MPI学习——jacabi迭代（非阻塞通信与重复阻塞通信）

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原创最新推荐文章于 2026-07-05 10:28:47 发布 1.4k 阅读 AI 写同款· GEO 优化 ›

史上最完整的MPI实现Jacobi(雅可比)迭代算法[C++] 史上最详细的MPI 雅可比迭代算法实现(c++) 阅读详情

为了实现计算与通信的最大重叠一个通用的原则就是尽早开始通信尽晚完成通信
在开始通信和完成通信之间进行计算这样通信启动得越早完成得越晚就有可能有更多
的计算任务可以和通信重叠也使通信可以在计算任务执行期间完成而不需要专门的等待
时间
为此修改Jacobi迭代过程如下
1 计算迭代任务中下次需要通信的数据
2 启动非阻塞通信传递这些数据转下一次迭代
3 计算剩余的迭代部分

4 完成非阻塞通信

#include<mpi.h>
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 8;
const int SIZE = N / 4;
const int T = 2;


int main()
{
    double matrix1[SIZE+2][N], matrix[SIZE+2][N];
    int myid;
    MPI_Status status[4];
    MPI_Request request[4];


    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);


    memset(matrix1, 0, sizeof matrix1);
    memset(matrix2, 0, sizeof matrix2);


    //赋值边界数据
    if(0 == myid)
        for(int j = 0; j < N; j++)
            matrix1[1][j] = matrix[2][j] = N;
    if(3 == myid)
        for(int j = 0; j < N; j++)
            matrix1[SIZE][j] = matrix2[SIZE][j] = N;
    for(int i = 1; i < SIZE+1; i++)
        matrix1[i][0] = matrix1[i][N-1] = matrix2[0] = matrix2[N-1] = N;

      
    //引入虚拟进程简化代码
    int up_proc_id = myid==0 ? MPI_PROC_NULL : myid - 1;
    int down_proc_id = myid==3 ? MPI_PROC_NULL : myid + 1;
    //jacobi迭代
    int t, row, col;
    for(t = 0; t < T; t++)
    {
        if(0 == myid)
            for(col = 1; col < N-1; col++)
                matrix2[SIZE][col] = 0.25 * (matrix1[SIZE][col-1] + matrix1[SIZE][col+1] + matrix1[SIZE-1][col] + matrix[SIZE+1][col]);
        else if(3 == myid)
            for(col = 1; col < N-1; col++)
                matrix2[1][col] = 0.25 * (matrix1[1][col-1] + matrix1[1][col+1] + matrix1[0][col] + matrix1[2][col]);;
        else
            for(col = 1; col < N-1; col++) // 中间的矩阵块
                matrix2[SIZE][col] = 0.25 * (matrix1[SIZE][col-1] + matrix1[SIZE][col+1] + matrix1[SIZE+1][col] + matrix1[SIZE-1][col]);
                matrix2[1][col] = 0.25 * (matrix1[1][col-1] + matrix1[1][col+1] + matrix1[2][col] + matrix1[0][col]);
        //利用非阻塞通信传递边界数据
        int tag1 = 1, tag2 = 2;
        MPI_Isend(&matrix2[1][0], N, MPI_DOUBLE, up_proc_id, tag1, MPI_COMM_WORLD, request[0]);
        MPI_Isend(&matrix2[SIZE][0], N, MPI_DOUBLE, down_proc_id, tag2, MPI_COMM_WORLD, request[1]);
        MPI_Irecv(&matrix1[SIZE+1][0], N, MPI_DOUBLE, down_proc_id, tag1, MPI_COMM_WORLD, request[2]);
        MPI_Irecv(&matrix1[0][0], N, MPI_DOUBLE, up_proc_id, tag1, MPI_COMM_WORLD, request[3]);


        //利用通信的时间计算矩阵中间值
        int begin_row = 0==myid ? 2 : 1;
        int end_row = 3==myid ? (SIZE-1) : (SIZE);
        for (row = begin_row; row < end_row; row++)
            for (col = 1; col < N-1; col++)
                matrix2[row][col] = 0.25 * (matrix1[row][col-1] + matrix1[row][col+1] + matrix1[row+1][col] + matrix1[row-1][col]);


        //利用通信的时间更新矩阵
        for(row = begin_row; row <= end_row; row++)
            for(col = 1; col < N-1; col++)
                matrix1[row][col] = matrix2[row][col];
        MPI_Waitall(4, &request[0], &status[0]);
    }
    MPI_Barrier(MPI_COMM_WORLD);
    MPI_Finalize();
    return 0;
}

