pylops.LinearRegression#
- class pylops.LinearRegression(taxis, dtype='float64', name='L')[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.
- taxis
- Raises
- TypeError
If
taxis
is notnumpy.ndarray
.
See also
Regression
Polynomial regression
Notes
The LinearRegression operator solves the following problem:
\[y_i = x_0 + x_1 t_i \qquad \forall i=0,1,\ldots,N-1\]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 withorder=1
.- Attributes
- shape
tuple
Operator shape
- explicit
bool
Operator contains a matrix that can be solved explicitly (
True
) or not (False
)
- shape
Methods
__init__
(taxis[, dtype, name])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, densesolver])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.
reset_count
()Reset counters
rmatmat
(X)Matrix-matrix multiplication.
rmatvec
(x)Adjoint matrix-vector multiplication.
todense
([backend])Return dense matrix.
toimag
([forw, adj])Imag operator
toreal
([forw, adj])Real operator
tosparse
()Return sparse matrix.
trace
([neval, method, backend])Trace of linear operator.
transpose
()