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MPI-Based Block Vectors and Matrices

PyNumero's MPI-based block vectors and matrices (:py~pyomo.contrib.pynumero.sparse.mpi_block_vector.MPIBlockVector and :py~pyomo.contrib.pynumero.sparse.mpi_block_matrix.MPIBlockMatrix) behave very similarly to BlockVector and BlockMatrix. The primary difference is in construction. With MPIBlockVector and MPIBlockMatrix, each block is owned by either a single process/rank or all processes/ranks.

Consider the following example (in a file called "parallel_vector_ops.py").

../../../../pyomo/contrib/pynumero/examples/parallel_vector_ops.py

This example can be run with

mpirun -np 3 python -m mpi4py parallel_vector_ops.py

The output is

[6. 6. 6. 2. 2. 2. 4. 4. 4. 2. 4. 6.]
56.0
3

Note that the make_local_copy() method is not efficient and should only be used for debugging.

The -1 in owners means that the block at that index (index 3 in this example) is owned by all processes. The non-negative integer values indicate that the block at that index is owned by the process with rank equal to the value. In this example, rank 0 owns block 1, rank 1 owns block 2, and rank 2 owns block 0. Block 3 is owned by all ranks. Note that blocks should only be set if the process/rank owns that block.

The operations performed with MPIBlockVector are identical to the same operations performed with BlockVector (or even NumPy arrays), except that the operations are now performed in parallel.

MPIBlockMatrix construction is very similar. Consider the following example in a file called "parallel_matvec.py".

../../../../pyomo/contrib/pynumero/examples/parallel_matvec.py

Which can be run with

mpirun -np 3 python -m mpi4py parallel_matvec.py

The output is

error:  4.440892098500626e-16

The most difficult part of using MPIBlockVector and MPIBlockMatrix is determining the best structure and rank ownership to maximize parallel efficiency.