Colour 0.3
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Extrapolation
=============
Defines classes for extrapolating variables:
- :class:`Extrapolator1d`: 1-D function extrapolation.
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import is_numeric, as_array
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['Extrapolator1d']
[docs]class Extrapolator1d(object):
"""
Extrapolates the 1-D function of given interpolator.
The Extrapolator1d acts as a wrapper around a given *Colour* or *scipy*
interpolator class instance with compatible signature. Two extrapolation
methods are available:
- *Linear*: Linearly extrapolates given points using the slope defined by
the interpolator boundaries (xi[0], xi[1]) if x < xi[0] and
(xi[-1], xi[-2]) if x > xi[-1].
- *Constant*: Extrapolates given points by assigning the interpolator
boundaries values xi[0] if x < xi[0] and xi[-1] if x > xi[-1].
Specifying the *left* and *right* arguments takes precedence on the chosen
extrapolation method and will assign the respective *left* and *right*
values to the given points.
Parameters
----------
interpolator : object
Interpolator object.
method : unicode, optional
{'Linear', 'Constant'},
Extrapolation method.
left : numeric, optional
Value to return for x < xi[0].
right : numeric, optional
Value to return for x > xi[-1].
Methods
-------
__class__
Notes
-----
The interpolator must define *x* and *y* attributes.
References
----------
.. [1] sastanin. (n.d.). How to make scipy.interpolate give an
extrapolated result beyond the input range? Retrieved August 08,
2014, from http://stackoverflow.com/a/2745496/931625
Examples
--------
Extrapolating a single numeric variable:
>>> from colour.algebra import LinearInterpolator1d
>>> x = np.array([3, 4, 5])
>>> y = np.array([1, 2, 3])
>>> interpolator = LinearInterpolator1d(x, y)
>>> extrapolator = Extrapolator1d(interpolator)
>>> extrapolator(1)
-1.0
Extrapolating an *array_like* variable:
>>> extrapolator(np.array([6, 7 , 8]))
array([ 4., 5., 6.])
Using the *Constant* extrapolation method:
>>> x = np.array([3, 4, 5])
>>> y = np.array([1, 2, 3])
>>> interpolator = LinearInterpolator1d(x, y)
>>> extrapolator = Extrapolator1d(interpolator, method='Constant')
>>> extrapolator(np.array([0.1, 0.2, 8, 9]))
array([ 1., 1., 3., 3.])
Using defined *left* boundary and *Constant* extrapolation method:
>>> x = np.array([3, 4, 5])
>>> y = np.array([1, 2, 3])
>>> interpolator = LinearInterpolator1d(x, y)
>>> extrapolator = Extrapolator1d(interpolator, method='Constant', left=0)
>>> extrapolator(np.array([0.1, 0.2, 8, 9]))
array([ 0., 0., 3., 3.])
"""
def __init__(self,
interpolator=None,
method='Linear',
left=None,
right=None):
self.__interpolator = None
self.interpolator = interpolator
self.__method = None
self.method = method
self.__right = None
self.right = right
self.__left = None
self.left = left
@property
def interpolator(self):
"""
Property for **self.__interpolator** private attribute.
Returns
-------
object
self.__interpolator
"""
return self.__interpolator
@interpolator.setter
[docs] def interpolator(self, value):
"""
Setter for **self.__interpolator** private attribute.
Parameters
----------
value : object
Attribute value.
"""
if value is not None:
assert hasattr(value, 'x'), (
'"{0}" interpolator has no "x" attribute!'.format(value))
assert hasattr(value, 'y'), (
'"{0}" interpolator has no "y" attribute!'.format(value))
self.__interpolator = value
@property
def method(self):
"""
Property for **self.__method** private attribute.
Returns
-------
unicode
self.__method
"""
return self.__method
@method.setter
[docs] def method(self, value):
"""
Setter for **self.__method** private attribute.
Parameters
----------
value : unicode
Attribute value.
"""
if value is not None:
assert type(value) in (str, unicode), (
('"{0}" attribute: "{1}" type is not '
'"str" or "unicode"!').format('method', value))
value = value.lower()
self.__method = value
@property
def left(self):
"""
Property for **self.__left** private attribute.
Returns
-------
numeric
self.__left
"""
return self.__left
@left.setter
[docs] def left(self, value):
"""
Setter for **self.__left** private attribute.
Parameters
----------
value : numeric
Attribute value.
"""
if value is not None:
assert is_numeric(value), (
'"{0}" attribute: "{1}" type is not "numeric"!').format(
'left', value)
self.__left = value
@property
def right(self):
"""
Property for **self.__right** private attribute.
Returns
-------
numeric
self.__right
"""
return self.__right
@right.setter
[docs] def right(self, value):
"""
Setter for **self.__right** private attribute.
Parameters
----------
value : numeric
Attribute value.
"""
if value is not None:
assert is_numeric(value), (
'"{0}" attribute: "{1}" type is not "numeric"!').format(
'right', value)
self.__right = value
[docs] def __call__(self, x):
"""
Evaluates the Extrapolator1d at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the Extrapolator1d at.
Returns
-------
float or ndarray
Extrapolated points value(s).
"""
xe = self.__evaluate(as_array(x))
if is_numeric(x):
return float(xe)
else:
return xe
def __evaluate(self, x):
"""
Performs the extrapolating evaluation at given points.
Parameters
----------
x : ndarray
Points to evaluate the Extrapolator1d at.
Returns
-------
ndarray
Extrapolated points values.
"""
xi = self.__interpolator.x
yi = self.__interpolator.y
y = np.empty_like(x)
if self.__method == 'linear':
y[x < xi[0]] = (yi[0] + (x[x < xi[0]] - xi[0]) *
(yi[1] - yi[0]) / (xi[1] - xi[0]))
y[x > xi[-1]] = (yi[-1] + (x[x > xi[-1]] - xi[-1]) *
(yi[-1] - yi[-2]) / (xi[-1] - xi[-2]))
elif self.__method == 'constant':
y[x < xi[0]] = yi[0]
y[x > xi[-1]] = yi[-1]
if self.__left is not None:
y[x < xi[0]] = self.__left
if self.__right is not None:
y[x > xi[-1]] = self.__right
in_range = np.logical_and(x >= xi[0], x <= xi[-1])
y[in_range] = self.__interpolator(x[in_range])
return y