pylops.LinearRegression¶
-
pylops.
LinearRegression
(taxis, dtype='float64')[source]¶ Linear regression.
Creates an operator that applies linear regression to a set of points. Values along the 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 in adjoint mode.
Parameters: - taxis :
numpy.ndarray
Elements along the t-axis.
- dtype :
str
, optional Type of elements in input array.
Raises: - TypeError
If
t
is notnumpy.ndarray
.
See also
Regression
- Polynomial regression
Notes
The LinearRegression operator solves the following problem:
\[y_i = x_0 + x_1 t_i \qquad \forall i=1,2,...,N\]We can express this problem in a matrix form
\[\mathbf{y}= \mathbf{A} \mathbf{x}\]where
\[\mathbf{y}= [y_1, y_2,...,y_N]^T, \qquad \mathbf{x}= [x_0, x_1]^T\]and
\[\begin{split}\mathbf{A} = \begin{bmatrix} 1 & t_{1} \\ 1 & t_{2} \\ .. & .. \\ 1 & t_{N} \end{bmatrix}\end{split}\]Note that this is a particular case of the
pylops.Regression
operator and it is in fact just a lazy call of that operator withorder=1
.Attributes: - taxis :