PR summary

In the current implementation, symlog axes only get major ticks by default. Depending on the data range, this can lead to too few or even no ticks at all. When "subticks" between decades are specified manually, those are sometimes labeled in an unintended manner (when they are at a decade).

This PR re-implements the tick placement and formatting for symlog axes to remedy these problems. If I am not mistaken, this closes #17402, closes #18757 and closes #25994.

I am submitting this as a PR now to get some general feedback on the approach and pointers if I need to consider anything regarding style or conventions that I missed. If I get a thumbs up, I would polish some things off (like making _SymmetricalLogUtil's methods work with np.arrays and have .firstdec() cache results) before merging.

My approach for the tick locator

I was aiming for SymmetricalLogLocator to behave identically to LogLocator as long as the data range is outside of the linear part of the scale and extend this reasonably to the linear part if it's present. What I came up with is this (I'm describing the positive half axis here for simplicity, everything works the same on the negative side):

• Major ticks at decades, where the first decade to be considered for labelling must be at least half the length of a decade from 0 (otherwise there would be infinitely many labeled decades close to 0).
• That decade receives the decade number 1, the next larger one 2 and so on. 0 gets the "decade" number 0. Values between those decades get interpolated decade numbers.
• We now have an obvious definition of the number of decades in the data range and can basically copy the logic from LogLocator, the only caveat being that 0 should always receive a tick if it is in the range.
• In the linear part of the scale, we add the same minor ticks below the first decade as below any other and add the next lower decade as a minor tick. That is, if with base b one gets minor ticks 2 to b-1 between larger decades one gets 1 to b-1 below the first one, effectively producing linear ticks between the first decade and 0.

LogFormatter (which is also used for symlog axes) is adapted accordingly.

• I added a separate field _firstsublabels for placing sublabels below the first decade.
• As with log axes it can sometimes happen that there is only one major tick with unlabeled minor ticks around it. This is fine (one can still identify the unlabeled positions) as long as the major tick is at some decade and not at 0, which can happen with symlog axes. In that case, we need to label at least one of the minor ticks to allow reading values off the axis.

Since both the locator and the formatter need the calculation of the first decade I placed the code regarding this into a helper class _SymmetricalLogUtil.

Finally, SymmetricalLogScale is adapted to actually use the new functionality by default.

I checked all parameter ranges I could think of and this seems to work out quite nicely.

import numpy as np
from matplotlib import pyplot as plt

def showcase_scales(axs, *plotargs, **plotkwargs):
    for ax, scale in zip(axs, ['linear', 'symlog', 'log']):
        ax.set_yscale(scale)
        ax.yaxis.grid()
        ax.plot(*plotargs, **plotkwargs)

values = [
    np.linspace(3, 150),
    np.linspace(20, 60),
    np.linspace(0.5, 12),
    np.linspace(0.5, 5),
    np.linspace(0.6, 3),
    np.linspace(1e-4, 1e-2),
    np.linspace(0, 40),
    np.linspace(-0.8, 0.9),
    np.linspace(-4, 4),
    np.linspace(-22, 22),
    np.linspace(0, 0),
    np.linspace(1, 1),
    np.linspace(2, 2),
    np.linspace(10, 10),
    np.linspace(13, 13),
]
fig, axs = plt.subplots(len(values), 3, squeeze=False, sharex=True,
                        figsize=(9, 2 * len(values)))
for a, v in zip(axs, values):
    showcase_scales(a, v)
axs[0, 0].set_title('linear')
axs[0, 1].set_title('symlog')
axs[0, 2].set_title('log')
fig.tight_layout()
fig.savefig('showcase.png')

Requested feedback

There are some details regarding which I would like feedback/guidance from you.

• When computing stride (i.e. the number of decades between major ticks) a possible forced tick at 0 is not considered. This may lead to an off-by-one error regarding numticks (i.e. a stride value smaller by one would have been possible) but I feel like preventing this is not worth the complication of taking it into account. Do you agree?
• subs=None is equivalent to subs='auto' in LogLocator but to subs=(1.0,) in SymmetricalLogLocator. Is that on purpose? I left it like that.
• For some reason, base came after linthresh in SymmetricalLogLocator's signature, contrary to most other occurences. In adding linscale I reordered those. While this is strictly a backwards incompatible change (whereas I just appended linscale everywhere else), I don't expect it to have ever been used in an incompatible way: providing base only make sense when transform (the first argument) is not given, so it's most probably always been don by keyword argument, though it is in principle possible to say SymmetricalLogLocator(None, None, 2, 10) to get SymmetricalLogLocator(linthresh=2, base=10). Should I switch it back for backwards compatibility or do we care more about consistent argument order?
• LogFormatter threw away the sign of any value, even though it is used for negative values with symlog axes. This was no problem because LogFormatterMathtext overwrites __call__ and preserves the sign, so it didn't actually show up on any axis (with the default configuration). I fixed this. Is it fine to just leave it in this PR or should it be a separate one?
• In test_ticker.py the test TestSymmetricalLogLocator.test_extending() relies on rcParams['axes.autolimit_mode'] being set to round_numbers but this is not set up in the test itself. I assume that this configuration is left in place by some previous test, though I can't tell where. Is this by design or should an rc_context be used, like in some other tests?
• The checklist below tells me to note API changes (which the new linscale argument to the locator and the formatter as well as the changed default value of SymmetricalLogScale's subs argument qualify as, I think) with a directive and release note, but the linked section does not seem to exist. What do I need to do?

PR checklist

• "closes #0000" is in the body of the PR description to link the related issue
• new and changed code is tested
• Plotting related features are demonstrated in an example
• New Features and API Changes are noted with a directive and release note
• Documentation complies with general and docstring guidelines