text: """
  Tick locating and formatting
  ============================
  
  This module contains classes to support completely configurable tick locating
  and formatting.  Although the locators know nothing about major or minor
  ticks, they are used by the Axis class to support major and minor tick
  locating and formatting.  Generic tick locators and formatters are provided,
  as well as domain specific custom ones..
  
  
  Tick locating
  -------------
  
  The Locator class is the base class for all tick locators.  The locators
  handle autoscaling of the view limits based on the data limits, and the
  choosing of tick locations.  A useful semi-automatic tick locator is
  MultipleLocator.  You initialize this with a base, eg 10, and it picks axis
  limits and ticks that are multiples of your base.
  
  The Locator subclasses defined here are
  
  :class:`NullLocator`
      No ticks
  
  :class:`FixedLocator`
      Tick locations are fixed
  
  :class:`IndexLocator`
      locator for index plots (eg. where x = range(len(y)))
  
  :class:`LinearLocator`
      evenly spaced ticks from min to max
  
  :class:`LogLocator`
      logarithmically ticks from min to max
  
  :class:`MultipleLocator`
      ticks and range are a multiple of base;
                    either integer or float
  :class:`OldAutoLocator`
      choose a MultipleLocator and dyamically reassign it for
      intelligent ticking during navigation
  
  :class:`MaxNLocator`
      finds up to a max number of ticks at nice  locations
  
  :class:`AutoLocator`
      :class:`MaxNLocator` with simple defaults. This is the default
      tick locator for most plotting.
  
  :class:`AutoMinorLocator`
      locator for minor ticks when the axis is linear and the
      major ticks are uniformly spaced.  It subdivides the major
      tick interval into a specified number of minor intervals,
      defaulting to 4 or 5 depending on the major interval.
  
  
  There are a number of locators specialized for date locations - see
  the dates module
  
  You can define your own locator by deriving from Locator.  You must
  override the __call__ method, which returns a sequence of locations,
  and you will probably want to override the autoscale method to set the
  view limits from the data limits.
  
  If you want to override the default locator, use one of the above or a
  custom locator and pass it to the x or y axis instance.  The relevant
  methods are::
  
    ax.xaxis.set_major_locator( xmajorLocator )
    ax.xaxis.set_minor_locator( xminorLocator )
    ax.yaxis.set_major_locator( ymajorLocator )
    ax.yaxis.set_minor_locator( yminorLocator )
  
  The default minor locator is the NullLocator, eg no minor ticks on by
  default.
  
  Tick formatting
  ---------------
  
  Tick formatting is controlled by classes derived from Formatter.  The
  formatter operates on a single tick value and returns a string to the
  axis.
  
  :class:`NullFormatter`
      no labels on the ticks
  
  :class:`IndexFormatter`
      set the strings from a list of labels
  
  :class:`FixedFormatter`
      set the strings manually for the labels
  
  :class:`FuncFormatter`
      user defined function sets the labels
  
  :class:`FormatStrFormatter`
      use a sprintf format string
  
  :class:`ScalarFormatter`
      default formatter for scalars; autopick the fmt string
  
  :class:`LogFormatter`
      formatter for log axes
  
  
  You can derive your own formatter from the Formatter base class by
  simply overriding the ``__call__`` method.  The formatter class has access
  to the axis view and data limits.
  
  To control the major and minor tick label formats, use one of the
  following methods::
  
    ax.xaxis.set_major_formatter( xmajorFormatter )
    ax.xaxis.set_minor_formatter( xminorFormatter )
    ax.yaxis.set_major_formatter( ymajorFormatter )
    ax.yaxis.set_minor_formatter( yminorFormatter )
  
  See :ref:`pylab_examples-major_minor_demo1` for an example of setting
  major an minor ticks.  See the :mod:`matplotlib.dates` module for
  more information and examples of using date locators and formatters.
  """
  
  
  import decimal
  import locale
  import math
  import numpy as np
  from matplotlib import rcParams
  from matplotlib import cbook
  from matplotlib import transforms as mtransforms
  
  
  class _DummyAxis(object):
      def __init__(self, minpos=0):
          self.dataLim = mtransforms.Bbox.unit()
          self.viewLim = mtransforms.Bbox.unit()
          self._minpos = minpos
  
      def get_view_interval(self):
          return self.viewLim.intervalx
  
      def set_view_interval(self, vmin, vmax):
          self.viewLim.intervalx = vmin, vmax
  
      def get_minpos(self):
          return self._minpos
  
      def get_data_interval(self):
          return self.dataLim.intervalx
  
      def set_data_interval(self, vmin, vmax):
          self.dataLim.intervalx = vmin, vmax
  
  
  class TickHelper(object):
      axis = None
  
      def set_axis(self, axis):
          self.axis = axis
  
      def create_dummy_axis(self, **kwargs):
          if self.axis is None:
              self.axis = _DummyAxis(**kwargs)
  
      def set_view_interval(self, vmin, vmax):
          self.axis.set_view_interval(vmin, vmax)
  
      def set_data_interval(self, vmin, vmax):
          self.axis.set_data_interval(vmin, vmax)
  
      def set_bounds(self, vmin, vmax):
          self.set_view_interval(vmin, vmax)
          self.set_data_interval(vmin, vmax)
  
  
  class Formatter(TickHelper):
      """
      Convert the tick location to a string
      """
      # some classes want to see all the locs to help format
      # individual ones
      locs = []
  
      def __call__(self, x, pos=None):
          """Return the format for tick val x at position pos; pos=None
             indicated unspecified"""
          raise NotImplementedError('Derived must override')
  
      def format_data(self, value):
          return self.__call__(value)
  
      def format_data_short(self, value):
          """return a short string version"""
          return self.format_data(value)
  
      def get_offset(self):
          return ''
  
      def set_locs(self, locs):
          self.locs = locs
  
      def fix_minus(self, s):
          """
          some classes may want to replace a hyphen for minus with the
          proper unicode symbol as described `here
          <http://sourceforge.net/tracker/index.php?func=detail&aid=1962574&group_id=80706&atid=560720>`_.
          The default is to do nothing
  
