Matplotlib

Matplotlib#

Data Visualization#

It is said that a picture is worth a 1000 words

In technical communication, a good figure is worth a 1000 words

Minard’s map of Napoleon’s Russian campaign of 1812 is often described as the best graphic ever produced
- Includes information of the troop size, location, temperature, travel direction and time

Minard's map
Source: Wikimedia

Matplotlib #

Matplotlib is a data visualization library built on numpy and designed to work seamlessly with scipy
Originally, it was intended as an interface for Matlab-style plotting in Python notebooks

2D plotting
- Point data - function in one variable, \(y = f(x)\)
  - Line plots, scatter plots, etc.
- Scalar fields – functions in two variables, \(z = f(x, y)\)
  - Contour plots, images
- Vector fields – vector functions \(\bar{V}(x, y) = (u(x, y), v(x, y))\)
  - Quiver plots, stream plots, etc.

3D plotting - 3D counterparts of point data, scalar fields, vector fields
Statistical plots - Histograms, box plots, violin plots, pie charts, etc.

Anatomy of a Figure#

Source: matplotlib.org

All matplotlib plots have three main elements

A Figure object
- The main canvas or stage
- All the other figure elements are artists that act to create the final graphic
Axis objects (x, y, z axes)
- Control the limits of the plots
- Contains the ticks and tick labels
Axes objects
- The actual data to be visualized
…

Matplotlib Examples #

See https://matplotlib.org/stable/gallery/index.html for more examples

A simple plot
- \(V(t) = 1 + sin(2\pi t)\)

Multiple Line Plots

Subplots

2D Scatter Plot

3D Scatter Plot

3D Parametric Curve

3D Surface and Wireframe Plots

_images/3d_surface_and_wireframe_plots.png

Contour Plots

Quiver Plot

Stream Plot

Histogram

Box Plots

Errorbar Plots

Pie Chart

Plotting Guidelines#

Always label axes
- Always include units where applicable

Legends only used with multiple datasets
Consider what it looks like in black and white

Include a title or a caption, but never both
- Titles/captions should give more information than is already provided by the rest of the plot

Each plot should tell a self-contained story
- Information from rest of the document should not be required reading to understand a plot
- Consider splitting very busy plots or combining several simple plots if they are related

Example

Bad Plot

Better Plot

Experimental data is NEVER connected with lines (just use markers)
- Lines are used for mathematical functions or trend lines (curve fits)
- Use error bars when available

Pay attention to font size
- If it looks good on the computer screen it’s good for written reports
- Increase the font size a few points for presentations

Example

Bad Plot

Better Plot

Matplotlib Plotting Interfaces#

Matplotlib provides two interfaces for plotting: matlab-style and object-oriented interfaces

A Matlab-style interface
- Uses the pyplot sub-module to create plots
- This interface imitates Matlab plotting – the original goal of matplotlib
- Works with an active figure that is modified as needed across different function calls until the figure is either closed or a new figure is explicitly created

The object-oriented interface
- Uses the Axes object for plotting
- No notion of an active figure
- Provides better control over the figure

Pyplot Interface: Example#

# backend for rendering the plots, replace widget with inline if you do not see the plot in the output
%matplotlib widget

import numpy as np
import matplotlib.pyplot as plt

# Data to be plotted
x = np.linspace(-2,2,20)
y = x**2

# Create a new figure and plot
fig = plt.figure()
plt.plot(x, y, linestyle='solid', color='k', label='$x^2$')
plt.plot(x, 2 + np.sin(x), color='b', marker='o', label='$2 + sin(x)$')

# Decorate
plt.xlabel('x')
plt.ylabel('y')
plt.title('Pyplot Interface')
plt.xlim(-2.2, 2.2)
plt.ylim(-0.2, 4.2)

# Add legend
plt.legend()

# Show/save figure - optional
plt.savefig("pyplot_simple.png")
plt.show()

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Cell In[1], line 2
      1 # backend for rendering the plots, replace widget with inline if you do not see the plot in the output
----> 2 get_ipython().run_line_magic('matplotlib', 'widget')
      4 import numpy as np
      5 import matplotlib.pyplot as plt

