>>> """
========================
Exploring normalizations
========================

Various normalization on a multivariate normal distribution.

"""
... 
... import matplotlib.pyplot as plt
... import matplotlib.colors as mcolors
... import numpy as np
... from numpy.random import multivariate_normal
... 
... 
... # Fixing random state for reproducibility.
... np.random.seed(19680801)
... 
... data = np.vstack([
...     multivariate_normal([10, 10], [[3, 2], [2, 3]], size=100000),
...     multivariate_normal([30, 20], [[3, 1], [1, 3]], size=1000)
... ])
... 
... gammas = [0.8, 0.5, 0.3]
... 
... fig, axs = plt.subplots(nrows=2, ncols=2)
... 
... axs[0, 0].set_title('Linear normalization')
... axs[0, 0].hist2d(data[:, 0], data[:, 1], bins=100)
... 
... for ax, gamma in zip(axs.flat[1:], gammas):
...     ax.set_title(r'Power law $(\gamma=%1.1f)$' % gamma)
...     ax.hist2d(data[:, 0], data[:, 1], bins=100, norm=mcolors.PowerNorm(gamma))
... 
... fig.tight_layout()
... 
... plt.show()
... 
... #############################################################################
... #
... # .. admonition:: References
... #
... #    The use of the following functions, methods, classes and modules is shown
... #    in this example:
... #
... #    - `matplotlib.colors`
... #    - `matplotlib.colors.PowerNorm`
... #    - `matplotlib.axes.Axes.hist2d`
... #    - `matplotlib.pyplot.hist2d`
...