Pyplot

Plotting

Plotting

Basic (low-level) library for plotting: matplotlib

Higher-level interfaces:

• pyplot (contained in matplotlib, similar to matlab's plotting interface)
• pandas plotting functions (based on pyplot)
• seaborn

Simple plot with pyplot

import numpy as np
import matplotlib.pyplot as plt

x = np.array([0, 1, 2, 3])

y1 = x*2
y2 = x**2

plt.plot(x, y1)
plt.plot(x, y2)

In Jupyter plots are shown automatically

In a regular terminal / program:

plt.show()

Simple plot with pyplot

results:

Example

We'll create a plot that shows the sine and cosine functions in the interval from 0 to 2π

Example

x = np.linspace(0, 2*3.1415, 200)

plt.plot(x, np.sin(x))
plt.plot(x, np.cos(x))

Exercise

Create a Python function that plots a gaussian function based on its parameters mu and sigma:

plot_gaussian_function(mu, sigma)

Pyplot: Configuration and Styling

Styling

Predefined stylesheets are available via:

plt.style.use("stylename")

see plt.style.available for a list of available styles (online reference)

Styling graphs

graph styling example:

plt.plot(x, y, color="C0", marker="X", linestyle="dashed")

Styling graphs

specifying colors:

• theme color (C0 ... C9)
• color name (green / lightblue / ...)
• short name (r / g / b / c / m / y / k)
• hex code (e.g. #FFAA00)
• RGB tuple (e.g. (1, 0.7, 0))

Styling graphs

line style:

• "none" or ""
• "solid" or "-"
• "dashed" or "--"
• "dotted" or ":"
• "dashdot" or "-."

Styling graphs

marker:

• "" (none)
• "." (small dot)
• "o" (large dot)
• "s" (square)
• "X"
• "+"
• "," (pixel)
• ...

Styling graphs

important parameters:

• color
• linestyle
• linewidth
• marker
• markersize

Styling graphs

long form:

plt.plot(x, y, color="C0", marker="X", linestyle="dashed")

short form (less flexible):

plt.plot(x, y, "C0X--")

Labels

• plt.title("Trigonometric functions")
• plt.xlabel("x (radians)")
• plt.ylabel("y")

Labels

labelling individual graphs:

plt.plot(x, np.sin(x), label='sin(x)')
plt.plot(x, np.cos(x), label='cos(x)')

plt.legend()

Axes

disabling axes:

plt.axis("off")

Axes limits

Fit axes (without gaps):

plt.axis("tight")

Show a specific region:

plt.axis([-1, 1, -1, 1])

Show a specific region of one axis:

plt.xlim(-1, 1)

Scaling

Equal distances on both axes:

plt.axis("equal")

Equal distances on both axes, restricting plot area to used data ranges:

plt.axis("scaled")

Grid

plt.grid(True)

Ticks

plt.yticks([-1, 0, 1])
plt.xticks(np.linspace(0, 2*np.pi, 5))

Exercises

• sine and cosine with extended options
• n-th prime and approximation via n * ln(n)
• estimating pi via random points

Exercise: sine and cosine with extended options

possible result:

Exercise: sine and cosine with extended options

import matplotlib.pyplot as plt
import numpy as np

plt.style.use("seaborn")

x = np.linspace(0, 2*np.pi, 100)
sin = np.sin(x)
cos = np.cos(x)
plt.plot(x, sin, "C0--", label="sin(x)")
plt.plot(x, cos, "C1:", label="cos(x)")

pi_multiples = np.array([0, 0.5, 1, 1.5, 2]) * np.pi
sin_points = np.sin(pi_multiples)
cos_points = np.cos(pi_multiples)
plt.plot(pi_multiples, sin_points, "C0o")
plt.plot(pi_multiples, cos_points, "C1o")

plt.title("Trigonometric functions")
plt.xlabel("x (radians)")
plt.xticks(np.linspace(0, 2*np.pi, 5))
plt.legend()
plt.axis("scaled")

Custom stylesheets

plt.style.use("./mystyle.mplstyle")

