content: """
  Classes for the ticks and x and y axis
  """
  from __future__ import (absolute_import, division, print_function,
                          unicode_literals)
  
  import six
  
  from matplotlib import rcParams
  import matplotlib.artist as artist
  from matplotlib.artist import allow_rasterization
  import matplotlib.cbook as cbook
  import matplotlib.font_manager as font_manager
  import matplotlib.lines as mlines
  import matplotlib.patches as mpatches
  import matplotlib.scale as mscale
  import matplotlib.text as mtext
  import matplotlib.ticker as mticker
  import matplotlib.transforms as mtransforms
  import matplotlib.units as munits
  import numpy as np
  import warnings
  
  GRIDLINE_INTERPOLATION_STEPS = 180
  
  
  class Tick(artist.Artist):
      """
      Abstract base class for the axis ticks, grid lines and labels
  
      1 refers to the bottom of the plot for xticks and the left for yticks
      2 refers to the top of the plot for xticks and the right for yticks
  
      Publicly accessible attributes:
  
        :attr:`tick1line`
            a Line2D instance
  
        :attr:`tick2line`
            a Line2D instance
  
        :attr:`gridline`
            a Line2D instance
  
        :attr:`label1`
            a Text instance
  
        :attr:`label2`
            a Text instance
  
        :attr:`gridOn`
            a boolean which determines whether to draw the tickline
  
        :attr:`tick1On`
            a boolean which determines whether to draw the 1st tickline
  
        :attr:`tick2On`
            a boolean which determines whether to draw the 2nd tickline
  
        :attr:`label1On`
            a boolean which determines whether to draw tick label
  
        :attr:`label2On`
            a boolean which determines whether to draw tick label
  
      """
      def __init__(self, axes, loc, label,
                   size=None,  # points
                   width=None,
                   color=None,
                   tickdir=None,
                   pad=None,
                   labelsize=None,
                   labelcolor=None,
                   zorder=None,
                   gridOn=None,  # defaults to axes.grid depending on
                                 # axes.grid.which
                   tick1On=True,
                   tick2On=True,
                   label1On=True,
                   label2On=False,
                   major=True,
                   ):
          """
          bbox is the Bound2D bounding box in display coords of the Axes
          loc is the tick location in data coords
          size is the tick size in points
          """
          artist.Artist.__init__(self)
  
          if gridOn is None:
              if major and (rcParams['axes.grid.which'] in ('both', 'major')):
                  gridOn = rcParams['axes.grid']
              elif (not major) and (rcParams['axes.grid.which']
                                    in ('both', 'minor')):
                  gridOn = rcParams['axes.grid']
              else:
                  gridOn = False
  
          self.set_figure(axes.figure)
          self.axes = axes
  
          name = self.__name__.lower()
          self._name = name
  
          self._loc = loc
  
          if size is None:
              if major:
                  size = rcParams['%s.major.size' % name]
              else:
                  size = rcParams['%s.minor.size' % name]
          self._size = size
  
          if width is None:
              if major:
                  width = rcParams['%s.major.width' % name]
              else:
                  width = rcParams['%s.minor.width' % name]
          self._width = width
  
          if color is None:
              color = rcParams['%s.color' % name]
          self._color = color
  
          if pad is None:
              if major:
                  pad = rcParams['%s.major.pad' % name]
              else:
                  pad = rcParams['%s.minor.pad' % name]
          self._base_pad = pad
  
          if labelcolor is None:
              labelcolor = rcParams['%s.color' % name]
          self._labelcolor = labelcolor
  
          if labelsize is None:
              labelsize = rcParams['%s.labelsize' % name]
          self._labelsize = labelsize
  
          if zorder is None:
              if major:
                  zorder = mlines.Line2D.zorder + 0.01
              else:
                  zorder = mlines.Line2D.zorder
          self._zorder = zorder
  
          self.apply_tickdir(tickdir)
  
          self.tick1line = self._get_tick1line()
          self.tick2line = self._get_tick2line()
          self.gridline = self._get_gridline()
  
          self.label1 = self._get_text1()
          self.label = self.label1  # legacy name
          self.label2 = self._get_text2()
  
          self.gridOn = gridOn
          self.tick1On = tick1On
          self.tick2On = tick2On
          self.label1On = label1On
          self.label2On = label2On
  
          self.update_position(loc)
  
      def apply_tickdir(self, tickdir):
          """
          Calculate self._pad and self._tickmarkers
          """
          pass
  
      def get_tickdir(self):
          return self._tickdir
  
      def get_tick_padding(self):
          """
          Get the length of the tick outside of the axes.
          """
          padding = {
              'in': 0.0,
              'inout': 0.5,
              'out': 1.0
          }
          return self._size * padding[self._tickdir]
  
      def get_children(self):
          children = [self.tick1line, self.tick2line,
                      self.gridline, self.label1, self.label2]
          return children
  
      def set_clip_path(self, clippath, transform=None):
          artist.Artist.set_clip_path(self, clippath, transform)
          self.gridline.set_clip_path(clippath, transform)
          self.stale = True
  
      set_clip_path.__doc__ = artist.Artist.set_clip_path.__doc__
  
      def get_pad_pixels(self):
          return self.figure.dpi * self._base_pad / 72.0
  
      def contains(self, mouseevent):
          """
          Test whether the mouse event occurred in the Tick marks.
  
          This function always returns false.  It is more useful to test if the
          axis as a whole contains the mouse rather than the set of tick marks.
          """
          if six.callable(self._contains):
              return self._contains(self, mouseevent)
          return False, {}
  
      def set_pad(self, val):
          """
          Set the tick label pad in points
  
          ACCEPTS: float
          """
          self._apply_params(pad=val)
          self.stale = True
  
      def get_pad(self):
          'Get the value of the tick label pad in points'
          return self._base_pad
  
      def _get_text1(self):
          'Get the default Text 1 instance'
          pass
  
      def _get_text2(self):
          'Get the default Text 2 instance'
          pass
  
      def _get_tick1line(self):
          'Get the default line2D instance for tick1'
          pass
  
      def _get_tick2line(self):
          'Get the default line2D instance for tick2'
          pass
  
      def _get_gridline(self):
          'Get the default grid Line2d instance for this tick'
          pass
  
      def get_loc(self):
          'Return the tick location (data coords) as a scalar'
          return self._loc
  
      @allow_rasterization
      def draw(self, renderer):
          if not self.get_visible():
              self.stale = False
              return
  
          renderer.open_group(self.__name__)
          if self.gridOn:
              self.gridline.draw(renderer)
          if self.tick1On:
              self.tick1line.draw(renderer)
          if self.tick2On:
              self.tick2line.draw(renderer)
  
          if self.label1On:
              self.label1.draw(renderer)
          if self.label2On:
              self.label2.draw(renderer)
          renderer.close_group(self.__name__)
  
          self.stale = False
  
      def set_label1(self, s):
          """
          Set the text of ticklabel
  
          ACCEPTS: str
          """
          self.label1.set_text(s)
          self.stale = True
  
      set_label = set_label1
  
      def set_label2(self, s):
          """
          Set the text of ticklabel2
  
          ACCEPTS: str
          """
          self.label2.set_text(s)
          self.stale = True
  
      def _set_artist_props(self, a):
          a.set_figure(self.figure)
  
      def get_view_interval(self):
          'return the view Interval instance for the axis this tick is ticking'
          raise NotImplementedError('Derived must override')
  
      def _apply_params(self, **kw):
          switchkw = ['gridOn', 'tick1On', 'tick2On', 'label1On', 'label2On']
          switches = [k for k in kw if k in switchkw]
          for k in switches:
              setattr(self, k, kw.pop(k))
          newmarker = [k for k in kw if k in ['size', 'width', 'pad', 'tickdir']]
          if newmarker:
              self._size = kw.pop('size', self._size)
              # Width could be handled outside this block, but it is
              # convenient to leave it here.
              self._width = kw.pop('width', self._width)
              self._base_pad = kw.pop('pad', self._base_pad)
              # apply_tickdir uses _size and _base_pad to make _pad,
              # and also makes _tickmarkers.
              self.apply_tickdir(kw.pop('tickdir', self._tickdir))
              self.tick1line.set_marker(self._tickmarkers[0])
              self.tick2line.set_marker(self._tickmarkers[1])
              for line in (self.tick1line, self.tick2line):
                  line.set_markersize(self._size)
                  line.set_markeredgewidth(self._width)
              # _get_text1_transform uses _pad from apply_tickdir.
              trans = self._get_text1_transform()[0]
              self.label1.set_transform(trans)
              trans = self._get_text2_transform()[0]
              self.label2.set_transform(trans)
          tick_kw = dict([kv for kv in six.iteritems(kw)
                          if kv[0] in ['color', 'zorder']])
          if tick_kw:
              self.tick1line.set(**tick_kw)
              self.tick2line.set(**tick_kw)
              for k, v in six.iteritems(tick_kw):
                  setattr(self, '_' + k, v)
          label_list = [k for k in six.iteritems(kw)
                        if k[0] in ['labelsize', 'labelcolor']]
          if label_list:
              label_kw = dict([(k[5:], v) for (k, v) in label_list])
              self.label1.set(**label_kw)
              self.label2.set(**label_kw)
              for k, v in six.iteritems(label_kw):
                  # for labelsize the text objects covert str ('small')
                  # -> points. grab the integer from the `Text` object
                  # instead of saving the string representation
                  v = getattr(self.label1, 'get_' + k)()
                  setattr(self, '_label' + k, v)
  
