"""
Tick locating and formatting
============================
This module contains classes for configuring tick locating and formatting.
Generic tick locators and formatters are provided, as well as domain specific
custom ones.
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.
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`. It is initialized with a base, e.g., 10, and it picks
axis limits and ticks that are multiples of that base.
The Locator subclasses defined here are:
======================= =======================================================
`AutoLocator` `MaxNLocator` with simple defaults. This is the default
tick locator for most plotting.
`MaxNLocator` Finds up to a max number of intervals with ticks at
nice locations.
`LinearLocator` Space ticks evenly from min to max.
`LogLocator` Space ticks logarithmically from min to max.
`MultipleLocator` Ticks and range are a multiple of base; either integer
or float.
`FixedLocator` Tick locations are fixed.
`IndexLocator` Locator for index plots (e.g., where
``x = range(len(y))``).
`NullLocator` No ticks.
`SymmetricalLogLocator` Locator for use with the symlog norm; works like
`LogLocator` for the part outside of the threshold and
adds 0 if inside the limits.
`AsinhLocator` Locator for use with the asinh norm, attempting to
space ticks approximately uniformly.
`LogitLocator` Locator for logit scaling.
`AutoMinorLocator` Locator for minor ticks when the axis is linear and the
major ticks are uniformly spaced. 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 :mod:`.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(xmajor_locator)
ax.xaxis.set_minor_locator(xminor_locator)
ax.yaxis.set_major_locator(ymajor_locator)
ax.yaxis.set_minor_locator(yminor_locator)
The default minor locator is `NullLocator`, i.e., no minor ticks on by default.
.. note::
`Locator` instances should not be used with more than one
`~matplotlib.axis.Axis` or `~matplotlib.axes.Axes`. So instead of::
locator = MultipleLocator(5)
ax.xaxis.set_major_locator(locator)
ax2.xaxis.set_major_locator(locator)
do the following instead::
ax.xaxis.set_major_locator(MultipleLocator(5))
ax2.xaxis.set_major_locator(MultipleLocator(5))
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.
========================= =====================================================
`NullFormatter` No labels on the ticks.
`FixedFormatter` Set the strings manually for the labels.
`FuncFormatter` User defined function sets the labels.
`StrMethodFormatter` Use string `format` method.
`FormatStrFormatter` Use an old-style sprintf format string.
`ScalarFormatter` Default formatter for scalars: autopick the format
string.
`LogFormatter` Formatter for log axes.
`LogFormatterExponent` Format values for log axis using
``exponent = log_base(value)``.
`LogFormatterMathtext` Format values for log axis using
``exponent = log_base(value)`` using Math text.
`LogFormatterSciNotation` Format values for log axis using scientific notation.
`LogitFormatter` Probability formatter.
`EngFormatter` Format labels in engineering notation.
`PercentFormatter` Format labels as a percentage.
========================= =====================================================
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(xmajor_formatter)
ax.xaxis.set_minor_formatter(xminor_formatter)
ax.yaxis.set_major_formatter(ymajor_formatter)
ax.yaxis.set_minor_formatter(yminor_formatter)
In addition to a `.Formatter` instance, `~.Axis.set_major_formatter` and
`~.Axis.set_minor_formatter` also accept a ``str`` or function. ``str`` input
will be internally replaced with an autogenerated `.StrMethodFormatter` with
the input ``str``. For function input, a `.FuncFormatter` with the input
function will be generated and used.
See :doc:`/gallery/ticks/major_minor_demo` for an example of setting major
and minor ticks. See the :mod:`matplotlib.dates` module for more information
and examples of using date locators and formatters.
"""
import itertools
import logging
import locale
import math
from numbers import Integral
import numpy as np
import matplotlib as mpl
from matplotlib import _api, cbook
from matplotlib import transforms as mtransforms
_log = logging.getLogger(__name__)
__all__ = ('TickHelper', 'Formatter', 'FixedFormatter',
'NullFormatter', 'FuncFormatter', 'FormatStrFormatter',
'StrMethodFormatter', 'ScalarFormatter', 'LogFormatter',
'LogFormatterExponent', 'LogFormatterMathtext',
'LogFormatterSciNotation',
'LogitFormatter', 'EngFormatter', 'PercentFormatter',
'Locator', 'IndexLocator', 'FixedLocator', 'NullLocator',
'LinearLocator', 'LogLocator', 'AutoLocator',
'MultipleLocator', 'MaxNLocator', 'AutoMinorLocator',
'SymmetricalLogLocator', 'AsinhLocator', 'LogitLocator')
class _DummyAxis:
__name__ = "dummy"
# Once the deprecation elapses, replace dataLim and viewLim by plain
# _view_interval and _data_interval private tuples.
dataLim = _api.deprecate_privatize_attribute(
"3.6", alternative="get_data_interval() and set_data_interval()")
viewLim = _api.deprecate_privatize_attribute(
"3.6", alternative="get_view_interval() and set_view_interval()")
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
def get_tick_space(self):
# Just use the long-standing default of nbins==9
return 9
class TickHelper:
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)
class Formatter(TickHelper):
"""
Create a string based on a tick value and location.
"""
# 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 value *x* at position pos.
``pos=None`` indicates an unspecified location.
"""
raise NotImplementedError('Derived must override')
def format_ticks(self, values):
"""Return the tick labels for all the ticks at once."""
self.set_locs(values)
return [self(value, i) for i, value in enumerate(values)]
def format_data(self, value):
"""
Return the full string representation of the value with the
position unspecified.
"""
return self.__call__(value)
def format_data_short(self, value):
"""
Return a short string version of the tick value.
Defaults to the position-independent long value.
"""
return self.format_data(value)
def get_offset(self):
return ''
def set_locs(self, locs):
"""
Set the locations of the ticks.
This method is called before computing the tick labels because some
formatters need to know all tick locations to do so.
"""
self.locs = locs
@staticmethod
def fix_minus(s):
"""
Some classes may want to replace a hyphen for minus with the proper
Unicode symbol (U+2212) for typographical correctness. This is a
helper method to perform such a replacement when it is enabled via
:rc:`axes.unicode_minus`.
"""
return (s.replace('-', '\N{MINUS SIGN}')
if mpl.rcParams['axes.unicode_minus']
else s)
def _set_locator(self, locator):
"""Subclasses may want to override this to set a locator."""
pass
class NullFormatter(Formatter):
"""Always return the empty string."""
def __call__(self, x, pos=None):
# docstring inherited
return ''
class FixedFormatter(Formatter):
"""
Return fixed strings for tick labels based only on position, not value.
.. note::
`.FixedFormatter` should only be used together with `.FixedLocator`.
Otherwise, the labels may end up in unexpected positions.
"""
def __init__(self, seq):
"""Set the sequence *seq* of strings that will be used for labels."""
self.seq = seq
self.offset_string = ''
def __call__(self, x, pos=None):
"""
Return the label that matches the position, regardless of the value.
For positions ``pos < len(seq)``, return ``seq[i]`` regardless of
*x*. Otherwise return empty string. ``seq`` is the sequence of
strings that this object was initialized with.
"""
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):
"""
Use a user-defined function for formatting.
The function should take in two inputs (a tick value ``x`` and a
position ``pos``), and return a string containing the corresponding
tick label.
"""
def __init__(self, func):
self.func = func
self.offset_string = ""
def __call__(self, x, pos=None):
"""
Return the value of the user defined function.
*x* and *pos* are passed through as-is.
"""
return self.func(x, pos)
def get_offset(self):
return self.offset_string
def set_offset_string(self, ofs):
self.offset_string = ofs
class FormatStrFormatter(Formatter):
"""
Use an old-style ('%' operator) format string to format the tick.
The format string should have a single variable format (%) in it.
It will be applied to the value (not the position) of the tick.
Negative numeric values will use a dash, not a Unicode minus; use mathtext
to get a Unicode minus by wrapping the format specifier with $ (e.g.
"$%g$").
"""
def __init__(self, fmt):
self.fmt = fmt
def __call__(self, x, pos=None):
"""
Return the formatted label string.
Only the value *x* is formatted. The position is ignored.
"""
return self.fmt % x
class StrMethodFormatter(Formatter):
"""
Use a new-style format string (as used by `str.format`) to format the tick.
The field used for the tick value must be labeled *x* and the field used
for the tick position must be labeled *pos*.
"""
def __init__(self, fmt):
self.fmt = fmt
def __call__(self, x, pos=None):
"""
Return the formatted label string.
*x* and *pos* are passed to `str.format` as keyword arguments
with those exact names.
"""
return self.fmt.format(x=x, pos=pos)
class ScalarFormatter(Formatter):
"""
Format tick values as a number.
Parameters
----------
useOffset : bool or float, default: :rc:`axes.formatter.useoffset`
Whether to use offset notation. See `.set_useOffset`.
useMathText : bool, default: :rc:`axes.formatter.use_mathtext`
Whether to use fancy math formatting. See `.set_useMathText`.
useLocale : bool, default: :rc:`axes.formatter.use_locale`.
Whether to use locale settings for decimal sign and positive sign.
See `.set_useLocale`.
Notes
-----
In addition to the parameters above, the formatting of scientific vs.
floating point representation can be configured via `.set_scientific`
and `.set_powerlimits`).
**Offset notation and scientific notation**
Offset notation and scientific notation look quite similar at first sight.
Both split some information from the formatted tick values and display it
at the end of the axis.
- The scientific notation splits up the order of magnitude, i.e. a
multiplicative scaling factor, e.g. ``1e6``.
