Simple Line Plot with Matplotlib

Introduction

This tutorial demonstrates how to use Python's Matplotlib library to create a simple line plot with a shaded region representing the area under the curve. The plot includes a text label, axis labels, and custom tick placement and labels.

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Define the function

First, define the function that will be plotted. In this example, the function is (x - 3) _ (x - 5) _ (x - 7) + 85.

def func(x):
    return (x - 3) * (x - 5) * (x - 7) + 85

Define the integral limits

Next, define the limits of the integral. In this example, the limits are a = 2 and b = 9.

a, b = 2, 9

Create the x and y values

Generate a range of x values using the numpy linspace function. Then, use the function defined in step 1 to generate the corresponding y values.

import numpy as np

x = np.linspace(0, 10)
y = func(x)

Create the plot

Create a figure and axis object using subplots. Plot the x and y values using plot. Set the y-axis limits to start at 0 using set_ylim.

fig, ax = plt.subplots()
ax.plot(x, y, 'r', linewidth=2)
ax.set_ylim(bottom=0)

Create the shaded region

Create the shaded region using a Polygon patch. Generate x and y values for the region using linspace and the function defined in step 1. Then, define the vertices of the region as a list of tuples. Finally, create the Polygon object and add it to the axis using add_patch.

from matplotlib.patches import Polygon

ix = np.linspace(a, b)
iy = func(ix)
verts = [(a, 0), *zip(ix, iy), (b, 0)]
poly = Polygon(verts, facecolor='0.9', edgecolor='0.5')
ax.add_patch(poly)

Add the integral label

Add the integral label to the plot using text. The label should be centered at the midpoint between a and b and should be formatted using mathtext.

ax.text(0.5 * (a + b), 30, r"$\int_a^b f(x)\mathrm{d}x$",
        horizontalalignment='center', fontsize=20)

Add axis labels and tick labels

Add the x and y-axis labels using figtext. Hide the top and right spines using spines. Set custom tick placement and labels using set_xticks and set_yticks.

fig.text(0.9, 0.05, '$x$')
fig.text(0.1, 0.9, '$y$')

ax.spines[['top', 'right']].set_visible(False)
ax.set_xticks([a, b], labels=['$a$', '$b$'])
ax.set_yticks([])

Show the plot

Use show to display the plot.

plt.show()

Summary

This tutorial demonstrated how to use Python's Matplotlib library to create a simple line plot with a shaded region representing the area under the curve. The plot included a text label, axis labels, and custom tick placement and labels. By following the steps outlined in this tutorial, you can create similar plots for your own data.