208 lines
8.9 KiB
Fortran
208 lines
8.9 KiB
Fortran
! $Id: decomp.f,v 1.1 2009/06/09 21:51:53 daven Exp $
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SUBROUTINE DECOMP
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!
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!******************************************************************************
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! Subroutine DECOMP decomposes the sparse matrix for the SMVGEAR II solver.
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! (M. Jacobson, 1997; bdf, bmy, 4/18/03)
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!
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! NOTES:
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! (1 ) Now use & as F90 continuation character. Now also force double
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! precision with the "D" exponent. (bmy, 4/18/03)
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! (2 ) Comment out counter variable NUM_BACKSUB, you can get the same info
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! w/ a profiling run. (bmy, 7/9/03)
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!******************************************************************************
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!
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IMPLICIT NONE
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# include "CMN_SIZE"
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# include "comode.h"
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C
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C *********************************************************************
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C ************ WRITTEN BY MARK JACOBSON (1993) ************
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C *** (C) COPYRIGHT, 1993 BY MARK Z. JACOBSON ***
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C *** U.S. COPYRIGHT OFFICE REGISTRATION NO. TXu 670-279 ***
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C *** (650) 723-6836 ***
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C *********************************************************************
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C
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C DDDDDDD EEEEEEE CCCCCCC OOOOOOO M M PPPPPPP
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C D D E C O O MM MM P P
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C D D EEEEEEE C O O M M M M PPPPPPP
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C D D E C O O M M M P
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C DDDDDDD EEEEEEE CCCCCCC OOOOOOO M M P
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C
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C *********************************************************************
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C ************** DECOMPOSE THE SPARSE MATRIX **************************
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C *********************************************************************
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C
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C *********************************************************************
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C * THIS SUBROUTINE DECOMPOSES THE MATRIX "P" INTO THE MATRIX "A" IN *
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C * ORDER TO SOLVE THE LINEAR SET OF EQUATIONS Ax = B FOR x, WHICH IS *
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C * A CORRECTION VECTOR. Ax = B IS SOLVED IN SUBROUTINE BACKSUB.F *
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C * ABOVE, THE ORIGINAL MATRIX "P" IS *
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C * *
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C * P = I - H x Bo x J, *
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C * *
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C * WHERE I = IDENTITY MATRIX, H = TIME-STEP, Bo = A COEFFICIENT THAT *
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C * DEPENDS ON THE ORDER OF THE INTEGRATION METHOD, AND J IS THE *
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C * MATRIX OF PARTIAL DERIVATIVES. SEE PRESS ET AL. (1992) NUMERICAL *
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C * RECIPES CAMBRIDGE UNIVERSITY PRESS, FOR A BETTER DESCRIPTION OF *
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C * THE L-U DECOMPOSTION PROCESS *
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C * *
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C * THIS L-U DECOMPOSTION PROCESS USES SPARSE-MATRIX TECHNIQUES, *
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C * VECTORIZES AROUND THE GRID-CELL DIMENSION, AND USES NO PARTIAL *
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C * PIVOTING. TESTS BY SHERMAN & HINDMARSH (1980) LAWRENCE LIVERMORE *
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C * REP. UCRL-84102 AND BY US HAVE CONFIRMED THAT THE REMOVAL OF *
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C * PARTIAL PIVOTING HAS LITTLE EFFECT ON RESULTS. *
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C * *
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C * HOW TO CALL SUBROUTINE: *
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C * ---------------------- *
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C * CALL DECOMP.F FROM SMVGEAR.F WITH *
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C * NCS = 1..NCSGAS FOR GAS CHEMISTRY *
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C * NCSP = NCS FOR DAYTIME GAS CHEM *
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C * NCSP = NCS +ICS FOR NIGHTTIME GAS CHEM *
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C *********************************************************************
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C
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C KTLOOP = NUMBER OF GRID-CELLS IN A GRID-BLOCK
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C ISCHAN = ORIGINAL ORDER OF MATRIX
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C CC2 = ARRAY OF IARRAY UNITS HOLDING VALUES OF EACH MATRIX
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C POSITION ACTUALLY USED. ORIGINALLY,
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C CC2 = P = I - DELT * ASET(NQQ,1) * PARTIAL DERIVATIVES.