          Note, if you use this method, eg in :meth`format_data` or
          call, you probably don't want to use it for
          :meth:`format_data_short` since the toolbar uses this for
          interactive coord reporting and I doubt we can expect GUIs
          across platforms will handle the unicode correctly.  So for
          now the classes that override :meth:`fix_minus` should have an
          explicit :meth:`format_data_short` method
          """
          return s
  
  
  class IndexFormatter(Formatter):
      """
      format the position x to the nearest i-th label where i=int(x+0.5)
      """
      def __init__(self, labels):
          self.labels = labels
          self.n = len(labels)
  
      def __call__(self, x, pos=None):
          """Return the format for tick val x at position pos; pos=None
          indicated unspecified"""
          i = int(x + 0.5)
          if i < 0:
              return ''
          elif i >= self.n:
              return ''
          else:
              return self.labels[i]
  
  
  class NullFormatter(Formatter):
      'Always return the empty string'
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          return ''
  
  
  class FixedFormatter(Formatter):
      'Return fixed strings for tick labels'
      def __init__(self, seq):
          """
          *seq* is a sequence of strings.  For positions ``i < len(seq)`` return
          *seq[i]* regardless of *x*.  Otherwise return ''
          """
          self.seq = seq
          self.offset_string = ''
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          if pos is None or pos >= len(self.seq):
              return ''
          else:
              return self.seq[pos]
  
      def get_offset(self):
          return self.offset_string
  
      def set_offset_string(self, ofs):
          self.offset_string = ofs
  
  
  class FuncFormatter(Formatter):
      """
      User defined function for formatting
      """
      def __init__(self, func):
          self.func = func
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          return self.func(x, pos)
  
  
  class FormatStrFormatter(Formatter):
      """
      Use a format string to format the tick
      """
      def __init__(self, fmt):
          self.fmt = fmt
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          return self.fmt % x
  
  
  class OldScalarFormatter(Formatter):
      """
      Tick location is a plain old number.
      """
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          xmin, xmax = self.axis.get_view_interval()
          d = abs(xmax - xmin)
  
          return self.pprint_val(x, d)
  
      def pprint_val(self, x, d):
          #if the number is not too big and it's an int, format it as an
          #int
          if abs(x) < 1e4 and x == int(x):
              return '%d' % x
  
          if d < 1e-2:
              fmt = '%1.3e'
          elif d < 1e-1:
              fmt = '%1.3f'
          elif d > 1e5:
              fmt = '%1.1e'
          elif d > 10:
              fmt = '%1.1f'
          elif d > 1:
              fmt = '%1.2f'
          else:
              fmt = '%1.3f'
          s = fmt % x
          #print d, x, fmt, s
          tup = s.split('e')
          if len(tup) == 2:
              mantissa = tup[0].rstrip('0').rstrip('.')
              sign = tup[1][0].replace('+', '')
              exponent = tup[1][1:].lstrip('0')
              s = '%se%s%s' % (mantissa, sign, exponent)
          else:
              s = s.rstrip('0').rstrip('.')
          return s
  
  
  class ScalarFormatter(Formatter):
      """
      Tick location is a plain old number.  If useOffset==True and the data range
      is much smaller than the data average, then an offset will be determined
      such that the tick labels are meaningful. Scientific notation is used for
      data < 10^-n or data >= 10^m, where n and m are the power limits set using
      set_powerlimits((n,m)). The defaults for these are controlled by the
      axes.formatter.limits rc parameter.
  
      """
  
      def __init__(self, useOffset=True, useMathText=None, useLocale=None):
          # useOffset allows plotting small data ranges with large offsets: for
          # example: [1+1e-9,1+2e-9,1+3e-9] useMathText will render the offset
          # and scientific notation in mathtext
  
          self.set_useOffset(useOffset)
          self._usetex = rcParams['text.usetex']
          if useMathText is None:
              useMathText = rcParams['axes.formatter.use_mathtext']
          self._useMathText = useMathText
          self.orderOfMagnitude = 0
          self.format = ''
          self._scientific = True
          self._powerlimits = rcParams['axes.formatter.limits']
          if useLocale is None:
              useLocale = rcParams['axes.formatter.use_locale']
          self._useLocale = useLocale
  
      def get_useOffset(self):
          return self._useOffset
  
      def set_useOffset(self, val):
          if val in [True, False]:
              self.offset = 0
              self._useOffset = val
          else:
              self._useOffset = False
              self.offset = val
  
      useOffset = property(fget=get_useOffset, fset=set_useOffset)
  
      def get_useLocale(self):
          return self._useLocale
  
      def set_useLocale(self, val):
          if val is None:
              self._useLocale = rcParams['axes.formatter.use_locale']
          else:
              self._useLocale = val
  
      useLocale = property(fget=get_useLocale, fset=set_useLocale)
  
      def fix_minus(self, s):
          """use a unicode minus rather than hyphen"""
          if rcParams['text.usetex'] or not rcParams['axes.unicode_minus']:
              return s
          else:
              return s.replace('-', '\u2212')
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          if len(self.locs) == 0:
              return ''
          else:
              s = self.pprint_val(x)
              return self.fix_minus(s)
  
      def set_scientific(self, b):
          '''True or False to turn scientific notation on or off
          see also :meth:`set_powerlimits`
          '''
          self._scientific = bool(b)
  
      def set_powerlimits(self, lims):
          '''
          Sets size thresholds for scientific notation.
  
          e.g. ``formatter.set_powerlimits((-3, 4))`` sets the pre-2007 default
          in which scientific notation is used for numbers less than 1e-3 or
          greater than 1e4.
          See also :meth:`set_scientific`.
          '''
          assert len(lims) == 2, "argument must be a sequence of length 2"
          self._powerlimits = lims
  
      def format_data_short(self, value):
          """return a short formatted string representation of a number"""
          if self._useLocale:
              return locale.format_string('%-12g', (value,))
          else:
              return '%-12g' % value
  
      def format_data(self, value):
          'return a formatted string representation of a number'
          if self._useLocale:
              s = locale.format_string('%1.10e', (value,))
          else:
              s = '%1.10e' % value
          s = self._formatSciNotation(s)
          return self.fix_minus(s)
  
      def get_offset(self):
          """Return scientific notation, plus offset"""
          if len(self.locs) == 0:
              return ''
          s = ''
          if self.orderOfMagnitude or self.offset:
              offsetStr = ''
              sciNotStr = ''
              if self.offset:
                  offsetStr = self.format_data(self.offset)
                  if self.offset > 0:
                      offsetStr = '+' + offsetStr
              if self.orderOfMagnitude:
                  if self._usetex or self._useMathText:
                      sciNotStr = self.format_data(10 ** self.orderOfMagnitude)
                  else:
                      sciNotStr = '1e%d' % self.orderOfMagnitude
              if self._useMathText:
                  if sciNotStr != '':
                      sciNotStr = r'\times\mathdefault{%s}' % sciNotStr
                  s = ''.join(('$', sciNotStr,
                               r'\mathdefault{', offsetStr, '}$'))
              elif self._usetex:
                  if sciNotStr != '':
                      sciNotStr = r'\times%s' % sciNotStr
                  s = ''.join(('$', sciNotStr, offsetStr, '$'))
              else:
                  s = ''.join((sciNotStr, offsetStr))
  