File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/IPython/core/interactiveshell.py:2480, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
   2478     kwargs['local_ns'] = self.get_local_scope(stack_depth)
   2479 with self.builtin_trap:
-> 2480     result = fn(*args, **kwargs)
   2482 # The code below prevents the output from being displayed
   2483 # when using magics with decorator @output_can_be_silenced
   2484 # when the last Python token in the expression is a ';'.
   2485 if getattr(fn, magic.MAGIC_OUTPUT_CAN_BE_SILENCED, False):

File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/IPython/core/magics/pylab.py:103, in PylabMagics.matplotlib(self, line)
     98     print(
     99         "Available matplotlib backends: %s"
    100         % _list_matplotlib_backends_and_gui_loops()
    101     )
    102 else:
--> 103     gui, backend = self.shell.enable_matplotlib(args.gui.lower() if isinstance(args.gui, str) else args.gui)
    104     self._show_matplotlib_backend(args.gui, backend)

File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3665, in InteractiveShell.enable_matplotlib(self, gui)
   3662     import matplotlib_inline.backend_inline
   3664 from IPython.core import pylabtools as pt
-> 3665 gui, backend = pt.find_gui_and_backend(gui, self.pylab_gui_select)
   3667 if gui != None:
   3668     # If we have our first gui selection, store it
   3669     if self.pylab_gui_select is None:

File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/IPython/core/pylabtools.py:338, in find_gui_and_backend(gui, gui_select)
    321 def find_gui_and_backend(gui=None, gui_select=None):
    322     """Given a gui string return the gui and mpl backend.
    323 
    324     Parameters
   (...)
    335     'WXAgg','Qt4Agg','module://matplotlib_inline.backend_inline','agg').
    336     """
--> 338     import matplotlib
    340     if _matplotlib_manages_backends():
    341         backend_registry = matplotlib.backends.registry.backend_registry

ModuleNotFoundError: No module named 'matplotlib'

Object Oriented Interface: Example#

#import numpy as np
#import matplotlib.pyplot as plt

# Data to be plotted
x = np.linspace(-2,2,20)
y = x**2

# Plot
fig, ax = plt.subplots(1, 1)
ax.plot(x, y, linestyle='solid', color='k', label='$x^2$')
ax.plot(x, 2 + np.sin(x), color='b', marker='o', label='$2 + sin(x)$')

# Decorate
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('OO Interface')
ax.set_xlim(-2.2, 2.2)
ax.set_ylim(-0.2, 4.2)

# Alternate method for decoration
#ax.set(xlabel='x', ylabel='y', title='OO Interface', xlim=(-2.2, 2.2), ylim=(-0.2, 4.2))

# Add legend
ax.legend()

# Show/save figure - optional
fig.savefig("OO_simple.png")

Plot Parameters#

The plot function in pyplot and the plot method of the Axes object are used to plot data of the form \(y = f(x)\)

Both take in optional formatting parameters of color, marker, and linestyle
- If not specified, these will be automatically determined
These parameters can be combined into a single string to specify the plot formatting

color

marker

linestyle


Black	‘k’
Blue	‘b’
Green	‘g’
Red	‘r’
Cyan	‘c’
Magenta	‘m’
Yellow	‘y’
White	‘w’


Point	‘.’
Circle	‘o’
Square	‘s’
Star	‘*’
Plus	‘+’
x	‘x’
Diamond	‘D’
Down Triangle	‘v’
Up Triangle	‘^’


Solid	‘-’	‘solid’
Dashed	‘–’	‘dashed’
Dash-dot	‘-.’	‘dashdot’
Dotted	‘:’	‘dotted’

These parameters can be combined into a single string to specify the plot formatting

x = np.linspace(-2, 2, 20)
fig = plt.figure()
plt.plot(x,     x, '-g') # solid green
plt.plot(x, x + 1, '--c') # dashed cyan
plt.plot(x, x + 2, '-.k') # dashdot black
plt.plot(x, x + 3, ':r') # dotted red

plt.show()