- The offset notation separates an additive constant, e.g. ``+1e6``. The
offset notation label is always prefixed with a ``+`` or ``-`` sign
and is thus distinguishable from the order of magnitude label.
The following plot with x limits ``1_000_000`` to ``1_000_010`` illustrates
the different formatting. Note the labels at the right edge of the x axis.
.. plot::
lim = (1_000_000, 1_000_010)
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, gridspec_kw={'hspace': 2})
ax1.set(title='offset_notation', xlim=lim)
ax2.set(title='scientific notation', xlim=lim)
ax2.xaxis.get_major_formatter().set_useOffset(False)
ax3.set(title='floating point notation', xlim=lim)
ax3.xaxis.get_major_formatter().set_useOffset(False)
ax3.xaxis.get_major_formatter().set_scientific(False)
"""
def __init__(self, useOffset=None, useMathText=None, useLocale=None):
if useOffset is None:
useOffset = mpl.rcParams['axes.formatter.useoffset']
self._offset_threshold = \
mpl.rcParams['axes.formatter.offset_threshold']
self.set_useOffset(useOffset)
self._usetex = mpl.rcParams['text.usetex']
self.set_useMathText(useMathText)
self.orderOfMagnitude = 0
self.format = ''
self._scientific = True
self._powerlimits = mpl.rcParams['axes.formatter.limits']
self.set_useLocale(useLocale)
def get_useOffset(self):
"""
Return whether automatic mode for offset notation is active.
This returns True if ``set_useOffset(True)``; it returns False if an
explicit offset was set, e.g. ``set_useOffset(1000)``.
See Also
--------
ScalarFormatter.set_useOffset
"""
return self._useOffset
def set_useOffset(self, val):
"""
Set whether to use offset notation.
When formatting a set numbers whose value is large compared to their
range, the formatter can separate an additive constant. This can
shorten the formatted numbers so that they are less likely to overlap
when drawn on an axis.
Parameters
----------
val : bool or float
- If False, do not use offset notation.
- If True (=automatic mode), use offset notation if it can make
the residual numbers significantly shorter. The exact behavior
is controlled by :rc:`axes.formatter.offset_threshold`.
- If a number, force an offset of the given value.
Examples
--------
With active offset notation, the values
``100_000, 100_002, 100_004, 100_006, 100_008``
will be formatted as ``0, 2, 4, 6, 8`` plus an offset ``+1e5``, which
is written to the edge of the axis.
"""
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 whether locale settings are used for formatting.
See Also
--------
ScalarFormatter.set_useLocale
"""
return self._useLocale
def set_useLocale(self, val):
"""
Set whether to use locale settings for decimal sign and positive sign.
Parameters
----------
val : bool or None
*None* resets to :rc:`axes.formatter.use_locale`.
"""
if val is None:
self._useLocale = mpl.rcParams['axes.formatter.use_locale']
else:
self._useLocale = val
useLocale = property(fget=get_useLocale, fset=set_useLocale)
def _format_maybe_minus_and_locale(self, fmt, arg):
"""
Format *arg* with *fmt*, applying Unicode minus and locale if desired.
"""
return self.fix_minus(locale.format_string(fmt, (arg,), True)
if self._useLocale else fmt % arg)
def get_useMathText(self):
"""
Return whether to use fancy math formatting.
See Also
--------
ScalarFormatter.set_useMathText
"""
return self._useMathText
def set_useMathText(self, val):
r"""
Set whether to use fancy math formatting.
If active, scientific notation is formatted as :math:`1.2 \times 10^3`.
Parameters
----------
val : bool or None
*None* resets to :rc:`axes.formatter.use_mathtext`.
"""
if val is None:
self._useMathText = mpl.rcParams['axes.formatter.use_mathtext']
if self._useMathText is False:
try:
from matplotlib import font_manager
ufont = font_manager.findfont(
font_manager.FontProperties(
mpl.rcParams["font.family"]
),
fallback_to_default=False,
)
except ValueError:
ufont = None
if ufont == str(cbook._get_data_path("fonts/ttf/cmr10.ttf")):
_api.warn_external(
"cmr10 font should ideally be used with "
"mathtext, set axes.formatter.use_mathtext to True"
)
else:
self._useMathText = val
useMathText = property(fget=get_useMathText, fset=set_useMathText)
def __call__(self, x, pos=None):
"""
Return the format for tick value *x* at position *pos*.
"""
if len(self.locs) == 0:
return ''
else:
xp = (x - self.offset) / (10. ** self.orderOfMagnitude)
if abs(xp) < 1e-8:
xp = 0
return self._format_maybe_minus_and_locale(self.format, xp)
def set_scientific(self, b):
"""
Turn scientific notation on or off.
See Also
--------
ScalarFormatter.set_powerlimits
"""
self._scientific = bool(b)
def set_powerlimits(self, lims):
r"""
Set size thresholds for scientific notation.
Parameters
----------
lims : (int, int)
A tuple *(min_exp, max_exp)* containing the powers of 10 that
determine the switchover threshold. For a number representable as
:math:`a \times 10^\mathrm{exp}` with :math:`1 <= |a| < 10`,
scientific notation will be used if ``exp <= min_exp`` or
``exp >= max_exp``.
The default limits are controlled by :rc:`axes.formatter.limits`.
In particular numbers with *exp* equal to the thresholds are
written in scientific notation.
Typically, *min_exp* will be negative and *max_exp* will be
positive.
For example, ``formatter.set_powerlimits((-3, 4))`` will provide
the following formatting:
:math:`1 \times 10^{-3}, 9.9 \times 10^{-3}, 0.01,`
:math:`9999, 1 \times 10^4`.
See Also
--------
ScalarFormatter.set_scientific
"""
if len(lims) != 2:
raise ValueError("'lims' must be a sequence of length 2")
self._powerlimits = lims
def format_data_short(self, value):
# docstring inherited
if value is np.ma.masked:
return ""
if isinstance(value, Integral):
fmt = "%d"
else:
if getattr(self.axis, "__name__", "") in ["xaxis", "yaxis"]:
if self.axis.__name__ == "xaxis":
axis_trf = self.axis.axes.get_xaxis_transform()
axis_inv_trf = axis_trf.inverted()
screen_xy = axis_trf.transform((value, 0))
neighbor_values = axis_inv_trf.transform(
screen_xy + [[-1, 0], [+1, 0]])[:, 0]
else: # yaxis:
axis_trf = self.axis.axes.get_yaxis_transform()
axis_inv_trf = axis_trf.inverted()
screen_xy = axis_trf.transform((0, value))
neighbor_values = axis_inv_trf.transform(
screen_xy + [[0, -1], [0, +1]])[:, 1]
delta = abs(neighbor_values - value).max()
else:
# Rough approximation: no more than 1e4 divisions.
a, b = self.axis.get_view_interval()
delta = (b - a) / 1e4
fmt = "%-#.{}g".format(cbook._g_sig_digits(value, delta))
return self._format_maybe_minus_and_locale(fmt, value)
def format_data(self, value):
# docstring inherited
e = math.floor(math.log10(abs(value)))
s = round(value / 10**e, 10)
exponent = self._format_maybe_minus_and_locale("%d", e)
significand = self._format_maybe_minus_and_locale(
"%d" if s % 1 == 0 else "%1.10g", s)
if e == 0:
return significand
elif self._useMathText or self._usetex:
exponent = "10^{%s}" % exponent
return (exponent if s == 1 # reformat 1x10^y as 10^y
else rf"{significand} \times {exponent}")
else:
return f"{significand}e{exponent}"
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 or self._usetex:
if sciNotStr != '':
sciNotStr = r'\times\mathdefault{%s}' % sciNotStr
s = r'$%s\mathdefault{%s}$' % (sciNotStr, offsetStr)
else:
s = ''.join((sciNotStr, offsetStr))
return self.fix_minus(s)
def set_locs(self, locs):
# docstring inherited
self.locs = locs
if len(self.locs) > 0:
if self._useOffset:
self._compute_offset()
self._set_order_of_magnitude()
self._set_format()
def _compute_offset(self):
locs = self.locs
# Restrict to visible ticks.
vmin, vmax = sorted(self.axis.get_view_interval())
locs = np.asarray(locs)
locs = locs[(vmin <= locs) & (locs <= vmax)]
if not len(locs):
self.offset = 0
return
lmin, lmax = locs.min(), locs.max()
# Only use offset if there are at least two ticks and every tick has
# the same sign.
if lmin == lmax or lmin <= 0 <= lmax:
self.offset = 0
return
# min, max comparing absolute values (we want division to round towards
# zero so we work on absolute values).
abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
sign = math.copysign(1, lmin)
# What is the smallest power of ten such that abs_min and abs_max are
# equal up to that precision?
# Note: Internally using oom instead of 10 ** oom avoids some numerical
# accuracy issues.
oom_max = np.ceil(math.log10(abs_max))
oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
if abs_min // 10 ** oom != abs_max // 10 ** oom)
if (abs_max - abs_min) / 10 ** oom <= 1e-2:
# Handle the case of straddling a multiple of a large power of ten
# (relative to the span).
# What is the smallest power of ten such that abs_min and abs_max
# are no more than 1 apart at that precision?
oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
if abs_max // 10 ** oom - abs_min // 10 ** oom > 1)
# Only use offset if it saves at least _offset_threshold digits.
n = self._offset_threshold - 1
self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
if abs_max // 10 ** oom >= 10**n
else 0)
def _set_order_of_magnitude(self):
# if scientific notation is to be used, find the appropriate exponent
# if using a numerical offset, find the exponent after applying the
# offset. When lower power limit = upper <> 0, use provided exponent.
if not self._scientific:
self.orderOfMagnitude = 0
return
if self._powerlimits[0] == self._powerlimits[1] != 0:
# fixed scaling when lower power limit = upper <> 0.
self.orderOfMagnitude = self._powerlimits[0]
return
# restrict to visible ticks
vmin, vmax = sorted(self.axis.get_view_interval())
locs = np.asarray(self.locs)
locs = locs[(vmin <= locs) & (locs <= vmax)]
locs = np.abs(locs)
if not len(locs):
self.orderOfMagnitude = 0
return
if self.offset:
oom = math.floor(math.log10(vmax - vmin))
else:
val = locs.max()
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
if len(self.locs) < 2:
# Temporarily augment the locations with the axis end points.
_locs = [*self.locs, *self.axis.get_view_interval()]
else:
_locs = self.locs
locs = (np.asarray(_locs) - self.offset) / 10. ** self.orderOfMagnitude
loc_range = np.ptp(locs)
# Curvilinear coordinates can yield two identical points.
if loc_range == 0:
loc_range = np.max(np.abs(locs))
# Both points might be zero.
if loc_range == 0:
loc_range = 1
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 = f'%1.{sigfigs}f'
if self._usetex or self._useMathText:
self.format = r'$\mathdefault{%s}$' % self.format
class LogFormatter(Formatter):
"""
Base class for formatting ticks on a log or symlog scale.
