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C $Header: /u/gcmpack/MITgcm/model/src/solve_pentadiagonal.F,v 1.12 2016/09/29 13:02:13 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_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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#ifdef SOLVE_DIAGONAL_LOWMEMORY |
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C | o Allows 2 types of call: |
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C | 1) with INPUT errCode < 0 (first call): |
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C | Solve system A*X=Y by LU decomposition and return |
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C | inverse matrix as output (in a5d,b5d,c5d,d5d,e5d) |
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C | 2) with INPUT errCode = 0 (subsequent calls): |
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C | Solve system A*Xp=Yp by using inverse matrix coeff |
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C | from first call output. |
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#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
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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 -- 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 errCode :: > 0 if singular matrix |
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#ifdef SOLVE_DIAGONAL_LOWMEMORY |
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C a5d,b5d,c5d,d5d,e5d :: inverse matrix coeff to enable to find Xp solution |
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C of A*Xp=Yp with subsequent call to this routine |
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#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
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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) |
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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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#ifndef SOLVE_DIAGONAL_LOWMEMORY |
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_RL tmpVar, recVar |
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_RL y5d_m1(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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# ifdef SOLVE_DIAGONAL_KINNER |
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_RL c5d_prime(Nr) |
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_RL d5d_prime(Nr) |
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_RL e5d_prime(Nr) |
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_RL y5d_prime(Nr) |
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_RL y5d_update(Nr) |
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# else |
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_RL c5d_prime(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL d5d_prime(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL e5d_prime(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL y5d_prime(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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#ifdef SOLVE_DIAGONAL_LOWMEMORY |
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|
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IF ( errCode .LT. 0 ) THEN |
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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) part-1: matrix L.U decomposition |
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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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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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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-- end if errCode < 0 |
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ENDIF |
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|
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DO k=2,Nr |
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C-- forward sweep (starting from top) part-2: process RHS |
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IF (k.EQ.2) 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) = y5d(i,j,k) - b5d(i,j,k)*y5d(i,j,k-1) |
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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) = y5d(i,j,k) - b5d(i,j,k)*y5d(i,j,k-1) |
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& - a5d(i,j,k)*y5d(i,j,k-2) |
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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) = y5d(i,j,k)*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) = ( y5d(i,j,k) |
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& - d5d(i,j,k)*y5d(i,j,k+1) |
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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) = ( y5d(i,j,k) |
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& - d5d(i,j,k)*y5d(i,j,k+1) |
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& - e5d(i,j,k)*y5d(i,j,k+2) |
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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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|
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#else /* ndef SOLVE_DIAGONAL_LOWMEMORY */ |
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|
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errCode = 0 |
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|
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#ifdef SOLVE_DIAGONAL_KINNER |
