Symmetric Log scale: linscale < 1 ?

[sergey-ns]

summary

1. remove limitation linscale>=1.0 in SymmetricLogScale;
2. set linscale=1.0/math.log(base) or multiply linscale*=1.0/math.log(base) internally

explanation

currently one cannot set linscale values less than 1 in
Axes.set_{x,y}scale
due to
(matplotlib/scale.py:449) assert linscale >= 1.0

Setting linscale=1.0/math.log(base) (which is < 1.0) ensures that the symlog transformation function is smooth, i.e. its derivative is continuous at the border between linear and logarithmic regions. Smoothness of the transformation function is necessary&sufficient to avoid kinks in plots of smooth curves, i.e a smooth curve (with a continuous derivative) will be shown as a smooth curve. (see pictures). It makes sense then to set linscale=1.0/log(base) by default, or multiply it by this appropriate factor internally.

examples

(default)

(smooth, generated with patched matplotlib/scale.py sans 'assert linscale >= 1.0')

(kink)

generated with the following script

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import math

x   = np.r_[-1:1:2000j]
y   = 1e2**(-x) - 0.02

# default
ax  = plt.figure().add_axes([0.1, 0.1, 0.8, 0.8])
ax.plot(x, y, ls='-')
ax.set_yscale('symlog')
ax.figure.savefig('fig_default.png')

# smooth
ax  = plt.figure().add_axes([0.1, 0.1, 0.8, 0.8])
ax.plot(x, y, ls='-')
ax.set_yscale('symlog', linscaley=1./math.log(10))
ax.figure.savefig('fig_smooth.png')

# rough
ax  = plt.figure().add_axes([0.1, 0.1, 0.8, 0.8])
ax.plot(x, y, ls='-')
ax.set_yscale('symlog', linscaley=math.log(10))
ax.figure.savefig('fig_kink.png')

[Tillsten]

This should be 1.4 milestone. I will try to solve this tomorrow.

[Tillsten]

To be more exact, i think we should allow linscale to be smaller than 1, does anybody see why this is enforced. For the rest of the issuse: the smoothness depends not only one linscale, but also on linthresh. I also think it is a little bit late to change defaults.

[Tillsten]

It is probably fine to just change the assert to > 0?

[tacaswell]

milestoned an requested, but did not really read/understand what is going on.

[Tillsten]

linscale defines the space ratio between a decade in the log-plot and halve of the linear part.
I actually need a ratio smaller than 1, else the log-part is to small for my case.

[Tillsten]

pinging @mdboom

[tacaswell]

Closing as #3053 is merged.