pylops_mpi.basicoperators.MPIBlockDiag

class pylops_mpi.basicoperators.MPIBlockDiag(ops, base_comm=<mpi4py.MPI.Intracomm object>, dtype=None)

MPI Block-diagonal operator.

Create a block-diagonal operator from a set of linear operators using MPI. Each rank must initialize this operator by providing one or more linear operators which will be computed within such rank.

Both model and data vectors must be of pylops_mpi.DistributedArray type and partitioned between ranks according to the shapes of the different linear operators.

Parameters:

opslist

One or more pylops.LinearOperator to be stacked.

base_commmpi4py.MPI.Comm, optional

Base MPI Communicator. Defaults to mpi4py.MPI.COMM_WORLD.

dtypestr, optional

Type of elements in input array.

Attributes:

shapetuple

Operator shape

Notes

An MPI Block Diagonal operator is composed of N linear operators, represented by L. Each rank has one or more pylops.LinearOperator, which we represent here compactly as \(\mathbf{L}_i\) for rank \(i\).

Each operator performs forward mode operations using its corresponding model vector, denoted as m. This vector is effectively a pylops_mpi.DistributedArray partitioned at each rank in such a way that its local shapes agree with those of the corresponding linear operators. The forward mode of each operator is then collected from all ranks as a DistributedArray, referred to as d.

\[\begin{split}\begin{bmatrix} \mathbf{d}_1 \\ \mathbf{d}_2 \\ \vdots \\ \mathbf{d}_n \end{bmatrix} = \begin{bmatrix} \mathbf{L}_1 & \mathbf{0} & \ldots & \mathbf{0} \\ \mathbf{0} & \mathbf{L}_2 & \ldots & \mathbf{0} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_n \end{bmatrix} \begin{bmatrix} \mathbf{m}_1 \\ \mathbf{m}_2 \\ \vdots \\ \mathbf{m}_n \end{bmatrix}\end{split}\]

Likewise, for the adjoint mode, each operator executes operations in the adjoint mode, the adjoint mode of each operator is then collected from all ranks as a DistributedArray referred as d.

\[\begin{split}\begin{bmatrix} \mathbf{d}_1 \\ \mathbf{d}_2 \\ \vdots \\ \mathbf{d}_n \end{bmatrix} = \begin{bmatrix} \mathbf{L}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\ \mathbf{0} & \mathbf{L}_2^H & \ldots & \mathbf{0} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_n^H \end{bmatrix} \begin{bmatrix} \mathbf{m}_1 \\ \mathbf{m}_2 \\ \vdots \\ \mathbf{m}_n \end{bmatrix}\end{split}\]

Methods

__init__(ops[, base_comm, dtype])
adjoint()	Adjoint MPI LinearOperator
conj()	Complex conjugate operator
dot(x)	Matrix Vector Multiplication
matvec(x)	Matrix-vector multiplication.
rmatvec(x)	Adjoint Matrix-vector multiplication.
transpose()	Transposition of MPI LinearOperator