778 lines
24 KiB
Python
778 lines
24 KiB
Python
import inspect
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import textwrap
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import numpy as np
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from numpy import ma
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from matplotlib import cbook, docstring, rcParams
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from matplotlib.ticker import (
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NullFormatter, ScalarFormatter, LogFormatterSciNotation, LogitFormatter,
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NullLocator, LogLocator, AutoLocator, AutoMinorLocator,
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SymmetricalLogLocator, LogitLocator)
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from matplotlib.transforms import Transform, IdentityTransform
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class ScaleBase(object):
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"""
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The base class for all scales.
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Scales are separable transformations, working on a single dimension.
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Any subclasses will want to override:
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- :attr:`name`
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- :meth:`get_transform`
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- :meth:`set_default_locators_and_formatters`
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And optionally:
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- :meth:`limit_range_for_scale`
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"""
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def __init__(self, axis, **kwargs):
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r"""
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Construct a new scale.
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Notes
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-----
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The following note is for scale implementors.
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For back-compatibility reasons, scales take an `~matplotlib.axis.Axis`
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object as first argument. However, this argument should not
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be used: a single scale object should be usable by multiple
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`~matplotlib.axis.Axis`\es at the same time.
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"""
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def get_transform(self):
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"""
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Return the :class:`~matplotlib.transforms.Transform` object
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associated with this scale.
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"""
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raise NotImplementedError()
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def set_default_locators_and_formatters(self, axis):
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"""
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Set the :class:`~matplotlib.ticker.Locator` and
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:class:`~matplotlib.ticker.Formatter` objects on the given
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axis to match this scale.
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"""
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raise NotImplementedError()
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def limit_range_for_scale(self, vmin, vmax, minpos):
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"""
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Returns the range *vmin*, *vmax*, possibly limited to the
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domain supported by this scale.
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*minpos* should be the minimum positive value in the data.
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This is used by log scales to determine a minimum value.
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"""
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return vmin, vmax
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class LinearScale(ScaleBase):
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"""
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The default linear scale.
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"""
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name = 'linear'
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def __init__(self, axis, **kwargs):
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# This method is present only to prevent inheritance of the base class'
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# constructor docstring, which would otherwise end up interpolated into
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# the docstring of Axis.set_scale.
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"""
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"""
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super().__init__(axis, **kwargs)
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def set_default_locators_and_formatters(self, axis):
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"""
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Set the locators and formatters to reasonable defaults for
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linear scaling.
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"""
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axis.set_major_locator(AutoLocator())
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axis.set_major_formatter(ScalarFormatter())
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axis.set_minor_formatter(NullFormatter())
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# update the minor locator for x and y axis based on rcParams
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if (axis.axis_name == 'x' and rcParams['xtick.minor.visible']
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or axis.axis_name == 'y' and rcParams['ytick.minor.visible']):
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axis.set_minor_locator(AutoMinorLocator())
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else:
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axis.set_minor_locator(NullLocator())
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def get_transform(self):
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"""
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The transform for linear scaling is just the
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:class:`~matplotlib.transforms.IdentityTransform`.
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"""
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return IdentityTransform()
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class FuncTransform(Transform):
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"""
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A simple transform that takes and arbitrary function for the
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forward and inverse transform.
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"""
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, forward, inverse):
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"""
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Parameters
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----------
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forward : callable
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The forward function for the transform. This function must have
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an inverse and, for best behavior, be monotonic.
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It must have the signature::
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def forward(values: array-like) -> array-like
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inverse : callable
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The inverse of the forward function. Signature as ``forward``.
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"""
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super().__init__()
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if callable(forward) and callable(inverse):
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self._forward = forward
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self._inverse = inverse
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else:
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raise ValueError('arguments to FuncTransform must '
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'be functions')
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def transform_non_affine(self, values):
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return self._forward(values)
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def inverted(self):
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return FuncTransform(self._inverse, self._forward)
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class FuncScale(ScaleBase):
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"""
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Provide an arbitrary scale with user-supplied function for the axis.
