<gh_stars>1-10
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
Spectrum
========

Defines the classes handling spectral data computation:

-   :class:`SpectralShape`
-   :class:`SpectralPowerDistribution`
-   :class:`TriSpectralPowerDistribution`

See Also
--------
`Spectrum IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/spectrum.ipynb>`_  # noqa
"""

from __future__ import division, unicode_literals

import copy
import itertools
import math
import numpy as np

from colour.algebra import (
    is_iterable,
    is_numeric,
    is_uniform,
    steps,
    to_ndarray)
from colour.algebra import (
    Extrapolator1d,
    LinearInterpolator1d,
    SplineInterpolator,
    SpragueInterpolator)
from colour.utilities import is_string

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = '<EMAIL>'
__status__ = 'Production'

__all__ = ['SpectralShape',
           'SpectralPowerDistribution',
           'TriSpectralPowerDistribution',
           'DEFAULT_SPECTRAL_SHAPE',
           'constant_spd',
           'zeros_spd',
           'ones_spd']


class SpectralShape(object):
    """
    Defines the base object for spectral power distribution shape.

    Parameters
    ----------
    start : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range start in nm.
    end : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range end in nm.
    steps : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range steps.

    Attributes
    ----------
    start
    end
    steps

    Methods
    -------
    __repr__
    __contains__
    __len__
    __eq__
    __ne__
    range

    Examples
    --------
    >>> SpectralShape(360, 830, 1)
    SpectralShape(360, 830, 1)
    """

    def __init__(self, start=None, end=None, steps=None):
        # Attribute storing the spectral shape range for caching purpose.
        self.__range = None

        self.__start = None
        self.__end = None
        self.__steps = None
        self.start = start
        self.end = end
        self.steps = steps

    @property
    def start(self):
        """
        Property for **self.__start** private attribute.

        Returns
        -------
        numeric
            self.__start.
        """

        return self.__start

    @start.setter
    def start(self, value):
        """
        Setter for **self.__start** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'start', value))
            if self.__end is not None:
                assert value < self.__end, (
                    '"{0}" attribute value must be strictly less than '
                    '"{1}"!'.format('start', self.__end))

        # Invalidating the *range* cache.
        if value != self.__start:
            self.__range = None

        self.__start = value

    @property
    def end(self):
        """
        Property for **self.__end** private attribute.

        Returns
        -------
        numeric
            self.__end.
        """

        return self.__end

    @end.setter
    def end(self, value):
        """
        Setter for **self.__end** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'end', value))
            if self.__start is not None:
                assert value > self.__start, (
                    '"{0}" attribute value must be strictly greater than '
                    '"{1}"!'.format('end', self.__start))

        # Invalidating the *range* cache.
        if value != self.__end:
            self.__range = None

        self.__end = value

    @property
    def steps(self):
        """
        Property for **self.__steps** private attribute.

        Returns
        -------
        numeric
            self.__steps.
        """

        return self.__steps

    @steps.setter
    def steps(self, value):
        """
        Setter for **self.__steps** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'steps', value))

        # Invalidating the *range* cache.
        if value != self.__steps:
            self.__range = None

        self.__steps = value

    def __str__(self):
        """
        Returns a nice formatted string representation.

        Returns
        -------
        unicode
            Nice formatted string representation.
        """

        return '({0}, {1}, {2})'.format(self.__start,
                                        self.__end,
                                        self.__steps)

    def __repr__(self):
        """
        Returns a formatted string representation.

        Returns
        -------
        unicode
            Formatted string representation.
        """

        return 'SpectralShape({0}, {1}, {2})'.format(self.__start,
                                                     self.__end,
                                                     self.__steps)

    def __iter__(self):
        """
        Returns a generator for the spectral power distribution data.

        Returns
        -------
        generator
            Spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> shape = SpectralShape(0, 10, 1)
        >>> for wavelength in shape: print(wavelength)
        0
        1
        2
        3
        4
        5
        6
        7
        8
        9
        10
        """

        return iter(self.range())

    def __contains__(self, wavelength):
        """
        Returns if the spectral shape contains the given wavelength
        :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the spectral shape.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> 0.5 in SpectralShape(0, 10, 0.1)
        True
        >>> 0.51 in SpectralShape(0, 10, 0.1)
        False
        """

        return wavelength in self.range()

    def __len__(self):
        """
        Returns the spectral shape wavelengths :math:`\lambda_n`
        count.

        Returns
        -------
        int
            Spectral shape wavelengths :math:`\lambda_n` count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> len(SpectralShape(0, 10, 0.1))
        101
        """

        return len(self.range())

    def __eq__(self, shape):
        """
        Returns the spectral shape equality with given other spectral shape.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape to compare for equality.

        Returns
        -------
        bool
            Spectral shape equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 0.1)
        True
        >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 1)
        False
        """

        return isinstance(shape, self.__class__) and np.array_equal(
            self.range(), shape.range())

    def __ne__(self, shape):
        """
        Returns the spectral shape inequality with given other spectral shape.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape to compare for inequality.

        Returns
        -------
        bool
            Spectral shape inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__ne__` method.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 0.1)
        False
        >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 1)
        True
        """

        return not (self == shape)

    def range(self):
        """
        Returns an iterable range for the spectral power distribution shape.

        Returns
        -------
        ndarray
            Iterable range for the spectral power distribution shape

        Raises
        ------
        RuntimeError
            If one of spectral shape *start*, *end* or *steps* attributes is
            not defined.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1).range()
        array([  0. ,   0.1,   0.2,   0.3,   0.4,   0.5,   0.6,   0.7,   0.8,
                 0.9,   1. ,   1.1,   1.2,   1.3,   1.4,   1.5,   1.6,   1.7,
                 1.8,   1.9,   2. ,   2.1,   2.2,   2.3,   2.4,   2.5,   2.6,
                 2.7,   2.8,   2.9,   3. ,   3.1,   3.2,   3.3,   3.4,   3.5,
                 3.6,   3.7,   3.8,   3.9,   4. ,   4.1,   4.2,   4.3,   4.4,
                 4.5,   4.6,   4.7,   4.8,   4.9,   5. ,   5.1,   5.2,   5.3,
                 5.4,   5.5,   5.6,   5.7,   5.8,   5.9,   6. ,   6.1,   6.2,
                 6.3,   6.4,   6.5,   6.6,   6.7,   6.8,   6.9,   7. ,   7.1,
                 7.2,   7.3,   7.4,   7.5,   7.6,   7.7,   7.8,   7.9,   8. ,
                 8.1,   8.2,   8.3,   8.4,   8.5,   8.6,   8.7,   8.8,   8.9,
                 9. ,   9.1,   9.2,   9.3,   9.4,   9.5,   9.6,   9.7,   9.8,
                 9.9,  10. ])
        """

        if None in (self.__start, self.__end, self.__steps):
            raise RuntimeError(('One of the spectral shape "start", "end" or '
                                '"steps" attributes is not defined!'))

        if self.__range is None:
            self.__range = np.arange(self.__start,
                                     self.__end + self.__steps,
                                     self.__steps)

        return self.__range


class SpectralPowerDistribution(object):
    """
    Defines the base object for spectral data computations.

    Parameters
    ----------
    name : str or unicode
        Spectral power distribution name.
    data : dict
        Spectral power distribution data in a *dict* as follows:
        {wavelength :math:`\lambda_{i}`: value,
        wavelength :math:`\lambda_{i+1}`,
        ...,
        wavelength :math:`\lambda_{i+n}`}

    Attributes
    ----------
    name
    data
    wavelengths
    values
    items
    shape

    Methods
    -------
    __getitem__
    __init__
    __setitem__
    __iter__
    __contains__
    __len__
    __eq__
    __ne__
    __add__
    __sub__
    __mul__
    __div__
    __truediv__
    get
    is_uniform
    extrapolate
    interpolate
    align
    zeros
    normalise
    clone

    Examples
    --------
    >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
    >>> spd = SpectralPowerDistribution('Spd', data)
    >>> spd.wavelengths
    array([510, 520, 530, 540])
    >>> spd.values
    array([ 49.67,  69.59,  81.73,  88.19])
    >>> spd.shape
    SpectralShape(510, 540, 10)
    """

    def __init__(self, name, data):
        self.__name = None
        self.name = name
        self.__data = None
        self.data = data

    @property
    def name(self):
        """
        Property for **self.__name** private attribute.

        Returns
        -------
        str or unicode
            self.__name.
        """

        return self.__name

    @name.setter
    def name(self, value):
        """
        Setter for **self.__name** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert type(value) in (str, unicode), (
                ('"{0}" attribute: "{1}" type is not '
                 '"str" or "unicode"!').format('name', value))
        self.__name = value

    @property
    def data(self):
        """
        Property for **self.__data** private attribute.

        Returns
        -------
        dict
            self.__data.
        """

        return self.__data

    @data.setter
    def data(self, value):
        """
        Setter for **self.__data** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'data', value))
        self.__data = value

    @property
    def wavelengths(self):
        """
        Property for **self.wavelengths** attribute.

        Returns
        -------
        ndarray
            Spectral power distribution wavelengths :math:`\lambda_n`.

        Warning
        -------
        :attr:`SpectralPowerDistribution.wavelengths` is read only.
        """

        return np.array(sorted(self.__data.keys()))

    @wavelengths.setter
    def wavelengths(self, value):
        """
        Setter for **self.wavelengths** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError(
            '"{0}" attribute is read only!'.format('wavelengths'))

    @property
    def values(self):
        """
        Property for **self.values** attribute.

        Returns
        -------
        ndarray
            Spectral power distribution wavelengths :math:`\lambda_n` values.

        Warning
        -------
        :attr:`SpectralPowerDistribution.values` is read only.
        """

        return np.array([self.get(wavelength)
                         for wavelength in self.wavelengths])

    @values.setter
    def values(self, value):
        """
        Setter for **self.values** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('values'))

    @property
    def items(self):
        """
        Property for **self.items** attribute. This is a convenient attribute
        used to iterate over the spectral power distribution.

        Returns
        -------
        generator
            Spectral power distribution data generator.
        """

        return self.__iter__()

    @items.setter
    def items(self, value):
        """
        Setter for **self.items** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('items'))

    @property
    def shape(self):
        """
        Property for **self.shape** attribute.

        Returns the shape of the spectral power distribution in the form of a
        :class:`SpectralShape` class instance.

        Returns
        -------
        SpectralShape
            Spectral power distribution shape.

        See Also
        --------
        SpectralPowerDistribution.is_uniform

        Notes
        -----
        -   A non uniform spectral power distribution may will have multiple
            different steps, in that case
            :attr:`SpectralPowerDistribution.shape` returns the *minimum* steps
            size.

        Warning
        -------
        :attr:`SpectralPowerDistribution.shape` is read only.

        Examples
        --------
        Uniform spectral power distribution:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> SpectralPowerDistribution('Spd', data).shape
        SpectralShape(510, 540, 10)

        Non uniform spectral power distribution:

        >>> data = {512.3: 49.67, 524.5: 69.59, 532.4: 81.73, 545.7: 88.19}
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> SpectralPowerDistribution('Spd', data).shape  # doctest: +ELLIPSIS
        SpectralShape(512.3, 545.7, 7...)
        """

        return SpectralShape(min(self.data.keys()),
                             max(self.data.keys()),
                             min(steps(self.wavelengths)))

    @shape.setter
    def shape(self, value):
        """
        Setter for **self.shape** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('shape'))

    def __hash__(self):
        """
        Returns the spectral power distribution hash value.

        Returns
        -------
        int
            Object hash.

        Notes
        -----
        -   Reimplements the :meth:`object.__hash__` method.

        Warning
        -------
        :class:`SpectralPowerDistribution` class is mutable and should not be
        hashable. However, so that it can be used as a key in some data caches,
        we provide a *__hash__* implementation, **assuming that the underlying
        data will not change for those specific cases**.

        References
        ----------
        .. [1]  http://stackoverflow.com/a/16162138/931625
                (Last accessed 8 August 2014)
        """

        return hash(frozenset(self.__data))

    def __getitem__(self, wavelength):
        """
        Returns the value for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength: numeric
            Wavelength :math:`\lambda` to retrieve the value.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` value.

        See Also
        --------
        SpectralPowerDistribution.get

        Notes
        -----
        -   Reimplements the :meth:`object.__getitem__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[510]  # doctest: +ELLIPSIS
        49.67...
        """

        return self.__data.__getitem__(wavelength)

    def __setitem__(self, wavelength, value):
        """
        Sets the wavelength :math:`\lambda` with given value.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to set.
        value : numeric
            Value for wavelength :math:`\lambda`.

        Notes
        -----
        -   Reimplements the :meth:`object.__setitem__` method.

        Examples
        --------
        >>> spd = SpectralPowerDistribution('Spd', {})
        >>> spd[510] = 49.6700
        >>> spd.values
        array([ 49.67])
        """

        self.__data.__setitem__(wavelength, value)

    def __iter__(self):
        """
        Returns a generator for the spectral power distribution data.

        Returns
        -------
        generator
            Spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> for wavelength, value in spd: print((wavelength, value))  # noqa  # doctest: +ELLIPSIS
        (510, 49.6...)
        (520, 69.5...)
        (530, 81.7...)
        (540, 88.1...)
        """

        return iter(sorted(self.__data.items()))

    def __contains__(self, wavelength):
        """
        Returns if the spectral power distribution contains the given
        wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the spectral power distribution.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> 510 in spd
        True
        """

        return wavelength in self.__data

    def __len__(self):
        """
        Returns the spectral power distribution wavelengths :math:`\lambda_n`
        count.

        Returns
        -------
        int
            Spectral power distribution wavelengths :math:`\lambda_n` count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> len(spd)
        4
        """

        return len(self.__data)

    def __eq__(self, spd):
        """
        Returns the spectral power distribution equality with given other
        spectral power distribution.

        Parameters
        ----------
        spd : SpectralPowerDistribution
            Spectral power distribution to compare for equality.

        Returns
        -------
        bool
            Spectral power distribution equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}
        >>> spd1 = SpectralPowerDistribution('Spd', data1)
        >>> spd2 = SpectralPowerDistribution('Spd', data2)
        >>> spd3 = SpectralPowerDistribution('Spd', data2)
        >>> spd1 == spd2
        False
        >>> spd2 == spd3
        True
        """

        return isinstance(spd, self.__class__) and spd.data == self.data

    def __ne__(self, spd):
        """
        Returns the spectral power distribution inequality with given other
        spectral power distribution.

        Parameters
        ----------
        spd : SpectralPowerDistribution
            Spectral power distribution to compare for inequality.

        Returns
        -------
        bool
            Spectral power distribution inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__ne__` method.

        Examples
        --------
        >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}
        >>> spd1 = SpectralPowerDistribution('Spd', data1)
        >>> spd2 = SpectralPowerDistribution('Spd', data2)
        >>> spd3 = SpectralPowerDistribution('Spd', data2)
        >>> spd1 != spd2
        True
        >>> spd2 != spd3
        False
        """

        return not (self == spd)

    def __format_operand(self, x):
        """
        Formats given :math:`x` variable operand to *numeric* or *ndarray*.

        This method is a convenient method to prepare the given :math:`x`
        variable for the arithmetic operations below.

        Parameters
        ----------
        x : numeric or ndarray or SpectralPowerDistribution
            Variable to format.

        Returns
        -------
        numeric or ndarray
            Formatted operand.
        """

        if issubclass(type(x), SpectralPowerDistribution):
            x = x.values
        elif is_iterable(x):
            x = to_ndarray(x)

        return x

    def __add__(self, x):
        """
        Implements support for spectral power distribution addition.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to add.

        Returns
        -------
        SpectralPowerDistribution
            Variable added spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__sub__, SpectralPowerDistribution.__mul__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__add__` method.

        Warning
        -------
        The addition operation happens in place.

        Examples
        --------
        Adding a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd + 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 59.67,  79.59,  91.73,  98.19])

        Adding an *array_like* variable:

        >>> spd + [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  60.67,   81.59,   94.73,  102.19])

        Adding a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd + spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 110.34,  151.18,  176.46,  190.38])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values + self.__format_operand(x)))

        return self

    def __sub__(self, x):
        """
        Implements support for spectral power distribution subtraction.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to subtract.

        Returns
        -------
        SpectralPowerDistribution
            Variable subtracted spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__mul__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__sub__` method.

        Warning
        -------
        The subtraction operation happens in place.

        Examples
        --------
        Subtracting a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd - 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 39.67,  59.59,  71.73,  78.19])

        Subtracting an *array_like* variable:

        >>> spd - [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 38.67,  57.59,  68.73,  74.19])

        Subtracting a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd - spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([-11., -12., -13., -14.])
        """

        return self + (-self.__format_operand(x))

    def __mul__(self, x):
        """
        Implements support for spectral power distribution multiplication.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to multiply.

        Returns
        -------
        SpectralPowerDistribution
            Variable multiplied spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The multiplication operation happens in place.

        Examples
        --------
        Multiplying a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd * 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 496.7,  695.9,  817.3,  881.9])

        Multiplying an *array_like* variable:

        >>> spd * [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  496.7,  1391.8,  2451.9,  3527.6])

        Multiplying a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd * spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  24671.089,   96855.362,  200393.787,  311099.044])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values * self.__format_operand(x)))

        return self

    def __div__(self, x):
        """
        Implements support for spectral power distribution division.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to divide.

        Returns
        -------
        SpectralPowerDistribution
            Variable divided spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,
        SpectralPowerDistribution.__mul__

        Notes
        -----
        -   Reimplements the :meth:`object.__div__` method.

        Warning
        -------
        The division operation happens in place.

        Examples
        --------
        Dividing a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd / 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 4.967,  6.959,  8.173,  8.819])

        Dividing an *array_like* variable:

        >>> spd / [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 4.967     ,  3.4795    ,  2.72433333,  2.20475   ])

        Dividing a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd / spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 0.1       ,  0.05      ,  0.0333333...,  0.025     ])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values * (1 / self.__format_operand(x))))

        return self

    # Python 3 compatibility.
    __truediv__ = __div__

    def get(self, wavelength, default=None):
        """
        Returns the value for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to retrieve the value.
        default : None or numeric, optional
            Wavelength :math:`\lambda` default value.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` value.

        See Also
        --------
        SpectralPowerDistribution.__getitem__

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd.get(510)  # doctest: +ELLIPSIS
        49.67...
        >>> spd.get(511)  # doctest: +SKIP
        None
        """

        try:
            return self.__getitem__(wavelength)
        except KeyError:
            return default

    def is_uniform(self):
        """
        Returns if the spectral power distribution has uniformly spaced data.

        Returns
        -------
        bool
            Is uniform.

        See Also
        --------
        SpectralPowerDistribution.shape

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.is_uniform()
        True

        Breaking the steps by introducing a new wavelength :math:`\lambda`
        value:

        >>> spd[511] = 3.1415
        >>> spd.is_uniform()
        False
        """

        return is_uniform(self.wavelengths)

    def extrapolate(self,
                    shape,
                    method='Constant',
                    left=None,
                    right=None):
        """
        Extrapolates the spectral power distribution following *CIE 15:2004*
        recommendation.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for extrapolation.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        SpectralPowerDistribution
            Extrapolated spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.align

        References
        ----------
        .. [2]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation
                <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa
                ISBN-13: 978-3-901-90633-6

        .. [3]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 10. EXTRAPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.extrapolate(SpectralShape(400, 700)).shape
        SpectralShape(400, 700, 10)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[400]  # doctest: +ELLIPSIS
        49.67...
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[700]  # doctest: +ELLIPSIS
        88.1...
        """

        extrapolator = Extrapolator1d(
            LinearInterpolator1d(self.wavelengths,
                                 self.values),
            method=method,
            left=left,
            right=right)

        spd_shape = self.shape
        for i in np.arange(spd_shape.start,
                           shape.start - spd_shape.steps,
                           -spd_shape.steps):
            self[i] = extrapolator(float(i))
        for i in np.arange(spd_shape.end,
                           shape.end + spd_shape.steps,
                           spd_shape.steps):
            self[i] = extrapolator(float(i))

        return self

    def interpolate(self, shape=SpectralShape(), method=None):
        """
        Interpolates the spectral power distribution following
        *CIE 167:2005* recommendations: the method developed by
        *Sprague (1880)* should be used for interpolating functions having a
        uniformly spaced independent variable and a *Cubic Spline* method for
        non-uniformly spaced independent variable.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for interpolation.
        method : unicode, optional
            ('Sprague', 'Cubic Spline', 'Linear'),
            Enforce given interpolation method.

