pylops.Restriction#

class pylops.Restriction(dims, iava, axis=-1, inplace=True, forceflat=None, dtype='float64', name='R')[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

dimslist or int: Number of samples for each dimension
iavalist or numpy.ndarray: Integer indices of available samples for data selection.
axisint, optional: New in version 2.0.0.

Axis along which restriction is applied to 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).
forceflatbool, optional: New in version 2.2.0.

Force an array to be flattened after rmatvec. Note that this is only required when len(dims)=2, otherwise pylops will detect whether to return a 1d or nd array.
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)

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 indices 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

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening.

For example, y_reshaped = (Op * x.ravel()).reshape(Op.dimsd).

iavamasknumpy.ndarray

Mask of indices used in adjoint mode when iava is a CuPy array.

iavareshapenumpy.ndarray

Shape used to reshape iava to be compatible with dims.

shapetuple

Operator shape.

Methods

`__init__`(dims, iava[, axis, inplace, ...])
`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.
`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`()