It may be instantiated directly, or subclassed.
Parameters
----------
base : float, default: 10.
Base of the logarithm used in all calculations.
labelOnlyBase : bool, default: False
If True, label ticks only at integer powers of base.
This is normally True for major ticks and False for
minor ticks.
minor_thresholds : (subset, all), default: (1, 0.4)
If labelOnlyBase is False, these two numbers control
the labeling of ticks that are not at integer powers of
base; normally these are the minor ticks. The controlling
parameter is the log of the axis data range. In the typical
case where base is 10 it is the number of decades spanned
by the axis, so we can call it 'numdec'. If ``numdec <= all``,
all minor ticks will be labeled. If ``all < numdec <= subset``,
then only a subset of minor ticks will be labeled, so as to
avoid crowding. If ``numdec > subset`` then no minor ticks will
be labeled.
linthresh : None or float, default: None
If a symmetric log scale is in use, its ``linthresh``
parameter must be supplied here.
Notes
-----
The `set_locs` method must be called to enable the subsetting
logic controlled by the ``minor_thresholds`` parameter.
In some cases such as the colorbar, there is no distinction between
major and minor ticks; the tick locations might be set manually,
or by a locator that puts ticks at integer powers of base and
at intermediate locations. For this situation, disable the
minor_thresholds logic by using ``minor_thresholds=(np.inf, np.inf)``,
so that all ticks will be labeled.
To disable labeling of minor ticks when 'labelOnlyBase' is False,
use ``minor_thresholds=(0, 0)``. This is the default for the
"classic" style.
Examples
--------
To label a subset of minor ticks when the view limits span up
to 2 decades, and all of the ticks when zoomed in to 0.5 decades
or less, use ``minor_thresholds=(2, 0.5)``.
To label all minor ticks when the view limits span up to 1.5
decades, use ``minor_thresholds=(1.5, 1.5)``.
"""
def __init__(self, base=10.0, labelOnlyBase=False,
minor_thresholds=None,
linthresh=None):
self.set_base(base)
self.set_label_minor(labelOnlyBase)
if minor_thresholds is None:
if mpl.rcParams['_internal.classic_mode']:
minor_thresholds = (0, 0)
else:
minor_thresholds = (1, 0.4)
self.minor_thresholds = minor_thresholds
self._sublabels = None
self._linthresh = linthresh
@_api.deprecated("3.6", alternative='set_base()')
def base(self, base):
"""
Change the *base* for labeling.
.. warning::
Should always match the base used for :class:`LogLocator`
"""
self.set_base(base)
def set_base(self, base):
"""
Change the *base* for labeling.
.. warning::
Should always match the base used for :class:`LogLocator`
"""
self._base = float(base)
@_api.deprecated("3.6", alternative='set_label_minor()')
def label_minor(self, labelOnlyBase):
"""
Switch minor tick labeling on or off.
Parameters
----------
labelOnlyBase : bool
If True, label ticks only at integer powers of base.
"""
self.set_label_minor(labelOnlyBase)
def set_label_minor(self, labelOnlyBase):
"""
Switch minor tick labeling on or off.
Parameters
----------
labelOnlyBase : bool
If True, label ticks only at integer powers of base.
"""
self.labelOnlyBase = labelOnlyBase
def set_locs(self, locs=None):
"""
Use axis view limits to control which ticks are labeled.
The *locs* parameter is ignored in the present algorithm.
"""
if np.isinf(self.minor_thresholds[0]):
self._sublabels = None
return
# Handle symlog case:
linthresh = self._linthresh
if linthresh is None:
try:
linthresh = self.axis.get_transform().linthresh
except AttributeError:
pass
vmin, vmax = self.axis.get_view_interval()
if vmin > vmax:
vmin, vmax = vmax, vmin
if linthresh is None and vmin <= 0:
# It's probably a colorbar with
# a format kwarg setting a LogFormatter in the manner
# that worked with 1.5.x, but that doesn't work now.
self._sublabels = {1} # label powers of base
return
b = self._base
if linthresh is not None: # symlog
# Only compute the number of decades in the logarithmic part of the
# axis
numdec = 0
if vmin < -linthresh:
rhs = min(vmax, -linthresh)
numdec += math.log(vmin / rhs) / math.log(b)
if vmax > linthresh:
lhs = max(vmin, linthresh)
numdec += math.log(vmax / lhs) / math.log(b)
else:
vmin = math.log(vmin) / math.log(b)
vmax = math.log(vmax) / math.log(b)
numdec = abs(vmax - vmin)
if numdec > self.minor_thresholds[0]:
# Label only bases
self._sublabels = {1}
elif numdec > self.minor_thresholds[1]:
# Add labels between bases at log-spaced coefficients;
# include base powers in case the locations include
# "major" and "minor" points, as in colorbar.
c = np.geomspace(1, b, int(b)//2 + 1)
self._sublabels = set(np.round(c))
# For base 10, this yields (1, 2, 3, 4, 6, 10).
else:
# Label all integer multiples of base**n.
self._sublabels = set(np.arange(1, b + 1))
def _num_to_string(self, x, vmin, vmax):
if x > 10000:
s = '%1.0e' % x
elif x < 1:
s = '%1.0e' % x
else:
s = self._pprint_val(x, vmax - vmin)
return s
def __call__(self, x, pos=None):
# docstring inherited
if x == 0.0: # Symlog
return '0'
x = abs(x)
b = self._base
# only label the decades
fx = math.log(x) / math.log(b)
is_x_decade = _is_close_to_int(fx)
exponent = round(fx) if is_x_decade else np.floor(fx)
coeff = round(b ** (fx - exponent))
if self.labelOnlyBase and not is_x_decade:
return ''
if self._sublabels is not None and coeff not in self._sublabels:
return ''
vmin, vmax = self.axis.get_view_interval()
vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=0.05)
s = self._num_to_string(x, vmin, vmax)
return self.fix_minus(s)
def format_data(self, value):
with cbook._setattr_cm(self, labelOnlyBase=False):
return cbook.strip_math(self.__call__(value))
def format_data_short(self, value):
# docstring inherited
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
fmt = ('%1.3e' if d < 1e-2 else
'%1.3f' if d <= 1 else
'%1.2f' if d <= 10 else
'%1.1f' if d <= 1e5 else
'%1.1e')
s = fmt % x
tup = s.split('e')
if len(tup) == 2:
mantissa = tup[0].rstrip('0').rstrip('.')
exponent = int(tup[1])
if exponent:
s = '%se%d' % (mantissa, exponent)
else:
s = mantissa
else:
s = s.rstrip('0').rstrip('.')
return s
class LogFormatterExponent(LogFormatter):
"""
Format values for log axis using ``exponent = log_base(value)``.
"""
def _num_to_string(self, x, vmin, vmax):
fx = math.log(x) / math.log(self._base)
if abs(fx) > 10000:
s = '%1.0g' % fx
elif abs(fx) < 1:
s = '%1.0g' % fx
else:
fd = math.log(vmax - vmin) / math.log(self._base)
s = self._pprint_val(fx, fd)
return s
class LogFormatterMathtext(LogFormatter):
"""
Format values for log axis using ``exponent = log_base(value)``.
"""
def _non_decade_format(self, sign_string, base, fx, usetex):
"""Return string for non-decade locations."""
return r'$\mathdefault{%s%s^{%.2f}}$' % (sign_string, base, fx)
def __call__(self, x, pos=None):
# docstring inherited
usetex = mpl.rcParams['text.usetex']
min_exp = mpl.rcParams['axes.formatter.min_exponent']
if x == 0: # Symlog
return r'$\mathdefault{0}$'
sign_string = '-' if x < 0 else ''
x = abs(x)
b = self._base
# only label the decades
fx = math.log(x) / math.log(b)
is_x_decade = _is_close_to_int(fx)
exponent = round(fx) if is_x_decade else np.floor(fx)
coeff = round(b ** (fx - exponent))
if is_x_decade:
fx = round(fx)
if self.labelOnlyBase and not is_x_decade:
return ''
if self._sublabels is not None and coeff not in self._sublabels:
return ''
# 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 abs(fx) < min_exp:
return r'$\mathdefault{%s%g}$' % (sign_string, x)
elif not is_x_decade:
return self._non_decade_format(sign_string, base, fx, usetex)
else:
return r'$\mathdefault{%s%s^{%d}}$' % (sign_string, base, fx)
class LogFormatterSciNotation(LogFormatterMathtext):
"""
Format values following scientific notation in a logarithmic axis.