        Returns
        -------
        SpectralPowerDistribution
            Interpolated spectral power distribution.

        Raises
        ------
        RuntimeError
            If the *Sprague* interpolation method is forced with a
            non-uniformly spaced independent variable.
        ValueError
            If the interpolation method is not defined.

        See Also
        --------
        SpectralPowerDistribution.align

        Notes
        -----
        -   Interpolation will be conducted over boundaries range, if you need
            to extend the range of the spectral power distribution use the
            :meth:`SpectralPowerDistribution.extrapolate` or
            :meth:`SpectralPowerDistribution.align` methods.
        -   *Sprague* interpolator cannot be used for interpolating
            functions having a non-uniformly spaced independent variable.

        Warning
        -------
        -   If *scipy* is not unavailable the *Cubic Spline* method will
            fallback to legacy *Linear* interpolation.
        -   *Linear* interpolator requires at least 2 wavelengths
            :math:`\lambda_n` for interpolation.
        -   *Cubic Spline* interpolator requires at least 3 wavelengths
            :math:`\lambda_n` for interpolation.
        -   *Sprague* interpolator requires at least 6 wavelengths
            :math:`\lambda_n` for interpolation.

        References
        ----------
        .. [4]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 9. INTERPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        Uniform data is using *Sprague* interpolation by default:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd[515]  # doctest: +ELLIPSIS
        60.3121800...

        Non uniform data is using *Cubic Spline* interpolation by default:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd[511] = 31.41
        >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd[515]  # doctest: +ELLIPSIS
        21.4792222...

        Enforcing *Linear* interpolation:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[515]  # doctest: +ELLIPSIS
        59.63...
        """

        spd_shape = self.shape
        boundaries = zip((shape.start, shape.end, shape.steps),
                         (spd_shape.start, spd_shape.end, spd_shape.steps))
        boundaries = [x[0] if x[0] is not None else x[1] for x in boundaries]
        shape = SpectralShape(*boundaries)

        # Defining proper interpolation bounds.
        # TODO: Provide support for fractional steps like 0.1, etc...
        shape.start = max(shape.start, math.ceil(spd_shape.start))
        shape.end = min(shape.end, math.floor(spd_shape.end))

        wavelengths, values = self.wavelengths, self.values
        is_uniform = self.is_uniform()

        if is_string(method):
            method = method.lower()

        if method is None:
            if is_uniform:
                interpolator = SpragueInterpolator(wavelengths, values)
            else:
                interpolator = SplineInterpolator(wavelengths, values)
        elif method == 'sprague':
            if is_uniform:
                interpolator = SpragueInterpolator(wavelengths, values)
            else:
                raise RuntimeError(
                    ('"Sprague" interpolator can only be used for '
                     'interpolating functions having a uniformly spaced '
                     'independent variable!'))
        elif method == 'cubic spline':
            interpolator = SplineInterpolator(wavelengths, values)
        elif method == 'linear':
            interpolator = LinearInterpolator1d(wavelengths, values)
        else:
            raise ValueError(
                'Undefined "{0}" interpolator!'.format(method))

        self.__data = dict([(wavelength, float(interpolator(wavelength)))
                            for wavelength in shape])
        return self

    def align(self,
              shape,
              method='Constant',
              left=None,
              right=None):
        """
        Aligns the spectral power distribution to given spectral shape:
        Interpolates first then extrapolates to fit the given range.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for alignment.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        SpectralPowerDistribution
            Aligned spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.extrapolate,
        SpectralPowerDistribution.interpolate

        Examples
        --------
        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> # Doctests skip for Python 2.x compatibility.
        >>> spd.wavelengths  # doctest: +SKIP
        array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,
               518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,
               531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,
               544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,
               557, 558, 559, 560, 561, 562, 563, 564, 565])
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 49.67     ...,  49.67     ...,  49.67     ...,  49.67     ...,
                49.67     ...,  49.67     ...,  51.8341162...,  53.9856467...,
                56.1229464...,  58.2366197...,  60.3121800...,  62.3327095...,
                64.2815187...,  66.1448055...,  67.9143153...,  69.59     ...,
                71.1759958...,  72.6627938...,  74.0465756...,  75.3329710...,
                76.5339542...,  77.6647421...,  78.7406907...,  79.7741932...,
                80.7715767...,  81.73     ...,  82.6407518...,  83.507872 ...,
                84.3326333...,  85.109696 ...,  85.8292968...,  86.47944  ...,
                87.0480863...,  87.525344 ...,  87.9056578...,  88.19     ...,
                88.3858347...,  88.4975634...,  88.5258906...,  88.4696570...,
                88.3266460...,  88.0943906...,  87.7709802...,  87.3558672...,
                86.8506741...,  86.26     ...,  85.5911699...,  84.8503430...,
                84.0434801...,  83.1771110...,  82.2583874...,  81.2951360...,
                80.2959122...,  79.2700525...,  78.2277286...,  77.18     ...,
                77.18     ...,  77.18     ...,  77.18     ...,  77.18     ...,  77.18      ])
        """

        self.interpolate(shape)
        self.extrapolate(shape, method, left, right)

        return self

    def zeros(self, shape=SpectralShape()):
        """
        Zeros fills the spectral power distribution: Missing values will be
        replaced with zeros to fit the defined range.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for zeros fill.

        Returns
        -------
        SpectralPowerDistribution
            Zeros filled spectral power distribution.

        Examples
        --------
        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  49.67,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  69.59,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,  81.73,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,  88.19,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  86.26,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  77.18,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ])
        """

        spd_shape = self.shape
        boundaries = zip((shape.start, shape.end, shape.steps),
                         (spd_shape.start, spd_shape.end, spd_shape.end))
        boundaries = [x[0] if x[0] is not None else x[1] for x in boundaries]
        shape = SpectralShape(*boundaries)

        self.__data = dict(
            [(wavelength, self.get(wavelength, 0)) for wavelength in shape])

        return self

    def normalise(self, factor=1):
        """
        Normalises the spectral power distribution with given normalization
        factor.

        Parameters
        ----------
        factor : numeric, optional
            Normalization factor

        Returns
        -------
        SpectralPowerDistribution
            Normalised spectral power distribution.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.normalise()  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 0.5632157...,  0.7890917...,  0.9267490...,  1.        ])
        """

        return (self * (1 / max(self.values))) * factor

    def clone(self):
        """
        Clones the spectral power distribution.

        Most of the :class:`SpectralPowerDistribution` class operations are
        conducted in-place. The :meth:`SpectralPowerDistribution.clone` method
        provides a convenient way to copy the spectral power distribution to a
        new object.

        Returns
        -------
        SpectralPowerDistribution
            Cloned spectral power distribution.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> print(spd)  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd_clone = spd.clone()
        >>> print(spd_clone)  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        """

        return copy.deepcopy(self)


class TriSpectralPowerDistribution(object):
    """
    Defines the base object for colour matching functions.

    A compound of three :class:`SpectralPowerDistribution` is used to store
    the underlying axis data.

    Parameters
    ----------
    name : str or unicode
        Tri-spectral power distribution name.
    data : dict
        Tri-spectral power distribution data.
    mapping : dict
        Tri-spectral power distribution attributes mapping.
    labels : dict
        Tri-spectral power distribution axis labels mapping.

    Attributes
    ----------
    name
    mapping
    data
    labels
    x
    y
    z
    wavelengths
    values
    items
    shape

    Methods
    -------
    __init__
    __getitem__
    __setitem__
    __iter__
    __contains__
    __len__
    __eq__
    __ne__
    __add__
    __sub__
    __mul__
    __div__
    __truediv__
    get
    is_uniform
    extrapolate
    interpolate
    align
    zeros
    normalise
    clone

    See Also
    --------
    colour.colorimetry.cmfs.LMS_ConeFundamentals,
    colour.colorimetry.cmfs.RGB_ColourMatchingFunctions,
    colour.colorimetry.cmfs.XYZ_ColourMatchingFunctions

    Examples
    --------
    >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
    >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
    >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
    >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
    >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
    >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
    >>> tri_spd.wavelengths
    array([510, 520, 530, 540])
    >>> tri_spd.values
    array([[ 49.67,  90.56,  12.43],
           [ 69.59,  87.34,  23.15],
           [ 81.73,  45.76,  67.98],
           [ 88.19,  23.45,  90.28]])
    >>> tri_spd.shape
    SpectralShape(510, 540, 10)
    """

    def __init__(self, name, data, mapping, labels):
        self.__name = None
        self.name = name
        self.__mapping = mapping
        self.__data = None
        self.data = data
        self.__labels = labels

    @property
    def name(self):
        """
        Property for **self.__name** private attribute.

        Returns
        -------
        str or unicode
            self.__name.
        """

        return self.__name

    @name.setter
    def name(self, value):
        """
        Setter for **self.__name** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert type(value) in (str, unicode), (
                ('"{0}" attribute: "{1}" type is not '
                 '"str" or "unicode"!').format('name', value))
        self.__name = value

    @property
    def mapping(self):
        """
        Property for **self.__mapping** private attribute.

        Returns
        -------
        dict
            self.__mapping.
        """

        return self.__mapping

    @mapping.setter
    def mapping(self, value):
        """
        Setter for **self.__mapping** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'mapping', value))
            for axis in ('x', 'y', 'z'):
                assert axis in value.keys(), (
                    '"{0}" attribute: "{1}" axis label is missing!'.format(
                        'mapping', axis))
        self.__mapping = value

    @property
    def data(self):
        """
        Property for **self.__data** private attribute.

        Returns
        -------
        dict
            self.__data.
        """

        return self.__data

    @data.setter
    def data(self, value):
        """
        Setter for **self.__data** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'data', value))
            for axis in ('x', 'y', 'z'):
                assert self.__mapping.get(axis) in value.keys(), (
                    '"{0}" attribute: "{1}" axis is missing!'.format(
                        'data', axis))

            data = {}
            for axis in ('x', 'y', 'z'):
                data[axis] = SpectralPowerDistribution(
                    self.__mapping.get(axis),
                    value.get(self.__mapping.get(axis)))

            np.testing.assert_almost_equal(
                data['x'].wavelengths,
                data['y'].wavelengths,
                err_msg=('"{0}" attribute: "{1}" and "{2}" wavelengths are '
                         'different!').format('data',
                                              self.__mapping.get('x'),
                                              self.__mapping.get('y')))
            np.testing.assert_almost_equal(
                data['x'].wavelengths,
                data['z'].wavelengths,
                err_msg=('"{0}" attribute: "{1}" and "{2}" wavelengths are '
                         'different!').format('data',
                                              self.__mapping.get('x'),
                                              self.__mapping.get('z')))

            self.__data = data
        else:
            self.__data = None

    @property
    def labels(self):
        """
        Property for **self.__labels** private attribute.

        Returns
        -------
        dict
            self.__labels.
        """

        return self.__labels

    @labels.setter
    def labels(self, value):
        """
        Setter for **self.__labels** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'labels', value))
            for axis in ('x', 'y', 'z'):
                assert axis in value.keys(), (
                    '"{0}" attribute: "{1}" axis label is missing!'.format(
                        'labels', axis))
        self.__labels = value

    @property
    def x(self):
        """
        Property for **self.x** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *x* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.x` is read only.
        """

        return self.__data.get('x')

    @x.setter
    def x(self, value):
        """
        Setter for **self.x** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('x'))

    @property
    def y(self):
        """
        Property for **self.y** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *y* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.y` is read only.
        """

        return self.__data.get('y')

    @y.setter
    def y(self, value):
        """
        Setter for **self.y** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('y'))

    @property
    def z(self):
        """
        Property for **self.z** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *z* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.z` is read only.
        """

        return self.__data.get('z')

    @z.setter
    def z(self, value):
        """
        Setter for **self.z** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('z'))

    @property
    def wavelengths(self):
        """
        Property for **self.wavelengths** attribute.

        Returns
        -------
        ndarray
            Tri-spectral power distribution wavelengths :math:`\lambda_n`.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.wavelengths` is read only.
        """

        return self.x.wavelengths

    @wavelengths.setter
    def wavelengths(self, value):
        """
        Setter for **self.wavelengths** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError(
            '"{0}" attribute is read only!'.format('wavelengths'))

    @property
    def values(self):
        """
        Property for **self.values** attribute.

        Returns
        -------
        ndarray
            Tri-spectral power distribution wavelengths :math:`\lambda_n`
            values.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.values` is read only.
        """

        return np.array([self.get(wavelength)
                         for wavelength in self.wavelengths])

    @values.setter
    def values(self, value):
        """
        Setter for **self.values** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('values'))

    @property
    def items(self):
        """
        Property for **self.items** attribute. This is a convenient attribute
        used to iterate over the tri-spectral power distribution.

        Returns
        -------
        generator
            Tri-spectral power distribution data generator.
        """

        return self.__iter__()

    @items.setter
    def items(self, value):
        """
        Setter for **self.items** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('items'))

    @property
    def shape(self):
        """
        Property for **self.shape** attribute.

        Returns the shape of the tri-spectral power distribution in the form of
        a :class:`SpectralShape` class instance.

        Returns
        -------
        SpectralShape
            Tri-spectral power distribution shape.

        See Also
        --------
        SpectralPowerDistribution.is_uniform,
        TriSpectralPowerDistribution.is_uniform

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.shape` is read only.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.shape
        SpectralShape(510, 540, 10)
        """

        return self.x.shape

    @shape.setter
    def shape(self, value):
        """
        Setter for **self.shape** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('shape'))

    def __hash__(self):
        """
        Returns the spectral power distribution hash value.

        Returns
        -------
        int
            Object hash.

        Notes
        -----
        -   Reimplements the :meth:`object.__hash__` method.

        Warning
        -------
        See :meth:`SpectralPowerDistribution.__hash__` method warning section.

        References
        ----------
        .. [5]  http://stackoverflow.com/a/16162138/931625
                (Last accessed 8 August 2014)
        """

        return hash((frozenset(self.__data.get('x')),
                     frozenset(self.__data.get('y')),
                     frozenset(self.__data.get('z'))))

    def __getitem__(self, wavelength):
        """
        Returns the values for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength: numeric
            Wavelength :math:`\lambda` to retrieve the values.

        Returns
        -------
        ndarray, (3,)
            Wavelength :math:`\lambda` values.

        See Also
        --------
        TriSpectralPowerDistribution.get

        Notes
        -----
        -   Reimplements the :meth:`object.__getitem__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510]
        array([ 49.67,  90.56,  12.43])
        """

        return np.array((self.x[wavelength],
                         self.y[wavelength],
                         self.z[wavelength]))

    def __setitem__(self, wavelength, value):
        """
        Sets the wavelength :math:`\lambda` with given value.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to set.
        value : array_like
            Value for wavelength :math:`\lambda`.

        Notes
        -----
        -   Reimplements the :meth:`object.__setitem__` method.

        Examples
        --------
        >>> x_bar = {}
        >>> y_bar = {}
        >>> z_bar = {}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510] = (49.6700, 49.6700, 49.6700)
        >>> tri_spd.values
        array([[ 49.67,  49.67,  49.67]])
        """

        x, y, z = np.ravel(value)

        self.x.__setitem__(wavelength, x)
        self.y.__setitem__(wavelength, y)
        self.z.__setitem__(wavelength, z)

    def __iter__(self):
        """
        Returns a generator for the tri-spectral power distribution data.

        Returns
        -------
        generator
            Tri-spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> for wavelength, value in tri_spd: print((wavelength, value))
        (510, array([ 49.67,  90.56,  12.43]))
        (520, array([ 69.59,  87.34,  23.15]))
        (530, array([ 81.73,  45.76,  67.98]))
        (540, array([ 88.19,  23.45,  90.28]))
        """

        return itertools.izip(self.wavelengths, self.values)

    def __contains__(self, wavelength):
        """
        Returns if the tri-spectral power distribution contains the given
        wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the tri-spectral power
            distribution.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> 510 in tri_spd
        True

        """

        return wavelength in self.x

    def __len__(self):
        """
        Returns the tri-spectral power distribution wavelengths
        :math:`\lambda_n` count.

        Returns
        -------
        int
            Tri-Spectral power distribution wavelengths :math:`\lambda_n`
            count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> len(tri_spd)
        4
        """

        return len(self.x)

    def __eq__(self, tri_spd):
        """
        Returns the tri-spectral power distribution equality with given other
        tri-spectral power distribution.

        Parameters
        ----------
        spd : TriSpectralPowerDistribution
            Tri-spectral power distribution to compare for equality.

        Returns
        -------
        bool
            Tri-spectral power distribution equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)
        >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd1 == tri_spd2
        False
        >>> tri_spd1 == tri_spd3
        True
        """

        if not isinstance(tri_spd, self.__class__):
            return False

        equality = True
        for axis in self.__mapping:
            equality *= getattr(self, axis) == getattr(tri_spd, axis)

        return bool(equality)

    def __ne__(self, tri_spd):
        """
        Returns the tri-spectral power distribution inequality with given other
        tri-spectral power distribution.

        Parameters
        ----------
        spd : TriSpectralPowerDistribution
            Tri-spectral power distribution to compare for inequality.

        Returns
        -------
        bool
            Tri-spectral power distribution inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)
        >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd1 != tri_spd2
        True
        >>> tri_spd1 != tri_spd3
        False
        """

        return not (self == tri_spd)

    def __format_operand(self, x):
        """
        Formats given :math:`x` variable operand to *numeric* or *ndarray*.

        This method is a convenient method to prepare the given :math:`x`
        variable for the arithmetic operations below.

        Parameters
        ----------
        x : numeric or ndarray or TriSpectralPowerDistribution
            Variable to format.

        Returns
        -------
        numeric or ndarray
            Formatted operand.
        """

        if issubclass(type(x), TriSpectralPowerDistribution):
            x = x.values
        elif is_iterable(x):
            x = to_ndarray(x)

        return x

    def __add__(self, x):
        """
        Implements support for tri-spectral power distribution addition.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to add.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable added tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__mul__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__add__` method.

        Warning
        -------
        The addition operation happens in place.

        Examples
        --------
        Adding a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd + 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  59.67,  100.56,   22.43],
               [  79.59,   97.34,   33.15],
               [  91.73,   55.76,   77.98],
               [  98.19,   33.45,  100.28]])

        Adding an *array_like* variable:

        >>> tri_spd + [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  60.67,  102.56,   25.43],
               [  80.59,   99.34,   36.15],
               [  92.73,   57.76,   80.98],
               [  99.19,   35.45,  103.28]])

        Adding a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd + tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  73.1 ,  152.23,  115.99],
               [ 103.74,  168.93,  123.49],
               [ 160.71,  139.49,  126.74],
               [ 189.47,  123.64,  126.73]])
        """

        values = self.values + self.__format_operand(x)

        for i, axis in enumerate(('x', 'y', 'z')):
            self.__data[axis].data = dict(zip(self.wavelengths, values[:, i]))

        return self

    def __sub__(self, x):
        """
        Implements support for tri-spectral power distribution subtraction.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to subtract.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable subtracted tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__mul__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__sub__` method.

        Warning
        -------
        The subtraction operation happens in place.

        Examples
        --------
        Subtracting a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd - 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 39.67,  80.56,   2.43],
               [ 59.59,  77.34,  13.15],
               [ 71.73,  35.76,  57.98],
               [ 78.19,  13.45,  80.28]])

        Subtracting an *array_like* variable:

        >>> tri_spd - [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 38.67,  78.56,  -0.57],
               [ 58.59,  75.34,  10.15],
               [ 70.73,  33.76,  54.98],
               [ 77.19,  11.45,  77.28]])

        Subtracting a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd - tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 26.24,  28.89, -91.13],
               [ 35.44,   5.75, -77.19],
               [  2.75, -47.97,   9.22],
               [-13.09, -76.74,  53.83]])
        """

        return self + (-self.__format_operand(x))

    def __mul__(self, x):
        """
        Implements support for tri-spectral power distribution multiplication.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to multiply.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable multiplied tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The multiplication operation happens in place.