      def update_position(self, loc):
          'Set the location of tick in data coords with scalar *loc*'
          raise NotImplementedError('Derived must override')
  
      def _get_text1_transform(self):
          raise NotImplementedError('Derived must override')
  
      def _get_text2_transform(self):
          raise NotImplementedError('Derived must override')
  
  
  class XTick(Tick):
      """
      Contains all the Artists needed to make an x tick - the tick line,
      the label text and the grid line
      """
      __name__ = 'xtick'
  
      def _get_text1_transform(self):
          return self.axes.get_xaxis_text1_transform(self._pad)
  
      def _get_text2_transform(self):
          return self.axes.get_xaxis_text2_transform(self._pad)
  
      def apply_tickdir(self, tickdir):
          if tickdir is None:
              tickdir = rcParams['%s.direction' % self._name]
          self._tickdir = tickdir
  
          if self._tickdir == 'in':
              self._tickmarkers = (mlines.TICKUP, mlines.TICKDOWN)
          elif self._tickdir == 'inout':
              self._tickmarkers = ('|', '|')
          else:
              self._tickmarkers = (mlines.TICKDOWN, mlines.TICKUP)
          self._pad = self._base_pad + self.get_tick_padding()
          self.stale = True
  
      def _get_text1(self):
          'Get the default Text instance'
          # the y loc is 3 points below the min of y axis
          # get the affine as an a,b,c,d,tx,ty list
          # x in data coords, y in axes coords
          trans, vert, horiz = self._get_text1_transform()
          t = mtext.Text(
              x=0, y=0,
              fontproperties=font_manager.FontProperties(size=self._labelsize),
              color=self._labelcolor,
              verticalalignment=vert,
              horizontalalignment=horiz,
              )
          t.set_transform(trans)
          self._set_artist_props(t)
          return t
  
      def _get_text2(self):
  
          'Get the default Text 2 instance'
          # x in data coords, y in axes coords
          trans, vert, horiz = self._get_text2_transform()
          t = mtext.Text(
              x=0, y=1,
              fontproperties=font_manager.FontProperties(size=self._labelsize),
              color=self._labelcolor,
              verticalalignment=vert,
              horizontalalignment=horiz,
              )
          t.set_transform(trans)
          self._set_artist_props(t)
          return t
  
      def _get_tick1line(self):
          'Get the default line2D instance'
          # x in data coords, y in axes coords
          l = mlines.Line2D(xdata=(0,), ydata=(0,), color=self._color,
                            linestyle='None', marker=self._tickmarkers[0],
                            markersize=self._size,
                            markeredgewidth=self._width, zorder=self._zorder)
          l.set_transform(self.axes.get_xaxis_transform(which='tick1'))
          self._set_artist_props(l)
          return l
  
      def _get_tick2line(self):
          'Get the default line2D instance'
          # x in data coords, y in axes coords
          l = mlines.Line2D(xdata=(0,), ydata=(1,),
                            color=self._color,
                            linestyle='None',
                            marker=self._tickmarkers[1],
                            markersize=self._size,
                            markeredgewidth=self._width,
                            zorder=self._zorder)
  
          l.set_transform(self.axes.get_xaxis_transform(which='tick2'))
          self._set_artist_props(l)
          return l
  
      def _get_gridline(self):
          'Get the default line2D instance'
          # x in data coords, y in axes coords
          l = mlines.Line2D(xdata=(0.0, 0.0), ydata=(0, 1.0),
                            color=rcParams['grid.color'],
                            linestyle=rcParams['grid.linestyle'],
                            linewidth=rcParams['grid.linewidth'],
                            alpha=rcParams['grid.alpha'],
                            markersize=0)
          l.set_transform(self.axes.get_xaxis_transform(which='grid'))
          l.get_path()._interpolation_steps = GRIDLINE_INTERPOLATION_STEPS
          self._set_artist_props(l)
  
          return l
  
      def update_position(self, loc):
          'Set the location of tick in data coords with scalar *loc*'
          x = loc
  
          nonlinear = (hasattr(self.axes, 'yaxis') and
                       self.axes.yaxis.get_scale() != 'linear' or
                       hasattr(self.axes, 'xaxis') and
                       self.axes.xaxis.get_scale() != 'linear')
  
          if self.tick1On:
              self.tick1line.set_xdata((x,))
          if self.tick2On:
              self.tick2line.set_xdata((x,))
          if self.gridOn:
              self.gridline.set_xdata((x,))
          if self.label1On:
              self.label1.set_x(x)
          if self.label2On:
              self.label2.set_x(x)
  
          if nonlinear:
              self.tick1line._invalid = True
              self.tick2line._invalid = True
              self.gridline._invalid = True
  
          self._loc = loc
          self.stale = True
  
      def get_view_interval(self):
          'return the Interval instance for this axis view limits'
          return self.axes.viewLim.intervalx
  
  
  class YTick(Tick):
      """
      Contains all the Artists needed to make a Y tick - the tick line,
      the label text and the grid line
      """
      __name__ = 'ytick'
  
      def _get_text1_transform(self):
          return self.axes.get_yaxis_text1_transform(self._pad)
  
      def _get_text2_transform(self):
          return self.axes.get_yaxis_text2_transform(self._pad)
  
      def apply_tickdir(self, tickdir):
          if tickdir is None:
              tickdir = rcParams['%s.direction' % self._name]
          self._tickdir = tickdir
  
          if self._tickdir == 'in':
              self._tickmarkers = (mlines.TICKRIGHT, mlines.TICKLEFT)
          elif self._tickdir == 'inout':
              self._tickmarkers = ('_', '_')
          else:
              self._tickmarkers = (mlines.TICKLEFT, mlines.TICKRIGHT)
          self._pad = self._base_pad + self.get_tick_padding()
          self.stale = True
  
      # how far from the y axis line the right of the ticklabel are
      def _get_text1(self):
          'Get the default Text instance'
          # x in axes coords, y in data coords
          trans, vert, horiz = self._get_text1_transform()
          t = mtext.Text(
              x=0, y=0,
              fontproperties=font_manager.FontProperties(size=self._labelsize),
              color=self._labelcolor,
              verticalalignment=vert,
              horizontalalignment=horiz,
              )
          t.set_transform(trans)
          self._set_artist_props(t)
          return t
  
      def _get_text2(self):
          'Get the default Text instance'
          # x in axes coords, y in data coords
          trans, vert, horiz = self._get_text2_transform()
          t = mtext.Text(
              x=1, y=0,
              fontproperties=font_manager.FontProperties(size=self._labelsize),
              color=self._labelcolor,
              verticalalignment=vert,
              horizontalalignment=horiz,
              )
          t.set_transform(trans)
          self._set_artist_props(t)
          return t
  
      def _get_tick1line(self):
          'Get the default line2D instance'
          # x in axes coords, y in data coords
  
          l = mlines.Line2D((0,), (0,),
                            color=self._color,
                            marker=self._tickmarkers[0],
                            linestyle='None',
                            markersize=self._size,
                            markeredgewidth=self._width,
                            zorder=self._zorder)
          l.set_transform(self.axes.get_yaxis_transform(which='tick1'))
          self._set_artist_props(l)
          return l
  
      def _get_tick2line(self):
          'Get the default line2D instance'
          # x in axes coords, y in data coords
          l = mlines.Line2D((1,), (0,),
                            color=self._color,
                            marker=self._tickmarkers[1],
                            linestyle='None',
                            markersize=self._size,
                            markeredgewidth=self._width,
                            zorder=self._zorder)
          l.set_transform(self.axes.get_yaxis_transform(which='tick2'))
          self._set_artist_props(l)
          return l
  
      def _get_gridline(self):
          'Get the default line2D instance'
          # x in axes coords, y in data coords
          l = mlines.Line2D(xdata=(0, 1), ydata=(0, 0),
                            color=rcParams['grid.color'],
                            linestyle=rcParams['grid.linestyle'],
                            linewidth=rcParams['grid.linewidth'],
                            alpha=rcParams['grid.alpha'],
                            markersize=0)
  
          l.set_transform(self.axes.get_yaxis_transform(which='grid'))
          l.get_path()._interpolation_steps = GRIDLINE_INTERPOLATION_STEPS
          self._set_artist_props(l)
          return l
  
      def update_position(self, loc):
          'Set the location of tick in data coords with scalar loc'
          y = loc
  
          nonlinear = (hasattr(self.axes, 'yaxis') and
                       self.axes.yaxis.get_scale() != 'linear' or
                       hasattr(self.axes, 'xaxis') and
                       self.axes.xaxis.get_scale() != 'linear')
  
          if self.tick1On:
              self.tick1line.set_ydata((y,))
          if self.tick2On:
              self.tick2line.set_ydata((y,))
          if self.gridOn:
              self.gridline.set_ydata((y, ))
          if self.label1On:
              self.label1.set_y(y)
          if self.label2On:
              self.label2.set_y(y)
          if nonlinear:
              self.tick1line._invalid = True
              self.tick2line._invalid = True
              self.gridline._invalid = True
  
          self._loc = loc
          self.stale = True
  
      def get_view_interval(self):
          'return the Interval instance for this axis view limits'
          return self.axes.viewLim.intervaly
  
  
  class Ticker(object):
      locator = None
      formatter = None
  
  
  class Axis(artist.Artist):
      """
      Public attributes
  
      * :attr:`axes.transData` - transform data coords to display coords
      * :attr:`axes.transAxes` - transform axis coords to display coords
      * :attr:`labelpad` - number of points between the axis and its label
      """
      OFFSETTEXTPAD = 3
  
      def __str__(self):
          return self.__class__.__name__ \
              + "(%f,%f)" % tuple(self.axes.transAxes.transform_point((0, 0)))
  
      def __init__(self, axes, pickradius=15):
          """
          Init the axis with the parent Axes instance
          """
          artist.Artist.__init__(self)
          self.set_figure(axes.figure)
  
