How to add third level of ticks in python matplotlib

Question

Matplotlib axes have Major and Minor ticks. How do I add a third level of tick below Minor?

For example

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.ticker

t = np.arange(0.0, 100.0, 0.1)
s = np.sin(0.1*np.pi*t)*np.exp(-t*0.01)

fig, ax = plt.subplots()
plt.plot(t, s)

ax1 = ax.twiny()
ax1.plot(t, s)

ax1.xaxis.set_ticks_position('bottom')

majors = np.linspace(0, 100, 6)
minors = np.linspace(0, 100, 11)
thirds = np.linspace(0, 100, 101)

ax.xaxis.set_major_locator(matplotlib.ticker.FixedLocator(majors))
ax.xaxis.set_minor_locator(matplotlib.ticker.FixedLocator(minors))
ax1.xaxis.set_major_locator(matplotlib.ticker.FixedLocator([]))
ax1.xaxis.set_minor_locator(matplotlib.ticker.FixedLocator(thirds))
ax1.tick_params(which='minor', length=2)
ax.tick_params(which='minor', length=4)
ax.tick_params(which='major', length=6)
ax.grid(which='both',axis='x',linestyle='--')

plt.axhline(color='gray')

plt.show()

produces the effect I want using twinned x-axes.

Is there a better way?

Answer 1

As I stated that you can achieve what you want by deriving from some key classes, I decided to do so (but as I said, it's probably not worth the effort). Anyway, here is what I've got:

from matplotlib import pyplot as plt
from matplotlib import axes as maxes
from matplotlib import axis as maxis
import matplotlib.ticker as mticker
import matplotlib.cbook as cbook
from matplotlib.projections import register_projection


from matplotlib import ticker
import numpy as np

class SubMinorXAxis(maxis.XAxis):
    def __init__(self,*args,**kwargs):
        self.subminor = maxis.Ticker()
        self.subminorTicks = []
        self._subminor_tick_kw = dict()

        super(SubMinorXAxis,self).__init__(*args,**kwargs)


    def reset_ticks(self):
        cbook.popall(self.subminorTicks)
        ##self.subminorTicks.extend([self._get_tick(major=False)])
        self.subminorTicks.extend([maxis.XTick(self.axes, 0, '', major=False, **self._subminor_tick_kw)])
        self._lastNumSubminorTicks = 1
        super(SubMinorXAxis,self).reset_ticks()


    def set_subminor_locator(self, locator):
        """
        Set the locator of the subminor ticker

        ACCEPTS: a :class:`~matplotlib.ticker.Locator` instance
        """
        self.isDefault_minloc = False
        self.subminor.locator = locator
        locator.set_axis(self)
        self.stale = True


    def set_subminor_formatter(self, formatter):
        """
        Set the formatter of the subminor ticker

        ACCEPTS: A :class:`~matplotlib.ticker.Formatter` instance
        """
        self.isDefault_minfmt = False
        self.subminor.formatter = formatter
        formatter.set_axis(self)
        self.stale = True


    def get_subminor_ticks(self, numticks=None):
        'get the subminor tick instances; grow as necessary'
        if numticks is None:
            numticks = len(self.get_subminor_locator()())

        if len(self.subminorTicks) < numticks:
            # update the new tick label properties from the old
            for i in range(numticks - len(self.subminorTicks)):
                ##tick = self._get_tick(major=False)
                tick = maxis.XTick(self.axes, 0, '', major=False, **self._subminor_tick_kw)
                self.subminorTicks.append(tick)

        if self._lastNumSubminorTicks < numticks:
            protoTick = self.subminorTicks[0]
            for i in range(self._lastNumSubminorTicks, len(self.subminorTicks)):
                tick = self.subminorTicks[i]
                tick.gridOn = False
                self._copy_tick_props(protoTick, tick)

        self._lastNumSubminorTicks = numticks
        ticks = self.subminorTicks[:numticks]