        Examples
        --------
        Multiplying a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd * 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 496.7,  905.6,  124.3],
               [ 695.9,  873.4,  231.5],
               [ 817.3,  457.6,  679.8],
               [ 881.9,  234.5,  902.8]])

        Multiplying an *array_like* variable:

        >>> tri_spd * [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  1986.8,   7244.8,   1491.6],
               [  2783.6,   6987.2,   2778. ],
               [  3269.2,   3660.8,   8157.6],
               [  3527.6,   1876. ,  10833.6]])

        Multiplying a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd * tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  24695.924,  359849.216,  135079.296],
               [  64440.34 ,  486239.248,  242630.52 ],
               [ 222240.216,  299197.184,  373291.776],
               [ 318471.728,  165444.44 ,  254047.92 ]])
        """

        values = self.values * self.__format_operand(x)

        for i, axis in enumerate(('x', 'y', 'z')):
            self.__data[axis].data = dict(zip(self.wavelengths, values[:, i]))

        return self

    def __div__(self, x):
        """
        Implements support for tri-spectral power distribution division.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to divide.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable divided tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__mul__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The division operation happens in place.

        Examples
        --------
        Dividing a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd / 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 4.967,  9.056,  1.243],
               [ 6.959,  8.734,  2.315],
               [ 8.173,  4.576,  6.798],
               [ 8.819,  2.345,  9.028]])

        Dividing an *array_like* variable:

        >>> tri_spd / [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 19.868     ,  18.112     ,   1.6573333...],
               [ 27.836     ,  17.468     ,   3.0866666...],
               [ 32.692     ,   9.152     ,   9.064    ...],
               [ 35.276     ,   4.69      ,  12.0373333...]])

        Dividing a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd / tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 1.5983909...,  0.3646466...,  0.0183009...],
               [ 1.2024190...,  0.2510130...,  0.0353408...],
               [ 0.4809061...,  0.1119784...,  0.1980769...],
               [ 0.3907399...,  0.0531806...,  0.5133191...]])
        """

        return self * (1 / self.__format_operand(x))

    # Python 3 compatibility.
    __truediv__ = __div__

    def get(self, wavelength, default=None):
        """
        Returns the values for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to retrieve the values.
        default : None or numeric, optional
            Wavelength :math:`\lambda` default values.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` values.

        See Also
        --------
        TriSpectralPowerDistribution.__getitem__

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510]
        array([ 49.67,  90.56,  12.43])
        >>> tri_spd.get(511)  # doctest: +SKIP
        None
        """

        try:
            return self.__getitem__(wavelength)
        except KeyError:
            return default

    def is_uniform(self):
        """
        Returns if the tri-spectral power distribution has uniformly spaced
        data.

        Returns
        -------
        bool
            Is uniform.

        See Also
        --------
        TriSpectralPowerDistribution.shape

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.is_uniform()
        True

        Breaking the steps by introducing new wavelength :math:`\lambda`
        values:

        >>> tri_spd[511] = (49.6700, 49.6700, 49.6700)
        >>> tri_spd.is_uniform()
        False
        """

        for i in self.__mapping.keys():
            if not getattr(self, i).is_uniform():
                return False
        return True

    def extrapolate(self,
                    shape,
                    method='Constant',
                    left=None,
                    right=None):
        """
        Extrapolates the tri-spectral power distribution following
        *CIE 15:2004* recommendation.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for extrapolation.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        TriSpectralPowerDistribution
            Extrapolated tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.align

        References
        ----------

        .. [6]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation
                <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa
                ISBN-13: 978-3-901-90633-6
        .. [7]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 10. EXTRAPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.extrapolate(SpectralShape(400, 700)).shape
        SpectralShape(400, 700, 10)
        >>> tri_spd[400]
        array([ 49.67,  90.56,  12.43])
        >>> tri_spd[700]
        array([ 88.19,  23.45,  90.28])
        """

        for i in self.__mapping.keys():
            getattr(self, i).extrapolate(shape, method, left, right)

        return self

    def interpolate(self, shape=SpectralShape(), method=None):
        """
        Interpolates the tri-spectral power distribution following
        *CIE 167:2005* recommendations: the method developed by
        *Sprague (1880)* should be used for interpolating functions having a
        uniformly spaced independent variable and a *Cubic Spline* method for
        non-uniformly spaced independent variable.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for interpolation.
        method : unicode, optional
            ('Sprague', 'Cubic Spline', 'Linear'),
            Enforce given interpolation method.

        Returns
        -------
        TriSpectralPowerDistribution
            Interpolated tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.align

        Notes
        -----
        -   See :meth:`SpectralPowerDistribution.interpolate` method
            notes section.

        Warning
        -------
        See :meth:`SpectralPowerDistribution.interpolate` method warning
        section.

        References
        ----------
        .. [8]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 9. INTERPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        Uniform data is using *Sprague* interpolation by default:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([ 60.30332087,  93.27163315,  13.86051361])

        Non uniform data is using *Cubic Spline* interpolation by default:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[511] = (31.41, 95.27, 15.06)
        >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([  21.47104053,  100.64300155,   18.8165196 ])

        Enforcing *Linear* interpolation:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([ 59.63,  88.95,  17.79])
        """

        for i in self.__mapping.keys():
            getattr(self, i).interpolate(shape, method)

        return self

    def align(self,
              shape,
              method='Constant',
              left=None,
              right=None):
        """
        Aligns the tri-spectral power distribution to given shape: Interpolates
        first then extrapolates to fit the given range.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for alignment.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        TriSpectralPowerDistribution
            Aligned tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.extrapolate,
        TriSpectralPowerDistribution.interpolate

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> # Doctests skip for Python 2.x compatibility.
        >>> tri_spd.wavelengths  # doctest: +SKIP
        array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,
               518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,
               531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,
               544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,
               557, 558, 559, 560, 561, 562, 563, 564, 565])
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 51.8325938...,  91.2994928...,  12.5377184...],
               [ 53.9841952...,  91.9502387...,  12.7233193...],
               [ 56.1205452...,  92.5395463...,  12.9651679...],
               [ 58.2315395...,  93.0150037...,  13.3123777...],
               [ 60.3033208...,  93.2716331...,  13.8605136...],
               [ 62.3203719...,  93.1790455...,  14.7272944...],
               [ 64.2676077...,  92.6085951...,  16.0282961...],
               [ 66.1324679...,  91.4605335...,  17.8526544...],
               [ 67.9070097...,  89.6911649...,  20.2387677...],
               [ 69.59     ...,  87.34     ...,  23.15     ...],
               [ 71.1837378...,  84.4868033...,  26.5150469...],
               [ 72.6800056...,  81.0666018...,  30.3964852...],
               [ 74.0753483...,  77.0766254...,  34.7958422...],
               [ 75.3740343...,  72.6153870...,  39.6178858...],
               [ 76.5856008...,  67.8490714...,  44.7026805...],
               [ 77.7223995...,  62.9779261...,  49.8576432...],
               [ 78.7971418...,  58.2026503...,  54.8895997...],
               [ 79.8204447...,  53.6907852...,  59.6368406...],
               [ 80.798376 ...,  49.5431036...,  64.0011777...],
               [ 81.73     ...,  45.76     ...,  67.98     ...],
               [ 82.6093606...,  42.2678534...,  71.6460893...],
               [ 83.439232 ...,  39.10608  ...,  74.976976 ...],
               [ 84.2220071...,  36.3063728...,  77.9450589...],
               [ 84.956896 ...,  33.85464  ...,  80.552    ...],
               [ 85.6410156...,  31.7051171...,  82.8203515...],
               [ 86.27048  ...,  29.79448  ...,  84.785184 ...],
               [ 86.8414901...,  28.0559565...,  86.4857131...],
               [ 87.351424 ...,  26.43344  ...,  87.956928 ...],
               [ 87.7999266...,  24.8956009...,  89.2212178...],
               [ 88.19     ...,  23.45     ...,  90.28     ...],
               [ 88.5265036...,  22.1424091...,  91.1039133...],
               [ 88.8090803...,  20.9945234...,  91.6538035...],
               [ 89.0393279...,  20.0021787...,  91.9333499...],
               [ 89.2222817...,  19.1473370...,  91.9858818...],
               [ 89.3652954...,  18.4028179...,  91.8811002...],
               [ 89.4769231...,  17.7370306...,  91.7018000...],
               [ 89.5657996...,  17.1187058...,  91.5305910...],
               [ 89.6395227...,  16.5216272...,  91.4366204...],
               [ 89.7035339...,  15.9293635...,  91.4622944...],
               [ 89.76     ...,  15.34     ...,  91.61     ...],
               [ 89.8094041...,  14.7659177...,  91.8528616...],
               [ 89.8578890...,  14.2129190...,  92.2091737...],
               [ 89.9096307...,  13.6795969...,  92.6929664...],
               [ 89.9652970...,  13.1613510...,  93.2988377...],
               [ 90.0232498...,  12.6519811...,  94.0078786...],
               [ 90.0807467...,  12.1452800...,  94.7935995...],
               [ 90.1351435...,  11.6366269...,  95.6278555...],
               [ 90.1850956...,  11.1245805...,  96.4867724...],
               [ 90.2317606...,  10.6124724...,  97.3566724...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...]])
        """

        for i in self.__mapping.keys():
            getattr(self, i).align(shape, method, left, right)

        return self

    def zeros(self, shape=SpectralShape()):
        """
        Zeros fills the tri-spectral power distribution: Missing values will be
        replaced with zeros to fit the defined range.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for zeros fill.

        Returns
        -------
        TriSpectralPowerDistribution
            Zeros filled tri-spectral power distribution.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 49.67,  90.56,  12.43],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 69.59,  87.34,  23.15],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 81.73,  45.76,  67.98],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 88.19,  23.45,  90.28],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 89.76,  15.34,  91.61],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 90.28,  10.11,  98.24],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ]])
        """

        for i in self.__mapping.keys():
            getattr(self, i).zeros(shape)

        return self

    def normalise(self, factor=1):
        """
        Normalises the tri-spectral power distribution with given normalization
        factor.

        Parameters
        ----------
        factor : numeric, optional
            Normalization factor

        Returns
        -------
        TriSpectralPowerDistribution
            Normalised tri- spectral power distribution.

        Notes
        -----
        -   The implementation uses the maximum value for all axis.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.normalise()  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 0.5055985...,  0.9218241...,  0.1265268...],
               [ 0.7083672...,  0.8890472...,  0.2356473...],
               [ 0.8319421...,  0.4657980...,  0.6919788...],
               [ 0.8976995...,  0.2387011...,  0.9189739...],
               [ 0.9136807...,  0.1561482...,  0.9325122...],
               [ 0.9189739...,  0.1029112...,  1.       ...]])
        """

        maximum = max(np.ravel(self.values))
        for i in self.__mapping.keys():
            getattr(self, i) * (1 / maximum) * factor

        return self

    def clone(self):
        """
        Clones the tri-spectral power distribution.

        Most of the :class:`TriSpectralPowerDistribution` class operations are
        conducted in-place. The :meth:`TriSpectralPowerDistribution.clone`
        method provides a convenient way to copy the tri-spectral power
        distribution to a new object.

        Returns
        -------
        TriSpectralPowerDistribution
            Cloned tri-spectral power distribution.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> print(tri_spd)  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd_clone = tri_spd.clone()
        >>> print(tri_spd_clone)  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        """

        return copy.deepcopy(self)


DEFAULT_SPECTRAL_SHAPE = SpectralShape(360, 830, 1)
"""
Default spectral shape using the shape of
*CIE 1931 2 Degree Standard Observer*.

DEFAULT_SPECTRAL_SHAPE : SpectralShape
"""


def constant_spd(k,
                 shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    constant :math:`k` values.

    Parameters
    ----------
    k : numeric
        Constant :math:`k` to fill the spectral power distribution with.
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Constant :math:`k` to filled spectral power distribution.

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = constant_spd(100)
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    100.0
    """

    wavelengths = shape.range()
    values = np.full(len(wavelengths), k)

    name = '{0} Constant'.format(k)
    return SpectralPowerDistribution(name, dict(zip(wavelengths, values)))


def zeros_spd(shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    zeros.

    Parameters
    ----------
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Zeros filled spectral power distribution.

    See Also
    --------
    constant_spd

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = zeros_spd()
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    0.0
    """

    return constant_spd(0, shape)


def ones_spd(shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    ones.

    Parameters
    ----------
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Ones filled spectral power distribution.

    See Also
    --------
    constant_spd

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = ones_spd()
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    1.0
    """

    return constant_spd(1, shape)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
Spectrum
========

Defines the classes handling spectral data computation:

-   :class:`SpectralShape`
-   :class:`SpectralPowerDistribution`
-   :class:`TriSpectralPowerDistribution`

See Also
--------
`Spectrum IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/spectrum.ipynb>`_  # noqa
"""

from __future__ import division, unicode_literals

import copy
import itertools
import math
import numpy as np

from colour.algebra import (
    is_iterable,
    is_numeric,
    is_uniform,
    steps,
    to_ndarray)
from colour.algebra import (
    Extrapolator1d,
    LinearInterpolator1d,
    SplineInterpolator,
    SpragueInterpolator)
from colour.utilities import is_string

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = '<EMAIL>'
__status__ = 'Production'

__all__ = ['SpectralShape',
           'SpectralPowerDistribution',
           'TriSpectralPowerDistribution',
           'DEFAULT_SPECTRAL_SHAPE',
           'constant_spd',
           'zeros_spd',
           'ones_spd']


class SpectralShape(object):
    """
    Defines the base object for spectral power distribution shape.

    Parameters
    ----------
    start : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range start in nm.
    end : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range end in nm.
    steps : numeric, optional
        Wavelengths :math:`\lambda_{i}`: range steps.

    Attributes
    ----------
    start
    end
    steps

    Methods
    -------
    __repr__
    __contains__
    __len__
    __eq__
    __ne__
    range

    Examples
    --------
    >>> SpectralShape(360, 830, 1)
    SpectralShape(360, 830, 1)
    """

    def __init__(self, start=None, end=None, steps=None):
        # Attribute storing the spectral shape range for caching purpose.
        self.__range = None

        self.__start = None
        self.__end = None
        self.__steps = None
        self.start = start
        self.end = end
        self.steps = steps

    @property
    def start(self):
        """
        Property for **self.__start** private attribute.

        Returns
        -------
        numeric
            self.__start.
        """

        return self.__start

    @start.setter
    def start(self, value):
        """
        Setter for **self.__start** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'start', value))
            if self.__end is not None:
                assert value < self.__end, (
                    '"{0}" attribute value must be strictly less than '
                    '"{1}"!'.format('start', self.__end))

        # Invalidating the *range* cache.
        if value != self.__start:
            self.__range = None

        self.__start = value

    @property
    def end(self):
        """
        Property for **self.__end** private attribute.

        Returns
        -------
        numeric
            self.__end.
        """

        return self.__end

    @end.setter
    def end(self, value):
        """
        Setter for **self.__end** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'end', value))
            if self.__start is not None:
                assert value > self.__start, (
                    '"{0}" attribute value must be strictly greater than '
                    '"{1}"!'.format('end', self.__start))

        # Invalidating the *range* cache.
        if value != self.__end:
            self.__range = None

        self.__end = value

    @property
    def steps(self):
        """
        Property for **self.__steps** private attribute.

        Returns
        -------
        numeric
            self.__steps.
        """

        return self.__steps

    @steps.setter
    def steps(self, value):
        """
        Setter for **self.__steps** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert is_numeric(value), (
                '"{0}" attribute: "{1}" type is not "numeric"!'.format(
                    'steps', value))

        # Invalidating the *range* cache.
        if value != self.__steps:
            self.__range = None

        self.__steps = value

    def __str__(self):
        """
        Returns a nice formatted string representation.

        Returns
        -------
        unicode
            Nice formatted string representation.
        """

        return '({0}, {1}, {2})'.format(self.__start,
                                        self.__end,
                                        self.__steps)

    def __repr__(self):
        """
        Returns a formatted string representation.

        Returns
        -------
        unicode
            Formatted string representation.
        """

        return 'SpectralShape({0}, {1}, {2})'.format(self.__start,
                                                     self.__end,
                                                     self.__steps)

    def __iter__(self):
        """
        Returns a generator for the spectral power distribution data.

        Returns
        -------
        generator
            Spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> shape = SpectralShape(0, 10, 1)
        >>> for wavelength in shape: print(wavelength)
        0
        1
        2
        3
        4
        5
        6
        7
        8
        9
        10
        """

        return iter(self.range())

    def __contains__(self, wavelength):
        """
        Returns if the spectral shape contains the given wavelength
        :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the spectral shape.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> 0.5 in SpectralShape(0, 10, 0.1)
        True
        >>> 0.51 in SpectralShape(0, 10, 0.1)
        False
        """

        return wavelength in self.range()

    def __len__(self):
        """
        Returns the spectral shape wavelengths :math:`\lambda_n`
        count.

        Returns
        -------
        int
            Spectral shape wavelengths :math:`\lambda_n` count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> len(SpectralShape(0, 10, 0.1))
        101
        """

        return len(self.range())

    def __eq__(self, shape):
        """
        Returns the spectral shape equality with given other spectral shape.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape to compare for equality.

        Returns
        -------
        bool
            Spectral shape equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 0.1)
        True
        >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 1)
        False
        """

        return isinstance(shape, self.__class__) and np.array_equal(
            self.range(), shape.range())

    def __ne__(self, shape):
        """
        Returns the spectral shape inequality with given other spectral shape.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape to compare for inequality.

        Returns
        -------
        bool
            Spectral shape inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__ne__` method.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 0.1)
        False
        >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 1)
        True
        """

        return not (self == shape)

    def range(self):
        """
        Returns an iterable range for the spectral power distribution shape.

        Returns
        -------
        ndarray
            Iterable range for the spectral power distribution shape

        Raises
        ------
        RuntimeError
            If one of spectral shape *start*, *end* or *steps* attributes is
            not defined.

        Examples
        --------
        >>> SpectralShape(0, 10, 0.1).range()
        array([  0. ,   0.1,   0.2,   0.3,   0.4,   0.5,   0.6,   0.7,   0.8,
                 0.9,   1. ,   1.1,   1.2,   1.3,   1.4,   1.5,   1.6,   1.7,
                 1.8,   1.9,   2. ,   2.1,   2.2,   2.3,   2.4,   2.5,   2.6,
                 2.7,   2.8,   2.9,   3. ,   3.1,   3.2,   3.3,   3.4,   3.5,
                 3.6,   3.7,   3.8,   3.9,   4. ,   4.1,   4.2,   4.3,   4.4,
                 4.5,   4.6,   4.7,   4.8,   4.9,   5. ,   5.1,   5.2,   5.3,
                 5.4,   5.5,   5.6,   5.7,   5.8,   5.9,   6. ,   6.1,   6.2,
                 6.3,   6.4,   6.5,   6.6,   6.7,   6.8,   6.9,   7. ,   7.1,
                 7.2,   7.3,   7.4,   7.5,   7.6,   7.7,   7.8,   7.9,   8. ,
                 8.1,   8.2,   8.3,   8.4,   8.5,   8.6,   8.7,   8.8,   8.9,
                 9. ,   9.1,   9.2,   9.3,   9.4,   9.5,   9.6,   9.7,   9.8,
                 9.9,  10. ])
        """

        if None in (self.__start, self.__end, self.__steps):
            raise RuntimeError(('One of the spectral shape "start", "end" or '
                                '"steps" attributes is not defined!'))

        if self.__range is None:
            self.__range = np.arange(self.__start,
                                     self.__end + self.__steps,
                                     self.__steps)

        return self.__range


class SpectralPowerDistribution(object):
    """
    Defines the base object for spectral data computations.

