<reponame>canavandl/colour
#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
Interpolation
=============

Defines classes for interpolating variables.

-   :class:`LinearInterpolator1d`: 1-D function linear interpolation.
-   :class:`SpragueInterpolator`: 1-D function fifth-order polynomial
    interpolation.
"""

from __future__ import division, unicode_literals

import bisect
import numpy as np

from colour.algebra import steps, is_numeric, is_uniform, to_ndarray
from colour.utilities import is_scipy_installed, warning

__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__ = ['LinearInterpolator1d',
           'SplineInterpolator',
           'SpragueInterpolator']


class LinearInterpolator1d(object):
    """
    Linearly interpolates a 1-D function.

    Parameters
    ----------
    x : ndarray
        Independent :math:`x` variable values corresponding with :math:`y`
        variable.
    y : ndarray
        Dependent and already known :math:`y` variable values to
        interpolate.

    Methods
    -------
    __call__

    Notes
    -----
    This class is a wrapper around *numpy.interp* definition.

    See Also
    --------
    SpragueInterpolator

    Examples
    --------
    Interpolating a single numeric variable:

    >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa
    >>> x = np.arange(len(y))
    >>> f = LinearInterpolator1d(x, y)
    >>> # Doctests ellipsis for Python 2.x compatibility.
    >>> f(0.5)  # doctest: +ELLIPSIS
    7.64...

    Interpolating an *array_like* variable:

    >>> f([0.25, 0.75])
    array([ 6.7825,  8.5075])
    """

    def __init__(self, x=None, y=None):
        self.__x = None
        self.x = x
        self.__y = None
        self.y = y

        self.__validate_dimensions()

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

        Returns
        -------
        array_like
            self.__x
        """

        return self.__x

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"x" independent variable must have exactly one dimension!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

        self.__x = value

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

        Returns
        -------
        array_like
            self.__y
        """

        return self.__y

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"y" dependent variable must have exactly one dimension!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

        self.__y = value

    def __call__(self, x):
        """
        Evaluates the interpolating polynomial at given point(s).


        Parameters
        ----------
        x : numeric or array_like
            Point(s) to evaluate the interpolant at.

        Returns
        -------
        float or ndarray
            Interpolated value(s).
        """

        xi = self.__evaluate(to_ndarray(x))
        if is_numeric(x):
            return float(xi)
        else:
            return xi

    def __evaluate(self, x):
        """
        Performs the interpolating polynomial evaluation at given points.

        Parameters
        ----------
        x : ndarray
            Points to evaluate the interpolant at.

        Returns
        -------
        ndarray
            Interpolated points values.
        """

        self.__validate_dimensions()
        self.__validate_interpolation_range(x)

        return np.interp(x, self.__x, self.__y)

    def __validate_dimensions(self):
        """
        Validates variables dimensions to be the same.
        """

        if len(self.__x) != len(self.__y):
            raise ValueError(
                ('"x" independent and "y" dependent variables have different '
                 'dimensions: "{0}", "{1}"').format(len(self.__x),
                                                    len(self.__y)))

    def __validate_interpolation_range(self, x):
        """
        Validates given point to be in interpolation range.
        """

        below_interpolation_range = x < self.__x[0]
        above_interpolation_range = x > self.__x[-1]

        if below_interpolation_range.any():
            raise ValueError('"{0}" is below interpolation range.'.format(x))

        if above_interpolation_range.any():
            raise ValueError('"{0}" is above interpolation range.'.format(x))


if is_scipy_installed():
    from scipy.interpolate import interp1d

    class SplineInterpolator(interp1d):
        """
        Interpolates a 1-D function using cubic spline interpolation.

        Notes
        -----
        This class is a wrapper around *scipy.interpolate.interp1d* class.
        """

        def __init__(self, *args, **kwargs):
            # TODO: Implements proper wrapper to ensure return values
            # consistency and avoid having to cast to numeric in
            # :meth:`SpectralPowerDistribution.interpolate` method.
            super(SplineInterpolator, self).__init__(
                kind='cubic', *args, **kwargs)
else:
    warning(('"scipy.interpolate.interp1d" interpolator is unavailable, using '
             '"LinearInterpolator1d" instead!'))

    SplineInterpolator = LinearInterpolator1d


class SpragueInterpolator(object):
    """
    Constructs a fifth-order polynomial that passes through :math:`y` dependent
    variable.

