2.5. Plotting with matplotlib

2.5.1. Learning Goals

After going through this notebook, you should be able to:

1. import matplotlib in a Jupyter Notebook

2. Make a basic plot of a 1D function with matplotlib

3. Change the size of a maplotlib plot

4. Change font sizes in matplotlib

5. Change tickmarks

6. Add a legend

7. Add labels to axes

2.5.2. Importing libraries

matplotlib is a python library used for making plots. It is not native to python and thus we must tell our python kernel to import it. In addition, and something specific to Jupyter Notebooks, we will have to tell the notebook that we want to display the plot inline

import matplotlib.pyplot as plt
%matplotlib inline

while we are at it we will import numpy

import numpy as np

2.5.3. Basic plotting

Let’s plot \(f(x) = x^2\). To have a computer do this, we must explicitly define our \(x\) values and compute the corresponding \(f(x)\) value.

# create a list of x values
xValues = []   # initialize list
for i in range(100):
    xValues.append(-5 + i*0.1)
print(xValues)

[-5.0, -4.9, -4.8, -4.7, -4.6, -4.5, -4.4, -4.3, -4.2, -4.1, -4.0, -3.9, -3.8, -3.7, -3.5999999999999996, -3.5, -3.4, -3.3, -3.2, -3.0999999999999996, -3.0, -2.9, -2.8, -2.6999999999999997, -2.5999999999999996, -2.5, -2.4, -2.3, -2.1999999999999997, -2.0999999999999996, -2.0, -1.9, -1.7999999999999998, -1.6999999999999997, -1.5999999999999996, -1.5, -1.4, -1.2999999999999998, -1.1999999999999997, -1.0999999999999996, -1.0, -0.8999999999999995, -0.7999999999999998, -0.7000000000000002, -0.5999999999999996, -0.5, -0.39999999999999947, -0.2999999999999998, -0.1999999999999993, -0.09999999999999964, 0.0, 0.10000000000000053, 0.20000000000000018, 0.3000000000000007, 0.40000000000000036, 0.5, 0.6000000000000005, 0.7000000000000002, 0.8000000000000007, 0.9000000000000004, 1.0, 1.1000000000000005, 1.2000000000000002, 1.3000000000000007, 1.4000000000000004, 1.5, 1.6000000000000005, 1.7000000000000002, 1.8000000000000007, 1.9000000000000004, 2.0, 2.1000000000000005, 2.2, 2.3000000000000007, 2.4000000000000004, 2.5, 2.6000000000000005, 2.7, 2.8000000000000007, 2.9000000000000004, 3.0, 3.0999999999999996, 3.200000000000001, 3.3000000000000007, 3.4000000000000004, 3.5, 3.5999999999999996, 3.700000000000001, 3.8000000000000007, 3.9000000000000004, 4.0, 4.1, 4.200000000000001, 4.300000000000001, 4.4, 4.5, 4.600000000000001, 4.700000000000001, 4.800000000000001, 4.9]

# determine f(x) values
yValues = []   # initialize list
for i in range(100):
    yValues.append(xValues[i]*xValues[i])   # f(x) = x^2 = x*x
print(yValues)

[25.0, 24.010000000000005, 23.04, 22.090000000000003, 21.159999999999997, 20.25, 19.360000000000003, 18.49, 17.64, 16.81, 16.0, 15.209999999999999, 14.44, 13.690000000000001, 12.959999999999997, 12.25, 11.559999999999999, 10.889999999999999, 10.240000000000002, 9.609999999999998, 9.0, 8.41, 7.839999999999999, 7.289999999999998, 6.759999999999998, 6.25, 5.76, 5.289999999999999, 4.839999999999999, 4.409999999999998, 4.0, 3.61, 3.2399999999999993, 2.8899999999999992, 2.5599999999999987, 2.25, 1.9599999999999997, 1.6899999999999995, 1.4399999999999993, 1.2099999999999993, 1.0, 0.809999999999999, 0.6399999999999997, 0.49000000000000027, 0.3599999999999996, 0.25, 0.1599999999999996, 0.0899999999999999, 0.039999999999999716, 0.009999999999999929, 0.0, 0.010000000000000106, 0.04000000000000007, 0.09000000000000043, 0.16000000000000028, 0.25, 0.36000000000000065, 0.49000000000000027, 0.6400000000000011, 0.8100000000000006, 1.0, 1.210000000000001, 1.4400000000000004, 1.690000000000002, 1.960000000000001, 2.25, 2.560000000000002, 2.8900000000000006, 3.2400000000000024, 3.610000000000001, 4.0, 4.410000000000002, 4.840000000000001, 5.290000000000004, 5.760000000000002, 6.25, 6.7600000000000025, 7.290000000000001, 7.840000000000004, 8.410000000000002, 9.0, 9.609999999999998, 10.240000000000007, 10.890000000000004, 11.560000000000002, 12.25, 12.959999999999997, 13.690000000000008, 14.440000000000005, 15.210000000000003, 16.0, 16.81, 17.640000000000008, 18.490000000000006, 19.360000000000003, 20.25, 21.160000000000014, 22.09000000000001, 23.040000000000006, 24.010000000000005]

# plot
plt.plot(xValues,yValues)

[<matplotlib.lines.Line2D at 0x7f89d82675b0>]

The above lists and plots could also be all done in one code snippet. I will do so below and also use numpy routines and operations to make the code look cleaner.

x_vals = np.arange(-5,5,0.1)
y_vals = x_vals**2
plt.plot(x_vals,y_vals)

[<matplotlib.lines.Line2D at 0x7f8998300880>]

2.5.4. Multiple curves on the same plot

x_vals = np.arange(-5,5,0.1)
y_vals_1 = x_vals**2
y_vals_2 = x_vals**3
plt.plot(x_vals,y_vals_1)
plt.plot(x_vals,y_vals_2)

[<matplotlib.lines.Line2D at 0x7f89d8479f70>]

2.5.5. Changing linewidth

x_vals = np.arange(-5,5,0.1)
y_vals_1 = x_vals**2
y_vals_2 = x_vals**3
plt.plot(x_vals,y_vals_1,lw=2)
plt.plot(x_vals,y_vals_2,lw=5)

[<matplotlib.lines.Line2D at 0x7f89d839c9a0>]

2.5.6. Changing the size of the plot

What I mean by size, here, is the image size. If you want to plot a larger domain/range you must simply change the number of x and y values you compute.

There are likely an almost infinite number of ways of changing the image size of a matplotlib plot. Here we will use the approach of declaring a figure object and then modifying that object.

# declare a figure object and set the figure size
fig = plt.figure(figsize=(6,6),dpi=80)
plt.plot(x_vals,y_vals)

[<matplotlib.lines.Line2D at 0x7f8998207b80>]

2.5.7. Changing the font size in matplotlib plots

Changing the fontsizes in matplotlib can be tricky because one can change the font size of different parts of the plot in different spots. For the current plot, we only have text for along our axes so we will modify those. We will, however, modify the default fontsize which will affect our subsequent plots as well.

# update default font size to 16
plt.rcParams.update({'font.size': 16})

# declare a figure object and set the figure size
fig = plt.figure(figsize=(6,6),dpi=80)
plt.plot(x_vals,y_vals)

[<matplotlib.lines.Line2D at 0x7f899828a550>]