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C $Header: /u/gcmpack/MITgcm/model/src/solve_pentadiagonal.F,v 1.3 2010/03/16 00:08:27 jmc Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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C o Switch to code that has the k-loop inside the |
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C ij-loops, which matters in adjoint mode. |
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#ifdef ALLOW_AUTODIFF |
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#define ALLOW_SOLVERS_KLOOPINSIDE |
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#endif |
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|
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CBOP |
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C !ROUTINE: SOLVE_PENTADIAGONAL |
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C !INTERFACE: |
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SUBROUTINE SOLVE_PENTADIAGONAL( |
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I iMin,iMax, jMin,jMax, |
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U a5d, b5d, c5d, d5d, e5d, |
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U y5d, |
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O errCode, |
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I bi, bj, myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | S/R SOLVE_PENTADIAGONAL |
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C | o Solve a penta-diagonal system A*X=Y (dimension Nr) |
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C *==========================================================* |
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C | o Used to solve implicitly vertical advection & diffusion |
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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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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine Arguments == |
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C INPUT: |
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C iMin,iMax,jMin,jMax :: computational domain |
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C a5d :: 2nd lower diagonal of the pentadiagonal matrix |
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C b5d :: 1rst lower diagonal of the pentadiagonal matrix |
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C c5d :: main diagonal of the pentadiagonal matrix |
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C d5d :: 1rst upper diagonal of the pentadiagonal matrix |
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C e5d :: 2nd upper diagonal of the pentadiagonal matrix |
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C y5d :: Y vector (R.H.S.); |
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C bi,bj :: tile indices |
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C myThid :: thread number |
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C OUTPUT: |
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C y5d :: X = solution of A*X=Y |
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C a5d,b5d,c5d,d5d,e5d :: modified to enable to find Xp solution of |
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C A*Xp=Yp without solving the full system again |
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C errCode :: > 0 if singular matrix |
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INTEGER iMin,iMax,jMin,jMax |
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_RL a5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL b5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL c5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL d5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL e5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL y5d(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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INTEGER errCode |
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INTEGER bi, bj, myThid |
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|
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C !LOCAL VARIABLES: |
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C == Local variables == |
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INTEGER i,j,k |
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#ifdef ALLOW_SOLVERS_KLOOPINSIDE |
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_RL y5d_m1(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL a5d_prime(Nr), b5d_prime(Nr) |
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_RL c5d_prime(Nr), d5d_prime(Nr), e5d_prime(Nr) |
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_RL y5d_prime(Nr), y5d_update(Nr), tmpval |
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#endif |
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CEOP |
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|
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#ifndef ALLOW_SOLVERS_KLOOPINSIDE |
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|
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errCode = 0 |
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|
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DO k=1,Nr |
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C-- forward sweep (starting from top) |
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IF (k.EQ.1) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( c5d(i,j,k).NE.0. _d 0 ) THEN |
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c5d(i,j,k) = 1. _d 0 / c5d(i,j,k) |
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ELSE |
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c5d(i,j,k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ENDDO |
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ENDDO |
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|
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ELSEIF (k.EQ.2) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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C-- [k] <- [k] - b_k/c_k-1 * [k-1] |
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b5d(i,j,k) = b5d(i,j,k)*c5d(i,j,k-1) |
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c5d(i,j,k) = c5d(i,j,k) - b5d(i,j,k)*d5d(i,j,k-1) |
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d5d(i,j,k) = d5d(i,j,k) - b5d(i,j,k)*e5d(i,j,k-1) |
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y5d(i,j,k,bi,bj) = y5d(i,j,k,bi,bj) |
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& - b5d(i,j,k)*y5d(i,j,k-1,bi,bj) |
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IF ( c5d(i,j,k).NE.0. _d 0 ) THEN |
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c5d(i,j,k) = 1. _d 0 / c5d(i,j,k) |
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ELSE |
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c5d(i,j,k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ENDDO |
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ENDDO |
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|
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ELSE |
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C-- Middle of forward sweep |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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C-- [k] <- [k] - a_k/c_k-2 * [k-2] |
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a5d(i,j,k) = a5d(i,j,k)*c5d(i,j,k-2) |
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b5d(i,j,k) = b5d(i,j,k) - a5d(i,j,k)*d5d(i,j,k-2) |
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c5d(i,j,k) = c5d(i,j,k) - a5d(i,j,k)*e5d(i,j,k-2) |
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C-- [k] <- [k] - b_k/c_k-1 * [k-1] |
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b5d(i,j,k) = b5d(i,j,k)*c5d(i,j,k-1) |
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c5d(i,j,k) = c5d(i,j,k) - b5d(i,j,k)*d5d(i,j,k-1) |
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d5d(i,j,k) = d5d(i,j,k) - b5d(i,j,k)*e5d(i,j,k-1) |
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y5d(i,j,k,bi,bj) = y5d(i,j,k,bi,bj) |
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& - b5d(i,j,k)*y5d(i,j,k-1,bi,bj) |
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& - a5d(i,j,k)*y5d(i,j,k-2,bi,bj) |
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IF ( c5d(i,j,k).NE.0. _d 0 ) THEN |
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c5d(i,j,k) = 1. _d 0 / c5d(i,j,k) |
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ELSE |
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c5d(i,j,k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ENDDO |
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ENDDO |
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C- end if k= .. ; end of k loop |
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ENDIF |
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ENDDO |
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|
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C-- Backward sweep (starting from bottom) |
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DO k=Nr,1,-1 |
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IF (k.EQ.Nr) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y5d(i,j,k,bi,bj) = y5d(i,j,k,bi,bj)*c5d(i,j,k) |
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ENDDO |
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ENDDO |
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ELSEIF (k.EQ.Nr-1) THEN |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y5d(i,j,k,bi,bj) = ( y5d(i,j,k,bi,bj) |
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& - d5d(i,j,k)*y5d(i,j,k+1,bi,bj) |
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& )*c5d(i,j,k) |
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ENDDO |
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ENDDO |
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ELSE |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y5d(i,j,k,bi,bj) = ( y5d(i,j,k,bi,bj) |
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& - d5d(i,j,k)*y5d(i,j,k+1,bi,bj) |
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& - e5d(i,j,k)*y5d(i,j,k+2,bi,bj) |
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& )*c5d(i,j,k) |
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ENDDO |
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ENDDO |
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C- end if k= .. ; end of k loop |
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ENDIF |
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ENDDO |
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#else /* ALLOW_SOLVERS_KLOOPINSIDE */ |
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errCode = 0 |
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|
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C-- Temporary array |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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DO k=1,Nr |
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y5d_m1(i,j,k) = y5d(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C-- Main loop |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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|
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DO k=1,Nr |
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a5d_prime(k) = 0. _d 0 |
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b5d_prime(k) = 0. _d 0 |
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c5d_prime(k) = 0. _d 0 |
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d5d_prime(k) = 0. _d 0 |
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e5d_prime(k) = 0. _d 0 |
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y5d_prime(k) = 0. _d 0 |
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y5d_update(k) = 0. _d 0 |
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ENDDO |
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|
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DO k=1,Nr |
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C-- forward sweep (starting from top) |
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|
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IF (k.EQ.1) THEN |
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c just copy terms |
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a5d_prime(k) = 0. _d 0 |
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b5d_prime(k) = 0. _d 0 |
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c5d_prime(k) = c5d(i,j,k) |
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d5d_prime(k) = d5d(i,j,k) |
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e5d_prime(k) = e5d(i,j,k) |
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y5d_prime(k) = y5d_m1(i,j,k) |
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ELSEIF (k.EQ.2) THEN |
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c subtract one term |
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a5d_prime(k) = 0. _d 0 |
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b5d_prime(k) = 0. _d 0 |
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c5d_prime(k) = c5d(i,j,k) |
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& -b5d(i,j,k)*d5d_prime(k-1) |
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d5d_prime(k) = d5d(i,j,k) |
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& -b5d(i,j,k)*e5d_prime(k-1) |
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e5d_prime(k) = e5d(i,j,k) |
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y5d_prime(k) = y5d_m1(i,j,k) |
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& -b5d(i,j,k)*y5d_prime(k-1) |
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ELSE |
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c subtract two terms |
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a5d_prime(k) = 0. _d 0 |
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b5d_prime(k) = 0. _d 0 |
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c5d_prime(k) = c5d(i,j,k) |
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& -a5d(i,j,k)*e5d_prime(k-2) |
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& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(k-2))*d5d_prime(k-1) |
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d5d_prime(k) = d5d(i,j,k) |
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& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(k-2))*e5d_prime(k-1) |
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e5d_prime(k) = e5d(i,j,k) |
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y5d_prime(k) = y5d_m1(i,j,k) |
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& -a5d(i,j,k)*y5d_prime(k-2) |
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& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(k-2))*y5d_prime(k-1) |
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ENDIF |
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|
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c normalization |
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tmpval=c5d_prime(k) |
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IF ( tmpval.NE.0. _d 0 ) THEN |
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a5d_prime(k) = a5d_prime(k) / tmpval |
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b5d_prime(k) = b5d_prime(k) / tmpval |
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c5d_prime(k) = 1. _d 0 |
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d5d_prime(k) = d5d_prime(k) / tmpval |
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e5d_prime(k) = e5d_prime(k) / tmpval |
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y5d_prime(k) = y5d_prime(k) / tmpval |
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ELSE |
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a5d_prime(k) = 0. _d 0 |
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b5d_prime(k) = 0. _d 0 |
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c5d_prime(k) = 0. _d 0 |
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d5d_prime(k) = 0. _d 0 |
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e5d_prime(k) = 0. _d 0 |
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y5d_prime(k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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|
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ENDDO |
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|
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C-- Backward sweep (starting from bottom) |
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DO k=Nr,1,-1 |
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IF (k.EQ.Nr) THEN |
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y5d_update(k) = y5d_prime(k) |
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ELSEIF (k.EQ.Nr-1) THEN |
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y5d_update(k) = y5d_prime(k) |
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& - y5d_update(k+1)*d5d_prime(k) |
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ELSE |
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y5d_update(k) = y5d_prime(k) |
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& - y5d_update(k+1)*d5d_prime(k) |
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& - y5d_update(k+2)*e5d_prime(k) |
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ENDIF |
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ENDDO |
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|
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C-- Update array |
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DO k=1,Nr |
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y5d(i,j,k,bi,bj)=y5d_update(k) |
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ENDDO |
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|
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ENDDO |
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ENDDO |
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|
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#endif /* ALLOW_SOLVERS_KLOOPINSIDE */ |
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|
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RETURN |
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END |
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