          # Keep track of setting to the default value, this allows use to know
          # if any of the following values is explicitly set by the user, so as
          # to not overwrite their settings with any of our 'auto' settings.
          self.isDefault_majloc = True
          self.isDefault_minloc = True
          self.isDefault_majfmt = True
          self.isDefault_minfmt = True
          self.isDefault_label = True
  
          self.axes = axes
          self.major = Ticker()
          self.minor = Ticker()
          self.callbacks = cbook.CallbackRegistry()
  
          self._autolabelpos = True
          self._smart_bounds = False
  
          self.label = self._get_label()
          self.labelpad = rcParams['axes.labelpad']
          self.offsetText = self._get_offset_text()
          self.majorTicks = []
          self.minorTicks = []
          self.pickradius = pickradius
  
          # Initialize here for testing; later add API
          self._major_tick_kw = dict()
          self._minor_tick_kw = dict()
  
          self.cla()
          self._set_scale('linear')
  
      def set_label_coords(self, x, y, transform=None):
          """
          Set the coordinates of the label.  By default, the x
          coordinate of the y label is determined by the tick label
          bounding boxes, but this can lead to poor alignment of
          multiple ylabels if there are multiple axes.  Ditto for the y
          coodinate of the x label.
  
          You can also specify the coordinate system of the label with
          the transform.  If None, the default coordinate system will be
          the axes coordinate system (0,0) is (left,bottom), (0.5, 0.5)
          is middle, etc
  
          """
  
          self._autolabelpos = False
          if transform is None:
              transform = self.axes.transAxes
  
          self.label.set_transform(transform)
          self.label.set_position((x, y))
          self.stale = True
  
      def get_transform(self):
          return self._scale.get_transform()
  
      def get_scale(self):
          return self._scale.name
  
      def _set_scale(self, value, **kwargs):
          self._scale = mscale.scale_factory(value, self, **kwargs)
          self._scale.set_default_locators_and_formatters(self)
  
          self.isDefault_majloc = True
          self.isDefault_minloc = True
          self.isDefault_majfmt = True
          self.isDefault_minfmt = True
  
      def limit_range_for_scale(self, vmin, vmax):
          return self._scale.limit_range_for_scale(vmin, vmax, self.get_minpos())
  
      def get_children(self):
          children = [self.label, self.offsetText]
          majorticks = self.get_major_ticks()
          minorticks = self.get_minor_ticks()
  
          children.extend(majorticks)
          children.extend(minorticks)
          return children
  
      def cla(self):
          'clear the current axis'
          self.set_major_locator(mticker.AutoLocator())
          self.set_major_formatter(mticker.ScalarFormatter())
          self.set_minor_locator(mticker.NullLocator())
          self.set_minor_formatter(mticker.NullFormatter())
  
          self.set_label_text('')
          self._set_artist_props(self.label)
  
          # Keep track of setting to the default value, this allows use to know
          # if any of the following values is explicitly set by the user, so as
          # to not overwrite their settings with any of our 'auto' settings.
          self.isDefault_majloc = True
          self.isDefault_minloc = True
          self.isDefault_majfmt = True
          self.isDefault_minfmt = True
          self.isDefault_label = True
  
          # Clear the callback registry for this axis, or it may "leak"
          self.callbacks = cbook.CallbackRegistry()
  
          # whether the grids are on
          self._gridOnMajor = (rcParams['axes.grid'] and
                               rcParams['axes.grid.which'] in ('both', 'major'))
          self._gridOnMinor = (rcParams['axes.grid'] and
                               rcParams['axes.grid.which'] in ('both', 'minor'))
  
          self.label.set_text('')
          self._set_artist_props(self.label)
  
          self.reset_ticks()
  
          self.converter = None
          self.units = None
          self.set_units(None)
          self.stale = True
  
      def reset_ticks(self):
          # build a few default ticks; grow as necessary later; only
          # define 1 so properties set on ticks will be copied as they
          # grow
          cbook.popall(self.majorTicks)
          cbook.popall(self.minorTicks)
  
          self.majorTicks.extend([self._get_tick(major=True)])
          self.minorTicks.extend([self._get_tick(major=False)])
          self._lastNumMajorTicks = 1
          self._lastNumMinorTicks = 1
  
      def set_tick_params(self, which='major', reset=False, **kw):
          """
          Set appearance parameters for ticks and ticklabels.
  
          For documentation of keyword arguments, see
          :meth:`matplotlib.axes.Axes.tick_params`.
          """
          dicts = []
          if which == 'major' or which == 'both':
              dicts.append(self._major_tick_kw)
          if which == 'minor' or which == 'both':
              dicts.append(self._minor_tick_kw)
          kwtrans = self._translate_tick_kw(kw, to_init_kw=True)
          for d in dicts:
              if reset:
                  d.clear()
              d.update(kwtrans)
          if reset:
              self.reset_ticks()
          else:
              if which == 'major' or which == 'both':
                  for tick in self.majorTicks:
                      tick._apply_params(**self._major_tick_kw)
              if which == 'minor' or which == 'both':
                  for tick in self.minorTicks:
                      tick._apply_params(**self._minor_tick_kw)
              if 'labelcolor' in kwtrans:
                  self.offsetText.set_color(kwtrans['labelcolor'])
          self.stale = True
  
      @staticmethod
      def _translate_tick_kw(kw, to_init_kw=True):
          # We may want to move the following function to
          # a more visible location; or maybe there already
          # is something like this.
          def _bool(arg):
              if cbook.is_string_like(arg):
                  if arg.lower() == 'on':
                      return True
                  if arg.lower() == 'off':
                      return False
                  raise ValueError('String "%s" should be "on" or "off"' % arg)
              return bool(arg)
          # The following lists may be moved to a more
          # accessible location.
          kwkeys0 = ['size', 'width', 'color', 'tickdir', 'pad',
                     'labelsize', 'labelcolor', 'zorder', 'gridOn',
                     'tick1On', 'tick2On', 'label1On', 'label2On']
          kwkeys1 = ['length', 'direction', 'left', 'bottom', 'right', 'top',
                     'labelleft', 'labelbottom', 'labelright', 'labeltop']
          kwkeys = kwkeys0 + kwkeys1
          kwtrans = dict()
          if to_init_kw:
              if 'length' in kw:
                  kwtrans['size'] = kw.pop('length')
              if 'direction' in kw:
                  kwtrans['tickdir'] = kw.pop('direction')
              if 'left' in kw:
                  kwtrans['tick1On'] = _bool(kw.pop('left'))
              if 'bottom' in kw:
                  kwtrans['tick1On'] = _bool(kw.pop('bottom'))
              if 'right' in kw:
                  kwtrans['tick2On'] = _bool(kw.pop('right'))
              if 'top' in kw:
                  kwtrans['tick2On'] = _bool(kw.pop('top'))
  
              if 'labelleft' in kw:
                  kwtrans['label1On'] = _bool(kw.pop('labelleft'))
              if 'labelbottom' in kw:
                  kwtrans['label1On'] = _bool(kw.pop('labelbottom'))
              if 'labelright' in kw:
                  kwtrans['label2On'] = _bool(kw.pop('labelright'))
              if 'labeltop' in kw:
                  kwtrans['label2On'] = _bool(kw.pop('labeltop'))
              if 'colors' in kw:
                  c = kw.pop('colors')
                  kwtrans['color'] = c
                  kwtrans['labelcolor'] = c
              # Maybe move the checking up to the caller of this method.
              for key in kw:
                  if key not in kwkeys:
                      raise ValueError(
                          "keyword %s is not recognized; valid keywords are %s"
                          % (key, kwkeys))
              kwtrans.update(kw)
          else:
              raise NotImplementedError("Inverse translation is deferred")
          return kwtrans
  
      def set_clip_path(self, clippath, transform=None):
          artist.Artist.set_clip_path(self, clippath, transform)
          for child in self.majorTicks + self.minorTicks:
              child.set_clip_path(clippath, transform)
          self.stale = True
  
      def get_view_interval(self):
          'return the Interval instance for this axis view limits'
          raise NotImplementedError('Derived must override')
  
      def set_view_interval(self, vmin, vmax, ignore=False):
          raise NotImplementedError('Derived must override')
  
      def get_data_interval(self):
          'return the Interval instance for this axis data limits'
          raise NotImplementedError('Derived must override')
  
      def set_data_interval(self):
          '''set the axis data limits'''
          raise NotImplementedError('Derived must override')
  
      def set_default_intervals(self):
          '''set the default limits for the axis data and view interval if they
          are not mutated'''
  
