MPI_Reduce(3)                      Open MPI                      MPI_Reduce(3)



NAME
       MPI_Reduce - Reduces values on all processes within a group.


SYNTAX
C Syntax
       #include <mpi.h>
       int MPI_Reduce(void *sendbuf, void *recvbuf, int count,
            MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm)


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


C++ Syntax
       #include <mpi.h>
       void MPI::Intracomm::Reduce(const void* sendbuf, void* recvbuf,
            int count, const MPI::Datatype& datatype, const MPI::Op& op,
            int root) const


INPUT PARAMETERS
       sendbuf   Address of send buffer (choice).

       count     Number of elements in send buffer (integer).

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

       op        Reduce operation (handle).

       root      Rank of root process (integer).

       comm      Communicator (handle).


OUTPUT PARAMETERS
       recvbuf   Address of receive buffer (choice, significant only at root).

       IERROR    Fortran only: Error status (integer).


DESCRIPTION
       The global reduce functions (MPI_Reduce, MPI_Op_create, MPI_Op_free,
       MPI_Allreduce, MPI_Reduce_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 combines the elements provided in the input buffer of each
       process in the group, using the operation op, and returns the combined
       value in the output buffer of the process with rank root. The input
       buffer is defined by the arguments sendbuf, count, and datatype; the
       output buffer is defined by the arguments recvbuf, count, and datatype;
       both have the same number of elements, with the same type. The routine
       is called by all group members using the same arguments for count,
       datatype, op, root, and comm. Thus, all processes provide input buffers
       and output buffers of the same length, with elements of the same type.
       Each 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 send
       buffer contains two elements that are floating-point numbers (count = 2
       and datatype = MPI_FLOAT), then recvbuf(1) = global max (sendbuf(1))
       and recvbuf(2) = global max(sendbuf(2)).


USE OF IN-PLACE OPTION
       When the communicator is an intracommunicator, you can perform a reduce
       operation in-place (the output buffer is used as the input buffer).
       Use the variable MPI_IN_PLACE as the value of the root process sendbuf.
       In this case, the input data is taken at the root from the receive
       buffer, where it will be replaced by the output data.

       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 root process in the
       first group combines data from all the processes in the second group
       and then performs the op operation.  The first group defines the root
       process.  That process uses MPI_ROOT as the value of its root argument.
       The remaining processes use MPI_PROC_NULL as the value of their root
       argument.  All processes in the second group use the rank of that root
       process in the first group as the value of their root argument.  Only
       the send buffer arguments are significant in the second group, and only
       the receive buffer arguments are significant in the root process of the
       first group.


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 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

       Example 1: A routine that computes the dot product of two vectors that
       are distributed across a  group of processes and returns the answer at
       process zero.

           SUBROUTINE PAR_BLAS1(m, a, b, c, comm)
           REAL a(m), b(m)       ! local slice of array
           REAL c                ! result (at process zero)
           REAL sum
           INTEGER m, comm, i, ierr

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

           ! global sum
           CALL MPI_REDUCE(sum, c, 1, MPI_REAL, MPI_SUM, 0, comm, ierr)
           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 process 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 process zero (and garbage at the other nodes)
           RETURN


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 = max(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.

       Example 3: Each process has an array of 30 doubles, in C. For each of
       the 30 locations, compute the value and rank of the process containing
       the largest value.

               ...
               /* each process has an array of 30 double: ain[30]
                */
               double ain[30], aout[30];
               int  ind[30];
               struct {
                   double val;
                   int   rank;
               } in[30], out[30];
               int i, myrank, root;

               MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
               for (i=0; i<30; ++i) {
                   in[i].val = ain[i];
                   in[i].rank = myrank;
               }
               MPI_Reduce( in, out, 30, MPI_DOUBLE_INT, MPI_MAXLOC, root, comm );
               /* At this point, the answer resides on process root
                */
               if (myrank == root) {
                   /* read ranks out
                    */
                   for (i=0; i<30; ++i) {
                       aout[i] = out[i].val;
                       ind[i] = out[i].rank;
                   }
               }

       Example 4:  Same example, in Fortran.

           ...
           ! each process has an array of 30 double: ain(30)

           DOUBLE PRECISION ain(30), aout(30)
           INTEGER ind(30);
           DOUBLE PRECISION in(2,30), out(2,30)
           INTEGER i, myrank, root, ierr;

           MPI_COMM_RANK(MPI_COMM_WORLD, myrank);
               DO I=1, 30
                   in(1,i) = ain(i)
                   in(2,i) = myrank    ! myrank is coerced to a double
               END DO

           MPI_REDUCE( in, out, 30, MPI_2DOUBLE_PRECISION, MPI_MAXLOC, root,
                                                                     comm, ierr );
           ! At this point, the answer resides on process root

           IF (myrank .EQ. root) THEN
                   ! read ranks out
                   DO I= 1, 30
                       aout(i) = out(1,i)
                       ind(i) = out(2,i)  ! rank is coerced back to an integer
                   END DO
               END IF

       Example 5: Each process has a nonempty array of values.  Find the
       minimum global value, the rank of the process that holds it, and its
       index on this process.

           #define  LEN   1000

           float val[LEN];        /* local array of values */
           int count;             /* local number of values */
           int myrank, minrank, minindex;
           float minval;

           struct {
               float value;
               int   index;
           } in, out;

           /* local minloc */
           in.value = val[0];
           in.index = 0;
           for (i=1; i < count; i++)
               if (in.value > val[i]) {
                   in.value = val[i];
                   in.index = i;
               }

           /* global minloc */
           MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
           in.index = myrank*LEN + in.index;
           MPI_Reduce( in, out, 1, MPI_FLOAT_INT, MPI_MINLOC, root, comm );
               /* At this point, the answer resides on process root
                */
           if (myrank == root) {
               /* read answer out
                */
               minval = out.value;
               minrank = out.index / LEN;
               minindex = out.index % LEN;

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

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.

       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_scatter
       MPI_Scan
       MPI_Op_create
       MPI_Op_free






1.4.1                            Jan 14, 2010                    MPI_Reduce(3)
