FM / matplotlib

/usr/lib64/python2.6/site-packages/matplotlib/

/usr/lib64/python2.6/site-packages/matplotlib

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Edit: /usr/lib64/python2.6/site-packages/matplotlib/ticker.py (40428B)

"""
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.

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.
"""

from __future__ import division
import math
import numpy as np
from matplotlib import rcParams
from matplotlib import cbook
from matplotlib import transforms as mtransforms

class TickHelper:
    axis = None
    class DummyAxis:
        def __init__(self):
            self.dataLim = mtransforms.Bbox.unit()
            self.viewLim = mtransforms.Bbox.unit()

def get_view_interval(self):
            return self.viewLim.intervalx

def set_view_interval(self, vmin, vmax):
            self.viewLim.intervalx = vmin, vmax

def get_data_interval(self):
            return self.dataLim.intervalx

def set_data_interval(self, vmin, vmax):
            self.dataLim.intervalx = vmin, vmax

def set_axis(self, axis):
        self.axis = axis

def create_dummy_axis(self):
        if self.axis is None:
            self.axis = self.DummyAxis()

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 overide')

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
        interative 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:
    """
    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 < 1e-3 or data >= 1e4.
    """

def __init__(self, useOffset=True, useMathText=False):
        # 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._useOffset = useOffset
        self._usetex = rcParams['text.usetex']
        self._useMathText = useMathText
        self.offset = 0
        self.orderOfMagnitude = 0
        self.format = ''
        self._scientific = True
        self._powerlimits = rcParams['axes.formatter.limits']

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('-', u'\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. ``xaxis.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'
        return '%-12g'%value

def format_data(self,value):
        'return a formatted string representation of a number'
        s =  self._formatSciNotation('%1.10e'% value)
        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()

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
                if ave_loc < 0:
                    self.offset = math.ceil(np.max(locs)/10**range_oom)*10**range_oom
                else:
                    self.offset = math.floor(np.min(locs)/10**(range_oom))*10**(range_oom)
            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):
        # set the format string to format all the ticklabels
        # The floating point black magic (adding 1e-15 and formatting
        # to 8 digits) may warrant review and cleanup.
        locs = (np.asarray(self.locs)-self.offset) / 10**self.orderOfMagnitude+1e-15
        sigfigs = [len(str('%1.8f'% loc).split('.')[1].rstrip('0')) \
                   for loc in locs]
        sigfigs.sort()
        self.format = '%1.' + str(sigfigs[-1]) + '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
        return self.format % xp

def _formatSciNotation(self, s):
        # transform 1e+004 into 1e4, for example
        tup = s.split('e')
        try:
            significand = tup[0].rstrip('0').rstrip('.')
            sign = tup[1][0].replace('+', '')
            exponent = tup[1][1:].lstrip('0')
            if self._useMathText or self._usetex:
                if significand == '1':
                    # 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, msg:
            return s

class LogFormatter(Formatter):
    """
    Format values for log axis;

if attribute *decadeOnly* is True, only the decades will be labelled.
    """
    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
        self.decadeOnly = True

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 = self.is_decade(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):
        self.labelOnlyBase = False
        value = cbook.strip_math(self.__call__(value))
        self.labelOnlyBase = True
        return value

def format_data_short(self,value):
        'return a short formatted string representation of a number'
        return '%-12g'%value

def is_decade(self, x):
        n = self.nearest_long(x)
        return abs(x-n)<1e-10

def nearest_long(self, x):
        if x==0: return 0L
        elif x>0: return long(x+0.5)
        else: return long(x-0.5)

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

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 = self.is_decade(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
        # only label the decades
        if x == 0:
            return '$0$'
        sign = np.sign(x)
        fx = math.log(abs(x))/math.log(b)
        isDecade = self.is_decade(fx)

usetex = rcParams['text.usetex']

if sign == -1:
            sign_string = '-'
        else:
            sign_string = ''

if not isDecade and self.labelOnlyBase: s = ''
        elif not isDecade:
            if usetex:
                s = r'$%s%d^{%.2f}$'% (sign_string, b, fx)
            else:
                s = '$\mathdefault{%s%d^{%.2f}}$'% (sign_string, b, fx)
        else:
            if usetex:
                s = r'$%s%d^{%d}$'% (sign_string, b, self.nearest_long(fx))
            else:
                s = r'$\mathdefault{%s%d^{%d}}$'% (sign_string, b, self.nearest_long(fx))

return s

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
    """

def __call__(self):
        'Return the locations of the ticks'
        raise NotImplementedError('Derived must override')

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 np.arange(dmin + self.offset, dmax+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 the locations of the ticks'
        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 ticks

class NullLocator(Locator):
    """
    No ticks
    """

def __call__(self):
        'Return the locations of the ticks'
        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()
        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 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()
        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 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)
    maxabsv = max(abs(vmin), abs(vmax))
    if maxabsv == 0 or dv/maxabsv < 1e-12:
        return 1.0, 0.0
    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.
    """

def __init__(self, nbins = 10, steps = None,
                 trim = True,
                 integer=False,
                 symmetric=False,
                 prune=None):
        """
        Keyword args:
        *prune*
            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.  One of 'lower' | 'upper' |
            'both' | None.  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.

