# Source code for pylops.basicoperators.LinearRegression

import logging

from pylops.basicoperators import Regression

logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)

[docs]def LinearRegression(taxis, dtype="float64"):
r"""Linear regression.

Creates an operator that applies linear regression to a set of points.
Values along the :math:t-axis  must be provided while initializing the operator.
Intercept and gradient form the model vector to be provided in forward
mode, while the values of the regression line curve shall be provided

Parameters
----------
taxis : :obj:numpy.ndarray
Elements along the :math:t-axis.
dtype : :obj:str, optional
Type of elements in input array.

Attributes
----------
shape : :obj:tuple
Operator shape
explicit : :obj:bool
Operator contains a matrix that can be solved explicitly
(True) or not (False)

Raises
------
TypeError
If taxis is not :obj:numpy.ndarray.

--------
Regression: Polynomial regression

Notes
-----
The LinearRegression operator solves the following problem:

.. math::
y_i = x_0 + x_1 t_i  \qquad \forall i=0,1,\ldots,N-1

We can express this problem in a matrix form

.. math::
\mathbf{y}=  \mathbf{A} \mathbf{x}

where

.. math::
\mathbf{y}= [y_0, y_1,\ldots,y_{N-1}]^T, \qquad \mathbf{x}= [x_0, x_1]^T

and

.. math::
\mathbf{A}
= \begin{bmatrix}
1       & t_{0}  \\
1       & t_{1}  \\
\vdots      & \vdots     \\
1       & t_{N-1}
\end{bmatrix}

Note that this is a particular case of the :py:class:pylops.Regression
operator and it is in fact just a lazy call of that operator with
order=1.
"""
return Regression(taxis, order=1, dtype=dtype)