Source code for pylops.basicoperators.symmetrize

__all__ = ["Symmetrize"]

from typing import Union

import numpy as np

from pylops import LinearOperator
from pylops.utils._internal import _value_or_sized_to_tuple
from pylops.utils.backend import get_array_module
from pylops.utils.decorators import reshaped
from pylops.utils.typing import DTypeLike, InputDimsLike, NDArray

[docs]class Symmetrize(LinearOperator): r"""Symmetrize along an axis. Symmetrize a multi-dimensional array along ``axis``. Parameters ---------- dims : :obj:`list` or :obj:`int` Number of samples for each dimension (``None`` if only one dimension is available) axis : :obj:`int`, optional .. versionadded:: 2.0.0 Axis along which model is symmetrized. dtype : :obj:`str`, optional Type of elements in input array name : :obj:`str`, optional .. versionadded:: 2.0.0 Name of operator (to be used by :func:`pylops.utils.describe.describe`) Attributes ---------- shape : :obj:`tuple` Operator shape explicit : :obj:`bool` Operator contains a matrix that can be solved explicitly (``True``) or not (``False``) Notes ----- The Symmetrize operator constructs a symmetric array given an input model in forward mode, by pre-pending the input model in reversed order. For simplicity, given a one dimensional array, the forward operation can be expressed as: .. math:: y[i] = \begin{cases} x[i-N+1],& i\geq N\\ x[N-1-i],& \text{otherwise} \end{cases} for :math:`i=0,1,2,\ldots,2N-2`, where :math:`N` is the dimension of the input model. In adjoint mode, the Symmetrize operator assigns the sums of the elements in position :math:`N-1-i` and :math:`N-1+i` to position :math:`i` as follows: .. math:: \begin{multline} x[i] = y[N-1-i]+y[N-1+i] \quad \forall i=0,2,\ldots,N-1 \end{multline} apart from the central sample where :math:`x[0] = y[N-1]`. """ def __init__( self, dims: Union[int, InputDimsLike], axis: int = -1, dtype: DTypeLike = "float64", name: str = "S", ) -> None: dims = _value_or_sized_to_tuple(dims) self.axis = axis self.nsym = dims[self.axis] dimsd = list(dims) dimsd[self.axis] = 2 * dims[self.axis] - 1 super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dimsd, name=name) @reshaped(swapaxis=True) def _matvec(self, x: NDArray) -> NDArray: ncp = get_array_module(x) y = ncp.zeros(self.dimsd, dtype=self.dtype) y = y.swapaxes(self.axis, -1) y[..., self.nsym - 1 :] = x y[..., : self.nsym - 1] = x[..., -1:0:-1] return y @reshaped(swapaxis=True) def _rmatvec(self, x: NDArray) -> NDArray: y = x[..., self.nsym - 1 :].copy() y[..., 1:] += x[..., self.nsym - 2 :: -1] return y