    Parameters
    ----------
    name : str or unicode
        Spectral power distribution name.
    data : dict
        Spectral power distribution data in a *dict* as follows:
        {wavelength :math:`\lambda_{i}`: value,
        wavelength :math:`\lambda_{i+1}`,
        ...,
        wavelength :math:`\lambda_{i+n}`}

    Attributes
    ----------
    name
    data
    wavelengths
    values
    items
    shape

    Methods
    -------
    __getitem__
    __init__
    __setitem__
    __iter__
    __contains__
    __len__
    __eq__
    __ne__
    __add__
    __sub__
    __mul__
    __div__
    __truediv__
    get
    is_uniform
    extrapolate
    interpolate
    align
    zeros
    normalise
    clone

    Examples
    --------
    >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
    >>> spd = SpectralPowerDistribution('Spd', data)
    >>> spd.wavelengths
    array([510, 520, 530, 540])
    >>> spd.values
    array([ 49.67,  69.59,  81.73,  88.19])
    >>> spd.shape
    SpectralShape(510, 540, 10)
    """

    def __init__(self, name, data):
        self.__name = None
        self.name = name
        self.__data = None
        self.data = data

    @property
    def name(self):
        """
        Property for **self.__name** private attribute.

        Returns
        -------
        str or unicode
            self.__name.
        """

        return self.__name

    @name.setter
    def name(self, value):
        """
        Setter for **self.__name** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert type(value) in (str, unicode), (
                ('"{0}" attribute: "{1}" type is not '
                 '"str" or "unicode"!').format('name', value))
        self.__name = value

    @property
    def data(self):
        """
        Property for **self.__data** private attribute.

        Returns
        -------
        dict
            self.__data.
        """

        return self.__data

    @data.setter
    def data(self, value):
        """
        Setter for **self.__data** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'data', value))
        self.__data = value

    @property
    def wavelengths(self):
        """
        Property for **self.wavelengths** attribute.

        Returns
        -------
        ndarray
            Spectral power distribution wavelengths :math:`\lambda_n`.

        Warning
        -------
        :attr:`SpectralPowerDistribution.wavelengths` is read only.
        """

        return np.array(sorted(self.__data.keys()))

    @wavelengths.setter
    def wavelengths(self, value):
        """
        Setter for **self.wavelengths** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError(
            '"{0}" attribute is read only!'.format('wavelengths'))

    @property
    def values(self):
        """
        Property for **self.values** attribute.

        Returns
        -------
        ndarray
            Spectral power distribution wavelengths :math:`\lambda_n` values.

        Warning
        -------
        :attr:`SpectralPowerDistribution.values` is read only.
        """

        return np.array([self.get(wavelength)
                         for wavelength in self.wavelengths])

    @values.setter
    def values(self, value):
        """
        Setter for **self.values** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('values'))

    @property
    def items(self):
        """
        Property for **self.items** attribute. This is a convenient attribute
        used to iterate over the spectral power distribution.

        Returns
        -------
        generator
            Spectral power distribution data generator.
        """

        return self.__iter__()

    @items.setter
    def items(self, value):
        """
        Setter for **self.items** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('items'))

    @property
    def shape(self):
        """
        Property for **self.shape** attribute.

        Returns the shape of the spectral power distribution in the form of a
        :class:`SpectralShape` class instance.

        Returns
        -------
        SpectralShape
            Spectral power distribution shape.

        See Also
        --------
        SpectralPowerDistribution.is_uniform

        Notes
        -----
        -   A non uniform spectral power distribution may will have multiple
            different steps, in that case
            :attr:`SpectralPowerDistribution.shape` returns the *minimum* steps
            size.

        Warning
        -------
        :attr:`SpectralPowerDistribution.shape` is read only.

        Examples
        --------
        Uniform spectral power distribution:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> SpectralPowerDistribution('Spd', data).shape
        SpectralShape(510, 540, 10)

        Non uniform spectral power distribution:

        >>> data = {512.3: 49.67, 524.5: 69.59, 532.4: 81.73, 545.7: 88.19}
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> SpectralPowerDistribution('Spd', data).shape  # doctest: +ELLIPSIS
        SpectralShape(512.3, 545.7, 7...)
        """

        return SpectralShape(min(self.data.keys()),
                             max(self.data.keys()),
                             min(steps(self.wavelengths)))

    @shape.setter
    def shape(self, value):
        """
        Setter for **self.shape** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('shape'))

    def __hash__(self):
        """
        Returns the spectral power distribution hash value.

        Returns
        -------
        int
            Object hash.

        Notes
        -----
        -   Reimplements the :meth:`object.__hash__` method.

        Warning
        -------
        :class:`SpectralPowerDistribution` class is mutable and should not be
        hashable. However, so that it can be used as a key in some data caches,
        we provide a *__hash__* implementation, **assuming that the underlying
        data will not change for those specific cases**.

        References
        ----------
        .. [1]  http://stackoverflow.com/a/16162138/931625
                (Last accessed 8 August 2014)
        """

        return hash(frozenset(self.__data))

    def __getitem__(self, wavelength):
        """
        Returns the value for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength: numeric
            Wavelength :math:`\lambda` to retrieve the value.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` value.

        See Also
        --------
        SpectralPowerDistribution.get

        Notes
        -----
        -   Reimplements the :meth:`object.__getitem__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[510]  # doctest: +ELLIPSIS
        49.67...
        """

        return self.__data.__getitem__(wavelength)

    def __setitem__(self, wavelength, value):
        """
        Sets the wavelength :math:`\lambda` with given value.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to set.
        value : numeric
            Value for wavelength :math:`\lambda`.

        Notes
        -----
        -   Reimplements the :meth:`object.__setitem__` method.

        Examples
        --------
        >>> spd = SpectralPowerDistribution('Spd', {})
        >>> spd[510] = 49.6700
        >>> spd.values
        array([ 49.67])
        """

        self.__data.__setitem__(wavelength, value)

    def __iter__(self):
        """
        Returns a generator for the spectral power distribution data.

        Returns
        -------
        generator
            Spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> for wavelength, value in spd: print((wavelength, value))  # noqa  # doctest: +ELLIPSIS
        (510, 49.6...)
        (520, 69.5...)
        (530, 81.7...)
        (540, 88.1...)
        """

        return iter(sorted(self.__data.items()))

    def __contains__(self, wavelength):
        """
        Returns if the spectral power distribution contains the given
        wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the spectral power distribution.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> 510 in spd
        True
        """

        return wavelength in self.__data

    def __len__(self):
        """
        Returns the spectral power distribution wavelengths :math:`\lambda_n`
        count.

        Returns
        -------
        int
            Spectral power distribution wavelengths :math:`\lambda_n` count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> len(spd)
        4
        """

        return len(self.__data)

    def __eq__(self, spd):
        """
        Returns the spectral power distribution equality with given other
        spectral power distribution.

        Parameters
        ----------
        spd : SpectralPowerDistribution
            Spectral power distribution to compare for equality.

        Returns
        -------
        bool
            Spectral power distribution equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}
        >>> spd1 = SpectralPowerDistribution('Spd', data1)
        >>> spd2 = SpectralPowerDistribution('Spd', data2)
        >>> spd3 = SpectralPowerDistribution('Spd', data2)
        >>> spd1 == spd2
        False
        >>> spd2 == spd3
        True
        """

        return isinstance(spd, self.__class__) and spd.data == self.data

    def __ne__(self, spd):
        """
        Returns the spectral power distribution inequality with given other
        spectral power distribution.

        Parameters
        ----------
        spd : SpectralPowerDistribution
            Spectral power distribution to compare for inequality.

        Returns
        -------
        bool
            Spectral power distribution inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__ne__` method.

        Examples
        --------
        >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}
        >>> spd1 = SpectralPowerDistribution('Spd', data1)
        >>> spd2 = SpectralPowerDistribution('Spd', data2)
        >>> spd3 = SpectralPowerDistribution('Spd', data2)
        >>> spd1 != spd2
        True
        >>> spd2 != spd3
        False
        """

        return not (self == spd)

    def __format_operand(self, x):
        """
        Formats given :math:`x` variable operand to *numeric* or *ndarray*.

        This method is a convenient method to prepare the given :math:`x`
        variable for the arithmetic operations below.

        Parameters
        ----------
        x : numeric or ndarray or SpectralPowerDistribution
            Variable to format.

        Returns
        -------
        numeric or ndarray
            Formatted operand.
        """

        if issubclass(type(x), SpectralPowerDistribution):
            x = x.values
        elif is_iterable(x):
            x = to_ndarray(x)

        return x

    def __add__(self, x):
        """
        Implements support for spectral power distribution addition.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to add.

        Returns
        -------
        SpectralPowerDistribution
            Variable added spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__sub__, SpectralPowerDistribution.__mul__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__add__` method.

        Warning
        -------
        The addition operation happens in place.

        Examples
        --------
        Adding a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd + 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 59.67,  79.59,  91.73,  98.19])

        Adding an *array_like* variable:

        >>> spd + [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  60.67,   81.59,   94.73,  102.19])

        Adding a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd + spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 110.34,  151.18,  176.46,  190.38])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values + self.__format_operand(x)))

        return self

    def __sub__(self, x):
        """
        Implements support for spectral power distribution subtraction.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to subtract.

        Returns
        -------
        SpectralPowerDistribution
            Variable subtracted spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__mul__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__sub__` method.

        Warning
        -------
        The subtraction operation happens in place.

        Examples
        --------
        Subtracting a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd - 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 39.67,  59.59,  71.73,  78.19])

        Subtracting an *array_like* variable:

        >>> spd - [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 38.67,  57.59,  68.73,  74.19])

        Subtracting a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd - spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([-11., -12., -13., -14.])
        """

        return self + (-self.__format_operand(x))

    def __mul__(self, x):
        """
        Implements support for spectral power distribution multiplication.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to multiply.

        Returns
        -------
        SpectralPowerDistribution
            Variable multiplied spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,
        SpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The multiplication operation happens in place.

        Examples
        --------
        Multiplying a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd * 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 496.7,  695.9,  817.3,  881.9])

        Multiplying an *array_like* variable:

        >>> spd * [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  496.7,  1391.8,  2451.9,  3527.6])

        Multiplying a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd * spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  24671.089,   96855.362,  200393.787,  311099.044])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values * self.__format_operand(x)))

        return self

    def __div__(self, x):
        """
        Implements support for spectral power distribution division.

        Parameters
        ----------
        x : numeric or array_like or SpectralPowerDistribution
            Variable to divide.

        Returns
        -------
        SpectralPowerDistribution
            Variable divided spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,
        SpectralPowerDistribution.__mul__

        Notes
        -----
        -   Reimplements the :meth:`object.__div__` method.

        Warning
        -------
        The division operation happens in place.

        Examples
        --------
        Dividing a single *numeric* variable:

        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd / 10  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 4.967,  6.959,  8.173,  8.819])

        Dividing an *array_like* variable:

        >>> spd / [1, 2, 3, 4]  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([ 4.967     ,  3.4795    ,  2.72433333,  2.20475   ])

        Dividing a :class:`SpectralPowerDistribution` class variable:

        >>> spd_alternate = SpectralPowerDistribution('Spd', data)
        >>> spd / spd_alternate  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 0.1       ,  0.05      ,  0.0333333...,  0.025     ])
        """

        self.__data = dict(zip(self.wavelengths,
                               self.values * (1 / self.__format_operand(x))))

        return self

    # Python 3 compatibility.
    __truediv__ = __div__

    def get(self, wavelength, default=None):
        """
        Returns the value for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to retrieve the value.
        default : None or numeric, optional
            Wavelength :math:`\lambda` default value.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` value.

        See Also
        --------
        SpectralPowerDistribution.__getitem__

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd.get(510)  # doctest: +ELLIPSIS
        49.67...
        >>> spd.get(511)  # doctest: +SKIP
        None
        """

        try:
            return self.__getitem__(wavelength)
        except KeyError:
            return default

    def is_uniform(self):
        """
        Returns if the spectral power distribution has uniformly spaced data.

        Returns
        -------
        bool
            Is uniform.

        See Also
        --------
        SpectralPowerDistribution.shape

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.is_uniform()
        True

        Breaking the steps by introducing a new wavelength :math:`\lambda`
        value:

        >>> spd[511] = 3.1415
        >>> spd.is_uniform()
        False
        """

        return is_uniform(self.wavelengths)

    def extrapolate(self,
                    shape,
                    method='Constant',
                    left=None,
                    right=None):
        """
        Extrapolates the spectral power distribution following *CIE 15:2004*
        recommendation.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for extrapolation.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        SpectralPowerDistribution
            Extrapolated spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.align

        References
        ----------
        .. [2]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation
                <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa
                ISBN-13: 978-3-901-90633-6

        .. [3]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 10. EXTRAPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.extrapolate(SpectralShape(400, 700)).shape
        SpectralShape(400, 700, 10)
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[400]  # doctest: +ELLIPSIS
        49.67...
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[700]  # doctest: +ELLIPSIS
        88.1...
        """

        extrapolator = Extrapolator1d(
            LinearInterpolator1d(self.wavelengths,
                                 self.values),
            method=method,
            left=left,
            right=right)

        spd_shape = self.shape
        for i in np.arange(spd_shape.start,
                           shape.start - spd_shape.steps,
                           -spd_shape.steps):
            self[i] = extrapolator(float(i))
        for i in np.arange(spd_shape.end,
                           shape.end + spd_shape.steps,
                           spd_shape.steps):
            self[i] = extrapolator(float(i))

        return self

    def interpolate(self, shape=SpectralShape(), method=None):
        """
        Interpolates the spectral power distribution following
        *CIE 167:2005* recommendations: the method developed by
        *Sprague (1880)* should be used for interpolating functions having a
        uniformly spaced independent variable and a *Cubic Spline* method for
        non-uniformly spaced independent variable.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for interpolation.
        method : unicode, optional
            ('Sprague', 'Cubic Spline', 'Linear'),
            Enforce given interpolation method.

        Returns
        -------
        SpectralPowerDistribution
            Interpolated spectral power distribution.

        Raises
        ------
        RuntimeError
            If the *Sprague* interpolation method is forced with a
            non-uniformly spaced independent variable.
        ValueError
            If the interpolation method is not defined.

        See Also
        --------
        SpectralPowerDistribution.align

        Notes
        -----
        -   Interpolation will be conducted over boundaries range, if you need
            to extend the range of the spectral power distribution use the
            :meth:`SpectralPowerDistribution.extrapolate` or
            :meth:`SpectralPowerDistribution.align` methods.
        -   *Sprague* interpolator cannot be used for interpolating
            functions having a non-uniformly spaced independent variable.

        Warning
        -------
        -   If *scipy* is not unavailable the *Cubic Spline* method will
            fallback to legacy *Linear* interpolation.
        -   *Linear* interpolator requires at least 2 wavelengths
            :math:`\lambda_n` for interpolation.
        -   *Cubic Spline* interpolator requires at least 3 wavelengths
            :math:`\lambda_n` for interpolation.
        -   *Sprague* interpolator requires at least 6 wavelengths
            :math:`\lambda_n` for interpolation.

        References
        ----------
        .. [4]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 9. INTERPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        Uniform data is using *Sprague* interpolation by default:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd[515]  # doctest: +ELLIPSIS
        60.3121800...

        Non uniform data is using *Cubic Spline* interpolation by default:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd[511] = 31.41
        >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd[515]  # doctest: +ELLIPSIS
        21.4792222...

        Enforcing *Linear* interpolation:

        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> # Doctests ellipsis for Python 2.x compatibility.
        >>> spd[515]  # doctest: +ELLIPSIS
        59.63...
        """

        spd_shape = self.shape
        boundaries = zip((shape.start, shape.end, shape.steps),
                         (spd_shape.start, spd_shape.end, spd_shape.steps))
        boundaries = [x[0] if x[0] is not None else x[1] for x in boundaries]
        shape = SpectralShape(*boundaries)

        # Defining proper interpolation bounds.
        # TODO: Provide support for fractional steps like 0.1, etc...
        shape.start = max(shape.start, math.ceil(spd_shape.start))
        shape.end = min(shape.end, math.floor(spd_shape.end))

        wavelengths, values = self.wavelengths, self.values
        is_uniform = self.is_uniform()

        if is_string(method):
            method = method.lower()

        if method is None:
            if is_uniform:
                interpolator = SpragueInterpolator(wavelengths, values)
            else:
                interpolator = SplineInterpolator(wavelengths, values)
        elif method == 'sprague':
            if is_uniform:
                interpolator = SpragueInterpolator(wavelengths, values)
            else:
                raise RuntimeError(
                    ('"Sprague" interpolator can only be used for '
                     'interpolating functions having a uniformly spaced '
                     'independent variable!'))
        elif method == 'cubic spline':
            interpolator = SplineInterpolator(wavelengths, values)
        elif method == 'linear':
            interpolator = LinearInterpolator1d(wavelengths, values)
        else:
            raise ValueError(
                'Undefined "{0}" interpolator!'.format(method))

        self.__data = dict([(wavelength, float(interpolator(wavelength)))
                            for wavelength in shape])
        return self

    def align(self,
              shape,
              method='Constant',
              left=None,
              right=None):
        """
        Aligns the spectral power distribution to given spectral shape:
        Interpolates first then extrapolates to fit the given range.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for alignment.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        SpectralPowerDistribution
            Aligned spectral power distribution.

        See Also
        --------
        SpectralPowerDistribution.extrapolate,
        SpectralPowerDistribution.interpolate

        Examples
        --------
        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> # Doctests skip for Python 2.x compatibility.
        >>> spd.wavelengths  # doctest: +SKIP
        array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,
               518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,
               531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,
               544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,
               557, 558, 559, 560, 561, 562, 563, 564, 565])
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 49.67     ...,  49.67     ...,  49.67     ...,  49.67     ...,
                49.67     ...,  49.67     ...,  51.8341162...,  53.9856467...,
                56.1229464...,  58.2366197...,  60.3121800...,  62.3327095...,
                64.2815187...,  66.1448055...,  67.9143153...,  69.59     ...,
                71.1759958...,  72.6627938...,  74.0465756...,  75.3329710...,
                76.5339542...,  77.6647421...,  78.7406907...,  79.7741932...,
                80.7715767...,  81.73     ...,  82.6407518...,  83.507872 ...,
                84.3326333...,  85.109696 ...,  85.8292968...,  86.47944  ...,
                87.0480863...,  87.525344 ...,  87.9056578...,  88.19     ...,
                88.3858347...,  88.4975634...,  88.5258906...,  88.4696570...,
                88.3266460...,  88.0943906...,  87.7709802...,  87.3558672...,
                86.8506741...,  86.26     ...,  85.5911699...,  84.8503430...,
                84.0434801...,  83.1771110...,  82.2583874...,  81.2951360...,
                80.2959122...,  79.2700525...,  78.2277286...,  77.18     ...,
                77.18     ...,  77.18     ...,  77.18     ...,  77.18     ...,  77.18      ])
        """

        self.interpolate(shape)
        self.extrapolate(shape, method, left, right)

        return self

    def zeros(self, shape=SpectralShape()):
        """
        Zeros fills the spectral power distribution: Missing values will be
        replaced with zeros to fit the defined range.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for zeros fill.

        Returns
        -------
        SpectralPowerDistribution
            Zeros filled spectral power distribution.

        Examples
        --------
        >>> data = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 86.26,
        ...     560: 77.18}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values
        array([  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  49.67,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  69.59,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,  81.73,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,  88.19,   0.  ,   0.  ,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  86.26,   0.  ,   0.  ,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  77.18,
                 0.  ,   0.  ,   0.  ,   0.  ,   0.  ])
        """

        spd_shape = self.shape
        boundaries = zip((shape.start, shape.end, shape.steps),
                         (spd_shape.start, spd_shape.end, spd_shape.end))
        boundaries = [x[0] if x[0] is not None else x[1] for x in boundaries]
        shape = SpectralShape(*boundaries)

        self.__data = dict(
            [(wavelength, self.get(wavelength, 0)) for wavelength in shape])

        return self

    def normalise(self, factor=1):
        """
        Normalises the spectral power distribution with given normalization
        factor.

