To visualize data in Python we will use the library Matplotlib. Matplotlib is a Python 2D plotting library with a variety of vizualisation tools. To see the full gallery of possibilities inluding tutorials, we highly recommend you to visit the offical Matplotlib page. In the following examples we will only cover some of the basic and most often used tools when visualizing data.

If you have not already installed Matplotlib, read our Matplotlib installation instructions. As NumPy is used a lot when working with Matplotlib, we also recommend checking it out.

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Tips and tricks

Data visualization is mainly about making your data easy to understand in a fast, interesting manner. It is therefore important to present your plots as clean, informative and proffesional as possible. We will now look at some small changes to your code that will help you achieve this.

Figure and plot appearance

Use the fact that the appearance of your figures and plots are changeable. The easiest and most important are such as xlabel(), ylabel() and title() that will help you describe your plot, while legend(), colors and linestyles will seperate different plots from eachother. More advanced changes may be making the axes log-scaled, or using markers to specify a certain area of the plot. In order to get better at this, look at other plots to see what they have done well, and what could have been done better. A great place to look for inspiration is the offical Matplotlib webpage, where a number of examples are already made.

Mathematical text

Matplotlib supports using TeX when writing mathematical expressions. This makes math text very presentable while beeing easy to write. We recommend you to visit Matplotlib's "Writing mathematical expressions" to get a complete tutorial. Here is an example:

plt.title(r'$\phi = \frac{\zeta_{a} g}{\omega} e^{k z} cos(\omega t + k x)$')

produces .

Image formats

When working with images, it is of great help to know the difference between different image formats, especially between PNG, JPG/JPEG and PDF. The following is a summary from the article "JPG vs PNG vs PDF: Which File Format Should You Use?

JPG images are ideal for posting photos and images online, as they keep file size down without much overall quality loss. They are also great for emailing preview images to clients, and for printing artwork and photographs at high resolution.
PNG images are ideal for web graphics, especially logos, illustrations, and graphs. They can shrink to very small file sizes when colors and elements are limited, which is another plus. The greatest advantage of a PNG is that the image can be fully transparent, allowing you to place illustrations and designs atop backgrounds effortlessly. PNG is also a top choice if images will be edited and saved multiple times.

PDF images are ideal for printing, especially for graphic design, posters, and flyers. PDF images are also an ideal choice for storing images online when you intend them to be downloaded. PDFs keep your images in one packet so viewers can print and save designs and booklets easily.

When writing in LaTeX, if you have two versions of the same image, it is prefered to use the low-resolution (.png) while developing the report for fast compilation of the preview, and changing to the high-resolution (.pdf) version once the report has been developed.

Simple plot

Visit this page for full documentation on simple plots using pyplot.

Simple plot code

import numpy as np
import matplotlib.pyplot as plt

# Evenly sampled time from 0s to 10s at 200ms intervals
t = np.arange(0.0, 10.0, 0.2)

# Plotting t at x-axis and sin(t) at y-axis
plt.plot(t, np.sin(t))

# Naming the title and both axis
plt.title('Sinus function')
plt.ylabel('sin(t)')
plt.xlabel('t [s]')

# Need to call the show() function at the end to display our figure
plt.show()

Multiple plots in same figure

import numpy as np
import matplotlib.pyplot as plt

# Evenly sampled time at 200ms intervals
t = np.arange(0.0, 5.0, 0.2)

# plot() can plot several lines in the same figure. To seperate the different lines 
# from eachother, we may change the line style and format strings.
# See the plot() documentation for a complete list of line styles and format strings.
# The following lines have red dashes, blue squares and green triangles
plt.plot(t, t, 'r--', label='Linear line')
plt.plot(t, t**2, color='blue', linestyle='none', marker='s', label='Second degree polynom')
plt.plot(t, t**3, 'g^', label='Third degree polynom')

# To describe our plot even more detailed we can draw the labels we previously gave our lines using legend.
# Specifying the location of legend is optionally, but may be 'left', 'lower right' or 'best'.
plt.legend(loc='upper left')

# The function axis() sets the axis sizes, and takes the argument [xmin, xmax, ymin, ymax]
plt.axis([0, 5, 0, 100])

plt.title('Mulitple polynoms')
plt.show()

More in-depth plot() documentation and legend() documentation.

Multiple figures and subplots

A very good and more detailed guide on subplots and figures can be found here.

import matplotlib.pyplot as plt
import numpy as np

# Some example data to display
x = np.linspace(0, 2 * np.pi, 400)
y = np.sin(x ** 2)

A single plot

subplots() without arguments return a Figure and a single Axes. When dealing with multiple plots in the same figure, the different axes will seperate the different subplots from eachother within the figure.

