# -*- coding: utf-8 -*-
"""
Regression
==========
Defines various objects to perform regression:
- :func:`colour.algebra.least_square_mapping_MoorePenrose`: *Least-squares*
mapping using *Moore-Penrose* inverse.
References
----------
- :cite:`Finlayson2015` : Finlayson, G. D., MacKiewicz, M., & Hurlbert, A.
(2015). Color Correction Using Root-Polynomial Regression. IEEE
Transactions on Image Processing, 24(5), 1460-1470.
doi:10.1109/TIP.2015.2405336
"""
from __future__ import division, unicode_literals
import numpy as np
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - Colour Developers'
__license__ = 'New BSD License - https://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-developers@colour-science.org'
__status__ = 'Production'
__all__ = ['least_square_mapping_MoorePenrose']
[docs]def least_square_mapping_MoorePenrose(y, x):
"""
Computes the *least-squares* mapping from dependent variable :math:`y` to
independent variable :math:`x` using *Moore-Penrose* inverse.
Parameters
----------
y : array_like
Dependent and already known :math:`y` variable.
x : array_like, optional
Independent :math:`x` variable(s) values corresponding with :math:`y`
variable.
Returns
-------
ndarray
*Least-squares* mapping.
References
----------
:cite:`Finlayson2015`
Examples
--------
>>> prng = np.random.RandomState(2)
>>> y = prng.random_sample((24, 3))
>>> x = y + (prng.random_sample((24, 3)) - 0.5) * 0.5
>>> least_square_mapping_MoorePenrose(y, x) # doctest: +ELLIPSIS
array([[ 1.0526376..., 0.1378078..., -0.2276339...],
[ 0.0739584..., 1.0293994..., -0.1060115...],
[ 0.0572550..., -0.2052633..., 1.1015194...]])
"""
y = np.atleast_2d(y)
x = np.atleast_2d(x)
return np.dot(np.transpose(x), np.linalg.pinv(np.transpose(y)))