        Parameters
        ----------
        factor : numeric, optional
            Normalization factor

        Returns
        -------
        SpectralPowerDistribution
            Normalised spectral power distribution.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> spd.normalise()  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd.values  # doctest: +ELLIPSIS
        array([ 0.5632157...,  0.7890917...,  0.9267490...,  1.        ])
        """

        return (self * (1 / max(self.values))) * factor

    def clone(self):
        """
        Clones the spectral power distribution.

        Most of the :class:`SpectralPowerDistribution` class operations are
        conducted in-place. The :meth:`SpectralPowerDistribution.clone` method
        provides a convenient way to copy the spectral power distribution to a
        new object.

        Returns
        -------
        SpectralPowerDistribution
            Cloned spectral power distribution.

        Examples
        --------
        >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> spd = SpectralPowerDistribution('Spd', data)
        >>> print(spd)  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        >>> spd_clone = spd.clone()
        >>> print(spd_clone)  # doctest: +ELLIPSIS
        <...SpectralPowerDistribution object at 0x...>
        """

        return copy.deepcopy(self)


class TriSpectralPowerDistribution(object):
    """
    Defines the base object for colour matching functions.

    A compound of three :class:`SpectralPowerDistribution` is used to store
    the underlying axis data.

    Parameters
    ----------
    name : str or unicode
        Tri-spectral power distribution name.
    data : dict
        Tri-spectral power distribution data.
    mapping : dict
        Tri-spectral power distribution attributes mapping.
    labels : dict
        Tri-spectral power distribution axis labels mapping.

    Attributes
    ----------
    name
    mapping
    data
    labels
    x
    y
    z
    wavelengths
    values
    items
    shape

    Methods
    -------
    __init__
    __getitem__
    __setitem__
    __iter__
    __contains__
    __len__
    __eq__
    __ne__
    __add__
    __sub__
    __mul__
    __div__
    __truediv__
    get
    is_uniform
    extrapolate
    interpolate
    align
    zeros
    normalise
    clone

    See Also
    --------
    colour.colorimetry.cmfs.LMS_ConeFundamentals,
    colour.colorimetry.cmfs.RGB_ColourMatchingFunctions,
    colour.colorimetry.cmfs.XYZ_ColourMatchingFunctions

    Examples
    --------
    >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
    >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
    >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
    >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
    >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
    >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
    >>> tri_spd.wavelengths
    array([510, 520, 530, 540])
    >>> tri_spd.values
    array([[ 49.67,  90.56,  12.43],
           [ 69.59,  87.34,  23.15],
           [ 81.73,  45.76,  67.98],
           [ 88.19,  23.45,  90.28]])
    >>> tri_spd.shape
    SpectralShape(510, 540, 10)
    """

    def __init__(self, name, data, mapping, labels):
        self.__name = None
        self.name = name
        self.__mapping = mapping
        self.__data = None
        self.data = data
        self.__labels = labels

    @property
    def name(self):
        """
        Property for **self.__name** private attribute.

        Returns
        -------
        str or unicode
            self.__name.
        """

        return self.__name

    @name.setter
    def name(self, value):
        """
        Setter for **self.__name** private attribute.

        Parameters
        ----------
        value : str or unicode
            Attribute value.
        """

        if value is not None:
            assert type(value) in (str, unicode), (
                ('"{0}" attribute: "{1}" type is not '
                 '"str" or "unicode"!').format('name', value))
        self.__name = value

    @property
    def mapping(self):
        """
        Property for **self.__mapping** private attribute.

        Returns
        -------
        dict
            self.__mapping.
        """

        return self.__mapping

    @mapping.setter
    def mapping(self, value):
        """
        Setter for **self.__mapping** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'mapping', value))
            for axis in ('x', 'y', 'z'):
                assert axis in value.keys(), (
                    '"{0}" attribute: "{1}" axis label is missing!'.format(
                        'mapping', axis))
        self.__mapping = value

    @property
    def data(self):
        """
        Property for **self.__data** private attribute.

        Returns
        -------
        dict
            self.__data.
        """

        return self.__data

    @data.setter
    def data(self, value):
        """
        Setter for **self.__data** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'data', value))
            for axis in ('x', 'y', 'z'):
                assert self.__mapping.get(axis) in value.keys(), (
                    '"{0}" attribute: "{1}" axis is missing!'.format(
                        'data', axis))

            data = {}
            for axis in ('x', 'y', 'z'):
                data[axis] = SpectralPowerDistribution(
                    self.__mapping.get(axis),
                    value.get(self.__mapping.get(axis)))

            np.testing.assert_almost_equal(
                data['x'].wavelengths,
                data['y'].wavelengths,
                err_msg=('"{0}" attribute: "{1}" and "{2}" wavelengths are '
                         'different!').format('data',
                                              self.__mapping.get('x'),
                                              self.__mapping.get('y')))
            np.testing.assert_almost_equal(
                data['x'].wavelengths,
                data['z'].wavelengths,
                err_msg=('"{0}" attribute: "{1}" and "{2}" wavelengths are '
                         'different!').format('data',
                                              self.__mapping.get('x'),
                                              self.__mapping.get('z')))

            self.__data = data
        else:
            self.__data = None

    @property
    def labels(self):
        """
        Property for **self.__labels** private attribute.

        Returns
        -------
        dict
            self.__labels.
        """

        return self.__labels

    @labels.setter
    def labels(self, value):
        """
        Setter for **self.__labels** private attribute.

        Parameters
        ----------
        value : dict
            Attribute value.
        """

        if value is not None:
            assert type(value) is dict, (
                '"{0}" attribute: "{1}" type is not "dict"!'.format(
                    'labels', value))
            for axis in ('x', 'y', 'z'):
                assert axis in value.keys(), (
                    '"{0}" attribute: "{1}" axis label is missing!'.format(
                        'labels', axis))
        self.__labels = value

    @property
    def x(self):
        """
        Property for **self.x** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *x* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.x` is read only.
        """

        return self.__data.get('x')

    @x.setter
    def x(self, value):
        """
        Setter for **self.x** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('x'))

    @property
    def y(self):
        """
        Property for **self.y** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *y* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.y` is read only.
        """

        return self.__data.get('y')

    @y.setter
    def y(self, value):
        """
        Setter for **self.y** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('y'))

    @property
    def z(self):
        """
        Property for **self.z** attribute.

        Returns
        -------
        SpectralPowerDistribution
            Spectral power distribution for *z* axis.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.z` is read only.
        """

        return self.__data.get('z')

    @z.setter
    def z(self, value):
        """
        Setter for **self.z** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('z'))

    @property
    def wavelengths(self):
        """
        Property for **self.wavelengths** attribute.

        Returns
        -------
        ndarray
            Tri-spectral power distribution wavelengths :math:`\lambda_n`.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.wavelengths` is read only.
        """

        return self.x.wavelengths

    @wavelengths.setter
    def wavelengths(self, value):
        """
        Setter for **self.wavelengths** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError(
            '"{0}" attribute is read only!'.format('wavelengths'))

    @property
    def values(self):
        """
        Property for **self.values** attribute.

        Returns
        -------
        ndarray
            Tri-spectral power distribution wavelengths :math:`\lambda_n`
            values.

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.values` is read only.
        """

        return np.array([self.get(wavelength)
                         for wavelength in self.wavelengths])

    @values.setter
    def values(self, value):
        """
        Setter for **self.values** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('values'))

    @property
    def items(self):
        """
        Property for **self.items** attribute. This is a convenient attribute
        used to iterate over the tri-spectral power distribution.

        Returns
        -------
        generator
            Tri-spectral power distribution data generator.
        """

        return self.__iter__()

    @items.setter
    def items(self, value):
        """
        Setter for **self.items** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('items'))

    @property
    def shape(self):
        """
        Property for **self.shape** attribute.

        Returns the shape of the tri-spectral power distribution in the form of
        a :class:`SpectralShape` class instance.

        Returns
        -------
        SpectralShape
            Tri-spectral power distribution shape.

        See Also
        --------
        SpectralPowerDistribution.is_uniform,
        TriSpectralPowerDistribution.is_uniform

        Warning
        -------
        :attr:`TriSpectralPowerDistribution.shape` is read only.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.shape
        SpectralShape(510, 540, 10)
        """

        return self.x.shape

    @shape.setter
    def shape(self, value):
        """
        Setter for **self.shape** attribute.

        Parameters
        ----------
        value : object
            Attribute value.
        """

        raise AttributeError('"{0}" attribute is read only!'.format('shape'))

    def __hash__(self):
        """
        Returns the spectral power distribution hash value.

        Returns
        -------
        int
            Object hash.

        Notes
        -----
        -   Reimplements the :meth:`object.__hash__` method.

        Warning
        -------
        See :meth:`SpectralPowerDistribution.__hash__` method warning section.

        References
        ----------
        .. [5]  http://stackoverflow.com/a/16162138/931625
                (Last accessed 8 August 2014)
        """

        return hash((frozenset(self.__data.get('x')),
                     frozenset(self.__data.get('y')),
                     frozenset(self.__data.get('z'))))

    def __getitem__(self, wavelength):
        """
        Returns the values for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength: numeric
            Wavelength :math:`\lambda` to retrieve the values.

        Returns
        -------
        ndarray, (3,)
            Wavelength :math:`\lambda` values.

        See Also
        --------
        TriSpectralPowerDistribution.get

        Notes
        -----
        -   Reimplements the :meth:`object.__getitem__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510]
        array([ 49.67,  90.56,  12.43])
        """

        return np.array((self.x[wavelength],
                         self.y[wavelength],
                         self.z[wavelength]))

    def __setitem__(self, wavelength, value):
        """
        Sets the wavelength :math:`\lambda` with given value.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to set.
        value : array_like
            Value for wavelength :math:`\lambda`.

        Notes
        -----
        -   Reimplements the :meth:`object.__setitem__` method.

        Examples
        --------
        >>> x_bar = {}
        >>> y_bar = {}
        >>> z_bar = {}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510] = (49.6700, 49.6700, 49.6700)
        >>> tri_spd.values
        array([[ 49.67,  49.67,  49.67]])
        """

        x, y, z = np.ravel(value)

        self.x.__setitem__(wavelength, x)
        self.y.__setitem__(wavelength, y)
        self.z.__setitem__(wavelength, z)

    def __iter__(self):
        """
        Returns a generator for the tri-spectral power distribution data.

        Returns
        -------
        generator
            Tri-spectral power distribution data generator.

        Notes
        -----
        -   Reimplements the :meth:`object.__iter__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> for wavelength, value in tri_spd: print((wavelength, value))
        (510, array([ 49.67,  90.56,  12.43]))
        (520, array([ 69.59,  87.34,  23.15]))
        (530, array([ 81.73,  45.76,  67.98]))
        (540, array([ 88.19,  23.45,  90.28]))
        """

        return itertools.izip(self.wavelengths, self.values)

    def __contains__(self, wavelength):
        """
        Returns if the tri-spectral power distribution contains the given
        wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda`.

        Returns
        -------
        bool
            Is wavelength :math:`\lambda` in the tri-spectral power
            distribution.

        Notes
        -----
        -   Reimplements the :meth:`object.__contains__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> 510 in tri_spd
        True

        """

        return wavelength in self.x

    def __len__(self):
        """
        Returns the tri-spectral power distribution wavelengths
        :math:`\lambda_n` count.

        Returns
        -------
        int
            Tri-Spectral power distribution wavelengths :math:`\lambda_n`
            count.

        Notes
        -----
        -   Reimplements the :meth:`object.__len__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> len(tri_spd)
        4
        """

        return len(self.x)

    def __eq__(self, tri_spd):
        """
        Returns the tri-spectral power distribution equality with given other
        tri-spectral power distribution.

        Parameters
        ----------
        spd : TriSpectralPowerDistribution
            Tri-spectral power distribution to compare for equality.

        Returns
        -------
        bool
            Tri-spectral power distribution equality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)
        >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd1 == tri_spd2
        False
        >>> tri_spd1 == tri_spd3
        True
        """

        if not isinstance(tri_spd, self.__class__):
            return False

        equality = True
        for axis in self.__mapping:
            equality *= getattr(self, axis) == getattr(tri_spd, axis)

        return bool(equality)

    def __ne__(self, tri_spd):
        """
        Returns the tri-spectral power distribution inequality with given other
        tri-spectral power distribution.

        Parameters
        ----------
        spd : TriSpectralPowerDistribution
            Tri-spectral power distribution to compare for inequality.

        Returns
        -------
        bool
            Tri-spectral power distribution inequality.

        Notes
        -----
        -   Reimplements the :meth:`object.__eq__` method.

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)
        >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd1 != tri_spd2
        True
        >>> tri_spd1 != tri_spd3
        False
        """

        return not (self == tri_spd)

    def __format_operand(self, x):
        """
        Formats given :math:`x` variable operand to *numeric* or *ndarray*.

        This method is a convenient method to prepare the given :math:`x`
        variable for the arithmetic operations below.

        Parameters
        ----------
        x : numeric or ndarray or TriSpectralPowerDistribution
            Variable to format.

        Returns
        -------
        numeric or ndarray
            Formatted operand.
        """

        if issubclass(type(x), TriSpectralPowerDistribution):
            x = x.values
        elif is_iterable(x):
            x = to_ndarray(x)

        return x

    def __add__(self, x):
        """
        Implements support for tri-spectral power distribution addition.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to add.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable added tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__mul__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__add__` method.

        Warning
        -------
        The addition operation happens in place.

        Examples
        --------
        Adding a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd + 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  59.67,  100.56,   22.43],
               [  79.59,   97.34,   33.15],
               [  91.73,   55.76,   77.98],
               [  98.19,   33.45,  100.28]])

        Adding an *array_like* variable:

        >>> tri_spd + [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  60.67,  102.56,   25.43],
               [  80.59,   99.34,   36.15],
               [  92.73,   57.76,   80.98],
               [  99.19,   35.45,  103.28]])

        Adding a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd + tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  73.1 ,  152.23,  115.99],
               [ 103.74,  168.93,  123.49],
               [ 160.71,  139.49,  126.74],
               [ 189.47,  123.64,  126.73]])
        """

        values = self.values + self.__format_operand(x)

        for i, axis in enumerate(('x', 'y', 'z')):
            self.__data[axis].data = dict(zip(self.wavelengths, values[:, i]))

        return self

    def __sub__(self, x):
        """
        Implements support for tri-spectral power distribution subtraction.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to subtract.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable subtracted tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__mul__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__sub__` method.

        Warning
        -------
        The subtraction operation happens in place.

        Examples
        --------
        Subtracting a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd - 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 39.67,  80.56,   2.43],
               [ 59.59,  77.34,  13.15],
               [ 71.73,  35.76,  57.98],
               [ 78.19,  13.45,  80.28]])

        Subtracting an *array_like* variable:

        >>> tri_spd - [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 38.67,  78.56,  -0.57],
               [ 58.59,  75.34,  10.15],
               [ 70.73,  33.76,  54.98],
               [ 77.19,  11.45,  77.28]])

        Subtracting a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd - tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 26.24,  28.89, -91.13],
               [ 35.44,   5.75, -77.19],
               [  2.75, -47.97,   9.22],
               [-13.09, -76.74,  53.83]])
        """

        return self + (-self.__format_operand(x))

    def __mul__(self, x):
        """
        Implements support for tri-spectral power distribution multiplication.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to multiply.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable multiplied tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__div__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The multiplication operation happens in place.

        Examples
        --------
        Multiplying a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd * 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 496.7,  905.6,  124.3],
               [ 695.9,  873.4,  231.5],
               [ 817.3,  457.6,  679.8],
               [ 881.9,  234.5,  902.8]])

        Multiplying an *array_like* variable:

        >>> tri_spd * [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  1986.8,   7244.8,   1491.6],
               [  2783.6,   6987.2,   2778. ],
               [  3269.2,   3660.8,   8157.6],
               [  3527.6,   1876. ,  10833.6]])

        Multiplying a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd * tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  24695.924,  359849.216,  135079.296],
               [  64440.34 ,  486239.248,  242630.52 ],
               [ 222240.216,  299197.184,  373291.776],
               [ 318471.728,  165444.44 ,  254047.92 ]])
        """

        values = self.values * self.__format_operand(x)

        for i, axis in enumerate(('x', 'y', 'z')):
            self.__data[axis].data = dict(zip(self.wavelengths, values[:, i]))

        return self

    def __div__(self, x):
        """
        Implements support for tri-spectral power distribution division.

        Parameters
        ----------
        x : numeric or array_like or TriSpectralPowerDistribution
            Variable to divide.

        Returns
        -------
        TriSpectralPowerDistribution
            Variable divided tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.__add__,
        TriSpectralPowerDistribution.__sub__,
        TriSpectralPowerDistribution.__mul__

        Notes
        -----
        -   Reimplements the :meth:`object.__mul__` method.

        Warning
        -------
        The division operation happens in place.

        Examples
        --------
        Dividing a single *numeric* variable:

        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd / 10  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[ 4.967,  9.056,  1.243],
               [ 6.959,  8.734,  2.315],
               [ 8.173,  4.576,  6.798],
               [ 8.819,  2.345,  9.028]])

        Dividing an *array_like* variable:

        >>> tri_spd / [(1, 2, 3)] * 4  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 19.868     ,  18.112     ,   1.6573333...],
               [ 27.836     ,  17.468     ,   3.0866666...],
               [ 32.692     ,   9.152     ,   9.064    ...],
               [ 35.276     ,   4.69      ,  12.0373333...]])

        Dividing a :class:`TriSpectralPowerDistribution` class variable:

        >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}
        >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)
        >>> tri_spd / tri_spd1  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 1.5983909...,  0.3646466...,  0.0183009...],
               [ 1.2024190...,  0.2510130...,  0.0353408...],
               [ 0.4809061...,  0.1119784...,  0.1980769...],
               [ 0.3907399...,  0.0531806...,  0.5133191...]])
        """

        return self * (1 / self.__format_operand(x))

    # Python 3 compatibility.
    __truediv__ = __div__

    def get(self, wavelength, default=None):
        """
        Returns the values for given wavelength :math:`\lambda`.

        Parameters
        ----------
        wavelength : numeric
            Wavelength :math:`\lambda` to retrieve the values.
        default : None or numeric, optional
            Wavelength :math:`\lambda` default values.

        Returns
        -------
        numeric
            Wavelength :math:`\lambda` values.

        See Also
        --------
        TriSpectralPowerDistribution.__getitem__

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[510]
        array([ 49.67,  90.56,  12.43])
        >>> tri_spd.get(511)  # doctest: +SKIP
        None
        """

        try:
            return self.__getitem__(wavelength)
        except KeyError:
            return default

    def is_uniform(self):
        """
        Returns if the tri-spectral power distribution has uniformly spaced
        data.

        Returns
        -------
        bool
            Is uniform.

        See Also
        --------
        TriSpectralPowerDistribution.shape

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.is_uniform()
        True

        Breaking the steps by introducing new wavelength :math:`\lambda`
        values:

        >>> tri_spd[511] = (49.6700, 49.6700, 49.6700)
        >>> tri_spd.is_uniform()
        False
        """

        for i in self.__mapping.keys():
            if not getattr(self, i).is_uniform():
                return False
        return True

    def extrapolate(self,
                    shape,
                    method='Constant',
                    left=None,
                    right=None):
        """
        Extrapolates the tri-spectral power distribution following
        *CIE 15:2004* recommendation.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for extrapolation.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        TriSpectralPowerDistribution
            Extrapolated tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.align

        References
        ----------

        .. [6]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation
                <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa
                ISBN-13: 978-3-901-90633-6
        .. [7]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 10. EXTRAPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}
        >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}
        >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.extrapolate(SpectralShape(400, 700)).shape
        SpectralShape(400, 700, 10)
        >>> tri_spd[400]
        array([ 49.67,  90.56,  12.43])
        >>> tri_spd[700]
        array([ 88.19,  23.45,  90.28])
        """

        for i in self.__mapping.keys():
            getattr(self, i).extrapolate(shape, method, left, right)

        return self

    def interpolate(self, shape=SpectralShape(), method=None):
        """
        Interpolates the tri-spectral power distribution following
        *CIE 167:2005* recommendations: the method developed by
        *Sprague (1880)* should be used for interpolating functions having a
        uniformly spaced independent variable and a *Cubic Spline* method for
        non-uniformly spaced independent variable.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for interpolation.
        method : unicode, optional
            ('Sprague', 'Cubic Spline', 'Linear'),
            Enforce given interpolation method.