A single plot

fig, ax = plt.subplots()
fig.suptitle('A single plot')
ax.plot(x, y)

Stacking subplots in one direction

The first two optional arguments of pyplot.subplots() define the number of rows and columns of the subplot grid.

When stacking in one direction only, the returned axs is a 1D numpy array containing the list of created Axes.

Vertically stacked subplots

fig, axs = plt.subplots(2)
fig.suptitle('Vertically stacked subplots')
axs[0].plot(x, y)
axs[1].plot(x, -y)

If you are creating just a few Axes, it's handy to unpack them immediately to dedicated variables for each Axes. That way, we can use ax1 instead of the more verbose axs[0].

Vertically stacked subplots (alternative)

fig, (ax1, ax2) = plt.subplots(2)
fig.suptitle('Vertically stacked subplots')
ax1.plot(x, y)
ax2.plot(x, -y)

To obtain side-by-side subplots, pass parameters 1, 2 for one row and two columns.

Horizontally stacked subplots

fig, (ax1, ax2) = plt.subplots(1, 2)
fig.suptitle('Horizontally stacked subplots')
ax1.plot(x, y)
ax2.plot(x, -y)

Stacking subplots in two directions

When stacking in two directions, the returned axs is a 2D numpy array. If you have to set parameters for each subplot it's handy to iterate over all subplots in a 2D grid using for ax in axs.flat:.

axes.flat is not a function, it's an atribute of the numpy.ndarray. ndarray.flat is a 1-D iterator over the array. This is a numpy.flatiter instance, which acts similarly to, but is not a subclass of Python’s built-in iterator object.

Stacking subplots in two directions

fig, axs = plt.subplots(2, 2)
fig.suptitle('Stacking subplots in two directions')
axs[0, 0].plot(x, y)
axs[0, 0].set_title('Axis [0,0]')
axs[0, 1].plot(x, y, 'tab:orange')
axs[0, 1].set_title('Axis [0,1]')
axs[1, 0].plot(x, -y, 'tab:green')
axs[1, 0].set_title('Axis [1,0]')
axs[1, 1].plot(x, -y, 'tab:red')
axs[1, 1].set_title('Axis [1,1]')


for ax in axs.flat:
    ax.set(xlabel='x-label', ylabel='y-label')

# Hide x labels and tick labels for top plots and y ticks for right plots.
# Try commenting out the next two lines to see what would happen if we did not hide the inner labels and ticks.
for ax in axs.flat:
    ax.label_outer()

Multiple figures with subplots

Creating multiple figures can be achieved in a number of ways. Below, we will demonstrate two different approaches.

To display all figures at once, only call plt.show() at the end of the last figure. As an extra practice, try moving the call or adding more, what happens, and why?

Multiple figures

fig1, ax1 = plt.subplots()
fig1.suptitle('A single plot')
ax1.plot(x, y)

fig2, ax2 = plt.subplots()
fig2.suptitle('Another single plot')
ax2.plot(x, y)

plt.show()

MATLAB, and pyplot, have the concept of the current figure and the current axes. All plotting commands apply to the current axes. You can create multiple figures by using multiple figure() calls with an increasing figure number. Of course, each figure can contain as many axes and subplots as your heart desires:

Multiple figures, current method

plt.figure(1)                # the first figure (now current figure)
plt.subplot(211)             # the first subplot in the first figure (now current subplot)
plt.plot([1, 2, 3])
plt.subplot(212)             # the second subplot in the first figure (new current subplot)
plt.plot([4, 5, 6])

plt.figure(2)                # a second figure (new current figure)
plt.plot([4, 5, 6])          # creates a subplot(111) by default

plt.figure(1)                # figure 1 current; subplot(212) still current
plt.subplot(211)             # make subplot(211) in figure 1 current
plt.title('Easy as 1, 2, 3') # subplot 211 title

A more detailed explanation of the subplot method used above is found in the code explaining Quiver autoscaling vs manually set axes.

Quiver plot

Quiver plots a 2D vector field of arrows.

More in-depth quiver documentation and functions.

Simple quiver plot

import numpy as np
import matplotlib.pyplot as plt

# X and Y define the arrow locations
X, Y = np.meshgrid(np.arange(0, 2 * np.pi, .2), np.arange(0, 2 * np.pi, .2))

# U and V define the arrow directions, respectively in x- and y-direction
U = np.cos(X)
V = np.sin(Y)

# Call signature: quiver([X, Y], U, V, [C]), where C optionally sets the color
plt.quiver(X, Y, U, V)
plt.title('Simple quiver plot')
plt.show()

The plot autoscaling does not take into account the arrows, so those on the boundaries may reach out of the picture. This is not an easy problem to solve in a perfectly general way. The recommended workaround is to manually set the Axes limits in such a case. An example showing autoscaling vs manually is shown below.

