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import textwrap
import numpy as np
from numpy import ma
MaskedArray = ma.MaskedArray
from cbook import dedent
from ticker import NullFormatter, ScalarFormatter, LogFormatterMathtext, Formatter
from ticker import NullLocator, LogLocator, AutoLocator, SymmetricalLogLocator, FixedLocator
from 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`
And optionally:
- :meth:`set_default_locators_and_formatters`
- :meth:`limit_range_for_scale`
"""
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):
pass
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_locator(NullLocator())
axis.set_minor_formatter(NullFormatter())
def get_transform(self):
"""
The transform for linear scaling is just the
:class:`~matplotlib.transforms.IdentityTransform`.
"""
return IdentityTransform()
def _mask_non_positives(a):
"""
Return a Numpy masked array where all non-positive values are
masked. If there are no non-positive values, the original array
is returned.
"""
mask = a <= 0.0
if mask.any():
return ma.MaskedArray(a, mask=mask)
return a
def _clip_non_positives(a):
a[a <= 0.0] = 1e-300
return a
class LogScale(ScaleBase):
"""
A standard logarithmic scale. Care is taken so non-positive
values are not plotted.
For computational efficiency (to push as much as possible to Numpy
C code in the common cases), this scale provides different
transforms depending on the base of the logarithm:
- base 10 (:class:`Log10Transform`)
- base 2 (:class:`Log2Transform`)
- base e (:class:`NaturalLogTransform`)
- arbitrary base (:class:`LogTransform`)
"""
name = 'log'
class LogTransformBase(Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, nonpos):
Transform.__init__(self)
if nonpos == 'mask':
self._handle_nonpos = _mask_non_positives
else:
self._handle_nonpos = _clip_non_positives
class Log10Transform(LogTransformBase):
base = 10.0
def transform(self, a):
a = self._handle_nonpos(a * 10.0)
if isinstance(a, MaskedArray):
return ma.log10(a)
return np.log10(a)
def inverted(self):
return LogScale.InvertedLog10Transform()
class InvertedLog10Transform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
base = 10.0
def transform(self, a):
return ma.power(10.0, a) / 10.0
def inverted(self):
return LogScale.Log10Transform()
class Log2Transform(LogTransformBase):
base = 2.0
def transform(self, a):
a = self._handle_nonpos(a * 2.0)
if isinstance(a, MaskedArray):
return ma.log(a) / np.log(2)
return np.log2(a)
def inverted(self):
return LogScale.InvertedLog2Transform()
class InvertedLog2Transform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
base = 2.0
def transform(self, a):
return ma.power(2.0, a) / 2.0
def inverted(self):
return LogScale.Log2Transform()
class NaturalLogTransform(LogTransformBase):
base = np.e
def transform(self, a):
a = self._handle_nonpos(a * np.e)
if isinstance(a, MaskedArray):
return ma.log(a)
return np.log(a)
def inverted(self):
return LogScale.InvertedNaturalLogTransform()
class InvertedNaturalLogTransform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
base = np.e
def transform(self, a):
return ma.power(np.e, a) / np.e
def inverted(self):
return LogScale.NaturalLogTransform()
class LogTransform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, base, nonpos):
Transform.__init__(self)
self.base = base
if nonpos == 'mask':
self._handle_nonpos = _mask_non_positives
else:
self._handle_nonpos = _clip_non_positives
def transform(self, a):
a = self._handle_nonpos(a * self.base)
if isinstance(a, MaskedArray):
return ma.log(a) / np.log(self.base)
return np.log(a) / np.log(self.base)
def inverted(self):
return LogScale.InvertedLogTransform(self.base)
class InvertedLogTransform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, base):
Transform.__init__(self)
self.base = base
def transform(self, a):
return ma.power(self.base, a) / self.base
def inverted(self):
return LogScale.LogTransform(self.base)
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: ``[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]``
will place 10 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', 'mask')
else:
base = kwargs.pop('basey', 10.0)
subs = kwargs.pop('subsy', None)
nonpos = kwargs.pop('nonposy', 'mask')
if nonpos not in ['mask', 'clip']:
raise ValueError("nonposx, nonposy kwarg must be 'mask' or 'clip'")
if base == 10.0:
self._transform = self.Log10Transform(nonpos)
elif base == 2.0:
self._transform = self.Log2Transform(nonpos)
elif base == np.e:
self._transform = self.NaturalLogTransform(nonpos)
else:
self._transform = self.LogTransform(base, nonpos)
self.base = base
self.subs = subs
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(LogFormatterMathtext(self.base))
axis.set_minor_locator(LogLocator(self.base, self.subs))
axis.set_minor_formatter(NullFormatter())
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.
