__all__ = ["Zero"]
import numpy as np
from pylops import LinearOperator
from pylops.utils.backend import get_array_module
from pylops.utils.typing import DTypeLike, InputDimsLike, 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` or :obj:`tuple`
Number of samples in data (and model, if ``M`` is not provided).
If a tuple is provided, this is interpreted as the data (and model)
are nd-arrays.
M : :obj:`int` or :obj:`tuple`, optional
Number of samples in model. If a tuple is provided, this is interpreted
as the model is an nd-array. Note that when `M` is a tuple, `N` must be
also a tuple with the same number of elements.
forceflat : :obj:`bool`, optional
.. versionadded:: 2.2.0
Force an array to be flattened after matvec and rmatvec. Note that this is only
required when `N` and `M` are tuples (input and output arrays are nd-arrays).
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
----------
dims : :obj:`tuple`
Shape of the array after the adjoint, but before flattening.
For example, ``x_reshaped = (Op.H * y.ravel()).reshape(Op.dims)``.
dimsd : :obj:`tuple`
Shape of the array after the forward, but before flattening.
For example, ``y_reshaped = (Op * x.ravel()).reshape(Op.dimsd)``.
shape : :obj:`tuple`
Operator shape.
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 | InputDimsLike,
M: int | InputDimsLike | None = None,
forceflat: bool | None = None,
dtype: DTypeLike = "float64",
name: str = "Z",
) -> None:
M = N if M is None else M
if isinstance(N, int) and isinstance(M, int):
# N and M are scalars (1d-arrays)
dims, dimsd = (M,), (N,)
elif isinstance(N, (tuple, list)) and isinstance(M, (tuple, list)):
# N and M are tuples (nd-arrays)
dims, dimsd = M, N
else:
msg = (
"N and M must have same type and equal to "
"int, tuple, or list, instead their types"
f" are type(N)={type(N)} and type(M)={type(M)}"
)
raise NotImplementedError(msg)
super().__init__(
dtype=np.dtype(dtype),
dims=dims,
dimsd=dimsd,
forceflat=forceflat,
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)
PyLops