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"""
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.
"""
from __future__ import division, print_function
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 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 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('-', 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. ``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
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, 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':
# 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: u"\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 = u"%g %s"
elif self.places == 0:
format_str = u"%i %s"
elif self.places > 0:
format_str = (u"%%.%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)
maxabsv = max(abs(vmin), abs(vmax))
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 -= 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()
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 0L
elif x > 0: return long(x+0.5)
else: return long(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',)
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