    The *Sprague (1880)* method is recommended by the *CIE* for interpolating
    functions having a uniformly spaced independent variable.

    Parameters
    ----------
    x : array_like
        Independent :math:`x` variable values corresponding with :math:`y`
        variable.
    y : array_like
        Dependent and already known :math:`y` variable values to
        interpolate.

    Methods
    -------
    __call__

    See Also
    --------
    LinearInterpolator1d

    Notes
    -----
    The minimum number :math:`k` of data points required along the
    interpolation axis is :math:`k=6`.

    References
    ----------
    .. [1]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data for
            Use in Colour Computations: 9.2.4 Method of interpolation for
            uniformly spaced independent variable
            <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
            ISBN-13: 978-3-901-90641-1
    .. [2]  **<NAME>, <NAME>, <NAME>**,
            *Computational Colour Science Using MATLAB, 2nd Edition*,
            The Wiley-IS&T Series in Imaging Science and Technology,
            published July 2012, ISBN-13: 978-0-470-66569-5, page  33.

    Examples
    --------
    Interpolating a single numeric variable:

    >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa
    >>> x = np.arange(len(y))
    >>> f = SpragueInterpolator(x, y)
    >>> f(0.5)  # doctest: +ELLIPSIS
    7.2185025...

    Interpolating an *array_like* variable:

    >>> f([0.25, 0.75])  # doctest: +ELLIPSIS
    array([ 6.7295161...,  7.8140625...])
    """

    SPRAGUE_C_COEFFICIENTS = np.array(
        [[884, -1960, 3033, -2648, 1080, -180],
         [508, -540, 488, -367, 144, -24],
         [-24, 144, -367, 488, -540, 508],
         [-180, 1080, -2648, 3033, -1960, 884]])
    """
    Defines the coefficients used to generate extra points for boundaries
    interpolation.

    SPRAGUE_C_COEFFICIENTS : array_like, (4, 6)

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

    def __init__(self, x=None, y=None):
        self.__xp = None
        self.__yp = None

        self.__x = None
        self.x = x
        self.__y = None
        self.y = y

        self.__validate_dimensions()

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

        Returns
        -------
        array_like
            self.__x
        """

        return self.__x

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"x" independent variable must have exactly one dimension!')

            assert is_uniform(value), (
                '"x" independent variable is not uniform!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

            value_steps = steps(value)[0]

            xp1 = value[0] - value_steps * 2
            xp2 = value[0] - value_steps
            xp3 = value[-1] + value_steps
            xp4 = value[-1] + value_steps * 2

            self.__xp = np.concatenate(((xp1, xp2), value, (xp3, xp4)))

        self.__x = value

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

        Returns
        -------
        array_like
            self.__y
        """

        return self.__y

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"y" dependent variable must have exactly one dimension!')

            assert len(value) >= 6, (
                '"y" dependent variable values count must be in domain [6:]!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

            yp1 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[0],
                np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
            yp2 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[1],
                np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
            yp3 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[2],
                np.array(value[-6:]).reshape((6, 1)))) / 209)[0]
            yp4 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[3],
                np.array(value[-6:]).reshape((6, 1)))) / 209)[0]

            self.__yp = np.concatenate(((yp1, yp2), value, (yp3, yp4)))

        self.__y = value

    def __call__(self, x):
        """
        Evaluates the interpolating polynomial at given point(s).

        Parameters
        ----------
        x : numeric or array_like
            Point(s) to evaluate the interpolant at.

        Returns
        -------
        numeric or ndarray
            Interpolated value(s).
        """

        try:
            return np.array([self.__evaluate(element) for element in x])
        except TypeError:
            return self.__evaluate(x)

    def __evaluate(self, x):
        """
        Performs the interpolating polynomial evaluation at given point.

        Parameters
        ----------
        x : numeric
            Point to evaluate the interpolant at.