          return self.fix_minus(s)
  
      def set_locs(self, locs):
          'set the locations of the ticks'
          self.locs = locs
          if len(self.locs) > 0:
              vmin, vmax = self.axis.get_view_interval()
              d = abs(vmax - vmin)
              if self._useOffset:
                  self._set_offset(d)
              self._set_orderOfMagnitude(d)
              self._set_format(vmin, vmax)
  
      def _set_offset(self, range):
          # offset of 20,001 is 20,000, for example
          locs = self.locs
  
          if locs is None or not len(locs) or range == 0:
              self.offset = 0
              return
          ave_loc = np.mean(locs)
          if ave_loc:  # dont want to take log10(0)
              ave_oom = math.floor(math.log10(np.mean(np.absolute(locs))))
              range_oom = math.floor(math.log10(range))
  
              if np.absolute(ave_oom - range_oom) >= 3:  # four sig-figs
                  p10 = 10 ** range_oom
                  if ave_loc < 0:
                      self.offset = (math.ceil(np.max(locs) / p10) * p10)
                  else:
                      self.offset = (math.floor(np.min(locs) / p10) * p10)
              else:
                  self.offset = 0
  
      def _set_orderOfMagnitude(self, range):
          # if scientific notation is to be used, find the appropriate exponent
          # if using an numerical offset, find the exponent after applying the
          # offset
          if not self._scientific:
              self.orderOfMagnitude = 0
              return
          locs = np.absolute(self.locs)
          if self.offset:
              oom = math.floor(math.log10(range))
          else:
              if locs[0] > locs[-1]:
                  val = locs[0]
              else:
                  val = locs[-1]
              if val == 0:
                  oom = 0
              else:
                  oom = math.floor(math.log10(val))
          if oom <= self._powerlimits[0]:
              self.orderOfMagnitude = oom
          elif oom >= self._powerlimits[1]:
              self.orderOfMagnitude = oom
          else:
              self.orderOfMagnitude = 0
  
      def _set_format(self, vmin, vmax):
          # set the format string to format all the ticklabels
          if len(self.locs) < 2:
              # Temporarily augment the locations with the axis end points.
              _locs = list(self.locs) + [vmin, vmax]
          else:
              _locs = self.locs
          locs = (np.asarray(_locs) - self.offset) / 10 ** self.orderOfMagnitude
          loc_range = np.ptp(locs)
          if len(self.locs) < 2:
              # We needed the end points only for the loc_range calculation.
              locs = locs[:-2]
          loc_range_oom = int(math.floor(math.log10(loc_range)))
          # first estimate:
          sigfigs = max(0, 3 - loc_range_oom)
          # refined estimate:
          thresh = 1e-3 * 10 ** loc_range_oom
          while sigfigs >= 0:
              if np.abs(locs - np.round(locs, decimals=sigfigs)).max() < thresh:
                  sigfigs -= 1
              else:
                  break
          sigfigs += 1
          self.format = '%1.' + str(sigfigs) + 'f'
          if self._usetex:
              self.format = '$%s$' % self.format
          elif self._useMathText:
              self.format = '$\mathdefault{%s}$' % self.format
  
      def pprint_val(self, x):
          xp = (x - self.offset) / (10 ** self.orderOfMagnitude)
          if np.absolute(xp) < 1e-8:
              xp = 0
          if self._useLocale:
              return locale.format_string(self.format, (xp,))
          else:
              return self.format % xp
  
      def _formatSciNotation(self, s):
          # transform 1e+004 into 1e4, for example
          if self._useLocale:
              decimal_point = locale.localeconv()['decimal_point']
              positive_sign = locale.localeconv()['positive_sign']
          else:
              decimal_point = '.'
              positive_sign = '+'
          tup = s.split('e')
          try:
              significand = tup[0].rstrip('0').rstrip(decimal_point)
              sign = tup[1][0].replace(positive_sign, '')
              exponent = tup[1][1:].lstrip('0')
              if self._useMathText or self._usetex:
                  if significand == '1' and exponent != '':
                      # reformat 1x10^y as 10^y
                      significand = ''
                  if exponent:
                      exponent = '10^{%s%s}' % (sign, exponent)
                  if significand and exponent:
                      return r'%s{\times}%s' % (significand, exponent)
                  else:
                      return r'%s%s' % (significand, exponent)
              else:
                  s = ('%se%s%s' % (significand, sign, exponent)).rstrip('e')
                  return s
          except IndexError:
              return s
  
  
  class LogFormatter(Formatter):
      """
      Format values for log axis;
  
      """
      def __init__(self, base=10.0, labelOnlyBase=True):
          """
          *base* is used to locate the decade tick,
          which will be the only one to be labeled if *labelOnlyBase*
          is ``False``
          """
          self._base = base + 0.0
          self.labelOnlyBase = labelOnlyBase
  
      def base(self, base):
          """change the *base* for labeling - warning: should always match the
             base used for :class:`LogLocator`"""
          self._base = base
  
      def label_minor(self, labelOnlyBase):
          'switch on/off minor ticks labeling'
          self.labelOnlyBase = labelOnlyBase
  
      def __call__(self, x, pos=None):
          """Return the format for tick val *x* at position *pos*"""
          vmin, vmax = self.axis.get_view_interval()
          d = abs(vmax - vmin)
          b = self._base
          if x == 0.0:
              return '0'
          sign = np.sign(x)
          # only label the decades
          fx = math.log(abs(x)) / math.log(b)
          isDecade = is_close_to_int(fx)
          if not isDecade and self.labelOnlyBase:
              s = ''
          elif x > 10000:
              s = '%1.0e' % x
          elif x < 1:
              s = '%1.0e' % x
          else:
              s = self.pprint_val(x, d)
          if sign == -1:
              s = '-%s' % s
  
          return self.fix_minus(s)
  
      def format_data(self, value):
          b = self.labelOnlyBase
          self.labelOnlyBase = False
          value = cbook.strip_math(self.__call__(value))
          self.labelOnlyBase = b
          return value
  
      def format_data_short(self, value):
          'return a short formatted string representation of a number'
          return '%-12g' % value
  
      def pprint_val(self, x, d):
          #if the number is not too big and it's an int, format it as an
          #int
          if abs(x) < 1e4 and x == int(x):
              return '%d' % x
  
