pylops.Regression¶
-
class
pylops.
Regression
(taxis, order, dtype='float64')[source]¶ Polynomial regression.
Creates an operator that applies polynomial regression to a set of points. Values along the t-axis must be provided while initializing the operator. The coefficients of the polynomial regression form the model vector to be provided in forward mode, while the values of the regression curve shall be provided in adjoint mode.
Parameters: - taxis :
numpy.ndarray
Elements along the t-axis.
- order :
int
Order of the regressed polynomial.
- dtype :
str
, optional Type of elements in input array.
Raises: - TypeError
If
t
is notnumpy.ndarray
.
See also
LinearRegression
- Linear regression
Notes
The Regression operator solves the following problem:
\[y_i = \sum_{n=0}^{order} x_n t_i^n \qquad \forall i=1,2,...,N\]where \(N\) represents the order of the chosen polynomial. We can express this problem in a matrix form
\[\mathbf{y}= \mathbf{A} \mathbf{x}\]where
\[\mathbf{y}= [y_1, y_2,...,y_N]^T, \qquad \mathbf{x}= [x_0, x_1,...,x_{order}]^T\]and
\[\begin{split}\mathbf{A} = \begin{bmatrix} 1 & t_{1} & t_{1}^2 & .. & t_{1}^{order} \\ 1 & t_{2} & t_{2}^2 & .. & t_{1}^{order} \\ .. & .. & .. & .. & .. \\ 1 & t_{N} & t_{N}^2 & .. & t_{N}^{order} \\ \end{bmatrix}\end{split}\]Attributes: Methods
__init__
(taxis, order[, dtype])Initialize this LinearOperator. adjoint
()Hermitian adjoint. apply
(t, x)Return values along y-axis given certain t
location(s) along t-axis and regression coefficientsx
apply_columns
(cols)Apply subset of columns of operator cond
([uselobpcg])Condition number of linear operator. conj
()Complex conjugate operator div
(y[, niter])Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\). dot
(x)Matrix-matrix or matrix-vector multiplication. eigs
([neigs, symmetric, niter, uselobpcg])Most significant eigenvalues of linear operator. matmat
(X)Matrix-matrix multiplication. matvec
(x)Matrix-vector multiplication. rmatmat
(X)Adjoint matrix-matrix multiplication. rmatvec
(x)Adjoint matrix-vector multiplication. todense
()Return dense matrix. tosparse
()Return sparse matrix. transpose
()Transpose this linear operator. -
apply
(t, x)[source]¶ Return values along y-axis given certain
t
location(s) along t-axis and regression coefficientsx
Parameters: - taxis :
numpy.ndarray
Elements along the t-axis.
- x :
numpy.ndarray
Regression coefficients
- dtype :
str
, optional - Returns
- ———-
- y :
numpy.ndarray
Values along y-axis
- taxis :
- taxis :