参考自：https://blog.csdn.net/lcx543576178/article/details/45892839

程序稍作修改，如下：

#include<iostream>
using namespace std;
#include<mpi.h>

int main(int argc, char * argv[] ){

    double start, stop;
    int *a, *b, *c, *buffer, *ans;
    int size = 1000;
    int rank, numprocs, line;

    MPI_Init(NULL,NULL);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &numprocs);

    line = size/numprocs;

    b = new int [ size * size ];
    ans = new int [ size * line ];

    start = MPI_Wtime();

    if( rank ==0 ){

        a = new int [ size * size ];
        c = new int [ size * size ];

        for(int i=0;i<size; i++)
        for(int j=0;j<size; j++){
            a[ i*size + j ] = i*j;
            b[ i*size + j ] = i + j;
        }

        for(int i=1;i<numprocs;i++){// send b
            MPI_Send( b, size*size, MPI_INT, i, 0, MPI_COMM_WORLD );
        }

        for(int i=1;i<numprocs;i++){// send part of a
            MPI_Send( a + (i-1)*line*size, size*line, MPI_INT, i, 1, MPI_COMM_WORLD);
        }

        for(int i = (numprocs-1)*line;i<size;i++){// calculate block 1
            for(int j=0;j<size;j++){
                int temp = 0;
                for(int k=0;k<size;k++)
                    temp += a[i*size+k]*b[k*size+j];
                c[i*size+j] = temp;
            }
        }

        for(int k=1;k<numprocs;k++){// recieve ans
            MPI_Recv( ans, line*size, MPI_INT, k, 3, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
            for(int i=0;i<line;i++){
                for(int j=0;j<size;j++){
                    c[ ((k-1)*line + i)*size + j] = ans[i*size+j];
                }
            }
        }

        FILE *fp = fopen("c.txt","w");
        for(int i=0;i<size;i++){
            for(int j=0;j<size;j++)
                fprintf(fp,"%d\t",c[i*size+j]);
            fputc('\n',fp);
        }
        fclose(fp);
        
        stop = MPI_Wtime();

        printf("rank:%d time:%lfs\n",rank,stop-start);

        delete [] a,c;

    }
    else{
        buffer = new int [ size * line ];

        MPI_Recv(b, size*size, MPI_INT, 0, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
        MPI_Recv(buffer, size*line, MPI_INT, 0, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
        for(int i=0;i<line;i++)
        for(int j=0;j<size;j++){
            int temp=0;
            for(int k=0;k<size;k++)
                temp += buffer[i*size+k]*b[k*size+j];
            ans[i*size+j] = temp;
        }
        MPI_Send(ans, line*size, MPI_INT, 0, 3, MPI_COMM_WORLD);

        delete [] buffer;
        delete [] ans;
    }

    delete [] b;

    MPI_Finalize();

    return 0;
}

线程 0 发送矩阵 b，以及 a 的分块矩阵给其他线程，然后自己做一部分矩阵乘法，然后接收其他线程的结果，然后输出最终答案。

 

2. 用 MPI_Scatter 和 MPI_Gather，代码同样参考自 https://blog.csdn.net/lcx543576178/article/details/45892839

稍作修改，如下：

#include<iostream>
using namespace std;
#include<mpi.h>

int main(){

    int my_rank;
    int num_procs;
    int size = 1000;
    double start, finish;

    MPI_Init(NULL,NULL);
    MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
    MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
    
    int line = size / num_procs;
    cout<<" line = "<<line<<endl;
    int * local_a = new int [ line * size ];
    int * b = new int [ size * size ];
    int * ans = new int [ line * size ];
    int * a = new int [ size * size ];
    int * c = new int [ size * size ];

    if( my_rank == 0 ){

        start = MPI_Wtime();

        for(int i=0;i<size;i++){
            for(int j=0;j<size;j++){
                a[ i*size + j ] = i*j;
                b[ i*size + j ] = i + j;
            }
        }

        MPI_Scatter(a, line * size, MPI_INT, local_a, line * size, MPI_INT, 0, MPI_COMM_WORLD );

        MPI_Bcast(b, size*size, MPI_INT, 0, MPI_COMM_WORLD);

        for(int i= 0; i< line;i++){
            for(int j=0;j<size;j++){
                int temp = 0;
                for(int k=0;k<size;k++)
                    temp += a[i*size+k] * b[k*size + j];
                ans[i*size + j ] = temp;
            }
        }

        MPI_Gather( ans, line * size, MPI_INT, c, line * size, MPI_INT, 0, MPI_COMM_WORLD );

        for(int i= num_procs *line; i< size;i++){
            for(int j=0;j<size;j++){
                int temp = 0;
                for(int k=0;k<size;k++)
                    temp += a[i*size+k] * b[k*size + j];
                c[i*size + j ] = temp;
            }
        }

        FILE *fp = fopen("c2.txt","w");
                for(int i=0;i<size;i++){
                        for(int j=0;j<size;j++)
                                fprintf(fp,"%d\t",c[i*size+j]);
                        fputc('\n',fp);
                }
                fclose(fp);

        finish = MPI_Wtime();
        printf(" time: %lf s \n", finish - start );
    }
    else{
        int * buffer = new int [ size * line ];
        MPI_Scatter(a, line * size, MPI_INT, buffer, line * size, MPI_INT, 0, MPI_COMM_WORLD );
        MPI_Bcast( b, size * size, MPI_INT, 0, MPI_COMM_WORLD );
        /*
        cout<<" b:"<<endl;
        for(int i=0;i<size;i++){
            for(int j=0;j<size;j++){
                cout<<b[i*size + j]<<",";
            }
            cout<<endl;
        }
        */

        for(int i=0;i<line;i++){
            for(int j=0;j<size;j++){
                int temp = 0;
                for(int k=0;k<size;k++)
                    temp += buffer[i*size+k] * b[k*size + j];
                //cout<<"i = "<<i<<"\t j= "<<j<<"\t temp = "<<temp<<endl;
                ans[i*size + j] = temp;
            }
        }

        /*
        cout<<" ans:"<<endl;
        for(int i=0;i<line;i++){
            for(int j=0;j<size;j++){
                cout<<ans[i*size + j]<<",";
            }
            cout<<endl;
        }
        */

        MPI_Gather(ans, line*size, MPI_INT, c, line*size, MPI_INT, 0, MPI_COMM_WORLD );
        delete [] buffer;
    }

    delete [] a, local_a, b, ans, c;

    MPI_Finalize();
    return 0;
}

进程 0 向所有进程（包括自己）分发（MPI_Scatter）a 矩阵的各个分块矩阵，并广播（MPI_Bcast）b 矩阵。其他进程接收 a 的分块矩阵与 b 矩阵，做乘法，并返回结果（MPI_Gather）。进程 0 收集所有结果（包括自己的）（MPI_Gather），如果 a 矩阵分块有剩余，进程 0 就做掉相关乘法，最后输出所有结果。

 

3. 测时间。下图为上面两种方法的耗时，

4. 总结：①确实进程越多，耗时越少。

　　　　②由于消息传递需要成本，而且不是每个进程都同时开始和结束，所以随着进程数的上升，平均每进程的效率下降。