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"""
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name = 'function'
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def __init__(self, axis, functions):
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"""
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Parameters
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----------
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axis: the axis for the scale
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functions : (callable, callable)
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two-tuple of the forward and inverse functions for the scale.
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The forward function must be monotonic.
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Both functions must have the signature::
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def forward(values: array-like) -> array-like
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"""
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forward, inverse = functions
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transform = FuncTransform(forward, inverse)
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self._transform = transform
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def get_transform(self):
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"""
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The transform for arbitrary scaling
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"""
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return self._transform
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def set_default_locators_and_formatters(self, axis):
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"""
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Set the locators and formatters to the same defaults as the
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linear scale.
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"""
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axis.set_major_locator(AutoLocator())
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axis.set_major_formatter(ScalarFormatter())
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axis.set_minor_formatter(NullFormatter())
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# update the minor locator for x and y axis based on rcParams
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if (axis.axis_name == 'x' and rcParams['xtick.minor.visible']
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or axis.axis_name == 'y' and rcParams['ytick.minor.visible']):
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axis.set_minor_locator(AutoMinorLocator())
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else:
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axis.set_minor_locator(NullLocator())
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@cbook.deprecated("3.1", alternative="LogTransform")
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class LogTransformBase(Transform):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, nonpos='clip'):
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Transform.__init__(self)
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self._clip = {"clip": True, "mask": False}[nonpos]
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def transform_non_affine(self, a):
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return LogTransform.transform_non_affine(self, a)
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def __str__(self):
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return "{}({!r})".format(
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type(self).__name__, "clip" if self._clip else "mask")
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@cbook.deprecated("3.1", alternative="InvertedLogTransform")
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class InvertedLogTransformBase(Transform):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def transform_non_affine(self, a):
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return ma.power(self.base, a)
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def __str__(self):
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return "{}()".format(type(self).__name__)
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@cbook.deprecated("3.1", alternative="LogTransform")
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class Log10Transform(LogTransformBase):
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base = 10.0
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def inverted(self):
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return InvertedLog10Transform()
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@cbook.deprecated("3.1", alternative="InvertedLogTransform")
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class InvertedLog10Transform(InvertedLogTransformBase):
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base = 10.0
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def inverted(self):
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return Log10Transform()
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@cbook.deprecated("3.1", alternative="LogTransform")
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class Log2Transform(LogTransformBase):
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base = 2.0
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def inverted(self):
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return InvertedLog2Transform()
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@cbook.deprecated("3.1", alternative="InvertedLogTransform")
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class InvertedLog2Transform(InvertedLogTransformBase):
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base = 2.0
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def inverted(self):
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return Log2Transform()
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@cbook.deprecated("3.1", alternative="LogTransform")
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class NaturalLogTransform(LogTransformBase):
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base = np.e
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def inverted(self):
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return InvertedNaturalLogTransform()
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@cbook.deprecated("3.1", alternative="InvertedLogTransform")
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class InvertedNaturalLogTransform(InvertedLogTransformBase):
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base = np.e
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def inverted(self):
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return NaturalLogTransform()
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class LogTransform(Transform):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, base, nonpos='clip'):
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Transform.__init__(self)
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self.base = base
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self._clip = {"clip": True, "mask": False}[nonpos]
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def __str__(self):
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return "{}(base={}, nonpos={!r})".format(
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type(self).__name__, self.base, "clip" if self._clip else "mask")
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def transform_non_affine(self, a):
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# Ignore invalid values due to nans being passed to the transform.
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with np.errstate(divide="ignore", invalid="ignore"):
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log = {np.e: np.log, 2: np.log2, 10: np.log10}.get(self.base)
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if log: # If possible, do everything in a single call to Numpy.
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out = log(a)
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else:
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out = np.log(a)
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out /= np.log(self.base)
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if self._clip:
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# SVG spec says that conforming viewers must support values up
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# to 3.4e38 (C float); however experiments suggest that
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# Inkscape (which uses cairo for rendering) runs into cairo's
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# 24-bit limit (which is apparently shared by Agg).
