在上一篇中我们介绍了 mpi4py 中的全收集操作方法，下面我们将介绍全规约操作。
对组内通信子上的全规约操作，组内所有进程都作为根执行一次规约操作，操作完毕后所有进程接收缓冲区的数据均相同。这个操作等价于以某个进程作为根首先进行一次规约操作，然后执行一次广播操作，最后每个进程都得到相同的结果。
对组间通信子上的全规约操作，其关联的两个组 group A 和 group B 都要执行该方法调用，该操作使得 group A 中进程提供的规约结果将保存到 group B 的各进程中，反之亦然。
方法接口
mpi4py 中的全规约操作的方法（MPI.Comm 类的方法）接口为：
allreduce(self, sendobj, op=SUM)
Allreduce(self, sendbuf, recvbuf, Op op=SUM)
这些方法的参数与规约操作对应方法的参数类似，不同的是对全规约操作没有了 root 参数。
对组内通信子对象的 Allreduce，可以将其 sendbuf 参数设置成 MPI.IN_PLACE，此时各进程将从自己的接收缓冲区中提取数据，经过规约操作后，将结果替换接收缓冲区中原来的内容。
例程
下面给出全规约操作的使用例程。
# allreduce.py
"""
Demonstrates the usage of allreduce, Allreduce.
Run this with 4 processes like:
$ mpiexec -n 4 python allreduce.py
"""
import numpy as np
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# ------------------------------------------------------------------------------
# reduce generic object from each process by using allreduce
if rank == 0:
send_obj = 0.5
elif rank == 1:
send_obj = 2.5
elif rank == 2:
send_obj = 3.5
else:
send_obj = 1.5
# reduce by SUM: 0.5 + 2.5 + 3.5 + 1.5 = 8.0
recv_obj = comm.allreduce(send_obj, op=MPI.SUM)
print 'allreduce by SUM: rank %d has %s' % (rank, recv_obj)
# reduce by MAX: max(0.5, 2.5, 3.5, 1.5) = 3.5
recv_obj = comm.allreduce(send_obj, op=MPI.MAX)
print 'allreduce by MAX: rank %d has %s' % (rank, recv_obj)
# ------------------------------------------------------------------------------
# reduce numpy arrays from each process by using Allreduce
send_buf = np.array([0, 1], dtype='i') + 2 * rank
recv_buf = np.empty(2, dtype='i')
# Reduce by SUM: [0, 1] + [2, 3] + [4, 5] + [6, 7] = [12, 16]
comm.Allreduce(send_buf, recv_buf, op=MPI.SUM)
print 'Allreduce by SUM: rank %d has %s' % (rank, recv_buf)
# ------------------------------------------------------------------------------
# reduce numpy arrays from each process by using Allreduce with MPI.IN_PLACE
recv_buf = np.array([0, 1], dtype='i') + 2 * rank
# Reduce by SUM with MPI.IN_PLACE: [0, 1] + [2, 3] + [5, 6] + [6, 7] = [12, 16]
# recv_buf used as both send buffer and receive buffer
comm.Allreduce(MPI.IN_PLACE, recv_buf, op=MPI.SUM)
print 'Allreduce by SUM with MPI.IN_PLACE: rank %d has %s' % (rank, recv_buf)
运行结果如下：
$ mpiexec -n 4 python allreduce.py
allreduce by SUM: rank 2 has 8.0
allreduce by SUM: rank 0 has 8.0
allreduce by SUM: rank 1 has 8.0
allreduce by SUM: rank 3 has 8.0
allreduce by MAX: rank 3 has 3.5
allreduce by MAX: rank 2 has 3.5
allreduce by MAX: rank 0 has 3.5
Allreduce by SUM: rank 0 has [12 16]
allreduce by MAX: rank 1 has 3.5
Allreduce by SUM: rank 1 has [12 16]
Allreduce by SUM with MPI.IN_PLACE: rank 0 has [12 16]
Allreduce by SUM: rank 3 has [12 16]
Allreduce by SUM with MPI.IN_PLACE: rank 3 has [12 16]
Allreduce by SUM: rank 2 has [12 16]
Allreduce by SUM with MPI.IN_PLACE: rank 2 has [12 16]
Allreduce by SUM with MPI.IN_PLACE: rank 1 has [12 16]
以上我们介绍了 mpi4py 中的全规约操作方法，在下一篇中我们将介绍规约发散操作。
