```c #include <stdio.h> #include <stdlib.h> #include <math.h> #include <mpi.h> #define N 1024 #define MAX_ITER 1000 #define EPSILON 0.001 // 定义子块的大小 #define BLOCK_SIZE (N / 8) int main(int argc, char *argv[]) { int rank, size; int i, j, iter; double diff, sum_diff, local_diff; double u[BLOCK_SIZE + 2][BLOCK_SIZE + 2], u_new[BLOCK_SIZE + 2][BLOCK_SIZE + 2]; double start_time, end_time; MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &rank); MPI_Comm_size(MPI_COMM_WORLD, &size); // 创建笛卡尔虚拟拓扑 int dims[2] = {8, 8}; // 二维网格的维度 int periods[2] = {0, 0}; // 周期性拓扑 int coords[2]; // 进程的坐标 MPI_Comm cart_comm; MPI_Cart_create(MPI_COMM_WORLD, 2, dims, periods, 0, &cart_comm); MPI_Cart_coords(cart_comm, rank, 2, coords); // 计算当前进程的子块在全局数组中的起始索引 int start_row = coords[0] * BLOCK_SIZE; int start_col = coords[1] * BLOCK_SIZE; // 初始化子块 for (i = 1; i <= BLOCK_SIZE; i++) { for (j = 1; j <= BLOCK_SIZE; j++) { u[i][j] = 0.0; } } // 执行Jacobi迭代 iter = 0; diff = EPSILON + 1; start_time = MPI_Wtime(); while (iter < MAX_ITER && diff > EPSILON) { // 保存上一次迭代的结果 for (i = 1; i <= BLOCK_SIZE; i++) { for (j = 1; j <= BLOCK_SIZE; j++) { u_new[i][j] = u[i][j]; } } // 进行Jacobi迭代计算 sum_diff = 0.0; for (i = 1; i <= BLOCK_SIZE; i++) { for (j = 1; j <= BLOCK_SIZE; j++) { u[i][j] = (u_new[i-1][j] + u_new[i+1][j] + u_new[i][j-1] + u_new[i][j+1]) * 0.25; local_diff = fabs(u[i][j] - u_new[i][j]); sum_diff += local_diff; } } // 全局计算总体差异 MPI_Allreduce(&sum_diff, &diff, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); // 进行进程间的数据交换 MPI_Request requests[8]; MPI_Status statuses[8]; // 向上邻居发送第一行 if (coords[0] > 0) { MPI_Isend(&u[1][1], BLOCK_SIZE, MPI_DOUBLE, rank - dims[1], 0, cart_comm, &requests[0]); } // 向下邻居发送最后一行 if (coords[0] < dims[0] - 1) { MPI_Isend(&u[BLOCK_SIZE][1], BLOCK_SIZE, MPI_DOUBLE, rank + dims[1], 0, cart_comm, &requests[1]); } // 从上邻居接收第一行 if (coords[0] > 0) { MPI_Irecv(&u[0][1], BLOCK_SIZE, MPI_DOUBLE, rank - dims[1], 0, cart_comm, &requests[2]); } // 从下邻居接收最后一行 if (coords[0] < dims[0] - 1) { MPI_Irecv(&u[BLOCK_SIZE + 1][1], BLOCK_SIZE, MPI_DOUBLE, rank + dims[1], 0, cart_comm, &requests[3]); } // 向左邻居发送第一列 if (coords[1] > 0) { MPI_Isend(&u[1][1], 1, MPI_DOUBLE, rank - 1, 0, cart_comm, &requests[4]); } // 向右邻居发送最后一列 if (coords[1] < dims[1] - 1) { MPI_Isend(&u[1][BLOCK_SIZE], 1, MPI_DOUBLE, rank + 1, 0, cart_comm, &requests[5]); } // 从左邻居接收第一列 if (coords[1] > 0) { MPI_Irecv(&u[1][0], 1, MPI_DOUBLE, rank - 1, 0, cart_comm, &requests[6]); } // 从右邻居接收最后一列 if (coords[1] < dims[1] - 1) { MPI_Irecv(&u[1][BLOCK_SIZE + 1], 1, MPI_DOUBLE, rank + 1, 0, cart_comm, &requests[7]); } // 等待通信完成 MPI_Waitall(8, requests, statuses); iter++; } end_time = MPI_Wtime(); // 打印每个进程的执行时间 double *execution_times = NULL; if (rank == 0) { execution_times = (double *)malloc(size * sizeof(double)); } MPI_Gather(&end_time, 1, MPI_DOUBLE, execution_times, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD); if (rank == 0) { printf("Execution Times:\n"); for (i = 0; i < size; i++) { printf("Process %d: %lf seconds\n", i, execution_times[i] - start_time); } free(execution_times); } MPI_Finalize(); return 0; } ``` 这是一个使用MPI实现Jacobi迭代算法的程序。程序使用了二维笛卡尔虚拟拓扑，将数据分解为多个二维子块，并使用非阻塞通信接口进行进程间的数据交换。每个进程负责计算和更新自己的子块。程序还打印了每个进程的执行时间。 请注意，该代码只提供了基本的框架和关键部分的代码示例，实际使用时需要根据具体的需求和问题进行适当的修改和优化。 |
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