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