"""
def _non_decade_format(self, sign_string, base, fx, usetex):
"""Return string for non-decade locations."""
b = float(base)
exponent = math.floor(fx)
coeff = b ** (fx - exponent)
if _is_close_to_int(coeff):
coeff = round(coeff)
return r'$\mathdefault{%s%g\times%s^{%d}}$' \
% (sign_string, coeff, base, exponent)
class LogitFormatter(Formatter):
"""
Probability formatter (using Math text).
"""
def __init__(
self,
*,
use_overline=False,
one_half=r"\frac{1}{2}",
minor=False,
minor_threshold=25,
minor_number=6,
):
r"""
Parameters
----------
use_overline : bool, default: False
If x > 1/2, with x = 1-v, indicate if x should be displayed as
$\overline{v}$. The default is to display $1-v$.
one_half : str, default: r"\frac{1}{2}"
The string used to represent 1/2.
minor : bool, default: False
Indicate if the formatter is formatting minor ticks or not.
Basically minor ticks are not labelled, except when only few ticks
are provided, ticks with most space with neighbor ticks are
labelled. See other parameters to change the default behavior.
minor_threshold : int, default: 25
Maximum number of locs for labelling some minor ticks. This
parameter have no effect if minor is False.
minor_number : int, default: 6
Number of ticks which are labelled when the number of ticks is
below the threshold.
"""
self._use_overline = use_overline
self._one_half = one_half
self._minor = minor
self._labelled = set()
self._minor_threshold = minor_threshold
self._minor_number = minor_number
def use_overline(self, use_overline):
r"""
Switch display mode with overline for labelling p>1/2.
Parameters
----------
use_overline : bool, default: False
If x > 1/2, with x = 1-v, indicate if x should be displayed as
$\overline{v}$. The default is to display $1-v$.
"""
self._use_overline = use_overline
def set_one_half(self, one_half):
r"""
Set the way one half is displayed.
one_half : str, default: r"\frac{1}{2}"
The string used to represent 1/2.
"""
self._one_half = one_half
def set_minor_threshold(self, minor_threshold):
"""
Set the threshold for labelling minors ticks.
Parameters
----------
minor_threshold : int
Maximum number of locations for labelling some minor ticks. This
parameter have no effect if minor is False.
"""
self._minor_threshold = minor_threshold
def set_minor_number(self, minor_number):
"""
Set the number of minor ticks to label when some minor ticks are
labelled.
Parameters
----------
minor_number : int
Number of ticks which are labelled when the number of ticks is
below the threshold.
"""
self._minor_number = minor_number
def set_locs(self, locs):
self.locs = np.array(locs)
self._labelled.clear()
if not self._minor:
return None
if all(
_is_decade(x, rtol=1e-7)
or _is_decade(1 - x, rtol=1e-7)
or (_is_close_to_int(2 * x) and
int(np.round(2 * x)) == 1)
for x in locs
):
# minor ticks are subsample from ideal, so no label
return None
if len(locs) < self._minor_threshold:
if len(locs) < self._minor_number:
self._labelled.update(locs)
else:
# we do not have a lot of minor ticks, so only few decades are
# displayed, then we choose some (spaced) minor ticks to label.
# Only minor ticks are known, we assume it is sufficient to
# choice which ticks are displayed.
# For each ticks we compute the distance between the ticks and
# the previous, and between the ticks and the next one. Ticks
# with smallest minimum are chosen. As tiebreak, the ticks
# with smallest sum is chosen.
diff = np.diff(-np.log(1 / self.locs - 1))
space_pessimistic = np.minimum(
np.concatenate(((np.inf,), diff)),
np.concatenate((diff, (np.inf,))),
)
space_sum = (
np.concatenate(((0,), diff))
+ np.concatenate((diff, (0,)))
)
good_minor = sorted(
range(len(self.locs)),
key=lambda i: (space_pessimistic[i], space_sum[i]),
)[-self._minor_number:]
self._labelled.update(locs[i] for i in good_minor)
def _format_value(self, x, locs, sci_notation=True):
if sci_notation:
exponent = math.floor(np.log10(x))
min_precision = 0
else:
exponent = 0
min_precision = 1
value = x * 10 ** (-exponent)
if len(locs) < 2:
precision = min_precision
else:
diff = np.sort(np.abs(locs - x))[1]
precision = -np.log10(diff) + exponent
precision = (
int(np.round(precision))
if _is_close_to_int(precision)
else math.ceil(precision)
)
if precision < min_precision:
precision = min_precision
mantissa = r"%.*f" % (precision, value)
if not sci_notation:
return mantissa
s = r"%s\cdot10^{%d}" % (mantissa, exponent)
return s
def _one_minus(self, s):
if self._use_overline:
return r"\overline{%s}" % s
else:
return "1-{}".format(s)
def __call__(self, x, pos=None):
if self._minor and x not in self._labelled:
return ""
if x <= 0 or x >= 1:
return ""
if _is_close_to_int(2 * x) and round(2 * x) == 1:
s = self._one_half
elif x < 0.5 and _is_decade(x, rtol=1e-7):
exponent = round(math.log10(x))
s = "10^{%d}" % exponent
elif x > 0.5 and _is_decade(1 - x, rtol=1e-7):
exponent = round(math.log10(1 - x))
s = self._one_minus("10^{%d}" % exponent)
elif x < 0.1:
s = self._format_value(x, self.locs)
elif x > 0.9:
s = self._one_minus(self._format_value(1-x, 1-self.locs))
else:
s = self._format_value(x, self.locs, sci_notation=False)
return r"$\mathdefault{%s}$" % s
def format_data_short(self, value):
# docstring inherited
# Thresholds chosen to use scientific notation iff exponent <= -2.
if value < 0.1:
return "{:e}".format(value)
if value < 0.9:
return "{:f}".format(value)
return "1-{:e}".format(1 - value)
class EngFormatter(Formatter):
"""
Format axis values using engineering prefixes to represent powers
of 1000, plus a specified unit, e.g., 10 MHz instead of 1e7.
"""
# The SI engineering prefixes
ENG_PREFIXES = {
-24: "y",
-21: "z",
-18: "a",
-15: "f",
-12: "p",
-9: "n",
-6: "\N{MICRO SIGN}",
-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, sep=" ", *, usetex=None,
useMathText=None):
r"""
Parameters
----------
unit : str, default: ""
Unit symbol to use, suitable for use with single-letter
representations of powers of 1000. For example, 'Hz' or 'm'.
places : int, default: None
Precision with which to display the number, specified in
digits after the decimal point (there will be between one
and three digits before the decimal point). If it is None,
the formatting falls back to the floating point format '%g',
which displays up to 6 *significant* digits, i.e. the equivalent
value for *places* varies between 0 and 5 (inclusive).
sep : str, default: " "
Separator used between the value and the prefix/unit. For
example, one get '3.14 mV' if ``sep`` is " " (default) and
'3.14mV' if ``sep`` is "". Besides the default behavior, some
other useful options may be:
* ``sep=""`` to append directly the prefix/unit to the value;
* ``sep="\N{THIN SPACE}"`` (``U+2009``);
* ``sep="\N{NARROW NO-BREAK SPACE}"`` (``U+202F``);
* ``sep="\N{NO-BREAK SPACE}"`` (``U+00A0``).
usetex : bool, default: :rc:`text.usetex`
To enable/disable the use of TeX's math mode for rendering the
numbers in the formatter.
useMathText : bool, default: :rc:`axes.formatter.use_mathtext`
To enable/disable the use mathtext for rendering the numbers in
the formatter.
"""
self.unit = unit
self.places = places
self.sep = sep
self.set_usetex(usetex)
self.set_useMathText(useMathText)
def get_usetex(self):
return self._usetex
def set_usetex(self, val):
if val is None:
self._usetex = mpl.rcParams['text.usetex']
else:
self._usetex = val
usetex = property(fget=get_usetex, fset=set_usetex)
def get_useMathText(self):
return self._useMathText
def set_useMathText(self, val):
if val is None:
self._useMathText = mpl.rcParams['axes.formatter.use_mathtext']
else:
self._useMathText = val
useMathText = property(fget=get_useMathText, fset=set_useMathText)
def __call__(self, x, pos=None):
s = "%s%s" % (self.format_eng(x), self.unit)
# Remove the trailing separator when there is neither prefix nor unit
if self.sep and s.endswith(self.sep):
s = s[:-len(self.sep)]
return self.fix_minus(s)
def format_eng(self, num):
"""
Format 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
'-1.00 \N{MICRO SIGN}'
"""
sign = 1
fmt = "g" if self.places is None else ".{:d}f".format(self.places)
if num < 0:
sign = -1
num = -num
if num != 0:
pow10 = int(math.floor(math.log10(num) / 3) * 3)
else:
pow10 = 0
# Force num to zero, to avoid inconsistencies like
# format_eng(-0) = "0" and format_eng(0.0) = "0"
# but format_eng(-0.0) = "-0.0"
num = 0.0
pow10 = np.clip(pow10, min(self.ENG_PREFIXES), max(self.ENG_PREFIXES))
mant = sign * num / (10.0 ** pow10)
# Taking care of the cases like 999.9..., which may be rounded to 1000
# instead of 1 k. Beware of the corner case of values that are beyond
# the range of SI prefixes (i.e. > 'Y').
if (abs(float(format(mant, fmt))) >= 1000
and pow10 < max(self.ENG_PREFIXES)):
mant /= 1000
pow10 += 3
prefix = self.ENG_PREFIXES[int(pow10)]
if self._usetex or self._useMathText:
formatted = "${mant:{fmt}}${sep}{prefix}".format(
mant=mant, sep=self.sep, prefix=prefix, fmt=fmt)
else:
formatted = "{mant:{fmt}}{sep}{prefix}".format(
mant=mant, sep=self.sep, prefix=prefix, fmt=fmt)
return formatted
class PercentFormatter(Formatter):
"""
Format numbers as a percentage.
