pylops_mpi.basicoperators.MPIVStack

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

MPI VStack Operator

Create a vertical stack of 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 each rank. Both model and data vectors are of pylops_mpi.DistributedArray type.

Parameters:

opslist

One or more pylops.LinearOperator to be vertically 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

Raises:

ValueError

If ops have different number of columns

Notes

An MPIVStack is composed of N linear operators stacked vertically, 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 with pylops_mpi.Partition.BROADCAST i.e. broadcasted at all ranks in such a way that the global shape is equal to the local shape of the array and these local shapes agree with the corresponding linear operators.

Afterwards, the forward mode of each operator is collected from each rank in a pylops_mpi.DistributedArray, represented by d.

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

Likewise for the adjoint mode, each operator performs adjoint operations using its corresponding model vector, denoted as m which is a pylops_mpi.DistributedArray with pylops_mpi.Partition.SCATTER i.e. partitioned at each rank.

Afterwards, a collective reduction operation is performed where adjoint values from linear operators are summed up, and the final sum is broadcasted to all processes in the communicator, represented by d.

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

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