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C $Header: /u/gcmpack/MITgcm/model/src/cg2d_nsa.F,v 1.3 2009/07/11 21:45:44 jmc Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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#ifdef ALLOW_USE_MPI |
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C HACK to avoid global_max |
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# define ALLOW_CONST_RHSMAX |
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#endif |
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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 alpha_aux :: 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 |
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_RL eta_qrN |
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_RL eta_qrNM1 |
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_RL recip_eta_qrNM1 |
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_RL cgBeta |
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_RL alpha |
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_RL alpha_aux |
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_RL sumRHS |
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_RL rhsMax, rhsMaxGlobal |
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_RL 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(standardMessageUnit,'(A,I10)') |
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& 'CG2D_NSA: numIters > numItersMax = ', numItersMax |
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STOP 'NON-NORMAL in 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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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ STORE cg2d_b = comlev1_cg2d, key = ikey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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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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IF (cg2dNormaliseRHS) THEN |
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C - Normalise RHS : |
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#ifdef ALLOW_CONST_RHSMAX |
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rhsMaxGlobal=1. |
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#else |
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rhsMaxGlobal=rhsMax |
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_GLOBAL_MAX_RL( rhsMaxGlobal, myThid ) |
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#endif /* ALLOW_CONST_RHSMAX */ |
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#ifdef ALLOW_AUTODIFF_TAMC |
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CADJ STORE rhsNorm = comlev1_cg2d, key = ikey, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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IF ( rhsMaxGlobal .NE. 0. ) THEN |
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rhsNorm = 1. _d 0 / rhsMaxGlobal |
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ELSE |
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rhsNorm = 1. _d 0 |
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ENDIF |
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|
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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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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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|
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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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err_sq = 0. _d 0 |
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sumRHS = 0. _d 0 |
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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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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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err_sq = err_sq + |
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& cg2d_r(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
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sumRHS = sumRHS + |
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& 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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_GLOBAL_SUM_RL( sumRHS, myThid ) |
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_GLOBAL_SUM_RL( err_sq, 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,rhsMaxGlobal |
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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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eta_qrN = 0. _d 0 |
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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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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_qrN = eta_qrN |
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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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_GLOBAL_SUM_RL(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 |
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Cml (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./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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alpha = 0. _d 0 |
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alpha_aux = 0. _d 0 |
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#ifdef ALLOW_AUTODIFF_TAMC |
| 320 |
#ifndef ALLOW_LOOP_DIRECTIVE |
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CADJ STORE cg2d_s = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
| 322 |
#endif /* not ALLOW_LOOP_DIRECTIVE */ |
| 323 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 324 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 325 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 326 |
DO j=1,sNy |
| 327 |
DO i=1,sNx |
| 328 |
cg2d_q(i,j,bi,bj) = |
| 329 |
& aW2d(i ,j ,bi,bj)*cg2d_s(i-1,j ,bi,bj) |
| 330 |
& +aW2d(i+1,j ,bi,bj)*cg2d_s(i+1,j ,bi,bj) |
| 331 |
& +aS2d(i ,j ,bi,bj)*cg2d_s(i ,j-1,bi,bj) |
| 332 |