        return ticks

    def set_tick_params(self, which='major', reset=False, **kwargs):
        if which == 'subminor':
            kwtrans = self._translate_tick_kw(kwargs, to_init_kw=True)
            if reset:
                self.reset_ticks()
                self._subminor_tick_kw.clear()
            self._subminor_tick_kw.update(kwtrans)

            for tick in self.subminorTicks:
                tick._apply_params(**self._subminor_tick_kw)
        else:
            super(SubMinorXAxis, self).set_tick_params(which=which, reset=reset, **kwargs)

    def cla(self):
        'clear the current axis'
        self.set_subminor_locator(mticker.NullLocator())
        self.set_subminor_formatter(mticker.NullFormatter())

        super(SubMinorXAxis,self).cla()


    def iter_ticks(self):
        """
        Iterate through all of the major and minor ticks.
        ...and through the subminors
        """
        majorLocs = self.major.locator()
        majorTicks = self.get_major_ticks(len(majorLocs))
        self.major.formatter.set_locs(majorLocs)
        majorLabels = [self.major.formatter(val, i)
                       for i, val in enumerate(majorLocs)]

        minorLocs = self.minor.locator()
        minorTicks = self.get_minor_ticks(len(minorLocs))
        self.minor.formatter.set_locs(minorLocs)
        minorLabels = [self.minor.formatter(val, i)
                       for i, val in enumerate(minorLocs)]

        subminorLocs = self.subminor.locator()
        subminorTicks = self.get_subminor_ticks(len(subminorLocs))
        self.subminor.formatter.set_locs(subminorLocs)
        subminorLabels = [self.subminor.formatter(val, i)
                       for i, val in enumerate(subminorLocs)]

        major_minor = [
            (majorTicks, majorLocs, majorLabels),
            (minorTicks, minorLocs, minorLabels),
            (subminorTicks, subminorLocs, subminorLabels),
        ]

        for group in major_minor:
            for tick in zip(*group):
                yield tick


class SubMinorAxes(maxes.Axes):
    name = 'subminor'

    def _init_axis(self):
        self.xaxis = SubMinorXAxis(self)
        self.spines['top'].register_axis(self.xaxis)
        self.spines['bottom'].register_axis(self.xaxis)
        self.yaxis = maxis.YAxis(self)
        self.spines['left'].register_axis(self.yaxis)
        self.spines['right'].register_axis(self.yaxis)

register_projection(SubMinorAxes)




if __name__ == '__main__':
    fig = plt.figure()
    ax = fig.add_subplot(111,projection = 'subminor')

    t = np.arange(0.0, 100.0, 0.1)
    s = np.sin(0.1*np.pi*t)*np.exp(-t*0.01)

    majors = np.linspace(0, 100, 6)
    minors = np.linspace(0, 100, 11)
    thirds = np.linspace(0, 100, 101)

    ax.plot(t, s)

    ax.xaxis.set_ticks_position('bottom')

    ax.xaxis.set_major_locator(ticker.FixedLocator(majors))
    ax.xaxis.set_minor_locator(ticker.FixedLocator(minors))
    ax.xaxis.set_subminor_locator(ticker.FixedLocator(thirds))

    ##some things in set_tick_params are not being set correctly
    ##by default. For instance 'top=False' must be stated
    ##explicitly
    ax.tick_params(which='subminor', length=2, top=False)
    ax.tick_params(which='minor', length=4)
    ax.tick_params(which='major', length=6)
    ax.grid(which='both',axis='x',linestyle='--')

    plt.show()

It's not perfect, but for the use case you provided it's working fine. I drew some ideas from this matplotlib example and by going through the source codes directly. The result looks like this:

I tested the code on both Python 2.7 and Python 3.5.

EDIT:

I noticed that the subminor gridlines would always be drawn if the grid is turned on (while I had intended for it not to be drawn at all). I rectified this in the code above, i.e. the subminor ticks should never produce grid lines. If gridlines should be implemented properly, some more work will be needed.