matplotlib/lib/matplotlib/scale.py at master · feisuo/matplotlib · GitHub

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from __future__ import (absolute_import, division, print_function,

unicode_literals)

import six

import numpy as np

from numpy import ma

from matplotlib.cbook import dedent

from matplotlib.ticker import (NullFormatter, ScalarFormatter,

LogFormatterMathtext, LogitFormatter)

from matplotlib.ticker import (NullLocator, LogLocator, AutoLocator,

SymmetricalLogLocator, LogitLocator)

from matplotlib.transforms import Transform, IdentityTransform

from matplotlib import docstring

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 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 array where all non-positive values are

replaced with NaNs. If there are no non-positive values, the

original array is returned.

"""

mask = a <= 0.0

if mask.any():

return np.where(mask, np.nan, a)

return a

def _clip_non_positives(a):

a = np.array(a, float)

a[a <= 0.0] = 1e-300

return a

class LogTransformBase(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = 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_non_affine(self, a):

a = self._handle_nonpos(a * 10.0)

return np.log10(a)

def inverted(self):

return InvertedLog10Transform()

class InvertedLog10Transform(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

base = 10.0

def transform_non_affine(self, a):

return ma.power(10.0, a) / 10.0

def inverted(self):

return Log10Transform()

class Log2Transform(LogTransformBase):

base = 2.0

def transform_non_affine(self, a):

a = self._handle_nonpos(a * 2.0)

return np.log2(a)

def inverted(self):

return InvertedLog2Transform()

class InvertedLog2Transform(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

base = 2.0

def transform_non_affine(self, a):

return ma.power(2.0, a) / 2.0

def inverted(self):

return Log2Transform()

class NaturalLogTransform(LogTransformBase):

base = np.e

def transform_non_affine(self, a):

a = self._handle_nonpos(a * np.e)

return np.log(a)

def inverted(self):

return InvertedNaturalLogTransform()

class InvertedNaturalLogTransform(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

base = np.e

def transform_non_affine(self, a):

return ma.power(np.e, a) / 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):

Transform.__init__(self)

self.base = base

if nonpos == 'mask':

self._handle_nonpos = _mask_non_positives

else:

self._handle_nonpos = _clip_non_positives

def transform_non_affine(self, a):

a = self._handle_nonpos(a * self.base)

return np.log(a) / np.log(self.base)

def inverted(self):

return InvertedLogTransform(self.base)

class InvertedLogTransform(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

def __init__(self, base):

Transform.__init__(self)

self.base = base

def transform_non_affine(self, a):

return ma.power(self.base, a) / self.base

def inverted(self):

return LogTransform(self.base)

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'

# 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', '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 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*:

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: ``[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(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

def _mask_non_logit(a):

"""

Return a Numpy array where all values outside ]0, 1[ are

replaced with NaNs. If all values are inside ]0, 1[, the original

array is returned.

"""

mask = (a <= 0.0) | (a >= 1.0)

if mask.any():

return np.where(mask, np.nan, a)

return a

def _clip_non_logit(a):

a = np.array(a, float)

a[a <= 0.0] = 1e-300

a[a >= 1.0] = 1 - 1e-300

return a

class LogitTransform(Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

def __init__(self, nonpos):

Transform.__init__(self)

if nonpos == 'mask':

self._handle_nonpos = _mask_non_logit

else:

self._handle_nonpos = _clip_non_logit

self._nonpos = nonpos

def transform_non_affine(self, a):

"""logit transform (base 10), masked or clipped"""

a = self._handle_nonpos(a)

return np.log10(1.0 * a / (1.0 - a))

def inverted(self):

return LogisticTransform(self._nonpos)

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)

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

"""

if nonpos not in ['mask', 'clip']:

raise ValueError("nonposx, nonposy kwarg must be 'mask' or 'clip'")

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).

"""

return (vmin <= 0 and minpos or vmin,

vmax >= 1 and (1 - minpos) or vmax)

_scale_mapping = {

'linear': LinearScale,

'log': LogScale,

'symlog': SymmetricalLogScale,

'logit': LogitScale,

}

def get_scale_names():

names = list(six.iterkeys(_scale_mapping))

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):

"""

*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)

docstring.interpd.update(

scale=' | '.join([repr(x) for x in get_scale_names()]),

scale_docs=get_scale_docs().rstrip(),

)

matplotlib/lib/matplotlib/scale.py at master · feisuo/matplotlib · GitHub

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