>>> """
======
Scales
======

Illustrate the scale transformations applied to axes, e.g. log, symlog, logit.

The last two examples are examples of using the ``'function'`` scale by
supplying forward and inverse functions for the scale transformation.
"""
... 
... import numpy as np
... import matplotlib.pyplot as plt
... from matplotlib.ticker import NullFormatter, FixedLocator
... 
... # Fixing random state for reproducibility
... np.random.seed(19680801)
... 
... # make up some data in the interval ]0, 1[
... y = np.random.normal(loc=0.5, scale=0.4, size=1000)
... y = y[(y > 0) & (y < 1)]
... y.sort()
... x = np.arange(len(y))
... 
... # plot with various axes scales
... fig, axs = plt.subplots(3, 2, figsize=(6, 8),
...                         constrained_layout=True)
... 
... # linear
... ax = axs[0, 0]
... ax.plot(x, y)
... ax.set_yscale('linear')
... ax.set_title('linear')
... ax.grid(True)
... 
... 
... # log
... ax = axs[0, 1]
... ax.plot(x, y)
... ax.set_yscale('log')
... ax.set_title('log')
... ax.grid(True)
... 
... 
... # symmetric log
... ax = axs[1, 1]
... ax.plot(x, y - y.mean())
... ax.set_yscale('symlog', linthresh=0.02)
... ax.set_title('symlog')
... ax.grid(True)
... 
... # logit
... ax = axs[1, 0]
... ax.plot(x, y)
... ax.set_yscale('logit')
... ax.set_title('logit')
... ax.grid(True)
... 
... 
... # Function x**(1/2)
... def forward(x):
...     return x**(1/2)
... 
... 
... def inverse(x):
...     return x**2
... 
... 
... ax = axs[2, 0]
... ax.plot(x, y)
... ax.set_yscale('function', functions=(forward, inverse))
... ax.set_title('function: $x^{1/2}$')
... ax.grid(True)
... ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 1, 0.2)**2))
... ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 1, 0.2)))
... 
... 
... # Function Mercator transform
... def forward(a):
...     a = np.deg2rad(a)
...     return np.rad2deg(np.log(np.abs(np.tan(a) + 1.0 / np.cos(a))))
... 
... 
... def inverse(a):
...     a = np.deg2rad(a)
...     return np.rad2deg(np.arctan(np.sinh(a)))
... 
... ax = axs[2, 1]
... 
... t = np.arange(0, 170.0, 0.1)
... s = t / 2.
... 
... ax.plot(t, s, '-', lw=2)
... 
... ax.set_yscale('function', functions=(forward, inverse))
... ax.set_title('function: Mercator')
... ax.grid(True)
... ax.set_xlim([0, 180])
... ax.yaxis.set_minor_formatter(NullFormatter())
... ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 90, 10)))
... 
... plt.show()
... 
... #############################################################################
... #
... # .. admonition:: References
... #
... #    The use of the following functions, methods, classes and modules is shown
... #    in this example:
... #
... #    - `matplotlib.axes.Axes.set_xscale`
... #    - `matplotlib.axes.Axes.set_yscale`
... #    - `matplotlib.axis.Axis.set_major_locator`
... #    - `matplotlib.scale.LinearScale`
... #    - `matplotlib.scale.LogScale`
... #    - `matplotlib.scale.SymmetricalLogScale`
... #    - `matplotlib.scale.LogitScale`
... #    - `matplotlib.scale.FuncScale`
...