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# Ghostscript (used for pdf rendering appears to overflow even
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# earlier, with the max value around 2 ** 15 for the tests to
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# pass. On the other hand, in practice, we want to clip beyond
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# np.log10(np.nextafter(0, 1)) ~ -323
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# so 1000 seems safe.
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out[a <= 0] = -1000
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return out
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def inverted(self):
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return InvertedLogTransform(self.base)
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class InvertedLogTransform(InvertedLogTransformBase):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, base):
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Transform.__init__(self)
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self.base = base
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def __str__(self):
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return "{}(base={})".format(type(self).__name__, self.base)
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def transform_non_affine(self, a):
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return ma.power(self.base, a)
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def inverted(self):
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return LogTransform(self.base)
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class LogScale(ScaleBase):
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"""
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A standard logarithmic scale. Care is taken to only plot positive values.
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"""
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name = 'log'
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# compatibility shim
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LogTransformBase = LogTransformBase
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Log10Transform = Log10Transform
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InvertedLog10Transform = InvertedLog10Transform
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Log2Transform = Log2Transform
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InvertedLog2Transform = InvertedLog2Transform
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NaturalLogTransform = NaturalLogTransform
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InvertedNaturalLogTransform = InvertedNaturalLogTransform
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LogTransform = LogTransform
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InvertedLogTransform = InvertedLogTransform
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def __init__(self, axis, **kwargs):
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"""
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*basex*/*basey*:
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The base of the logarithm
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*nonposx*/*nonposy*: {'mask', 'clip'}
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non-positive values in *x* or *y* can be masked as
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invalid, or clipped to a very small positive number
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*subsx*/*subsy*:
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Where to place the subticks between each major tick.
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Should be a sequence of integers. For example, in a log10
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scale: ``[2, 3, 4, 5, 6, 7, 8, 9]``
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will place 8 logarithmically spaced minor ticks between
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each major tick.
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"""
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if axis.axis_name == 'x':
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base = kwargs.pop('basex', 10.0)
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subs = kwargs.pop('subsx', None)
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nonpos = kwargs.pop('nonposx', 'clip')
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cbook._check_in_list(['mask', 'clip'], nonposx=nonpos)
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else:
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base = kwargs.pop('basey', 10.0)
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subs = kwargs.pop('subsy', None)
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nonpos = kwargs.pop('nonposy', 'clip')
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cbook._check_in_list(['mask', 'clip'], nonposy=nonpos)
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if len(kwargs):
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raise ValueError(("provided too many kwargs, can only pass "
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"{'basex', 'subsx', nonposx'} or "
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"{'basey', 'subsy', nonposy'}. You passed ") +
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"{!r}".format(kwargs))
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if base <= 0 or base == 1:
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raise ValueError('The log base cannot be <= 0 or == 1')
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self._transform = self.LogTransform(base, nonpos)
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self.subs = subs
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@property
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def base(self):
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return self._transform.base
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def set_default_locators_and_formatters(self, axis):
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"""
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Set the locators and formatters to specialized versions for
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log scaling.
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"""
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axis.set_major_locator(LogLocator(self.base))
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axis.set_major_formatter(LogFormatterSciNotation(self.base))
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axis.set_minor_locator(LogLocator(self.base, self.subs))
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axis.set_minor_formatter(
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LogFormatterSciNotation(self.base,
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labelOnlyBase=(self.subs is not None)))
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def get_transform(self):
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"""
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Return a :class:`~matplotlib.transforms.Transform` instance
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appropriate for the given logarithm base.
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"""
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return self._transform
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def limit_range_for_scale(self, vmin, vmax, minpos):
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"""
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Limit the domain to positive values.
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"""
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if not np.isfinite(minpos):
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minpos = 1e-300 # This value should rarely if ever
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# end up with a visible effect.
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return (minpos if vmin <= 0 else vmin,
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minpos if vmax <= 0 else vmax)
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class FuncScaleLog(LogScale):
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"""
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Provide an arbitrary scale with user-supplied function for the axis and
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then put on a logarithmic axes.
