2D-plotting

2D-plotting in matplotlib

As discussed before, matplotlib is the workhorse of visualization in Python and therefore, it should always be your first choice, before trying anything else. To see how plotting with matplotlib works, let’s start with a simple example of 2D curve plotting,

import numpy as np
import matplotlib.pyplot as plt
def f(x):
    return x**2*np.exp(-x**2)
x = np.linspace ( start = 0.    # lower limit
                , stop = 3      # upper limit
                , num = 51      # generate 51 points between 0 and 3
                )
y = f(x)    # This is already vectorized, that is, y will be a vector!
plt.plot(x, y)
plt.show()

If you try the above code in IPython, the out on screen would be something like the following,

matplotlib.pyplot is a collection of command-style functions and methods that have been intentionally made to work similar to MATLAB plotting functions. Each pyplot function makes some changes to a figure. For example, it can create a figure, like plt.plot() in the above example, or decorates the plot with labels, texts, etc, as will be seen below.

In matplotlib.pyplot various states are preserved across function calls. Therefore, any further plotting commands will add to the existing tasks that have been so far performed on the current figure and plotting area, and the plotting functions are directed to the current axes (i.e., the axes part of a figure).

Plotting multiple curves in one figure

Now, suppose you want to add another curve to the same figure that you created in the previous section, for example, the curve corresponding to the following mathematical function,

Then, all you would need to do is to add the follwing lines of code to your previous code snippet,

def g(x):
    return x*np.exp(-x)
xx = np.arange  ( start = 0.
                , stop = 3.
                , step = 0.05
                ) # generate points between start and stop with distances of step apart from each other
yy = g(xx)
plt.plot( xx
        , yy
        , 'r-'  # plot with the color red, as line
        )

This will modify your existing figure to something like the following,

Setting the limits of the plot’s axes

The plot of the above figure has an obvious problem: It does not seem to show the entire important range of the new function that is represented by the red-curve. To fix this issue, we should increase our curve data (xx, yy) to cover the range of interest, and then set the limits of both X and Y axes to our desired ranges,

xx = np.arange  ( start = 0.
                , stop = 6.
                , step = 0.05
                ) # generate points between start and stop with distances of step apart from each other
plt.plot( xx
        , g(xx)
        , 'r-'  # plot with color red, as line
        )
plt.axis([0, 6, -0.05, 0.6]) # [xmin, xmax, ymin, ymax]

which will modify the existing open figure in IPython (Jupyter) environment to the following,

Adding the axis-labels, figure-title, and legends

We can further decorate the generated figure by adding the relevantr information to it like the following,

plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.legend( [ 'f(x) = x^2*exp(-x^2)'   # This is f(x)
            , 'g(x) = x*exp(-x)'       # This is g(x)
            ] )
plt.title('multiple Matplotlib curves in a single decorated figure');

This will modify the existing figure to the following,

Saving figures as external files

Finally, we can save the generated figure in the file-format of our interest, for example, PDF, by the following command,

plt.savefig('multipleCurvesFullRangeDecorated.pdf') # produces a PDF file containing the figure

This will generate a PDF file that will be located in the current working directory of your Python environment. Alternatively, you could save it as a PNG file or any other popular image format by simply using the image format file-extension, like the following,

plt.savefig('multipleCurvesFullRangeDecorated.png') # produces a PNG file containing the figure

Working simultaneously with multiple open figures

There are times that you want to plot multiple curves, but each one in a separate figure. To do so, you can use plt.figure() whenever you want to create a new figure environment. For example, the two curves superposed on each other in the previous plots could be separated from each other with the following code,

def g(x):
    return x*np.exp(-x)
def f(x):
    return x**2*np.exp(-x**2)
x = np.arange   ( start = 0.    # upper limit
                , stop  = 6.    # lower limit
                , step  = 0.05  # step-size (distance between the points)
                ) # generate points between start and stop with distances of step apart from each other
plt.figure(1)
plt.plot( x, f(x) )    # plot f(x)
plt.figure(2)
plt.plot( x, g(x) )  # plot g(x)

This will generate the following two separate figures in the Python environment,

Adding transparency to the plot objects

It may happen frequently that you may need to represent some lines or objects in your plots at varying levels of transparency. This can be done by the alpha optional argument to the plot() function,

import matplotlib as mpl
x = np.arange   ( start = 0.    # upper limit
                , stop  = 6.    # lower limit
                , step  = 0.05  # step-size (distance between the points)
                ) # generate points between start and stop with distances of step apart from each other
thisLegend = []
mpl.use('Agg')   # avoid displaying the figure in Python environment
for thisAlpha in [0.2,0.4,0.6,0.8,1.0]:
    plt.plot( x, thisAlpha*x, 'b-.', alpha = thisAlpha );   # -. represents dashed-dotted line-style
    thisLegend.append("alpha = {}".format(thisAlpha))
plt.legend( thisLegend );
plt.savefig("transparency.png")

This will export the following figure to an external PNG file in the current working directory of Python, like the following,

Plotting line-styles and symbols

Just as in MATLAB, there are several line-style options available also in Python,

Similarly, one can use different symbols to generate scatter plots, instead of lines, using either scatter() or plot() functions,

Execise

Modify the following code to generate a figure like the following,

Subplots in matplotlib

Suppose you wanted to generate the same curves as in the above example, but each in a different plot, but with all of the plots in the same figure. One way to do this would be like the following,

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.arange   ( start = 0.    # upper limit
                , stop  = 6.    # lower limit
                , step  = 0.1   # step-size (distance between the points)
                ) # generate points between start and stop with distances of step apart from each other
def g(x):
    return x*np.exp(-x)
def f(x):
    return x**2*np.exp(-x**2)

plt.figure()            # generates a new figure as in MATLAB

plt.subplot(2,1,1)      # create a 2-row, 1-column subplot, and this is the 1st subplot.
plt.plot(x, f(x), 'r-') # plot with color red, as line

plt.subplot(2,1,2)      # create a 2-row, 1-column subplot, and this is the 2nd subplot.
plt.plot(x, g(x), 'bo') # plot with color blue, as points

plt.xlabel('x')
plt.ylabel('y')
plt.legend(['x*exp(-x)'])
plt.axis([0, 3, -0.05, 0.6]) # [xmin, xmax, ymin, ymax]
plt.title('an example Matplotlib subplot')

plt.savefig('two_by_one_subplot.png')
plt.show()

The output of the code is a PNG figure available here,

Note that since the decorations (i.e., axis labels, legend, title, …) appeared only for the second subplot, only the second one in the figure above is decorated with plot title, legend, etc. Also, note again that, the figure() method creates a new plot window on the screen that will contain both subplots.

Also, note that the subplots in the above figure look a bit too-squished and overlap each other. In such cases, one could use tight_layout() method to automatically adjust the paddings of the subplots and their organization within the figure. For example, by simply typing,

plt.tight_layout()

one would automatically get the following padded subplots that peacefully coexist,