          if d < 1e-2:
              fmt = '%1.3e'
          elif d < 1e-1:
              fmt = '%1.3f'
          elif d > 1e5:
              fmt = '%1.1e'
          elif d > 10:
              fmt = '%1.1f'
          elif d > 1:
              fmt = '%1.2f'
          else:
              fmt = '%1.3f'
          s = fmt % x
          #print d, x, fmt, s
          tup = s.split('e')
          if len(tup) == 2:
              mantissa = tup[0].rstrip('0').rstrip('.')
              sign = tup[1][0].replace('+', '')
              exponent = tup[1][1:].lstrip('0')
              s = '%se%s%s' % (mantissa, sign, exponent)
          else:
              s = s.rstrip('0').rstrip('.')
          return s
  
  
  class LogFormatterExponent(LogFormatter):
      """
      Format values for log axis; using ``exponent = log_base(value)``
      """
  
      def __call__(self, x, pos=None):
          """Return the format for tick val *x* at position *pos*"""
  
          vmin, vmax = self.axis.get_view_interval()
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
          d = abs(vmax - vmin)
          b = self._base
          if x == 0:
              return '0'
          sign = np.sign(x)
          # only label the decades
          fx = math.log(abs(x)) / math.log(b)
          isDecade = is_close_to_int(fx)
          if not isDecade and self.labelOnlyBase:
              s = ''
          #if 0: pass
          elif fx > 10000:
              s = '%1.0e' % fx
          #elif x<1: s = '$10^{%d}$'%fx
          #elif x<1: s =  '10^%d'%fx
          elif fx < 1:
              s = '%1.0e' % fx
          else:
              s = self.pprint_val(fx, d)
          if sign == -1:
              s = '-%s' % s
  
          return self.fix_minus(s)
  
  
  class LogFormatterMathtext(LogFormatter):
      """
      Format values for log axis; using ``exponent = log_base(value)``
      """
  
      def __call__(self, x, pos=None):
          'Return the format for tick val *x* at position *pos*'
          b = self._base
          usetex = rcParams['text.usetex']
  
          # only label the decades
          if x == 0:
              if usetex:
                  return '$0$'
              else:
                  return '$\mathdefault{0}$'
  
          fx = math.log(abs(x)) / math.log(b)
          is_decade = is_close_to_int(fx)
  
          sign_string = '-' if x < 0 else ''
  
          # use string formatting of the base if it is not an integer
          if b % 1 == 0.0:
              base = '%d' % b
          else:
              base = '%s' % b
  
          if not is_decade and self.labelOnlyBase:
              return ''
          elif not is_decade:
              if usetex:
                  return (r'$%s%s^{%.2f}$') % \
                                              (sign_string, base, fx)
              else:
                  return ('$\mathdefault{%s%s^{%.2f}}$') % \
                                              (sign_string, base, fx)
          else:
              if usetex:
                  return (r'$%s%s^{%d}$') % (sign_string,
                                             base,
                                             nearest_long(fx))
              else:
                  return (r'$\mathdefault{%s%s^{%d}}$') % (sign_string,
                                                           base,
                                                           nearest_long(fx))
  
  
  class EngFormatter(Formatter):
      """
      Formats axis values using engineering prefixes to represent powers of 1000,
      plus a specified unit, eg. 10 MHz instead of 1e7.
      """
  
      # The SI engineering prefixes
      ENG_PREFIXES = {
          -24: "y",
          -21: "z",
          -18: "a",
          -15: "f",
          -12: "p",
           -9: "n",
           -6: "\u03bc",  # Greek letter mu
           -3: "m",
            0: "",
            3: "k",
            6: "M",
            9: "G",
           12: "T",
           15: "P",
           18: "E",
           21: "Z",
           24: "Y"
        }
  
      def __init__(self, unit="", places=None):
          self.unit = unit
          self.places = places
  
      def __call__(self, x, pos=None):
          s = "%s%s" % (self.format_eng(x), self.unit)
          return self.fix_minus(s)
  
      def format_eng(self, num):
          """ Formats a number in engineering notation, appending a letter
          representing the power of 1000 of the original number. Some examples:
  
          >>> format_eng(0)       for self.places = 0
          '0'
  
          >>> format_eng(1000000) for self.places = 1
          '1.0 M'
  
          >>> format_eng("-1e-6") for self.places = 2
          u'-1.00 \u03bc'
  
          @param num: the value to represent
          @type num: either a numeric value or a string that can be converted to
                     a numeric value (as per decimal.Decimal constructor)
  
          @return: engineering formatted string
          """
  
          dnum = decimal.Decimal(str(num))
  
          sign = 1
  
          if dnum < 0:
              sign = -1
              dnum = -dnum
  
          if dnum != 0:
              pow10 = decimal.Decimal(int(math.floor(dnum.log10() / 3) * 3))
          else:
              pow10 = decimal.Decimal(0)
  
          pow10 = pow10.min(max(self.ENG_PREFIXES.keys()))
          pow10 = pow10.max(min(self.ENG_PREFIXES.keys()))
  
          prefix = self.ENG_PREFIXES[int(pow10)]
  
          mant = sign * dnum / (10 ** pow10)
  
          if self.places is None:
              format_str = "%g %s"
          elif self.places == 0:
              format_str = "%i %s"
          elif self.places > 0:
              format_str = ("%%.%if %%s" % self.places)
  
          formatted = format_str % (mant, prefix)
  
          return formatted.strip()
  
  
  class Locator(TickHelper):
      """
      Determine the tick locations;
  
      Note, you should not use the same locator between different
      :class:`~matplotlib.axis.Axis` because the locator stores references to
      the Axis data and view limits
      """
  
      # some automatic tick locators can generate so many ticks they
      # kill the machine when you try and render them, see eg sf bug
      # report
      # https://sourceforge.net/tracker/index.php?func=detail&aid=2715172&group_id=80706&atid=560720.
      # This parameter is set to cause locators to raise an error if too
      # many ticks are generated
      MAXTICKS = 1000
  
      def tick_values(self, vmin, vmax):
          """
          Return the values of the located ticks given **vmin** and **vmax**.
  