        Returns
        -------
        TriSpectralPowerDistribution
            Interpolated tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.align

        Notes
        -----
        -   See :meth:`SpectralPowerDistribution.interpolate` method
            notes section.

        Warning
        -------
        See :meth:`SpectralPowerDistribution.interpolate` method warning
        section.

        References
        ----------
        .. [8]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data
                for Use in Colour Computations: 9. INTERPOLATION
                <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
                ISBN-13: 978-3-901-90641-1

        Examples
        --------
        Uniform data is using *Sprague* interpolation by default:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([ 60.30332087,  93.27163315,  13.86051361])

        Non uniform data is using *Cubic Spline* interpolation by default:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd[511] = (31.41, 95.27, 15.06)
        >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([  21.47104053,  100.64300155,   18.8165196 ])

        Enforcing *Linear* interpolation:

        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd[515]
        array([ 59.63,  88.95,  17.79])
        """

        for i in self.__mapping.keys():
            getattr(self, i).interpolate(shape, method)

        return self

    def align(self,
              shape,
              method='Constant',
              left=None,
              right=None):
        """
        Aligns the tri-spectral power distribution to given shape: Interpolates
        first then extrapolates to fit the given range.

        Parameters
        ----------
        shape : SpectralShape
            Spectral shape used for alignment.
        method : unicode, optional
            ('Linear', 'Constant'),
            Extrapolation method.
        left : numeric, optional
            Value to return for low extrapolation range.
        right : numeric, optional
            Value to return for high extrapolation range.

        Returns
        -------
        TriSpectralPowerDistribution
            Aligned tri-spectral power distribution.

        See Also
        --------
        TriSpectralPowerDistribution.extrapolate,
        TriSpectralPowerDistribution.interpolate

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> # Doctests skip for Python 2.x compatibility.
        >>> tri_spd.wavelengths  # doctest: +SKIP
        array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,
               518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,
               531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,
               544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,
               557, 558, 559, 560, 561, 562, 563, 564, 565])
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 49.67     ...,  90.56     ...,  12.43     ...],
               [ 51.8325938...,  91.2994928...,  12.5377184...],
               [ 53.9841952...,  91.9502387...,  12.7233193...],
               [ 56.1205452...,  92.5395463...,  12.9651679...],
               [ 58.2315395...,  93.0150037...,  13.3123777...],
               [ 60.3033208...,  93.2716331...,  13.8605136...],
               [ 62.3203719...,  93.1790455...,  14.7272944...],
               [ 64.2676077...,  92.6085951...,  16.0282961...],
               [ 66.1324679...,  91.4605335...,  17.8526544...],
               [ 67.9070097...,  89.6911649...,  20.2387677...],
               [ 69.59     ...,  87.34     ...,  23.15     ...],
               [ 71.1837378...,  84.4868033...,  26.5150469...],
               [ 72.6800056...,  81.0666018...,  30.3964852...],
               [ 74.0753483...,  77.0766254...,  34.7958422...],
               [ 75.3740343...,  72.6153870...,  39.6178858...],
               [ 76.5856008...,  67.8490714...,  44.7026805...],
               [ 77.7223995...,  62.9779261...,  49.8576432...],
               [ 78.7971418...,  58.2026503...,  54.8895997...],
               [ 79.8204447...,  53.6907852...,  59.6368406...],
               [ 80.798376 ...,  49.5431036...,  64.0011777...],
               [ 81.73     ...,  45.76     ...,  67.98     ...],
               [ 82.6093606...,  42.2678534...,  71.6460893...],
               [ 83.439232 ...,  39.10608  ...,  74.976976 ...],
               [ 84.2220071...,  36.3063728...,  77.9450589...],
               [ 84.956896 ...,  33.85464  ...,  80.552    ...],
               [ 85.6410156...,  31.7051171...,  82.8203515...],
               [ 86.27048  ...,  29.79448  ...,  84.785184 ...],
               [ 86.8414901...,  28.0559565...,  86.4857131...],
               [ 87.351424 ...,  26.43344  ...,  87.956928 ...],
               [ 87.7999266...,  24.8956009...,  89.2212178...],
               [ 88.19     ...,  23.45     ...,  90.28     ...],
               [ 88.5265036...,  22.1424091...,  91.1039133...],
               [ 88.8090803...,  20.9945234...,  91.6538035...],
               [ 89.0393279...,  20.0021787...,  91.9333499...],
               [ 89.2222817...,  19.1473370...,  91.9858818...],
               [ 89.3652954...,  18.4028179...,  91.8811002...],
               [ 89.4769231...,  17.7370306...,  91.7018000...],
               [ 89.5657996...,  17.1187058...,  91.5305910...],
               [ 89.6395227...,  16.5216272...,  91.4366204...],
               [ 89.7035339...,  15.9293635...,  91.4622944...],
               [ 89.76     ...,  15.34     ...,  91.61     ...],
               [ 89.8094041...,  14.7659177...,  91.8528616...],
               [ 89.8578890...,  14.2129190...,  92.2091737...],
               [ 89.9096307...,  13.6795969...,  92.6929664...],
               [ 89.9652970...,  13.1613510...,  93.2988377...],
               [ 90.0232498...,  12.6519811...,  94.0078786...],
               [ 90.0807467...,  12.1452800...,  94.7935995...],
               [ 90.1351435...,  11.6366269...,  95.6278555...],
               [ 90.1850956...,  11.1245805...,  96.4867724...],
               [ 90.2317606...,  10.6124724...,  97.3566724...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...],
               [ 90.28     ...,  10.11     ...,  98.24     ...]])
        """

        for i in self.__mapping.keys():
            getattr(self, i).align(shape, method, left, right)

        return self

    def zeros(self, shape=SpectralShape()):
        """
        Zeros fills the tri-spectral power distribution: Missing values will be
        replaced with zeros to fit the defined range.

        Parameters
        ----------
        shape : SpectralShape, optional
            Spectral shape used for zeros fill.

        Returns
        -------
        TriSpectralPowerDistribution
            Zeros filled tri-spectral power distribution.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values
        array([[  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 49.67,  90.56,  12.43],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 69.59,  87.34,  23.15],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 81.73,  45.76,  67.98],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 88.19,  23.45,  90.28],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 89.76,  15.34,  91.61],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [ 90.28,  10.11,  98.24],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ],
               [  0.  ,   0.  ,   0.  ]])
        """

        for i in self.__mapping.keys():
            getattr(self, i).zeros(shape)

        return self

    def normalise(self, factor=1):
        """
        Normalises the tri-spectral power distribution with given normalization
        factor.

        Parameters
        ----------
        factor : numeric, optional
            Normalization factor

        Returns
        -------
        TriSpectralPowerDistribution
            Normalised tri- spectral power distribution.

        Notes
        -----
        -   The implementation uses the maximum value for all axis.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> tri_spd.normalise()  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd.values  # doctest: +ELLIPSIS
        array([[ 0.5055985...,  0.9218241...,  0.1265268...],
               [ 0.7083672...,  0.8890472...,  0.2356473...],
               [ 0.8319421...,  0.4657980...,  0.6919788...],
               [ 0.8976995...,  0.2387011...,  0.9189739...],
               [ 0.9136807...,  0.1561482...,  0.9325122...],
               [ 0.9189739...,  0.1029112...,  1.       ...]])
        """

        maximum = max(np.ravel(self.values))
        for i in self.__mapping.keys():
            getattr(self, i) * (1 / maximum) * factor

        return self

    def clone(self):
        """
        Clones the tri-spectral power distribution.

        Most of the :class:`TriSpectralPowerDistribution` class operations are
        conducted in-place. The :meth:`TriSpectralPowerDistribution.clone`
        method provides a convenient way to copy the tri-spectral power
        distribution to a new object.

        Returns
        -------
        TriSpectralPowerDistribution
            Cloned tri-spectral power distribution.

        Examples
        --------
        >>> x_bar = {
        ...     510: 49.67,
        ...     520: 69.59,
        ...     530: 81.73,
        ...     540: 88.19,
        ...     550: 89.76,
        ...     560: 90.28}
        >>> y_bar = {
        ...     510: 90.56,
        ...     520: 87.34,
        ...     530: 45.76,
        ...     540: 23.45,
        ...     550: 15.34,
        ...     560: 10.11}
        >>> z_bar = {
        ...     510: 12.43,
        ...     520: 23.15,
        ...     530: 67.98,
        ...     540: 90.28,
        ...     550: 91.61,
        ...     560: 98.24}
        >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}
        >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}
        >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)
        >>> print(tri_spd)  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        >>> tri_spd_clone = tri_spd.clone()
        >>> print(tri_spd_clone)  # doctest: +ELLIPSIS
        <...TriSpectralPowerDistribution object at 0x...>
        """

        return copy.deepcopy(self)


DEFAULT_SPECTRAL_SHAPE = SpectralShape(360, 830, 1)
"""
Default spectral shape using the shape of
*CIE 1931 2 Degree Standard Observer*.

DEFAULT_SPECTRAL_SHAPE : SpectralShape
"""


def constant_spd(k,
                 shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    constant :math:`k` values.

    Parameters
    ----------
    k : numeric
        Constant :math:`k` to fill the spectral power distribution with.
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Constant :math:`k` to filled spectral power distribution.

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = constant_spd(100)
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    100.0
    """

    wavelengths = shape.range()
    values = np.full(len(wavelengths), k)

    name = '{0} Constant'.format(k)
    return SpectralPowerDistribution(name, dict(zip(wavelengths, values)))


def zeros_spd(shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    zeros.

    Parameters
    ----------
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Zeros filled spectral power distribution.

    See Also
    --------
    constant_spd

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = zeros_spd()
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    0.0
    """

    return constant_spd(0, shape)


def ones_spd(shape=DEFAULT_SPECTRAL_SHAPE):
    """
    Returns a spectral power distribution of given spectral shape filled with
    ones.

    Parameters
    ----------
    shape : SpectralShape, optional
        Spectral shape used to create the spectral power distribution.

    Returns
    -------
    SpectralPowerDistribution
        Ones filled spectral power distribution.

    See Also
    --------
    constant_spd

    Notes
    -----
    -   By default, the spectral power distribution will use the shape given
        by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.

    Examples
    --------
    >>> spd = ones_spd()
    >>> spd.shape
    SpectralShape(360, 830, 1)
    >>> spd[400]
    1.0
    """