          # this is mainly in support of custom object plotting.  For
          # example, if someone passes in a datetime object, we do not
          # know automagically how to set the default min/max of the
          # data and view limits.  The unit conversion AxisInfo
          # interface provides a hook for custom types to register
          # default limits through the AxisInfo.default_limits
          # attribute, and the derived code below will check for that
          # and use it if is available (else just use 0..1)
          pass
  
      def _set_artist_props(self, a):
          if a is None:
              return
          a.set_figure(self.figure)
  
      def iter_ticks(self):
          """
          Iterate through all of the major and minor ticks.
          """
          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)]
  
          major_minor = [
              (majorTicks, majorLocs, majorLabels),
              (minorTicks, minorLocs, minorLabels)]
  
          for group in major_minor:
              for tick in zip(*group):
                  yield tick
  
      def get_ticklabel_extents(self, renderer):
          """
          Get the extents of the tick labels on either side
          of the axes.
          """
  
          ticks_to_draw = self._update_ticks(renderer)
          ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
                                                                  renderer)
  
          if len(ticklabelBoxes):
              bbox = mtransforms.Bbox.union(ticklabelBoxes)
          else:
              bbox = mtransforms.Bbox.from_extents(0, 0, 0, 0)
          if len(ticklabelBoxes2):
              bbox2 = mtransforms.Bbox.union(ticklabelBoxes2)
          else:
              bbox2 = mtransforms.Bbox.from_extents(0, 0, 0, 0)
          return bbox, bbox2
  
      def set_smart_bounds(self, value):
          """set the axis to have smart bounds"""
          self._smart_bounds = value
          self.stale = True
  
      def get_smart_bounds(self):
          """get whether the axis has smart bounds"""
          return self._smart_bounds
  
      def _update_ticks(self, renderer):
          """
          Update ticks (position and labels) using the current data
          interval of the axes. Returns a list of ticks that will be
          drawn.
          """
  
          interval = self.get_view_interval()
          tick_tups = [t for t in self.iter_ticks()]
          if self._smart_bounds:
              # handle inverted limits
              view_low, view_high = min(*interval), max(*interval)
              data_low, data_high = self.get_data_interval()
              if data_low > data_high:
                  data_low, data_high = data_high, data_low
              locs = [ti[1] for ti in tick_tups]
              locs.sort()
              locs = np.array(locs)
              if len(locs):
                  if data_low <= view_low:
                      # data extends beyond view, take view as limit
                      ilow = view_low
                  else:
                      # data stops within view, take best tick
                      cond = locs <= data_low
                      good_locs = locs[cond]
                      if len(good_locs) > 0:
                          # last tick prior or equal to first data point
                          ilow = good_locs[-1]
                      else:
                          # No ticks (why not?), take first tick
                          ilow = locs[0]
                  if data_high >= view_high:
                      # data extends beyond view, take view as limit
                      ihigh = view_high
                  else:
                      # data stops within view, take best tick
                      cond = locs >= data_high
                      good_locs = locs[cond]
                      if len(good_locs) > 0:
                          # first tick after or equal to last data point
                          ihigh = good_locs[0]
                      else:
                          # No ticks (why not?), take last tick
                          ihigh = locs[-1]
                  tick_tups = [ti for ti in tick_tups
                               if (ti[1] >= ilow) and (ti[1] <= ihigh)]
  
          # so that we don't lose ticks on the end, expand out the interval ever
          # so slightly.  The "ever so slightly" is defined to be the width of a
          # half of a pixel.  We don't want to draw a tick that even one pixel
          # outside of the defined axis interval.
          if interval[0] <= interval[1]:
              interval_expanded = interval
          else:
              interval_expanded = interval[1], interval[0]
  
          if hasattr(self, '_get_pixel_distance_along_axis'):
              # normally, one does not want to catch all exceptions that
              # could possibly happen, but it is not clear exactly what
              # exceptions might arise from a user's projection (their
              # rendition of the Axis object).  So, we catch all, with
              # the idea that one would rather potentially lose a tick
              # from one side of the axis or another, rather than see a
              # stack trace.
              # We also catch users warnings here. These are the result of
              # invalid numpy calculations that may be the result of out of
              # bounds on axis with finite allowed intervals such as geo
              # projections i.e. Mollweide.
              with np.errstate(invalid='ignore'):
                  try:
                      ds1 = self._get_pixel_distance_along_axis(
                          interval_expanded[0], -0.5)
                  except:
                      warnings.warn("Unable to find pixel distance along axis "
                                    "for interval padding of ticks; assuming no "
                                    "interval padding needed.")
                      ds1 = 0.0
                  if np.isnan(ds1):
                      ds1 = 0.0
                  try:
                      ds2 = self._get_pixel_distance_along_axis(
                          interval_expanded[1], +0.5)
                  except:
                      warnings.warn("Unable to find pixel distance along axis "
                                    "for interval padding of ticks; assuming no "
                                    "interval padding needed.")
                      ds2 = 0.0
                  if np.isnan(ds2):
                      ds2 = 0.0
              interval_expanded = (interval_expanded[0] - ds1,
                                   interval_expanded[1] + ds2)
  
          ticks_to_draw = []
          for tick, loc, label in tick_tups:
              if tick is None:
                  continue
              if not mtransforms.interval_contains(interval_expanded, loc):
                  continue
              tick.update_position(loc)
              tick.set_label1(label)
              tick.set_label2(label)
              ticks_to_draw.append(tick)
  
          return ticks_to_draw
  
      def _get_tick_bboxes(self, ticks, renderer):
          """
          Given the list of ticks, return two lists of bboxes. One for
          tick lable1's and another for tick label2's.
          """
  
          ticklabelBoxes = []
          ticklabelBoxes2 = []
  
          for tick in ticks:
              if tick.label1On and tick.label1.get_visible():
                  extent = tick.label1.get_window_extent(renderer)
                  ticklabelBoxes.append(extent)
              if tick.label2On and tick.label2.get_visible():
                  extent = tick.label2.get_window_extent(renderer)
                  ticklabelBoxes2.append(extent)
          return ticklabelBoxes, ticklabelBoxes2
  
      def get_tightbbox(self, renderer):
          """
          Return a bounding box that encloses the axis. It only accounts
          tick labels, axis label, and offsetText.
          """
          if not self.get_visible():
              return
  
          ticks_to_draw = self._update_ticks(renderer)
          ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
                                                                  renderer)
  
          self._update_label_position(ticklabelBoxes, ticklabelBoxes2)
  
          self._update_offset_text_position(ticklabelBoxes, ticklabelBoxes2)
          self.offsetText.set_text(self.major.formatter.get_offset())
  
          bb = []
  
          for a in [self.label, self.offsetText]:
              if a.get_visible():
                  bb.append(a.get_window_extent(renderer))
  
          bb.extend(ticklabelBoxes)
          bb.extend(ticklabelBoxes2)
  
          bb = [b for b in bb if b.width != 0 or b.height != 0]
          if bb:
              _bbox = mtransforms.Bbox.union(bb)
              return _bbox
          else:
              return None
  
      def get_tick_padding(self):
          values = []
          if len(self.majorTicks):
              values.append(self.majorTicks[0].get_tick_padding())
          if len(self.minorTicks):
              values.append(self.minorTicks[0].get_tick_padding())
          if len(values):
              return max(values)
          return 0.0
  
      @allow_rasterization
      def draw(self, renderer, *args, **kwargs):
          'Draw the axis lines, grid lines, tick lines and labels'
  
          if not self.get_visible():
              return
          renderer.open_group(__name__)
  
          ticks_to_draw = self._update_ticks(renderer)
          ticklabelBoxes, ticklabelBoxes2 = self._get_tick_bboxes(ticks_to_draw,
                                                                  renderer)
  
          for tick in ticks_to_draw:
              tick.draw(renderer)
  
          # scale up the axis label box to also find the neighbors, not
          # just the tick labels that actually overlap note we need a
          # *copy* of the axis label box because we don't wan't to scale
          # the actual bbox
  
          self._update_label_position(ticklabelBoxes, ticklabelBoxes2)
  
          self.label.draw(renderer)
  
          self._update_offset_text_position(ticklabelBoxes, ticklabelBoxes2)
          self.offsetText.set_text(self.major.formatter.get_offset())
          self.offsetText.draw(renderer)
  
          if 0:  # draw the bounding boxes around the text for debug
              for tick in self.majorTicks:
                  label = tick.label1
                  mpatches.bbox_artist(label, renderer)
              mpatches.bbox_artist(self.label, renderer)
  
          renderer.close_group(__name__)
          self.stale = False
  
      def _get_label(self):
          raise NotImplementedError('Derived must override')
  
      def _get_offset_text(self):
          raise NotImplementedError('Derived must override')
  
      def get_gridlines(self):
          'Return the grid lines as a list of Line2D instance'
          ticks = self.get_major_ticks()
          return cbook.silent_list('Line2D gridline',
                                   [tick.gridline for tick in ticks])
  
      def get_label(self):
          'Return the axis label as a Text instance'
          return self.label
  
      def get_offset_text(self):
          'Return the axis offsetText as a Text instance'
          return self.offsetText
  
      def get_pickradius(self):
          'Return the depth of the axis used by the picker'
          return self.pickradius
  
      def get_majorticklabels(self):
          'Return a list of Text instances for the major ticklabels'
          ticks = self.get_major_ticks()
          labels1 = [tick.label1 for tick in ticks if tick.label1On]
          labels2 = [tick.label2 for tick in ticks if tick.label2On]
          return cbook.silent_list('Text major ticklabel', labels1 + labels2)
  
      def get_minorticklabels(self):
          'Return a list of Text instances for the minor ticklabels'
          ticks = self.get_minor_ticks()
          labels1 = [tick.label1 for tick in ticks if tick.label1On]
          labels2 = [tick.label2 for tick in ticks if tick.label2On]
          return cbook.silent_list('Text minor ticklabel', labels1 + labels2)
  
      def get_ticklabels(self, minor=False, which=None):
          """
          Get the x tick labels as a list of :class:`~matplotlib.text.Text`
          instances.
  