Parameters
----------
xmax : float
Determines how the number is converted into a percentage.
*xmax* is the data value that corresponds to 100%.
Percentages are computed as ``x / xmax * 100``. So if the data is
already scaled to be percentages, *xmax* will be 100. Another common
situation is where *xmax* is 1.0.
decimals : None or int
The number of decimal places to place after the point.
If *None* (the default), the number will be computed automatically.
symbol : str or None
A string that will be appended to the label. It may be
*None* or empty to indicate that no symbol should be used. LaTeX
special characters are escaped in *symbol* whenever latex mode is
enabled, unless *is_latex* is *True*.
is_latex : bool
If *False*, reserved LaTeX characters in *symbol* will be escaped.
"""
def __init__(self, xmax=100, decimals=None, symbol='%', is_latex=False):
self.xmax = xmax + 0.0
self.decimals = decimals
self._symbol = symbol
self._is_latex = is_latex
def __call__(self, x, pos=None):
"""Format the tick as a percentage with the appropriate scaling."""
ax_min, ax_max = self.axis.get_view_interval()
display_range = abs(ax_max - ax_min)
return self.fix_minus(self.format_pct(x, display_range))
def format_pct(self, x, display_range):
"""
Format the number as a percentage number with the correct
number of decimals and adds the percent symbol, if any.
If ``self.decimals`` is `None`, the number of digits after the
decimal point is set based on the *display_range* of the axis
as follows:
============= ======== =======================
display_range decimals sample
============= ======== =======================
>50 0 ``x = 34.5`` => 35%
>5 1 ``x = 34.5`` => 34.5%
>0.5 2 ``x = 34.5`` => 34.50%
... ... ...
============= ======== =======================
This method will not be very good for tiny axis ranges or
extremely large ones. It assumes that the values on the chart
are percentages displayed on a reasonable scale.
"""
x = self.convert_to_pct(x)
if self.decimals is None:
# conversion works because display_range is a difference
scaled_range = self.convert_to_pct(display_range)
if scaled_range <= 0:
decimals = 0
else:
# Luckily Python's built-in ceil rounds to +inf, not away from
# zero. This is very important since the equation for decimals
# starts out as `scaled_range > 0.5 * 10**(2 - decimals)`
# and ends up with `decimals > 2 - log10(2 * scaled_range)`.
decimals = math.ceil(2.0 - math.log10(2.0 * scaled_range))
if decimals > 5:
decimals = 5
elif decimals < 0:
decimals = 0
else:
decimals = self.decimals
s = '{x:0.{decimals}f}'.format(x=x, decimals=int(decimals))
return s + self.symbol
def convert_to_pct(self, x):
return 100.0 * (x / self.xmax)
@property
def symbol(self):
r"""
The configured percent symbol as a string.
If LaTeX is enabled via :rc:`text.usetex`, the special characters
``{'#', '$', '%', '&', '~', '_', '^', '\', '{', '}'}`` are
automatically escaped in the string.
"""
symbol = self._symbol
if not symbol:
symbol = ''
elif mpl.rcParams['text.usetex'] and not self._is_latex:
# Source: http://www.personal.ceu.hu/tex/specchar.htm
# Backslash must be first for this to work correctly since
# it keeps getting added in
for spec in r'\#$%&~_^{}':
symbol = symbol.replace(spec, '\\' + spec)
return symbol
@symbol.setter
def symbol(self, symbol):
self._symbol = symbol
class Locator(TickHelper):
"""
Determine the tick locations;
Note that the same locator should not be used across multiple
`~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.
# 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 ``axis`` simply call
the Locator instance::
>>> print(type(loc))
<type 'Locator'>
>>> print(loc())
[1, 2, 3, 4]
"""
raise NotImplementedError('Derived must override')
def set_params(self, **kwargs):
"""
Do nothing, and raise a warning. Any locator class not supporting the
set_params() function will call this.
"""
_api.warn_external(
"'set_params()' not defined for locator of type " +
str(type(self)))
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):
"""
Log at WARNING level if *locs* is longer than `Locator.MAXTICKS`.
This is intended to be called immediately before returning *locs* from
``__call__`` to inform users in case their Locator returns a huge
number of ticks, causing Matplotlib to run out of memory.
The "strange" name of this method dates back to when it would raise an
exception instead of emitting a log.
"""
if len(locs) >= self.MAXTICKS:
_log.warning(
"Locator attempting to generate %s ticks ([%s, ..., %s]), "
"which exceeds Locator.MAXTICKS (%s).",
len(locs), locs[0], locs[-1], self.MAXTICKS)
return locs
def nonsingular(self, v0, v1):
"""
Adjust a range as needed to avoid singularities.
This method gets called during autoscaling, with ``(v0, v1)`` set to
the data limits on the axes if the axes contains any data, or
``(-inf, +inf)`` if not.
- If ``v0 == v1`` (possibly up to some floating point slop), this
method returns an expanded interval around this value.
- If ``(v0, v1) == (-inf, +inf)``, this method returns appropriate
default view limits.
- Otherwise, ``(v0, v1)`` is returned without modification.
"""
return mtransforms.nonsingular(v0, v1, expander=.05)
def view_limits(self, vmin, vmax):
"""
Select a scale for the range from vmin to vmax.
Subclasses should override this method to change locator behaviour.
"""
return mtransforms.nonsingular(vmin, vmax)
class IndexLocator(Locator):
"""
Place a tick on every multiple of some base number of points
plotted, e.g., on every 5th point. It is assumed that you are doing
index plotting; i.e., the axis is 0, len(data). This is mainly
useful for x ticks.
"""
def __init__(self, base, offset):
"""Place ticks every *base* data point, starting at *offset*."""
self._base = base
self.offset = offset
def set_params(self, base=None, offset=None):
"""Set parameters within this locator"""
if base is not None:
self._base = base
if offset is not None:
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 at *locs*. If *nbins* is not None,
the *locs* array of possible positions will be subsampled to
keep the number of ticks <= *nbins* +1.
The subsampling will be done 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)
_api.check_shape((None,), locs=self.locs)
self.nbins = max(nbins, 2) if nbins is not None else None
def set_params(self, nbins=None):
"""Set parameters within this locator."""
if nbins is not None:
self.nbins = nbins
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(np.ceil(len(self.locs) / self.nbins)), 1)
ticks = self.locs[::step]
for i in range(1, step):
ticks1 = self.locs[i::step]
if np.abs(ticks1).min() < np.abs(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):
"""
Parameters
----------
numticks : int or None, default None
Number of ticks. If None, *numticks* = 11.
presets : dict or None, default: None
Dictionary mapping ``(vmin, vmax)`` to an array of locations.
Overrides *numticks* if there is an entry for the current
``(vmin, vmax)``.
"""
self.numticks = numticks
if presets is None:
self.presets = {}
else:
self.presets = presets
@property
def numticks(self):
# Old hard-coded default.
return self._numticks if self._numticks is not None else 11
@numticks.setter
def numticks(self, numticks):
self._numticks = numticks
def set_params(self, numticks=None, presets=None):
"""Set parameters within this locator."""
if presets is not None:
self.presets = presets
if numticks is not None:
self.numticks = numticks
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 == 0:
return []
ticklocs = np.linspace(vmin, vmax, self.numticks)
return self.raise_if_exceeds(ticklocs)
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
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
exponent, remainder = divmod(
math.log10(vmax - vmin), math.log10(max(self.numticks - 1, 1)))
exponent -= (remainder < .5)
scale = max(self.numticks - 1, 1) ** (-exponent)
vmin = math.floor(scale * vmin) / scale
vmax = math.ceil(scale * vmax) / scale
return mtransforms.nonsingular(vmin, vmax)
class MultipleLocator(Locator):
"""
Set a tick on each integer multiple of the *base* within the view
interval.
"""
def __init__(self, base=1.0):
self._edge = _Edge_integer(base, 0)
def set_params(self, base):
"""Set parameters within this locator."""
if base is not None:
self._edge = _Edge_integer(base, 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):
if vmax < vmin:
vmin, vmax = vmax, vmin
step = self._edge.step
vmin = self._edge.ge(vmin) * step
n = (vmax - vmin + 0.001 * step) // step
locs = vmin - step + np.arange(n + 3) * step
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.
"""
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
vmin = self._edge.le(dmin) * self._edge.step
vmax = self._edge.ge(dmax) * self._edge.step
if vmin == vmax:
vmin -= 1
vmax += 1
else:
vmin = dmin
vmax = dmax
return mtransforms.nonsingular(vmin, vmax)
def scale_range(vmin, vmax, n=1, threshold=100):
dv = abs(vmax - vmin) # > 0 as nonsingular is called before.
meanv = (vmax + vmin) / 2
if abs(meanv) / dv < threshold:
offset = 0
else:
offset = math.copysign(10 ** (math.log10(abs(meanv)) // 1), meanv)
scale = 10 ** (math.log10(dv / n) // 1)
return scale, offset
class _Edge_integer:
"""
Helper for `.MaxNLocator`, `.MultipleLocator`, etc.