如果一个通信会被重复执行比如循环结构内的通信调用 MPI提供了特殊的实现方式对这样的通信进行优化以降低不必要的通信开销它将通信参数和MPI的内部对象建立固定的联系然后通过该对象完成重复通信的任务。大致步骤如下
1 通信的初始化比如MPI_SEND_INIT
2 启动通信 MPI_START
3 完成通信 MPI_WAIT
4 释放查询对象 MPI_REQUEST_FREE

#include<mpi.h>
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N = 8;
const int SIZE = N / 4;
const int T = 2;

int main()
{
    double matrix1[SIZE+2][N], matrix[SIZE+2][N];
    int myid;
    MPI_Status status[4];
    MPI_Request request[4];

    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);

    memset(matrix1, 0, sizeof matrix1);
    memset(matrix2, 0, sizeof matrix2);

    //赋值边界数据
    if(0 == myid)
        for(int j = 0; j < N; j++)
            matrix1[1][j] = matrix[2][j] = N;
    if(3 == myid)
        for(int j = 0; j < N; j++)
            matrix1[SIZE][j] = matrix2[SIZE][j] = N;
    for(int i = 1; i < SIZE+1; i++)
        matrix1[i][0] = matrix1[i][N-1] = matrix2[0] = matrix2[N-1] = N;
    //引入虚拟进程简化代码
    int up_proc_id = myid==0 ? MPI_PROC_NULL : myid - 1;
    int down_proc_id = myid==3 ? MPI_PROC_NULL : myid + 1;
    //初始化重复非阻塞通信
    int tag1 = 1, tag2 = 2;
    MPI_Send_init(&matrix2[1][0], N, MPI_DOUBLE, up_proc_id, tag1, MPI_COMM_WORLD, request[0]);
    MPI_Send_init(&matrix2[SIZE][0], N, MPI_DOUBLE, down_proc_id, tag2, MPI_COMM_WORLD, request[1]);
    MPI_Recv_init(&matrix1[SIZE+1][0], N, MPI_DOUBLE, down_proc_id, tag1, MPI_COMM_WORLD, request[2]);
    MPI_Recv_init(&matrix1[0][0], N, MPI_DOUBLE, up_proc_id, tag1, MPI_COMM_WORLD, request[3]);
    //jacobi迭代
    int t, row, col;
    for(t = 0; t < T; t++)
    {
        if(0 == myid)
            for(col = 1; col < N-1; col++)
                matrix2[SIZE][col] = 0.25 * (matrix1[SIZE][col-1] + matrix1[SIZE][col+1] + matrix1[SIZE-1][col] + matrix[SIZE+1][col]);
        else if(3 == myid)
            for(col = 1; col < N-1; col++)
                matrix2[1][col] = 0.25 * (matrix1[1][col-1] + matrix1[1][col+1] + matrix1[0][col] + matrix1[2][col]);;
        else
            for(col = 1; col < N-1; col++) // 中间的矩阵块
                matrix2[SIZE][col] = 0.25 * (matrix1[SIZE][col-1] + matrix1[SIZE][col+1] + matrix1[SIZE+1][col] + matrix1[SIZE-1][col]);
                matrix2[1][col] = 0.25 * (matrix1[1][col-1] + matrix1[1][col+1] + matrix1[2][col] + matrix1[0][col]);
        //启动非阻塞通信传递边界数据
        MPI_Startall(4, &request[0]);

        //利用通信的时间计算矩阵中间值
        int begin_row = 0==myid ? 2 : 1;
        int end_row = 3==myid ? (SIZE-1) : (SIZE);
        for (row = begin_row; row < end_row; row++)
            for (col = 1; col < N-1; col++)
                matrix2[row][col] = 0.25 * (matrix1[row][col-1] + matrix1[row][col+1] + matrix1[row+1][col] + matrix1[row-1][col]);

        //利用通信的时间更新矩阵
        for(row = begin_row; row <= end_row; row++)
            for(col = 1; col < N-1; col++)
                matrix1[row][col] = matrix2[row][col];
        MPI_Waitall(4, &request[0], &status[0]);
    }
    //释放非阻塞通信对象
    for(int i = 0; i < 4; i++) MPI_Request_free(&request[i]);
    MPI_Barrier(MPI_COMM_WORLD);
    MPI_Finalize();
    return 0;
}

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