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C $Header: /u/gcmpack/MITgcm/model/src/cg2d.F,v 1.55 2012/05/11 23:28:10 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 TARGET_NEC_SX |
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C set a sensible default for the outer loop unrolling parameter that can |
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C be overriden in the Makefile with the DEFINES macro or in CPP_OPTIONS.h |
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#ifndef CG2D_OUTERLOOPITERS |
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# define CG2D_OUTERLOOPITERS 10 |
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#endif |
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#endif /* TARGET_NEC_SX */ |
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|
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CBOP |
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C !ROUTINE: CG2D_EX0 |
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C !INTERFACE: |
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SUBROUTINE CG2D_EX0( |
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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_EX0 |
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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 | This is the disconnected-tile version (each tile treated |
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C | independently as a small domain, with locally periodic |
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C | BC at the edges. |
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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 matrix |
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C | of the form that arises in the discrete representation of |
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C | the del^2 operator in a two-dimensional space. |
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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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|
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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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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 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 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(nSx,nSy) |
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INTEGER minResIter(nSx,nSy) |
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_RL cg2dTolerance_sq |
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_RL err_sq, errTile(nSx,nSy) |
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_RL eta_qrNtile(nSx,nSy) |
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_RL eta_qrNM1(nSx,nSy) |
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_RL cgBeta |
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_RL alpha, alphaTile(nSx,nSy) |
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_RL sumRHS, sumRHStile(nSx,nSy) |
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_RL rhsMax, rhsMaxLoc |
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_RL rhsNorm(nSx,nSy) |
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_RL minResTile(nSx,nSy) |
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_RL cg2d_min(1:sNx,1:sNy,nSx,nSy) |
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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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C-- Initialise auxiliary constant, some output variable |
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cg2dTolerance_sq = cg2dTolerance*cg2dTolerance |
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|
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C-- Initialise inverter and 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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|
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actualIts(bi,bj) = 0 |
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minResIter(bi,bj) = 0 |
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minResTile(bi,bj) = -1. _d 0 |
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eta_qrNM1(bi,bj) = 1. _d 0 |
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rhsMaxLoc = 0. _d 0 |
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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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rhsMaxLoc = MAX(ABS(cg2d_b(i,j,bi,bj)),rhsMaxLoc) |
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ENDDO |
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ENDDO |
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rhsNorm(bi,bj) = 1. _d 0 |
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IF ( rhsMaxLoc .NE. 0. ) rhsNorm(bi,bj) = 1. _d 0 / rhsMaxLoc |
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IF (cg2dNormaliseRHS) THEN |
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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(bi,bj) |
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cg2d_x(i,j,bi,bj) = cg2d_x(i,j,bi,bj)*rhsNorm(bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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rhsMax = MAX( rhsMaxLoc, rhsMax ) |
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|
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ENDDO |
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ENDDO |
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_GLOBAL_MAX_RL( rhsMax, myThid ) |
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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. |
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sumRHS = 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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IF ( nIterMin.GE.0 ) THEN |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_min(i,j,bi,bj) = cg2d_x(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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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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sumRHStile(bi,bj) = 0. _d 0 |
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errTile(bi,bj) = 0. _d 0 |
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#ifdef TARGET_NEC_SX |
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!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
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#endif /* TARGET_NEC_SX */ |
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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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IF ( nIterMin.GE.0 ) THEN |
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minResTile(bi,bj) = errTile(bi,bj) |
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ENDIF |
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err_sq = MAX( errTile(bi,bj), err_sq ) |
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sumRHS = MAX( ABS(sumRHStile(bi,bj)), sumRHS ) |
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|
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ENDDO |
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ENDDO |
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CALL EXCH_S3D_RL( cg2d_r, 1, myThid ) |
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_GLOBAL_MAX_RL( err_sq, myThid ) |
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_GLOBAL_MAX_RL( sumRHS, myThid ) |
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firstResidual = SQRT(err_sq) |
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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 IF ( err_sq .LT. cg2dTolerance_sq ) GOTO 11 |
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|
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C >>>>>>>>>>>>>>> BEGIN SOLVER <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< |
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DO it2d=1, numIters |
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IF ( err_sq.GE.cg2dTolerance_sq ) THEN |
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err_sq = 0. _d 0 |
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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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IF ( errTile(bi,bj).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_qrNtile(bi,bj) = 0. _d 0 |
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#ifdef TARGET_NEC_SX |
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!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
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#endif /* TARGET_NEC_SX */ |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_q(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_q(i,j,bi,bj)*cg2d_r(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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|
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cgBeta = eta_qrNtile(bi,bj)/eta_qrNM1(bi,bj) |
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eta_qrNM1(bi,bj) = eta_qrNtile(bi,bj) |
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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,bi,bj) = cg2d_q(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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|
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C-- Do exchanges that require messages i.e. between processes. |
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CALL FILL_HALO_LOCAL_RL( |
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U cg2d_s(0,0,bi,bj), |
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I 1, 1, 1, 1, 1, |
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I EXCH_IGNORE_CORNERS, bi, bj, 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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alphaTile(bi,bj) = 0. _d 0 |
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#ifdef TARGET_NEC_SX |
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!CDIR OUTERUNROLL=CG2D_OUTERLOOPITERS |
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#endif /* TARGET_NEC_SX */ |
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DO j=1,sNy |
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DO i=1,sNx |
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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 |
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ENDDO |
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alpha = eta_qrNtile(bi,bj)/alphaTile(bi,bj) |
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|
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C== Update simultaneously solution and residual vectors (and Iter number) |
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C Now compute "interior" points. |
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errTile(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_x(i,j,bi,bj)=cg2d_x(i,j,bi,bj)+alpha*cg2d_s(i,j,bi,bj) |
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cg2d_r(i,j,bi,bj)=cg2d_r(i,j,bi,bj)-alpha*cg2d_q(i,j,bi,bj) |
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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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ENDDO |
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ENDDO |
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actualIts(bi,bj) = it2d |
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|
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IF ( printResidual ) THEN |
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IF ( MOD( it2d-1, printResidualFreq ).EQ.0 ) THEN |
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WRITE(msgBuf,'(A,2I4,A,I6,A,1PE21.14)') ' cg2d(bi,bj=', bi, |
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& bj, '): iter=', it2d, ' ; resid.= ', SQRT(errTile(bi,bj)) |
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CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
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& SQUEEZE_RIGHT, myThid ) |
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ENDIF |
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ENDIF |
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IF ( errTile(bi,bj) .GE. cg2dTolerance_sq .AND. |
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& errTile(bi,bj) .LT. minResTile(bi,bj) ) THEN |
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C- Store lowest residual solution |
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minResTile(bi,bj) = errTile(bi,bj) |
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minResIter(bi,bj) = it2d |
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DO j=1,sNy |
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DO i=1,sNx |
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cg2d_min(i,j,bi,bj) = cg2d_x(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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CALL FILL_HALO_LOCAL_RL( |
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U cg2d_r(0,0,bi,bj), |
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I 1, 1, 1, 1, 1, |
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I EXCH_IGNORE_CORNERS, bi, bj, myThid ) |
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|
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ENDIF |
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err_sq = MAX( errTile(bi,bj), err_sq ) |
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C- end bi,bj loops |
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ENDDO |
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ENDDO |
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C- end cg-2d iteration loop |
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ENDIF |
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ENDDO |
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|
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c 11 CONTINUE |
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|
| 312 |
IF ( nIterMin.GE.0 ) THEN |
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C- use the lowest residual solution (instead of current one = last residual) |
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DO bj=myByLo(myThid),myByHi(myThid) |
| 315 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 316 |
c minResidualSq = MAX( minResTile(bi,bj), minResidualSq ) |
| 317 |
c nIterMin = MAX( minResIter(bi,bj), nIterMin ) |
| 318 |
IF ( errTile(bi,bj) .GT. minResTile(bi,bj) ) THEN |
| 319 |
DO j=1,sNy |
| 320 |
DO i=1,sNx |
| 321 |
cg2d_x(i,j,bi,bj) = cg2d_min(i,j,bi,bj) |
| 322 |
ENDDO |
| 323 |
ENDDO |
| 324 |
ENDIF |
| 325 |
ENDDO |
| 326 |
ENDDO |
| 327 |
ENDIF |
| 328 |
|
| 329 |
IF (cg2dNormaliseRHS) THEN |
| 330 |
C-- Un-normalise the answer |
| 331 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 332 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 333 |
DO j=1,sNy |
| 334 |
DO i=1,sNx |
| 335 |
cg2d_x(i,j,bi,bj) = cg2d_x(i,j,bi,bj)/rhsNorm(bi,bj) |
| 336 |
ENDDO |
| 337 |
ENDDO |
| 338 |
ENDDO |
| 339 |
ENDDO |
| 340 |
ENDIF |
| 341 |
|
| 342 |
C-- Return parameters to caller |
| 343 |
C return largest Iter # and Max residual in numIters and lastResidual |
| 344 |
C return lowest Iter # and Min residual(^2) in nIterMin and minResidualSq |
| 345 |
_GLOBAL_MAX_RL( err_sq, myThid ) |
| 346 |
nIterMin = numIters |
| 347 |
numIters = 0 |
| 348 |
minResidualSq = err_sq |
| 349 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 350 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 351 |
nIterMin = MIN( actualIts(bi,bj), nIterMin ) |
| 352 |
numIters = MAX( actualIts(bi,bj), numIters ) |
| 353 |
minResidualSq = MIN( errTile(bi,bj), minResidualSq ) |
| 354 |
ENDDO |
| 355 |
ENDDO |
| 356 |
lastResidual = SQRT(err_sq) |
| 357 |
alpha = -nIterMin |
| 358 |
_GLOBAL_MAX_RL( alpha, myThid ) |
| 359 |
nIterMin = NINT( -alpha ) |
| 360 |
alpha = numIters |
| 361 |
_GLOBAL_MAX_RL( alpha, myThid ) |
| 362 |
numIters = NINT( alpha ) |
| 363 |
alpha = -minResidualSq |
| 364 |
_GLOBAL_MAX_RL( alpha, myThid ) |
| 365 |
minResidualSq = -alpha |
| 366 |
|
| 367 |
RETURN |
| 368 |
END |
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