一、Jacobi迭代

#include<stdio.h>
#include<mpi.h>
#include<stdlib.h>

#define totalsize 16
#define mysize totalsize / 4
#define steps 10
int main(int argc, char** argv)
{
    int rank, size, i, j, begin_col, end_col;
    //除分块大小外，还包括左右两边各一列
    float a[totalsize][mysize + 2], b[totalsize][mysize + 2];
    float temp[totalsize];//临时数组
    MPI_Status status;
    MPI_Init(&argc, &argv);
    MPI_Comm_size(MPI_COMM_WORLD, &size);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);

    printf("Process %d of %d is alive\n", rank, size);

    //数组初始化
    for (i = 0; i < totalsize; i++)
        for (j = 0; j < mysize + 2; j++)
            a[i][j] = 0;
    if (rank == 0)
    {
        for (i = 0; i < totalsize; i++)
            a[i][1] = 8.0;
    }
    if (rank == 3)
    {
        for (i = 0; i < totalsize; i++)
            a[i][mysize] = 8.0;
    }
    for (i = 1; i < mysize + 1; i++)
    {
        a[0][i] = 8.0;
        a[totalsize - 1][i] = 8.0;
    }
    //Jacobi 迭代
    for (int n = 1; n <= steps; n++)
    {
        //从右边的邻居得到数据
        if (rank < 3)
        {
            MPI_Recv(&temp[0], totalsize, MPI_FLOAT, rank + 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][mysize + 1] = temp[i];
        }
        //向左侧的邻居发送数据
        if (rank > 0)
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][1];
            MPI_Send(&temp[0], totalsize, MPI_FLOAT, rank - 1, 10, MPI_COMM_WORLD);
        }
        //向右侧的邻居发送数据
        if (rank < 3)
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][mysize];
            MPI_Send(&temp[0], totalsize, MPI_FLOAT, rank + 1, 10, MPI_COMM_WORLD);
        }
        //从左侧的邻居得到数据
        if (rank > 0)
        {
            MPI_Recv(&temp[0], totalsize, MPI_FLOAT, rank - 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][0] = temp[i];
        }
        begin_col = 1;
        end_col = mysize;
        if (rank == 0) begin_col = 2;
        if (rank == 3) end_col = mysize - 1;
        for (i = 1; i < totalsize - 1; i++)
            for (j = begin_col; j <= end_col; j++)
                b[i][j] = 0.25 * (a[i][j + 1] + a[i][j - 1] + a[i + 1][j] + a[i - 1][j]);
        for (i = 1; i < totalsize - 1; i++)
            for (j = begin_col; j <= end_col; j++)
                a[i][j] = b[i][j];
    }
    MPI_Barrier(MPI_COMM_WORLD);
    printf("Process %d:\n", rank);
    for (i = 0; i < totalsize; i++)
    {
        for (j = 1; j <= mysize; j++)
            printf("%.2fP%d\t", a[i][j], rank);
        printf("\n");
    }
    MPI_Finalize();
    return 0;
}

二、用捆绑发送接收实现Jacobi 迭代

#include<stdio.h>
#include<mpi.h>
#include<stdlib.h>

#define totalsize 16
#define mysize totalsize / 4
#define steps 10
int main(int argc, char** argv)
{
    int rank, size, i, j, begin_col, end_col;
    //除分块大小外，还包括左右两边各一列
    float a[totalsize][mysize + 2], b[totalsize][mysize + 2];
    float temp[totalsize],temp1[totalsize];//临时数组
    MPI_Status status;
    MPI_Init(&argc, &argv);
    MPI_Comm_size(MPI_COMM_WORLD, &size);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);

    printf("Process %d of %d is alive\n", rank, size);

    //数组初始化
    for (i = 0; i < totalsize; i++)
        for (j = 0; j < mysize + 2; j++)
            a[i][j] = 0;
    if (rank == 0)
    {
        for (i = 0; i < totalsize; i++)
            a[i][1] = 8.0;
    }
    if (rank == 3)
    {
        for (i = 0; i < totalsize; i++)
            a[i][mysize] = 8.0;
    }
    for (i = 1; i < mysize + 1; i++)
    {
        a[0][i] = 8.0;
        a[totalsize - 1][i] = 8.0;
    }
    //Jacobi 迭代
    for (int n = 1; n <= steps; n++)
    {
        //从左向右平移数据
        if (rank == 0)
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][mysize];
            MPI_Send(&temp[0], totalsize, MPI_FLOAT, rank + 1, 10, MPI_COMM_WORLD);

        }
        else if (rank == 3)
        {
            MPI_Recv(&temp[0], totalsize, MPI_FLOAT, rank - 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][1] = temp[i];
        }
        else
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][1];
            MPI_Sendrecv(&temp[0], totalsize, MPI_FLOAT, rank - 1, 10, &temp1[0], totalsize, MPI_FLOAT, \
                rank + 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][1] = temp1[i];
        }
        //从右向左平移数据
        if (rank == 0)
        {
            MPI_Recv(&temp[0], totalsize, MPI_FLOAT, rank + 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][mysize] = temp[i];
        }
        else if (rank == 3)
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][1];
            MPI_Send(&temp, totalsize, MPI_FLOAT, rank - 1, 10, MPI_COMM_WORLD);
        }
        else
        {
            for (i = 0; i < totalsize; i++)
                temp[i] = a[i][1];
            MPI_Sendrecv(&temp[0], totalsize, MPI_FLOAT, rank + 1, 10, &temp1[0], totalsize, MPI_FLOAT, \
                rank - 1, 10, MPI_COMM_WORLD, &status);
            for (i = 0; i < totalsize; i++)
                a[i][mysize] = temp1[i];
        }
        begin_col = 1;
        end_col = mysize;
        if (rank == 0) begin_col = 2;
        if (rank == 3) end_col = mysize - 1;
        for (i = 1; i < totalsize - 1; i++)
            for (j = begin_col; j <= end_col; j++)
                b[i][j] = 0.25 * (a[i][j + 1] + a[i][j - 1] + a[i + 1][j] + a[i - 1][j]);
        for (i = 1; i < totalsize - 1; i++)
            for (j = begin_col; j <= end_col; j++)
                a[i][j] = b[i][j];
    }
    MPI_Barrier(MPI_COMM_WORLD);
    printf("Process %d:\n", rank);
    for (i = 0; i < totalsize; i++)
    {
        for (j = 1; j <= mysize; j++)
            printf("%.2fP%d\t", a[i][j], rank);
        printf("\n");
    }
    MPI_Finalize();
    return 0;
}

矩阵乘

#include <stdio.h>
#include "mpi.h"
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

#define SIZE 5
//生成随机矩阵
int** generate_matrix(int size)
{
    int num = 0, m;
    int** matrix;
    matrix = (int**)malloc(sizeof(int*) * size);
    for (m = 0; m < size; m++)
        matrix[m] = (int*)malloc(sizeof(int) * size);
    int i, j;
    srand(time(NULL) + rand());
    for (i = 0; i < size; i++)
    {
        for (j = 0; j < size; j++)
        {
            matrix[i][j] = rand() % 20;
        }
    }
    return matrix;
}
//输出矩阵
void print_matrx(int** a, int size)
{
    int i, j;
    for (i = 0; i < size; i++)
    {
        for (j = 0; j < size; j++)
        {
            printf("%d ", a[i][j]);
        }
        printf("\n");
    }
    printf("\n");
}
//矩阵相乘([参考](https://blog.csdn.net/qq_35614920/article/details/80570839))
int* Multiplication(int** a, int b[], int size)
{
    int* result;
    result = (int*)malloc(sizeof(int) * size);
    int i, m, n, sum = 0;
    for (m = 0; m < size; m++)
    {
        for (n = 0; n < size; n++)
        {
            sum += a[n][m] * b[n];
        }
        result[m] = sum;
        sum = 0;
    }
    return result;
}
int main(int argc, char** argv)
{
    int size, rank, dest;
    MPI_Comm comm = MPI_COMM_WORLD;
    MPI_Status status;
    MPI_Init(&argc, &argv);
    MPI_Comm_size(comm, &size);
    MPI_Comm_rank(comm, &rank);

    int** matrix1;
    int** matrix2;
    int send_buff[SIZE* SIZE];
    matrix1 = generate_matrix(size);
    matrix2 = generate_matrix(size);
    if (rank == 0)
    {
        printf("matrix1 is :\n");
        print_matrx((int**)matrix1, size);

        printf("matrix2 is :\n");
        print_matrx((int**)matrix2, size);

        int j, k, tmp = 0;
        for (j = 0; j < size; j++)
            for (k = 0; k < size; k++)
            {
                send_buff[tmp] = matrix1[j][k];
                tmp++;
            }
    }
    int rbuf[SIZE];
    int* result;
    result = (int*)malloc(sizeof(int) * size);
    //分发列
    MPI_Scatter(send_buff, size, MPI_INT, rbuf, size, MPI_INT, 0, comm);
    result = Multiplication((int**)matrix2, rbuf, size);
    MPI_Barrier(comm);//等待所有进程计算结束
    int* recv_buff;
    recv_buff = (int*)malloc(sizeof(int) * size * size);
    MPI_Barrier(comm);
    MPI_Gather(result, size, MPI_INT, recv_buff, size, MPI_INT, 0, comm);//收集各列数据
    //根进程进行输出
    if (rank == 0)
    {
        printf("\nresult is :\n");
        int m, n, tmp = 0;
        for (m = 0; m < size; m++)
        {
            for (n = 0; n < size; n++)
            {
                printf("%d ", recv_buff[tmp]);
                tmp++;
            }
            printf("\n");
        }
        printf("\n");
    }
    MPI_Finalize();
    return 0;
}