"""
        self._nbins = int(nbins)
        self._trim = trim
        self._integer = integer
        self._symmetric = symmetric
        self._prune = prune
        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:
            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 -= offset
        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()
        vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander = 0.05)
        locs = self.bin_boundaries(vmin, vmax)
        #print 'locs=', locs
        prune = self._prune
        if prune=='lower':
            locs = locs[1:]
        elif prune=='upper':
            locs = locs[:-1]
        elif prune=='both':
            locs = locs[1:-1]
        return 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 = 0.05)
        return np.take(self.bin_boundaries(dmin, dmax), [0,-1])

def decade_down(x, base=10):
    'floor x to the nearest lower decade'

lx = math.floor(math.log(x)/math.log(base))
    return base**lx

def decade_up(x, base=10):
    'ceil x to the nearest higher decade'
    lx = math.ceil(math.log(x)/math.log(base))
    return base**lx

def is_decade(x,base=10):
    lx = math.log(x)/math.log(base)
    return lx==int(lx)

class LogLocator(Locator):
    """
    Determine the tick locations for log axes
    """

def __init__(self, base=10.0, subs=[1.0]):
        """
        place ticks on the location= base**i*subs[j]
        """
        self.base(base)
        self.subs(subs)
        self.numticks = 15

def base(self,base):
        """
        set the base of the log scaling (major tick every base**i, i interger)
        """
        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 _set_numticks(self):
        self.numticks = 15  # todo; be smart here; this is just for dev

def __call__(self):
        'Return the locations of the ticks'
        b=self._base

vmin, vmax = self.axis.get_view_interval()
        if vmin <= 0.0:
            vmin = self.axis.get_minpos()
            if vmin <= 0.0:
                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 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 np.array(ticklocs)

def view_limits(self, vmin, vmax):
        'Try to choose the view limits intelligently'

if vmax<vmin:
            vmin, vmax = vmax, vmin

minpos = self.axis.get_minpos()

if minpos<=0:
            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=[1.0]):
        """
        place ticks on the location= base**i*subs[j]
        """
        self._transform = transform
        self._subs = subs
        self.numticks = 15

def _set_numticks(self):
        self.numticks = 15  # todo; be smart here; this is just for dev

def __call__(self):
        'Return the locations of the ticks'
        b = self._transform.base

vmin, vmax = self.axis.get_view_interval()
        vmin, vmax = self._transform.transform((vmin, vmax))

if vmax<vmin:
            vmin, vmax = vmax, vmin
        numdec = math.floor(vmax)-math.ceil(vmin)

if self._subs is None:
            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 = np.asarray(self._subs)

stride = 1
        while numdec/stride+1 > self.numticks:
            stride += 1

decades = np.arange(math.floor(vmin), math.ceil(vmax)+stride, stride)
        if len(subs) > 1 or subs[0] != 1.0:
            ticklocs = []
            for decade in decades:
                ticklocs.extend(subs * (np.sign(decade) * b ** np.abs(decade)))
        else:
            ticklocs = np.sign(decades) * b ** np.abs(decades)
        return 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 __call__(self):
        'Return the locations of the ticks'
        majorlocs = self.axis.get_majorticklocs()
        try:
            majorstep = majorlocs[1] - majorlocs[0]
        except IndexError:
            raise ValueError('Need at least two major ticks to find minor '
                             'tick locations')
        # see whether major step should be divided by 5, 4 or 2. This
        # should cover most cases.
        temp = float(('%e' % majorstep).split('e')[0])
        if temp % 5 < 1e-10:
            minorstep = majorstep / 5.
        elif temp % 2 < 1e-10:
            minorstep = majorstep / 4.
        else:
            minorstep = majorstep / 2.

tmin = majorlocs[0] - majorstep
        tmax = majorlocs[-1] + majorstep
        locs = np.arange(tmin, tmax, minorstep)
        vmin, vmax = self.axis.get_view_interval()
        if vmin > vmax:
            vmin,vmax = vmax,vmin

return locs[(vmin < locs) & (locs < vmax)]

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._locator()

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', )

cmd: