Source code for pylops.basicoperators.Block

from pylops.basicoperators import HStack, VStack

def _Block(
    ops, dtype=None, _HStack=HStack, _VStack=VStack, args_HStack={}, args_VStack={}
    """Block operator.

    Used to be able to provide operators from different libraries to
    hblocks = [_HStack(hblock, dtype=dtype, **args_HStack) for hblock in ops]
    return _VStack(hblocks, dtype=dtype, **args_VStack)

[docs]def Block(ops, nproc=1, dtype=None): 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. 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} """ return _Block(ops, dtype=dtype, args_VStack={"nproc": nproc})