===============
Sample solution                   [TOC]
===============

This solution works with additional template functions in
`hpc/mpi/matrix.hpp` that support scatter and gather operations
for matrices. These are one-to-many communications where
a master distributes partitions of a matrix to other processes
(scatter) and where the other processes send back their updated
partitions which are sent back to the master process and merged
(gather). MPI supports following operations:

---- CODE (type=cpp) ----------------------------------------------------------
int MPI_Scatterv(const void* sendbuf, int* sendcounts, int* displs,
		 MPI_Datatype sendtype, void* recvbuf, int recvcount,
		 MPI_Datatype recvtype, int root, MPI_Comm comm);
int MPI_Gatherv(const void* sendbuf, int sendcount, MPI_Datatype sendtype,
		void* recvbuf, int* recvcounts, int* displs,
		MPI_Datatype recvtype, int root, MPI_Comm comm);
-------------------------------------------------------------------------------

There exists also operations `MPI_Scatter` and `MPI_Gather` which
unfortunately do not support cases where slices can differ in their
extents.

These two operations are wrapped into `scatter_by_row` and `gather_by_row`:

---- CODE (type=cpp) ----------------------------------------------------------
template<typename T,
   template<typename> typename MA,
   template<typename> typename MB,
   Require<Ge<MA<T>>> = true, Require<Ge<MB<T>>> = true>
int scatter_by_row(const MA<T>& A, MB<T>& B, int root, MPI_Comm comm) {
   /* ... */
}

template<typename T,
   template<typename> typename MA,
   template<typename> typename MB,
   Require<Ge<MA<T>>> = true, Require<Ge<MB<T>>> = true>
int gather_by_row(const MA<T>& A, MB<T>& B, int root, MPI_Comm comm) {
   /* ... */
}
-------------------------------------------------------------------------------

We will see more about this communication pattern in the next session.

:import:session06/jacobi.cpp
:import:session06/step03/hpc/mpi/matrix.hpp

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