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.