Source code for pylops.basicoperators.BlockDiag

import multiprocessing as mp

import numpy as np
import scipy as sp
from scipy.sparse.linalg.interface import LinearOperator as spLinearOperator

# 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 _get_dtype
else:
    from scipy.sparse.linalg._interface import _get_dtype

from pylops import LinearOperator
from pylops.basicoperators import MatrixMult
from pylops.utils.backend import get_array_module


def _matvec_rmatvec_map(op, x):
    """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. 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, nproc=1, dtype=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) # create pool for multiprocessing self._nproc = nproc self.pool = None if self.nproc > 1: self.pool = mp.Pool(processes=nproc) self.shape = (self.nops, self.mops) if dtype is None: self.dtype = _get_dtype(ops) else: self.dtype = np.dtype(dtype) self.explicit = False self.clinear = all([getattr(oper, "clinear", True) for oper in self.ops]) @property def nproc(self): return self._nproc @nproc.setter def nproc(self, nprocnew): if self._nproc > 1: self.pool.close() if nprocnew > 1: self.pool = mp.Pool(processes=nprocnew) self._nproc = nprocnew def _matvec_serial(self, x): 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): 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): 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): 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): if self.nproc == 1: y = self._matvec_serial(x) else: y = self._matvec_multiproc(x) return y def _rmatvec(self, x): if self.nproc == 1: y = self._rmatvec_serial(x) else: y = self._rmatvec_multiproc(x) return y