Take floating-point precision limitations into account when calculating
tick locations as integer multiples of a step.
"""
def __init__(self, step, offset):
"""
Parameters
----------
step : float > 0
Interval between ticks.
offset : float
Offset subtracted from the data limits prior to calculating tick
locations.
"""
if step <= 0:
raise ValueError("'step' must be positive")
self.step = step
self._offset = abs(offset)
def closeto(self, ms, edge):
# Allow more slop when the offset is large compared to the step.
if self._offset > 0:
digits = np.log10(self._offset / self.step)
tol = max(1e-10, 10 ** (digits - 12))
tol = min(0.4999, tol)
else:
tol = 1e-10
return abs(ms - edge) < tol
def le(self, x):
"""Return the largest n: n*step <= x."""
d, m = divmod(x, self.step)
if self.closeto(m / self.step, 1):
return d + 1
return d
def ge(self, x):
"""Return the smallest n: n*step >= x."""
d, m = divmod(x, self.step)
if self.closeto(m / self.step, 0):
return d
return d + 1
class MaxNLocator(Locator):
"""
Find nice tick locations with no more than *nbins* + 1 being within the
view limits. Locations beyond the limits are added to support autoscaling.
"""
default_params = dict(nbins=10,
steps=None,
integer=False,
symmetric=False,
prune=None,
min_n_ticks=2)
def __init__(self, nbins=None, **kwargs):
"""
Parameters
----------
nbins : int or 'auto', default: 10
Maximum number of intervals; one less than max number of
ticks. If the string 'auto', the number of bins will be
automatically determined based on the length of the axis.
steps : array-like, optional
Sequence of nice numbers starting with 1 and ending with 10;
e.g., [1, 2, 4, 5, 10], where the values are acceptable
tick multiples. i.e. for the example, 20, 40, 60 would be
an acceptable set of ticks, as would 0.4, 0.6, 0.8, because
they are multiples of 2. However, 30, 60, 90 would not
be allowed because 3 does not appear in the list of steps.
integer : bool, default: False
If True, ticks will take only integer values, provided at least
*min_n_ticks* integers are found within the view limits.
symmetric : bool, default: False
If True, autoscaling will result in a range symmetric about zero.
prune : {'lower', 'upper', 'both', None}, default: 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, primarily when :rc:`axes.autolimit_mode` is
``'round_numbers'``. 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* is *None*, no ticks will be removed.
min_n_ticks : int, default: 2
Relax *nbins* and *integer* constraints if necessary to obtain
this minimum number of ticks.
"""
if nbins is not None:
kwargs['nbins'] = nbins
self.set_params(**{**self.default_params, **kwargs})
@staticmethod
def _validate_steps(steps):
if not np.iterable(steps):
raise ValueError('steps argument must be an increasing sequence '
'of numbers between 1 and 10 inclusive')
steps = np.asarray(steps)
if np.any(np.diff(steps) <= 0) or steps[-1] > 10 or steps[0] < 1:
raise ValueError('steps argument must be an increasing sequence '
'of numbers between 1 and 10 inclusive')
if steps[0] != 1:
steps = np.concatenate([[1], steps])
if steps[-1] != 10:
steps = np.concatenate([steps, [10]])
return steps
@staticmethod
def _staircase(steps):
# Make an extended staircase within which the needed step will be
# found. This is probably much larger than necessary.
return np.concatenate([0.1 * steps[:-1], steps, [10 * steps[1]]])
def set_params(self, **kwargs):
"""
Set parameters for this locator.
Parameters
----------
nbins : int or 'auto', optional
see `.MaxNLocator`
steps : array-like, optional
see `.MaxNLocator`
integer : bool, optional
see `.MaxNLocator`
symmetric : bool, optional
see `.MaxNLocator`
prune : {'lower', 'upper', 'both', None}, optional
see `.MaxNLocator`
min_n_ticks : int, optional
see `.MaxNLocator`
"""
if 'nbins' in kwargs:
self._nbins = kwargs.pop('nbins')
if self._nbins != 'auto':
self._nbins = int(self._nbins)
if 'symmetric' in kwargs:
self._symmetric = kwargs.pop('symmetric')
if 'prune' in kwargs:
prune = kwargs.pop('prune')
_api.check_in_list(['upper', 'lower', 'both', None], prune=prune)
self._prune = prune
if 'min_n_ticks' in kwargs:
self._min_n_ticks = max(1, kwargs.pop('min_n_ticks'))
if 'steps' in kwargs:
steps = kwargs.pop('steps')
if steps is None:
self._steps = np.array([1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10])
else:
self._steps = self._validate_steps(steps)
self._extended_steps = self._staircase(self._steps)
if 'integer' in kwargs:
self._integer = kwargs.pop('integer')
if kwargs:
raise _api.kwarg_error("set_params", kwargs)
def _raw_ticks(self, vmin, vmax):
"""
Generate a list of tick locations including the range *vmin* to
*vmax*. In some applications, one or both of the end locations
will not be needed, in which case they are trimmed off
elsewhere.
"""
if self._nbins == 'auto':
if self.axis is not None:
nbins = np.clip(self.axis.get_tick_space(),
max(1, self._min_n_ticks - 1), 9)
else:
nbins = 9
else:
nbins = self._nbins
scale, offset = scale_range(vmin, vmax, nbins)
_vmin = vmin - offset
_vmax = vmax - offset
raw_step = (_vmax - _vmin) / nbins
steps = self._extended_steps * scale
if self._integer:
# For steps > 1, keep only integer values.
igood = (steps < 1) | (np.abs(steps - np.round(steps)) < 0.001)
steps = steps[igood]
istep = np.nonzero(steps >= raw_step)[0][0]
# Classic round_numbers mode may require a larger step.
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
for istep in range(istep, len(steps)):
step = steps[istep]
best_vmin = (_vmin // step) * step
best_vmax = best_vmin + step * nbins
if best_vmax >= _vmax:
break
# This is an upper limit; move to smaller steps if necessary.
for istep in reversed(range(istep + 1)):
step = steps[istep]
if (self._integer and
np.floor(_vmax) - np.ceil(_vmin) >= self._min_n_ticks - 1):
step = max(1, step)
best_vmin = (_vmin // step) * step
# Find tick locations spanning the vmin-vmax range, taking into
# account degradation of precision when there is a large offset.
# The edge ticks beyond vmin and/or vmax are needed for the
# "round_numbers" autolimit mode.
edge = _Edge_integer(step, offset)
low = edge.le(_vmin - best_vmin)
high = edge.ge(_vmax - best_vmin)
ticks = np.arange(low, high + 1) * step + best_vmin
# Count only the ticks that will be displayed.
nticks = ((ticks <= _vmax) & (ticks >= _vmin)).sum()
if nticks >= self._min_n_ticks:
break
return ticks + offset
def __call__(self):
vmin, vmax = self.axis.get_view_interval()
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
if self._symmetric:
vmax = max(abs(vmin), abs(vmax))
vmin = -vmax
vmin, vmax = mtransforms.nonsingular(
vmin, vmax, expander=1e-13, tiny=1e-14)
locs = self._raw_ticks(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:
dmax = max(abs(dmin), abs(dmax))
dmin = -dmax
dmin, dmax = mtransforms.nonsingular(
dmin, dmax, expander=1e-12, tiny=1e-13)
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
return self._raw_ticks(dmin, dmax)[[0, -1]]
else:
return dmin, dmax
@_api.deprecated("3.6")
def is_decade(x, base=10, *, rtol=1e-10):
if not np.isfinite(x):
return False
if x == 0.0:
return True
lx = np.log(abs(x)) / np.log(base)
return is_close_to_int(lx, atol=rtol)
def _is_decade(x, *, base=10, rtol=None):
"""Return True if *x* is an integer power of *base*."""
if not np.isfinite(x):
return False
if x == 0.0:
return True
lx = np.log(abs(x)) / np.log(base)
if rtol is None:
return np.isclose(lx, np.round(lx))
else:
return np.isclose(lx, np.round(lx), rtol=rtol)
def _decade_less_equal(x, base):
"""
Return the largest integer power of *base* that's less or equal to *x*.
If *x* is negative, the exponent will be *greater*.
"""
return (x if x == 0 else
-_decade_greater_equal(-x, base) if x < 0 else
base ** np.floor(np.log(x) / np.log(base)))
def _decade_greater_equal(x, base):
"""
Return the smallest integer power of *base* that's greater or equal to *x*.
If *x* is negative, the exponent will be *smaller*.
"""
return (x if x == 0 else
-_decade_less_equal(-x, base) if x < 0 else
base ** np.ceil(np.log(x) / np.log(base)))
def _decade_less(x, base):
"""
Return the largest integer power of *base* that's less than *x*.
If *x* is negative, the exponent will be *greater*.
"""
if x < 0:
return -_decade_greater(-x, base)
less = _decade_less_equal(x, base)
if less == x:
less /= base
return less
def _decade_greater(x, base):
"""
Return the smallest integer power of *base* that's greater than *x*.
If *x* is negative, the exponent will be *smaller*.
"""
if x < 0:
return -_decade_less(-x, base)
greater = _decade_greater_equal(x, base)
if greater == x:
greater *= base
return greater
@_api.deprecated("3.6")
def is_close_to_int(x, *, atol=1e-10):
return abs(x - np.round(x)) < atol
def _is_close_to_int(x):
return math.isclose(x, round(x))
class LogLocator(Locator):
"""
Determine the tick locations for log axes.
