pylops.Identity#

class pylops.Identity(*args, **kwargs)[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
Nint

Number of samples in data (and model, if M is not provided).

Mint, optional

Number of samples in model.

inplacebool, 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).

dtypestr, optional

Type of elements in input array.

namestr, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

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:

\[y_i = x_i \quad \forall i=1,2,\ldots,N\]

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

\[y_i = x_i \quad \forall i=1,2,\ldots,N\]

and all the elements of the data \(\mathbf{y}\) into the first \(M\) elements of model in adjoint mode (other elements are O):

\[ \begin{align}\begin{aligned}x_i = y_i \quad \forall i=1,2,\ldots,M\\x_i = 0 \quad \forall i=M+1,\ldots,N\end{aligned}\end{align} \]
Attributes
shapetuple

Operator shape

explicitbool

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

Methods

__init__(N[, M, inplace, dtype, name])

Initialize this LinearOperator.

adjoint()

Hermitian adjoint.

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()

Transpose this linear operator.

Examples using pylops.Identity#

Identity

Identity

Identity
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Operators concatenation

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04. Bayesian Inversion

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