        Returns
        -------
        float
            Interpolated point values.
        """

        self.__validate_dimensions()
        self.__validate_interpolation_range(x)

        if x in self.__x:
            return self.__y[np.where(self.__x == x)][0]

        i = bisect.bisect(self.__xp, x) - 1
        X = (x - self.__xp[i]) / (self.__xp[i + 1] - self.__xp[i])

        r = self.__yp

        a0p = r[i]
        a1p = ((2 * r[i - 2] - 16 * r[i - 1] + 16 * r[i + 1] - 2 *
                r[i + 2]) / 24)
        a2p = ((-r[i - 2] + 16 * r[i - 1] - 30 * r[i] + 16 * r[i + 1] -
                r[i + 2]) / 24)
        a3p = ((-9 * r[i - 2] + 39 * r[i - 1] - 70 * r[i] + 66 *
                r[i + 1] - 33 * r[i + 2] + 7 * r[i + 3]) / 24)
        a4p = ((13 * r[i - 2] - 64 * r[i - 1] + 126 * r[i] - 124 *
                r[i + 1] + 61 * r[i + 2] - 12 * r[i + 3]) / 24)
        a5p = ((-5 * r[i - 2] + 25 * r[i - 1] - 50 * r[i] + 50 *
                r[i + 1] - 25 * r[i + 2] + 5 * r[i + 3]) / 24)

        y = (a0p + a1p * X + a2p * X ** 2 + a3p * X ** 3 + a4p * X ** 4 +
             a5p * X ** 5)

        return y

    def __validate_dimensions(self):
        """
        Validates variables dimensions to be the same.
        """

        if len(self.__x) != len(self.__y):
            raise ValueError(
                ('"x" independent and "y" dependent variables have different '
                 'dimensions: "{0}", "{1}"').format(len(self.__x),
                                                    len(self.__y)))

    def __validate_interpolation_range(self, x):
        """
        Validates given point to be in interpolation range.
        """

        below_interpolation_range = x < self.__x[0]
        above_interpolation_range = x > self.__x[-1]

        if below_interpolation_range.any():
            raise ValueError('"{0}" is below interpolation range.'.format(x))

        if above_interpolation_range.any():
            raise ValueError('"{0}" is above interpolation range.'.format(x))

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

"""
Interpolation
=============

Defines classes for interpolating variables.

-   :class:`LinearInterpolator1d`: 1-D function linear interpolation.
-   :class:`SpragueInterpolator`: 1-D function fifth-order polynomial
    interpolation.
"""

from __future__ import division, unicode_literals

import bisect
import numpy as np

from colour.algebra import steps, is_numeric, is_uniform, to_ndarray
from colour.utilities import is_scipy_installed, warning

__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__ = ['LinearInterpolator1d',
           'SplineInterpolator',
           'SpragueInterpolator']


class LinearInterpolator1d(object):
    """
    Linearly interpolates a 1-D function.

    Parameters
    ----------
    x : ndarray
        Independent :math:`x` variable values corresponding with :math:`y`
        variable.
    y : ndarray
        Dependent and already known :math:`y` variable values to
        interpolate.

    Methods
    -------
    __call__

    Notes
    -----
    This class is a wrapper around *numpy.interp* definition.

    See Also
    --------
    SpragueInterpolator

    Examples
    --------
    Interpolating a single numeric variable:

    >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa
    >>> x = np.arange(len(y))
    >>> f = LinearInterpolator1d(x, y)
    >>> # Doctests ellipsis for Python 2.x compatibility.
    >>> f(0.5)  # doctest: +ELLIPSIS
    7.64...

    Interpolating an *array_like* variable:

    >>> f([0.25, 0.75])
    array([ 6.7825,  8.5075])
    """

    def __init__(self, x=None, y=None):
        self.__x = None
        self.x = x
        self.__y = None
        self.y = y

        self.__validate_dimensions()

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

        Returns
        -------
        array_like
            self.__x
        """

        return self.__x

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"x" independent variable must have exactly one dimension!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

        self.__x = value

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

        Returns
        -------
        array_like
            self.__y
        """

        return self.__y

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"y" dependent variable must have exactly one dimension!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

        self.__y = value

    def __call__(self, x):
        """
        Evaluates the interpolating polynomial at given point(s).


        Parameters
        ----------
        x : numeric or array_like
            Point(s) to evaluate the interpolant at.

        Returns
        -------
        float or ndarray
            Interpolated value(s).
        """

        xi = self.__evaluate(to_ndarray(x))
        if is_numeric(x):
            return float(xi)
        else:
            return xi

    def __evaluate(self, x):
        """
        Performs the interpolating polynomial evaluation at given points.

        Parameters
        ----------
        x : ndarray
            Points to evaluate the interpolant at.

