# Plots with matplotlib¶

## Basic plotting¶

We can create plots with Python using matplotlib.pyplot module. First we import the module:

import matplotlib.pyplot as plt


Each function in matplotlib.pyplot can be now accessed by typing plt.function_name.

Here are the main functions we will use. Click on the function description to see its full documentation:

function

usage

plot

creates a plot

title

sets a title of the plot

xlabel

sets label of the x-axis

ylabel

sets label of the y-axis

xlim

set the range of x values displayed

ylim

set the range of y values displayed

show

displays the plot

The syntax of the plot function is plot(xl, yl, options) where:

• xl is the list of x-coordinates of points we want to plot

• yl is the list of y-coordinates

• other options may specify how we want the plot to look like.

The show function must be executed to display a plot.

xl = range(-10, 11)                  #x-coordinates
yl = [x**2 for x in xl]              #y-coordinates
plt.plot(xl, yl)                     #create plot
plt.ylim(-10, 110)                   #set the range of y-values displayed
plt.title('My first plot')           #set the plot title
plt.xlabel('This is the x-axis')     #set the label of the x-axis
plt.ylabel('This is the y-axis')     #set the label of the y-axis
plt.show()                           #show plot - not necessary in the inline mode


Notice that on the plot above the x-axis and the y-axis have different scales: the distance between 0 and 5 on the x-axis is bigger than the distance between 0 and 20 on the y-axis. In order to set the same scale for both axes we can use the axis function:

plt.plot(xl, yl)           #create plot
plt.axis('equal')          #equalize axes
plt.ylim(-10, 100)         #set the range of y-values displayed
plt.show()


The axis function has other options that can be used to control properties of coordinate axes of a plot. See matplotlib documentation for details.

## More plotting options¶

By default the plot function joins the specified points by straight lines. If, instead, we want to plot individual points as red circles we can add the 'ro' option ('r' specifies the color, and 'o' the shape of markers):

plt.plot(xl, yl, 'ro')
plt.xlim()
plt.ylim(-10, 110)
plt.show()


Here are same other options for shapes and colors of markers:

shape

meaning

color

meaning

'-'

solid line

'b'

blue

'--'

dashed line

'g'

green

'.'

point marker

'r'

red

'o'

circle marker

'c'

cyan

's'

square marker

'w'

white

'+'

plus marker

'm'

magenta

'x'

x marker

'y'

yellow

'D'

diamond marker

'k'

black

Here are some examples:

x_list = range(20)
y1_list = 20*[1]
y2_list = 20*[2]
y3_list = 20*[3]
y4_list = 20*[4]

plt.xlim(-1,20)
plt.ylim(0,5)
plt.plot(x_list, y1_list, 'b.',)
plt.plot(x_list, y2_list, 'gx')
plt.plot(x_list, y3_list, 'm.')
plt.plot(x_list, y4_list, 'rs')
plt.title('Shapes and colors')

plt.show()


The parameter ms of the plot function can be used to set the size of markers:

plt.xlim(-1,20)
plt.ylim(0,5)

plt.plot(x_list, y1_list, 'rD', ms=2)
plt.plot(x_list, y2_list, 'rD', ms=4)
plt.plot(x_list, y3_list, 'rD', ms=8)
plt.plot(x_list, y4_list, 'rD', ms=12)
plt.title('Sizes of markers')

plt.show()


The parameter alpha controls transparency of plots. The value of alpha can vary between 0 (completely transparent) to 1 (opaque):

plt.xlim(-1,20)
plt.ylim(0,5)

plt.plot(x_list, y1_list, 'rD', ms=20, alpha= 0.25)
plt.plot(x_list, y2_list, 'rD', ms=20, alpha= 0.5)
plt.plot(x_list, y3_list, 'rD', ms=20, alpha= 0.75)
plt.plot(x_list, y4_list, 'rD', ms=20, alpha= 1.0)
plt.title('Transparency')

plt.show()


## Plot legend¶

If more than one graph is plotted on a single figure a legend can be used to label graphs:

x_list =  [0.01*x for x in range(-200, 201)]
y2_list = [x**2 for x in x_list]
y4_list = [-x**2 for x in x_list]
y6_list = [-x**3 + x for x in x_list]

plt.plot(x_list, y2_list, 'b-', label='$y=x^2$')    # label specifies the plot description in the legend
plt.plot(x_list, y4_list, 'r-', label='$y=-x^2$')   # LaTeX can be used to typeset formulas in matplotlib labels and titles
plt.plot(x_list, y6_list, 'g-', label='$y=x^3+x$')

plt.ylim(-1, 1)
plt.xlim(-3, 3)

plt.legend(fontsize=13) # creates the legend; fontsize specifies the size of fonts in the legend

plt.show()


Exercise 1. Plot the function $$y = \sin(6x)$$ for $$0\leq x \leq 6$$. The Python function sin which computes values of sine is a part of the math module:

from math import sin, pi
sin(pi/2)


1.0