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MPI_Alltoallv, MPI_Ialltoallv - All processes send different amount
of data to, and receive different amount of data from, all processes 
 
 #include <mpi.h>
int MPI_Alltoallv(const void *sendbuf, const int sendcounts[],
    const int sdispls]P, MPI_Datatype sendtype,
    void *recvbuf, const int recvcounts[],
    const int rdispls[], MPI_Datatype recvtype, MPI_Comm comm)
int MPI_Ialltoallv(const void *sendbuf, const int sendcounts[],
    const int sdispls]P, MPI_Datatype sendtype,
    void *recvbuf, const int recvcounts[],
    const int rdispls[], MPI_Datatype recvtype, MPI_Comm comm,
    MPI_Request *request)
 
 INCLUDE ’mpif.h’
MPI_ALLTOALLV(SENDBUF, SENDCOUNTS, SDISPLS, SENDTYPE,
    RECVBUF, RECVCOUNTS, RDISPLS, RECVTYPE, COMM, IERROR)
    <type>    SENDBUF(*), RECVBUF(*)
    INTEGER    SENDCOUNTS(*), SDISPLS(*), SENDTYPE
    INTEGER    RECVCOUNTS(*), RDISPLS(*), RECVTYPE
    INTEGER    COMM, IERROR
MPI_IALLTOALLV(SENDBUF, SENDCOUNTS, SDISPLS, SENDTYPE,
    RECVBUF, RECVCOUNTS, RDISPLS, RECVTYPE, REQUEST, COMM, IERROR)
    <type>    SENDBUF(*), RECVBUF(*)
    INTEGER    SENDCOUNTS(*), SDISPLS(*), SENDTYPE
    INTEGER    RECVCOUNTS(*), RDISPLS(*), RECVTYPE
    INTEGER    COMM, REQUEST, IERROR
 
 #include <mpi.h>
void MPI::Comm::Alltoallv(const void* sendbuf,
    const int sendcounts[], const int displs[],
    const MPI::Datatype& sendtype, void* recvbuf,
    const int recvcounts[], const int rdispls[],
    const MPI::Datatype& recvtype)
 
 import mpi.*;
void MPI.COMM_WORLD.Alltoallv(Object sendbuf, int sendoffset, int sendcount[],
                              int sdispls[], MPI.Datatype sendtype,
                              Object recvbuf, int recvoffset, int recvcount[],
                              int rdispls[], MPI.Datatype recvtype)
sendbuf Starting address of send buffer. sendoffset
Initial number of elements to skip at beginning of buffer (integer, Java-only).
sendcounts Integer array, where entry i specifies the number of elements
to send to rank i. sdispls Integer array, where entry i specifies the displacement
(offset from sendbuf, in units of sendtype) from which to send data to
rank i. sendtype Datatype of send buffer elements. recvoffset     Initial
number of elements to skip at beginning of buffer (integer, Java-only). recvcounts
Integer array, where entry j specifies the number of elements to receive
from rank j. rdispls Integer array, where entry j specifies the displacement
(offset from recvbuf, in units of recvtype) to which data from rank j should
be written. recvtype Datatype of receive buffer elements. comm Communicator
over which data is to be exchanged.
  
MPI_Alltoallv is a generalized collective
operation in which all processes send data to and receive data from all
other processes. It adds flexibility to MPI_Alltoall by allowing the user
to specify data to send and receive vector-style (via a displacement and
element count). The operation of this routine can be thought of 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).recvbuf Address of
receive buffer. request Request (handle, non-blocking only). IERROR Fortran
only: Error status.
  
     MPI_Comm_size(comm, &n);
    for (i = 0, i < n; i++)
        MPI_Send(sendbuf + sdispls[i] * extent(sendtype),
            sendcounts[i], sendtype, i, ..., comm);
    for (i = 0, i < n; i++)
        MPI_Recv(recvbuf + rdispls[i] * extent(recvtype),
            recvcounts[i], recvtype, i, ..., comm);
 
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.   
When a pair of processes
exchanges data, each may pass different element count and datatype arguments
so long as the sender specifies the same amount of data to send (in bytes)
as the receiver expects to receive.  
Note that process i may send a different
amount of data to process j than it receives from process j. Also, a process
may send entirely different amounts of data to different processes in the
communicator.
   
WHEN COMMUNICATOR IS AN INTER-COMMUNICATOR  
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.  
 
When the communicator is an intracommunicator,
you can perform an all-to-all operation in-place (the output buffer is used
as the input buffer).  Use the variable MPI_IN_PLACE as the value of sendbuf.
 In this case, sendcounts, sdispls, and sendtype are ignored.  The input
data of each process is assumed to be in the area where that process would
receive its own contribution to the receive buffer. 
 
The specification
of counts and displacements should not cause any location to be written
more than once.  
All arguments on all processes are significant. The comm
argument, in particular, must describe the same communicator on all processes.
 
The offsets of sdispls and rdispls are measured in units of sendtype and
recvtype, respectively. Compare this to MPI_Alltoallw, where these offsets
are measured in bytes.
 
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.
 
 
 MPI_Alltoall
MPI_Alltoallw
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