__all__ = ["BlockDiag"]
import multiprocessing as mp
import numpy as np
import scipy as sp
# need to check scipy version since the interface submodule changed into
# _interface from scipy>=1.8.0
sp_version = sp.__version__.split(".")
if int(sp_version[0]) <= 1 and int(sp_version[1]) < 8:
from scipy.sparse.linalg.interface import LinearOperator as spLinearOperator
from scipy.sparse.linalg.interface import _get_dtype
else:
from scipy.sparse.linalg._interface import (
_get_dtype,
LinearOperator as spLinearOperator,
)
from typing import Optional, Sequence
from pylops import LinearOperator
from pylops.basicoperators import MatrixMult
from pylops.utils.backend import get_array_module
from pylops.utils.typing import DTypeLike, NDArray
def _matvec_rmatvec_map(op, x: NDArray) -> NDArray:
"""matvec/rmatvec for multiprocessing"""
return op(x).squeeze()
[docs]class BlockDiag(LinearOperator):
r"""Block-diagonal operator.
Create a block-diagonal operator from N linear operators.
Parameters
----------
ops : :obj:`list`
Linear operators to be stacked. 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 matvec and 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
-----
A block-diagonal operator composed of N linear operators is created such
as its application in forward mode leads to
.. math::
\begin{bmatrix}
\mathbf{L}_1 & \mathbf{0} & \ldots & \mathbf{0} \\
\mathbf{0} & \mathbf{L}_2 & \ldots & \mathbf{0} \\
\vdots & \vdots & \ddots & \vdots \\
\mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_N
\end{bmatrix}
\begin{bmatrix}
\mathbf{x}_{1} \\
\mathbf{x}_{2} \\
\vdots \\
\mathbf{x}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L}_1 \mathbf{x}_{1} \\
\mathbf{L}_2 \mathbf{x}_{2} \\
\vdots \\
\mathbf{L}_N \mathbf{x}_{N}
\end{bmatrix}
while its application in adjoint mode leads to
.. math::
\begin{bmatrix}
\mathbf{L}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\
\mathbf{0} & \mathbf{L}_2^H & \ldots & \mathbf{0} \\
\vdots & \vdots & \ddots & \vdots \\
\mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_N^H
\end{bmatrix}
\begin{bmatrix}
\mathbf{y}_{1} \\
\mathbf{y}_{2} \\
\vdots \\
\mathbf{y}_{N}
\end{bmatrix} =
\begin{bmatrix}
\mathbf{L}_1^H \mathbf{y}_{1} \\
\mathbf{L}_2^H \mathbf{y}_{2} \\
\vdots \\
\mathbf{L}_N^H \mathbf{y}_{N}
\end{bmatrix}
"""
def __init__(
self,
ops: Sequence[LinearOperator],
nproc: int = 1,
forceflat: bool = None,
dtype: Optional[DTypeLike] = None,
) -> None:
self.ops = ops
mops = np.zeros(len(ops), dtype=int)
nops = np.zeros(len(ops), dtype=int)
for iop, oper in enumerate(ops):
if not isinstance(oper, (LinearOperator, spLinearOperator)):
self.ops[iop] = MatrixMult(oper, dtype=oper.dtype)
nops[iop] = self.ops[iop].shape[0]
mops[iop] = self.ops[iop].shape[1]
self.nops = int(nops.sum())
self.mops = int(mops.sum())
self.nnops = np.insert(np.cumsum(nops), 0, 0)
self.mmops = np.insert(np.cumsum(mops), 0, 0)
# define dims (check if all operators have the same,
# otherwise make same as self.mops and forceflat=True)
dims = [op.dims for op in self.ops]
if len(set(dims)) == 1:
dims = (len(ops), *dims[0])
else:
dims = (self.mops,)
forceflat = True
# define dimsd (check if all operators have the same,
# otherwise make same as self.nops and forceflat=True)
dimsd = [op.dimsd for op in self.ops]
if len(set(dimsd)) == 1:
dimsd = (len(ops), *dimsd[0])
else:
dimsd = (self.nops,)
forceflat = True
# create pool for multiprocessing
self._nproc = nproc
self.pool: Optional[mp.pool.Pool] = None
if self.nproc > 1:
self.pool = mp.Pool(processes=nproc)
dtype = _get_dtype(ops) if dtype is None else np.dtype(dtype)
clinear = all([getattr(oper, "clinear", True) for oper in self.ops])
super().__init__(
dtype=dtype,
dims=dims,
dimsd=dimsd,
clinear=clinear,
forceflat=forceflat,
)
@property
def nproc(self) -> int:
return self._nproc
@nproc.setter
def nproc(self, nprocnew: int) -> None:
if self._nproc > 1 and self.pool is not None:
self.pool.close()
if nprocnew > 1:
self.pool = mp.Pool(processes=nprocnew)
self._nproc = nprocnew
def _matvec_serial(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
y = ncp.zeros(self.nops, dtype=self.dtype)
for iop, oper in enumerate(self.ops):
y[self.nnops[iop] : self.nnops[iop + 1]] = oper.matvec(
x[self.mmops[iop] : self.mmops[iop + 1]]
).squeeze()
return y
def _rmatvec_serial(self, x: NDArray) -> NDArray:
ncp = get_array_module(x)
y = ncp.zeros(self.mops, dtype=self.dtype)
for iop, oper in enumerate(self.ops):
y[self.mmops[iop] : self.mmops[iop + 1]] = oper.rmatvec(
x[self.nnops[iop] : self.nnops[iop + 1]]
).squeeze()
return y
def _matvec_multiproc(self, x: NDArray) -> NDArray:
if self.pool is None:
raise ValueError
ys = self.pool.starmap(
_matvec_rmatvec_map,
[
(oper._matvec, x[self.mmops[iop] : self.mmops[iop + 1]])
for iop, oper in enumerate(self.ops)
],
)
y = np.hstack(ys)
return y
def _rmatvec_multiproc(self, x: NDArray) -> NDArray:
if self.pool is None:
raise ValueError
ys = self.pool.starmap(
_matvec_rmatvec_map,
[
(oper._rmatvec, x[self.nnops[iop] : self.nnops[iop + 1]])
for iop, oper in enumerate(self.ops)
],
)
y = np.hstack(ys)
return y
def _matvec(self, x: NDArray) -> NDArray:
if self.nproc == 1:
y = self._matvec_serial(x)
else:
y = self._matvec_multiproc(x)
return y
def _rmatvec(self, x: NDArray) -> NDArray:
if self.nproc == 1:
y = self._rmatvec_serial(x)
else:
y = self._rmatvec_multiproc(x)
return y
