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NAME

       MPI_Reduce_local - Perform a local reduction

SYNTAX

C Syntax

       #include <mpi.h>
       int MPI_Reduce_local(void *inbuf, void *inoutbuf, int count,
            MPI_Datatype datatype, MPI_Op op)

Fortran Syntax

       INCLUDE 'mpif.h'
       MPI_REDUCE_LOCAL(INBUF, INOUTBUF, COUNT, DATATYPE, OP, IERROR)
            <type>    INBUF(*), INOUTBUF(*)
            INTEGER   COUNT, DATATYPE, OP, IERROR

C++ Syntax

       #include <mpi.h>
       void MPI::Op::Reduce_local(const void* inbuf, void* inoutbuf,
            int count, const MPI::Datatype& datatype, const MPI::Op& op) const

INPUT PARAMETERS

       inbuf     Address of input buffer (choice).

       count     Number of elements in input buffer (integer).

       datatype  Data type of elements of input buffer (handle).

       op        Reduce operation (handle).

OUTPUT PARAMETERS

       inoutbuf  Address of in/out buffer (choice).

       IERROR    Fortran only: Error status (integer).

DESCRIPTION

       The  MPI_Reduce_local function is proposed for MPI-2.2 and (as of 10 Jan 2009) has not yet been ratified.
       Use at your own risk. See https://svn.mpi-forum.org/trac/mpi-forum-web/ticket/24.

       The   global   reduce   functions   (MPI_Reduce_local,   MPI_Op_create,    MPI_Op_free,    MPI_Allreduce,
       MPI_Reduce_local_scatter,  MPI_Scan)  perform  a  global reduce operation (such as sum, max, logical AND,
       etc.) across all the members of a group. The reduction operation can be either one of a  predefined  list
       of  operations,  or  a  user-defined operation. The global reduction functions come in several flavors: a
       reduce that returns the result of the reduction at one node, an all-reduce that returns  this  result  at
       all  nodes,  and a scan (parallel prefix) operation. In addition, a reduce-scatter operation combines the
       functionality of a reduce and a scatter operation.

       MPI_Reduce_local combines the elements provided in the  input  and  input/output  buffers  of  the  local
       process,  using  the  operation  op, and returns the combined value in the inout/output buffer. The input
       buffer is defined by the arguments inbuf, count, and datatype;  the  output  buffer  is  defined  by  the
       arguments  inoutbuf,  count, and datatype; both have the same number of elements, with the same type. The
       routine is a local call.  The process can provide one element, or a sequence of elements, in  which  case
       the  combine  operation  is  executed  element-wise  on  each  entry of the sequence. For example, if the
       operation is MPI_MAX and the input buffer contains two elements that are floating-point numbers (count  =
       2  and  datatype  =  MPI_FLOAT),  then  inoutbuf(1)  =  global  max  (inbuf(1))  and inoutbuf(2) = global
       max(inbuf(2)).

USE OF IN-PLACE OPTION

       The use of MPI_IN_PLACE is disallowed with MPI_Reduce_local.

PREDEFINED REDUCE OPERATIONS

       The set of predefined operations provided by MPI is listed below  (Predefined  Reduce  Operations).  That
       section  also  enumerates  the  datatypes each operation can be applied to. In addition, users may define
       their own operations that can be overloaded to operate on several datatypes,  either  basic  or  derived.
       This  is  further  explained  in  the  description  of the user-defined operations (see the man pages for
       MPI_Op_create and MPI_Op_free).

       The operation op is always assumed to be associative. All predefined operations are also  assumed  to  be
       commutative.  Users  may  define  operations that are assumed to be associative, but not commutative. The
       ``canonical'' evaluation order of a reduction is determined by the ranks of the processes in  the  group.
       However,  the  implementation can take advantage of associativity, or associativity and commutativity, in
       order to change the order of evaluation. This may change the result of the reduction for operations  that
       are not strictly associative and commutative, such as floating point addition.

       Predefined  operators  work  only  with the MPI types listed below (Predefined Reduce Operations, and the
       section MINLOC and MAXLOC, below).  User-defined operators may operate on general, derived datatypes.  In
       this  case,  each  argument  that  the  reduce operation is applied to is one element described by such a
       datatype, which may contain several basic values. This is further explained in Section 4.9.4 of  the  MPI
       Standard, "User-Defined Operations."

       The   following   predefined   operations   are  supplied  for  MPI_Reduce_local  and  related  functions
       MPI_Allreduce, MPI_Reduce_scatter, and MPI_Scan. These operations are invoked by placing the following in
       op:

            Name                Meaning
            ---------           --------------------
            MPI_MAX             maximum
            MPI_MIN             minimum
            MPI_SUM             sum
            MPI_PROD            product
            MPI_LAND            logical and
            MPI_BAND            bit-wise and
            MPI_LOR             logical or
            MPI_BOR             bit-wise or
            MPI_LXOR            logical xor
            MPI_BXOR            bit-wise xor
            MPI_MAXLOC          max value and location
            MPI_MINLOC          min value and location

       The  two operations MPI_MINLOC and MPI_MAXLOC are discussed separately below (MINLOC and MAXLOC). For the
       other predefined operations, we enumerate below the allowed combinations of op  and  datatype  arguments.
       First, define groups of MPI basic datatypes in the following way:

            C integer:            MPI_INT, MPI_LONG, MPI_SHORT,
                                  MPI_UNSIGNED_SHORT, MPI_UNSIGNED,
                                  MPI_UNSIGNED_LONG
            Fortran integer:      MPI_INTEGER
            Floating-point:       MPI_FLOAT, MPI_DOUBLE, MPI_REAL,
                                  MPI_DOUBLE_PRECISION, MPI_LONG_DOUBLE
            Logical:              MPI_LOGICAL
            Complex:              MPI_COMPLEX
            Byte:                 MPI_BYTE

       Now, the valid datatypes for each option is specified below.