        Returns
        -------
        ndarray
            Interpolated points values.
        """

        self.__validate_dimensions()
        self.__validate_interpolation_range(x)

        return np.interp(x, self.__x, self.__y)

    def __validate_dimensions(self):
        """
        Validates variables dimensions to be the same.
        """

        if len(self.__x) != len(self.__y):
            raise ValueError(
                ('"x" independent and "y" dependent variables have different '
                 'dimensions: "{0}", "{1}"').format(len(self.__x),
                                                    len(self.__y)))

    def __validate_interpolation_range(self, x):
        """
        Validates given point to be in interpolation range.
        """

        below_interpolation_range = x < self.__x[0]
        above_interpolation_range = x > self.__x[-1]

        if below_interpolation_range.any():
            raise ValueError('"{0}" is below interpolation range.'.format(x))

        if above_interpolation_range.any():
            raise ValueError('"{0}" is above interpolation range.'.format(x))


if is_scipy_installed():
    from scipy.interpolate import interp1d

    class SplineInterpolator(interp1d):
        """
        Interpolates a 1-D function using cubic spline interpolation.

        Notes
        -----
        This class is a wrapper around *scipy.interpolate.interp1d* class.
        """

        def __init__(self, *args, **kwargs):
            # TODO: Implements proper wrapper to ensure return values
            # consistency and avoid having to cast to numeric in
            # :meth:`SpectralPowerDistribution.interpolate` method.
            super(SplineInterpolator, self).__init__(
                kind='cubic', *args, **kwargs)
else:
    warning(('"scipy.interpolate.interp1d" interpolator is unavailable, using '
             '"LinearInterpolator1d" instead!'))

    SplineInterpolator = LinearInterpolator1d


class SpragueInterpolator(object):
    """
    Constructs a fifth-order polynomial that passes through :math:`y` dependent
    variable.

    The *Sprague (1880)* method is recommended by the *CIE* for interpolating
    functions having a uniformly spaced independent variable.

    Parameters
    ----------
    x : array_like
        Independent :math:`x` variable values corresponding with :math:`y`
        variable.
    y : array_like
        Dependent and already known :math:`y` variable values to
        interpolate.

    Methods
    -------
    __call__

    See Also
    --------
    LinearInterpolator1d

    Notes
    -----
    The minimum number :math:`k` of data points required along the
    interpolation axis is :math:`k=6`.

    References
    ----------
    .. [1]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data for
            Use in Colour Computations: 9.2.4 Method of interpolation for
            uniformly spaced independent variable
            <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,
            ISBN-13: 978-3-901-90641-1
    .. [2]  **<NAME>, <NAME>, <NAME>**,
            *Computational Colour Science Using MATLAB, 2nd Edition*,
            The Wiley-IS&T Series in Imaging Science and Technology,
            published July 2012, ISBN-13: 978-0-470-66569-5, page  33.

    Examples
    --------
    Interpolating a single numeric variable:

    >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa
    >>> x = np.arange(len(y))
    >>> f = SpragueInterpolator(x, y)
    >>> f(0.5)  # doctest: +ELLIPSIS
    7.2185025...

    Interpolating an *array_like* variable:

    >>> f([0.25, 0.75])  # doctest: +ELLIPSIS
    array([ 6.7295161...,  7.8140625...])
    """

    SPRAGUE_C_COEFFICIENTS = np.array(
        [[884, -1960, 3033, -2648, 1080, -180],
         [508, -540, 488, -367, 144, -24],
         [-24, 144, -367, 488, -540, 508],
         [-180, 1080, -2648, 3033, -1960, 884]])
    """
    Defines the coefficients used to generate extra points for boundaries
    interpolation.

    SPRAGUE_C_COEFFICIENTS : array_like, (4, 6)

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

    def __init__(self, x=None, y=None):
        self.__xp = None
        self.__yp = None

        self.__x = None
        self.x = x
        self.__y = None
        self.y = y

        self.__validate_dimensions()

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

        Returns
        -------
        array_like
            self.__x
        """

        return self.__x

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"x" independent variable must have exactly one dimension!')

            assert is_uniform(value), (
                '"x" independent variable is not uniform!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

            value_steps = steps(value)[0]

            xp1 = value[0] - value_steps * 2
            xp2 = value[0] - value_steps
            xp3 = value[-1] + value_steps
            xp4 = value[-1] + value_steps * 2

            self.__xp = np.concatenate(((xp1, xp2), value, (xp3, xp4)))

        self.__x = value

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

        Returns
        -------
        array_like
            self.__y
        """

        return self.__y

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

        Parameters
        ----------
        value : array_like
            Attribute value.
        """

        if value is not None:
            value = to_ndarray(value)

            assert value.ndim == 1, (
                '"y" dependent variable must have exactly one dimension!')

