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C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_fgmres.F,v 1.16 2013/02/13 09:14:58 mlosch Exp $ |
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C $Name: $ |
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|
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#include "SEAICE_OPTIONS.h" |
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|
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C-- File seaice_fgmres.F: seaice fgmres dynamical (linear) solver S/R: |
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C-- Contents |
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C-- o SEAICE_FGMRES_DRIVER |
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C-- o SEAICE_MAP2VEC |
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C-- o SEAICE_MAP_RS2VEC |
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C-- o SEAICE_FGMRES |
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C-- o SEAICE_SCALPROD |
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|
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CBOP |
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C !ROUTINE: SEAICE_FGMRES_DRIVER |
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C !INTERFACE: |
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|
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SUBROUTINE SEAICE_FGMRES_DRIVER( |
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I uIceRes, vIceRes, |
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U duIce, dvIce, |
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U iCode, |
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I FGMRESeps, iOutFGMRES, |
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I newtonIter, |
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U krylovIter, |
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I myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SEAICE_FGMRES_DRIVER |
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C | o driver routine for fgmres |
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C | o does the conversion between 2D fields and 1D vector |
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C | back and forth |
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C *==========================================================* |
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C | written by Martin Losch, Oct 2012 |
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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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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "SEAICE_SIZE.h" |
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#include "SEAICE_PARAMS.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 myTime :: Simulation time |
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C myIter :: Simulation timestep number |
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C myThid :: my Thread Id. number |
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C newtonIter :: current iterate of Newton iteration (for diagnostics) |
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C krylovIter :: current iterate of Newton iteration (updated) |
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C iCode :: FGMRES parameter to determine next step |
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C iOutFGMRES :: control output of fgmres |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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INTEGER newtonIter |
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INTEGER krylovIter |
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INTEGER iOutFGMRES |
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INTEGER iCode |
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C FGMRESeps :: tolerance for FGMRES |
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_RL FGMRESeps |
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C du/vIce :: solution vector |
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_RL duIce(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL dvIce(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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C u/vIceRes :: residual F(u) |
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_RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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|
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#if ( defined (SEAICE_CGRID) && \ |
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defined (SEAICE_ALLOW_JFNK) && \ |
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defined (SEAICE_ALLOW_DYNAMICS) ) |
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C Local variables: |