    return constant_spd(1, shape)
#!/usr/bin/env python # -*- coding: utf-8 -*- Spectrum ========  Defines the classes handling spectral data computation:  -   :class:`SpectralShape` -   :class:`SpectralPowerDistribution` -   :class:`TriSpectralPowerDistribution`  See Also -------- `Spectrum IPython Notebook <http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/spectrum.ipynb>`_  # noqa Defines the base object for spectral power distribution shape.      Parameters     ----------     start : numeric, optional         Wavelengths :math:`\lambda_{i}`: range start in nm.     end : numeric, optional         Wavelengths :math:`\lambda_{i}`: range end in nm.     steps : numeric, optional         Wavelengths :math:`\lambda_{i}`: range steps.      Attributes     ----------     start     end     steps      Methods     -------     __repr__     __contains__     __len__     __eq__     __ne__     range      Examples     --------     >>> SpectralShape(360, 830, 1)     SpectralShape(360, 830, 1) # Attribute storing the spectral shape range for caching purpose. Property for **self.__start** private attribute.          Returns         -------         numeric             self.__start. Setter for **self.__start** private attribute.          Parameters         ----------         value : str or unicode             Attribute value. # Invalidating the *range* cache. Property for **self.__end** private attribute.          Returns         -------         numeric             self.__end. Setter for **self.__end** private attribute.          Parameters         ----------         value : str or unicode             Attribute value. # Invalidating the *range* cache. Property for **self.__steps** private attribute.          Returns         -------         numeric             self.__steps. Setter for **self.__steps** private attribute.          Parameters         ----------         value : str or unicode             Attribute value. # Invalidating the *range* cache. Returns a nice formatted string representation.          Returns         -------         unicode             Nice formatted string representation. Returns a formatted string representation.          Returns         -------         unicode             Formatted string representation. Returns a generator for the spectral power distribution data.          Returns         -------         generator             Spectral power distribution data generator.          Notes         -----         -   Reimplements the :meth:`object.__iter__` method.          Examples         --------         >>> shape = SpectralShape(0, 10, 1)         >>> for wavelength in shape: print(wavelength)         0         1         2         3         4         5         6         7         8         9         10 Returns if the spectral shape contains the given wavelength         :math:`\lambda`.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda`.          Returns         -------         bool             Is wavelength :math:`\lambda` in the spectral shape.          Notes         -----         -   Reimplements the :meth:`object.__contains__` method.          Examples         --------         >>> 0.5 in SpectralShape(0, 10, 0.1)         True         >>> 0.51 in SpectralShape(0, 10, 0.1)         False Returns the spectral shape wavelengths :math:`\lambda_n`         count.          Returns         -------         int             Spectral shape wavelengths :math:`\lambda_n` count.          Notes         -----         -   Reimplements the :meth:`object.__len__` method.          Examples         --------         >>> len(SpectralShape(0, 10, 0.1))         101 Returns the spectral shape equality with given other spectral shape.          Parameters         ----------         shape : SpectralShape             Spectral shape to compare for equality.          Returns         -------         bool             Spectral shape equality.          Notes         -----         -   Reimplements the :meth:`object.__eq__` method.          Examples         --------         >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 0.1)         True         >>> SpectralShape(0, 10, 0.1) == SpectralShape(0, 10, 1)         False Returns the spectral shape inequality with given other spectral shape.          Parameters         ----------         shape : SpectralShape             Spectral shape to compare for inequality.          Returns         -------         bool             Spectral shape inequality.          Notes         -----         -   Reimplements the :meth:`object.__ne__` method.          Examples         --------         >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 0.1)         False         >>> SpectralShape(0, 10, 0.1) != SpectralShape(0, 10, 1)         True Returns an iterable range for the spectral power distribution shape.          Returns         -------         ndarray             Iterable range for the spectral power distribution shape          Raises         ------         RuntimeError             If one of spectral shape *start*, *end* or *steps* attributes is             not defined.          Examples         --------         >>> SpectralShape(0, 10, 0.1).range()         array([  0. ,   0.1,   0.2,   0.3,   0.4,   0.5,   0.6,   0.7,   0.8,                  0.9,   1. ,   1.1,   1.2,   1.3,   1.4,   1.5,   1.6,   1.7,                  1.8,   1.9,   2. ,   2.1,   2.2,   2.3,   2.4,   2.5,   2.6,                  2.7,   2.8,   2.9,   3. ,   3.1,   3.2,   3.3,   3.4,   3.5,                  3.6,   3.7,   3.8,   3.9,   4. ,   4.1,   4.2,   4.3,   4.4,                  4.5,   4.6,   4.7,   4.8,   4.9,   5. ,   5.1,   5.2,   5.3,                  5.4,   5.5,   5.6,   5.7,   5.8,   5.9,   6. ,   6.1,   6.2,                  6.3,   6.4,   6.5,   6.6,   6.7,   6.8,   6.9,   7. ,   7.1,                  7.2,   7.3,   7.4,   7.5,   7.6,   7.7,   7.8,   7.9,   8. ,                  8.1,   8.2,   8.3,   8.4,   8.5,   8.6,   8.7,   8.8,   8.9,                  9. ,   9.1,   9.2,   9.3,   9.4,   9.5,   9.6,   9.7,   9.8,                  9.9,  10. ]) Defines the base object for spectral data computations.      Parameters     ----------     name : str or unicode         Spectral power distribution name.     data : dict         Spectral power distribution data in a *dict* as follows:         {wavelength :math:`\lambda_{i}`: value,         wavelength :math:`\lambda_{i+1}`,         ...,         wavelength :math:`\lambda_{i+n}`}      Attributes     ----------     name     data     wavelengths     values     items     shape      Methods     -------     __getitem__     __init__     __setitem__     __iter__     __contains__     __len__     __eq__     __ne__     __add__     __sub__     __mul__     __div__     __truediv__     get     is_uniform     extrapolate     interpolate     align     zeros     normalise     clone      Examples     --------     >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}     >>> spd = SpectralPowerDistribution('Spd', data)     >>> spd.wavelengths     array([510, 520, 530, 540])     >>> spd.values     array([ 49.67,  69.59,  81.73,  88.19])     >>> spd.shape     SpectralShape(510, 540, 10) Property for **self.__name** private attribute.          Returns         -------         str or unicode             self.__name. Setter for **self.__name** private attribute.          Parameters         ----------         value : str or unicode             Attribute value. Property for **self.__data** private attribute.          Returns         -------         dict             self.__data. Setter for **self.__data** private attribute.          Parameters         ----------         value : dict             Attribute value. Property for **self.wavelengths** attribute.          Returns         -------         ndarray             Spectral power distribution wavelengths :math:`\lambda_n`.          Warning         -------         :attr:`SpectralPowerDistribution.wavelengths` is read only. Setter for **self.wavelengths** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.values** attribute.          Returns         -------         ndarray             Spectral power distribution wavelengths :math:`\lambda_n` values.          Warning         -------         :attr:`SpectralPowerDistribution.values` is read only. Setter for **self.values** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.items** attribute. This is a convenient attribute         used to iterate over the spectral power distribution.          Returns         -------         generator             Spectral power distribution data generator. Setter for **self.items** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.shape** attribute.          Returns the shape of the spectral power distribution in the form of a         :class:`SpectralShape` class instance.          Returns         -------         SpectralShape             Spectral power distribution shape.          See Also         --------         SpectralPowerDistribution.is_uniform          Notes         -----         -   A non uniform spectral power distribution may will have multiple             different steps, in that case             :attr:`SpectralPowerDistribution.shape` returns the *minimum* steps             size.          Warning         -------         :attr:`SpectralPowerDistribution.shape` is read only.          Examples         --------         Uniform spectral power distribution:          >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> SpectralPowerDistribution('Spd', data).shape         SpectralShape(510, 540, 10)          Non uniform spectral power distribution:          >>> data = {512.3: 49.67, 524.5: 69.59, 532.4: 81.73, 545.7: 88.19}         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> SpectralPowerDistribution('Spd', data).shape  # doctest: +ELLIPSIS         SpectralShape(512.3, 545.7, 7...) Setter for **self.shape** attribute.          Parameters         ----------         value : object             Attribute value. Returns the spectral power distribution hash value.          Returns         -------         int             Object hash.          Notes         -----         -   Reimplements the :meth:`object.__hash__` method.          Warning         -------         :class:`SpectralPowerDistribution` class is mutable and should not be         hashable. However, so that it can be used as a key in some data caches,         we provide a *__hash__* implementation, **assuming that the underlying         data will not change for those specific cases**.          References         ----------         .. [1]  http://stackoverflow.com/a/16162138/931625                 (Last accessed 8 August 2014) Returns the value for given wavelength :math:`\lambda`.          Parameters         ----------         wavelength: numeric             Wavelength :math:`\lambda` to retrieve the value.          Returns         -------         numeric             Wavelength :math:`\lambda` value.          See Also         --------         SpectralPowerDistribution.get          Notes         -----         -   Reimplements the :meth:`object.__getitem__` method.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> spd[510]  # doctest: +ELLIPSIS         49.67... Sets the wavelength :math:`\lambda` with given value.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda` to set.         value : numeric             Value for wavelength :math:`\lambda`.          Notes         -----         -   Reimplements the :meth:`object.__setitem__` method.          Examples         --------         >>> spd = SpectralPowerDistribution('Spd', {})         >>> spd[510] = 49.6700         >>> spd.values         array([ 49.67]) Returns a generator for the spectral power distribution data.          Returns         -------         generator             Spectral power distribution data generator.          Notes         -----         -   Reimplements the :meth:`object.__iter__` method.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> for wavelength, value in spd: print((wavelength, value))  # noqa  # doctest: +ELLIPSIS         (510, 49.6...)         (520, 69.5...)         (530, 81.7...)         (540, 88.1...) Returns if the spectral power distribution contains the given         wavelength :math:`\lambda`.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda`.          Returns         -------         bool             Is wavelength :math:`\lambda` in the spectral power distribution.          Notes         -----         -   Reimplements the :meth:`object.__contains__` method.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> 510 in spd         True Returns the spectral power distribution wavelengths :math:`\lambda_n`         count.          Returns         -------         int             Spectral power distribution wavelengths :math:`\lambda_n` count.          Notes         -----         -   Reimplements the :meth:`object.__len__` method.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> len(spd)         4 Returns the spectral power distribution equality with given other         spectral power distribution.          Parameters         ----------         spd : SpectralPowerDistribution             Spectral power distribution to compare for equality.          Returns         -------         bool             Spectral power distribution equality.          Notes         -----         -   Reimplements the :meth:`object.__eq__` method.          Examples         --------         >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}         >>> spd1 = SpectralPowerDistribution('Spd', data1)         >>> spd2 = SpectralPowerDistribution('Spd', data2)         >>> spd3 = SpectralPowerDistribution('Spd', data2)         >>> spd1 == spd2         False         >>> spd2 == spd3         True Returns the spectral power distribution inequality with given other         spectral power distribution.          Parameters         ----------         spd : SpectralPowerDistribution             Spectral power distribution to compare for inequality.          Returns         -------         bool             Spectral power distribution inequality.          Notes         -----         -   Reimplements the :meth:`object.__ne__` method.          Examples         --------         >>> data1 = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> data2 = {510: 48.6700, 520: 69.5900, 530: 81.7300, 540: 88.1900}         >>> spd1 = SpectralPowerDistribution('Spd', data1)         >>> spd2 = SpectralPowerDistribution('Spd', data2)         >>> spd3 = SpectralPowerDistribution('Spd', data2)         >>> spd1 != spd2         True         >>> spd2 != spd3         False Formats given :math:`x` variable operand to *numeric* or *ndarray*.          This method is a convenient method to prepare the given :math:`x`         variable for the arithmetic operations below.          Parameters         ----------         x : numeric or ndarray or SpectralPowerDistribution             Variable to format.          Returns         -------         numeric or ndarray             Formatted operand. Implements support for spectral power distribution addition.          Parameters         ----------         x : numeric or array_like or SpectralPowerDistribution             Variable to add.          Returns         -------         SpectralPowerDistribution             Variable added spectral power distribution.          See Also         --------         SpectralPowerDistribution.__sub__, SpectralPowerDistribution.__mul__,         SpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__add__` method.          Warning         -------         The addition operation happens in place.          Examples         --------         Adding a single *numeric* variable:          >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd + 10  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 59.67,  79.59,  91.73,  98.19])          Adding an *array_like* variable:          >>> spd + [1, 2, 3, 4]  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([  60.67,   81.59,   94.73,  102.19])          Adding a :class:`SpectralPowerDistribution` class variable:          >>> spd_alternate = SpectralPowerDistribution('Spd', data)         >>> spd + spd_alternate  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 110.34,  151.18,  176.46,  190.38]) Implements support for spectral power distribution subtraction.          Parameters         ----------         x : numeric or array_like or SpectralPowerDistribution             Variable to subtract.          Returns         -------         SpectralPowerDistribution             Variable subtracted spectral power distribution.          See Also         --------         SpectralPowerDistribution.__add__, SpectralPowerDistribution.__mul__,         SpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__sub__` method.          Warning         -------         The subtraction operation happens in place.          Examples         --------         Subtracting a single *numeric* variable:          >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd - 10  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 39.67,  59.59,  71.73,  78.19])          Subtracting an *array_like* variable:          >>> spd - [1, 2, 3, 4]  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 38.67,  57.59,  68.73,  74.19])          Subtracting a :class:`SpectralPowerDistribution` class variable:          >>> spd_alternate = SpectralPowerDistribution('Spd', data)         >>> spd - spd_alternate  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([-11., -12., -13., -14.]) Implements support for spectral power distribution multiplication.          Parameters         ----------         x : numeric or array_like or SpectralPowerDistribution             Variable to multiply.          Returns         -------         SpectralPowerDistribution             Variable multiplied spectral power distribution.          See Also         --------         SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,         SpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__mul__` method.          Warning         -------         The multiplication operation happens in place.          Examples         --------         Multiplying a single *numeric* variable:          >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd * 10  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 496.7,  695.9,  817.3,  881.9])          Multiplying an *array_like* variable:          >>> spd * [1, 2, 3, 4]  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([  496.7,  1391.8,  2451.9,  3527.6])          Multiplying a :class:`SpectralPowerDistribution` class variable:          >>> spd_alternate = SpectralPowerDistribution('Spd', data)         >>> spd * spd_alternate  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([  24671.089,   96855.362,  200393.787,  311099.044]) Implements support for spectral power distribution division.          Parameters         ----------         x : numeric or array_like or SpectralPowerDistribution             Variable to divide.          Returns         -------         SpectralPowerDistribution             Variable divided spectral power distribution.          See Also         --------         SpectralPowerDistribution.__add__, SpectralPowerDistribution.__sub__,         SpectralPowerDistribution.__mul__          Notes         -----         -   Reimplements the :meth:`object.__div__` method.          Warning         -------         The division operation happens in place.          Examples         --------         Dividing a single *numeric* variable:          >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd / 10  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 4.967,  6.959,  8.173,  8.819])          Dividing an *array_like* variable:          >>> spd / [1, 2, 3, 4]  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([ 4.967     ,  3.4795    ,  2.72433333,  2.20475   ])          Dividing a :class:`SpectralPowerDistribution` class variable:          >>> spd_alternate = SpectralPowerDistribution('Spd', data)         >>> spd / spd_alternate  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values  # doctest: +ELLIPSIS         array([ 0.1       ,  0.05      ,  0.0333333...,  0.025     ]) # Python 3 compatibility. Returns the value for given wavelength :math:`\lambda`.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda` to retrieve the value.         default : None or numeric, optional             Wavelength :math:`\lambda` default value.          Returns         -------         numeric             Wavelength :math:`\lambda` value.          See Also         --------         SpectralPowerDistribution.__getitem__          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> spd.get(510)  # doctest: +ELLIPSIS         49.67...         >>> spd.get(511)  # doctest: +SKIP         None Returns if the spectral power distribution has uniformly spaced data.          Returns         -------         bool             Is uniform.          See Also         --------         SpectralPowerDistribution.shape          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.is_uniform()         True          Breaking the steps by introducing a new wavelength :math:`\lambda`         value:          >>> spd[511] = 3.1415         >>> spd.is_uniform()         False Extrapolates the spectral power distribution following *CIE 15:2004*         recommendation.          Parameters         ----------         shape : SpectralShape             Spectral shape used for extrapolation.         method : unicode, optional             ('Linear', 'Constant'),             Extrapolation method.         left : numeric, optional             Value to return for low extrapolation range.         right : numeric, optional             Value to return for high extrapolation range.          Returns         -------         SpectralPowerDistribution             Extrapolated spectral power distribution.          See Also         --------         SpectralPowerDistribution.align          References         ----------         .. [2]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation                 <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa                 ISBN-13: 978-3-901-90633-6          .. [3]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data                 for Use in Colour Computations: 10. EXTRAPOLATION                 <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,                 ISBN-13: 978-3-901-90641-1          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.extrapolate(SpectralShape(400, 700)).shape         SpectralShape(400, 700, 10)         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> spd[400]  # doctest: +ELLIPSIS         49.67...         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> spd[700]  # doctest: +ELLIPSIS         88.1... Interpolates the spectral power distribution following         *CIE 167:2005* recommendations: the method developed by         *Sprague (1880)* should be used for interpolating functions having a         uniformly spaced independent variable and a *Cubic Spline* method for         non-uniformly spaced independent variable.          Parameters         ----------         shape : SpectralShape, optional             Spectral shape used for interpolation.         method : unicode, optional             ('Sprague', 'Cubic Spline', 'Linear'),             Enforce given interpolation method.          Returns         -------         SpectralPowerDistribution             Interpolated spectral power distribution.          Raises         ------         RuntimeError             If the *Sprague* interpolation method is forced with a             non-uniformly spaced independent variable.         ValueError             If the interpolation method is not defined.          See Also         --------         SpectralPowerDistribution.align          Notes         -----         -   Interpolation will be conducted over boundaries range, if you need             to extend the range of the spectral power distribution use the             :meth:`SpectralPowerDistribution.extrapolate` or             :meth:`SpectralPowerDistribution.align` methods.         -   *Sprague* interpolator cannot be used for interpolating             functions having a non-uniformly spaced independent variable.          Warning         -------         -   If *scipy* is not unavailable the *Cubic Spline* method will             fallback to legacy *Linear* interpolation.         -   *Linear* interpolator requires at least 2 wavelengths             :math:`\lambda_n` for interpolation.         -   *Cubic Spline* interpolator requires at least 3 wavelengths             :math:`\lambda_n` for interpolation.         -   *Sprague* interpolator requires at least 6 wavelengths             :math:`\lambda_n` for interpolation.          References         ----------         .. [4]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data                 for Use in Colour Computations: 9. INTERPOLATION                 <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,                 ISBN-13: 978-3-901-90641-1          Examples         --------         Uniform data is using *Sprague* interpolation by default:          >>> data = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 86.26,         ...     560: 77.18}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd[515]  # doctest: +ELLIPSIS         60.3121800...          Non uniform data is using *Cubic Spline* interpolation by default:          >>> data = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 86.26,         ...     560: 77.18}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd[511] = 31.41         >>> spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd[515]  # doctest: +ELLIPSIS         21.4792222...          Enforcing *Linear* interpolation:          >>> data = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 86.26,         ...     560: 77.18}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> # Doctests ellipsis for Python 2.x compatibility.         >>> spd[515]  # doctest: +ELLIPSIS         59.63... # Defining proper interpolation bounds. # TODO: Provide support for fractional steps like 0.1, etc... Aligns the spectral power distribution to given spectral shape:         Interpolates first then extrapolates to fit the given range.          Parameters         ----------         shape : SpectralShape             Spectral shape used for alignment.         method : unicode, optional             ('Linear', 'Constant'),             Extrapolation method.         left : numeric, optional             Value to return for low extrapolation range.         right : numeric, optional             Value to return for high extrapolation range.          Returns         -------         SpectralPowerDistribution             Aligned spectral power distribution.          See Also         --------         SpectralPowerDistribution.extrapolate,         SpectralPowerDistribution.interpolate          Examples         --------         >>> data = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 86.26,         ...     560: 77.18}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> # Doctests skip for Python 2.x compatibility.         >>> spd.wavelengths  # doctest: +SKIP         array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,                518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,                531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,                544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,                557, 558, 559, 560, 561, 562, 563, 564, 565])         >>> spd.values  # doctest: +ELLIPSIS         array([ 49.67     ...,  49.67     ...,  49.67     ...,  49.67     ...,                 49.67     ...,  49.67     ...,  51.8341162...,  53.9856467...,                 56.1229464...,  58.2366197...,  60.3121800...,  62.3327095...,                 64.2815187...,  66.1448055...,  67.9143153...,  69.59     ...,                 71.1759958...,  72.6627938...,  74.0465756...,  75.3329710...,                 76.5339542...,  77.6647421...,  78.7406907...,  79.7741932...,                 80.7715767...,  81.73     ...,  82.6407518...,  83.507872 ...,                 84.3326333...,  85.109696 ...,  85.8292968...,  86.47944  ...,                 87.0480863...,  87.525344 ...,  87.9056578...,  88.19     ...,                 88.3858347...,  88.4975634...,  88.5258906...,  88.4696570...,                 88.3266460...,  88.0943906...,  87.7709802...,  87.3558672...,                 86.8506741...,  86.26     ...,  85.5911699...,  84.8503430...,                 84.0434801...,  83.1771110...,  82.2583874...,  81.2951360...,                 80.2959122...,  79.2700525...,  78.2277286...,  77.18     ...,                 77.18     ...,  77.18     ...,  77.18     ...,  77.18     ...,  77.18      ]) Zeros fills the spectral power distribution: Missing values will be         replaced with zeros to fit the defined range.          Parameters         ----------         shape : SpectralShape, optional             Spectral shape used for zeros fill.          Returns         -------         SpectralPowerDistribution             Zeros filled spectral power distribution.          Examples         --------         >>> data = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 86.26,         ...     560: 77.18}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values         array([  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  49.67,   0.  ,   0.  ,                  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  69.59,                  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,                  0.  ,  81.73,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,                  0.  ,   0.  ,   0.  ,  88.19,   0.  ,   0.  ,   0.  ,   0.  ,                  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  86.26,   0.  ,   0.  ,                  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ,  77.18,                  0.  ,   0.  ,   0.  ,   0.  ,   0.  ]) Normalises the spectral power distribution with given normalization         factor.          Parameters         ----------         factor : numeric, optional             Normalization factor          Returns         -------         SpectralPowerDistribution             Normalised spectral power distribution.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> spd.normalise()  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd.values  # doctest: +ELLIPSIS         array([ 0.5632157...,  0.7890917...,  0.9267490...,  1.        ]) Clones the spectral power distribution.          Most of the :class:`SpectralPowerDistribution` class operations are         conducted in-place. The :meth:`SpectralPowerDistribution.clone` method         provides a convenient way to copy the spectral power distribution to a         new object.          Returns         -------         SpectralPowerDistribution             Cloned spectral power distribution.          Examples         --------         >>> data = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> spd = SpectralPowerDistribution('Spd', data)         >>> print(spd)  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...>         >>> spd_clone = spd.clone()         >>> print(spd_clone)  # doctest: +ELLIPSIS         <...SpectralPowerDistribution object at 0x...> Defines the base object for colour matching functions.      A compound of three :class:`SpectralPowerDistribution` is used to store     the underlying axis data.      Parameters     ----------     name : str or unicode         Tri-spectral power distribution name.     data : dict         Tri-spectral power distribution data.     mapping : dict         Tri-spectral power distribution attributes mapping.     labels : dict         Tri-spectral power distribution axis labels mapping.      Attributes     ----------     name     mapping     data     labels     x     y     z     wavelengths     values     items     shape      Methods     -------     __init__     __getitem__     __setitem__     __iter__     __contains__     __len__     __eq__     __ne__     __add__     __sub__     __mul__     __div__     __truediv__     get     is_uniform     extrapolate     interpolate     align     zeros     normalise     clone      See Also     --------     colour.colorimetry.cmfs.LMS_ConeFundamentals,     colour.colorimetry.cmfs.RGB_ColourMatchingFunctions,     colour.colorimetry.cmfs.XYZ_ColourMatchingFunctions      Examples     --------     >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}     >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}     >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}     >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}     >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}     >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)     >>> tri_spd.wavelengths     array([510, 520, 530, 540])     >>> tri_spd.values     array([[ 49.67,  90.56,  12.43],            [ 69.59,  87.34,  23.15],            [ 81.73,  45.76,  67.98],            [ 88.19,  23.45,  90.28]])     >>> tri_spd.shape     SpectralShape(510, 540, 10) Property for **self.__name** private attribute.          Returns         -------         str or unicode             self.__name. Setter for **self.__name** private attribute.          Parameters         ----------         value : str or unicode             Attribute value. Property for **self.__mapping** private attribute.          Returns         -------         dict             self.__mapping. Setter for **self.__mapping** private attribute.          Parameters         ----------         value : dict             Attribute value. Property for **self.__data** private attribute.          Returns         -------         dict             self.__data. Setter for **self.__data** private attribute.          Parameters         ----------         value : dict             Attribute value. Property for **self.__labels** private attribute.          Returns         -------         dict             self.__labels. Setter for **self.__labels** private attribute.          Parameters         ----------         value : dict             Attribute value. Property for **self.x** attribute.          Returns         -------         SpectralPowerDistribution             Spectral power distribution for *x* axis.          Warning         -------         :attr:`TriSpectralPowerDistribution.x` is read only. Setter for **self.x** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.y** attribute.          Returns         -------         SpectralPowerDistribution             Spectral power distribution for *y* axis.          Warning         -------         :attr:`TriSpectralPowerDistribution.y` is read only. Setter for **self.y** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.z** attribute.          Returns         -------         SpectralPowerDistribution             Spectral power distribution for *z* axis.          Warning         -------         :attr:`TriSpectralPowerDistribution.z` is read only. Setter for **self.z** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.wavelengths** attribute.          Returns         -------         ndarray             Tri-spectral power distribution wavelengths :math:`\lambda_n`.          Warning         -------         :attr:`TriSpectralPowerDistribution.wavelengths` is read only. Setter for **self.wavelengths** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.values** attribute.          Returns         -------         ndarray             Tri-spectral power distribution wavelengths :math:`\lambda_n`             values.          Warning         -------         :attr:`TriSpectralPowerDistribution.values` is read only. Setter for **self.values** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.items** attribute. This is a convenient attribute         used to iterate over the tri-spectral power distribution.          Returns         -------         generator             Tri-spectral power distribution data generator. Setter for **self.items** attribute.          Parameters         ----------         value : object             Attribute value. Property for **self.shape** attribute.          Returns the shape of the tri-spectral power distribution in the form of         a :class:`SpectralShape` class instance.          Returns         -------         SpectralShape             Tri-spectral power distribution shape.          See Also         --------         SpectralPowerDistribution.is_uniform,         TriSpectralPowerDistribution.is_uniform          Warning         -------         :attr:`TriSpectralPowerDistribution.shape` is read only.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.shape         SpectralShape(510, 540, 10) Setter for **self.shape** attribute.          Parameters         ----------         value : object             Attribute value. Returns the spectral power distribution hash value.          Returns         -------         int             Object hash.          Notes         -----         -   Reimplements the :meth:`object.__hash__` method.          Warning         -------         See :meth:`SpectralPowerDistribution.__hash__` method warning section.          References         ----------         .. [5]  http://stackoverflow.com/a/16162138/931625                 (Last accessed 8 August 2014) Returns the values for given wavelength :math:`\lambda`.          Parameters         ----------         wavelength: numeric             Wavelength :math:`\lambda` to retrieve the values.          Returns         -------         ndarray, (3,)             Wavelength :math:`\lambda` values.          See Also         --------         TriSpectralPowerDistribution.get          Notes         -----         -   Reimplements the :meth:`object.__getitem__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd[510]         array([ 49.67,  90.56,  12.43]) Sets the wavelength :math:`\lambda` with given value.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda` to set.         value : array_like             Value for wavelength :math:`\lambda`.          Notes         -----         -   Reimplements the :meth:`object.__setitem__` method.          Examples         --------         >>> x_bar = {}         >>> y_bar = {}         >>> z_bar = {}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd[510] = (49.6700, 49.6700, 49.6700)         >>> tri_spd.values         array([[ 49.67,  49.67,  49.67]]) Returns a generator for the tri-spectral power distribution data.          Returns         -------         generator             Tri-spectral power distribution data generator.          Notes         -----         -   Reimplements the :meth:`object.__iter__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> for wavelength, value in tri_spd: print((wavelength, value))         (510, array([ 49.67,  90.56,  12.43]))         (520, array([ 69.59,  87.34,  23.15]))         (530, array([ 81.73,  45.76,  67.98]))         (540, array([ 88.19,  23.45,  90.28])) Returns if the tri-spectral power distribution contains the given         wavelength :math:`\lambda`.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda`.          Returns         -------         bool             Is wavelength :math:`\lambda` in the tri-spectral power             distribution.          Notes         -----         -   Reimplements the :meth:`object.__contains__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> 510 in tri_spd         True Returns the tri-spectral power distribution wavelengths         :math:`\lambda_n` count.          Returns         -------         int             Tri-Spectral power distribution wavelengths :math:`\lambda_n`             count.          Notes         -----         -   Reimplements the :meth:`object.__len__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> len(tri_spd)         4 Returns the tri-spectral power distribution equality with given other         tri-spectral power distribution.          Parameters         ----------         spd : TriSpectralPowerDistribution             Tri-spectral power distribution to compare for equality.          Returns         -------         bool             Tri-spectral power distribution equality.          Notes         -----         -   Reimplements the :meth:`object.__eq__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)         >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd1 == tri_spd2         False         >>> tri_spd1 == tri_spd3         True Returns the tri-spectral power distribution inequality with given other         tri-spectral power distribution.          Parameters         ----------         spd : TriSpectralPowerDistribution             Tri-spectral power distribution to compare for inequality.          Returns         -------         bool             Tri-spectral power distribution inequality.          Notes         -----         -   Reimplements the :meth:`object.__eq__` method.          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data1 = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> data2 = {'x_bar': y_bar, 'y_bar': x_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd2 = TriSpectralPowerDistribution('Tri Spd', data2, mpg, lbl)         >>> tri_spd3 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd1 != tri_spd2         True         >>> tri_spd1 != tri_spd3         False Formats given :math:`x` variable operand to *numeric* or *ndarray*.          This method is a convenient method to prepare the given :math:`x`         variable for the arithmetic operations below.          Parameters         ----------         x : numeric or ndarray or TriSpectralPowerDistribution             Variable to format.          Returns         -------         numeric or ndarray             Formatted operand. Implements support for tri-spectral power distribution addition.          Parameters         ----------         x : numeric or array_like or TriSpectralPowerDistribution             Variable to add.          Returns         -------         TriSpectralPowerDistribution             Variable added tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.__sub__,         TriSpectralPowerDistribution.__mul__,         TriSpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__add__` method.          Warning         -------         The addition operation happens in place.          Examples         --------         Adding a single *numeric* variable:          >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd + 10  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  59.67,  100.56,   22.43],                [  79.59,   97.34,   33.15],                [  91.73,   55.76,   77.98],                [  98.19,   33.45,  100.28]])          Adding an *array_like* variable:          >>> tri_spd + [(1, 2, 3)] * 4  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  60.67,  102.56,   25.43],                [  80.59,   99.34,   36.15],                [  92.73,   57.76,   80.98],                [  99.19,   35.45,  103.28]])          Adding a :class:`TriSpectralPowerDistribution` class variable:          >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd + tri_spd1  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  73.1 ,  152.23,  115.99],                [ 103.74,  168.93,  123.49],                [ 160.71,  139.49,  126.74],                [ 189.47,  123.64,  126.73]]) Implements support for tri-spectral power distribution subtraction.          Parameters         ----------         x : numeric or array_like or TriSpectralPowerDistribution             Variable to subtract.          Returns         -------         TriSpectralPowerDistribution             Variable subtracted tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.__add__,         TriSpectralPowerDistribution.__mul__,         TriSpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__sub__` method.          Warning         -------         The subtraction operation happens in place.          Examples         --------         Subtracting a single *numeric* variable:          >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd - 10  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[ 39.67,  80.56,   2.43],                [ 59.59,  77.34,  13.15],                [ 71.73,  35.76,  57.98],                [ 78.19,  13.45,  80.28]])          Subtracting an *array_like* variable:          >>> tri_spd - [(1, 2, 3)] * 4  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[ 38.67,  78.56,  -0.57],                [ 58.59,  75.34,  10.15],                [ 70.73,  33.76,  54.98],                [ 77.19,  11.45,  77.28]])          Subtracting a :class:`TriSpectralPowerDistribution` class variable:          >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd - tri_spd1  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[ 26.24,  28.89, -91.13],                [ 35.44,   5.75, -77.19],                [  2.75, -47.97,   9.22],                [-13.09, -76.74,  53.83]]) Implements support for tri-spectral power distribution multiplication.          Parameters         ----------         x : numeric or array_like or TriSpectralPowerDistribution             Variable to multiply.          Returns         -------         TriSpectralPowerDistribution             Variable multiplied tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.__add__,         TriSpectralPowerDistribution.__sub__,         TriSpectralPowerDistribution.__div__          Notes         -----         -   Reimplements the :meth:`object.__mul__` method.          Warning         -------         The multiplication operation happens in place.          Examples         --------         Multiplying a single *numeric* variable:          >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd * 10  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[ 496.7,  905.6,  124.3],                [ 695.9,  873.4,  231.5],                [ 817.3,  457.6,  679.8],                [ 881.9,  234.5,  902.8]])          Multiplying an *array_like* variable:          >>> tri_spd * [(1, 2, 3)] * 4  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  1986.8,   7244.8,   1491.6],                [  2783.6,   6987.2,   2778. ],                [  3269.2,   3660.8,   8157.6],                [  3527.6,   1876. ,  10833.6]])          Multiplying a :class:`TriSpectralPowerDistribution` class variable:          >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd * tri_spd1  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  24695.924,  359849.216,  135079.296],                [  64440.34 ,  486239.248,  242630.52 ],                [ 222240.216,  299197.184,  373291.776],                [ 318471.728,  165444.44 ,  254047.92 ]]) Implements support for tri-spectral power distribution division.          Parameters         ----------         x : numeric or array_like or TriSpectralPowerDistribution             Variable to divide.          Returns         -------         TriSpectralPowerDistribution             Variable divided tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.__add__,         TriSpectralPowerDistribution.__sub__,         TriSpectralPowerDistribution.__mul__          Notes         -----         -   Reimplements the :meth:`object.__mul__` method.          Warning         -------         The division operation happens in place.          Examples         --------         Dividing a single *numeric* variable:          >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd / 10  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[ 4.967,  9.056,  1.243],                [ 6.959,  8.734,  2.315],                [ 8.173,  4.576,  6.798],                [ 8.819,  2.345,  9.028]])          Dividing an *array_like* variable:          >>> tri_spd / [(1, 2, 3)] * 4  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values  # doctest: +ELLIPSIS         array([[ 19.868     ,  18.112     ,   1.6573333...],                [ 27.836     ,  17.468     ,   3.0866666...],                [ 32.692     ,   9.152     ,   9.064    ...],                [ 35.276     ,   4.69      ,  12.0373333...]])          Dividing a :class:`TriSpectralPowerDistribution` class variable:          >>> data1 = {'x_bar': z_bar, 'y_bar': x_bar, 'z_bar': y_bar}         >>> tri_spd1 = TriSpectralPowerDistribution('Tri Spd', data1, mpg, lbl)         >>> tri_spd / tri_spd1  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values  # doctest: +ELLIPSIS         array([[ 1.5983909...,  0.3646466...,  0.0183009...],                [ 1.2024190...,  0.2510130...,  0.0353408...],                [ 0.4809061...,  0.1119784...,  0.1980769...],                [ 0.3907399...,  0.0531806...,  0.5133191...]]) # Python 3 compatibility. Returns the values for given wavelength :math:`\lambda`.          Parameters         ----------         wavelength : numeric             Wavelength :math:`\lambda` to retrieve the values.         default : None or numeric, optional             Wavelength :math:`\lambda` default values.          Returns         -------         numeric             Wavelength :math:`\lambda` values.          See Also         --------         TriSpectralPowerDistribution.__getitem__          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd[510]         array([ 49.67,  90.56,  12.43])         >>> tri_spd.get(511)  # doctest: +SKIP         None Returns if the tri-spectral power distribution has uniformly spaced         data.          Returns         -------         bool             Is uniform.          See Also         --------         TriSpectralPowerDistribution.shape          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.is_uniform()         True          Breaking the steps by introducing new wavelength :math:`\lambda`         values:          >>> tri_spd[511] = (49.6700, 49.6700, 49.6700)         >>> tri_spd.is_uniform()         False Extrapolates the tri-spectral power distribution following         *CIE 15:2004* recommendation.          Parameters         ----------         shape : SpectralShape             Spectral shape used for extrapolation.         method : unicode, optional             ('Linear', 'Constant'),             Extrapolation method.         left : numeric, optional             Value to return for low extrapolation range.         right : numeric, optional             Value to return for high extrapolation range.          Returns         -------         TriSpectralPowerDistribution             Extrapolated tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.align          References         ----------          .. [6]  `CIE 015:2004 Colorimetry, 3rd edition: 7.2.2.1 Extrapolation                 <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_,  # noqa                 ISBN-13: 978-3-901-90633-6         .. [7]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data                 for Use in Colour Computations: 10. EXTRAPOLATION                 <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,                 ISBN-13: 978-3-901-90641-1          Examples         --------         >>> x_bar = {510: 49.67, 520: 69.59, 530: 81.73, 540: 88.19}         >>> y_bar = {510: 90.56, 520: 87.34, 530: 45.76, 540: 23.45}         >>> z_bar = {510: 12.43, 520: 23.15, 530: 67.98, 540: 90.28}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.extrapolate(SpectralShape(400, 700)).shape         SpectralShape(400, 700, 10)         >>> tri_spd[400]         array([ 49.67,  90.56,  12.43])         >>> tri_spd[700]         array([ 88.19,  23.45,  90.28]) Interpolates the tri-spectral power distribution following         *CIE 167:2005* recommendations: the method developed by         *Sprague (1880)* should be used for interpolating functions having a         uniformly spaced independent variable and a *Cubic Spline* method for         non-uniformly spaced independent variable.          Parameters         ----------         shape : SpectralShape, optional             Spectral shape used for interpolation.         method : unicode, optional             ('Sprague', 'Cubic Spline', 'Linear'),             Enforce given interpolation method.          Returns         -------         TriSpectralPowerDistribution             Interpolated tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.align          Notes         -----         -   See :meth:`SpectralPowerDistribution.interpolate` method             notes section.          Warning         -------         See :meth:`SpectralPowerDistribution.interpolate` method warning         section.          References         ----------         .. [8]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data                 for Use in Colour Computations: 9. INTERPOLATION                 <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,                 ISBN-13: 978-3-901-90641-1          Examples         --------         Uniform data is using *Sprague* interpolation by default:          >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd[515]         array([ 60.30332087,  93.27163315,  13.86051361])          Non uniform data is using *Cubic Spline* interpolation by default:          >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd[511] = (31.41, 95.27, 15.06)         >>> tri_spd.interpolate(SpectralShape(steps=1))  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd[515]         array([  21.47104053,  100.64300155,   18.8165196 ])          Enforcing *Linear* interpolation:          >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.interpolate(SpectralShape(steps=1), method='Linear')  # noqa  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd[515]         array([ 59.63,  88.95,  17.79]) Aligns the tri-spectral power distribution to given shape: Interpolates         first then extrapolates to fit the given range.          Parameters         ----------         shape : SpectralShape             Spectral shape used for alignment.         method : unicode, optional             ('Linear', 'Constant'),             Extrapolation method.         left : numeric, optional             Value to return for low extrapolation range.         right : numeric, optional             Value to return for high extrapolation range.          Returns         -------         TriSpectralPowerDistribution             Aligned tri-spectral power distribution.          See Also         --------         TriSpectralPowerDistribution.extrapolate,         TriSpectralPowerDistribution.interpolate          Examples         --------         >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.align(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> # Doctests skip for Python 2.x compatibility.         >>> tri_spd.wavelengths  # doctest: +SKIP         array([505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517,                518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530,                531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543,                544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,                557, 558, 559, 560, 561, 562, 563, 564, 565])         >>> tri_spd.values  # doctest: +ELLIPSIS         array([[ 49.67     ...,  90.56     ...,  12.43     ...],                [ 49.67     ...,  90.56     ...,  12.43     ...],                [ 49.67     ...,  90.56     ...,  12.43     ...],                [ 49.67     ...,  90.56     ...,  12.43     ...],                [ 49.67     ...,  90.56     ...,  12.43     ...],                [ 49.67     ...,  90.56     ...,  12.43     ...],                [ 51.8325938...,  91.2994928...,  12.5377184...],                [ 53.9841952...,  91.9502387...,  12.7233193...],                [ 56.1205452...,  92.5395463...,  12.9651679...],                [ 58.2315395...,  93.0150037...,  13.3123777...],                [ 60.3033208...,  93.2716331...,  13.8605136...],                [ 62.3203719...,  93.1790455...,  14.7272944...],                [ 64.2676077...,  92.6085951...,  16.0282961...],                [ 66.1324679...,  91.4605335...,  17.8526544...],                [ 67.9070097...,  89.6911649...,  20.2387677...],                [ 69.59     ...,  87.34     ...,  23.15     ...],                [ 71.1837378...,  84.4868033...,  26.5150469...],                [ 72.6800056...,  81.0666018...,  30.3964852...],                [ 74.0753483...,  77.0766254...,  34.7958422...],                [ 75.3740343...,  72.6153870...,  39.6178858...],                [ 76.5856008...,  67.8490714...,  44.7026805...],                [ 77.7223995...,  62.9779261...,  49.8576432...],                [ 78.7971418...,  58.2026503...,  54.8895997...],                [ 79.8204447...,  53.6907852...,  59.6368406...],                [ 80.798376 ...,  49.5431036...,  64.0011777...],                [ 81.73     ...,  45.76     ...,  67.98     ...],                [ 82.6093606...,  42.2678534...,  71.6460893...],                [ 83.439232 ...,  39.10608  ...,  74.976976 ...],                [ 84.2220071...,  36.3063728...,  77.9450589...],                [ 84.956896 ...,  33.85464  ...,  80.552    ...],                [ 85.6410156...,  31.7051171...,  82.8203515...],                [ 86.27048  ...,  29.79448  ...,  84.785184 ...],                [ 86.8414901...,  28.0559565...,  86.4857131...],                [ 87.351424 ...,  26.43344  ...,  87.956928 ...],                [ 87.7999266...,  24.8956009...,  89.2212178...],                [ 88.19     ...,  23.45     ...,  90.28     ...],                [ 88.5265036...,  22.1424091...,  91.1039133...],                [ 88.8090803...,  20.9945234...,  91.6538035...],                [ 89.0393279...,  20.0021787...,  91.9333499...],                [ 89.2222817...,  19.1473370...,  91.9858818...],                [ 89.3652954...,  18.4028179...,  91.8811002...],                [ 89.4769231...,  17.7370306...,  91.7018000...],                [ 89.5657996...,  17.1187058...,  91.5305910...],                [ 89.6395227...,  16.5216272...,  91.4366204...],                [ 89.7035339...,  15.9293635...,  91.4622944...],                [ 89.76     ...,  15.34     ...,  91.61     ...],                [ 89.8094041...,  14.7659177...,  91.8528616...],                [ 89.8578890...,  14.2129190...,  92.2091737...],                [ 89.9096307...,  13.6795969...,  92.6929664...],                [ 89.9652970...,  13.1613510...,  93.2988377...],                [ 90.0232498...,  12.6519811...,  94.0078786...],                [ 90.0807467...,  12.1452800...,  94.7935995...],                [ 90.1351435...,  11.6366269...,  95.6278555...],                [ 90.1850956...,  11.1245805...,  96.4867724...],                [ 90.2317606...,  10.6124724...,  97.3566724...],                [ 90.28     ...,  10.11     ...,  98.24     ...],                [ 90.28     ...,  10.11     ...,  98.24     ...],                [ 90.28     ...,  10.11     ...,  98.24     ...],                [ 90.28     ...,  10.11     ...,  98.24     ...],                [ 90.28     ...,  10.11     ...,  98.24     ...],                [ 90.28     ...,  10.11     ...,  98.24     ...]]) Zeros fills the tri-spectral power distribution: Missing values will be         replaced with zeros to fit the defined range.          Parameters         ----------         shape : SpectralShape, optional             Spectral shape used for zeros fill.          Returns         -------         TriSpectralPowerDistribution             Zeros filled tri-spectral power distribution.          Examples         --------         >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.zeros(SpectralShape(505, 565, 1))  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values         array([[  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 49.67,  90.56,  12.43],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 69.59,  87.34,  23.15],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 81.73,  45.76,  67.98],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 88.19,  23.45,  90.28],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 89.76,  15.34,  91.61],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [ 90.28,  10.11,  98.24],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ],                [  0.  ,   0.  ,   0.  ]]) Normalises the tri-spectral power distribution with given normalization         factor.          Parameters         ----------         factor : numeric, optional             Normalization factor          Returns         -------         TriSpectralPowerDistribution             Normalised tri- spectral power distribution.          Notes         -----         -   The implementation uses the maximum value for all axis.          Examples         --------         >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> tri_spd.normalise()  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd.values  # doctest: +ELLIPSIS         array([[ 0.5055985...,  0.9218241...,  0.1265268...],                [ 0.7083672...,  0.8890472...,  0.2356473...],                [ 0.8319421...,  0.4657980...,  0.6919788...],                [ 0.8976995...,  0.2387011...,  0.9189739...],                [ 0.9136807...,  0.1561482...,  0.9325122...],                [ 0.9189739...,  0.1029112...,  1.       ...]]) Clones the tri-spectral power distribution.          Most of the :class:`TriSpectralPowerDistribution` class operations are         conducted in-place. The :meth:`TriSpectralPowerDistribution.clone`         method provides a convenient way to copy the tri-spectral power         distribution to a new object.          Returns         -------         TriSpectralPowerDistribution             Cloned tri-spectral power distribution.          Examples         --------         >>> x_bar = {         ...     510: 49.67,         ...     520: 69.59,         ...     530: 81.73,         ...     540: 88.19,         ...     550: 89.76,         ...     560: 90.28}         >>> y_bar = {         ...     510: 90.56,         ...     520: 87.34,         ...     530: 45.76,         ...     540: 23.45,         ...     550: 15.34,         ...     560: 10.11}         >>> z_bar = {         ...     510: 12.43,         ...     520: 23.15,         ...     530: 67.98,         ...     540: 90.28,         ...     550: 91.61,         ...     560: 98.24}         >>> data = {'x_bar': x_bar, 'y_bar': y_bar, 'z_bar': z_bar}         >>> mpg = lbl = {'x': 'x_bar', 'y': 'y_bar', 'z': 'z_bar'}         >>> tri_spd = TriSpectralPowerDistribution('Tri Spd', data, mpg, lbl)         >>> print(tri_spd)  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...>         >>> tri_spd_clone = tri_spd.clone()         >>> print(tri_spd_clone)  # doctest: +ELLIPSIS         <...TriSpectralPowerDistribution object at 0x...> Default spectral shape using the shape of *CIE 1931 2 Degree Standard Observer*.  DEFAULT_SPECTRAL_SHAPE : SpectralShape Returns a spectral power distribution of given spectral shape filled with     constant :math:`k` values.      Parameters     ----------     k : numeric         Constant :math:`k` to fill the spectral power distribution with.     shape : SpectralShape, optional         Spectral shape used to create the spectral power distribution.      Returns     -------     SpectralPowerDistribution         Constant :math:`k` to filled spectral power distribution.      Notes     -----     -   By default, the spectral power distribution will use the shape given         by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.      Examples     --------     >>> spd = constant_spd(100)     >>> spd.shape     SpectralShape(360, 830, 1)     >>> spd[400]     100.0 Returns a spectral power distribution of given spectral shape filled with     zeros.      Parameters     ----------     shape : SpectralShape, optional         Spectral shape used to create the spectral power distribution.      Returns     -------     SpectralPowerDistribution         Zeros filled spectral power distribution.      See Also     --------     constant_spd      Notes     -----     -   By default, the spectral power distribution will use the shape given         by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.      Examples     --------     >>> spd = zeros_spd()     >>> spd.shape     SpectralShape(360, 830, 1)     >>> spd[400]     0.0 Returns a spectral power distribution of given spectral shape filled with     ones.      Parameters     ----------     shape : SpectralShape, optional         Spectral shape used to create the spectral power distribution.      Returns     -------     SpectralPowerDistribution         Ones filled spectral power distribution.      See Also     --------     constant_spd      Notes     -----     -   By default, the spectral power distribution will use the shape given         by :attr:`DEFAULT_SPECTRAL_SHAPE` attribute.      Examples     --------     >>> spd = ones_spd()     >>> spd.shape     SpectralShape(360, 830, 1)     >>> spd[400]     1.0