& +aS2d(i ,j+1,bi,bj)*cg2d_s(i ,j+1,bi,bj) |
| 333 |
& +aC2d(i ,j ,bi,bj)*cg2d_s(i ,j ,bi,bj) |
| 334 |
alpha_aux = alpha_aux+cg2d_s(i,j,bi,bj)*cg2d_q(i,j,bi,bj) |
| 335 |
ENDDO |
| 336 |
ENDDO |
| 337 |
ENDDO |
| 338 |
ENDDO |
| 339 |
_GLOBAL_SUM_RL(alpha_aux,myThid) |
| 340 |
alpha = eta_qrN/alpha_aux |
| 341 |
|
| 342 |
C== Update simultaneously solution and residual vectors (and Iter number) |
| 343 |
C Now compute "interior" points. |
| 344 |
err_sq = 0. _d 0 |
| 345 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 346 |
#ifndef ALLOW_LOOP_DIRECTIVE |
| 347 |
CADJ STORE cg2d_r = comlev1_cg2d_iter, key = icg2dkey, byte = isbyte |
| 348 |
#endif /* ALLOW_LOOP_DIRECTIVE */ |
| 349 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 350 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 351 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 352 |
DO j=1,sNy |
| 353 |
DO i=1,sNx |
| 354 |
cg2d_x(i,j,bi,bj)=cg2d_x(i,j,bi,bj)+alpha*cg2d_s(i,j,bi,bj) |
| 355 |
cg2d_r(i,j,bi,bj)=cg2d_r(i,j,bi,bj)-alpha*cg2d_q(i,j,bi,bj) |
| 356 |
err_sq = err_sq+cg2d_r(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
| 357 |
ENDDO |
| 358 |
ENDDO |
| 359 |
ENDDO |
| 360 |
ENDDO |
| 361 |
actualIts = it2d |
| 362 |
|
| 363 |
_GLOBAL_SUM_RL( err_sq , myThid ) |
| 364 |
IF ( printResidual ) THEN |
| 365 |
IF ( MOD( it2d-1, printResidualFreq ).EQ.0 ) THEN |
| 366 |
WRITE(msgBuf,'(A,I6,A,1PE21.14)') |
| 367 |
& ' cg2d: iter=', it2d, ' ; resid.= ', SQRT(err_sq) |
| 368 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 369 |
& SQUEEZE_RIGHT, myThid ) |
| 370 |
ENDIF |
| 371 |
ENDIF |
| 372 |
|
| 373 |
c CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
| 374 |
CALL EXCH_XY_RL ( cg2d_r, myThid ) |
| 375 |
|
| 376 |
Cml end of if "err >= cg2dTolerance" block ; end main solver loop |
| 377 |
ENDIF |
| 378 |
ENDDO |
| 379 |
|
| 380 |
IF (cg2dNormaliseRHS) THEN |
| 381 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 382 |
CADJ STORE rhsNorm = comlev1_cg2d, key = ikey, byte = isbyte |
| 383 |
CADJ STORE cg2d_x = comlev1_cg2d, key = ikey, byte = isbyte |
| 384 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 385 |
C-- Un-normalise the answer |
| 386 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 387 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 388 |
DO j=1,sNy |
| 389 |
DO i=1,sNx |
| 390 |
cg2d_x(i,j,bi,bj) = cg2d_x(i,j,bi,bj)/rhsNorm |
| 391 |
ENDDO |
| 392 |
ENDDO |
| 393 |
ENDDO |
| 394 |
ENDDO |
| 395 |
ENDIF |
| 396 |
|
| 397 |
C-- Return parameters to caller |
| 398 |
IF ( err_sq .NE. 0. ) THEN |
| 399 |
lastResidual = SQRT(err_sq) |
| 400 |
ELSE |
| 401 |
lastResidual = 0. |
| 402 |
ENDIF |
| 403 |
numIters = actualIts |
| 404 |
|
| 405 |
#endif /* ALLOW_CG2D_NSA */ |
| 406 |
RETURN |
| 407 |
END |
| 408 |
|
| 409 |
#if ((defined ALLOW_AUTODIFF_TAMC) && (defined ALLOW_LOOP_DIRECTIVE)) |
| 410 |
C |
| 411 |
C These routines are routinely part of the TAMC/TAF library that is |
| 412 |
C not included in the MITcgm, therefore they are mimicked here. |
| 413 |
C |
| 414 |
subroutine adstore(chardum,int1,idow,int2,int3,icount) |
| 415 |
|
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implicit none |
| 417 |
|
| 418 |
#include "SIZE.h" |
| 419 |
#include "tamc.h" |
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|
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character*(*) chardum |
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integer int1, int2, int3, idow, icount |
| 423 |
|
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C the length of this vector must be greater or equal |
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C twice the number of timesteps |
| 426 |
integer nidow |
| 427 |
#ifdef ALLOW_TAMC_CHECKPOINTING |
| 428 |
parameter ( nidow = 2*nchklev_1*nchklev_2*nchklev_3 ) |
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#else |
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parameter ( nidow = 1000000 ) |
| 431 |
#endif /* ALLOW_TAMC_CHECKPOINTING */ |
| 432 |
integer istoreidow(nidow) |
| 433 |
common /istorecommon/ istoreidow |
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|
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print *, 'adstore: ', chardum, int1, idow, int2, int3, icount |
| 436 |
|
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if ( icount .gt. nidow ) then |
| 438 |
print *, 'adstore: error: icount > nidow = ', nidow |
| 439 |
stop 'ABNORMAL STOP in adstore' |
| 440 |
endif |
| 441 |
|
| 442 |
istoreidow(icount) = idow |
| 443 |
|
| 444 |
return |
| 445 |
end |
| 446 |
|
| 447 |
subroutine adresto(chardum,int1,idow,int2,int3,icount) |
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|
| 449 |
implicit none |
| 450 |
|
| 451 |
#include "SIZE.h" |
| 452 |
#include "tamc.h" |
| 453 |
|
| 454 |
character*(*) chardum |
| 455 |
integer int1, int2, int3, idow, icount |
| 456 |
|
| 457 |
|
| 458 |
C the length of this vector must be greater or equal |
| 459 |
C twice the number of timesteps |
| 460 |
integer nidow |
| 461 |
#ifdef ALLOW_TAMC_CHECKPOINTING |
| 462 |
parameter ( nidow = 2*nchklev_1*nchklev_2*nchklev_3 ) |
| 463 |
#else |
| 464 |
parameter ( nidow = 1000000 ) |
| 465 |
#endif /* ALLOW_TAMC_CHECKPOINTING */ |
| 466 |
integer istoreidow(nidow) |
| 467 |
common /istorecommon/ istoreidow |
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|
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print *, 'adresto: ', chardum, int1, idow, int2, int3, icount |
| 470 |
|
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if ( icount .gt. nidow ) then |
| 472 |
print *, 'adstore: error: icount > nidow = ', nidow |
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stop 'ABNORMAL STOP in adstore' |
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endif |
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|
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idow = istoreidow(icount) |
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|
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return |
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end |
| 480 |
#endif /* ALLOW_AUTODIFF_TAMC and ALLOW_LOOP_DIRECTIVE */ |
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