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C k :: loop indices |
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INTEGER k, bi, bj |
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C FGMRES parameters |
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C nVec :: size of the input vector(s) |
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C im :: size of Krylov space |
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C ifgmres :: interation counter |
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INTEGER nVec |
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PARAMETER ( nVec = 2*sNx*sNy ) |
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INTEGER im |
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PARAMETER ( im = 50 ) |
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INTEGER ifgmres |
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C work arrays |
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_RL rhs(nVec,nSx,nSy), sol(nVec,nSx,nSy) |
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_RL vv(nVec,im+1,nSx,nSy), w(nVec,im,nSx,nSy) |
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_RL wk1(nVec,nSx,nSy), wk2(nVec,nSx,nSy) |
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C need to store some of the fgmres parameters and fields so that |
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C they are not forgotten between Krylov iterations |
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COMMON /FGMRES_I/ ifgmres |
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COMMON /FGMRES_RL/ sol, rhs, vv, w |
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CEOP |
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|
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IF ( iCode .EQ. 0 ) THEN |
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C The first guess is zero because it is a correction, but this |
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C is implemented by setting du/vIce=0 outside of this routine; |
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C this make it possible to restart FGMRES with a nonzero sol |
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CALL SEAICE_MAP2VEC(nVec,duIce,dvIce,sol,.TRUE.,myThid) |
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C wk2 needs to be reset for iCode = 0, because it may contain |
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C remains of the previous Krylov iteration |
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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 k=1,nVec |
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wk2(k,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSEIF ( iCode .EQ. 3 ) THEN |
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CALL SEAICE_MAP2VEC(nVec,uIceRes,vIceRes,rhs,.TRUE.,myThid) |
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C change sign of rhs because we are solving J*u = -F |
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C wk2 needs to be initialised for iCode = 3, because it may contain |
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C garbage |
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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 k=1,nVec |
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rhs(k,bi,bj) = -rhs(k,bi,bj) |
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wk2(k,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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C map preconditioner results or Jacobian times vector, |
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C stored in du/vIce to wk2 |
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CALL SEAICE_MAP2VEC(nVec,duIce,dvIce,wk2,.TRUE.,myThid) |
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ENDIF |
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C |
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CALL SEAICE_FGMRES (nVec,im,rhs,sol,ifgmres,krylovIter, |
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U vv,w,wk1,wk2, |
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I FGMRESeps,SEAICEkrylovIterMax,iOutFGMRES, |
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U iCode, |
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I myThid) |
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C |
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IF ( iCode .EQ. 0 ) THEN |
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C map sol(ution) vector to du/vIce |
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CALL SEAICE_MAP2VEC(nVec,duIce,dvIce,sol,.FALSE.,myThid) |
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ELSE |
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C map work vector to du/vIce to either compute a preconditioner |