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C HOWEVER, CC2 IS DECOMPOSED HERE
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C
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C *********************************************************************
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C *** FIRST LOOP OF L-U DECOMPOSTION ***
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C *********************************************************************
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C SUM 1,2,3,4, OR 5 TERMS AT A TIME TO IMPROVE VECTORIZATION
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C
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INTEGER J,IJT,IJ,IL5,IH5,IL4,IH4,IL3,IH3,IL2,IH2,IL1,IH1
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INTEGER IC,IK0,IK1,IK2,IK3,IK4,KJ0,KJ1,KJ2,KJ3,KJ4,K,IAR
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INTEGER JL,JH,JC,IJA
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DO 510 J = 1, ISCHAN
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DO 310 IJT = IJTLO(J,NCSP), IJTHI(J,NCSP)
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IJ = IJVAL(IJT)
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IL5 = IDL5( IJT)
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IH5 = IDH5( IJT)
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IL4 = IDL4( IJT)
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IH4 = IDH4( IJT)
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IL3 = IDL3( IJT)
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IH3 = IDH3( IJT)
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IL2 = IDL2( IJT)
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IH2 = IDH2( IJT)
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IL1 = IDL1( IJT)
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IH1 = IDH1( IJT)
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C ********************* SUM 5 TERMS AT A TIME *************************
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C
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DO 105 IC = IL5, IH5
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IK0 = IKDECA(IC)
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IK1 = IKDECB(IC)
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IK2 = IKDECC(IC)
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IK3 = IKDECD(IC)
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IK4 = IKDECE(IC)
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KJ0 = KJDECA(IC)
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KJ1 = KJDECB(IC)
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KJ2 = KJDECC(IC)
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KJ3 = KJDECD(IC)
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KJ4 = KJDECE(IC)
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DO 100 K = 1, KTLOOP
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CC2(K,IJ) = CC2(K,IJ) - CC2(K,IK0) * CC2(K,KJ0)
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& - CC2(K,IK1) * CC2(K,KJ1)
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& - CC2(K,IK2) * CC2(K,KJ2)
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& - CC2(K,IK3) * CC2(K,KJ3)
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& - CC2(K,IK4) * CC2(K,KJ4)
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100 CONTINUE
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105 CONTINUE
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C
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C ********************* SUM 4 TERMS AT A TIME *************************
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C
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DO 155 IC = IL4, IH4
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IK0 = IKDECA(IC)
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IK1 = IKDECB(IC)
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IK2 = IKDECC(IC)
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IK3 = IKDECD(IC)
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KJ0 = KJDECA(IC)
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KJ1 = KJDECB(IC)
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KJ2 = KJDECC(IC)
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KJ3 = KJDECD(IC)
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DO 150 K = 1, KTLOOP
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CC2(K,IJ) = CC2(K,IJ) - CC2(K,IK0) * CC2(K,KJ0)
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& - CC2(K,IK1) * CC2(K,KJ1)
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& - CC2(K,IK2) * CC2(K,KJ2)
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& - CC2(K,IK3) * CC2(K,KJ3)
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150 CONTINUE
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155 CONTINUE
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C
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C ********************* SUM 3 TERMS AT A TIME *************************
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C
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DO 205 IC = IL3, IH3
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IK0 = IKDECA(IC)
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IK1 = IKDECB(IC)
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IK2 = IKDECC(IC)
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KJ0 = KJDECA(IC)
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KJ1 = KJDECB(IC)
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KJ2 = KJDECC(IC)
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DO 200 K = 1, KTLOOP
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CC2(K,IJ) = CC2(K,IJ) - CC2(K,IK0) * CC2(K,KJ0)
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& - CC2(K,IK1) * CC2(K,KJ1)
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& - CC2(K,IK2) * CC2(K,KJ2)
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200 CONTINUE
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205 CONTINUE
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C
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C ********************* SUM 2 TERMS AT A TIME *************************
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C
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DO 255 IC = IL2, IH2
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IK0 = IKDECA(IC)
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IK1 = IKDECB(IC)
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KJ0 = KJDECA(IC)
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KJ1 = KJDECB(IC)
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DO 250 K = 1, KTLOOP
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CC2(K,IJ) = CC2(K,IJ) - CC2(K,IK0) * CC2(K,KJ0)
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& - CC2(K,IK1) * CC2(K,KJ1)
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250 CONTINUE
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255 CONTINUE
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C
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C ********************* SUM 1 TERM AT A TIME *************************
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C
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DO 305 IC = IL1, IH1
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IK0 = IKDECA(IC)
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KJ0 = KJDECA(IC)
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DO 300 K = 1, KTLOOP
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CC2(K,IJ) = CC2(K,IJ) - CC2(K,IK0) * CC2(K,KJ0)
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300 CONTINUE
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305 CONTINUE
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C
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310 CONTINUE
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C
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C *********************************************************************
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C * VDIAG = 1 / CURRENT DIAGONAL TERM OF THE DECOMPOSED MATRIX *
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C *********************************************************************
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C
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IAR = JARRDIAG(J,NCSP)
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DO 400 K = 1, KTLOOP
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VDIAG(K,J) = 1.0d0 / CC2(K,IAR)
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400 CONTINUE
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C
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C *********************************************************************
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C *** SECOND LOOP OF DECOMPOSTION ***
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C *********************************************************************
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C JZEROA = IDENTIFIES THE ARRAY POSITION OF EACH JLOZ1..JHIZ1 TERM
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C
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JL = JLOZ1(J,NCSP)
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JH = JHIZ1(J,NCSP)
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DO 505 JC = JL, JH
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IJA = JZEROA(JC)
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DO 500 K = 1, KTLOOP
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CC2(K,IJA) = CC2(K,IJA) * VDIAG(K,J)
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500 CONTINUE
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505 CONTINUE
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C
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510 CONTINUE
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C
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C *********************************************************************
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C ********************* END OF SUBROUTINE DECOMP *********************
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C *********************************************************************
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C
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RETURN
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END SUBROUTINE DECOMP
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