Place ticks on the locations : ``subs[j] * base**i``
Parameters
----------
base : float, default: 10.0
The base of the log used, so major ticks are placed at
``base**n``, where ``n`` is an integer.
subs : None or {'auto', 'all'} or sequence of float, default: (1.0,)
Gives the multiples of integer powers of the base at which
to place ticks. The default of ``(1.0, )`` places ticks only at
integer powers of the base.
Permitted string values are ``'auto'`` and ``'all'``.
Both of these use an algorithm based on the axis view
limits to determine whether and how to put ticks between
integer powers of the base. With ``'auto'``, ticks are
placed only between integer powers; with ``'all'``, the
integer powers are included. A value of None is
equivalent to ``'auto'``.
numticks : None or int, default: None
The maximum number of ticks to allow on a given axis. The default
of ``None`` will try to choose intelligently as long as this
Locator has already been assigned to an axis using
`~.axis.Axis.get_tick_space`, but otherwise falls back to 9.
"""
def __init__(self, base=10.0, subs=(1.0,), numdecs=4, numticks=None):
"""Place ticks on the locations : subs[j] * base**i."""
if numticks is None:
if mpl.rcParams['_internal.classic_mode']:
numticks = 15
else:
numticks = 'auto'
self._base = float(base)
self._set_subs(subs)
self.numdecs = numdecs
self.numticks = numticks
def set_params(self, base=None, subs=None, numdecs=None, numticks=None):
"""Set parameters within this locator."""
if base is not None:
self._base = float(base)
if subs is not None:
self._set_subs(subs)
if numdecs is not None:
self.numdecs = numdecs
if numticks is not None:
self.numticks = numticks
@_api.deprecated("3.6", alternative='set_params(base=...)')
def base(self, base):
"""Set the log base (major tick every ``base**i``, i integer)."""
self._base = float(base)
@_api.deprecated("3.6", alternative='set_params(subs=...)')
def subs(self, subs):
"""
Set the minor ticks for the log scaling every ``base**i*subs[j]``.
"""
self._set_subs(subs)
def _set_subs(self, subs):
"""
Set the minor ticks for the log scaling every ``base**i*subs[j]``.
"""
if subs is None: # consistency with previous bad API
self._subs = 'auto'
elif isinstance(subs, str):
_api.check_in_list(('all', 'auto'), subs=subs)
self._subs = subs
else:
try:
self._subs = np.asarray(subs, dtype=float)
except ValueError as e:
raise ValueError("subs must be None, 'all', 'auto' or "
"a sequence of floats, not "
"{}.".format(subs)) from e
if self._subs.ndim != 1:
raise ValueError("A sequence passed to subs must be "
"1-dimensional, not "
"{}-dimensional.".format(self._subs.ndim))
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 self.numticks == 'auto':
if self.axis is not None:
numticks = np.clip(self.axis.get_tick_space(), 2, 9)
else:
numticks = 9
else:
numticks = self.numticks
b = self._base
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.")
_log.debug('vmin %s vmax %s', vmin, vmax)
if vmax < vmin:
vmin, vmax = vmax, vmin
log_vmin = math.log(vmin) / math.log(b)
log_vmax = math.log(vmax) / math.log(b)
numdec = math.floor(log_vmax) - math.ceil(log_vmin)
if isinstance(self._subs, str):
_first = 2.0 if self._subs == 'auto' else 1.0
if numdec > 10 or b < 3:
if self._subs == 'auto':
return np.array([]) # no minor or major ticks
else:
subs = np.array([1.0]) # major ticks
else:
subs = np.arange(_first, b)
else:
subs = self._subs
# Get decades between major ticks.
stride = (max(math.ceil(numdec / (numticks - 1)), 1)
if mpl.rcParams['_internal.classic_mode'] else
(numdec + 1) // numticks + 1)
# if we have decided that the stride is as big or bigger than
# the range, clip the stride back to the available range - 1
# with a floor of 1. This prevents getting axis with only 1 tick
# visible.
if stride >= numdec:
stride = max(1, numdec - 1)
# Does subs include anything other than 1? Essentially a hack to know
# whether we're a major or a minor locator.
have_subs = len(subs) > 1 or (len(subs) == 1 and subs[0] != 1.0)
decades = np.arange(math.floor(log_vmin) - stride,
math.ceil(log_vmax) + 2 * stride, stride)
if hasattr(self, '_transform'):
ticklocs = self._transform.inverted().transform(decades)
if have_subs:
if stride == 1:
ticklocs = np.ravel(np.outer(subs, ticklocs))
else:
# No ticklocs if we have >1 decade between major ticks.
ticklocs = np.array([])
else:
if have_subs:
if stride == 1:
ticklocs = np.concatenate(
[subs * decade_start for decade_start in b ** decades])
else:
ticklocs = np.array([])
else:
ticklocs = b ** decades
_log.debug('ticklocs %r', ticklocs)
if (len(subs) > 1
and stride == 1
and ((vmin <= ticklocs) & (ticklocs <= vmax)).sum() <= 1):
# If we're a minor locator *that expects at least two ticks per
# decade* and the major locator stride is 1 and there's no more
# than one minor tick, switch to AutoLocator.
return AutoLocator().tick_values(vmin, vmax)
else:
return self.raise_if_exceeds(ticklocs)
def view_limits(self, vmin, vmax):
"""Try to choose the view limits intelligently."""
b = self._base
vmin, vmax = self.nonsingular(vmin, vmax)
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
vmin = _decade_less_equal(vmin, self._base)
vmax = _decade_greater_equal(vmax, self._base)
return vmin, vmax
def nonsingular(self, vmin, vmax):
if vmin > vmax:
vmin, vmax = vmax, vmin
if not np.isfinite(vmin) or not np.isfinite(vmax):
vmin, vmax = 1, 10 # Initial range, no data plotted yet.
elif vmax <= 0:
_api.warn_external(
"Data has no positive values, and therefore cannot be "
"log-scaled.")
vmin, vmax = 1, 10
else:
minpos = self.axis.get_minpos()
if not np.isfinite(minpos):
minpos = 1e-300 # This should never take effect.
if vmin <= 0:
vmin = minpos
if vmin == vmax:
vmin = _decade_less(vmin, self._base)
vmax = _decade_greater(vmax, self._base)
return vmin, vmax
class SymmetricalLogLocator(Locator):
"""
Determine the tick locations for symmetric log axes.
"""
def __init__(self, transform=None, subs=None, linthresh=None, base=None):
"""
Parameters
----------
transform : `~.scale.SymmetricalLogTransform`, optional
If set, defines the *base* and *linthresh* of the symlog transform.
base, linthresh : float, optional
The *base* and *linthresh* of the symlog transform, as documented
for `.SymmetricalLogScale`. These parameters are only used if
*transform* is not set.
subs : sequence of float, default: [1]
The multiples of integer powers of the base where ticks are placed,
i.e., ticks are placed at
``[sub * base**i for i in ... for sub in subs]``.
Notes
-----
Either *transform*, or both *base* and *linthresh*, must be given.
"""
if transform is not None:
self._base = transform.base
self._linthresh = transform.linthresh
elif linthresh is not None and base is not None:
self._base = base
self._linthresh = linthresh
else:
raise ValueError("Either transform, or both linthresh "
"and base, must be provided.")
if subs is None:
self._subs = [1.0]
else:
self._subs = subs
self.numticks = 15
def set_params(self, subs=None, numticks=None):
"""Set parameters within this locator."""
if numticks is not None:
self.numticks = numticks
if subs is not None:
self._subs = subs
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):
base = self._base
linthresh = self._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)
if -linthresh < vmin < vmax < linthresh:
# only the linear range is present
return [vmin, vmax]
# Lower log range is present
has_a = (vmin < -linthresh)
# Upper log range is present
has_c = (vmax > linthresh)
# Check if linear range is present
has_b = (has_a and vmax > -linthresh) or (has_c and vmin < linthresh)
def get_log_range(lo, hi):
lo = np.floor(np.log(lo) / np.log(base))
hi = np.ceil(np.log(hi) / np.log(base))
return lo, hi
# Calculate all the ranges, so we can determine striding
a_lo, a_hi = (0, 0)
if has_a:
a_upper_lim = min(-linthresh, vmax)
a_lo, a_hi = get_log_range(abs(a_upper_lim), abs(vmin) + 1)
c_lo, c_hi = (0, 0)
if has_c:
c_lower_lim = max(linthresh, vmin)
c_lo, c_hi = get_log_range(c_lower_lim, vmax + 1)
# Calculate the total number of integer exponents in a and c ranges
total_ticks = (a_hi - a_lo) + (c_hi - c_lo)
if has_b:
total_ticks += 1
stride = max(total_ticks // (self.numticks - 1), 1)
decades = []
if has_a:
decades.extend(-1 * (base ** (np.arange(a_lo, a_hi,
stride)[::-1])))
if has_b:
decades.append(0.0)
if has_c:
decades.extend(base ** (np.arange(c_lo, c_hi, stride)))
# Add the subticks if requested
if self._subs is None:
subs = np.arange(2.0, base)
else:
subs = np.asarray(self._subs)
if len(subs) > 1 or subs[0] != 1.0:
ticklocs = []
for decade in decades:
if decade == 0:
ticklocs.append(decade)
else:
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._base
if vmax < vmin:
vmin, vmax = vmax, vmin
if mpl.rcParams['axes.autolimit_mode'] == 'round_numbers':
vmin = _decade_less_equal(vmin, b)
vmax = _decade_greater_equal(vmax, b)
if vmin == vmax:
vmin = _decade_less(vmin, b)
vmax = _decade_greater(vmax, b)
result = mtransforms.nonsingular(vmin, vmax)
return result
class AsinhLocator(Locator):
"""
An axis tick locator specialized for the inverse-sinh scale
This is very unlikely to have any use beyond
the `~.scale.AsinhScale` class.