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C solution (wk1=rhs) or a Jacobian times wk1 |
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CALL SEAICE_MAP2VEC(nVec,duIce,dvIce,wk1,.FALSE.,myThid) |
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ENDIF |
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|
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C Fill overlaps in updated fields |
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CALL EXCH_UV_XY_RL( duIce, dvIce,.TRUE.,myThid) |
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|
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RETURN |
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END |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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CBOP |
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C !ROUTINE: SEAICE_MAP2VEC |
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C !INTERFACE: |
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|
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SUBROUTINE SEAICE_MAP2VEC( |
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I n, |
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O xfld2d, yfld2d, |
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U vector, |
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I map2vec, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SEAICE_MAP2VEC |
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C | o maps 2 2D-fields to vector and back |
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C *==========================================================* |
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C | written by Martin Losch, Oct 2012 |
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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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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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C === Routine arguments === |
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INTEGER n |
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LOGICAL map2vec |
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INTEGER myThid |
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_RL xfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL yfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vector (n,nSx,nSy) |
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C === local variables === |
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INTEGER I, J, bi, bj |
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INTEGER ii, jj, m |
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CEOP |
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|
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m = n/2 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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#ifdef SEAICE_JFNK_MAP_REORDER |
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ii = 0 |
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IF ( map2vec ) THEN |
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DO J=1,sNy |
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jj = 2*sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + 2*I |
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vector(ii-1,bi,bj) = xfld2d(I,J,bi,bj) |
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vector(ii, bi,bj) = yfld2d(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ELSE |
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DO J=1,sNy |
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jj = 2*sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + 2*I |
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xfld2d(I,J,bi,bj) = vector(ii-1,bi,bj) |
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yfld2d(I,J,bi,bj) = vector(ii, bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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#else |
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IF ( map2vec ) THEN |
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DO J=1,sNy |
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jj = sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + I |
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vector(ii, bi,bj) = xfld2d(I,J,bi,bj) |
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vector(ii+m,bi,bj) = yfld2d(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ELSE |
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DO J=1,sNy |
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jj = sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + I |
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xfld2d(I,J,bi,bj) = vector(ii, bi,bj) |
