# Source code for colour.algebra.interpolation

#!/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'
__maintainer__ = 'Colour Developers'
__status__ = 'Production'

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

[docs]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.

--------
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
[docs]    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
[docs]    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

[docs]    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

[docs]    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 '

SplineInterpolator = LinearInterpolator1d

[docs]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__

--------
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]  **Stephen Westland, Caterina Ripamonti, Vien Cheung**,
*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
[docs]    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
[docs]    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

[docs]    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))