          Parameters
          ----------
          minor : bool
             If True return the minor ticklabels,
             else return the major ticklabels
  
          which : None, ('minor', 'major', 'both')
             Overrides `minor`.
  
             Selects which ticklabels to return
  
          Returns
          -------
          ret : list
             List of :class:`~matplotlib.text.Text` instances.
          """
  
          if which is not None:
              if which == 'minor':
                  return self.get_minorticklabels()
              elif which == 'major':
                  return self.get_majorticklabels()
              elif which == 'both':
                  return self.get_majorticklabels() + self.get_minorticklabels()
              else:
                  raise ValueError("`which` must be one of ('minor', 'major', "
                                   "'both') not " + str(which))
          if minor:
              return self.get_minorticklabels()
          return self.get_majorticklabels()
  
      def get_majorticklines(self):
          'Return the major tick lines as a list of Line2D instances'
          lines = []
          ticks = self.get_major_ticks()
          for tick in ticks:
              lines.append(tick.tick1line)
              lines.append(tick.tick2line)
          return cbook.silent_list('Line2D ticklines', lines)
  
      def get_minorticklines(self):
          'Return the minor tick lines as a list of Line2D instances'
          lines = []
          ticks = self.get_minor_ticks()
          for tick in ticks:
              lines.append(tick.tick1line)
              lines.append(tick.tick2line)
          return cbook.silent_list('Line2D ticklines', lines)
  
      def get_ticklines(self, minor=False):
          'Return the tick lines as a list of Line2D instances'
          if minor:
              return self.get_minorticklines()
          return self.get_majorticklines()
  
      def get_majorticklocs(self):
          "Get the major tick locations in data coordinates as a numpy array"
          return self.major.locator()
  
      def get_minorticklocs(self):
          "Get the minor tick locations in data coordinates as a numpy array"
          return self.minor.locator()
  
      def get_ticklocs(self, minor=False):
          "Get the tick locations in data coordinates as a numpy array"
          if minor:
              return self.minor.locator()
          return self.major.locator()
  
      def _get_tick(self, major):
          'return the default tick instance'
          raise NotImplementedError('derived must override')
  
      def _copy_tick_props(self, src, dest):
          'Copy the props from src tick to dest tick'
          if src is None or dest is None:
              return
          dest.label1.update_from(src.label1)
          dest.label2.update_from(src.label2)
  
          dest.tick1line.update_from(src.tick1line)
          dest.tick2line.update_from(src.tick2line)
          dest.gridline.update_from(src.gridline)
  
          dest.tick1On = src.tick1On
          dest.tick2On = src.tick2On
          dest.label1On = src.label1On
          dest.label2On = src.label2On
  
      def get_label_text(self):
          'Get the text of the label'
          return self.label.get_text()
  
      def get_major_locator(self):
          'Get the locator of the major ticker'
          return self.major.locator
  
      def get_minor_locator(self):
          'Get the locator of the minor ticker'
          return self.minor.locator
  
      def get_major_formatter(self):
          'Get the formatter of the major ticker'
          return self.major.formatter
  
      def get_minor_formatter(self):
          'Get the formatter of the minor ticker'
          return self.minor.formatter
  
      def get_major_ticks(self, numticks=None):
          'get the tick instances; grow as necessary'
          if numticks is None:
              numticks = len(self.get_major_locator()())
          if len(self.majorTicks) < numticks:
              # update the new tick label properties from the old
              for i in range(numticks - len(self.majorTicks)):
                  tick = self._get_tick(major=True)
                  self.majorTicks.append(tick)
  
          if self._lastNumMajorTicks < numticks:
              protoTick = self.majorTicks[0]
              for i in range(self._lastNumMajorTicks, len(self.majorTicks)):
                  tick = self.majorTicks[i]
                  if self._gridOnMajor:
                      tick.gridOn = True
                  self._copy_tick_props(protoTick, tick)
  
          self._lastNumMajorTicks = numticks
          ticks = self.majorTicks[:numticks]
  
          return ticks
  
      def get_minor_ticks(self, numticks=None):
          'get the minor tick instances; grow as necessary'
          if numticks is None:
              numticks = len(self.get_minor_locator()())
  
          if len(self.minorTicks) < numticks:
              # update the new tick label properties from the old
              for i in range(numticks - len(self.minorTicks)):
                  tick = self._get_tick(major=False)
                  self.minorTicks.append(tick)
  
          if self._lastNumMinorTicks < numticks:
              protoTick = self.minorTicks[0]
              for i in range(self._lastNumMinorTicks, len(self.minorTicks)):
                  tick = self.minorTicks[i]
                  if self._gridOnMinor:
                      tick.gridOn = True
                  self._copy_tick_props(protoTick, tick)
  
          self._lastNumMinorTicks = numticks
          ticks = self.minorTicks[:numticks]
  
          return ticks
  
      def grid(self, b=None, which='major', **kwargs):
          """
          Set the axis grid on or off; b is a boolean. Use *which* =
          'major' | 'minor' | 'both' to set the grid for major or minor ticks.
  
          If *b* is *None* and len(kwargs)==0, toggle the grid state.  If
          *kwargs* are supplied, it is assumed you want the grid on and *b*
          will be set to True.
  
          *kwargs* are used to set the line properties of the grids, e.g.,
  
            xax.grid(color='r', linestyle='-', linewidth=2)
          """
          if len(kwargs):
              b = True
          which = which.lower()
          if which in ['minor', 'both']:
              if b is None:
                  self._gridOnMinor = not self._gridOnMinor
              else:
                  self._gridOnMinor = b
              for tick in self.minorTicks:  # don't use get_ticks here!
                  if tick is None:
                      continue
                  tick.gridOn = self._gridOnMinor
                  if len(kwargs):
                      tick.gridline.update(kwargs)
              self._minor_tick_kw['gridOn'] = self._gridOnMinor
          if which in ['major', 'both']:
              if b is None:
                  self._gridOnMajor = not self._gridOnMajor
              else:
                  self._gridOnMajor = b
              for tick in self.majorTicks:  # don't use get_ticks here!
                  if tick is None:
                      continue
                  tick.gridOn = self._gridOnMajor
                  if len(kwargs):
                      tick.gridline.update(kwargs)
              self._major_tick_kw['gridOn'] = self._gridOnMajor
          self.stale = True
  
      def update_units(self, data):
          """
          introspect *data* for units converter and update the
          axis.converter instance if necessary. Return *True*
          if *data* is registered for unit conversion.
          """
  
          converter = munits.registry.get_converter(data)
          if converter is None:
              return False
  
          neednew = self.converter != converter
          self.converter = converter
          default = self.converter.default_units(data, self)
          if default is not None and self.units is None:
              self.set_units(default)
  
          if neednew:
              self._update_axisinfo()
          self.stale = True
          return True
  
      def _update_axisinfo(self):
          """
          check the axis converter for the stored units to see if the
          axis info needs to be updated
          """
  
          if self.converter is None:
              return
  
          info = self.converter.axisinfo(self.units, self)
          if info is None:
              return
          if info.majloc is not None and \
             self.major.locator != info.majloc and self.isDefault_majloc:
              self.set_major_locator(info.majloc)
              self.isDefault_majloc = True
          if info.minloc is not None and \
             self.minor.locator != info.minloc and self.isDefault_minloc:
              self.set_minor_locator(info.minloc)
              self.isDefault_minloc = True
          if info.majfmt is not None and \
             self.major.formatter != info.majfmt and self.isDefault_majfmt:
              self.set_major_formatter(info.majfmt)
              self.isDefault_majfmt = True
          if info.minfmt is not None and \
             self.minor.formatter != info.minfmt and self.isDefault_minfmt:
              self.set_minor_formatter(info.minfmt)
              self.isDefault_minfmt = True
          if info.label is not None and self.isDefault_label:
              self.set_label_text(info.label)
              self.isDefault_label = True
  
          self.set_default_intervals()
  
      def have_units(self):
          return self.converter is not None or self.units is not None
  
      def convert_units(self, x):
          if self.converter is None:
              self.converter = munits.registry.get_converter(x)
  
          if self.converter is None:
              return x
  
          ret = self.converter.convert(x, self.units, self)
          return ret
  
      def set_units(self, u):
          """
          set the units for axis
  
          ACCEPTS: a units tag
          """
          pchanged = False
          if u is None:
              self.units = None
              pchanged = True
          else:
              if u != self.units:
                  self.units = u
                  pchanged = True
          if pchanged:
              self._update_axisinfo()
              self.callbacks.process('units')
              self.callbacks.process('units finalize')
          self.stale = True
  
      def get_units(self):
          'return the units for axis'
          return self.units
  
      def set_label_text(self, label, fontdict=None, **kwargs):
          """  Sets the text value of the axis label
  
          ACCEPTS: A string value for the label
          """
          self.isDefault_label = False
          self.label.set_text(label)
          if fontdict is not None:
              self.label.update(fontdict)
          self.label.update(kwargs)
          self.stale = True
          return self.label
  
      def set_major_formatter(self, formatter):
          """
          Set the formatter of the major ticker
  
          ACCEPTS: A :class:`~matplotlib.ticker.Formatter` instance
          """
          self.isDefault_majfmt = False
          self.major.formatter = formatter
          formatter.set_axis(self)
          self.stale = True
  
      def set_minor_formatter(self, formatter):
          """
          Set the formatter of the minor ticker
  
          ACCEPTS: A :class:`~matplotlib.ticker.Formatter` instance
          """
          self.isDefault_minfmt = False
          self.minor.formatter = formatter
          formatter.set_axis(self)
          self.stale = True
  
      def set_major_locator(self, locator):
          """
          Set the locator of the major ticker
  
          ACCEPTS: a :class:`~matplotlib.ticker.Locator` instance
          """
          self.isDefault_majloc = False
          self.major.locator = locator
          locator.set_axis(self)
          self.stale = True
  
      def set_minor_locator(self, locator):
          """
          Set the locator of the minor ticker
  
          ACCEPTS: a :class:`~matplotlib.ticker.Locator` instance
          """
          self.isDefault_minloc = False
          self.minor.locator = locator
          locator.set_axis(self)
          self.stale = True
  
      def set_pickradius(self, pickradius):
          """
          Set the depth of the axis used by the picker
  
          ACCEPTS: a distance in points
          """
          self.pickradius = pickradius
  
      def set_ticklabels(self, ticklabels, *args, **kwargs):
          """
          Set the text values of the tick labels. Return a list of Text
          instances.  Use *kwarg* *minor=True* to select minor ticks.
          All other kwargs are used to update the text object properties.
          As for get_ticklabels, label1 (left or bottom) is
          affected for a given tick only if its label1On attribute
          is True, and similarly for label2.  The list of returned
          label text objects consists of all such label1 objects followed
          by all such label2 objects.
  
          The input *ticklabels* is assumed to match the set of
          tick locations, regardless of the state of label1On and
          label2On.
  
          ACCEPTS: sequence of strings or Text objects
          """
          get_labels = []
          for t in ticklabels:
              # try calling get_text() to check whether it is Text object
              # if it is Text, get label content
              try:
                  get_labels.append(t.get_text())
              # otherwise add the label to the list directly
              except AttributeError:
                  get_labels.append(t)
          # replace the ticklabels list with the processed one
          ticklabels = get_labels
  
          minor = kwargs.pop('minor', False)
          if minor:
              self.set_minor_formatter(mticker.FixedFormatter(ticklabels))
              ticks = self.get_minor_ticks()
          else:
              self.set_major_formatter(mticker.FixedFormatter(ticklabels))
              ticks = self.get_major_ticks()
          ret = []
          for tick_label, tick in zip(ticklabels, ticks):
              # deal with label1
              tick.label1.set_text(tick_label)
              tick.label1.update(kwargs)
              # deal with label2
              tick.label2.set_text(tick_label)
              tick.label2.update(kwargs)
              # only return visible tick labels
              if tick.label1On:
                  ret.append(tick.label1)
              if tick.label2On:
                  ret.append(tick.label2)
  
          self.stale = True
          return ret
  
      def set_ticks(self, ticks, minor=False):
          """
          Set the locations of the tick marks from sequence ticks
  
          ACCEPTS: sequence of floats
          """
          # XXX if the user changes units, the information will be lost here
          ticks = self.convert_units(ticks)
          if len(ticks) > 1:
              xleft, xright = self.get_view_interval()
              if xright > xleft:
                  self.set_view_interval(min(ticks), max(ticks))
              else:
                  self.set_view_interval(max(ticks), min(ticks))
          if minor:
              self.set_minor_locator(mticker.FixedLocator(ticks))
              return self.get_minor_ticks(len(ticks))
          else:
              self.set_major_locator(mticker.FixedLocator(ticks))
              return self.get_major_ticks(len(ticks))
  
      def _update_label_position(self, bboxes, bboxes2):
          """
          Update the label position based on the bounding box enclosing
          all the ticklabels and axis spine
          """
          raise NotImplementedError('Derived must override')
  
      def _update_offset_text_postion(self, bboxes, bboxes2):
          """
          Update the label position based on the sequence of bounding
          boxes of all the ticklabels
          """
          raise NotImplementedError('Derived must override')
  
      def pan(self, numsteps):
          'Pan *numsteps* (can be positive or negative)'
          self.major.locator.pan(numsteps)
  
      def zoom(self, direction):
          "Zoom in/out on axis; if *direction* is >0 zoom in, else zoom out"
          self.major.locator.zoom(direction)
  
      def axis_date(self, tz=None):
          """
          Sets up x-axis ticks and labels that treat the x data as dates.
          *tz* is a :class:`tzinfo` instance or a timezone string.
          This timezone is used to create date labels.
          """
          # By providing a sample datetime instance with the desired
          # timezone, the registered converter can be selected,
          # and the "units" attribute, which is the timezone, can
          # be set.
          import datetime
          if isinstance(tz, six.string_types):
              import pytz
              tz = pytz.timezone(tz)
          self.update_units(datetime.datetime(2009, 1, 1, 0, 0, 0, 0, tz))
  
      def get_tick_space(self):
          """
          Return the estimated number of ticks that can fit on the axis.
          """
          # Must be overridden in the subclass
          raise NotImplementedError()
  
      def get_label_position(self):
          """
          Return the label position (top or bottom)
          """
          return self.label_position
  
      def set_label_position(self, position):
          """
          Set the label position (top or bottom)
  
          ACCEPTS: [ 'top' | 'bottom' ]
          """
          raise NotImplementedError()
  
      def get_minpos(self):
          raise NotImplementedError()
  
  
  class XAxis(Axis):
      __name__ = 'xaxis'
      axis_name = 'x'
  
      def contains(self, mouseevent):
          """Test whether the mouse event occured in the x axis.
          """
          if six.callable(self._contains):
              return self._contains(self, mouseevent)
  
          x, y = mouseevent.x, mouseevent.y
          try:
              trans = self.axes.transAxes.inverted()
              xaxes, yaxes = trans.transform_point((x, y))
          except ValueError:
              return False, {}
          l, b = self.axes.transAxes.transform_point((0, 0))
          r, t = self.axes.transAxes.transform_point((1, 1))
          inaxis = xaxes >= 0 and xaxes <= 1 and (
              (y < b and y > b - self.pickradius) or
              (y > t and y < t + self.pickradius))
          return inaxis, {}
  
      def _get_tick(self, major):
          if major:
              tick_kw = self._major_tick_kw
          else:
              tick_kw = self._minor_tick_kw
          return XTick(self.axes, 0, '', major=major, **tick_kw)
  
      def _get_label(self):
          # x in axes coords, y in display coords (to be updated at draw
          # time by _update_label_positions)
          label = mtext.Text(x=0.5, y=0,
                             fontproperties=font_manager.FontProperties(
                                 size=rcParams['axes.labelsize'],
                                 weight=rcParams['axes.labelweight']),
                             color=rcParams['axes.labelcolor'],
                             verticalalignment='top',
                             horizontalalignment='center')
  
          label.set_transform(mtransforms.blended_transform_factory(
              self.axes.transAxes, mtransforms.IdentityTransform()))
  
          self._set_artist_props(label)
          self.label_position = 'bottom'
          return label
  
      def _get_offset_text(self):
          # x in axes coords, y in display coords (to be updated at draw time)
          offsetText = mtext.Text(x=1, y=0,
                                  fontproperties=font_manager.FontProperties(
                                      size=rcParams['xtick.labelsize']),
                                  color=rcParams['xtick.color'],
                                  verticalalignment='top',
                                  horizontalalignment='right')
          offsetText.set_transform(mtransforms.blended_transform_factory(
              self.axes.transAxes, mtransforms.IdentityTransform())
          )
          self._set_artist_props(offsetText)
          self.offset_text_position = 'bottom'
          return offsetText
  
      def _get_pixel_distance_along_axis(self, where, perturb):
          """
          Returns the amount, in data coordinates, that a single pixel
          corresponds to in the locality given by "where", which is also given
          in data coordinates, and is an x coordinate. "perturb" is the amount
          to perturb the pixel.  Usually +0.5 or -0.5.
  
          Implementing this routine for an axis is optional; if present, it will
          ensure that no ticks are lost due to round-off at the extreme ends of
          an axis.
          """
  
          # Note that this routine does not work for a polar axis, because of
          # the 1e-10 below.  To do things correctly, we need to use rmax
          # instead of 1e-10 for a polar axis.  But since we do not have that
          # kind of information at this point, we just don't try to pad anything
          # for the theta axis of a polar plot.
          if self.axes.name == 'polar':
              return 0.0
  
          #
          # first figure out the pixel location of the "where" point.  We use
          # 1e-10 for the y point, so that we remain compatible with log axes.
  
          # transformation from data coords to display coords
          trans = self.axes.transData
          # transformation from display coords to data coords
          transinv = trans.inverted()
          pix = trans.transform_point((where, 1e-10))
          # perturb the pixel
          ptp = transinv.transform_point((pix[0] + perturb, pix[1]))
          dx = abs(ptp[0] - where)
  
          return dx
  
      def set_label_position(self, position):
          """
          Set the label position (top or bottom)
  
          ACCEPTS: [ 'top' | 'bottom' ]
          """
          if position == 'top':
              self.label.set_verticalalignment('baseline')
          elif position == 'bottom':
              self.label.set_verticalalignment('top')
          else:
              msg = "Position accepts only [ 'top' | 'bottom' ]"
              raise ValueError(msg)
          self.label_position = position
          self.stale = True
  
      def _update_label_position(self, bboxes, bboxes2):
          """
          Update the label position based on the bounding box enclosing
          all the ticklabels and axis spine
          """
          if not self._autolabelpos:
              return
          x, y = self.label.get_position()
          if self.label_position == 'bottom':
              try:
                  spine = self.axes.spines['bottom']
                  spinebbox = spine.get_transform().transform_path(
                      spine.get_path()).get_extents()
              except KeyError:
                  # use axes if spine doesn't exist
                  spinebbox = self.axes.bbox
              bbox = mtransforms.Bbox.union(bboxes + [spinebbox])
              bottom = bbox.y0
  
              self.label.set_position(
                  (x, bottom - self.labelpad * self.figure.dpi / 72.0)
              )
  
          else:
              try:
                  spine = self.axes.spines['top']
                  spinebbox = spine.get_transform().transform_path(
                      spine.get_path()).get_extents()
              except KeyError:
                  # use axes if spine doesn't exist
                  spinebbox = self.axes.bbox
              bbox = mtransforms.Bbox.union(bboxes2 + [spinebbox])
              top = bbox.y1
  
              self.label.set_position(
                  (x, top + self.labelpad * self.figure.dpi / 72.0)
              )
  
      def _update_offset_text_position(self, bboxes, bboxes2):
          """
          Update the offset_text position based on the sequence of bounding
          boxes of all the ticklabels
          """
          x, y = self.offsetText.get_position()
          if not len(bboxes):
              bottom = self.axes.bbox.ymin
          else:
              bbox = mtransforms.Bbox.union(bboxes)
              bottom = bbox.y0
          self.offsetText.set_position(
              (x, bottom - self.OFFSETTEXTPAD * self.figure.dpi / 72.0)
          )
  
      def get_text_heights(self, renderer):
          """
          Returns the amount of space one should reserve for text
          above and below the axes.  Returns a tuple (above, below)
          """
          bbox, bbox2 = self.get_ticklabel_extents(renderer)
          # MGDTODO: Need a better way to get the pad
          padPixels = self.majorTicks[0].get_pad_pixels()
  
          above = 0.0
          if bbox2.height:
              above += bbox2.height + padPixels
          below = 0.0
          if bbox.height:
              below += bbox.height + padPixels
  
          if self.get_label_position() == 'top':
              above += self.label.get_window_extent(renderer).height + padPixels
          else:
              below += self.label.get_window_extent(renderer).height + padPixels
          return above, below
  
      def set_ticks_position(self, position):
          """
          Set the ticks position (top, bottom, both, default or none)
          both sets the ticks to appear on both positions, but does not
          change the tick labels.  'default' resets the tick positions to
          the default: ticks on both positions, labels at bottom.  'none'
          can be used if you don't want any ticks. 'none' and 'both'
          affect only the ticks, not the labels.
  
          ACCEPTS: [ 'top' | 'bottom' | 'both' | 'default' | 'none' ]
          """
          if position == 'top':
              self.set_tick_params(which='both', top=True, labeltop=True,
                                   bottom=False, labelbottom=False)
          elif position == 'bottom':
              self.set_tick_params(which='both', top=False, labeltop=False,
                                   bottom=True, labelbottom=True)
          elif position == 'both':
              self.set_tick_params(which='both', top=True,
                                   bottom=True)
          elif position == 'none':
              self.set_tick_params(which='both', top=False,
                                   bottom=False)
          elif position == 'default':
              self.set_tick_params(which='both', top=True, labeltop=False,
                                   bottom=True, labelbottom=True)
          else:
              raise ValueError("invalid position: %s" % position)
          self.stale = True
  
      def tick_top(self):
          'use ticks only on top'
          self.set_ticks_position('top')
  
      def tick_bottom(self):
          'use ticks only on bottom'
          self.set_ticks_position('bottom')
  
      def get_ticks_position(self):
          """
          Return the ticks position (top, bottom, default or unknown)
          """
          majt = self.majorTicks[0]
          mT = self.minorTicks[0]
  
          majorTop = ((not majt.tick1On) and majt.tick2On and
                      (not majt.label1On) and majt.label2On)
          minorTop = ((not mT.tick1On) and mT.tick2On and
                      (not mT.label1On) and mT.label2On)
          if majorTop and minorTop:
              return 'top'
  
          MajorBottom = (majt.tick1On and (not majt.tick2On) and
                         majt.label1On and (not majt.label2On))
          MinorBottom = (mT.tick1On and (not mT.tick2On) and
                         mT.label1On and (not mT.label2On))
          if MajorBottom and MinorBottom:
              return 'bottom'
  
          majorDefault = (majt.tick1On and majt.tick2On and
                          majt.label1On and (not majt.label2On))
          minorDefault = (mT.tick1On and mT.tick2On and
                          mT.label1On and (not mT.label2On))
          if majorDefault and minorDefault:
              return 'default'
  
          return 'unknown'
  
      def get_view_interval(self):
          'return the Interval instance for this axis view limits'
          return self.axes.viewLim.intervalx
  
      def set_view_interval(self, vmin, vmax, ignore=False):
          """
          If *ignore* is *False*, the order of vmin, vmax
          does not matter; the original axis orientation will
          be preserved. In addition, the view limits can be
          expanded, but will not be reduced.  This method is
          for mpl internal use; for normal use, see
          :meth:`~matplotlib.axes.Axes.set_xlim`.
  
          """
          if ignore:
              self.axes.viewLim.intervalx = vmin, vmax
          else:
              Vmin, Vmax = self.get_view_interval()
              if Vmin < Vmax:
                  self.axes.viewLim.intervalx = (min(vmin, vmax, Vmin),
                                                 max(vmin, vmax, Vmax))
              else:
                  self.axes.viewLim.intervalx = (max(vmin, vmax, Vmin),
                                                 min(vmin, vmax, Vmax))
  
      def get_minpos(self):
          return self.axes.dataLim.minposx
  
      def get_data_interval(self):
          'return the Interval instance for this axis data limits'
          return self.axes.dataLim.intervalx
  
      def set_data_interval(self, vmin, vmax, ignore=False):
          'set the axis data limits'
          if ignore:
              self.axes.dataLim.intervalx = vmin, vmax
          else:
              Vmin, Vmax = self.get_data_interval()
              self.axes.dataLim.intervalx = min(vmin, Vmin), max(vmax, Vmax)
          self.stale = True
  
      def set_default_intervals(self):
          'set the default limits for the axis interval if they are not mutated'
          xmin, xmax = 0., 1.
          dataMutated = self.axes.dataLim.mutatedx()
          viewMutated = self.axes.viewLim.mutatedx()
          if not dataMutated or not viewMutated:
              if self.converter is not None:
                  info = self.converter.axisinfo(self.units, self)
                  if info.default_limits is not None:
                      valmin, valmax = info.default_limits
                      xmin = self.converter.convert(valmin, self.units, self)
                      xmax = self.converter.convert(valmax, self.units, self)
              if not dataMutated:
                  self.axes.dataLim.intervalx = xmin, xmax
              if not viewMutated:
                  self.axes.viewLim.intervalx = xmin, xmax
          self.stale = True
  
      def get_tick_space(self):
          ends = self.axes.transAxes.transform([[0, 0], [1, 0]])
          length = ((ends[1][0] - ends[0][0]) / self.axes.figure.dpi) * 72.0
          tick = self._get_tick(True)
          # There is a heuristic here that the aspect ratio of tick text
          # is no more than 3:1
          size = tick.label1.get_size() * 3
          if size > 0:
              return int(np.floor(length / size))
          else:
              return 2**31 - 1
  
  
  class YAxis(Axis):
      __name__ = 'yaxis'
      axis_name = 'y'
  
      def contains(self, mouseevent):
          """Test whether the mouse event occurred in the y axis.
  
          Returns *True* | *False*
          """
          if six.callable(self._contains):
              return self._contains(self, mouseevent)
  
          x, y = mouseevent.x, mouseevent.y
          try:
              trans = self.axes.transAxes.inverted()
              xaxes, yaxes = trans.transform_point((x, y))
          except ValueError:
              return False, {}
          l, b = self.axes.transAxes.transform_point((0, 0))
          r, t = self.axes.transAxes.transform_point((1, 1))
          inaxis = yaxes >= 0 and yaxes <= 1 and (
              (x < l and x > l - self.pickradius) or
              (x > r and x < r + self.pickradius))
          return inaxis, {}
  
      def _get_tick(self, major):
          if major:
              tick_kw = self._major_tick_kw
          else:
              tick_kw = self._minor_tick_kw
          return YTick(self.axes, 0, '', major=major, **tick_kw)
  
      def _get_label(self):
          # x in display coords (updated by _update_label_position)
          # y in axes coords
          label = mtext.Text(x=0, y=0.5,
                             # todo: get the label position
                             fontproperties=font_manager.FontProperties(
                                 size=rcParams['axes.labelsize'],
                                 weight=rcParams['axes.labelweight']),
                             color=rcParams['axes.labelcolor'],
                             verticalalignment='bottom',
                             horizontalalignment='center',
                             rotation='vertical',
                             rotation_mode='anchor')
          label.set_transform(mtransforms.blended_transform_factory(
              mtransforms.IdentityTransform(), self.axes.transAxes))
  
          self._set_artist_props(label)
          self.label_position = 'left'
          return label
  
      def _get_offset_text(self):
          # x in display coords, y in axes coords (to be updated at draw time)
          offsetText = mtext.Text(x=0, y=0.5,
                                  fontproperties=font_manager.FontProperties(
                                      size=rcParams['ytick.labelsize']
                                  ),
                                  color=rcParams['ytick.color'],
                                  verticalalignment='baseline',
                                  horizontalalignment='left')
          offsetText.set_transform(mtransforms.blended_transform_factory(
              self.axes.transAxes, mtransforms.IdentityTransform())
          )
          self._set_artist_props(offsetText)
          self.offset_text_position = 'left'
          return offsetText
  
      def _get_pixel_distance_along_axis(self, where, perturb):
          """
          Returns the amount, in data coordinates, that a single pixel
          corresponds to in the locality given by *where*, which is also given
          in data coordinates, and is a y coordinate.
  
          *perturb* is the amount to perturb the pixel.  Usually +0.5 or -0.5.
  
          Implementing this routine for an axis is optional; if present, it will
          ensure that no ticks are lost due to round-off at the extreme ends of
          an axis.
          """
  
          #
          # first figure out the pixel location of the "where" point.  We use
          # 1e-10 for the x point, so that we remain compatible with log axes.
  
          # transformation from data coords to display coords
          trans = self.axes.transData
          # transformation from display coords to data coords
          transinv = trans.inverted()
          pix = trans.transform_point((1e-10, where))
          # perturb the pixel
          ptp = transinv.transform_point((pix[0], pix[1] + perturb))
          dy = abs(ptp[1] - where)
          return dy
  
      def set_label_position(self, position):
          """
          Set the label position (left or right)
  
          ACCEPTS: [ 'left' | 'right' ]
          """
          self.label.set_rotation_mode('anchor')
          self.label.set_horizontalalignment('center')
          if position == 'left':
              self.label.set_verticalalignment('bottom')
          elif position == 'right':
              self.label.set_verticalalignment('top')
          else:
              msg = "Position accepts only [ 'left' | 'right' ]"
              raise ValueError(msg)
          self.label_position = position
          self.stale = True
  
      def _update_label_position(self, bboxes, bboxes2):
          """
          Update the label position based on the bounding box enclosing
          all the ticklabels and axis spine
          """
          if not self._autolabelpos:
              return
          x, y = self.label.get_position()
          if self.label_position == 'left':
              try:
                  spine = self.axes.spines['left']
                  spinebbox = spine.get_transform().transform_path(
                      spine.get_path()).get_extents()
              except KeyError:
                  # use axes if spine doesn't exist
                  spinebbox = self.axes.bbox
              bbox = mtransforms.Bbox.union(bboxes + [spinebbox])
              left = bbox.x0
  
              self.label.set_position(
                  (left - self.labelpad * self.figure.dpi / 72.0, y)
              )
  
          else:
              try:
                  spine = self.axes.spines['right']
                  spinebbox = spine.get_transform().transform_path(
                      spine.get_path()).get_extents()
              except KeyError:
                  # use axes if spine doesn't exist
                  spinebbox = self.axes.bbox
              bbox = mtransforms.Bbox.union(bboxes2 + [spinebbox])
              right = bbox.x1
  
              self.label.set_position(
                  (right + self.labelpad * self.figure.dpi / 72.0, y)
              )
  
      def _update_offset_text_position(self, bboxes, bboxes2):
          """
          Update the offset_text position based on the sequence of bounding
          boxes of all the ticklabels
          """
          x, y = self.offsetText.get_position()
          top = self.axes.bbox.ymax
          self.offsetText.set_position(
              (x, top + self.OFFSETTEXTPAD * self.figure.dpi / 72.0)
          )
  
      def set_offset_position(self, position):
          x, y = self.offsetText.get_position()
          if position == 'left':
              x = 0
          elif position == 'right':
              x = 1
          else:
              msg = "Position accepts only [ 'left' | 'right' ]"
              raise ValueError(msg)
  
          self.offsetText.set_ha(position)
          self.offsetText.set_position((x, y))
          self.stale = True
  
      def get_text_widths(self, renderer):
          bbox, bbox2 = self.get_ticklabel_extents(renderer)
          # MGDTODO: Need a better way to get the pad
          padPixels = self.majorTicks[0].get_pad_pixels()
  
          left = 0.0
          if bbox.width:
              left += bbox.width + padPixels
          right = 0.0
          if bbox2.width:
              right += bbox2.width + padPixels
  
          if self.get_label_position() == 'left':
              left += self.label.get_window_extent(renderer).width + padPixels
          else:
              right += self.label.get_window_extent(renderer).width + padPixels
          return left, right
  
      def set_ticks_position(self, position):
          """
          Set the ticks position (left, right, both, default or none)
          'both' sets the ticks to appear on both positions, but does not
          change the tick labels.  'default' resets the tick positions to
          the default: ticks on both positions, labels at left.  'none'
          can be used if you don't want any ticks. 'none' and 'both'
          affect only the ticks, not the labels.
  
          ACCEPTS: [ 'left' | 'right' | 'both' | 'default' | 'none' ]
          """
          if position == 'right':
              self.set_tick_params(which='both', right=True, labelright=True,
                                   left=False, labelleft=False)
              self.set_offset_position(position)
          elif position == 'left':
              self.set_tick_params(which='both', right=False, labelright=False,
                                   left=True, labelleft=True)
              self.set_offset_position(position)
          elif position == 'both':
              self.set_tick_params(which='both', right=True,
                                   left=True)
          elif position == 'none':
              self.set_tick_params(which='both', right=False,
                                   left=False)
          elif position == 'default':
              self.set_tick_params(which='both', right=True, labelright=False,
                                   left=True, labelleft=True)
          else:
              raise ValueError("invalid position: %s" % position)
          self.stale = True
  
      def tick_right(self):
          'use ticks only on right'
          self.set_ticks_position('right')
  
      def tick_left(self):
          'use ticks only on left'
          self.set_ticks_position('left')
  
      def get_ticks_position(self):
          """
          Return the ticks position (left, right, both or unknown)
          """
          majt = self.majorTicks[0]
          mT = self.minorTicks[0]
  
          majorRight = ((not majt.tick1On) and majt.tick2On and
                        (not majt.label1On) and majt.label2On)
          minorRight = ((not mT.tick1On) and mT.tick2On and
                        (not mT.label1On) and mT.label2On)
          if majorRight and minorRight:
              return 'right'
  
          majorLeft = (majt.tick1On and (not majt.tick2On) and
                       majt.label1On and (not majt.label2On))
          minorLeft = (mT.tick1On and (not mT.tick2On) and
                       mT.label1On and (not mT.label2On))
          if majorLeft and minorLeft:
              return 'left'
  
          majorDefault = (majt.tick1On and majt.tick2On and
                          majt.label1On and (not majt.label2On))
          minorDefault = (mT.tick1On and mT.tick2On and
                          mT.label1On and (not mT.label2On))
          if majorDefault and minorDefault:
              return 'default'
  
          return 'unknown'
  
      def get_view_interval(self):
          'return the Interval instance for this axis view limits'
          return self.axes.viewLim.intervaly
  
      def set_view_interval(self, vmin, vmax, ignore=False):
          """
          If *ignore* is *False*, the order of vmin, vmax
          does not matter; the original axis orientation will
          be preserved. In addition, the view limits can be
          expanded, but will not be reduced.  This method is
          for mpl internal use; for normal use, see
          :meth:`~matplotlib.axes.Axes.set_ylim`.
  
          """
          if ignore:
              self.axes.viewLim.intervaly = vmin, vmax
          else:
              Vmin, Vmax = self.get_view_interval()
              if Vmin < Vmax:
                  self.axes.viewLim.intervaly = (min(vmin, vmax, Vmin),
                                                 max(vmin, vmax, Vmax))
              else:
                  self.axes.viewLim.intervaly = (max(vmin, vmax, Vmin),
                                                 min(vmin, vmax, Vmax))
          self.stale = True
  
      def get_minpos(self):
          return self.axes.dataLim.minposy
  
      def get_data_interval(self):
          'return the Interval instance for this axis data limits'
          return self.axes.dataLim.intervaly
  
      def set_data_interval(self, vmin, vmax, ignore=False):
          'set the axis data limits'
          if ignore:
              self.axes.dataLim.intervaly = vmin, vmax
          else:
              Vmin, Vmax = self.get_data_interval()
              self.axes.dataLim.intervaly = min(vmin, Vmin), max(vmax, Vmax)
          self.stale = True
  
      def set_default_intervals(self):
          'set the default limits for the axis interval if they are not mutated'
          ymin, ymax = 0., 1.
          dataMutated = self.axes.dataLim.mutatedy()
          viewMutated = self.axes.viewLim.mutatedy()
          if not dataMutated or not viewMutated:
              if self.converter is not None:
                  info = self.converter.axisinfo(self.units, self)
                  if info.default_limits is not None:
                      valmin, valmax = info.default_limits
                      ymin = self.converter.convert(valmin, self.units, self)
                      ymax = self.converter.convert(valmax, self.units, self)
              if not dataMutated:
                  self.axes.dataLim.intervaly = ymin, ymax
              if not viewMutated:
                  self.axes.viewLim.intervaly = ymin, ymax
          self.stale = True
  
      def get_tick_space(self):
          ends = self.axes.transAxes.transform([[0, 0], [0, 1]])
          length = ((ends[1][1] - ends[0][1]) / self.axes.figure.dpi) * 72.0
          tick = self._get_tick(True)
          # Having a spacing of at least 2 just looks good.
          size = tick.label1.get_size() * 2.0
          if size > 0:
              return int(np.floor(length / size))
          else:
              return 2**31 - 1
  