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yfld2d(I,J,bi,bj) = vector(ii+m,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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#endif /* SEAICE_JFNK_MAP_REORDER */ |
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C bi,bj-loops |
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ENDDO |
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ENDDO |
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|
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RETURN |
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END |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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CBOP |
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C !ROUTINE: SEAICE_MAP_RS2VEC |
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C !INTERFACE: |
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|
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SUBROUTINE SEAICE_MAP_RS2VEC( |
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I n, |
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O xfld2d, yfld2d, |
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U vector, |
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I map2vec, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SEAICE_MAP_RS2VEC |
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C | o maps 2 2D-RS-fields to vector and back |
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C *==========================================================* |
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C | written by Martin Losch, Oct 2012 |
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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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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
| 267 |
C === Routine arguments === |
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INTEGER n |
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LOGICAL map2vec |
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INTEGER myThid |
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_RS xfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
| 272 |
_RS yfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vector (n,nSx,nSy) |
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C === local variables === |
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INTEGER I, J, bi, bj |
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INTEGER ii, jj, m |
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CEOP |
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|
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m = n/2 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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#ifdef SEAICE_JFNK_MAP_REORDER |
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ii = 0 |
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IF ( map2vec ) THEN |
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DO J=1,sNy |
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jj = 2*sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + 2*I |
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vector(ii-1,bi,bj) = xfld2d(I,J,bi,bj) |
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vector(ii, bi,bj) = yfld2d(I,J,bi,bj) |
| 291 |
ENDDO |
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ENDDO |
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ELSE |
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DO J=1,sNy |
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jj = 2*sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + 2*I |
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xfld2d(I,J,bi,bj) = vector(ii-1,bi,bj) |
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yfld2d(I,J,bi,bj) = vector(ii, bi,bj) |
| 300 |
ENDDO |
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ENDDO |
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ENDIF |
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#else |
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IF ( map2vec ) THEN |
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DO J=1,sNy |
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jj = sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + I |
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vector(ii, bi,bj) = xfld2d(I,J,bi,bj) |
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vector(ii+m,bi,bj) = yfld2d(I,J,bi,bj) |
| 311 |
ENDDO |
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ENDDO |
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ELSE |
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DO J=1,sNy |
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jj = sNx*(J-1) |
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DO I=1,sNx |
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ii = jj + I |
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xfld2d(I,J,bi,bj) = vector(ii, bi,bj) |
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yfld2d(I,J,bi,bj) = vector(ii+m,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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#endif /* SEAICE_JFNK_MAP_REORDER */ |
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C bi,bj-loops |
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ENDDO |
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ENDDO |
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|
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RETURN |
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END |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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CBOP |
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C !ROUTINE: SEAICE_FGMRES |
| 334 |
C !INTERFACE: |
| 335 |
SUBROUTINE SEAICE_FGMRES ( |
| 336 |
I n,im,rhs, |
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U sol,i,its,vv,w,wk1,wk2, |
| 338 |
I eps,maxits,iout, |
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U icode, |
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I myThid ) |
| 341 |
|
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C----------------------------------------------------------------------- |
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C mlosch Oct 2012: modified the routine further to be compliant with |
| 344 |
C MITgcm standards: |
| 345 |
C f90 -> F |
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C !-comment -> C-comment |
| 347 |
C add its to list of arguments |
| 348 |
C double precision -> _RL |
| 349 |
C implicit none |
| 350 |
C |
| 351 |
C jfl Dec 1st 2006. We modified the routine so that it is double precison. |
| 352 |
C Here are the modifications: |
| 353 |
C 1) implicit real (a-h,o-z) becomes implicit real*8 (a-h,o-z) |
| 354 |
C 2) real bocomes real*8 |
| 355 |
C 3) subroutine scopy.f has been changed for dcopy.f |
| 356 |
C 4) subroutine saxpy.f has been changed for daxpy.f |
| 357 |
C 5) function sdot.f has been changed for ddot.f |
| 358 |
C 6) 1e-08 becomes 1d-08 |
| 359 |
C |
| 360 |
C Be careful with the dcopy, daxpy and ddot code...there is a slight |
| 361 |
C difference with the single precision versions (scopy, saxpy and sdot). |
| 362 |
C In the single precision versions, the array are declared sightly differently. |
| 363 |
C It is written for single precision: |
| 364 |
C |
| 365 |
C modified 12/3/93, array(1) declarations changed to array(*) |
| 366 |
C----------------------------------------------------------------------- |
| 367 |
|
| 368 |
implicit none |
| 369 |
C === Global variables === |
| 370 |
#include "SIZE.h" |
| 371 |
#include "EEPARAMS.h" |
| 372 |
CML implicit double precision (a-h,o-z) !jfl modification |
| 373 |
integer myThid |
| 374 |
integer n, im, its, maxits, iout, icode |
| 375 |
_RL rhs(n,nSx,nSy), sol(n,nSx,nSy) |
| 376 |
_RL vv(n,im+1,nSx,nSy), w(n,im,nSx,nSy) |
| 377 |
_RL wk1(n,nSx,nSy), wk2(n,nSx,nSy), eps |
| 378 |
C----------------------------------------------------------------------- |
| 379 |
C flexible GMRES routine. This is a version of GMRES which allows a |
| 380 |
C a variable preconditioner. Implemented with a reverse communication |
| 381 |
C protocole for flexibility - |
| 382 |
C DISTRIBUTED VERSION (USES DISTDOT FOR DDOT) |
| 383 |
C explicit (exact) residual norms for restarts |
| 384 |
C written by Y. Saad, modified by A. Malevsky, version February 1, 1995 |
| 385 |
C----------------------------------------------------------------------- |
| 386 |
C This Is A Reverse Communication Implementation. |
| 387 |
C------------------------------------------------- |
| 388 |
C USAGE: (see also comments for icode below). FGMRES |
| 389 |
C should be put in a loop and the loop should be active for as |
| 390 |
C long as icode is not equal to 0. On return fgmres will |
| 391 |
C 1) either be requesting the new preconditioned vector applied |
| 392 |
C to wk1 in case icode.eq.1 (result should be put in wk2) |
| 393 |
C 2) or be requesting the product of A applied to the vector wk1 |
| 394 |
C in case icode.eq.2 (result should be put in wk2) |
| 395 |
C 3) or be terminated in case icode .eq. 0. |
| 396 |
C on entry always set icode = 0. So icode should be set back to zero |
| 397 |
C upon convergence. |
| 398 |
C----------------------------------------------------------------------- |
| 399 |
C Here is a typical way of running fgmres: |
| 400 |
C |
| 401 |
C icode = 0 |
| 402 |
C 1 continue |
| 403 |
C call fgmres (n,im,rhs,sol,i,vv,w,wk1,wk2,eps,maxits,iout, |
| 404 |
C & icode,its,mythid) |
| 405 |
C |
| 406 |
C if (icode .eq. 1) then |
| 407 |
C call precon(n, wk1, wk2) <--- user variable preconditioning |
| 408 |
C goto 1 |
| 409 |
C else if (icode .ge. 2) then |
| 410 |
C call matvec (n,wk1, wk2) <--- user matrix vector product. |
| 411 |
C goto 1 |
| 412 |
C else |
| 413 |
C ----- done ---- |
| 414 |
C ......... |
| 415 |
C----------------------------------------------------------------------- |
| 416 |
C list of parameters |
| 417 |
C------------------- |
| 418 |
C |
| 419 |
C n == integer. the dimension of the problem |
| 420 |
C im == size of Krylov subspace: should not exceed 50 in this |
| 421 |
C version (can be reset in code. looking at comment below) |
| 422 |
C rhs == vector of length n containing the right hand side |
| 423 |
C sol == initial guess on input, approximate solution on output |
| 424 |
C vv == work space of size n x (im+1) |
| 425 |
C w == work space of length n x im |
| 426 |
C wk1, |
| 427 |
C wk2, == two work vectors of length n each used for the reverse |
| 428 |
C communication protocole. When on return (icode .ne. 1) |
| 429 |
C the user should call fgmres again with wk2 = precon * wk1 |
| 430 |
C and icode untouched. When icode.eq.1 then it means that |
| 431 |
C convergence has taken place. |
| 432 |
C |
| 433 |
C eps == tolerance for stopping criterion. process is stopped |
| 434 |
C as soon as ( ||.|| is the euclidean norm): |
| 435 |
C || current residual||/||initial residual|| <= eps |
| 436 |
C |
| 437 |
C maxits== maximum number of iterations allowed |
| 438 |
C |
| 439 |
C i == internal iteration counter, updated in this routine |
| 440 |
C its == current (Krylov) iteration counter, updated in this routine |
| 441 |
C |
| 442 |
C iout == output unit number number for printing intermediate results |
| 443 |
C if (iout .le. 0) no statistics are printed. |
| 444 |
C |
| 445 |
C icode = integer. indicator for the reverse communication protocole. |
| 446 |
C ON ENTRY : icode should be set to icode = 0. |
| 447 |
C ON RETURN: |
| 448 |
C * icode .eq. 1 value means that fgmres has not finished |
| 449 |
C and that it is requesting a preconditioned vector before |
| 450 |
C continuing. The user must compute M**(-1) wk1, where M is |
| 451 |
C the preconditioing matrix (may vary at each call) and wk1 is |
| 452 |
C the vector as provided by fgmres upun return, and put the |
| 453 |
C result in wk2. Then fgmres must be called again without |
| 454 |
C changing any other argument. |
| 455 |
C * icode .eq. 2 value means that fgmres has not finished |
| 456 |
C and that it is requesting a matrix vector product before |
| 457 |
C continuing. The user must compute A * wk1, where A is the |
| 458 |
C coefficient matrix and wk1 is the vector provided by |
| 459 |
C upon return. The result of the operation is to be put in |
| 460 |
C the vector wk2. Then fgmres must be called again without |
| 461 |
C changing any other argument. |
| 462 |
C * icode .eq. 0 means that fgmres has finished and sol contains |
| 463 |
C the approximate solution. |
| 464 |
C comment: typically fgmres must be implemented in a loop |
| 465 |
C with fgmres being called as long icode is returned with |
| 466 |
C a value .ne. 0. |
| 467 |
C----------------------------------------------------------------------- |
| 468 |
C local variables -- !jfl modif |
| 469 |
integer imax |
| 470 |
parameter ( imax = 50 ) |
| 471 |
_RL hh(4*imax+1,4*imax),c(4*imax),s(4*imax) |
| 472 |
_RL rs(4*imax+1),t,ro |
| 473 |
C------------------------------------------------------------- |
| 474 |
C arnoldi size should not exceed 50 in this version.. |
| 475 |
C------------------------------------------------------------- |
| 476 |
integer i, i1, ii, j, jj, k, k1!, n1 |
| 477 |
integer bi, bj |
| 478 |
_RL r0, gam, epsmac, eps1 |
| 479 |
CHARACTER*(MAX_LEN_MBUF) msgBuf |
| 480 |
|
| 481 |
CEOP |
| 482 |
CML save |
| 483 |
C local common block to replace the save statement |
| 484 |
COMMON /SEAICE_FMRES_LOC_I/ i1 |
| 485 |
COMMON /SEAICE_FMRES_LOC_RL/ |
| 486 |
& hh, c, s, rs, t, ro, r0, gam, epsmac, eps1 |
| 487 |
data epsmac/1.d-16/ |
| 488 |
C |
| 489 |
C computed goto |
| 490 |
C |
| 491 |
if ( im .gt. imax ) stop 'size of krylov space > 50' |
| 492 |
goto (100,200,300,11) icode +1 |
| 493 |
100 continue |
| 494 |
CML n1 = n + 1 |
| 495 |
its = 0 |
| 496 |
C------------------------------------------------------------- |
| 497 |
C ** outer loop starts here.. |
| 498 |
C--------------compute initial residual vector -------------- |
| 499 |
C 10 continue |
| 500 |
CML call dcopy (n, sol, 1, wk1, 1) !jfl modification |
| 501 |
do bj=myByLo(myThid),myByHi(myThid) |
| 502 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 503 |
do j=1,n |
| 504 |
wk1(j,bi,bj)=sol(j,bi,bj) |
| 505 |
enddo |
| 506 |
enddo |
| 507 |
enddo |
| 508 |
icode = 3 |
| 509 |
RETURN |
| 510 |
11 continue |
| 511 |
do bj=myByLo(myThid),myByHi(myThid) |
| 512 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 513 |
do j=1,n |
| 514 |
vv(j,1,bi,bj) = rhs(j,bi,bj) - wk2(j,bi,bj) |
| 515 |
enddo |
| 516 |
enddo |
| 517 |
enddo |
| 518 |
20 continue |
| 519 |
CML ro = ddot(n, vv, 1, vv,1) !jfl modification |
| 520 |
call SEAICE_SCALPROD(n, im+1, 1, 1, vv, vv, ro, myThid) |
| 521 |
ro = sqrt(ro) |
| 522 |
if (ro .eq. 0.0 _d 0) goto 999 |
| 523 |
t = 1.0 _d 0/ ro |
| 524 |
do bj=myByLo(myThid),myByHi(myThid) |
| 525 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 526 |
do j=1, n |
| 527 |
vv(j,1,bi,bj) = vv(j,1,bi,bj)*t |
| 528 |
enddo |
| 529 |
enddo |
| 530 |
enddo |
| 531 |
if (its .eq. 0) eps1=eps |
| 532 |
C not sure what this is, r0 is never used again |
| 533 |
if (its .eq. 0) r0 = ro |
| 534 |
if (iout .gt. 0) then |
| 535 |
_BEGIN_MASTER( myThid ) |
| 536 |
write(msgBuf, 199) its, ro |
| 537 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 538 |
& SQUEEZE_RIGHT, myThid ) |
| 539 |
C print *,'chau',its, ro !write(iout, 199) its, ro |
| 540 |
_END_MASTER( myThid ) |
| 541 |
endif |
| 542 |
C |
| 543 |
C initialize 1-st term of rhs of hessenberg system.. |
| 544 |
C |
| 545 |
rs(1) = ro |
| 546 |
i = 0 |
| 547 |
4 continue |
| 548 |
i=i+1 |
| 549 |
its = its + 1 |
| 550 |
i1 = i + 1 |
| 551 |
do bj=myByLo(myThid),myByHi(myThid) |
| 552 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 553 |
do k=1, n |
| 554 |
wk1(k,bi,bj) = vv(k,i,bi,bj) |
| 555 |
enddo |
| 556 |
enddo |
| 557 |
enddo |
| 558 |
C |
| 559 |
C return |
| 560 |
C |
| 561 |
icode = 1 |
| 562 |
RETURN |
| 563 |
200 continue |
| 564 |
do bj=myByLo(myThid),myByHi(myThid) |
| 565 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 566 |
do k=1, n |
| 567 |
w(k,i,bi,bj) = wk2(k,bi,bj) |
| 568 |
enddo |
| 569 |
enddo |
| 570 |
enddo |
| 571 |
C |
| 572 |
C call matvec operation |
| 573 |
C |
| 574 |
CML call dcopy(n, wk2, 1, wk1, 1) !jfl modification |
| 575 |
do bj=myByLo(myThid),myByHi(myThid) |
| 576 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 577 |
do k=1,n |
| 578 |
wk1(k,bi,bj)=wk2(k,bi,bj) |
| 579 |
enddo |
| 580 |
enddo |
| 581 |
enddo |
| 582 |
C |
| 583 |
C return |
| 584 |
C |
| 585 |
icode = 2 |
| 586 |
RETURN |
| 587 |
300 continue |
| 588 |
C |
| 589 |
C first call to ope corresponds to intialization goto back to 11. |
| 590 |
C |
| 591 |
C if (icode .eq. 3) goto 11 |
| 592 |
CML call dcopy (n, wk2, 1, vv(1,i1), 1) !jfl modification |
| 593 |
do bj=myByLo(myThid),myByHi(myThid) |
| 594 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 595 |
do k=1,n |
| 596 |
vv(k,i1,bi,bj)=wk2(k,bi,bj) |
| 597 |
enddo |
| 598 |
enddo |
| 599 |
enddo |
| 600 |
C |
| 601 |
C modified gram - schmidt... |
| 602 |
C |
| 603 |
do j=1, i |
| 604 |
CML t = ddot(n, vv(1,j), 1, vv(1,i1), 1) !jfl modification |
| 605 |
call SEAICE_SCALPROD(n, im+1, j, i1, vv, vv, t, myThid) |
| 606 |
hh(j,i) = t |
| 607 |
CML call daxpy(n, -t, vv(1,j), 1, vv(1,i1), 1) !jfl modification |
| 608 |
CML enddo |
| 609 |
CML do j=1, i |
| 610 |
CML t = hh(j,i) |
| 611 |
do bj=myByLo(myThid),myByHi(myThid) |
| 612 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 613 |
do k=1,n |
| 614 |
vv(k,i1,bi,bj) = vv(k,i1,bi,bj) - t*vv(k,j,bi,bj) |
| 615 |
enddo |
| 616 |
enddo |
| 617 |
enddo |
| 618 |
enddo |
| 619 |
CML t = sqrt(ddot(n, vv(1,i1), 1, vv(1,i1), 1)) !jfl modification |
| 620 |
call SEAICE_SCALPROD(n, im+1, i1, i1, vv, vv, t, myThid) |
| 621 |
t = sqrt(t) |
| 622 |
hh(i1,i) = t |
| 623 |
if (t .ne. 0.0 _d 0) then |
| 624 |
t = 1.0 _d 0 / t |
| 625 |
do bj=myByLo(myThid),myByHi(myThid) |
| 626 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 627 |
do k=1,n |
| 628 |
vv(k,i1,bi,bj) = vv(k,i1,bi,bj)*t |
| 629 |
enddo |
| 630 |
enddo |
| 631 |
enddo |
| 632 |
endif |
| 633 |
C |
| 634 |
C done with modified gram schimd and arnoldi step. |
| 635 |
C now update factorization of hh |
| 636 |
C |
| 637 |
if (i .ne. 1) then |
| 638 |
C |
| 639 |
C perfrom previous transformations on i-th column of h |
| 640 |
C |
| 641 |
do k=2,i |
| 642 |
k1 = k-1 |
| 643 |
t = hh(k1,i) |
| 644 |
hh(k1,i) = c(k1)*t + s(k1)*hh(k,i) |
| 645 |
hh(k,i) = -s(k1)*t + c(k1)*hh(k,i) |
| 646 |
enddo |
| 647 |
endif |
| 648 |
gam = sqrt(hh(i,i)**2 + hh(i1,i)**2) |
| 649 |
if (gam .eq. 0.0 _d 0) gam = epsmac |
| 650 |
C-----------#determine next plane rotation #------------------- |
| 651 |
c(i) = hh(i,i)/gam |
| 652 |
s(i) = hh(i1,i)/gam |
| 653 |
C numerically more stable Givens rotation, but the results |
| 654 |
C are not better |
| 655 |
CML c(i)=1. _d 0 |
| 656 |
CML s(i)=0. _d 0 |
| 657 |
CML if ( abs(hh(i1,i)) .gt. 0.0 _d 0) then |
| 658 |
CML if ( abs(hh(i1,i)) .gt. abs(hh(i,i)) ) then |
| 659 |
CML gam = hh(i,i)/hh(i1,i) |
| 660 |
CML s(i) = 1./sqrt(1.+gam*gam) |
| 661 |
CML c(i) = s(i)*gam |
| 662 |
CML else |
| 663 |
CML gam = hh(i1,i)/hh(i,i) |
| 664 |
CML c(i) = 1./sqrt(1.+gam*gam) |
| 665 |
CML s(i) = c(i)*gam |
| 666 |
CML endif |
| 667 |
CML endif |
| 668 |
rs(i1) = -s(i)*rs(i) |
| 669 |
rs(i) = c(i)*rs(i) |
| 670 |
C |
| 671 |
C determine res. norm. and test for convergence |
| 672 |
C |
| 673 |
hh(i,i) = c(i)*hh(i,i) + s(i)*hh(i1,i) |
| 674 |
ro = abs(rs(i1)) |
| 675 |
if (iout .gt. 0) then |
| 676 |
_BEGIN_MASTER( myThid ) |
| 677 |
write(msgBuf, 199) its, ro |
| 678 |
CALL PRINT_MESSAGE( msgBuf, standardMessageUnit, |
| 679 |
& SQUEEZE_RIGHT, myThid ) |
| 680 |
_END_MASTER( myThid ) |
| 681 |
endif |
| 682 |
if (i .lt. im .and. (ro .gt. eps1)) goto 4 |
| 683 |
C |
| 684 |
C now compute solution. first solve upper triangular system. |
| 685 |
C |
| 686 |
rs(i) = rs(i)/hh(i,i) |
| 687 |
do ii=2,i |
| 688 |
k=i-ii+1 |
| 689 |
k1 = k+1 |
| 690 |
t=rs(k) |
| 691 |
do j=k1,i |
| 692 |
t = t-hh(k,j)*rs(j) |
| 693 |
enddo |
| 694 |
rs(k) = t/hh(k,k) |
| 695 |
enddo |
| 696 |
C |
| 697 |
C done with back substitution.. |
| 698 |
C now form linear combination to get solution |
| 699 |
C |
| 700 |
do j=1, i |
| 701 |
t = rs(j) |
| 702 |
CML call daxpy(n, t, w(1,j), 1, sol,1) !jfl modification |
| 703 |
do bj=myByLo(myThid),myByHi(myThid) |
| 704 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 705 |
do k=1,n |
| 706 |
sol(k,bi,bj) = sol(k,bi,bj) + t*w(k,j,bi,bj) |
| 707 |
enddo |
| 708 |
enddo |
| 709 |
enddo |
| 710 |
enddo |
| 711 |
C |
| 712 |
C test for return |
| 713 |
C |
| 714 |
if (ro .le. eps1 .or. its .ge. maxits) goto 999 |
| 715 |
C |
| 716 |
C else compute residual vector and continue.. |
| 717 |
C |
| 718 |
C goto 10 |
| 719 |
|
| 720 |
do j=1,i |
| 721 |
jj = i1-j+1 |
| 722 |
rs(jj-1) = -s(jj-1)*rs(jj) |
| 723 |
rs(jj) = c(jj-1)*rs(jj) |
| 724 |
enddo |
| 725 |
do j=1,i1 |
| 726 |
t = rs(j) |
| 727 |
if (j .eq. 1) t = t-1.0 _d 0 |
| 728 |
CML call daxpy (n, t, vv(1,j), 1, vv, 1) |
| 729 |
do bj=myByLo(myThid),myByHi(myThid) |
| 730 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 731 |
do k=1,n |
| 732 |
vv(k,1,bi,bj) = vv(k,1,bi,bj) + t*vv(k,j,bi,bj) |
| 733 |
enddo |
| 734 |
enddo |
| 735 |
enddo |
| 736 |
enddo |
| 737 |
C |
| 738 |
C restart outer loop. |
| 739 |
C |
| 740 |
goto 20 |
| 741 |
999 icode = 0 |
| 742 |
|
| 743 |
199 format(' SEAICE_FGMRES: its =', i4, ' res. norm =', d26.16) |
| 744 |
C |
| 745 |
RETURN |
| 746 |
C-----end-of-fgmres----------------------------------------------------- |
| 747 |
C----------------------------------------------------------------------- |
| 748 |
END |
| 749 |
|
| 750 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 751 |
CBOP |
| 752 |
C !ROUTINE: SEAICE_SCALPROD |
| 753 |
C !INTERFACE: |
| 754 |
|
| 755 |
subroutine SEAICE_SCALPROD(n,im,i1,i2,dx,dy,t,myThid) |
| 756 |
|
| 757 |
C forms the dot product of two vectors. |
| 758 |
C uses unrolled loops for increments equal to one. |
| 759 |
C jack dongarra, linpack, 3/11/78. |
| 760 |
C ML: code stolen from BLAS-ddot and adapted for parallel applications |
| 761 |
|
| 762 |
implicit none |
| 763 |
#include "SIZE.h" |
| 764 |
#include "EEPARAMS.h" |
| 765 |
#include "EESUPPORT.h" |
| 766 |
#include "SEAICE_SIZE.h" |
| 767 |
#include "SEAICE.h" |
| 768 |
integer n, im, i1, i2 |
| 769 |
_RL dx(n,im,nSx,nSy),dy(n,im,nSx,nSy) |
| 770 |
_RL t |
| 771 |
integer myThid |
| 772 |
C local arrays |
| 773 |
_RL dtemp(nSx,nSy) |
| 774 |
integer i,m,mp1,bi,bj |
| 775 |
CEOP |
| 776 |
|
| 777 |
m = mod(n,5) |
| 778 |
mp1 = m + 1 |
| 779 |
t = 0. _d 0 |
| 780 |
c if( m .eq. 0 ) go to 40 |
| 781 |
do bj=myByLo(myThid),myByHi(myThid) |
| 782 |
do bi=myBxLo(myThid),myBxHi(myThid) |
| 783 |
dtemp(bi,bj) = 0. _d 0 |
| 784 |
if ( m .ne. 0 ) then |
| 785 |
do i = 1,m |
| 786 |
dtemp(bi,bj) = dtemp(bi,bj) + dx(i,i1,bi,bj)*dy(i,i2,bi,bj) |
| 787 |
& * scalarProductMetric(i,1,bi,bj) |
| 788 |
enddo |
| 789 |
endif |
| 790 |
if ( n .ge. 5 ) then |
| 791 |
c if( n .lt. 5 ) go to 60 |
| 792 |
c40 mp1 = m + 1 |
| 793 |
do i = mp1,n,5 |
| 794 |
dtemp(bi,bj) = dtemp(bi,bj) + |
| 795 |
& dx(i, i1,bi,bj)*dy(i, i2,bi,bj) |
| 796 |
& * scalarProductMetric(i, 1, bi,bj) + |
| 797 |
& dx(i + 1,i1,bi,bj)*dy(i + 1,i2,bi,bj) |
| 798 |
& * scalarProductMetric(i + 1,1, bi,bj) + |
| 799 |
& dx(i + 2,i1,bi,bj)*dy(i + 2,i2,bi,bj) |
| 800 |
& * scalarProductMetric(i + 2,1, bi,bj) + |
| 801 |
& dx(i + 3,i1,bi,bj)*dy(i + 3,i2,bi,bj) |
| 802 |
& * scalarProductMetric(i + 3,1, bi,bj) + |
| 803 |
& dx(i + 4,i1,bi,bj)*dy(i + 4,i2,bi,bj) |
| 804 |
& * scalarProductMetric(i + 4,1, bi,bj) |
| 805 |
enddo |
| 806 |
c60 continue |
| 807 |
endif |
| 808 |
enddo |
| 809 |
enddo |
| 810 |
CALL GLOBAL_SUM_TILE_RL( dtemp,t,myThid ) |
| 811 |
|
| 812 |
#endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_JFNK */ |
| 813 |
|
| 814 |
RETURN |
| 815 |
END |
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