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       MPI_Alltoall - All processes send data to all processes


C Syntax

       #include <mpi.h>
       int MPI_Alltoall(void *sendbuf, int sendcount,
            MPI_Datatype sendtype, void *recvbuf, int recvcount,
            MPI_Datatype recvtype, MPI_Comm comm)

Fortran Syntax

       INCLUDE 'mpif.h'

            <type>    SENDBUF(*), RECVBUF(*)
            INTEGER   COMM, IERROR

C++ Syntax

       #include <mpi.h>
       void MPI::Comm::Alltoall(const void* sendbuf, int sendcount,
            const MPI::Datatype& sendtype, void* recvbuf,
            int recvcount, const MPI::Datatype& recvtype)


       sendbuf     Starting address of send buffer (choice).

       sendcount   Number of elements to send to each process (integer).

       sendtype    Datatype of send buffer elements (handle).

       recvcount   Number of elements to receive from each process (integer).

       recvtype    Datatype of receive buffer elements (handle).

       comm        Communicator over which data is to be exchanged (handle).


       recvbuf     Starting address of receive buffer (choice).

       IERROR      Fortran only: Error status (integer).


       MPI_Alltoall is a collective operation in which all processes send the same amount of data
       to each other, and receive the same amount of data from each other. The operation of  this
       routine  can be represented as follows, where each process performs 2n (n being the number
       of processes in communicator comm) independent  point-to-point  communications  (including
       communication with itself).

            MPI_Comm_size(comm, &n);
            for (i = 0, i < n; i++)
                MPI_Send(sendbuf + i * sendcount * extent(sendtype),
                    sendcount, sendtype, i, ..., comm);
            for (i = 0, i < n; i++)
                MPI_Recv(recvbuf + i * recvcount * extent(recvtype),
                    recvcount, recvtype, i, ..., comm);

       Each  process  breaks  up  its  local  sendbuf  into  n blocks - each containing sendcount
       elements of type sendtype - and divides its recvbuf similarly according to  recvcount  and
       recvtype.  Process  j sends the k-th block of its local sendbuf to process k, which places
       the data in the j-th block of its local recvbuf. The amount of data sent must be equal  to
       the amount of data received, pairwise, between every pair of processes.


       When the communicator is an inter-communicator, the gather operation occurs in two phases.
       The data is gathered from all the members of the first  group  and  received  by  all  the
       members of the second group.  Then the data is gathered 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.

       The  first group defines the root process.  The root process uses MPI_ROOT as the value of
       root.  All other processes in the first group use MPI_PROC_NULL as the value of root.  All
       processes  in  the second group use the rank of the root process in the first group as the
       value of root.

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


       The MPI_IN_PLACE option is not available for this function.

       All  arguments  on  all  processes are significant. The comm argument, in particular, must
       describe the same communicator on all processes.

       There are two MPI library functions that are more general than MPI_Alltoall. MPI_Alltoallv
       allows all-to-all communication to and from buffers that need not be contiguous; different
       processes  may  send  and  receive  different  amounts  of  data.  MPI_Alltoallw   expands
       MPI_Alltoallv's functionality to allow the exchange of data with different datatypes.


       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.