colour.algebra.extrapolation Module¶

Extrapolation¶

Defines classes for extrapolating variables:

• Extrapolator1d: 1-D function extrapolation.

class colour.algebra.extrapolation.Extrapolator1d(interpolator=None, method=u'Linear', left=None, right=None)[source]¶

Bases: 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].

__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.])

__call__(x)[source]¶

Evaluates the Extrapolator1d at given point(s).

Parameters:	x (numeric or array_like) – Point(s) to evaluate the Extrapolator1d at.
Returns:	Extrapolated points value(s).
Return type:	float or ndarray

interpolator[source]¶

Property for self.__interpolator private attribute.

Returns:	self.__interpolator
Return type:	object

left[source]¶

Property for self.__left private attribute.

Returns:	self.__left
Return type:	numeric

method[source]¶

Property for self.__method private attribute.

Returns:	self.__method
Return type:	unicode

right[source]¶

Property for self.__right private attribute.

Returns:	self.__right
Return type:	numeric