.legend()

# Show the data plt.show()

In this case we used abbreviations for the keywords, but it is clearer to use the full text and to write, for example

plt.plot(time,product_amplitude, color='blue', linestyle = 'line', marker='None', label='Sine', linewidth=1.5)

instead.

You may create two separate plots instead of one, in the previous example, by using pyplot this way:

# Create a figure fig = plt.figure()

# Adjust white space between plots fig.subplots_adjust(hspace=0.5)

# Create x-y plots of the data with labeled axes

data1 = fig.add_subplot(2,1,1) plt.xlabel('Time') plt.ylabel('Amplitude') plt.title('Damping') data1.plot(time,exp_amplitude,'r.', label='Exponential') plt.legend()

data2 = fig.add_subplot(2,1,2) plt.xlabel('Time') plt.ylabel('Amplitude') plt.title('A Damped Oscillator') data2.plot(time,product_amplitude, color='blue', linestyle='solid', marker='None', label='Sine', linewidth=1.5) plt.legend()

# Show the data plt.show()

We added subplots with the fig.add_subplot(a,b,c) function, which can also be written without the commas if there is no ambiguity in the numbers. The (a,b,c) mean an axb grid, and the cth subplot of that grid. So 111 is simply 1 plot, but 211 is a 2x1 grid and the first plot in the grid, while 212 is a 2x1 grid and the second plot.

Other one-line plotting options that would create subplot(1,1,1) by default include

import pyplot as plt plt.scatter plt.semilogx plt.semilogy plt.loglog

Errorbars may be included with x and y data using

plt.errorbar(x, y, yerr=None, xerr=None)

It takes the x and y arrays, an array of y errors that defaults to *None*, and an array of x errors that also defaults to *None*.

For more information on plot and other built-in plotting types, see the pyplot documentation.

You've noticed that when data are loaded as a list or tuple, the plot function automatically selects the data range for both axes, and supplies tick marks. You may add minor ticks and control their properties with

plt.minorticks_on() plt.tick_params(which='major', length=7) plt.tick_params(which='minor', length=4, color='r')

where the first one turns on the minor ticks (minorticks_off() is the default), and the others change their length and color.

You may also limit the range of data shown in the plot and retain the automatic tick marking by adding functions such as these *after creating the plot* for the example show above

oscillator = plt.plot(time,amplitude) plt.xlim(-10.,10.) plt.ylim(-200.,200.)

With these limits, the range of x shown will be from -10 to +10 instead of the range in the x-data, and y will be shown from -200 to +200.

It is often useful to view a function or processing operation interactively with a graph that shows the results of changing one or more variables. This is an example written by Michael Tague, a student in the Research Methods class in 2013. We begin by setting up matplotlib and numpy in the usual way:

import matplotlib.pyplot as plt import numpy as np from matplotlib.widgets import Slider

and you see in the last line we have added a useful "Slider" control. Next we create a series of time values as a numpy array

t = np.arange(0, 1, 0.001)

from 0 to 1 in steps of 0.001 which we take to be seconds. From this we create a matching series of amplitudes

y = np.sin(2*np.pi*t*f)/np.exp(t*d)

and a plot

p, = plt.plot(t,y)

You could stop here with "plt.show()" and be done with simple plot of the sinusoidal function. If you want to add controls to make the plot interactive, then rather than showing the plot now add adjustable subplots. The command

plt.subplots_adjust(bottom=0.25)

makes room for the sliders at the bottom of the plot. We add axes

fax = plt.axes([0.25, 0.14, 0.5, 0.03])

and a frequency Slider

fs = Slider(fax, 'Freq', 0.0, 10.0, valinit=f)

Now we create a function that updates the frequencies whenever the slider is changed

def f_update(val): global f, p f = val y = np.sin(2*np.pi*t*f)/np.exp(t*d) p.set_ydata(y) plt.draw();

fs.on_changed(f_update)

The decay constant slider is the same as this, but for the decay, d, we move it down a bit.

dax = plt.axes([0.25, 0.07, 0.5, 0.03]) ds = Slider(dax, 'Decay', 0.0, 10.0, valinit=d)

def d_update(val): global d d = val y = np.sin(2*np.pi*t*f)/np.exp(t*d) p.set_ydata(y) plt.draw();

ds.on_changed(d_update)

Now we show the interactive plot with

plt.show()

One of the features that makes Mathematica and Matlab so useful is their built-in 3D plotting for multivariable surfaces and objects. Matplotlib does this very easily in Python, but the features are so rich we can only sample a few of them here.

As an appetizer, consider surface3d_demo2.py from matplotlib:

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

fig = plt.figure() ax = fig.add_subplot(111, projection='3d')

u = np.linspace(0, 2 * np.pi, 100) v = np.linspace(0, np.pi, 100)

x = 10 * np.outer(np.cos(u), np.sin(v)) y = 10 * np.outer(np.sin(u), np.sin(v)) z = 10 * np.outer(np.ones(np.size(u)), np.cos(v)) ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b')

plt.show()

The first line imports a toolkit that provides 3d projection. For this one, you would need the mpl_tookits package.

