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from __future__ import print_function
import numpy as np
from numpy import ma
from matplotlib.cbook import dedent
from matplotlib.ticker import (NullFormatter, ScalarFormatter,
                               LogFormatterMathtext)
from matplotlib.ticker import (NullLocator, LogLocator, AutoLocator,
                               SymmetricalLogLocator)
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`
    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
        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)
            if isinstance(a, ma.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
        has_inverse = True
        base = 10.0
        def transform_non_affine(self, a):
            return ma.power(10.0, a) / 10.0
        def inverted(self):
            return LogScale.Log10Transform()
    class Log2Transform(LogTransformBase):
        base = 2.0
        def transform_non_affine(self, a):
            a = self._handle_nonpos(a * 2.0)
            if isinstance(a, ma.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
        has_inverse = True
        base = 2.0
        def transform_non_affine(self, a):
            return ma.power(2.0, a) / 2.0
        def inverted(self):
            return LogScale.Log2Transform()
    class NaturalLogTransform(LogTransformBase):
        base = np.e
        def transform_non_affine(self, a):
            a = self._handle_nonpos(a * np.e)
            if isinstance(a, ma.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
        has_inverse = True
        base = np.e
        def transform_non_affine(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
        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)
            if isinstance(a, ma.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
        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 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: ``[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 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
        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 SymmetricalLogScale.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 = SymmetricalLogScale.SymmetricalLogTransform(base,
            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 SymmetricalLogScale.SymmetricalLogTransform(
                self.base, self.linthresh, self.linscale)
    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)
        assert base > 1.0
        assert linthresh > 0.0
        assert linscale >= 1.0
        self._transform = self.SymmetricalLogTransform(base,
        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(),
        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)
docstring.interpd.update(
    scale=' | '.join([repr(x) for x in get_scale_names()]),
    scale_docs=get_scale_docs().strip(),
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