pylops.Identity¶
-
class
pylops.
Identity
(N, M=None, dtype='float64', inplace=True)[source]¶ Identity operator.
Simply move model to data in forward model and viceversa in adjoint mode if \(M = N\). If \(M > N\) removes last \(M - N\) elements from model in forward and pads with \(0\) in adjoint. If \(N > M\) removes last \(N - M\) elements from data in adjoint and pads with \(0\) in forward.
Parameters: - N :
int
Number of samples in data (and model, if
M
is not provided).- M :
int
, optional Number of samples in model.
- dtype :
str
, optional Type of elements in input array.
- inplace :
bool
, optional Work inplace (
True
) or make a new copy (False
). By default, data is a reference to the model (in forward) and model is a reference to the data (in adjoint).
Notes
For \(M = N\), an Identity operator simply moves the model \(\mathbf{x}\) to the data \(\mathbf{y}\) in forward mode and viceversa in adjoint mode:
\[y_i = x_i \quad \forall i=1,2,...,N\]or in matrix form:
\[\mathbf{y} = \mathbf{I} \mathbf{x} = \mathbf{x}\]and
\[\mathbf{x} = \mathbf{I} \mathbf{y} = \mathbf{y}\]For \(M > N\), the Identity operator takes the first \(M\) elements of the model \(\mathbf{x}\) into the data \(\mathbf{y}\) in forward mode
\[y_i = x_i \quad \forall i=1,2,...,N\]and all the elements of the data \(\mathbf{y}\) into the first \(M\) elements of model in adjoint mode (other elements are
O
):\[ \begin{align}\begin{aligned}x_i = y_i \quad \forall i=1,2,...,M\\x_i = 0 \quad \forall i=M+1,...,N\end{aligned}\end{align} \]Attributes: Methods
__init__
(self, N[, M, dtype, inplace])Initialize this LinearOperator. adjoint
(self)Hermitian adjoint. cond
(self, \*\*kwargs_eig)Condition number of linear operator. conj
(self)Complex conjugate operator div
(self, y[, niter])Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\). dot
(self, x)Matrix-matrix or matrix-vector multiplication. eigs
(self[, neigs, symmetric, niter])Most significant eigenvalues of linear operator. matmat
(self, X)Matrix-matrix multiplication. matvec
(self, x)Matrix-vector multiplication. rmatvec
(self, x)Adjoint matrix-vector multiplication. transpose
(self)Transpose this linear operator. - N :