# general configuration
axes.facecolor: EAEAF2

# line plot configuration
lines.linewidth: 1.5
lines.marker: o
lines.markersize: 4

# box plot configuration
boxplot.whiskers: 0, 100

Custom stylesheets

custom theme colors (C0 - C10):

axes.prop_cycle: cycler('color', ['4C72B0', '55A868', 'C44E52', '8172B2', 'CCB974', '64B5CD'])

Resources

• Python Data Science Handbook: Simple Line Plots
• list of Pyplot functions

Pyplot API

Pyplot API

see:

https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.html

Basic plot types

Basic plot types

• graph: plt.plot(x, y) / plt.plot(y)
• bar chart: plt.bar(x, y)
• scatter plot: plt.plot(x, y, ".") / plt.scatter(x, y, size, color)
• histogram: plt.hist(x)
• box plot: plt.boxplot(x)
• pie chart: plt.pie(x, labels=...)

Graph

Graph of associated values of x and y:

plt.plot(x, y)

Graph with automatic x (0, 1, ...):

plt.plot(y)

Bar charts

plt.bar(x, y, width=0.6)
plt.bar(x, y, width=1, align="edge")

plt.bar(
    [0, 1, 2],
    [9.6, 17, 9.8],
    tick_label=["China", "Russia", "USA"]
)

# horizontal
plt.barh([0, 1, 2], [9.6, 17, 9.8])

Scatter plot

creates data points with two (or more) values - one on the x-axis and the other on the y-axis

simple:

plt.plot(x, y, ".")

advanced:

plt.scatter(x, y, s=sizes, c=colors)

Histogram

Counts the occurence of certain values / ranges

plt.hist(many_simulated_dice_rolls_with_10_dice)

plt.hist(
    many_simulated_dice_rolls_with_10_dice,
    bins=[13, 18, 23, 28, 33, 38, 43, 48, 53, 58]
)

plt.hist(
    many_simulated_dice_rolls_with_10_dice,
    density=True
)

Box plot

Visualization of statistical data of a distribution (minimum, median, maximum, ...)

plt.boxplot(dice_simulation_1, whis=(0, 100))

plt.boxplot(
    [dice_simulation_1, dice_simulation_2],
    labels=["simulation 1", "simulation 2"]
)

Pie chart

plt.pie([3, 10, 17, 9], labels=["a", "b", "c", "d"])

plt.pie([3, 10, 17, 9], explode=[0, 0, 0, 0.1])

plt.pie([3, 10, 17, 9], startangle=90, counterclock=False)

Basic plot types: visualizing iris data

Iris data set

Iris data set: measurements of 150 Iris flowers (50 of type iris setosa, 50 of type iris versicolor and 50 of type iris virginica)

data entries: sepal length, sepal width, petal length, petal width

Loading the data

import pandas as pd
iris = pd.read_csv(
    "https://raw.githubusercontent.com/mwaskom/seaborn-data/master/iris.csv"
)
# get all rows and the first four columns as numpy data
iris = iris.iloc[:,:4].to_numpy()

sepal_length = iris[:,0]
sepal_width = iris[:,1]
petal_length = iris[:,2]
petal_width = iris[:,3]

Scatter plot 1

scatter plot of petal_length and petal_width

plot the first 50, the second 50 and the thrid 50 data points separately (in separate colors)

Scatter plot 2

scatter plot of all four iris properties

use the color and size to visualize sepal length and sepal width

Histogram and boxplot

histogram of the petal length

boxplot of all four measurements

Scatter plot: solutions

plt.plot(petal_length[:50], petal_width[:50], ".",
         label="setosa")
plt.plot(petal_length[50:100], petal_width[50:100], ".",
         label="versicolor")
plt.plot(petal_length[100:150], petal_width[100:150], ".",
         label="virginica")

plt.legend()

plt.scatter(petal_length, petal_width,
            sepal_length*10, sepal_width)

Histogram and boxplot: solutions

plt.hist(
    petal_length,
    bins=np.arange(0.5, 7.5, 0.5)
)

plt.boxplot(
    [petal_length, petal_width, sepal_length, sepal_width],
    labels=["petal length", "petal width", "sepal length",
            "sepal width"],
    whis=(0, 100)
)

Pyplot: figure, axes & subplots

Figure & axes

Figure = entire drawing

Axes = coordinate system that can display data

A figure can contain multiple axes objects next to one another

Figure

Every drawing in pyplot is created via a figure object (the figure is usually created automatically when plotting)

Manually creating a figure of size 800 x 600 px (assuming 100 dpi):

fig = plt.figure(
    figsize=(8, 6),
    facecolor="#eeeeee"
)

This will automatically become the active figure.

