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#include <mpi.h> #include <vector> // A function to perform local matrix multiplication. void local_matrix_multiply(const std::vector<int>& A, const std::vector<int>& B, std::vector<int>& C, int block_size) { // Implement your matrix multiplication logic here. // For example, a simple triple nested loop for matrix multiplication. } int main(int argc, char* argv[]) { MPI_Init(&argc, &argv); // Assuming we have Px * Px * Pz processors and square matrices of size N const int Px = 2; // Number of processors in each row/column in a 2D layer const int Pz = 2; // Number of layers const int N = 4; // Matrix size (N x N) int rank, size; MPI_Comm_rank(MPI_COMM_WORLD, &rank); MPI_Comm_size(MPI_COMM_WORLD, &size); // Validate our assumptions if(size != Px * Px * Pz) { if(rank == 0) { std::cerr << "The number of processors does not match Px * Px * Pz." << std::endl; } MPI_Finalize(); return -1; } // Create 3D Cartesian topology for processors int dims[3] = {Px, Px, Pz}; int periods[3] = {1, 1, 1}; // Enable wrapping for circular shifts MPI_Comm grid_comm; MPI_Cart_create(MPI_COMM_WORLD, 3, dims, periods, 1, &grid_comm); // Get new rank and coordinates in the grid int grid_rank, coords[3]; MPI_Comm_rank(grid_comm, &grid_rank); MPI_Cart_coords(grid_comm, grid_rank, 3, coords); // Calculate block size for each processor int block_size = N / (Px * Pz); // Assuming N is evenly divisible by Px * Pz // Allocate memory for local blocks of A, B, and C std::vector<int> A_block(block_size * block_size, 0); std::vector<int> B_block(block_size * block_size, 0); std::vector<int> C_block(block_size * block_size, 0); // Distribute initial blocks of A and B to processors (omitted for brevity) // ... // Perform initial local matrix multiplication local_matrix_multiply(A_block, B_block, C_block, block_size); // Get rank of right and downward neighbors for A and B shifting int right_src, right_dst, down_src, down_dst; MPI_Cart_shift(grid_comm, 1, 1, &right_src, &right_dst); // Shift along the second dimension (j) MPI_Cart_shift(grid_comm, 0, 1, &down_src, &down_dst); // Shift along the first dimension (i) // Circular shift and local multiplication for Pz steps for(int step = 0; step < Pz; ++step) { // Circularly shift A rightwards and B downwards std::vector<int> A_recv(block_size * block_size), B_recv(block_size * block_size); MPI_Status status; // Shift A rightwards MPI_Sendrecv_replace(A_block.data(), block_size * block_size, MPI_INT, right_dst, 0, right_src, 0, grid_comm, &status); // Shift B downwards MPI_Sendrecv_replace(B_block.data(), block_size * block_size, MPI_INT, down_dst, 1, down_src, 1, grid_comm, &status); // Perform local matrix multiplication with the received blocks local_matrix_multiply(A_block, B_block, C_block, block_size); } // Gather the local C blocks into the global C matrix (omitted for brevity) // ... // Clean up MPI_Comm_free(&grid_comm); MPI_Finalize(); return 0; }
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