10. Plotting

Saleh Rezaeiravesh, saleh.rezaeiravesh@manchester.ac.uk
Department of Mechanical and Aerospace Engineering, The University of Manchester, Manchester, UK

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Overview: In Python, there are various packages for visualisation of the data. One of the most frequently used package is `matplotlib`:

https://matplotlib.org/stable/index.html

In this notebook, elementary syntaxes for plotting 2D graphs in matplotlib are opresented.

10.1. Import matplotlib

matplotlib has several classes, but the main one that we use here is pyplot. This can be imported as below:

import matplotlib.pyplot as plt

10.2. 2D plot of a single graph

Assume we want to plot \(y\) versus \(x\), where we have numpy arrays for these two variables. First, we create some data:

#first create some test data
import numpy as np

x = np.linspace(0,2*np.pi,100)   #equi-spaced x-values
y = np.sin(3.*x)                    #y values at x

Plotting is simple, we use plot from class plt (imported above), and then we should use show() to see the plot.

plt.plot(x,y)
plt.show()

10.2.1. Line’s color and style

A plot has several attributes including:

• line style, ls: simply you can write - (solid line), : (dotted line), -- (dashed line)

• line color, color

• line width, lw

plt.plot(x,y,'--',color='red',lw=2)
plt.show()

You can see the list of some default colors in matplotlib in this link.

10.2.2. Add markers

You can use markers solely or with lines. By default, markers appear at values of x. There are different markers, such as o (circle), x (cross), s (square), etc. See the full list here.

plt.plot(x,y,'-ob')
plt.show()

Markers can have a different face color specified by mfc. Note that mfc='none' returns hollow markers.

plt.plot(x,y,'--or',mfc='k')
plt.show()

10.2.3. Axis label

For the axes label, we can use pure text as string, Latex math expressions (provided within $  $ as usual), or a combination of the two. If you are using the latter, make sure you add an r before the string. Also, the font size of the labels can be easily specified.

plt.plot(x,y,'-k')
plt.xlabel('$x$',fontsize=18)                   #x label
plt.ylabel(r'$y=\sin(3x)$',fontsize=12)         #y label
plt.show()

10.2.4. Figure size

This width and height of the figure can be set through the 1st and second arguments of figsize:

### control the figure size
plt.figure(figsize=(8,3))
plt.plot(x,y,'-k')
plt.show()

10.2.5. Size of the axes’ ticks

There are different ways to set the size of the ticks on the axes, including using plt.xticks() and plt.yticks():

plt.figure(figsize=(8,3))
plt.plot(x,y,'-k')
plt.xticks(fontsize=16)
plt.yticks(fontsize=16)
plt.show()

10.2.6. Add grid

plt.plot(x,y,'-k')
plt.grid()
plt.show()

10.3. Multiple graphs in one plot

Seomtimes we need to plot two or more graphs in one plot. To distinguish between multiple graphs, different line styles and coloes with and without markers can be used. A label can be assigned to each graph using label key in plot function. To show the labels as a legend, call plt.legend which has several parameters including loc (location of the legend on the plot) and fontsize. For a full list of parameters, see this link.

Let’s create another graph and plot it along the above curve in one plot.

y2=0.5*np.cos(0.5*x**2)

plt.figure(figsize=(8,4))

plt.plot(x,y,'-b',label=r'$\sin(3x)$')      #plotting the first graph 
plt.plot(x,y2,'--r',label=r'$0.5\cos(x^2/2)$')   #plotting the second graph

plt.xlabel(r'$x$',fontsize=16)      
plt.ylabel(r'$y$',fontsize=16)

plt.xticks(fontsize=16)
plt.yticks(fontsize=16)

plt.legend(loc='best',fontsize=14)   #add legend with location set to be the best one
plt.show()

10.4. Multiple graphs in subplots

We can have a set of subplots within each one or more plots are provided. Use plt.subplot(nRows, nColumn, id) to create an array of subplots, where:

• nRows: number of rows

• nColumn: number of columns

• id: plot id - it goes from 1 to nRows*nColumn.

Once all subplots are defined, write plt.show().

plt.figure(figsize=(10,5))

#subplot 1
plt.subplot(1,2,1)   #indices: 1 row, 2 column, first subplot
plt.plot(x,y,'-b',label=r'$\sin(x)$')
plt.xlabel(r'$x$',fontsize=16)
plt.ylabel(r'$y$',fontsize=16)
plt.xticks(fontsize=16)
plt.yticks(fontsize=16)
plt.legend(loc='best',fontsize=14)   #add legend

#subplot 2
plt.subplot(1,2,2)   #indices: 1 row, 2 column, second subplot
plt.plot(x,y2,'--r',label=r'$\cos(2x)$')
plt.xlabel(r'$x$',fontsize=16)
plt.ylabel(r'$y$',fontsize=16)
plt.xticks(fontsize=16)
plt.yticks(fontsize=16)
plt.legend(loc='best',fontsize=14)   #add legend

plt.show()  #show both subplots

We can add other graphs to each of these subplots. Let’s add an array and a list of discrete data, for instance (shown by markers).

#list of data
a=[0,0.5,4,2.8,5,1]
b=[-0.25,0,0.39,0.6,-0.4,0]

#a new function using numpy arrays as input
y2=np.cos(4*x)*np.sin(2*x)

plt.figure(figsize=(14,3))

#subplot 1
plt.subplot(1,2,1)   #indices: 1 row, 2 column, first subplot
plt.plot(x,y,'-b',label=r'$\sin(3x)$')
plt.plot(a,b,'o k',ms=7, label='Some random data')
plt.xlabel(r'$x$',fontsize=16)
plt.ylabel(r'$y_1$',fontsize=16)
plt.xticks(fontsize=16)
plt.yticks(fontsize=16)
plt.legend(loc='best',fontsize=10)   #add legend


#subplot 2
plt.subplot(1,2,2)   #indices: 1 row, 2 column, second subplot
plt.plot(x,y2,'--r',label=r'$0.5*\cos(x^2/2)$')
plt.xlabel(r'$x$',fontsize=16)
plt.ylabel(r'$y_2$',fontsize=16)
plt.xticks(fontsize=16)
plt.yticks(fontsize=16)
plt.legend(loc='best',fontsize=10)   #add legend
plt.show()  #show both subplots

10.4.1. Save a plot

To save a plot made by matplotlib, we can use savefig('PATH/figName'). Make sure the path exists on the disk. figName should contain the image type, like .png, .pdf, etc. If you want to show the plot, write plt.show() after plt.savefig().