Matplotlib.colors.BoundaryNorm class in Python

Matplotlib is an amazing visualization library in Python for 2D plots of arrays. Matplotlib is a multi-platform data visualization library built on NumPy arrays and designed to work with the broader SciPy stack.

matplotlib.colors.BoundaryNorm

The matplotlib.colors.BoundaryNorm class belongs to the matplotlib.colors module. The matplotlib.colors module is used for converting color or numbers arguments to RGBA or RGB.This module is used for mapping numbers to colors or color specification conversion in a 1-D array of colors also known as colormap.
The matplotlib.colors.BoundaryNorm class is used to create a colormap based on discrete intervals. BoundaryNorm maps values to integers, unlike Normalize or LogNorm which does mapping to the interval of 0 to 1. Piecewise linear interpolation can be used for mapping to the o- interval, however, using integers is simpler and leads to the reduction of the number of conversions back and forth among integer and floating points.
Parameters: 

1. boundaries: it is an array like object that monotonically increase sequence of boundaries
   
2. ncolor: It accepts an integer value that represents a number of colors in the colormap that will be used.
   
3. clip: It accepts a boolean value and is a optional parameter. If the clip is True, the values that are out of range and they are below the boundaries[0] are mapped to 0, whereas if they are above the boundaries[-1] they are mapped to ncolors-1. If the clip is set to False, the out of range values and they are below the boundaries[0] are mapped to -1, whereas if they are above boundaries[-1], they are mapped to ncolors. The Colormap.__call__() convert these into valid indices. 
   

Note: The edges of bins are defined by boundaries and the data falling within the bins are mapped to the same color index. If the ncolors are not equal to the number of bins, linear interpolation is used to choose color for them. 
Example 1:

Python3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from matplotlib.colors import ListedColormap, BoundaryNorm

a = np.linspace(0, 3 * np.pi, 500)
b = np.sin(a)
# this is the first derivative
dbda = np.cos(0.5 * (a[:-1] + a[1:]))

# Creating  line segments so
# to color them individually
points = np.array([a, b]).T.reshape(-1, 1, 2)
set_of_segments = np.concatenate([points[:-1],
                                  points[1:]],
                                 axis = 1)

figure, axes = plt.subplots(2, 1,
                            sharex = True,
                            sharey = True)

# Mapping the data points with
# continuous norm
continuous_norm = plt.Normalize(dbda.min(),
                               dbda.max())

line_collection = LineCollection(set_of_segments,
                                 cmap ='viridis',
                                 norm = continuous_norm)

# Set the values used for
# colormapping
line_collection.set_array(dbda)
line_collection.set_linewidth(2)
line = axes[0].add_collection(line_collection)
figure.colorbar(line, ax = axes[0])

# Use a boundary norm instead
cmap = ListedColormap(['r', 'g', 'b'])
boundary_norm = BoundaryNorm([-1, -0.5, 0.5, 1],
                             cmap.N)

line_collection = LineCollection(set_of_segments,
                                 cmap = cmap,
                                 norm = boundary_norm)

line_collection.set_array(dbda)
line_collection.set_linewidth(2)
line = axes[1].add_collection(line_collection)
figure.colorbar(line, ax = axes[1])

axes[0].set_xlim(a.min(), a.max())
axes[0].set_ylim(-1.1, 1.1)
plt.show()

Output:

Example 2:

Python3

import numpy as np
import matplotlib as mpl
import matplotlib.pylab as plt


# setup the plot
figure, axes = plt.subplots(1, 1,
                            figsize=(6, 6))

# defining random data
x = np.random.rand(20)
y = np.random.rand(20)
tag = np.random.randint(0, 20, 20)
tag[10:12] = 0

# defining the colormap
cmap = plt.cm.jet

# extracting all colors
cmaplist = [cmap(i) for i in range(cmap.N)]

# making first color entry  grey
cmaplist[0] = (.5, .5, .5, 1.0)

# new map
cmap = mpl.colors.LinearSegmentedColormap.from_list(
   'Custom cmap', cmaplist, cmap.N)

# defining the bins and norms
bounds = np.linspace(0, 20, 21)
norm = mpl.colors.BoundaryNorm(bounds,
                               cmap.N)

# the scatter
scat = axes.scatter(x, y, c=tag,
                    s=np.random.randint(100,
                                        500,
                                        20),
                    cmap=cmap, norm=norm)

# axes for the colorbar
ax2 = figure.add_axes([0.95, 0.1,
                       0.03, 0.8])


axes.set_title(' discrete colors')

Output: