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C $Id$ |
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SUBROUTINE CG2D |
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C /==========================================================\ |
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C | SUBROUTINE CG2D | |
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C | o Two-dimensional grid problem conjugate-gradient | |
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C | inverter (with preconditioner). | |
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C |==========================================================| |
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C | Con. grad is an iterative procedure for solving Ax = b. | |
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C | It requires the A be symmetric. | |
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C | This implementation assumes A is a five-diagonal | |
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C | matrix of the form that arises in the discrete | |
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C | representation of the del^2 operator in a | |
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C | two-dimensional space. | |
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C | Notes: | |
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C | ====== | |
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C | This implementation can support shared-memory | |
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C | multi-threaded execution. In order to do this COMMON | |
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C | blocks are used for many of the arrays - even ones that | |
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C | are only used for intermedaite results. This design is | |
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C | OK if you want to all the threads to collaborate on | |
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C | solving the same problem. On the other hand if you want | |
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C | the threads to solve several different problems | |
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C | concurrently this implementation will not work. | |
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C \==========================================================/ |
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IMPLICIT NONE |
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|
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C === Global data === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "CG2D.h" |
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#if defined(USE_PAPI_FLOPS) || defined(USE_PAPI_FLIPS) |
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#if defined(PAPI_PER_ITERATION) || defined(PAPI_PER_TIMESTEP) |
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#include "PAPI.h" |
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#endif |
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#endif |
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|
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C === Routine arguments === |
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C myThid - Thread on which I am working. |
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INTEGER myThid |
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|
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C === Local variables ==== |
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C actualIts - Number of iterations taken |
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C actualResidual - residual |
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C bi - Block index in X and Y. |
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C bj |
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C etaN - Used in computing search directions |
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C etaNM1 suffix N and NM1 denote current and |
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C beta previous iterations respectively. |
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C alpha |
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C sumRHS - Sum of right-hand-side. Sometimes this is a |
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C useful debuggin/trouble shooting diagnostic. |
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C For neumann problems sumRHS needs to be ~0. |
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C or they converge at a non-zero residual. |
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C err - Measure of residual of Ax - b, usually the norm. |
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C I, J, N - Loop counters ( N counts CG iterations ) |
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INTEGER actualIts |
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INTEGER bi, bj |
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INTEGER I, J, N |
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#ifdef USE_MIXED_PRECISION |
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REAL*8 actualResidual |
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REAL*8 err |
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REAL*8 errSum |
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REAL*8 etaN |
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REAL*8 etaNM1 |
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REAL*8 etaNSum |
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REAL*8 beta |
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REAL*8 alpha |
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REAL*8 alphaSum |
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REAL*8 sumRHS |
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REAL*8 temp |
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#else |
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Real actualResidual |
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Real err |
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Real errSum |
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Real etaN |
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Real etaNM1 |
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Real etaNSum |
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Real beta |
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Real alpha |
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Real alphaSum |
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Real sumRHS |
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Real temp |
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#endif |
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|
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C-- Initialise inverter |
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etaNM1 = 1. _d 0 |
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|
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C-- Initial residual calculation |
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err = 0. _d 0 |
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sumRHS = 0. _d 0 |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_s(I,J) = 0. _d 0 |
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cg2d_r(I,J) = cg2d_b(I,J) - |
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& ( aW2d(I ,J )*cg2d_x(I-1,J )+aW2d(I+1,J )*cg2d_x(I+1,J ) |
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& +aS2d(I ,J )*cg2d_x(I ,J-1)+aS2d(I ,J+1)*cg2d_x(I ,J+1) |
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& -aW2d(I ,J )*cg2d_x(I ,J )-aW2d(I+1,J )*cg2d_x(I ,J ) |
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& -aS2d(I ,J )*cg2d_x(I ,J )-aS2d(I ,J+1)*cg2d_x(I ,J ) |
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& ) |
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err = err + cg2d_r(I,J)*cg2d_r(I,J) |
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sumRHS = sumRHS + cg2d_b(I,J) |
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ENDDO |
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ENDDO |
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CALL EXCH_XY_R8( cg2d_r ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL GSUM_R8( temp, err ) |
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err = temp |
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CALL GSUM_R8( temp, sumRHS ) |
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sumRHS = temp |
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|
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actualIts = 0 |
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actualResidual = SQRT(err) |
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WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
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IF ( actualResidual .EQ. 0. _d 0) STOP 'ABNORMAL END: RESIDUAL 0' |
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|
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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DO 10 N=1, cg2dMaxIters |
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C-- Solve preconditioning equation and update |
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C-- conjugate direction vector "s". |
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etaN = 0. _d 0 |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_q(I,J) = |
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& pW(I ,J )*cg2d_r(I-1,J )+pW(I+1,J )*cg2d_r(I+1,J ) |
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& +pS(I ,J )*cg2d_r(I ,J-1)+pS(I ,J+1)*cg2d_r(I ,J+1) |
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& +pC(I ,J )*cg2d_r(I ,J ) |
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etaN = etaN+cg2d_q(I,J)*cg2d_r(I,J) |
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ENDDO |
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ENDDO |
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|
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CALL GSUM_R8( temp, etaN ) |
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etaN = temp |
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beta = etaN/etaNM1 |
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etaNM1 = etaN |
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|
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_s(I,J) = cg2d_q(I,J) + beta*cg2d_s(I,J) |
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ENDDO |
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ENDDO |
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|
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C-- Do exchanges that require messages i.e. between |
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C-- processes. |
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CALL EXCH_XY_R8( cg2d_s ) |
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|
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C-- Ten extra exchanges |
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#ifdef TEN_EXTRA_EXCHS |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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CALL EXCH_XY_R8( cg2d_s ) |
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#endif |
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|
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C== Evaluate laplace operator on conjugate gradient vector |
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C== q = A.s |
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alpha = 0. _d 0 |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_q(I,J) = |
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& aW2d(I ,J )*cg2d_s(I-1,J )+aW2d(I+1,J )*cg2d_s(I+1,J ) |
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& +aS2d(I ,J )*cg2d_s(I ,J-1)+aS2d(I ,J+1)*cg2d_s(I ,J+1) |
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& -aW2d(I ,J )*cg2d_s(I ,J )-aW2d(I+1,J )*cg2d_s(I ,J ) |
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& -aS2d(I ,J )*cg2d_s(I ,J )-aS2d(I ,J+1)*cg2d_s(I ,J ) |
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alpha = alpha+cg2d_s(I,J)*cg2d_q(I,J) |
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ENDDO |
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ENDDO |
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CALL GSUM_R8( temp, alpha ) |
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|
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#ifdef HUNDRED_EXTRA_SUMS |
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C-- Hundred extra global sums |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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CALL GSUM_R8( temp, alpha ) |
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#endif |
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|
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alpha = temp |
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alpha = etaN/alpha |
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|
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C== Update solution and residual vectors |
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C Now compute "interior" points. |
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err = 0. _d 0 |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_x(I,J)=cg2d_x(I,J)+alpha*cg2d_s(I,J) |
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cg2d_r(I,J)=cg2d_r(I,J)-alpha*cg2d_q(I,J) |
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err = err+cg2d_r(I,J)*cg2d_r(I,J) |
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ENDDO |
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ENDDO |
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|
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CALL GSUM_R8( temp, err ) |
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|
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err = temp |
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err = SQRT(err) |
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actualIts = N |
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actualResidual = err |
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#ifdef RESIDUAL_PER_ITERATION |
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WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
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#endif |
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IF ( err .LT. cg2dTargetResidual ) GOTO 11 |
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CALL EXCH_XY_R8(cg2d_r ) |
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#ifdef PAPI_PER_ITERATION |
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#ifdef USE_PAPI_FLOPS |
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call PAPIF_flops(real_time, proc_time, flpops, mflops, check) |
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WRITE(6,'(F10.3,A7,F10.3,A37,I8)') |
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$ mflops, ' user ', mflops*proc_time/real_time, |
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$ ' wallclock Mflop/s during iteration ', N |
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#else |
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#ifdef USE_PAPI_FLIPS |
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call PAPIF_flips(real_time, proc_time, flpops, mflops, check) |
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WRITE(6,'(F10.3,A7,F10.3,A37,I8)') |
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$ mflops, ' user ', mflops*proc_time/real_time, |
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$ ' wallclock Mflip/s during iteration ', N |
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#endif |
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#endif |
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#endif |
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10 CONTINUE |
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11 CONTINUE |
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CALL EXCH_XY_R8(cg2d_x ) |
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#ifdef PAPI_PER_TIMESTEP |
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#ifdef USE_PAPI_FLOPS |
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call PAPIF_flops(real_time, proc_time, flpops, mflops, check) |
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WRITE(6,'(F10.3,A7,F10.3,A37,I8)') |
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$ mflops, ' user ', mflops*proc_time/real_time, |
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$ ' wallclock Mflop/s during iteration ', N |
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#else |
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#ifdef USE_PAPI_FLIPS |
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call PAPIF_flips(real_time, proc_time, flpops, mflops, check) |
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WRITE(6,'(F10.3,A7,F10.3,A37,I8)') |
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$ mflops, ' user ', mflops*proc_time/real_time, |
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$ ' wallclock Mflip/s during iteration ', N |
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#endif |
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#endif |
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#endif |
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WRITE(6,*) ' CG2D iters, err = ', actualIts, actualResidual |
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|
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C Calc Ax to check result |
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DO J=1,sNy |
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DO I=1,sNx |
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cg2d_Ax(I,J) = |
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& ( aW2d(I ,J )*cg2d_x(I-1,J )+aW2d(I+1,J )*cg2d_x(I+1,J ) |
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& +aS2d(I ,J )*cg2d_x(I ,J-1)+aS2d(I ,J+1)*cg2d_x(I ,J+1) |
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& -aW2d(I ,J )*cg2d_x(I ,J )-aW2d(I+1,J )*cg2d_x(I ,J ) |
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& -aS2d(I ,J )*cg2d_x(I ,J )-aS2d(I ,J+1)*cg2d_x(I ,J ) |
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& ) |
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cg2d_r(I,J) = cg2d_b(I,J)-cg2d_Ax(I,J) |
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ENDDO |
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ENDDO |
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CALL EXCH_XY_R8(cg2d_Ax ) |
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CALL EXCH_XY_R8(cg2d_r ) |
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|
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END |
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