671 lines
22 KiB
Python
671 lines
22 KiB
Python
"""
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Scales define the distribution of data values on an axis, e.g. a log scaling.
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They are attached to an `~.axis.Axis` and hold a `.Transform`, which is
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responsible for the actual data transformation.
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See also `.axes.Axes.set_xscale` and the scales examples in the documentation.
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"""
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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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import matplotlib as mpl
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from matplotlib import _api, docstring
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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:
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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):
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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 locators and formatters of *axis* to instances suitable for
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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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Return the range *vmin*, *vmax*, restricted to the
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domain supported by this scale (if any).
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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):
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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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def set_default_locators_and_formatters(self, axis):
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# docstring inherited
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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 mpl.rcParams['xtick.minor.visible'] or
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axis.axis_name == 'y' and mpl.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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Return the transform for linear scaling, which is just the
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`~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 = output_dims = 1
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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 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 : `~matplotlib.axis.Axis`
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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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"""Return the `.FuncTransform` associated with this scale."""
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return self._transform
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def set_default_locators_and_formatters(self, axis):
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# docstring inherited
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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 mpl.rcParams['xtick.minor.visible'] or
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axis.axis_name == 'y' and mpl.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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class LogTransform(Transform):
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input_dims = output_dims = 1
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@_api.rename_parameter("3.3", "nonpos", "nonpositive")
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def __init__(self, base, nonpositive='clip'):
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super().__init__()
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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.base = base
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self._clip = _api.check_getitem(
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{"clip": True, "mask": False}, nonpositive=nonpositive)
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def __str__(self):
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return "{}(base={}, nonpositive={!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(Transform):
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input_dims = output_dims = 1
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def __init__(self, base):
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super().__init__()
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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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@_api.deprecated("3.3", alternative="scale.LogTransform")
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@property
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def LogTransform(self):
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return LogTransform
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@_api.deprecated("3.3", alternative="scale.InvertedLogTransform")
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@property
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def InvertedLogTransform(self):
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return InvertedLogTransform
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def __init__(self, axis, **kwargs):
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"""
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Parameters
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----------
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axis : `~matplotlib.axis.Axis`
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The axis for the scale.
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base : float, default: 10
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The base of the logarithm.
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nonpositive : {'clip', 'mask'}, default: 'clip'
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Determines the behavior for non-positive values. They can either
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be masked as invalid, or clipped to a very small positive number.
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subs : sequence of int, default: None
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Where to place the subticks between each major tick. For example,
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in a log10 scale, ``[2, 3, 4, 5, 6, 7, 8, 9]`` will place 8
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logarithmically spaced minor ticks between each major tick.
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"""
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# After the deprecation, the whole (outer) __init__ can be replaced by
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# def __init__(self, axis, *, base=10, subs=None, nonpositive="clip")
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# The following is to emit the right warnings depending on the axis
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# used, as the *old* kwarg names depended on the axis.
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axis_name = getattr(axis, "axis_name", "x")
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@_api.rename_parameter("3.3", f"base{axis_name}", "base")
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@_api.rename_parameter("3.3", f"subs{axis_name}", "subs")
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@_api.rename_parameter("3.3", f"nonpos{axis_name}", "nonpositive")
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def __init__(*, base=10, subs=None, nonpositive="clip"):
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return base, subs, nonpositive
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base, subs, nonpositive = __init__(**kwargs)
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self._transform = LogTransform(base, nonpositive)
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self.subs = subs
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base = property(lambda self: self._transform.base)
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def set_default_locators_and_formatters(self, axis):
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# docstring inherited
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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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"""Return the `.LogTransform` associated with this scale."""
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return self._transform
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def limit_range_for_scale(self, vmin, vmax, minpos):
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"""Limit the domain to positive values."""
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if not np.isfinite(minpos):
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minpos = 1e-300 # Should rarely (if ever) have 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 : `matplotlib.axis.Axis`
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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, default: 10
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Logarithmic base of the scale.
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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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"""Return the `.Transform` associated with this scale."""
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return self._transform
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class SymmetricalLogTransform(Transform):
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input_dims = output_dims = 1
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def __init__(self, base, linthresh, linscale):
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super().__init__()
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if base <= 1.0:
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raise ValueError("'base' must be larger than 1")
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if linthresh <= 0.0:
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raise ValueError("'linthresh' must be positive")
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if linscale <= 0.0:
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raise ValueError("'linscale' must be positive")
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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 = output_dims = 1
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def __init__(self, base, linthresh, linscale):
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super().__init__()
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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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base : float, default: 10
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The base of the logarithm.
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linthresh : float, default: 2
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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.
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subs : 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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linscale : 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
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decades to use for each half of the linear range. For example, when
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*linscale* == 1.0 (the default), the space used for the positive and
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negative halves of the linear range will be equal to one decade in
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the logarithmic range.
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"""
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name = 'symlog'
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@_api.deprecated("3.3", alternative="scale.SymmetricalLogTransform")
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@property
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def SymmetricalLogTransform(self):
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return SymmetricalLogTransform
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@_api.deprecated(
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"3.3", alternative="scale.InvertedSymmetricalLogTransform")
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@property
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def InvertedSymmetricalLogTransform(self):
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return InvertedSymmetricalLogTransform
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def __init__(self, axis, **kwargs):
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axis_name = getattr(axis, "axis_name", "x")
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# See explanation in LogScale.__init__.
