In order to illustrate the gather and scatter functions, we give a matrix-style depiction below:

Let's consider in detail how MPI_Gather might be used to facilitate a distributed matrix computation.

Example: matrix-vector multiplication

• Matrix is distributed by rows (i.e., row-major order)
• Product vector is needed in entirety by one process
• MPI_Gather will be used to collect the product from processes

Description of Sample Code

The problem associated with the following sample code is the multiplication of a matrix A, size 100x100, by a vector b of length 100. The example uses four MPI processes, so each process will work on its own chunk of 25 rows of A. Since b is the same for each process, it will simply be replicated across processes. The vector c will therefore have 25 elements calculated by each process; these are stored in cpart. Here is a picture of how the overall computation is distributed:

A

a matrix partitioned across rows and distributed to processes as Apart

b

a vector present on all processes

c

a partitioned vector updated by each process independently

The MPI_Gather routine will retrieve cpart from each process and store the result in ctotal, which is the complete vector c.

MPI_Gather Example

/* Compute a partition of matrix A multiplied by vector b */
float Apart[25,100], b[100], cpart[25], ctotal[100];
int root;
root=0;
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/* Code that initializes Apart and b */
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for(i=0; i<5; i++)
{
   cpart[i]=0;
   for(k=0; k<100; k++)
   {
      cpart[i] = cpart[i] + Apart[i,k] * b[k];
   }
}
MPI_Gather(cpart, 25, MPI_FLOAT, ctotal, 25, MPI_FLOAT,
    root, MPI_COMM_WORLD);

! Compute a partition of matrix A multiplied by vector b 
! Fortran, unlike C, stores matrices in column-major order,
! so for speed, each submatrix of A is stored as its transpose, ApartT 
REAL ApartT(100,25), b(100), cpart(25), ctotal(100)
INTEGER root
DATA root/0/
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! Code that initializes ApartT and b
⋮
DO I=1,25
     cpart(I) = 0.
     DO K=1,100
          cpart(I) = cpart(I) + ApartT(K,I) * b(K)
     END DO
END DO
CALL MPI_GATHER(cpart, 25, MPI_REAL, ctotal, 25, MPI_REAL, &
      root, MPI_COMM_WORLD, ierr)