# Source code for colour.algebra.regression

```"""
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 annotations

import numpy as np

from colour.hints import ArrayLike, NDArrayFloat

__author__ = "Colour Developers"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"

__all__ = [
"least_square_mapping_MoorePenrose",
]

[docs]
def least_square_mapping_MoorePenrose(
y: ArrayLike, x: ArrayLike
) -> NDArrayFloat:
"""
Compute the *least-squares* mapping from dependent variable :math:`y` to
independent variable :math:`x` using *Moore-Penrose* inverse.

Parameters
----------
y
Dependent and already known :math:`y` variable.
x
Independent :math:`x` variable(s) values corresponding with :math:`y`
variable.

Returns
-------
:class:`numpy.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)))

```