Source code for colour.algebra.regression

# -*- 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
"""

import numpy as np

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2021 - 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)))