矩阵每个元素都是其上下左右四个元素的平均值，矩阵四个边界的值不变。请使用MPI设计一个求该矩阵中所有值的程序。

下面是一个使用MPI实现的求矩阵平均值的程序：

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

#define N 1000
#define EPSILON 0.000001

double A[N][N];
double B[N][N];

int main(int argc, char *argv[]) {
    int rank, size, i, j, iters = 0;
    double diff, sum, local_sum;
    MPI_Status status;

    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    int rows_per_process = N / size;
    int extra_rows = N % size;

    if (rank == 0) {
        // Initialize the matrix A
        for (i = 0; i < N; i++) {
            for (j = 0; j < N; j++) {
                A[i][j] = rand() % 10;
            }
        }

        // Distribute the matrix A
        for (i = 1; i < size; i++) {
            int rows_to_send = rows_per_process + (i <= extra_rows ? 1 : 0);
            MPI_Send(&A[i * rows_per_process - extra_rows][0], rows_to_send * N, MPI_DOUBLE, i, 0, MPI_COMM_WORLD);
        }

        // Calculate the local sum for process 0
        local_sum = 0.0;
        for (i = 1; i < rows_per_process + 1; i++) {
            for (j = 1; j < N - 1; j++) {
                B[i][j] = (A[i-1][j] + A[i+1][j] + A[i][j-1] + A[i][j+1]) / 4.0;
                local_sum += B[i][j];
            }
        }

        // Receive the results from other processes and accumulate the sum
        sum = local_sum;
        for (i = 1; i < size; i++) {
            MPI_Recv(&local_sum, 1, MPI_DOUBLE, i, 0, MPI_COMM_WORLD, &status);
            sum += local_sum;
        }

        // Print the result
        printf("The average of all elements in the matrix is %f\n", sum / (N * N));
    } else {
        // Allocate memory for the local matrix
        int rows = rows_per_process + (rank <= extra_rows ? 1 : 0);
        double local_A[rows + 2][N];
        double local_B[rows + 2][N];

        // Receive the matrix A from process 0
        int rows_to_recv = rows + (rank <= extra_rows ? 1 : 0);
        MPI_Recv(&local_A[1][0], rows_to_recv * N, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD, &status);

        // Calculate the local sum
        local_sum = 0.0;
        for (i = 1; i < rows + 1; i++) {
            for (j = 1; j < N - 1; j++) {
                local_B[i][j] = (local_A[i-1][j] + local_A[i+1][j] + local_A[i][j-1] + local_A[i][j+1]) / 4.0;
                local_sum += local_B[i][j];
            }
        }

        // Send the result back to process 0
        MPI_Send(&local_sum, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);
    }

    MPI_Finalize();
    return 0;
}

该程序使用了MPI，在多个进程之间分配矩阵的不同部分，然后并行计算每个进程的部分，最后将结果收集到进程0中。