            Op                       Allowed Types
            ----------------         ---------------------------
            MPI_MAX, MPI_MIN         C integer, Fortran integer,
                                     floating-point

            MPI_SUM, MPI_PROD        C integer, Fortran integer,
                                     floating-point, complex

            MPI_LAND, MPI_LOR,       C integer, logical
            MPI_LXOR

            MPI_BAND, MPI_BOR,       C integer, Fortran integer, byte
            MPI_BXOR

MINLOC AND MAXLOC

       The  operator  MPI_MINLOC  is  used to compute a global minimum and also an index attached to the minimum
       value. MPI_MAXLOC similarly computes a global maximum and index. One application of these is to compute a
       global minimum (maximum) and the rank of the process containing this value.

       The operation that defines MPI_MAXLOC is

                ( u )    (  v )      ( w )
                (   )  o (    )   =  (   )
                ( i )    (  j )      ( k )

       where

           w = max(u, v)

       and

                ( i            if u > v
                (
          k   = ( min(i, j)    if u = v
                (
                (  j           if u < v)

       MPI_MINLOC is defined similarly:

                ( u )    (  v )      ( w )
                (   )  o (    )   =  (   )
                ( i )    (  j )      ( k )

       where

           w = min(u, v)

       and

                ( i            if u < v
                (
          k   = ( min(i, j)    if u = v
                (
                (  j           if u > v)

       Both  operations are associative and commutative. Note that if MPI_MAXLOC is applied to reduce a sequence
       of pairs (u(0), 0), (u(1), 1), ..., (u(n-1), n-1), then the value returned is (u , r),  where  u=  max(i)
       u(i)  and  r  is  the index of the first global maximum in the sequence. Thus, if each process supplies a
       value and its rank within the group, then a reduce operation with op = MPI_MAXLOC will return the maximum
       value  and  the  rank of the first process with that value. Similarly, MPI_MINLOC can be used to return a
       minimum and its index. More generally, MPI_MINLOC computes a lexicographic minimum,  where  elements  are
       ordered  according  to  the  first  component of each pair, and ties are resolved according to the second
       component.

       The reduce operation is defined to operate on arguments that consist of a pair: value and index. For both
       Fortran  and  C,  types  are  provided  to  describe  the pair. The potentially mixed-type nature of such
       arguments is a problem in Fortran. The problem is circumvented, for Fortran, by having  the  MPI-provided
       type  consist  of  a  pair of the same type as value, and coercing the index to this type also. In C, the
       MPI-provided pair type has distinct types and the index is an int.

       In order to use MPI_MINLOC and MPI_MAXLOC in a reduce operation, one must  provide  a  datatype  argument
       that  represents  a  pair  (value and index). MPI provides nine such predefined datatypes. The operations
       MPI_MAXLOC and MPI_MINLOC can be used with each of the following datatypes:

           Fortran:
           Name                     Description
           MPI_2REAL                pair of REALs
           MPI_2DOUBLE_PRECISION    pair of DOUBLE-PRECISION variables
           MPI_2INTEGER             pair of INTEGERs

           C:
           Name                 Description
           MPI_FLOAT_INT            float and int
           MPI_DOUBLE_INT           double and int
           MPI_LONG_INT             long and int
           MPI_2INT                 pair of ints
           MPI_SHORT_INT            short and int
           MPI_LONG_DOUBLE_INT      long double and int

       The data type MPI_2REAL is equivalent to:
           MPI_TYPE_CONTIGUOUS(2, MPI_REAL, MPI_2REAL)

       Similar statements apply for MPI_2INTEGER, MPI_2DOUBLE_PRECISION, and MPI_2INT.

       The datatype MPI_FLOAT_INT is as if defined by the following sequence of instructions.

           type[0] = MPI_FLOAT
           type[1] = MPI_INT
           disp[0] = 0
           disp[1] = sizeof(float)
           block[0] = 1
           block[1] = 1
           MPI_TYPE_STRUCT(2, block, disp, type, MPI_FLOAT_INT)

       Similar statements apply for MPI_LONG_INT and MPI_DOUBLE_INT.

       All MPI objects (e.g., MPI_Datatype, MPI_Comm) are of type INTEGER in Fortran.

NOTES ON COLLECTIVE OPERATIONS

       The reduction operators ( 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.

       The  reason for this is the performance problems in ensuring that all collective routines return the same
       error value.

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.

SEE ALSO

       MPI_Allreduce
       MPI_Reduce
       MPI_Reduce_scatter
       MPI_Scan
       MPI_Op_create
       MPI_Op_free