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"""
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name = 'functionlog'
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def __init__(self, axis, functions, base=10):
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"""
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Parameters
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----------
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axis: the axis for the scale
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functions : (callable, callable)
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two-tuple of the forward and inverse functions for the scale.
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The forward function must be monotonic.
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Both functions must have the signature::
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def forward(values: array-like) -> array-like
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base : float
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logarithmic base of the scale (default = 10)
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"""
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forward, inverse = functions
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self.subs = None
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self._transform = FuncTransform(forward, inverse) + LogTransform(base)
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@property
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def base(self):
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return self._transform._b.base # Base of the LogTransform.
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def get_transform(self):
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"""
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The transform for arbitrary scaling
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"""
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return self._transform
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class SymmetricalLogTransform(Transform):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, base, linthresh, linscale):
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Transform.__init__(self)
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self.base = base
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self.linthresh = linthresh
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self.linscale = linscale
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self._linscale_adj = (linscale / (1.0 - self.base ** -1))
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self._log_base = np.log(base)
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def transform_non_affine(self, a):
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abs_a = np.abs(a)
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with np.errstate(divide="ignore", invalid="ignore"):
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out = np.sign(a) * self.linthresh * (
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self._linscale_adj +
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np.log(abs_a / self.linthresh) / self._log_base)
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inside = abs_a <= self.linthresh
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out[inside] = a[inside] * self._linscale_adj
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return out
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def inverted(self):
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return InvertedSymmetricalLogTransform(self.base, self.linthresh,
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self.linscale)
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class InvertedSymmetricalLogTransform(Transform):
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input_dims = 1
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output_dims = 1
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is_separable = True
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has_inverse = True
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def __init__(self, base, linthresh, linscale):
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Transform.__init__(self)
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symlog = SymmetricalLogTransform(base, linthresh, linscale)
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self.base = base
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self.linthresh = linthresh
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self.invlinthresh = symlog.transform(linthresh)
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self.linscale = linscale
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self._linscale_adj = (linscale / (1.0 - self.base ** -1))
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def transform_non_affine(self, a):
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abs_a = np.abs(a)
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with np.errstate(divide="ignore", invalid="ignore"):
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out = np.sign(a) * self.linthresh * (
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np.power(self.base,
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abs_a / self.linthresh - self._linscale_adj))
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inside = abs_a <= self.invlinthresh
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out[inside] = a[inside] / self._linscale_adj
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return out
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def inverted(self):
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return SymmetricalLogTransform(self.base,
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self.linthresh, self.linscale)
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class SymmetricalLogScale(ScaleBase):
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"""
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The symmetrical logarithmic scale is logarithmic in both the
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positive and negative directions from the origin.
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Since the values close to zero tend toward infinity, there is a
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need to have a range around zero that is linear. The parameter
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*linthresh* allows the user to specify the size of this range
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(-*linthresh*, *linthresh*).
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Parameters
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----------
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basex, basey : float
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The base of the logarithm. Defaults to 10.
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linthreshx, linthreshy : float
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Defines the range ``(-x, x)``, within which the plot is linear.
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This avoids having the plot go to infinity around zero. Defaults to 2.
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subsx, subsy : sequence of int
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Where to place the subticks between each major tick.
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For example, in a log10 scale: ``[2, 3, 4, 5, 6, 7, 8, 9]`` will place
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8 logarithmically spaced minor ticks between each major tick.
