Department of Informatics V. HPC-Lab. Session 4: MPI, CG M. Bader, A. Breuer. Alex Breuer

Transcription

1 HPC-Lab Session 4: MPI, CG M. Bader, A. Breuer

2 Meetings Date Schedule 10/13/14 Kickoff 10/20/14 Q&A 10/27/14 Presentation 1 11/03/14 H. Bast, Intel 11/10/14 Presentation 2 12/01/14 Presentation 3 12/08/14 Q&A 12/15/14 Presentation 4 12/22/14 Q&A 01/12/15 Report: Project phase 01/19/15 Presentation Project 2

3 MPI: From Kindergarden to Large Scale Sandy Bridge CPU, /01/03/intel-sandy-bridge-review/1 SuperMUC docs/doc-3126 Stampede 3

4 Hello World #include <mpi.h> void 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); printf("hello World! (rank %d of %d)", rank, size); MPI_Finalize(); } Compile: mpicc -o hello hello.c Execute: mpiexec.hydra -n number_of_processes./hello 4

5 Hello World #include <mpi.h> void 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); printf("hello World! (rank %d of %d)", rank, size); MPI_Finalize(); } int MPI_Comm_size(MPI_Comm comm, int *size) Returns the number of processes in the communicator MPI_COMM_WORLD Predefined standard communicator; Includes all processes of a parallel application. int MPI_Comm_rank(MPI_Comm comm, int *size) Returns the process number of the executing process. 5

6 P2P MPI_Send( void *buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm communicator ); MPI_Recv( void *buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm communicator, MPI_Status *status ); Blocking operations (return when buffer can be reused) rank (dest/source) and tag of send- and recieve-call must match Wildcards for receive-calls: MPI_ANY_SOURCE, MPI_ANY_TAG, MPI_STATUS_IGNORE Messages with same destination rank do not overtake each other (order preservation) 6

7 Datatypes MPI MPI_CHAR MPI_SHORT MPI_INT MPI_LONG MPI_UNSIGNED_CHAR MPI_UNSIGNED C signed char signed short int signed int signed long int unsigned char unsigned int... MPI_FLOAT MPI_DOUBLE float double 7

8 Deadlocked Ring // int rank, size, dest, src; double *s_buf, *r_buf; MPI_Status status; // dest = (rank + 1) % size; src = (rank size) % size; MPI_Send( s_buf, 2, MPI_DOUBLE, dest, 0, MPI_COMM_WORLD ); MPI_Recv( r_buf, 2, MPI_DOUBLE, src, 0, MPI_COMM_WORLD, &status ); //

9 Non-Blocking MPI_Isend( void *buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm communicator, MPI_Request *request ); MPI_Irecv( void *buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm communicator, MPI_Request *request ); Returns immediately Separates communication into three phases Initiate communication Do something else Wait for communication to finish MPI_Request-object is used to test / wait for completition. 9

10 Non-Blocking MPI_Wait( MPI_Request *request, MPI_Status *status ); Waits until pending communication is finished MPI_Test( MPI_Request *request, int *flag, MPI_Status *status ); Tests if pending communication is finished MPI_Waitall, MPI_Testall, MPI_Waitany, MPI_Testany, MPI_Waitsome, MPI_Testsome There s more.. 10

11 Collectives Three types of collective operations Synchronization (MPI_Barrier, ) Communication (MPI_Bcast, ) Reduction (MPI_Allreduce,...) Must be executed by all processes of the communicator All collective operations are blocking operations MPI 3.0 will contain non-blocking collective operations 11

12 Network: BG/Q 12

13 Topologies Processes of a communicator (e.g. MPI_COMM_WORLD) can be mapped to cartesian topology graph topology Allow convenient process naming with cartesian process coordinates May lead to better performance (network aware programming) 13

14 Cartesian MPI_Cart_create( MPI_Comm comm old, int ndims, int *dims, int *periods, int reorder, MPI_Comm *comm cart ); Creates a communicator with cartesian topology MPI_Cart_sub( MPI_Comm comm, int *remain dims, MPI_Comm *newcomm ); Cuts a grid up into slices MPI, B. Barney, LLNL, computing.llnl.gov/tutorials/mpi/ #Virtual_Topologies 14

15 Cartesian MPI_Cart_rank( MPI_Comm comm, int *coords, int *rank ); Converts grid coordinates into process rank MPI_Cart_coords( MPI_Comm comm, int rank, int maxdims, int *coords ); Returns the grid coordinates of process rank MPI, B. Barney, LLNL, computing.llnl.gov/tutorials/mpi/ #Virtual_Topologies 15

16 Systems of Linear Equations Ax = b A regular, b known Direct methods: Gauß, LU-decomposition, QR-decomposition Iterative methods: Splitting methods (Jacobi, Gauß-Seidl, SOR), projection methods (CG, GMRES, BiCGSTAB), QR-decomposition 16

17 Conjugate Gradients Method Ax = b Solve SLEs with symmetric and positive definite matrices, equivalent to minimizing: f(x) = 1 2 xt Ax - b T x + c 17

18 The code given in this section represents efficient implementations of the algorithms discu (a) B1. Steepest Descent Algorithm Given the inputs,, a starting value, a maximum number of iterations, and 1: (b) While and 2 0 do (c) (d) 1 If is divisible by 50 else 1 Figure 6: The method of Steepest Descent. (a) Starting at 2 2, take a step in the direction of steepest J. R. Shewchuk, An Introduction to descent of. (b) Find the point on the intersection of these two surfaces that minimizes. (c) This parabola the Conjugate Gradient Method Without the Agonizing Pain, is the intersection of surfaces. The bottommost point is our target. (d) The gradient at the0. bottommost point is orthogonal to the gradient of the previous step. This algorithm terminates when the maximum number of iterations has been e 18

19 Laplace 4f(x) =0 x 2 R 2 Dirichlet boundary conditions regular full grid no need to assemble the matrix: Use an implicitly given operator finite differences; in 1D: f 00 (x) = f(x + h)-2f(x)+f(x - h) h 2 19