NAME

       MPI_Allreduce, MPI_Iallreduce - Combines values from all processes and distributes the result back to all
       processes.

SYNTAX

C Syntax

       #include <mpi.h>
       int MPI_Allreduce(const void *sendbuf, void *recvbuf, int count,
                         MPI_Datatype datatype, MPI_Op op, MPI_Comm comm)

       int MPI_Iallreduce(const void *sendbuf, void *recvbuf, int count,
                          MPI_Datatype datatype, MPI_Op op, MPI_Comm comm,
                          MPI_Request *request)

Fortran Syntax

       INCLUDE 'mpif.h'
       MPI_ALLREDUCE(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, COMM, IERROR)
            <type>    SENDBUF(*), RECVBUF(*)
            INTEGER   COUNT, DATATYPE, OP, COMM, IERROR

       MPI_IALLREDUCE(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, COMM, REQUEST, IERROR)
            <type>    SENDBUF(*), RECVBUF(*)
            INTEGER   COUNT, DATATYPE, OP, COMM, REQUEST, IERROR

C++ Syntax

       #include <mpi.h>
       void MPI::Comm::Allreduce(const void* sendbuf, void* recvbuf,
            int count, const MPI::Datatype& datatype, const
            MPI::Op& op) const=0

INPUT PARAMETERS

       sendbuf   Starting address of send buffer (choice).

       count     Number of elements in send buffer (integer).

       datatype  Datatype of elements of send buffer (handle).

       op        Operation (handle).

       comm      Communicator (handle).

OUTPUT PARAMETERS

       recvbuf   Starting address of receive buffer (choice).

       request   Request (handle, non-blocking only).

       IERROR    Fortran only: Error status (integer).

DESCRIPTION

       Same as MPI_Reduce except that the result appears in the receive buffer of all the group members.

       Example 1: A routine that computes the product of a vector and an array that  are  distributed  across  a
       group of processes and returns the answer at all nodes (compare with Example 2, with MPI_Reduce, below).

       SUBROUTINE PAR_BLAS2(m, n, a, b, c, comm)
       REAL a(m), b(m,n)    ! local slice of array
       REAL c(n)            ! result
       REAL sum(n)
       INTEGER n, comm, i, j, ierr

       ! local sum
       DO j= 1, n
         sum(j) = 0.0
         DO i = 1, m
           sum(j) = sum(j) + a(i)*b(i,j)
         END DO
       END DO

       ! global sum
       CALL MPI_ALLREDUCE(sum, c, n, MPI_REAL, MPI_SUM, comm, ierr)

       ! return result at all nodes
       RETURN

       Example  2:  A  routine  that computes the product of a vector and an array that are distributed across a
       group of processes and returns the answer at node zero.

       SUBROUTINE PAR_BLAS2(m, n, a, b, c, comm)
       REAL a(m), b(m,n)    ! local slice of array
       REAL c(n)            ! result
       REAL sum(n)
       INTEGER n, comm, i, j, ierr

       ! local sum
       DO j= 1, n
         sum(j) = 0.0
         DO i = 1, m
           sum(j) = sum(j) + a(i)*b(i,j)
         END DO
       END DO

       ! global sum
       CALL MPI_REDUCE(sum, c, n, MPI_REAL, MPI_SUM, 0, comm, ierr)

       ! return result at node zero (and garbage at the other nodes)
       RETURN

USE OF IN-PLACE OPTION

       When the communicator is an intracommunicator, you can perform  an  all-reduce  operation  in-place  (the
       output buffer is used as the input buffer).  Use the variable MPI_IN_PLACE as the value of sendbuf at all
       processes.

       Note that MPI_IN_PLACE is a special kind of value; it has the same restrictions on its use as MPI_BOTTOM.

       Because the in-place option converts the receive buffer into a send-and-receive buffer, a Fortran binding
       that includes INTENT must mark these as INOUT, not OUT.

WHEN COMMUNICATOR IS AN INTER-COMMUNICATOR

       When  the  communicator is an inter-communicator, the reduce operation occurs in two phases.  The data is
       reduced from all the members of the first group and received by all the  members  of  the  second  group.
       Then  the data is reduced from all the members of the second group and received by all the members of the
       first.  The operation exhibits a symmetric, full-duplex behavior.

       When the communicator is an intra-communicator, these groups are the same, and the operation occurs in  a
       single phase.

NOTES ON COLLECTIVE OPERATIONS

       The reduction functions ( MPI_Op ) do not return an error value.  As a result, if the functions detect an
       error, all they can do is either call MPI_Abort or silently skip the problem.  Thus, if  you  change  the
       error handler from MPI_ERRORS_ARE_FATAL to something else, for example, MPI_ERRORS_RETURN , then no error
       may be indicated.

ERRORS

       Almost all MPI routines return an error value; C routines as  the  value  of  the  function  and  Fortran
       routines in the last argument. C++ functions do not return errors. If the default error handler is set to
       MPI::ERRORS_THROW_EXCEPTIONS, then on error the  C++  exception  mechanism  will  be  used  to  throw  an
       MPI::Exception object.

       Before  the  error  value  is  returned,  the current MPI error handler is called. By default, this error
       handler aborts the MPI job, except for I/O function  errors.  The  error  handler  may  be  changed  with
       MPI_Comm_set_errhandler; the predefined error handler MPI_ERRORS_RETURN may be used to cause error values
       to be returned. Note that MPI does not guarantee that an MPI program can continue past an error.