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
taxisnumpy.ndarray

Elements along the \(t\)-axis.

dtypestr, optional

Type of elements in input array.

Raises
TypeError

If taxis is not numpy.ndarray.

See also

Regression

Polynomial regression

Notes

The LinearRegression operator solves the following problem:

\[y_i = x_0 + x_1 t_i \qquad \forall i=0,1,\ldots,N-1\]

We can express this problem in a matrix form

\[\mathbf{y}= \mathbf{A} \mathbf{x}\]

where

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

and

\[\begin{split}\mathbf{A} = \begin{bmatrix} 1 & t_{0} \\ 1 & t_{1} \\ \vdots & \vdots \\ 1 & t_{N-1} \end{bmatrix}\end{split}\]

Note that this is a particular case of the pylops.Regression operator and it is in fact just a lazy call of that operator with order=1.

Attributes
shapetuple

Operator shape

explicitbool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Examples using pylops.LinearRegression#

Linear Regression

Linear Regression

Linear Regression