__all__ = ["Block"]
import multiprocessing as mp
from typing import Iterable, Optional
from pylops import LinearOperator
from pylops.basicoperators import HStack, VStack
from pylops.utils.typing import DTypeLike, NDArray
class _Block(LinearOperator):
"""Block operator.
Used to be able to provide operators from different libraries to
Block.
"""
def __init__(
self,
ops: Iterable[Iterable[LinearOperator]],
forceflat: bool = None,
dtype: Optional[DTypeLike] = None,
_HStack=HStack,
_VStack=VStack,
args_HStack: Optional[dict] = None,
args_VStack: Optional[dict] = None,
name: str = "B",
):
if args_HStack is None:
self.args_HStack = {}
else:
self.args_HStack = args_HStack
if args_VStack is None:
self.args_VStack = {}
else:
self.args_VStack = args_VStack
hblocks = [_HStack(hblock, dtype=dtype, **self.args_HStack) for hblock in ops]
super().__init__(
Op=_VStack(
ops=hblocks, forceflat=forceflat, dtype=dtype, **self.args_VStack
),
name=name,
)
def _matvec(self, x: NDArray) -> NDArray:
return super()._matvec(x)
def _rmatvec(self, x: NDArray) -> NDArray:
return super()._rmatvec(x)
[docs]class Block(_Block):
r"""Block operator.
Create a block operator from N lists of M linear operators each.
Parameters
----------
ops : :obj:`list`
List of lists of operators to be combined in block fashion.
Alternatively, :obj:`numpy.ndarray` or :obj:`scipy.sparse` matrices
can be passed in place of one or more operators.
nproc : :obj:`int`, optional
Number of processes used to evaluate the N operators in parallel using
``multiprocessing``. If ``nproc=1``, work in serial mode.
forceflat : :obj:`bool`, optional
.. versionadded:: 2.2.0
Force an array to be flattened after rmatvec.
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
Notes
-----
In mathematics, a block or a partitioned matrix is a matrix that is
interpreted as being broken into sections called blocks or submatrices.
Similarly a block operator is composed of N sets of M linear operators
each such that its application in forward mode leads to
.. math::
\begin{bmatrix}
\mathbf{L}_{1,1} & \mathbf{L}_{1,2} & \ldots & \mathbf{L}_{1,M} \\
\mathbf{L}_{2,1} & \mathbf{L}_{2,2} & \ldots & \mathbf{L}_{2,M} \\
\vdots & \vdots & \ddots & \vdots \\
\mathbf{L}_{N,1} & \mathbf{L}_{N,2} & \ldots & \mathbf{L}_{N,M}
\end{bmatrix}
\begin{bmatrix}
\mathbf{x}_{1} \\
\mathbf{x}_{2} \\
\vdots \\
\mathbf{x}_{M}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L}_{1,1} \mathbf{x}_{1} + \mathbf{L}_{1,2} \mathbf{x}_{2} +
\mathbf{L}_{1,M} \mathbf{x}_{M} \\
\mathbf{L}_{2,1} \mathbf{x}_{1} + \mathbf{L}_{2,2} \mathbf{x}_{2} +
\mathbf{L}_{2,M} \mathbf{x}_{M} \\
\vdots \\
\mathbf{L}_{N,1} \mathbf{x}_{1} + \mathbf{L}_{N,2} \mathbf{x}_{2} +
\mathbf{L}_{N,M} \mathbf{x}_{M}
\end{bmatrix}
while its application in adjoint mode leads to
.. math::
\begin{bmatrix}
\mathbf{L}_{1,1}^H & \mathbf{L}_{2,1}^H & \ldots & \mathbf{L}_{N,1}^H \\
\mathbf{L}_{1,2}^H & \mathbf{L}_{2,2}^H & \ldots & \mathbf{L}_{N,2}^H \\
\vdots & \vdots & \ddots & \vdots \\
\mathbf{L}_{1,M}^H & \mathbf{L}_{2,M}^H & \ldots & \mathbf{L}_{N,M}^H
\end{bmatrix}
\begin{bmatrix}
\mathbf{y}_{1} \\
\mathbf{y}_{2} \\
\vdots \\
\mathbf{y}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L}_{1,1}^H \mathbf{y}_{1} +
\mathbf{L}_{2,1}^H \mathbf{y}_{2} +
\mathbf{L}_{N,1}^H \mathbf{y}_{N} \\
\mathbf{L}_{1,2}^H \mathbf{y}_{1} +
\mathbf{L}_{2,2}^H \mathbf{y}_{2} +
\mathbf{L}_{N,2}^H \mathbf{y}_{N} \\
\vdots \\
\mathbf{L}_{1,M}^H \mathbf{y}_{1} +
\mathbf{L}_{2,M}^H \mathbf{y}_{2} +
\mathbf{L}_{N,M}^H \mathbf{y}_{N}
\end{bmatrix}
"""
def __init__(
self,
ops: Iterable[Iterable[LinearOperator]],
nproc: int = 1,
forceflat: bool = None,
dtype: Optional[DTypeLike] = None,
):
if nproc > 1:
self.pool = mp.Pool(processes=nproc)
super().__init__(
ops=ops, forceflat=forceflat, dtype=dtype, args_VStack={"nproc": nproc}
)
