用MPI_Scatterv和MPI_Gatherv计算矩阵乘法

好的，下面是使用MPI_Scatterv和MPI_Gatherv来计算矩阵乘法的示例代码：

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

#define MATRIX_SIZE 4

int main(int argc, char* argv[]) {
    int rank, size;
    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    if (size != MATRIX_SIZE) {
        printf("Error: the number of processes must be %d\n", MATRIX_SIZE);
        MPI_Abort(MPI_COMM_WORLD, 1);
    }

    int matrix_a[MATRIX_SIZE][MATRIX_SIZE] = {
        {1, 2, 3, 4},
        {5, 6, 7, 8},
        {9, 10, 11, 12},
        {13, 14, 15, 16}
    };

    int matrix_b[MATRIX_SIZE][MATRIX_SIZE] = {
        {1, 2, 3, 4},
        {5, 6, 7, 8},
        {9, 10, 11, 12},
        {13, 14, 15, 16}
    };

    int local_matrix_a[MATRIX_SIZE][MATRIX_SIZE/MATRIX_SIZE];
    int local_matrix_b[MATRIX_SIZE/MATRIX_SIZE][MATRIX_SIZE];
    int local_matrix_c[MATRIX_SIZE/MATRIX_SIZE][MATRIX_SIZE/MATRIX_SIZE];

    int sendcounts[MATRIX_SIZE];
    int displs[MATRIX_SIZE];

    // scatter matrix_a
    for (int i = 0; i < MATRIX_SIZE; i++) {
        int local_cols = MATRIX_SIZE / size;
        sendcounts[i] = local_cols;
        displs[i] = i * local_cols;
    }
    MPI_Scatterv(matrix_a, sendcounts, displs, MPI_INT, local_matrix_a, MATRIX_SIZE * MATRIX_SIZE / size, MPI_INT, 0, MPI_COMM_WORLD);

    // scatter matrix_b
    for (int i = 0; i < MATRIX_SIZE; i++) {
        int local_rows = MATRIX_SIZE / size;
        sendcounts[i] = local_rows;
        displs[i] = i * local_rows;
    }
    MPI_Scatterv(matrix_b, sendcounts, displs, MPI_INT, local_matrix_b, MATRIX_SIZE * MATRIX_SIZE / size, MPI_INT, 0, MPI_COMM_WORLD);

    // calculate local_matrix_c
    for (int i = 0; i < MATRIX_SIZE/MATRIX_SIZE; i++) {
        for (int j = 0; j < MATRIX_SIZE/MATRIX_SIZE; j++) {
            local_matrix_c[i][j] = 0;
            for (int k = 0; k < MATRIX_SIZE; k++) {
                local_matrix_c[i][j] += local_matrix_a[i][k] * local_matrix_b[k][j];
            }
        }
    }

    // gather matrix_c
    MPI_Gatherv(local_matrix_c, MATRIX_SIZE * MATRIX_SIZE / size, MPI_INT, matrix_c, sendcounts, displs, MPI_INT, 0, MPI_COMM_WORLD);

    if (rank == 0) {
        printf("Matrix C:\n");
        for (int i = 0; i < MATRIX_SIZE; i++) {
            for (int j = 0; j < MATRIX_SIZE; j++) {
                printf("%d ", matrix_c[i][j]);
            }
            printf("\n");
        }
    }

    MPI_Finalize();
    return 0;
}

在这个示例中，矩阵A和矩阵B都是4x4的矩阵。我们将使用4个进程来计算矩阵乘积，每个进程计算结果的一部分。使用MPI_Scatterv将矩阵A和矩阵B分发到各个进程中，并使用MPI_Gatherv将结果收集回主进程。在每个进程中，我们使用双重循环计算局部矩阵的乘积，并将结果存储在局部矩阵C中。最后，我们在主进程中输出完整的矩阵C。