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linscalex, linscaley : float, optional
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This allows the linear range ``(-linthresh, linthresh)`` to be
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stretched relative to the logarithmic range. Its value is the number of
|
|
decades to use for each half of the linear range. For example, when
|
|
*linscale* == 1.0 (the default), the space used for the positive and
|
|
negative halves of the linear range will be equal to one decade in
|
|
the logarithmic range.
|
|
"""
|
|
name = 'symlog'
|
|
# compatibility shim
|
|
SymmetricalLogTransform = SymmetricalLogTransform
|
|
InvertedSymmetricalLogTransform = InvertedSymmetricalLogTransform
|
|
|
|
def __init__(self, axis, **kwargs):
|
|
if axis.axis_name == 'x':
|
|
base = kwargs.pop('basex', 10.0)
|
|
linthresh = kwargs.pop('linthreshx', 2.0)
|
|
subs = kwargs.pop('subsx', None)
|
|
linscale = kwargs.pop('linscalex', 1.0)
|
|
else:
|
|
base = kwargs.pop('basey', 10.0)
|
|
linthresh = kwargs.pop('linthreshy', 2.0)
|
|
subs = kwargs.pop('subsy', None)
|
|
linscale = kwargs.pop('linscaley', 1.0)
|
|
|
|
if base <= 1.0:
|
|
raise ValueError("'basex/basey' must be larger than 1")
|
|
if linthresh <= 0.0:
|
|
raise ValueError("'linthreshx/linthreshy' must be positive")
|
|
if linscale <= 0.0:
|
|
raise ValueError("'linscalex/linthreshy' must be positive")
|
|
|
|
self._transform = self.SymmetricalLogTransform(base,
|
|
linthresh,
|
|
linscale)
|
|
|
|
self.base = base
|
|
self.linthresh = linthresh
|
|
self.linscale = linscale
|
|
self.subs = subs
|
|
|
|
def set_default_locators_and_formatters(self, axis):
|
|
"""
|
|
Set the locators and formatters to specialized versions for
|
|
symmetrical log scaling.
|
|
"""
|
|
axis.set_major_locator(SymmetricalLogLocator(self.get_transform()))
|
|
axis.set_major_formatter(LogFormatterSciNotation(self.base))
|
|
axis.set_minor_locator(SymmetricalLogLocator(self.get_transform(),
|
|
self.subs))
|
|
axis.set_minor_formatter(NullFormatter())
|
|
|
|
def get_transform(self):
|
|
"""
|
|
Return a :class:`SymmetricalLogTransform` instance.
|
|
"""
|
|
return self._transform
|
|
|
|
|
|
class LogitTransform(Transform):
|
|
input_dims = 1
|
|
output_dims = 1
|
|
is_separable = True
|
|
has_inverse = True
|
|
|
|
def __init__(self, nonpos='mask'):
|
|
Transform.__init__(self)
|
|
self._nonpos = nonpos
|
|
self._clip = {"clip": True, "mask": False}[nonpos]
|
|
|
|
def transform_non_affine(self, a):
|
|
"""logit transform (base 10), masked or clipped"""
|
|
with np.errstate(divide="ignore", invalid="ignore"):
|
|
out = np.log10(a / (1 - a))
|
|
if self._clip: # See LogTransform for choice of clip value.
|
|
out[a <= 0] = -1000
|
|
out[1 <= a] = 1000
|
|
return out
|
|
|
|
def inverted(self):
|
|
return LogisticTransform(self._nonpos)
|
|
|
|
def __str__(self):
|
|
return "{}({!r})".format(type(self).__name__,
|
|
"clip" if self._clip else "mask")
|
|
|
|
|
|
class LogisticTransform(Transform):
|
|
input_dims = 1
|
|
output_dims = 1
|
|
is_separable = True
|
|
has_inverse = True
|
|
|
|
def __init__(self, nonpos='mask'):
|
|
Transform.__init__(self)
|
|
self._nonpos = nonpos
|
|
|
|
def transform_non_affine(self, a):
|
|
"""logistic transform (base 10)"""
|
|
return 1.0 / (1 + 10**(-a))
|
|
|
|
def inverted(self):
|
|
return LogitTransform(self._nonpos)
|
|
|
|
def __str__(self):
|
|
return "{}({!r})".format(type(self).__name__, self._nonpos)
|
|
|
|
|
|
class LogitScale(ScaleBase):
|
|
"""
|
|
Logit scale for data between zero and one, both excluded.