The second line imports matplotlib.pyplot and uses plt to stand for it in our code.

The third line imports numpy, numerical Python, which we are going to look at in more detail later. Here, it provides a way to handle the data transparently even if you do not know how the code works yet.

We create a figure called "fig", and we add one and only one subplot "ax" that will hold our work. Notice that the subplot is a "3d" projection.

Numpy is used to create two linear arrays, one from 0 to 2 Pi that we think of as Phi, the azimuth angle in spherical coordinates. The other, from 0 to Pi, is Theta, the altitude of spherical coordinates. From these we calculate a set of x, y, and z that are the coordinates of points on a surface. Here, "np.outer" means "outer product" of two linear arrays, that is each of x, y, and z are matrices that contain the coordinates (x,y,z) of points on the unit sphere or radius 10 selected by the angles u and v.

The plotting is done in one line from the mpl toolkit with plot_surface(), and then dislayed for us to use with show().

From that little program we get an interactive 3D display of a sphere that looks like this:

There's a 3D tutorial for matplotlib from their website illustrating other examples.

Bokeh is a visualization library that is not part of the standard Python core distribution, is included in Anaconda or Enthought versions. If you find it is missing from your computer, the installation website will tell you how to install it. The short instructions are to use pip if you are managing your own Python. The command line would

pip3 install bokeh

which on Linux may require root (or su) privileges. If you are using Anaconda or Canopy distributions, it is probably already installed.

Once you have it, read the Getting Started Guide on line and the other documentation as you gain confidence. This technology is still developing, and the Guide is only an introduction to a very rich set of features that are fully described in a complete User Guide. These pages provide interactive html that is produced with bokeh.

Rather than use the windowing software of your computer's operating system, say X-windows for Linux as an example, Bokeh prepares your data in a format that can be read by Javascript, the language of your computer's browser. While this may seem a roundabout way of getting a display, it is a rather brilliant technique to leverage the power of the browser and to make graphics universal across all platforms. It is also only one step removed from turning your desktop data processing into a website where you can share your work and collaborate with others. There is an alternative, coming from the world of Javascript (perversely often written JavaScript) and the HTML5 web language, where the work is done largely in the browser and Python is used on the "server side" to do the heavy lifting on the data. This is an entirely functional approach too, and lets us use the full featured web for data processing and visualization. However it is more cumbersome, and adds other languages to the toolchain, and requires running a web server. Before we go into that possibility, we look at what can be done with Python, this library, and a browser like Chrome or Firefox.

Let's start with a really simple example that quickly illustrates how useful this approach is, and how few lines of code are required to get an interactive plot. Start by importing the bokeh elements you will use

from bokeh.plotting import figure, output_file, show import math as m

and in this case also Python math. For more advanced work, you might use numpy and scipy or other packages as well, but here we are only going to plot something simple.

Next, create or import the data you want to plot. You need two lists, one for "x" and one for "y" starting like this

npoints = 1000 x = [] y = [] f1 = 100. f2 = 80. a1 = 5. a2 = 5.

which created empty lists of x and y, and defined some variables we will use to fill those lists with data, in this case the sum of two sine functions. Generate the lists point by point

for i in range(npoints): t = float(i)/10000. arg1 = 2.*m.pi*f1*t arg2 = 2.*m.pi*f2*t amplitude = a1*m.sin(arg1) + a2* m.sin(arg2) x.append(t) y.append(amplitude)

by appending values for each x and y. Lastly, give a file name that you want the program to use to store the output, create the graphics, and show the result.

output_file("sines.html") p = figure() p.line(x, y, line_width=2) show(p)

The rest is bokeh magic. The program will create an "html" file, that is a page that can be viewed in a browser. When you also have a default browser selected for your operating system and it is running, the browser will be directed to display this file. However, the file remains saved after you are done, and to review it again you would enter

file:///full_path_to/sines.html

in the browser target window. The "file:///" tells the browser to look locally, rather than on the web, and the file contains all the code needed to create an interactive plot that looks like this.

The html content that is produced is readable and can be edited if you are familiar with web programming and Javascript. A key feature is not only that you can display it later on your own computer, but you can put it on a website for others to use. Thus, the interactive graphics you create can be shared with colleagues or students. The first lines of the html file are

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <title>Bokeh Plot</title> <link rel="stylesheet" href="https://cdn.pydata.org/bokeh/release/bokeh-0.12.14.min.css" type="text/css" /> <script type="text/javascript" src="https://cdn.pydata.org/bokeh/release/bokeh-0.12.14.min.js"></script> <script type="text/javascript"> Bokeh.set_log_level("info"); </script>

which tell your browser to load the bokeh javascript and style from the web. The next lines invoke that code and display the data which are embedded in the html file as Javascript "json" data. The rest is between Firefox, Chrome or the browser of your choice and the web to get the display running.

One note of caution of course is that you must enable Javascript in your browser, which most users do by default, but some do not because of concern about security.

You will find most of these programs on our examples page for download. For recent additions or special cases, see the examples section of the wiki.

For the assigned homework to use these ideas, see the assignments section.