Matplotlib Colormap Normalization: Visualizing Nonlinear Data

Introduction

In data visualization, colormaps are used to represent numerical data through color. However, sometimes the data distribution may be nonlinear, which can make it difficult to discern the details of the data. In such cases, colormap normalization can be used to map colormaps onto data in nonlinear ways to help visualize the data more accurately. Matplotlib provides several normalization methods, including SymLogNorm and AsinhNorm, which can be used to normalize colormaps. This lab will demonstrate how to use SymLogNorm and AsinhNorm to map colormaps onto nonlinear data.

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Import Required Libraries

In this step, we will import the necessary libraries, including Matplotlib, NumPy, and Matplotlib colors.

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

Create Synthetic Data

In this step, we will create a synthetic dataset consisting of two humps, one negative and one positive, with the positive hump having an amplitude eight times greater than the negative hump. We will then apply SymLogNorm to visualize the data.

def rbf(x, y):
    return 1.0 / (1 + 5 * ((x ** 2) + (y ** 2)))

N = 200
gain = 8
X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)]
Z1 = rbf(X + 0.5, Y + 0.5)
Z2 = rbf(X - 0.5, Y - 0.5)
Z = gain * Z1 - Z2

shadeopts = {'cmap': 'PRGn', 'shading': 'gouraud'}
colormap = 'PRGn'
lnrwidth = 0.5

Apply SymLogNorm

In this step, we will apply SymLogNorm to the synthetic data and visualize the results.

fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)

pcm = ax[0].pcolormesh(X, Y, Z,
                       norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
                                              vmin=-gain, vmax=gain, base=10),
                       **shadeopts)
fig.colorbar(pcm, ax=ax[0], extend='both')
ax[0].text(-2.5, 1.5, 'symlog')

pcm = ax[1].pcolormesh(X, Y, Z, vmin=-gain, vmax=gain,
                       **shadeopts)
fig.colorbar(pcm, ax=ax[1], extend='both')
ax[1].text(-2.5, 1.5, 'linear')

plt.show()

Apply AsinhNorm

In this step, we will apply AsinhNorm to the synthetic data and visualize the results.

fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)

pcm = ax[0].pcolormesh(X, Y, Z,
                       norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
                                              vmin=-gain, vmax=gain, base=10),
                       **shadeopts)
fig.colorbar(pcm, ax=ax[0], extend='both')
ax[0].text(-2.5, 1.5, 'symlog')

pcm = ax[1].pcolormesh(X, Y, Z,
                       norm=colors.AsinhNorm(linear_width=lnrwidth,
                                             vmin=-gain, vmax=gain),
                       **shadeopts)
fig.colorbar(pcm, ax=ax[1], extend='both')
ax[1].text(-2.5, 1.5, 'asinh')

plt.show()

Summary

In this lab, we learned how to use SymLogNorm and AsinhNorm to map colormaps onto nonlinear data. By applying these normalization methods, we can visualize the data more accurately and discern the details of the data more easily.

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