.. note::
This API is provisional and may be revised in the future
based on early user feedback.
"""
def __init__(self, linear_width, numticks=11, symthresh=0.2,
base=10, subs=None):
"""
Parameters
----------
linear_width : float
The scale parameter defining the extent
of the quasi-linear region.
numticks : int, default: 11
The approximate number of major ticks that will fit
along the entire axis
symthresh : float, default: 0.2
The fractional threshold beneath which data which covers
a range that is approximately symmetric about zero
will have ticks that are exactly symmetric.
base : int, default: 10
The number base used for rounding tick locations
on a logarithmic scale. If this is less than one,
then rounding is to the nearest integer multiple
of powers of ten.
subs : tuple, default: None
Multiples of the number base, typically used
for the minor ticks, e.g. (2, 5) when base=10.
"""
super().__init__()
self.linear_width = linear_width
self.numticks = numticks
self.symthresh = symthresh
self.base = base
self.subs = subs
def set_params(self, numticks=None, symthresh=None,
base=None, subs=None):
"""Set parameters within this locator."""
if numticks is not None:
self.numticks = numticks
if symthresh is not None:
self.symthresh = symthresh
if base is not None:
self.base = base
if subs is not None:
self.subs = subs if len(subs) > 0 else None
def __call__(self):
vmin, vmax = self.axis.get_view_interval()
if (vmin * vmax) < 0 and abs(1 + vmax / vmin) < self.symthresh:
# Data-range appears to be almost symmetric, so round up:
bound = max(abs(vmin), abs(vmax))
return self.tick_values(-bound, bound)
else:
return self.tick_values(vmin, vmax)
def tick_values(self, vmin, vmax):
# Construct a set of "on-screen" locations
# that are uniformly spaced:
ymin, ymax = self.linear_width * np.arcsinh(np.array([vmin, vmax])
/ self.linear_width)
ys = np.linspace(ymin, ymax, self.numticks)
zero_dev = np.abs(ys / (ymax - ymin))
if (ymin * ymax) < 0:
# Ensure that the zero tick-mark is included,
# if the axis straddles zero
ys = np.hstack([ys[(zero_dev > 0.5 / self.numticks)], 0.0])
# Transform the "on-screen" grid to the data space:
xs = self.linear_width * np.sinh(ys / self.linear_width)
zero_xs = (ys == 0)
# Round the data-space values to be intuitive base-n numbers,
# keeping track of positive and negative values separately,
# but giving careful treatment to the zero value:
if self.base > 1:
log_base = math.log(self.base)
powers = (
np.where(zero_xs, 0, np.sign(xs)) *
np.power(self.base,
np.where(zero_xs, 0.0,
np.floor(np.log(np.abs(xs) + zero_xs*1e-6)
/ log_base)))
)
if self.subs:
qs = np.outer(powers, self.subs).flatten()
else:
qs = powers
else:
powers = (
np.where(xs >= 0, 1, -1) *
np.power(10, np.where(zero_xs, 0.0,
np.floor(np.log10(np.abs(xs)
+ zero_xs*1e-6))))
)
qs = powers * np.round(xs / powers)
ticks = np.array(sorted(set(qs)))
if len(ticks) >= 2:
return ticks
else:
return np.linspace(vmin, vmax, self.numticks)
class LogitLocator(MaxNLocator):
"""
Determine the tick locations for logit axes
"""
def __init__(self, minor=False, *, nbins="auto"):
"""
Place ticks on the logit locations
Parameters
----------
nbins : int or 'auto', optional
Number of ticks. Only used if minor is False.
minor : bool, default: False
Indicate if this locator is for minor ticks or not.
"""
self._minor = minor
super().__init__(nbins=nbins, steps=[1, 2, 5, 10])
def set_params(self, minor=None, **kwargs):
"""Set parameters within this locator."""
if minor is not None:
self._minor = minor
super().set_params(**kwargs)
@property
def minor(self):
return self._minor
@minor.setter
def minor(self, value):
self.set_params(minor=value)
def tick_values(self, vmin, vmax):
# dummy axis has no axes attribute
if hasattr(self.axis, "axes") and self.axis.axes.name == "polar":
raise NotImplementedError("Polar axis cannot be logit scaled yet")
if self._nbins == "auto":
if self.axis is not None:
nbins = self.axis.get_tick_space()
if nbins < 2:
nbins = 2
else:
nbins = 9
else:
nbins = self._nbins
# We define ideal ticks with their index:
# linscale: ... 1e-3 1e-2 1e-1 1/2 1-1e-1 1-1e-2 1-1e-3 ...
# b-scale : ... -3 -2 -1 0 1 2 3 ...
def ideal_ticks(x):
return 10 ** x if x < 0 else 1 - (10 ** (-x)) if x > 0 else 1 / 2
vmin, vmax = self.nonsingular(vmin, vmax)
binf = int(
np.floor(np.log10(vmin))
if vmin < 0.5
else 0
if vmin < 0.9
else -np.ceil(np.log10(1 - vmin))
)
bsup = int(
np.ceil(np.log10(vmax))
if vmax <= 0.5
else 1
if vmax <= 0.9
else -np.floor(np.log10(1 - vmax))
)
numideal = bsup - binf - 1
if numideal >= 2:
# have 2 or more wanted ideal ticks, so use them as major ticks
if numideal > nbins:
# to many ideal ticks, subsampling ideals for major ticks, and
# take others for minor ticks
subsampling_factor = math.ceil(numideal / nbins)
if self._minor:
ticklocs = [
ideal_ticks(b)
for b in range(binf, bsup + 1)
if (b % subsampling_factor) != 0
]
else:
ticklocs = [
ideal_ticks(b)
for b in range(binf, bsup + 1)
if (b % subsampling_factor) == 0
]
return self.raise_if_exceeds(np.array(ticklocs))
if self._minor:
ticklocs = []
for b in range(binf, bsup):
if b < -1:
ticklocs.extend(np.arange(2, 10) * 10 ** b)
elif b == -1:
ticklocs.extend(np.arange(2, 5) / 10)
elif b == 0:
ticklocs.extend(np.arange(6, 9) / 10)
else:
ticklocs.extend(
1 - np.arange(2, 10)[::-1] * 10 ** (-b - 1)
)
return self.raise_if_exceeds(np.array(ticklocs))
ticklocs = [ideal_ticks(b) for b in range(binf, bsup + 1)]
return self.raise_if_exceeds(np.array(ticklocs))
# the scale is zoomed so same ticks as linear scale can be used
if self._minor:
return []
return super().tick_values(vmin, vmax)
def nonsingular(self, vmin, vmax):
standard_minpos = 1e-7
initial_range = (standard_minpos, 1 - standard_minpos)
if vmin > vmax:
vmin, vmax = vmax, vmin
if not np.isfinite(vmin) or not np.isfinite(vmax):
vmin, vmax = initial_range # Initial range, no data plotted yet.
elif vmax <= 0 or vmin >= 1:
# vmax <= 0 occurs when all values are negative
# vmin >= 1 occurs when all values are greater than one
_api.warn_external(
"Data has no values between 0 and 1, and therefore cannot be "
"logit-scaled."
)
vmin, vmax = initial_range
else:
minpos = (
self.axis.get_minpos()
if self.axis is not None
else standard_minpos
)
if not np.isfinite(minpos):
minpos = standard_minpos # This should never take effect.
if vmin <= 0:
vmin = minpos
# NOTE: for vmax, we should query a property similar to get_minpos,
# but related to the maximal, less-than-one data point.
# Unfortunately, Bbox._minpos is defined very deep in the BBox and
# updated with data, so for now we use 1 - minpos as a substitute.
if vmax >= 1:
vmax = 1 - minpos
if vmin == vmax:
vmin, vmax = 0.1 * vmin, 1 - 0.1 * vmin
return vmin, vmax
class AutoLocator(MaxNLocator):
"""
Dynamically find major tick positions. This is actually a subclass
of `~matplotlib.ticker.MaxNLocator`, with parameters *nbins = 'auto'*
and *steps = [1, 2, 2.5, 5, 10]*.
"""
def __init__(self):
"""
To know the values of the non-public parameters, please have a
look to the defaults of `~matplotlib.ticker.MaxNLocator`.
"""
if mpl.rcParams['_internal.classic_mode']:
nbins = 9
steps = [1, 2, 5, 10]
else:
nbins = 'auto'
steps = [1, 2, 2.5, 5, 10]
super().__init__(nbins=nbins, steps=steps)
class AutoMinorLocator(Locator):
"""
Dynamically find minor tick positions based on the positions of
major ticks. The scale must be linear with major ticks 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."""
if self.axis.get_scale() == 'log':
_api.warn_external('AutoMinorLocator does not work with '
'logarithmic scale')
return []
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.
return []
if self.ndivs is None:
majorstep_no_exponent = 10 ** (np.log10(majorstep) % 1)
if np.isclose(majorstep_no_exponent, [1.0, 2.5, 5.0, 10.0]).any():
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
t0 = majorlocs[0]
tmin = ((vmin - t0) // minorstep + 1) * minorstep
tmax = ((vmax - t0) // minorstep + 1) * minorstep
locs = np.arange(tmin, tmax, minorstep) + t0
return self.raise_if_exceeds(locs)
def tick_values(self, vmin, vmax):
raise NotImplementedError('Cannot get tick locations for a '
'%s type.' % type(self))