          .. note::
              To get tick locations with the vmin and vmax values defined
              automatically for the associated :attr:`axis` simply call
              the Locator instance::
  
                  >>> print(type(loc))
                  <type 'Locator'>
                  >>> print(loc())
                  [1, 2, 3, 4]
  
          """
          raise NotImplementedError('Derived must override')
  
      def __call__(self):
          """Return the locations of the ticks"""
          # note: some locators return data limits, other return view limits,
          # hence there is no *one* interface to call self.tick_values.
          raise NotImplementedError('Derived must override')
  
      def raise_if_exceeds(self, locs):
          """raise a RuntimeError if Locator attempts to create more than
             MAXTICKS locs"""
          if len(locs) >= self.MAXTICKS:
              msg = ('Locator attempting to generate %d ticks from %s to %s: ' +
                     'exceeds Locator.MAXTICKS') % (len(locs), locs[0], locs[-1])
              raise RuntimeError(msg)
  
          return locs
  
      def view_limits(self, vmin, vmax):
          """
          select a scale for the range from vmin to vmax
  
          Normally This will be overridden.
          """
          return mtransforms.nonsingular(vmin, vmax)
  
      def autoscale(self):
          """autoscale the view limits"""
          return self.view_limits(*self.axis.get_view_interval())
  
      def pan(self, numsteps):
          """Pan numticks (can be positive or negative)"""
          ticks = self()
          numticks = len(ticks)
  
          vmin, vmax = self.axis.get_view_interval()
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
          if numticks > 2:
              step = numsteps * abs(ticks[0] - ticks[1])
          else:
              d = abs(vmax - vmin)
              step = numsteps * d / 6.
  
          vmin += step
          vmax += step
          self.axis.set_view_interval(vmin, vmax, ignore=True)
  
      def zoom(self, direction):
          "Zoom in/out on axis; if direction is >0 zoom in, else zoom out"
  
          vmin, vmax = self.axis.get_view_interval()
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
          interval = abs(vmax - vmin)
          step = 0.1 * interval * direction
          self.axis.set_view_interval(vmin + step, vmax - step, ignore=True)
  
      def refresh(self):
          """refresh internal information based on current lim"""
          pass
  
  
  class IndexLocator(Locator):
      """
      Place a tick on every multiple of some base number of points
      plotted, eg on every 5th point.  It is assumed that you are doing
      index plotting; ie the axis is 0, len(data).  This is mainly
      useful for x ticks.
      """
      def __init__(self, base, offset):
          'place ticks on the i-th data points where (i-offset)%base==0'
          self._base = base
          self.offset = offset
  
      def __call__(self):
          """Return the locations of the ticks"""
          dmin, dmax = self.axis.get_data_interval()
          return self.tick_values(dmin, dmax)
  
      def tick_values(self, vmin, vmax):
          return self.raise_if_exceeds(
              np.arange(vmin + self.offset, vmax + 1, self._base))
  
  
  class FixedLocator(Locator):
      """
      Tick locations are fixed.  If nbins is not None,
      the array of possible positions will be subsampled to
      keep the number of ticks <= nbins +1.
      The subsampling will be done so as to include the smallest
      absolute value; for example, if zero is included in the
      array of possibilities, then it is guaranteed to be one of
      the chosen ticks.
      """
  
      def __init__(self, locs, nbins=None):
          self.locs = np.asarray(locs)
          self.nbins = nbins
          if self.nbins is not None:
              self.nbins = max(self.nbins, 2)
  
      def __call__(self):
          return self.tick_values(None, None)
  
      def tick_values(self, vmin, vmax):
          """"
          Return the locations of the ticks.
  
          .. note::
  
              Because the values are fixed, vmin and vmax are not used in this
              method.
  
          """
          if self.nbins is None:
              return self.locs
          step = max(int(0.99 + len(self.locs) / float(self.nbins)), 1)
          ticks = self.locs[::step]
          for i in range(1, step):
              ticks1 = self.locs[i::step]
              if np.absolute(ticks1).min() < np.absolute(ticks).min():
                  ticks = ticks1
          return self.raise_if_exceeds(ticks)
  
  
  class NullLocator(Locator):
      """
      No ticks
      """
  
      def __call__(self):
          return self.tick_values(None, None)
  
      def tick_values(self, vmin, vmax):
          """"
          Return the locations of the ticks.
  
          .. note::
  
              Because the values are Null, vmin and vmax are not used in this
              method.
          """
          return []
  
  
  class LinearLocator(Locator):
      """
      Determine the tick locations
  
      The first time this function is called it will try to set the
      number of ticks to make a nice tick partitioning.  Thereafter the
      number of ticks will be fixed so that interactive navigation will
      be nice
  
      """
      def __init__(self, numticks=None, presets=None):
          """
          Use presets to set locs based on lom.  A dict mapping vmin, vmax->locs
          """
          self.numticks = numticks
          if presets is None:
              self.presets = {}
          else:
              self.presets = presets
  
      def __call__(self):
          'Return the locations of the ticks'
          vmin, vmax = self.axis.get_view_interval()
          return self.tick_values(vmin, vmax)
  
      def tick_values(self, vmin, vmax):
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          if (vmin, vmax) in self.presets:
              return self.presets[(vmin, vmax)]
  
          if self.numticks is None:
              self._set_numticks()
  
          if self.numticks == 0:
              return []
          ticklocs = np.linspace(vmin, vmax, self.numticks)
  
          return self.raise_if_exceeds(ticklocs)
  
      def _set_numticks(self):
          self.numticks = 11  # todo; be smart here; this is just for dev
  
      def view_limits(self, vmin, vmax):
          'Try to choose the view limits intelligently'
  
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          if vmin == vmax:
              vmin -= 1
              vmax += 1
  
          exponent, remainder = divmod(math.log10(vmax - vmin), 1)
  
          if remainder < 0.5:
              exponent -= 1
          scale = 10 ** (-exponent)
          vmin = math.floor(scale * vmin) / scale
          vmax = math.ceil(scale * vmax) / scale
  
          return mtransforms.nonsingular(vmin, vmax)
  
  
  def closeto(x, y):
      if abs(x - y) < 1e-10:
          return True
      else:
          return False
  
  
  class Base:
      'this solution has some hacks to deal with floating point inaccuracies'
      def __init__(self, base):
          assert(base > 0)
          self._base = base
  
      def lt(self, x):
          'return the largest multiple of base < x'
          d, m = divmod(x, self._base)
          if closeto(m, 0) and not closeto(m / self._base, 1):
              return (d - 1) * self._base
          return d * self._base
  
      def le(self, x):
          'return the largest multiple of base <= x'
          d, m = divmod(x, self._base)
          if closeto(m / self._base, 1):  # was closeto(m, self._base)
              #looks like floating point error
              return (d + 1) * self._base
          return d * self._base
  
      def gt(self, x):
          'return the smallest multiple of base > x'
          d, m = divmod(x, self._base)
          if closeto(m / self._base, 1):
              #looks like floating point error
              return (d + 2) * self._base
          return (d + 1) * self._base
  
