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**NAME**

MPI_Reduce,MPI_Ireduce- Reduces values on all processes within a group.

**SYNTAX**

**C** **Syntax**

#include <mpi.h> int MPI_Reduce(const void *sendbuf, void *recvbuf, intcount, MPI_Datatypedatatype, MPI_Opop, introot, MPI_Commcomm) int MPI_Ireduce(const void *sendbuf, void *recvbuf, intcount, MPI_Datatypedatatype, MPI_Opop, introot, MPI_Commcomm, MPI_Request*request)

**Fortran** **Syntax**

INCLUDE 'mpif.h' MPI_REDUCE(SENDBUF,RECVBUF,COUNT,DATATYPE,OP,ROOT,COMM,IERROR) <type>SENDBUF(*),RECVBUF(*)INTEGERCOUNT,DATATYPE,OP,ROOT,COMM,IERRORMPI_IREDUCE(SENDBUF,RECVBUF,COUNT,DATATYPE,OP,ROOT,COMM,REQUEST,IERROR) <type>SENDBUF(*),RECVBUF(*)INTEGERCOUNT,DATATYPE,OP,ROOT,COMM,REQUEST,IERROR

**C++** **Syntax**

#include <mpi.h> void MPI::Intracomm::Reduce(const void*sendbuf, void*recvbuf, intcount, const MPI::Datatype&datatype, const MPI::Op&op, introot) 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). request Request (handle, non-blocking only). 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 processsendbuf. 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 theopoperation. The first group defines the root process. That process uses MPI_ROOT as the value of itsrootargument. The remaining processes use MPI_PROC_NULL as the value of theirrootargument. All processes in the second group use the rank of that root process in the first group as the value of theirrootargument. 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_BXORExample1: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) RETURNExample2: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 = 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.Example3: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; } }Example4: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 IFExample5: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 callMPI_Abortor silently skip the problem. Thus, if you change the error handler fromMPI_ERRORS_ARE_FATALto 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