            assert len(value) >= 6, (
                '"y" dependent variable values count must be in domain [6:]!')

            if not issubclass(value.dtype.type, np.inexact):
                value = value.astype(np.float_)

            yp1 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[0],
                np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
            yp2 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[1],
                np.array(value[0:6]).reshape((6, 1)))) / 209)[0]
            yp3 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[2],
                np.array(value[-6:]).reshape((6, 1)))) / 209)[0]
            yp4 = np.ravel((np.dot(
                self.SPRAGUE_C_COEFFICIENTS[3],
                np.array(value[-6:]).reshape((6, 1)))) / 209)[0]

            self.__yp = np.concatenate(((yp1, yp2), value, (yp3, yp4)))

        self.__y = value

    def __call__(self, x):
        """
        Evaluates the interpolating polynomial at given point(s).

        Parameters
        ----------
        x : numeric or array_like
            Point(s) to evaluate the interpolant at.

        Returns
        -------
        numeric or ndarray
            Interpolated value(s).
        """

        try:
            return np.array([self.__evaluate(element) for element in x])
        except TypeError:
            return self.__evaluate(x)

    def __evaluate(self, x):
        """
        Performs the interpolating polynomial evaluation at given point.

        Parameters
        ----------
        x : numeric
            Point to evaluate the interpolant at.

        Returns
        -------
        float
            Interpolated point values.
        """

        self.__validate_dimensions()
        self.__validate_interpolation_range(x)

        if x in self.__x:
            return self.__y[np.where(self.__x == x)][0]

        i = bisect.bisect(self.__xp, x) - 1
        X = (x - self.__xp[i]) / (self.__xp[i + 1] - self.__xp[i])

        r = self.__yp

        a0p = r[i]
        a1p = ((2 * r[i - 2] - 16 * r[i - 1] + 16 * r[i + 1] - 2 *
                r[i + 2]) / 24)
        a2p = ((-r[i - 2] + 16 * r[i - 1] - 30 * r[i] + 16 * r[i + 1] -
                r[i + 2]) / 24)
        a3p = ((-9 * r[i - 2] + 39 * r[i - 1] - 70 * r[i] + 66 *
                r[i + 1] - 33 * r[i + 2] + 7 * r[i + 3]) / 24)
        a4p = ((13 * r[i - 2] - 64 * r[i - 1] + 126 * r[i] - 124 *
                r[i + 1] + 61 * r[i + 2] - 12 * r[i + 3]) / 24)
        a5p = ((-5 * r[i - 2] + 25 * r[i - 1] - 50 * r[i] + 50 *
                r[i + 1] - 25 * r[i + 2] + 5 * r[i + 3]) / 24)

        y = (a0p + a1p * X + a2p * X ** 2 + a3p * X ** 3 + a4p * X ** 4 +
             a5p * X ** 5)

        return y

    def __validate_dimensions(self):
        """
        Validates variables dimensions to be the same.
        """

        if len(self.__x) != len(self.__y):
            raise ValueError(
                ('"x" independent and "y" dependent variables have different '
                 'dimensions: "{0}", "{1}"').format(len(self.__x),
                                                    len(self.__y)))

    def __validate_interpolation_range(self, x):
        """
        Validates given point to be in interpolation range.
        """

        below_interpolation_range = x < self.__x[0]
        above_interpolation_range = x > self.__x[-1]

        if below_interpolation_range.any():
            raise ValueError('"{0}" is below interpolation range.'.format(x))

