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C $Header: /u/gcmpack/MITgcm/model/src/solve_tridiagonal.F,v 1.10 2012/03/15 15:25:18 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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CBOP |
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C !ROUTINE: SOLVE_TRIDIAGONAL |
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C !INTERFACE: |
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SUBROUTINE SOLVE_TRIDIAGONAL( |
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I iMin,iMax, jMin,jMax, |
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I a3d, b3d, c3d, |
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U y3d, |
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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_TRIDIAGONAL |
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C | o Solve a tri-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 a3d :: matrix lower diagnonal |
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C b3d :: matrix main diagnonal |
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C c3d :: matrix upper diagnonal |
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C y3d :: Input = Y vector ; Output = X = solution of A*X=Y |
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C errCode :: > 0 if singular matrix |
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INTEGER iMin,iMax,jMin,jMax |
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_RL a3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL b3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL c3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL y3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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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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_RL tmpVar |
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#ifndef SOLVE_DIAGONAL_LOWMEMORY |
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_RL recVar |
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_RL c3d_m1(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL y3d_m1(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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# ifdef SOLVE_DIAGONAL_KINNER |
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_RL c3d_prime(Nr) |
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_RL y3d_prime(Nr) |
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_RL y3d_update(Nr) |
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# else |
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_RL c3d_prime(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL y3d_prime(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL y3d_update(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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# endif |
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#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
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CEOP |
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|
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errCode = 0 |
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|
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#ifdef SOLVE_DIAGONAL_LOWMEMORY |
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|
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C-- Beginning of forward sweep (top level) |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( b3d(i,j,1).NE.0. _d 0 ) THEN |
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b3d(i,j,1) = 1. _d 0 / b3d(i,j,1) |
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ELSE |
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b3d(i,j,1) = 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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C-- Middle of forward sweep |
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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tmpVar = b3d(i,j,k) - a3d(i,j,k)*c3d(i,j,k-1)*b3d(i,j,k-1) |
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IF ( tmpVar .NE. 0. _d 0 ) THEN |
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b3d(i,j,k) = 1. _d 0 / tmpVar |
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ELSE |
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b3d(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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ENDDO |
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|
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y3d(i,j,1) = y3d(i,j,1)*b3d(i,j,1) |
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ENDDO |
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ENDDO |
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y3d(i,j,k) = ( y3d(i,j,k) |
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& - a3d(i,j,k)*y3d(i,j,k-1) |
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& )*b3d(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C-- Backward sweep |
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DO k=Nr-1,1,-1 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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y3d(i,j,k) = y3d(i,j,k) |
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& - c3d(i,j,k)*b3d(i,j,k)*y3d(i,j,k+1) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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#else /* ndef SOLVE_DIAGONAL_LOWMEMORY */ |
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|
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C-- Temporary array |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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c DO j=jMin,jMax |
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c DO i=iMin,iMax |
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c3d_m1(i,j,k) = c3d(i,j,k) |
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y3d_m1(i,j,k) = y3d(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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#ifdef SOLVE_DIAGONAL_KINNER |
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|
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C-- Main loop |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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|
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DO k=1,Nr |
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c3d_prime(k) = 0. _d 0 |
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y3d_prime(k) = 0. _d 0 |
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y3d_update(k) = 0. _d 0 |
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ENDDO |
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|
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C-- Forward sweep |
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DO k=1,Nr |
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IF ( k.EQ.1 ) THEN |
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IF ( b3d(i,j,1).NE.0. _d 0 ) THEN |
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c3d_prime(1) = c3d_m1(i,j,1) / b3d(i,j,1) |
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y3d_prime(1) = y3d_m1(i,j,1) / b3d(i,j,1) |
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ELSE |
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c3d_prime(1) = 0. _d 0 |
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y3d_prime(1) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ELSE |
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tmpVar = b3d(i,j,k) - a3d(i,j,k)*c3d_prime(k-1) |
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IF ( tmpVar .NE. 0. _d 0 ) THEN |
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recVar = 1. _d 0 / tmpVar |
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c3d_prime(k) = c3d_m1(i,j,k)*recVar |
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y3d_prime(k) = (y3d_m1(i,j,k) - y3d_prime(k-1)*a3d(i,j,k)) |
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& *recVar |
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ELSE |
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c3d_prime(k) = 0. _d 0 |
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y3d_prime(k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ENDIF |
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ENDDO |
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|
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C-- Backward sweep |
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DO k=Nr,1,-1 |
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IF ( k.EQ.Nr ) THEN |
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y3d_update(k)=y3d_prime(k) |
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ELSE |
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y3d_update(k)=y3d_prime(k)-c3d_prime(k)*y3d_update(k+1) |
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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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y3d(i,j,k) = y3d_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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#else /* ndef SOLVE_DIAGONAL_KINNER */ |
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|
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C-- Init. |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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c DO j=jMin,jMax |
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c DO i=iMin,iMax |
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c3d_prime(i,j,k) = 0. _d 0 |
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y3d_prime(i,j,k) = 0. _d 0 |
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y3d_update(i,j,k) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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CADJ loop = sequential |
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C-- Forward sweep |
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DO k=1,Nr |
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|
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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c DO j=jMin,jMax |
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c DO i=iMin,iMax |
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IF ( k.EQ.1 ) THEN |
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IF ( b3d(i,j,1).NE.0. _d 0 ) THEN |
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recVar = 1. _d 0 / b3d(i,j,1) |
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c3d_prime(i,j,1) = c3d_m1(i,j,1)*recVar |
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y3d_prime(i,j,1) = y3d_m1(i,j,1)*recVar |
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ELSE |
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c3d_prime(i,j,1) = 0. _d 0 |
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y3d_prime(i,j,1) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ELSE |
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tmpVar = b3d(i,j,k) - a3d(i,j,k)*c3d_prime(i,j,k-1) |
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IF ( tmpVar .NE. 0. _d 0 ) THEN |
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recVar = 1. _d 0 / tmpVar |
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c3d_prime(i,j,k) = c3d_m1(i,j,k)*recVar |
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y3d_prime(i,j,k) = ( y3d_m1(i,j,k) |
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& - a3d(i,j,k)*y3d_prime(i,j,k-1) |
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& )*recVar |
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ELSE |
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c3d_prime(i,j,k) = 0. _d 0 |
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y3d_prime(i,j,k) = 0. _d 0 |
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errCode = 1 |
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ENDIF |
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ENDIF |
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ENDDO |
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ENDDO |
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C-- k-loop |
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ENDDO |
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|
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CADJ loop = sequential |
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C-- Backward sweep |
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DO k=Nr,1,-1 |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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c DO j=jMin,jMax |
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c DO i=iMin,iMax |
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IF ( k.EQ.Nr ) THEN |
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y3d_update(i,j,k) = y3d_prime(i,j,k) |
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ELSE |
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y3d_update(i,j,k) = y3d_prime(i,j,k) |
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& - c3d_prime(i,j,k)*y3d_update(i,j,k+1) |
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ENDIF |
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ENDDO |
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ENDDO |
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C-- k-loop |
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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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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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c DO j=jMin,jMax |
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c DO i=iMin,iMax |
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y3d(i,j,k) = y3d_update(i,j,k) |
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ENDDO |
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ENDDO |
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C-- k-loop |
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ENDDO |
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|
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#endif /* SOLVE_DIAGONAL_KINNER */ |
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|
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#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
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|
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RETURN |
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END |
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