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C $Header: /u/gcmpack/MITgcm/model/src/cg2d_nsa.F,v 1.4 2012/05/11 23:29:13 jmc Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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CML THIS DOES NOT WORK +++++ |
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#undef ALLOW_LOOP_DIRECTIVE |
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CBOP |
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C !ROUTINE: CG2D_NSA |
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C !INTERFACE: |
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SUBROUTINE CG2D_NSA( |
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U cg2d_b, cg2d_x, |
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O firstResidual, minResidualSq, lastResidual, |
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U numIters, nIterMin, |
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I myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE CG2D_NSA |
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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 | o This version is used only in the case when the matrix |
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C | operator is not "self-adjoint" (NSA). Any remaining |
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C | residuals will immediately reported to the department |
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C | of homeland security. |
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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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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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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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#ifdef ALLOW_AUTODIFF_TAMC |
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# include "tamc.h" |
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# include "tamc_keys.h" |
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#endif |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C === Routine arguments === |
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C cg2d_b :: The source term or "right hand side" (Output: normalised RHS) |
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C cg2d_x :: The solution (Input: first guess) |
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C firstResidual :: the initial residual before any iterations |
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C minResidualSq :: the lowest residual reached (squared) |
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C lastResidual :: the actual residual reached |
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C numIters :: Inp: the maximum number of iterations allowed |
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C Out: the actual number of iterations used |
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C nIterMin :: Inp: decide to store (if >=0) or not (if <0) lowest res. sol. |
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C Out: iteration number corresponding to lowest residual |
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C myThid :: Thread on which I am working. |
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_RL cg2d_b(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL cg2d_x(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL firstResidual |
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_RL minResidualSq |
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_RL lastResidual |
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INTEGER numIters |
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INTEGER nIterMin |
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INTEGER myThid |
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|
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#ifdef ALLOW_CG2D_NSA |
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C !LOCAL VARIABLES: |
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C === Local variables ==== |
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C bi, bj :: tile index in X and Y. |
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C i, j, it2d :: Loop counters ( it2d counts CG iterations ) |
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C actualIts :: actual CG iteration number |
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C err_sq :: Measure of the square of the residual of Ax - b. |
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C eta_qrN :: Used in computing search directions; suffix N and NM1 |
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C eta_qrNM1 denote current and previous iterations respectively. |
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C recip_eta_qrNM1 :: reciprocal of eta_qrNM1 |
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C cgBeta :: coeff used to update conjugate direction vector "s". |
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C alpha :: coeff used to update solution & residual |
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C alphaSum :: to avoid the statement: alpha = 1./alpha (for TAMC/TAF) |
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C sumRHS :: Sum of right-hand-side. Sometimes this is a useful |
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C debugging/trouble shooting diagnostic. For neumann problems |
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C sumRHS needs to be ~0 or it converge at a non-zero residual. |
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C cg2d_min :: used to store solution corresponding to lowest residual. |
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C msgBuf :: Informational/error message buffer |
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INTEGER bi, bj |
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INTEGER i, j, it2d |
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INTEGER actualIts |
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_RL cg2dTolerance_sq |
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_RL err_sq, errTile(nSx,nSy) |
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_RL eta_qrN, eta_qrNtile(nSx,nSy) |
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_RL eta_qrNM1, recip_eta_qrNM1 |
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_RL cgBeta, alpha |
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_RL alphaSum,alphaTile(nSx,nSy) |
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_RL sumRHS, sumRHStile(nSx,nSy) |
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_RL rhsMax, rhsNorm |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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LOGICAL printResidual |
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CEOP |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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IF ( numIters .GT. numItersMax ) THEN |
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WRITE(msgBuf,'(A,I10)') |
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& 'CG2D_NSA: numIters > numItersMax =', numItersMax |
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CALL PRINT_ERROR( msgBuf, myThid ) |
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STOP 'ABNORMAL END: S/R CG2D_NSA' |
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ENDIF |
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IF ( cg2dNormaliseRHS ) THEN |
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WRITE(msgBuf,'(A)') 'CG2D_NSA: cg2dNormaliseRHS is disabled' |
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CALL PRINT_ERROR( msgBuf, myThid ) |
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WRITE(msgBuf,'(A)') |
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& 'set cg2dTargetResWunit (instead of cg2dTargetResidual)' |
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CALL PRINT_ERROR( msgBuf, myThid ) |
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STOP 'ABNORMAL END: S/R CG2D_NSA' |
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ENDIF |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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act1 = myThid - 1 |
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max1 = nTx*nTy |
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act2 = ikey_dynamics - 1 |
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ikey = (act1 + 1) + act2*max1 |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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C-- Initialise auxiliary constant, some output variable and inverter |
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cg2dTolerance_sq = cg2dTolerance*cg2dTolerance |
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minResidualSq = -1. _d 0 |
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eta_qrNM1 = 1. _d 0 |
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recip_eta_qrNM1= 1. _d 0 |
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|
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C-- Normalise RHS |
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rhsMax = 0. _d 0 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_b(i,j,bi,bj) = cg2d_b(i,j,bi,bj)*cg2dNorm |
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rhsMax = MAX(ABS(cg2d_b(i,j,bi,bj)),rhsMax) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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#ifndef ALLOW_AUTODIFF_TAMC |
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IF (cg2dNormaliseRHS) THEN |
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C- Normalise RHS : |
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_GLOBAL_MAX_RL( rhsMax, myThid ) |
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rhsNorm = 1. _d 0 |
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IF ( rhsMax .NE. 0. ) rhsNorm = 1. _d 0 / rhsMax |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_b(i,j,bi,bj) = cg2d_b(i,j,bi,bj)*rhsNorm |
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cg2d_x(i,j,bi,bj) = cg2d_x(i,j,bi,bj)*rhsNorm |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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C- end Normalise RHS |
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ENDIF |
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#endif /* ndef ALLOW_AUTODIFF_TAMC */ |
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|
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C-- Update overlaps |
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CALL EXCH_XY_RL( cg2d_x, myThid ) |
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|
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C-- Initial residual calculation |
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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ STORE cg2d_b = comlev1_cg2d, key = ikey, byte = isbyte |
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CADJ STORE cg2d_x = comlev1_cg2d, key = ikey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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errTile(bi,bj) = 0. _d 0 |
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sumRHStile(bi,bj) = 0. _d 0 |
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DO j=0,sNy+1 |
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DO i=0,sNx+1 |
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cg2d_s(i,j,bi,bj) = 0. |
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ENDDO |
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ENDDO |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_r(i,j,bi,bj) = cg2d_b(i,j,bi,bj) - |
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& (aW2d(i ,j ,bi,bj)*cg2d_x(i-1,j ,bi,bj) |
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& +aW2d(i+1,j ,bi,bj)*cg2d_x(i+1,j ,bi,bj) |
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& +aS2d(i ,j ,bi,bj)*cg2d_x(i ,j-1,bi,bj) |
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& +aS2d(i ,j+1,bi,bj)*cg2d_x(i ,j+1,bi,bj) |
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& +aC2d(i ,j ,bi,bj)*cg2d_x(i ,j ,bi,bj) |
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& ) |
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errTile(bi,bj) = errTile(bi,bj) |
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& + cg2d_r(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
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sumRHStile(bi,bj) = sumRHStile(bi,bj) + cg2d_b(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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c CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
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CALL EXCH_XY_RL ( cg2d_r, myThid ) |
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CALL GLOBAL_SUM_TILE_RL( errTile, err_sq, myThid ) |
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CALL GLOBAL_SUM_TILE_RL( sumRHStile, sumRHS, myThid ) |
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actualIts = 0 |
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IF ( err_sq .NE. 0. ) THEN |
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firstResidual = SQRT(err_sq) |
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ELSE |
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firstResidual = 0. |
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ENDIF |
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|
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printResidual = .FALSE. |
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IF ( debugLevel .GE. debLevZero ) THEN |
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_BEGIN_MASTER( myThid ) |
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printResidual = printResidualFreq.GE.1 |
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WRITE(standardmessageunit,'(A,1P2E22.14)') |
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& ' cg2d: Sum(rhs),rhsMax = ', sumRHS,rhsMax |
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_END_MASTER( myThid ) |
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ENDIF |
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|
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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Cml begin main solver loop |
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#if ((defined ALLOW_AUTODIFF_TAMC) && (defined ALLOW_LOOP_DIRECTIVE)) |
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CADJ LOOP = iteration, cg2d_x = comlev_cg2d_iter |
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#endif /* ALLOW_AUTODIFF_TAMC and ALLOW_LOOP_DIRECTIVE */ |
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DO it2d=1, numIters |
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#ifdef ALLOW_LOOP_DIRECTIVE |
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CML it2d = 0 |
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CML DO WHILE ( err_sq .GT. cg2dTolerance_sq .and. it2d .LT. numIters ) |
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CML it2d = it2d+1 |
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#endif /* ALLOW_LOOP_DIRECTIVE */ |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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icg2dkey = (ikey-1)*numItersMax + it2d |
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CADJ STORE err_sq = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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IF ( err_sq .GE. cg2dTolerance_sq ) THEN |
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|
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C-- Solve preconditioning equation and update |
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C-- conjugate direction vector "s". |
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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ STORE cg2d_r = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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CADJ STORE cg2d_s = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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eta_qrNtile(bi,bj) = 0. _d 0 |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_z(i,j,bi,bj) = |
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& pC(i ,j ,bi,bj)*cg2d_r(i ,j ,bi,bj) |
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& +pW(i ,j ,bi,bj)*cg2d_r(i-1,j ,bi,bj) |
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& +pW(i+1,j ,bi,bj)*cg2d_r(i+1,j ,bi,bj) |
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& +pS(i ,j ,bi,bj)*cg2d_r(i ,j-1,bi,bj) |
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& +pS(i ,j+1,bi,bj)*cg2d_r(i ,j+1,bi,bj) |
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eta_qrNtile(bi,bj) = eta_qrNtile(bi,bj) |
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& +cg2d_z(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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CALL GLOBAL_SUM_TILE_RL( eta_qrNtile,eta_qrN,myThid ) |
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#ifdef ALLOW_AUTODIFF_TAMC |
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CMLCADJ STORE eta_qrNM1 = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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CADJ STORE recip_eta_qrNM1 = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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CML cgBeta = eta_qrN/eta_qrNM1 |
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cgBeta = eta_qrN*recip_eta_qrNM1 |
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Cml store normalisation factor for the next interation (in case there is one). |
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CML store the inverse of the normalization factor for higher precision |
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CML eta_qrNM1 = eta_qrN |
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recip_eta_qrNM1 = 1. _d 0/eta_qrN |
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|
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_s(i,j,bi,bj) = cg2d_z(i,j,bi,bj) |
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& + cgBeta*cg2d_s(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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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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c CALL EXCH_S3D_RL( cg2d_s, 1, myThid ) |