        if above_interpolation_range.any():
            raise ValueError('"{0}" is above interpolation range.'.format(x))
#!/usr/bin/env python # -*- coding: utf-8 -*- Interpolation =============  Defines classes for interpolating variables.  -   :class:`LinearInterpolator1d`: 1-D function linear interpolation. -   :class:`SpragueInterpolator`: 1-D function fifth-order polynomial     interpolation. Linearly interpolates a 1-D function.      Parameters     ----------     x : ndarray         Independent :math:`x` variable values corresponding with :math:`y`         variable.     y : ndarray         Dependent and already known :math:`y` variable values to         interpolate.      Methods     -------     __call__      Notes     -----     This class is a wrapper around *numpy.interp* definition.      See Also     --------     SpragueInterpolator      Examples     --------     Interpolating a single numeric variable:      >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa     >>> x = np.arange(len(y))     >>> f = LinearInterpolator1d(x, y)     >>> # Doctests ellipsis for Python 2.x compatibility.     >>> f(0.5)  # doctest: +ELLIPSIS     7.64...      Interpolating an *array_like* variable:      >>> f([0.25, 0.75])     array([ 6.7825,  8.5075]) Property for **self.__x** private attribute.          Returns         -------         array_like             self.__x Setter for **self.__x** private attribute.          Parameters         ----------         value : array_like             Attribute value. Property for **self.__y** private attribute.          Returns         -------         array_like             self.__y Setter for **self.__y** private attribute.          Parameters         ----------         value : array_like             Attribute value. Evaluates the interpolating polynomial at given point(s).           Parameters         ----------         x : numeric or array_like             Point(s) to evaluate the interpolant at.          Returns         -------         float or ndarray             Interpolated value(s). Performs the interpolating polynomial evaluation at given points.          Parameters         ----------         x : ndarray             Points to evaluate the interpolant at.          Returns         -------         ndarray             Interpolated points values. Validates variables dimensions to be the same. Validates given point to be in interpolation range. Interpolates a 1-D function using cubic spline interpolation.          Notes         -----         This class is a wrapper around *scipy.interpolate.interp1d* class. # TODO: Implements proper wrapper to ensure return values # consistency and avoid having to cast to numeric in # :meth:`SpectralPowerDistribution.interpolate` method. Constructs a fifth-order polynomial that passes through :math:`y` dependent     variable.      The *Sprague (1880)* method is recommended by the *CIE* for interpolating     functions having a uniformly spaced independent variable.      Parameters     ----------     x : array_like         Independent :math:`x` variable values corresponding with :math:`y`         variable.     y : array_like         Dependent and already known :math:`y` variable values to         interpolate.      Methods     -------     __call__      See Also     --------     LinearInterpolator1d      Notes     -----     The minimum number :math:`k` of data points required along the     interpolation axis is :math:`k=6`.      References     ----------     .. [1]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data for             Use in Colour Computations: 9.2.4 Method of interpolation for             uniformly spaced independent variable             <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,             ISBN-13: 978-3-901-90641-1     .. [2]  **<NAME>, <NAME>, <NAME>**,             *Computational Colour Science Using MATLAB, 2nd Edition*,             The Wiley-IS&T Series in Imaging Science and Technology,             published July 2012, ISBN-13: 978-0-470-66569-5, page  33.      Examples     --------     Interpolating a single numeric variable:      >>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  # noqa     >>> x = np.arange(len(y))     >>> f = SpragueInterpolator(x, y)     >>> f(0.5)  # doctest: +ELLIPSIS     7.2185025...      Interpolating an *array_like* variable:      >>> f([0.25, 0.75])  # doctest: +ELLIPSIS     array([ 6.7295161...,  7.8140625...]) Defines the coefficients used to generate extra points for boundaries     interpolation.      SPRAGUE_C_COEFFICIENTS : array_like, (4, 6)      References     ----------     .. [3]  `CIE 167:2005 Recommended Practice for Tabulating Spectral Data for Use in Colour Computations: Table V <http://div1.cie.co.at/?i_ca_id=551&pubid=47>`_,  # noqa             ISBN-13: 978-3-901-90641-1 Property for **self.__x** private attribute.          Returns         -------         array_like             self.__x Setter for **self.__x** private attribute.          Parameters         ----------         value : array_like             Attribute value. Property for **self.__y** private attribute.          Returns         -------         array_like             self.__y Setter for **self.__y** private attribute.          Parameters         ----------         value : array_like             Attribute value. Evaluates the interpolating polynomial at given point(s).          Parameters         ----------         x : numeric or array_like             Point(s) to evaluate the interpolant at.          Returns         -------         numeric or ndarray             Interpolated value(s). Performs the interpolating polynomial evaluation at given point.          Parameters         ----------         x : numeric             Point to evaluate the interpolant at.          Returns         -------         float             Interpolated point values. Validates variables dimensions to be the same. Validates given point to be in interpolation range.