Added demo script for asinh axis scaling

Author: rwpenney

doc/users/next_whats_new/asinh_scale.rst

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+New axis scale ``asinh``
+------------------------
+
+The new ``asinh`` axis scale offers an alternative to ``symlog`` that
+smoothly transitions between the quasi-linear and asymptotically logarithmic
+regions of the scale. This is based on an arcsinh transformation that
+allows plotting both positive and negative values than span many orders
+of magnitude. A scale parameter ``a0`` is provided to allow the user
+to tune the width of the linear region of the scale.

examples/scales/asinh_demo.py

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+"""
+============
+Asinh Demo
+============
+"""
+
+import numpy
+import matplotlib.pyplot as plt
+
+# Prepare sample values for variations on y=x graph:
+x = numpy.linspace(-3, 6, 100)
+
+# Compare "symlog" and "asinh" behaviour on sample y=x graph:
+fig1 = plt.figure()
+ax0, ax1 = fig1.subplots(1, 2, sharex=True)
+
+ax0.plot(x, x)
+ax0.set_yscale('symlog')
+ax0.grid()
+ax0.set_title('symlog')
+
+ax1.plot(x, x)
+ax1.set_yscale('asinh')
+ax1.grid()
+ax1.set_title(r'$sinh^{-1}$')
+
+
+# Compare "asinh" graphs with different scale parameter "a0":
+fig2 = plt.figure()
+axs = fig2.subplots(1, 3, sharex=True)
+for ax, a0 in zip(axs, (0.2, 1.0, 5.0)):
+    ax.set_title('a0={:.3g}'.format(a0))
+    ax.plot(x, x, label='y=x')
+    ax.plot(x, 10*x, label='y=10x')
+    ax.plot(x, 100*x, label='y=100x')
+    ax.set_yscale('asinh', a0=a0)
+    ax.grid()
+    ax.legend(loc='best', fontsize='small')
+
+plt.show()