__all__ = ["Zero"]
from typing import Optional
import numpy as np
from pylops import LinearOperator
from pylops.utils.backend import get_array_module
from pylops.utils.typing import DTypeLike, NDArray
[docs]class Zero(LinearOperator):
r"""Zero operator.
Transform model into array of zeros of size :math:`N` in forward
and transform data into array of zeros of size :math:`N` in adjoint.
Parameters
----------
N : :obj:`int`
Number of samples in data (and model in M is not provided).
M : :obj:`int`, optional
Number of samples in model.
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
-----
An *Zero* operator simply creates a null data vector :math:`\mathbf{y}` in
forward mode:
.. math::
\mathbf{0} \mathbf{x} = \mathbf{0}_N
and a null model vector :math:`\mathbf{x}` in forward mode:
.. math::
\mathbf{0} \mathbf{y} = \mathbf{0}_M
"""
def __init__(
self,
N: int,
M: Optional[int] = None,
dtype: DTypeLike = "float64",
name: str = "Z",
) -> None:
M = N if M is None else M
super().__init__(dtype=np.dtype(dtype), shape=(N, M), name=name)
def _matvec(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
return ncp.zeros(self.shape[0], dtype=self.dtype)
def _rmatvec(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
return ncp.zeros(self.shape[1], dtype=self.dtype)