Figure objects

exporting the active figure:

plt.savefig("myplot.png")
plt.savefig("myplot.svg")

Axes objects

Creating and activating new axes objects:

# axes in the bottom left
ax1 = plt.axes(0, 0, 0.5, 0.5)
plt.plot([0, 1, 2], [0, 1, 0])

# axes in the top right
ax2 = plt.axes(0.5, 0.5, 0.5, 0.5)
plt.plot([0, 1, 2], [0, 1, 0])

Axes objects

getting the current active axes object:

# gca = get current axes
active_axes = plt.gca()

making an axes object the active axes:

# sca = set current axes
plt.sca(ax1)

Axes objects

creating axes with the the same x axis and a new y axis:

ax2 = ax1.twinx()

Axes objects

automatic creation of multiple Axes objects in a grid (here: 2 rows, 3 columns):

fig, ax = plt.subplots(2, 3)

ax0 = ax[0, 0]
ax1 = ax[0, 1]
ax5 = ax[1, 2]

Axis and Axes

naming to keep in mind:

• plt.axis: e.g. for setting scaling
• plt.axes: for creating a new coordinate system

actual meaning (from Latin): axis = singular, axes = plural

Object-oriented interface

Object-oriented interface

The Methods of plt that we've previously seen call methods of the active Axes object in the background:

ax.plot(...)
ax.set_title(...)
ax.set_xlabel(...)
ax.legend()
ax.set_aspect("equal")

Advanced plot types

Advanced plot types

• plotting data points with more than 2 features
• plotting z = f(x, y)
• plotting density of some distribution (1D and 2D)

Plotting data points with more than 2 features

• advanced scatter plot (size, color) - pyplot, pandas, seaborn
• scatter matrix - pandas, seaborn

Scatter matrix

Extra function in pandas: scatter matrix

creates several scatter plots in a grid

if there are 4 data series it will create 4x4=16 plots (scatter plots and histograms)

from pandas.plotting import scatter_matrix

scatter_matrix(iris)

Plotting z = f(x, y)

• contour plots - pyplot, pandas, seaborn
• 3d plots - matplotlib

• Python Data Science Handbook: Density and Contour Plots
• Python Data Science Handbook: Three-Dimensional Plotting in Matplotlib

Plotting density of some distribution

• (histogram)
• (box plot)
• KDE (kernel density estimation) - pandas, seaborn
• violin plot (box plot + KDE) - seaborn
• 2D histogram - pyplot (hist2d, hexbin)
• 2D KDE - seaborn

see Python Data Science Handbook: Histograms, Binnings, and Density

Showing images

Showing images

a grayscale image with 3x3 pixels:

image = np.array([[0, 1, 2],
                  [3, 4, 5],
                  [6, 7, 8]])
plt.imshow(image, cmap="gray")

an RGB image with 2x2 pixels:

colors = np.array([[[255, 0, 0], [0, 255, 0]],
                   [[0, 0, 255], [0, 0, 0]]])
plt.imshow(colors)

Artists

Artists

Artist = base class for elements in a figure

Artists

example: creating an artist (rectangle) explicitly

r = plt.Rectangle((0.25, 0.75), 0.1, 0.1, color="C0")

ax = plt.gca()
ax.add_artist(r)

Artists

examples: creating primitive artists:

r = plt.Rectangle((0.25, 0.75), 0.1, 0.1, color="C0")
c = plt.Circle((0.75, 0.75), 0.1, color="C1")
p = plt.Polygon(
    [[0.2, 0.2], [0.5, 0.1], [0.8, 0.2]],
    color="C2",
)
l = plt.Line2D(
    (0.5, 0.5), # x coordinates
    (0.25, 0.75), # y coordinates
    color="C3",
)
t = plt.Text(0, 0, "Hello!", size=40, color="C4")