Subplots with Pyplot Interface#

#data to be plotted
x = np.linspace(0, 10, 50)

# Create an empty figure, all arguments are optional
# figsize is the figure size in inches
plt.figure(figsize = (8,8))

# Add a plot to the left, upper left corner
# Assumes there are going to be 2 rows and 2 columns
plt.subplot(2, 2, 1)
plt.plot(x, -1 + 0.2*x, '-r') 
 
plt.subplot(2,2,2) 
plt.plot(x, -1 + 0.02*x**2, '--gs', markersize=4) 

plt.subplot(2,2,3)
plt.plot(x, np.cos(x), '-.b') 

plt.subplot(2,2,4)
plt.plot(x, np.sin(x), ':k') 

plt.show()

Subplots with Object-Oriented Interface#

# x values to be plotted
x = np.linspace(0, 10, 40)

# First create a grid of plots
# axs will be an array of 2D ndarray of Axes objects
fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)

# Call plot() method on the appropriate axes object
axs[0, 0].plot(x, -1 + 0.2*x, '-r')
axs[0, 1].plot(x, -1 + 0.02*x**2, '--gs', markersize=4)
axs[1, 0].plot(x, np.cos(x), '-.b')
axs[1, 1].plot(x, np.cos(x), ':k');

# Set figure size
fig.set_size_inches(8, 8)
#fig.savefig("OO_subplots.png")

Annotations#

# Create some data
x = [1, 2, 3, 4, 5]
y = [10, 15, 13, 17, 20]

# Create scatter plot
fig, ax = plt.subplots()
ax.scatter(x, y)

# Add annotations
for i, txt in enumerate(y):
    ax.annotate(txt, (x[i]+0.05, y[i]+0.5))

plt.show()

# Create some data
x = np.linspace(0, 2*np.pi, 100)
y_sin = np.sin(x)
y_cos = np.cos(x)

# Plot sin(x) and cos(x)
fig = plt.figure()
plt.plot(x, y_sin, label='sin(x)')
plt.plot(x, y_cos, label='cos(x)') 
 
# Add arrows and function labels
plt.annotate('sin(x)', xy=(np.pi/2, 1), xytext=(np.pi/2, .6), arrowprops=dict(facecolor='black', arrowstyle='->'))
plt.annotate('cos(x)', xy=(np.pi, -1), xytext=(np.pi, -0.7), arrowprops=dict(facecolor='black', arrowstyle='->'))

# Set axis labels
plt.xlabel('x')
plt.ylabel('y')

plt.show()

Text Boxes#

# Create some data
x = np.linspace(0,5,20)
y = -2*x**2 + 5*x + 10

# Create line plot
fig = plt.figure()
plt.plot(x, y)

# Add text box
textstr = f'Max value: {max(y):0.2f}'
props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
plt.text(0.5, -10, textstr, fontsize=14, bbox=props)
plt.grid(True)

plt.show()

Interactive Plots#

from ipywidgets import HBox, FloatSlider
plt.ioff()
plt.clf()
slider = FloatSlider(orientation='vertical', value=1.0, min=0.02, max=2.0)

fig, ax = plt.subplots()
x = np.linspace(0, 20, 500)
lines = ax.plot(x, np.sin(slider.value*x))
def update_lines(change):
    lines[0].set_data(x, np.sin(change.new * x))
    fig.canvas.draw()
    fig.canvas.flush_events()
slider.observe(update_lines, names='value')
HBox([slider, fig.canvas])

Matplotlib

Contents

Matplotlib#

Data Visualization#

Matplotlib#

Anatomy of a Figure#

Matplotlib Examples#

Plotting Guidelines#

Matplotlib Plotting Interfaces#

Pyplot Interface: Example#

Object Oriented Interface: Example#

Plot Parameters#

Subplots with Pyplot Interface#

Subplots with Object-Oriented Interface#

Annotations#

Text Boxes#

Interactive Plots#

Matplotlib #

Matplotlib Examples #