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@_api.rename_parameter("3.3", f"base{axis_name}", "base")
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@_api.rename_parameter("3.3", f"linthresh{axis_name}", "linthresh")
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@_api.rename_parameter("3.3", f"subs{axis_name}", "subs")
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@_api.rename_parameter("3.3", f"linscale{axis_name}", "linscale")
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def __init__(*, base=10, linthresh=2, subs=None, linscale=1):
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return base, linthresh, subs, linscale
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base, linthresh, subs, linscale = __init__(**kwargs)
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self._transform = SymmetricalLogTransform(base, linthresh, linscale)
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self.subs = subs
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base = property(lambda self: self._transform.base)
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linthresh = property(lambda self: self._transform.linthresh)
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linscale = property(lambda self: self._transform.linscale)
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def set_default_locators_and_formatters(self, axis):
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# docstring inherited
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axis.set_major_locator(SymmetricalLogLocator(self.get_transform()))
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axis.set_major_formatter(LogFormatterSciNotation(self.base))
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axis.set_minor_locator(SymmetricalLogLocator(self.get_transform(),
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self.subs))
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axis.set_minor_formatter(NullFormatter())
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def get_transform(self):
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"""Return the `.SymmetricalLogTransform` associated with this scale."""
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return self._transform
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class LogitTransform(Transform):
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input_dims = output_dims = 1
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@_api.rename_parameter("3.3", "nonpos", "nonpositive")
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def __init__(self, nonpositive='mask'):
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super().__init__()
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_api.check_in_list(['mask', 'clip'], nonpositive=nonpositive)
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self._nonpositive = nonpositive
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self._clip = {"clip": True, "mask": False}[nonpositive]
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def transform_non_affine(self, a):
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"""logit transform (base 10), masked or clipped"""
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with np.errstate(divide="ignore", invalid="ignore"):
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out = np.log10(a / (1 - a))
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if self._clip: # See LogTransform for choice of clip value.
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out[a <= 0] = -1000
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out[1 <= a] = 1000
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return out
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def inverted(self):
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return LogisticTransform(self._nonpositive)
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def __str__(self):
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return "{}({!r})".format(type(self).__name__, self._nonpositive)
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class LogisticTransform(Transform):
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input_dims = output_dims = 1
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@_api.rename_parameter("3.3", "nonpos", "nonpositive")
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def __init__(self, nonpositive='mask'):
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super().__init__()
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self._nonpositive = nonpositive
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def transform_non_affine(self, a):
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"""logistic transform (base 10)"""
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return 1.0 / (1 + 10**(-a))
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def inverted(self):
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return LogitTransform(self._nonpositive)
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def __str__(self):
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return "{}({!r})".format(type(self).__name__, self._nonpositive)
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|
|
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class LogitScale(ScaleBase):
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"""
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Logit scale for data between zero and one, both excluded.
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|
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This scale is similar to a log scale close to zero and to one, and almost
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linear around 0.5. It maps the interval ]0, 1[ onto ]-infty, +infty[.
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"""
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name = 'logit'
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@_api.rename_parameter("3.3", "nonpos", "nonpositive")
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def __init__(self, axis, nonpositive='mask', *,
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one_half=r"\frac{1}{2}", use_overline=False):
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r"""
|
|
Parameters
|
|
----------
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axis : `matplotlib.axis.Axis`
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|
Currently unused.
|
|
nonpositive : {'mask', 'clip'}
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|
Determines the behavior for values beyond the open interval ]0, 1[.
|
|
They can either be masked as invalid, or clipped to a number very
|
|
close to 0 or 1.
|
|
use_overline : bool, default: False
|
|
Indicate the usage of survival notation (\overline{x}) in place of
|
|
standard notation (1-x) for probability close to one.
|
|
one_half : str, default: r"\frac{1}{2}"
|
|
The string used for ticks formatter to represent 1/2.
|
|
"""
|
|
self._transform = LogitTransform(nonpositive)
|
|
self._use_overline = use_overline
|
|
self._one_half = one_half
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|
|
|
def get_transform(self):
|
|
"""Return the `.LogitTransform` associated with this scale."""
|
|
return self._transform
|
|
|
|
def set_default_locators_and_formatters(self, axis):
|
|
# docstring inherited
|
|
# ..., 0.01, 0.1, 0.5, 0.9, 0.99, ...
|
|
axis.set_major_locator(LogitLocator())
|
|
axis.set_major_formatter(
|
|
LogitFormatter(
|
|
one_half=self._one_half,
|
|
use_overline=self._use_overline
|
|
)
|
|
)
|
|
axis.set_minor_locator(LogitLocator(minor=True))
|
|
axis.set_minor_formatter(
|
|
LogitFormatter(
|
|
minor=True,
|
|
one_half=self._one_half,
|
|
use_overline=self._use_overline
|
|
)
|
|
)
|
|
|
|
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 # Should rarely (if ever) have 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 the names of the available scales."""
|
|
return sorted(_scale_mapping)
|
|
|
|
|
|
def scale_factory(scale, axis, **kwargs):
|
|
"""
|
|
Return a scale class by name.
|
|
|
|
Parameters
|
|
----------
|
|
scale : {%(names)s}
|
|
axis : `matplotlib.axis.Axis`
|
|
"""
|
|
scale = scale.lower()
|
|
_api.check_in_list(_scale_mapping, scale=scale)
|
|
return _scale_mapping[scale](axis, **kwargs)
|
|
|
|
|
|
if scale_factory.__doc__:
|
|
scale_factory.__doc__ = scale_factory.__doc__ % {
|
|
"names": ", ".join(map(repr, get_scale_names()))}
|
|
|
|
|
|
def register_scale(scale_class):
|
|
"""
|
|
Register a new kind of scale.
|
|
|
|
Parameters
|
|
----------
|
|
scale_class : subclass of `ScaleBase`
|
|
The scale to register.
|
|
"""
|
|
_scale_mapping[scale_class.name] = scale_class
|
|
|
|
|
|
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_type='{%s}' % ', '.join([repr(x) for x in get_scale_names()]),
|
|
scale_docs=_get_scale_docs().rstrip(),
|
|
)
|