      def ge(self, x):
          'return the smallest multiple of base >= x'
          d, m = divmod(x, self._base)
          if closeto(m, 0) and not closeto(m / self._base, 1):
              return d * self._base
          return (d + 1) * self._base
  
      def get_base(self):
          return self._base
  
  
  class MultipleLocator(Locator):
      """
      Set a tick on every integer that is multiple of base in the
      view interval
      """
  
      def __init__(self, base=1.0):
          self._base = Base(base)
  
      def __call__(self):
          'Return the locations of the ticks'
          vmin, vmax = self.axis.get_view_interval()
          return self.tick_values(vmin, vmax)
  
      def tick_values(self, vmin, vmax):
          if vmax < vmin:
              vmin, vmax = vmax, vmin
          vmin = self._base.ge(vmin)
          base = self._base.get_base()
          n = (vmax - vmin + 0.001 * base) // base
          locs = vmin + np.arange(n + 1) * base
          return self.raise_if_exceeds(locs)
  
      def view_limits(self, dmin, dmax):
          """
          Set the view limits to the nearest multiples of base that
          contain the data
          """
          vmin = self._base.le(dmin)
          vmax = self._base.ge(dmax)
          if vmin == vmax:
              vmin -= 1
              vmax += 1
  
          return mtransforms.nonsingular(vmin, vmax)
  
  
  def scale_range(vmin, vmax, n=1, threshold=100):
      dv = abs(vmax - vmin)
      if dv == 0:     # maxabsv == 0 is a special case of this.
          return 1.0, 0.0
          # Note: this should never occur because
          # vmin, vmax should have been checked by nonsingular(),
          # and spread apart if necessary.
      meanv = 0.5 * (vmax + vmin)
      if abs(meanv) / dv < threshold:
          offset = 0
      elif meanv > 0:
          ex = divmod(math.log10(meanv), 1)[0]
          offset = 10 ** ex
      else:
          ex = divmod(math.log10(-meanv), 1)[0]
          offset = -10 ** ex
      ex = divmod(math.log10(dv / n), 1)[0]
      scale = 10 ** ex
      return scale, offset
  
  
  class MaxNLocator(Locator):
      """
      Select no more than N intervals at nice locations.
      """
      default_params = dict(nbins=10,
                            steps=None,
                            trim=True,
                            integer=False,
                            symmetric=False,
                            prune=None)
  
      def __init__(self, *args, **kwargs):
          """
          Keyword args:
  
          *nbins*
              Maximum number of intervals; one less than max number of ticks.
  
          *steps*
              Sequence of nice numbers starting with 1 and ending with 10;
              e.g., [1, 2, 4, 5, 10]
  
          *integer*
              If True, ticks will take only integer values.
  
          *symmetric*
              If True, autoscaling will result in a range symmetric
              about zero.
  
          *prune*
              ['lower' | 'upper' | 'both' | None]
              Remove edge ticks -- useful for stacked or ganged plots
              where the upper tick of one axes overlaps with the lower
              tick of the axes above it.
              If prune=='lower', the smallest tick will
              be removed.  If prune=='upper', the largest tick will be
              removed.  If prune=='both', the largest and smallest ticks
              will be removed.  If prune==None, no ticks will be removed.
  
          """
          # I left "trim" out; it defaults to True, and it is not
          # clear that there is any use case for False, so we may
          # want to remove that kwarg.  EF 2010/04/18
          if args:
              kwargs['nbins'] = args[0]
              if len(args) > 1:
                  raise ValueError(
                      "Keywords are required for all arguments except 'nbins'")
          self.set_params(**self.default_params)
          self.set_params(**kwargs)
  
      def set_params(self, **kwargs):
          if 'nbins' in kwargs:
              self._nbins = int(kwargs['nbins'])
          if 'trim' in kwargs:
              self._trim = kwargs['trim']
          if 'integer' in kwargs:
              self._integer = kwargs['integer']
          if 'symmetric' in kwargs:
              self._symmetric = kwargs['symmetric']
          if 'prune' in kwargs:
              prune = kwargs['prune']
              if prune is not None and prune not in ['upper', 'lower', 'both']:
                  raise ValueError(
                      "prune must be 'upper', 'lower', 'both', or None")
              self._prune = prune
          if 'steps' in kwargs:
              steps = kwargs['steps']
              if steps is None:
                  self._steps = [1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10]
              else:
                  if int(steps[-1]) != 10:
                      steps = list(steps)
                      steps.append(10)
                  self._steps = steps
          if 'integer' in kwargs:
              self._integer = kwargs['integer']
          if self._integer:
              self._steps = [n for n in self._steps if divmod(n, 1)[1] < 0.001]
  
      def bin_boundaries(self, vmin, vmax):
          nbins = self._nbins
          scale, offset = scale_range(vmin, vmax, nbins)
          if self._integer:
              scale = max(1, scale)
          vmin = vmin - offset
          vmax = vmax - offset
          raw_step = (vmax - vmin) / nbins
          scaled_raw_step = raw_step / scale
          best_vmax = vmax
          best_vmin = vmin
  
          for step in self._steps:
              if step < scaled_raw_step:
                  continue
              step *= scale
              best_vmin = step * divmod(vmin, step)[0]
              best_vmax = best_vmin + step * nbins
              if (best_vmax >= vmax):
                  break
          if self._trim:
              extra_bins = int(divmod((best_vmax - vmax), step)[0])
              nbins -= extra_bins
          return (np.arange(nbins + 1) * step + best_vmin + offset)
  
      def __call__(self):
          vmin, vmax = self.axis.get_view_interval()
          return self.tick_values(vmin, vmax)
  
      def tick_values(self, vmin, vmax):
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=1e-13,
                                                           tiny=1e-14)
          locs = self.bin_boundaries(vmin, vmax)
          prune = self._prune
          if prune == 'lower':
              locs = locs[1:]
          elif prune == 'upper':
              locs = locs[:-1]
          elif prune == 'both':
              locs = locs[1:-1]
          return self.raise_if_exceeds(locs)
  
      def view_limits(self, dmin, dmax):
          if self._symmetric:
              maxabs = max(abs(dmin), abs(dmax))
              dmin = -maxabs
              dmax = maxabs
          dmin, dmax = mtransforms.nonsingular(dmin, dmax, expander=1e-12,
                                                          tiny=1.e-13)
          return np.take(self.bin_boundaries(dmin, dmax), [0, -1])
  
  
  def decade_down(x, base=10):
      'floor x to the nearest lower decade'
      if x == 0.0:
          return -base
      lx = np.floor(np.log(x) / np.log(base))
      return base ** lx
  
