pylops.Restriction¶

class pylops.Restriction(M, iava, dims=None, dir=0, dtype='float64', inplace=True)[source]¶

Restriction (or sampling) operator.

Extract subset of values from input vector at locations iava in forward mode and place those values at locations iava in an otherwise zero vector in adjoint mode.

Parameters:

M : int: Number of samples in model.
iava : list or numpy.ndarray: Integer indices of available samples for data selection.
dims : list: Number of samples for each dimension (None if only one dimension is available)
dir : int, optional: Direction along which restriction is applied.
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).

See also

pylops.signalprocessing.Interp: Interpolation operator

Notes

Extraction (or sampling) of a subset of \(N\) values at locations iava from an input (or model) vector \(\mathbf{x}\) of size \(M\) can be expressed as:

\[y_i = x_{l_i} \quad \forall i=0,1,\ldots,N-1\]

where \(\mathbf{l}=[l_0, l_1,\ldots, l_{N-1}]\) is a vector containing the indeces of the original array at which samples are taken.

Conversely, in adjoint mode the available values in the data vector \(\mathbf{y}\) are placed at locations \(\mathbf{l}=[l_0, l_1,\ldots, l_{M-1}]\) in the model vector:

\[x_{l_i} = y_i \quad \forall i=0,1,\ldots,N-1\]

and \(x_{j}=0\) for \(j \neq l_i\) (i.e., at all other locations in input vector).

Attributes:	shape : `tuple` Operator shape explicit : `bool` Operator contains a matrix that can be solved explicitly (`True`) or not (`False`)

Methods

`__init__`(M, iava[, dims, dir, dtype, inplace])	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.
`mask`(x)	Apply mask to input signal returning a signal of same size with values at `iava` locations and `0` at other locations
`matmat`(X)	Matrix-matrix multiplication.
`matvec`(x)	Matrix-vector multiplication.
`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.