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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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y5d_m1(i,j,k) = y5d(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-- 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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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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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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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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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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|
| 255 |
c normalization |
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tmpVar = c5d_prime(k) |
| 257 |
IF ( tmpVar.NE.0. _d 0 ) THEN |
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recVar = 1. _d 0 / tmpVar |
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d5d_prime(k) = d5d_prime(k)*recVar |
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e5d_prime(k) = e5d_prime(k)*recVar |
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y5d_prime(k) = y5d_prime(k)*recVar |
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ELSE |
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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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C-- k loop |
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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) |
| 276 |
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) |
| 279 |
ELSE |
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y5d_update(k) = y5d_prime(k) |
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& - y5d_update(k+1)*d5d_prime(k) |
| 282 |
& - y5d_update(k+2)*e5d_prime(k) |
| 283 |
ENDIF |
| 284 |
ENDDO |
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|
| 286 |
C-- Update array |
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DO k=1,Nr |
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y5d(i,j,k) = y5d_update(k) |
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ENDDO |
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|
| 291 |
C- end i,j loop |
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ENDDO |
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ENDDO |
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|
| 295 |
#else /* ndef SOLVE_DIAGONAL_KINNER */ |
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|
| 297 |
C-- Init. + copy to temp. array |
| 298 |
DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
| 300 |
DO i=1-OLx,sNx+OLx |
| 301 |
c5d_prime(i,j,k) = 0. _d 0 |
| 302 |
d5d_prime(i,j,k) = 0. _d 0 |
| 303 |
e5d_prime(i,j,k) = 0. _d 0 |
| 304 |
y5d_prime(i,j,k) = 0. _d 0 |
| 305 |
y5d_m1(i,j,k) = y5d(i,j,k) |
| 306 |
ENDDO |
| 307 |
ENDDO |
| 308 |
ENDDO |
| 309 |
|
| 310 |
CADJ loop = sequential |
| 311 |
DO k=1,Nr |
| 312 |
C-- Forward sweep (starting from top) |
| 313 |
|
| 314 |
DO j=1-OLy,sNy+OLy |
| 315 |
DO i=1-OLx,sNx+OLx |
| 316 |
c DO j=jMin,jMax |
| 317 |
c DO i=iMin,iMax |
| 318 |
|
| 319 |
IF (k.EQ.1) THEN |
| 320 |
C- just copy terms |
| 321 |
c5d_prime(i,j,k) = c5d(i,j,k) |
| 322 |
d5d_prime(i,j,k) = d5d(i,j,k) |
| 323 |
e5d_prime(i,j,k) = e5d(i,j,k) |
| 324 |
y5d_prime(i,j,k) = y5d_m1(i,j,k) |
| 325 |
ELSEIF (k.EQ.2) THEN |
| 326 |
C- subtract one term |
| 327 |
c5d_prime(i,j,k) = c5d(i,j,k) |
| 328 |
& -b5d(i,j,k)*d5d_prime(i,j,k-1) |
| 329 |
d5d_prime(i,j,k) = d5d(i,j,k) |
| 330 |
& -b5d(i,j,k)*e5d_prime(i,j,k-1) |
| 331 |
e5d_prime(i,j,k) = e5d(i,j,k) |
| 332 |
y5d_prime(i,j,k) = y5d_m1(i,j,k) |
| 333 |
& -b5d(i,j,k)*y5d_prime(i,j,k-1) |
| 334 |
ELSE |
| 335 |
C- subtract two terms |
| 336 |
c5d_prime(i,j,k) = c5d(i,j,k) |
| 337 |
& -a5d(i,j,k)*e5d_prime(i,j,k-2) |
| 338 |
& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(i,j,k-2)) |
| 339 |
& *d5d_prime(i,j,k-1) |
| 340 |
d5d_prime(i,j,k) = d5d(i,j,k) |
| 341 |
& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(i,j,k-2)) |
| 342 |
& *e5d_prime(i,j,k-1) |
| 343 |
e5d_prime(i,j,k) = e5d(i,j,k) |
| 344 |
y5d_prime(i,j,k) = y5d_m1(i,j,k) |
| 345 |
& -a5d(i,j,k)*y5d_prime(i,j,k-2) |
| 346 |
& -(b5d(i,j,k)-a5d(i,j,k)*d5d_prime(i,j,k-2)) |
| 347 |
& *y5d_prime(i,j,k-1) |
| 348 |
ENDIF |
| 349 |
|
| 350 |
C- normalization |
| 351 |
tmpVar = c5d_prime(i,j,k) |
| 352 |
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 353 |
recVar = 1. _d 0 / tmpVar |
| 354 |
d5d_prime(i,j,k) = d5d_prime(i,j,k)*recVar |
| 355 |
e5d_prime(i,j,k) = e5d_prime(i,j,k)*recVar |
| 356 |
y5d_prime(i,j,k) = y5d_prime(i,j,k)*recVar |
| 357 |
ELSE |
| 358 |
d5d_prime(i,j,k) = 0. _d 0 |
| 359 |
e5d_prime(i,j,k) = 0. _d 0 |
| 360 |
y5d_prime(i,j,k) = 0. _d 0 |
| 361 |
errCode = 1 |
| 362 |
ENDIF |
| 363 |
|
| 364 |
ENDDO |
| 365 |
ENDDO |
| 366 |
|
| 367 |
C- end k-loop |
| 368 |
ENDDO |
| 369 |
|
| 370 |
CADJ loop = sequential |
| 371 |
C-- Backward sweep (starting from bottom) |
| 372 |
DO k=Nr,1,-1 |
| 373 |
DO j=1-OLy,sNy+OLy |
| 374 |
DO i=1-OLx,sNx+OLx |
| 375 |
c DO j=jMin,jMax |
| 376 |
c DO i=iMin,iMax |
| 377 |
IF (k.EQ.Nr) THEN |
| 378 |
y5d(i,j,k) = y5d_prime(i,j,k) |
| 379 |
ELSEIF (k.EQ.Nr-1) THEN |
| 380 |
y5d(i,j,k) = y5d_prime(i,j,k) |
| 381 |
& - y5d(i,j,k+1)*d5d_prime(i,j,k) |
| 382 |
ELSE |
| 383 |
y5d(i,j,k) = y5d_prime(i,j,k) |
| 384 |
& - y5d(i,j,k+1)*d5d_prime(i,j,k) |
| 385 |
& - y5d(i,j,k+2)*e5d_prime(i,j,k) |
| 386 |
ENDIF |
| 387 |
ENDDO |
| 388 |
ENDDO |
| 389 |
C- end k-loop |
| 390 |
ENDDO |
| 391 |
|
| 392 |
#endif /* SOLVE_DIAGONAL_KINNER */ |
| 393 |
|
| 394 |
#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
| 395 |
|
| 396 |
RETURN |
| 397 |
END |
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