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CALL EXCH_XY_RL ( cg2d_s, myThid ) |
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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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#ifdef ALLOW_AUTODIFF_TAMC |
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#ifndef ALLOW_LOOP_DIRECTIVE |
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CADJ STORE cg2d_s = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
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#endif /* not ALLOW_LOOP_DIRECTIVE */ |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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alphaTile(bi,bj) = 0. _d 0 |
308 |
DO j=1,sNy |
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DO i=1,sNx |
310 |
cg2d_q(i,j,bi,bj) = |
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& aW2d(i ,j ,bi,bj)*cg2d_s(i-1,j ,bi,bj) |
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& +aW2d(i+1,j ,bi,bj)*cg2d_s(i+1,j ,bi,bj) |
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& +aS2d(i ,j ,bi,bj)*cg2d_s(i ,j-1,bi,bj) |
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& +aS2d(i ,j+1,bi,bj)*cg2d_s(i ,j+1,bi,bj) |
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& +aC2d(i ,j ,bi,bj)*cg2d_s(i ,j ,bi,bj) |
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alphaTile(bi,bj) = alphaTile(bi,bj) |
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& + cg2d_s(i,j,bi,bj)*cg2d_q(i,j,bi,bj) |
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ENDDO |
319 |
ENDDO |
320 |
ENDDO |
321 |
ENDDO |
322 |
CALL GLOBAL_SUM_TILE_RL( alphaTile, alphaSum, myThid ) |
323 |
alpha = eta_qrN/alphaSum |
324 |
|
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C== Update simultaneously solution and residual vectors (and Iter number) |
326 |
C Now compute "interior" points. |
327 |
#ifdef ALLOW_AUTODIFF_TAMC |
328 |
#ifndef ALLOW_LOOP_DIRECTIVE |
329 |
CADJ STORE cg2d_r = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
330 |
#endif /* ALLOW_LOOP_DIRECTIVE */ |
331 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
332 |
DO bj=myByLo(myThid),myByHi(myThid) |
333 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
334 |
errTile(bi,bj) = 0. _d 0 |
335 |
DO j=1,sNy |
336 |
DO i=1,sNx |
337 |
cg2d_x(i,j,bi,bj)=cg2d_x(i,j,bi,bj)+alpha*cg2d_s(i,j,bi,bj) |
338 |
cg2d_r(i,j,bi,bj)=cg2d_r(i,j,bi,bj)-alpha*cg2d_q(i,j,bi,bj) |
339 |
errTile(bi,bj) = errTile(bi,bj) |
340 |
& + cg2d_r(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
341 |
ENDDO |
342 |
ENDDO |
343 |
ENDDO |
344 |
ENDDO |
345 |
actualIts = it2d |
346 |
|
347 |
CALL GLOBAL_SUM_TILE_RL( errTile, err_sq, myThid ) |
348 |
IF ( printResidual ) THEN |
349 |
IF ( MOD( it2d-1, printResidualFreq ).EQ.0 ) THEN |
350 |
WRITE(msgBuf,'(A,I6,A,1PE21.14)') |
351 |
& ' cg2d: iter=', it2d, ' ; resid.= ', SQRT(err_sq) |
352 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
353 |
& SQUEEZE_RIGHT, myThid ) |
354 |
ENDIF |
355 |
ENDIF |
356 |
|
357 |
c CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
358 |
CALL EXCH_XY_RL ( cg2d_r, myThid ) |
359 |
|
360 |
Cml end of if "err >= cg2dTolerance" block ; end main solver loop |
361 |
ENDIF |
362 |
ENDDO |
363 |
|
364 |
#ifndef ALLOW_AUTODIFF_TAMC |
365 |
IF (cg2dNormaliseRHS) THEN |
366 |
C-- Un-normalise the answer |
367 |
DO bj=myByLo(myThid),myByHi(myThid) |
368 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
369 |
DO j=1,sNy |
370 |
DO i=1,sNx |
371 |
cg2d_x(i,j,bi,bj) = cg2d_x(i,j,bi,bj)/rhsNorm |
372 |
ENDDO |
373 |
ENDDO |
374 |
ENDDO |
375 |
ENDDO |
376 |
ENDIF |
377 |
#endif /* ndef ALLOW_AUTODIFF_TAMC */ |
378 |
|
379 |
C-- Return parameters to caller |
380 |
IF ( err_sq .NE. 0. ) THEN |
381 |
lastResidual = SQRT(err_sq) |
382 |
ELSE |
383 |
lastResidual = 0. |
384 |
ENDIF |
385 |
numIters = actualIts |
386 |
|
387 |
#endif /* ALLOW_CG2D_NSA */ |
388 |
RETURN |
389 |
END |
390 |
|
391 |
#if ((defined ALLOW_AUTODIFF_TAMC) && (defined ALLOW_LOOP_DIRECTIVE)) |
392 |
|
393 |
C These routines are routinely part of the TAMC/TAF library that is |
394 |
C not included in the MITcgm, therefore they are mimicked here. |
395 |
|
396 |
subroutine adstore(chardum,int1,idow,int2,int3,icount) |
397 |
|
398 |
implicit none |
399 |
|
400 |
#include "SIZE.h" |
401 |
#include "tamc.h" |
402 |
|
403 |
character*(*) chardum |
404 |
integer int1, int2, int3, idow, icount |
405 |
|
406 |
C the length of this vector must be greater or equal |
407 |
C twice the number of timesteps |
408 |
integer nidow |
409 |
#ifdef ALLOW_TAMC_CHECKPOINTING |
410 |
parameter ( nidow = 2*nchklev_1*nchklev_2*nchklev_3 ) |
411 |
#else |
412 |
parameter ( nidow = 1000000 ) |
413 |
#endif /* ALLOW_TAMC_CHECKPOINTING */ |
414 |
integer istoreidow(nidow) |
415 |
common /istorecommon/ istoreidow |
416 |
|
417 |
print *, 'adstore: ', chardum, int1, idow, int2, int3, icount |
418 |
|
419 |
if ( icount .gt. nidow ) then |
420 |
print *, 'adstore: error: icount > nidow = ', nidow |
421 |
stop 'ABNORMAL STOP in adstore' |
422 |
endif |
423 |
|
424 |
istoreidow(icount) = idow |
425 |
|
426 |
return |
427 |
end |
428 |
|
429 |
subroutine adresto(chardum,int1,idow,int2,int3,icount) |
430 |
|
431 |
implicit none |
432 |
|
433 |
#include "SIZE.h" |
434 |
#include "tamc.h" |
435 |
|
436 |
character*(*) chardum |
437 |
integer int1, int2, int3, idow, icount |
438 |
|
439 |
C the length of this vector must be greater or equal |
440 |
C twice the number of timesteps |
441 |
integer nidow |
442 |
#ifdef ALLOW_TAMC_CHECKPOINTING |
443 |
parameter ( nidow = 2*nchklev_1*nchklev_2*nchklev_3 ) |
444 |
#else |
445 |
parameter ( nidow = 1000000 ) |
446 |
#endif /* ALLOW_TAMC_CHECKPOINTING */ |
447 |
integer istoreidow(nidow) |
448 |
common /istorecommon/ istoreidow |
449 |
|
450 |
print *, 'adresto: ', chardum, int1, idow, int2, int3, icount |
451 |
|
452 |
if ( icount .gt. nidow ) then |
453 |
print *, 'adstore: error: icount > nidow = ', nidow |
454 |
stop 'ABNORMAL STOP in adstore' |
455 |
endif |
456 |
|
457 |
idow = istoreidow(icount) |
458 |
|
459 |
return |
460 |
end |
461 |
#endif /* ALLOW_AUTODIFF_TAMC and ALLOW_LOOP_DIRECTIVE */ |