  
  def decade_up(x, base=10):
      'ceil x to the nearest higher decade'
      if x == 0.0:
          return base
      lx = np.ceil(np.log(x) / np.log(base))
      return base ** lx
  
  
  def nearest_long(x):
      if x == 0:
          return 0
      elif x > 0:
          return int(x + 0.5)
      else:
          return int(x - 0.5)
  
  
  def is_decade(x, base=10):
      if not np.isfinite(x):
          return False
      if x == 0.0:
          return True
      lx = np.log(np.abs(x)) / np.log(base)
      return is_close_to_int(lx)
  
  
  def is_close_to_int(x):
      if not np.isfinite(x):
          return False
      return abs(x - nearest_long(x)) < 1e-10
  
  
  class LogLocator(Locator):
      """
      Determine the tick locations for log axes
      """
  
      def __init__(self, base=10.0, subs=[1.0], numdecs=4, numticks=15):
          """
          place ticks on the location= base**i*subs[j]
          """
          self.base(base)
          self.subs(subs)
          self.numticks = numticks
          self.numdecs = numdecs
  
      def base(self, base):
          """
          set the base of the log scaling (major tick every base**i, i integer)
          """
          self._base = base + 0.0
  
      def subs(self, subs):
          """
          set the minor ticks the log scaling every base**i*subs[j]
          """
          if subs is None:
              self._subs = None  # autosub
          else:
              self._subs = np.asarray(subs) + 0.0
  
      def __call__(self):
          'Return the locations of the ticks'
          vmin, vmax = self.axis.get_view_interval()
          return self.tick_values(vmin, vmax)
  
      def tick_values(self, vmin, vmax):
          b = self._base
          # dummy axis has no axes attribute
          if hasattr(self.axis, 'axes') and self.axis.axes.name == 'polar':
              vmax = math.ceil(math.log(vmax) / math.log(b))
              decades = np.arange(vmax - self.numdecs, vmax)
              ticklocs = b ** decades
  
              return ticklocs
  
          if vmin <= 0.0:
              if self.axis is not None:
                  vmin = self.axis.get_minpos()
  
              if vmin <= 0.0 or not np.isfinite(vmin):
                  raise ValueError(
                      "Data has no positive values, and therefore can not be "
                      "log-scaled.")
  
          vmin = math.log(vmin) / math.log(b)
          vmax = math.log(vmax) / math.log(b)
  
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          numdec = math.floor(vmax) - math.ceil(vmin)
  
          if self._subs is None:  # autosub
              if numdec > 10:
                  subs = np.array([1.0])
              elif numdec > 6:
                  subs = np.arange(2.0, b, 2.0)
              else:
                  subs = np.arange(2.0, b)
          else:
              subs = self._subs
  
          stride = 1
          while numdec / stride + 1 > self.numticks:
              stride += 1
  
          decades = np.arange(math.floor(vmin),
                              math.ceil(vmax) + stride, stride)
          if hasattr(self, '_transform'):
              ticklocs = self._transform.inverted().transform(decades)
              if len(subs) > 1 or (len(subs == 1) and subs[0] != 1.0):
                  ticklocs = np.ravel(np.outer(subs, ticklocs))
          else:
              if len(subs) > 1 or (len(subs == 1) and subs[0] != 1.0):
                  ticklocs = []
                  for decadeStart in b ** decades:
                      ticklocs.extend(subs * decadeStart)
              else:
                  ticklocs = b ** decades
  
          return self.raise_if_exceeds(np.asarray(ticklocs))
  
      def view_limits(self, vmin, vmax):
          'Try to choose the view limits intelligently'
          b = self._base
  
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          if self.axis.axes.name == 'polar':
              vmax = math.ceil(math.log(vmax) / math.log(b))
              vmin = b ** (vmax - self.numdecs)
              return vmin, vmax
  
          minpos = self.axis.get_minpos()
  
          if minpos <= 0 or not np.isfinite(minpos):
              raise ValueError(
                  "Data has no positive values, and therefore can not be "
                  "log-scaled.")
  
          if vmin <= minpos:
              vmin = minpos
  
          if not is_decade(vmin, self._base):
              vmin = decade_down(vmin, self._base)
          if not is_decade(vmax, self._base):
              vmax = decade_up(vmax, self._base)
  
          if vmin == vmax:
              vmin = decade_down(vmin, self._base)
              vmax = decade_up(vmax, self._base)
          result = mtransforms.nonsingular(vmin, vmax)
          return result
  
  
  class SymmetricalLogLocator(Locator):
      """
      Determine the tick locations for log axes
      """
  
      def __init__(self, transform, subs=None):
          """
          place ticks on the location= base**i*subs[j]
          """
          self._transform = transform
          if subs is None:
              self._subs = [1.0]
          else:
              self._subs = subs
          self.numticks = 15
  
      def __call__(self):
          'Return the locations of the ticks'
          # Note, these are untransformed coordinates
          vmin, vmax = self.axis.get_view_interval()
          return self.tick_values(vmin, vmax)
  
      def tick_values(self, vmin, vmax):
          b = self._transform.base
          t = self._transform.linthresh
  
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          # The domain is divided into three sections, only some of
          # which may actually be present.
          #
          # <======== -t ==0== t ========>
          # aaaaaaaaa    bbbbb   ccccccccc
          #
          # a) and c) will have ticks at integral log positions.  The
          # number of ticks needs to be reduced if there are more
          # than self.numticks of them.
          #
          # b) has a tick at 0 and only 0 (we assume t is a small
          # number, and the linear segment is just an implementation
          # detail and not interesting.)
          #
          # We could also add ticks at t, but that seems to usually be
          # uninteresting.
          #
          # "simple" mode is when the range falls entirely within (-t,
          # t) -- it should just display (vmin, 0, vmax)
  
          has_a = has_b = has_c = False
          if vmin < -t:
              has_a = True
              if vmax > -t:
                  has_b = True
                  if vmax > t:
                      has_c = True
          elif vmin < 0:
              if vmax > 0:
                  has_b = True
                  if vmax > t:
                      has_c = True
              else:
                  return [vmin, vmax]
          elif vmin < t:
              if vmax > t:
                  has_b = True
                  has_c = True
              else:
                  return [vmin, vmax]
          else:
              has_c = True
  
          def get_log_range(lo, hi):
              lo = np.floor(np.log(lo) / np.log(b))
              hi = np.ceil(np.log(hi) / np.log(b))
              return lo, hi
  