"""
return (vmin <= 0.0 and minpos or vmin,
vmax <= 0.0 and minpos or vmax)
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'
class SymmetricalLogTransform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, base, linthresh):
Transform.__init__(self)
self.base = base
self.linthresh = linthresh
self._log_base = np.log(base)
self._linadjust = (np.log(linthresh) / self._log_base) / linthresh
def transform(self, a):
a = np.asarray(a)
sign = np.sign(a)
masked = ma.masked_inside(a, -self.linthresh, self.linthresh, copy=False)
log = sign * ma.log(np.abs(masked)) / self._log_base
if masked.mask.any():
return np.asarray(ma.where(masked.mask,
a * self._linadjust,
log))
else:
return np.asarray(log)
def inverted(self):
return SymmetricalLogScale.InvertedSymmetricalLogTransform(self.base, self.linthresh)
class InvertedSymmetricalLogTransform(Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, base, linthresh):
Transform.__init__(self)
self.base = base
self.linthresh = linthresh
self._log_base = np.log(base)
self._log_linthresh = np.log(linthresh) / self._log_base
self._linadjust = linthresh / (np.log(linthresh) / self._log_base)
def transform(self, a):
a = np.asarray(a)
return np.where(a <= self._log_linthresh,
np.where(a >= -self._log_linthresh,
a * self._linadjust,
-(np.power(self.base, -a))),
np.power(self.base, a))
def inverted(self):
return SymmetricalLogScale.SymmetricalLogTransform(self.base)
def __init__(self, axis, **kwargs):
"""
*basex*/*basey*:
The base of the logarithm
*linthreshx*/*linthreshy*:
The range (-*x*, *x*) within which the plot is linear (to
avoid 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: ``[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]``
will place 10 logarithmically spaced minor ticks between
each major tick.
"""
if axis.axis_name == 'x':
base = kwargs.pop('basex', 10.0)
linthresh = kwargs.pop('linthreshx', 2.0)
subs = kwargs.pop('subsx', None)
else:
base = kwargs.pop('basey', 10.0)
linthresh = kwargs.pop('linthreshy', 2.0)
subs = kwargs.pop('subsy', None)
self._transform = self.SymmetricalLogTransform(base, linthresh)
self.base = base
self.linthresh = linthresh
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(LogFormatterMathtext(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
_scale_mapping = {
'linear' : LinearScale,
'log' : LogScale,
'symlog' : SymmetricalLogScale
}
def get_scale_names():
names = _scale_mapping.keys()
names.sort()
return names
def scale_factory(scale, axis, **kwargs):
"""
Return a scale class by name.
ACCEPTS: [ %(names)s ]
"""
scale = scale.lower()
if scale is None:
scale = 'linear'
if scale not in _scale_mapping:
raise ValueError("Unknown scale type '%s'" % scale)
return _scale_mapping[scale](axis, **kwargs)
scale_factory.__doc__ = dedent(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
def get_scale_docs():
"""
Helper function for generating docstrings related to scales.
"""
docs = []
for name in get_scale_names():
scale_class = _scale_mapping[name]
docs.append(" '%s'" % name)
docs.append("")
class_docs = dedent(scale_class.__init__.__doc__)
class_docs = "".join([" %s\n" %
x for x in class_docs.split("\n")])
docs.append(class_docs)
docs.append("")
return "\n".join(docs)
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