|
|
|
|
This scale is similar to a log scale close to zero and to one, and almost
|
|
linear around 0.5. It maps the interval ]0, 1[ onto ]-infty, +infty[.
|
|
"""
|
|
name = 'logit'
|
|
|
|
def __init__(self, axis, nonpos='mask'):
|
|
"""
|
|
*nonpos*: {'mask', 'clip'}
|
|
values beyond ]0, 1[ can be masked as invalid, or clipped to a number
|
|
very close to 0 or 1
|
|
"""
|
|
cbook._check_in_list(['mask', 'clip'], nonpos=nonpos)
|
|
self._transform = LogitTransform(nonpos)
|
|
|
|
def get_transform(self):
|
|
"""
|
|
Return a :class:`LogitTransform` instance.
|
|
"""
|
|
return self._transform
|
|
|
|
def set_default_locators_and_formatters(self, axis):
|
|
# ..., 0.01, 0.1, 0.5, 0.9, 0.99, ...
|
|
axis.set_major_locator(LogitLocator())
|
|
axis.set_major_formatter(LogitFormatter())
|
|
axis.set_minor_locator(LogitLocator(minor=True))
|
|
axis.set_minor_formatter(LogitFormatter())
|
|
|
|
def limit_range_for_scale(self, vmin, vmax, minpos):
|
|
"""
|
|
Limit the domain to values between 0 and 1 (excluded).
|
|
"""
|
|
if not np.isfinite(minpos):
|
|
minpos = 1e-7 # This value should rarely if ever
|
|
# end up with a visible effect.
|
|
return (minpos if vmin <= 0 else vmin,
|
|
1 - minpos if vmax >= 1 else vmax)
|
|
|
|
|
|
_scale_mapping = {
|
|
'linear': LinearScale,
|
|
'log': LogScale,
|
|
'symlog': SymmetricalLogScale,
|
|
'logit': LogitScale,
|
|
'function': FuncScale,
|
|
'functionlog': FuncScaleLog,
|
|
}
|
|
|
|
|
|
def get_scale_names():
|
|
return sorted(_scale_mapping)
|
|
|
|
|
|
def scale_factory(scale, axis, **kwargs):
|
|
"""
|
|
Return a scale class by name.
|
|
|
|
Parameters
|
|
----------
|
|
scale : {%(names)s}
|
|
axis : Axis
|
|
"""
|
|
scale = scale.lower()
|
|
if scale not in _scale_mapping:
|
|
raise ValueError("Unknown scale type '%s'" % scale)
|
|
return _scale_mapping[scale](axis, **kwargs)
|
|
|
|
if scale_factory.__doc__:
|
|
scale_factory.__doc__ = scale_factory.__doc__ % {
|
|
"names": ", ".join(get_scale_names())}
|
|
|
|
|
|
def register_scale(scale_class):
|
|
"""
|
|
Register a new kind of scale.
|
|
|
|
*scale_class* must be a subclass of :class:`ScaleBase`.
|
|
"""
|
|
_scale_mapping[scale_class.name] = scale_class
|
|
|
|
|
|
@cbook.deprecated(
|
|
'3.1', message='get_scale_docs() is considered private API since '
|
|
'3.1 and will be removed from the public API in 3.3.')
|
|
def get_scale_docs():
|
|
"""
|
|
Helper function for generating docstrings related to scales.
|
|
"""
|
|
return _get_scale_docs()
|
|
|
|
|
|
def _get_scale_docs():
|
|
"""
|
|
Helper function for generating docstrings related to scales.
|
|
"""
|
|
docs = []
|
|
for name, scale_class in _scale_mapping.items():
|
|
docs.extend([
|
|
f" {name!r}",
|
|
"",
|
|
textwrap.indent(inspect.getdoc(scale_class.__init__), " " * 8),
|
|
""
|
|
])
|
|
return "\n".join(docs)
|
|
|
|
|
|
docstring.interpd.update(
|
|
scale=' | '.join([repr(x) for x in get_scale_names()]),
|
|
scale_docs=_get_scale_docs().rstrip(),
|
|
)
|