Source code for pylops.basicoperators.VStack

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 VStack(LinearOperator): r"""Vertical stacking. Stack a set of N linear operators vertically. 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``) Raises ------ ValueError If ``ops`` have different number of rows Notes ----- A vertical stack of N linear operators is created such as its application in forward mode leads to .. math:: \begin{bmatrix} \mathbf{L}_{1} \\ \mathbf{L}_{2} \\ \vdots \\ \mathbf{L}_{N} \end{bmatrix} \mathbf{x} = \begin{bmatrix} \mathbf{L}_{1} \mathbf{x} \\ \mathbf{L}_{2} \mathbf{x} \\ \vdots \\ \mathbf{L}_{N} \mathbf{x} \end{bmatrix} = \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} while its application in adjoint mode leads to .. math:: \begin{bmatrix} \mathbf{L}_{1}^H & \mathbf{L}_{2}^H & \ldots & \mathbf{L}_{N}^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} = \mathbf{L}_{1}^H \mathbf{y}_1 + \mathbf{L}_{2}^H \mathbf{y}_2 + \ldots + \mathbf{L}_{N}^H \mathbf{y}_N """ def __init__(self, ops, nproc=1, dtype=None): self.ops = ops nops = np.zeros(len(self.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] self.nops = int(nops.sum()) mops = [oper.shape[1] for oper in self.ops] if len(set(mops)) > 1: raise ValueError("operators have different number of columns") self.mops = int(mops[0]) self.nnops = np.insert(np.cumsum(nops), 0, 0) # create pool for multiprocessing self._nproc = nproc self.pool = None if self.nproc > 1: self.pool = mp.Pool(processes=nproc) dtype = _get_dtype(self.ops) if dtype is None else np.dtype(dtype) clinear = all([getattr(oper, "clinear", True) for oper in self.ops]) super().__init__(dtype=dtype, shape=(self.nops, self.mops), clinear=clinear) @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).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 += 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) 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.sum(ys, axis=0) 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