          # First, calculate all the ranges, so we can determine striding
          if has_a:
              if has_b:
                  a_range = get_log_range(t, -vmin + 1)
              else:
                  a_range = get_log_range(-vmax, -vmin + 1)
          else:
              a_range = (0, 0)
  
          if has_c:
              if has_b:
                  c_range = get_log_range(t, vmax + 1)
              else:
                  c_range = get_log_range(vmin, vmax + 1)
          else:
              c_range = (0, 0)
  
          total_ticks = (a_range[1] - a_range[0]) + (c_range[1] - c_range[0])
          if has_b:
              total_ticks += 1
          stride = max(np.floor(float(total_ticks) / (self.numticks - 1)), 1)
  
          decades = []
          if has_a:
              decades.extend(-1 * (b ** (np.arange(a_range[0], a_range[1],
                                                   stride)[::-1])))
  
          if has_b:
              decades.append(0.0)
  
          if has_c:
              decades.extend(b ** (np.arange(c_range[0], c_range[1], stride)))
  
          # Add the subticks if requested
          if self._subs is None:
              subs = np.arange(2.0, b)
          else:
              subs = np.asarray(self._subs)
  
          if len(subs) > 1 or subs[0] != 1.0:
              ticklocs = []
              for decade in decades:
                  ticklocs.extend(subs * decade)
          else:
              ticklocs = decades
  
          return self.raise_if_exceeds(np.array(ticklocs))
  
      def view_limits(self, vmin, vmax):
          'Try to choose the view limits intelligently'
          b = self._transform.base
          if vmax < vmin:
              vmin, vmax = vmax, vmin
  
          if not is_decade(abs(vmin), b):
              if vmin < 0:
                  vmin = -decade_up(-vmin, b)
              else:
                  vmin = decade_down(vmin, b)
          if not is_decade(abs(vmax), b):
              if vmax < 0:
                  vmax = -decade_down(-vmax, b)
              else:
                  vmax = decade_up(vmax, b)
  
          if vmin == vmax:
              if vmin < 0:
                  vmin = -decade_up(-vmin, b)
                  vmax = -decade_down(-vmax, b)
              else:
                  vmin = decade_down(vmin, b)
                  vmax = decade_up(vmax, b)
          result = mtransforms.nonsingular(vmin, vmax)
          return result
  
  
  class AutoLocator(MaxNLocator):
      def __init__(self):
          MaxNLocator.__init__(self, nbins=9, steps=[1, 2, 5, 10])
  
  
  class AutoMinorLocator(Locator):
      """
      Dynamically find minor tick positions based on the positions of
      major ticks. Assumes the scale is linear and major ticks are
      evenly spaced.
      """
      def __init__(self, n=None):
          """
          *n* is the number of subdivisions of the interval between
          major ticks; e.g., n=2 will place a single minor tick midway
          between major ticks.
  
          If *n* is omitted or None, it will be set to 5 or 4.
          """
          self.ndivs = n
  
      def __call__(self):
          'Return the locations of the ticks'
          majorlocs = self.axis.get_majorticklocs()
          try:
              majorstep = majorlocs[1] - majorlocs[0]
          except IndexError:
              # Need at least two major ticks to find minor tick locations
              # TODO: Figure out a way to still be able to display minor
              # ticks without two major ticks visible. For now, just display
              # no ticks at all.
              majorstep = 0
  
          if self.ndivs is None:
              if majorstep == 0:
                  # TODO: Need a better way to figure out ndivs
                  ndivs = 1
              else:
                  x = int(round(10 ** (np.log10(majorstep) % 1)))
                  if x in [1, 5, 10]:
                      ndivs = 5
                  else:
                      ndivs = 4
          else:
              ndivs = self.ndivs
  
          minorstep = majorstep / ndivs
  
          vmin, vmax = self.axis.get_view_interval()
          if vmin > vmax:
              vmin, vmax = vmax, vmin
  
          if len(majorlocs) > 0:
              t0 = majorlocs[0]
              tmin = np.ceil((vmin - t0) / minorstep) * minorstep
              tmax = np.floor((vmax - t0) / minorstep) * minorstep
              locs = np.arange(tmin, tmax, minorstep) + t0
              cond = np.abs((locs - t0) % majorstep) > minorstep / 10.0
              locs = locs.compress(cond)
          else:
              locs = []
  
          return self.raise_if_exceeds(np.array(locs))
  
      def tick_values(self, vmin, vmax):
          raise NotImplementedError('Cannot get tick locations for a '
                                    '%s type.' % type(self))
  
  
  class OldAutoLocator(Locator):
      """
      On autoscale this class picks the best MultipleLocator to set the
      view limits and the tick locs.
  
      """
      def __init__(self):
          self._locator = LinearLocator()
  
      def __call__(self):
          'Return the locations of the ticks'
          self.refresh()
          return self.raise_if_exceeds(self._locator())
  
      def tick_values(self, vmin, vmax):
          raise NotImplementedError('Cannot get tick locations for a '
                                    '%s type.' % type(self))
  
      def refresh(self):
          'refresh internal information based on current lim'
          vmin, vmax = self.axis.get_view_interval()
          vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
          d = abs(vmax - vmin)
          self._locator = self.get_locator(d)
  
      def view_limits(self, vmin, vmax):
          'Try to choose the view limits intelligently'
  
          d = abs(vmax - vmin)
          self._locator = self.get_locator(d)
          return self._locator.view_limits(vmin, vmax)
  
      def get_locator(self, d):
          'pick the best locator based on a distance'
          d = abs(d)
          if d <= 0:
              locator = MultipleLocator(0.2)
          else:
  
              try:
                  ld = math.log10(d)
              except OverflowError:
                  raise RuntimeError('AutoLocator illegal data interval range')
  
              fld = math.floor(ld)
              base = 10 ** fld
  
              #if ld==fld:  base = 10**(fld-1)
              #else:        base = 10**fld
  
              if d >= 5 * base:
                  ticksize = base
              elif d >= 2 * base:
                  ticksize = base / 2.0
              else:
                  ticksize = base / 5.0
              locator = MultipleLocator(ticksize)
  
          return locator
  
  
  __all__ = ('TickHelper', 'Formatter', 'FixedFormatter',
             'NullFormatter', 'FuncFormatter', 'FormatStrFormatter',
             'ScalarFormatter', 'LogFormatter', 'LogFormatterExponent',
             'LogFormatterMathtext', 'Locator', 'IndexLocator',
             'FixedLocator', 'NullLocator', 'LinearLocator',
             'LogLocator', 'AutoLocator', 'MultipleLocator',
             'MaxNLocator', 'AutoMinorLocator',)
  