linscalex/linscaley (for symlog) behaviour and documentation #10369
Description
According to the documentation linscalex/linscaley "is the number of decades to use for each half of the linear range." This may be correct for base 10* (incidentally the documentation does not specify that this is the default base) but with a general base b it seems not to be, nor for a 'b-ade' as opposed to a decade. Also, there is a natural value log(e)/log(b) for this scaling (relative to the 'b-ade') which makes the scale continuous at the threshold and hence does not introduce gradient jumps in smooth curves. This may be a better default than 1.
- See also issue Suspected incorrect axis transformation of symlog #7008
import matplotlib.pyplot as plt
import numpy as np
b = 2. # Try 100. too
t = 1.
# Define some curves:
x = np.linspace(0.1,3.,100)
y1 = x
y2 = x**2
y3 = np.exp(x)/2.
y4 = np.log(x)*2.
plt.figure()
plt.subplot(1,3,1)
plt.title('base 10 default')
plt.ylim(-100,100)
plt.yscale('symlog',linthreshy=t) # should set decade = half-linear
plt.plot(x,y1)
plt.plot(x,y2)
plt.plot(x,y3)
plt.plot(x,y4)
plt.subplot(1,3,2)
plt.title('base 10 smooth?')
plt.ylim(-100,100)
plt.yscale('symlog',linthreshy=t,linscaley=np.log10(np.e)) # smooth match?
plt.plot(x,y1)
plt.plot(x,y2)
plt.plot(x,y3)
plt.plot(x,y4)
plt.subplot(1,3,3)
plt.title('base %d default' % (b))
plt.ylim(-100,100)
plt.yscale('symlog',linthreshy=t,basey=b) # doesn't set decade or b-ade = half-linear
plt.plot(x,y1)
plt.plot(x,y2)
plt.plot(x,y3)
plt.plot(x,y4)
plt.show()Linux; matplotlib 2.0.0, python 2.7.12 via conda
*actually not; see below