Quiver autoscaling vs manually set axes

import numpy as np
import matplotlib.pyplot as plt

# X and Y define the arrow locations
# This setup gives us 10 arrows in width and height, as our interval is from -5 to 5 with step 1
X = np.arange(-5, 5, 1)
Y = np.arange(-5, 5, 1)

# U and V define the arrow directions, respectively in x- and y-direction
U, V = np.meshgrid(3*X, 3*Y)

plt.figure()

# Argument 121 in subplot() below denotes 1 row, 2 columns, first subplot. sublot(121) is then current.
plt.subplot(121)
plt.quiver(X, Y, U, V)
plt.title('Only autoscaling')

# Argument 122 denotes 1 row, 2 columns, second subplot. Notice that the number of rows and columns has to be equal every time, 
# where as the last number is the position where we want our subplot.
plt.subplot(122)
plt.quiver(X, Y, U, V)
# Here we specify the axes. How much extra space you need depends on the arrow size and direction,
# and must therefore be adapted each time
plt.axis([-6.5, 5.5, -6.5, 5.5])
plt.title('Manually set axes')

plt.show()

Contour plot

Further demos on contour plots and contour labels.

In the example below two types of contour plots are used, where contour and contourf draw contour lines and filled contours, respectively.

The call signature is contour([X, Y,] Z, [levels]), where X and Y are the coordinates of the values in Z, and Z is the height values over which the contour is drawn. Levels is optional, and determines the number and positions of the contour lines / regions.

Contour plots

import matplotlib.pyplot as plt
import numpy as np

def f(x, y):
    return np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)
 
x = np.linspace(0, 5, 60)
y = np.linspace(0, 5, 50)

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

fig, axs = plt.subplots(1,3)
fig.suptitle('Three versions of the same contour plot')
axs[0].contour(X, Y, Z)
axs[1].contourf(X, Y, Z)
axs[2].contour(X, Y, Z, colors='black')

plt.show()

3D Plots

3D Plotting is not used in most courses, but may be used as a great tool of learning, as the visual aspects of plotting often are even more reinforced in 3D plots. In this chapter, we want to show you how easy it is to set up a simple 3D plot using Matplotlib. Check out Matplotlib's tutorial on 3D Plots if you want to learn more about the possibilities in 3D.

3D Plots as a tool of learning may be especially useful when learning about linear wave theory in the course TMR4247 - Marine Technology - Hydrodynamics.

3D Plot

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

fig = plt.figure()

# Setting the axes to 3D
ax = Axes3D(fig)        
X, Y = np.meshgrid(np.arange(0, 2*np.pi, 0.2), np.arange(0, 2*np.pi, 0.2))
Z = np.sin(X)

# Making the 3D plot as a surface plot, where X, Y and Z is data values as 2D arrays
# The arguments here are in the same format as used in Contour plots
# Also specifing a colormap to make our surface easier to interpet
ax.plot_surface(X, Y, Z, cmap='Blues')
ax.set_xlabel('X-label')
ax.set_ylabel('Y-label')
ax.set_zlabel('Z-label')
ax.set_title('3D Plot')

plt.show()

Plotting animation

Plots are often time-dependent, and even though most of them are easily interpeted by choosing a specific t_0,making a small animation may help you get some extra insight to how the plot actually changes with time. We will now set up a simple animation using the 3D plot as an example. Because our main goal with this animation is to get a better understanding of how our function changes with time, we will not put to much effort into the aesthetics of our animaiton.

Plotting animation

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


fig = plt.figure()
ax = Axes3D(fig)
X, Y = np.meshgrid(np.arange(0, 2*np.pi, 0.2), np.arange(0, 2*np.pi, 0.2))

# Setting a time interval
dt = 0.1                

# We have set our range from 0 to 10000 to make sure it runs as long as we want, and we'll then close it ourself
for i in range(0, 10000):
    # Our function for Z has to be dependent on some non-constant value
    # We have chosen to increase 'dt' each loop
    dt = dt + 0.1
    Z = np.sin(X + dt)

    # Our plotting has to be done inside the loop, as we want to redraw it mulitple times
    ax.plot_surface(X, Y, Z, cmap='Blues')

    # Since we are using the 'ax.clear()' at the end to clear all previous drawings, we need to specfiy all axes inside the loop
    # If we choose not to clear, we can move this outside the loop
    ax.set_xlabel('X-label')
    ax.set_ylabel('Y-label')
    ax.set_zlabel('Z-label')
    ax.set_title('3D Animation')

    # Here we pause the system for some time, in order for us to be able to watch as the plot changes
    plt.pause(1/60)

    # Lastly, we clear all previous drawings, as we usually only want to see the plot at the current time value
    ax.clear()
    
plt.show()

The animation below is slightly altered from the code above in order to make it a GIF.

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Data visualization in Python