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Xuesong (Steve)
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code/pderiv.f
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187
code/pderiv.f
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! $Id: pderiv.f,v 1.1 2009/06/09 21:51:53 daven Exp $
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SUBROUTINE PDERIV
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!
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!******************************************************************************
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! Subroutine PDERIV places the partial differential equations into a matrix
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! for SMVGEAR II. (M. Jacobson, 1997; bdf, bmy, 4/18/03)
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!
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! NOTES:
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! (1 ) Now force double-precision w/ "D" exponents (bmy, 4/18/03)
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!******************************************************************************
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!
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IMPLICIT NONE
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# include "CMN_SIZE" ! Size parameters
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# include "comode.h" ! SMVGEAR II arrays
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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 PPPPPPP DDDDDDD EEEEEEE RRRRRRR IIIIIII V V
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C P P D D E R R I V V
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C PPPPPPP D D EEEEEEE RRRRRRR I V V
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C P D D E R R I V V
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C P DDDDDDD EEEEEEE R R IIIIIII V
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C
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C *********************************************************************
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C * THIS SUBROUTINE PUTS THE PARTIAL DERIVATIVES OF EACH ORDINARY *
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C * DIFFERENTIAL EQUATION INTO A MATRIX. THE FORM OF THE MATRIX *
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C * EQUATION IS *
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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 = COEFFICIENT *
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C * CORRESPONDING TO THE ORDER OF THE METHOD, AND J IS THE JACOBIAN *
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C * MATRIX OF PARTIAL DERIVATIVES. *
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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 PDERIV.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 *********************************************************************
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C * INITIALIZE MATRIX *
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C *********************************************************************
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C CC2 = ARRAY OF IARRAY UNITS HOLDING VALUES OF EACH MAXTRIX
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C POSITION ACTUALLY USED.
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C CC2 = P = I - DELT * ASET(NQQ,1) * PARTIAL DERIVATIVES.
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C URATE = TERM OF JACOBIAN (J) = PARTIAL DERIVATIVE
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C IARRAY = TOTAL NUMBER OF MATRIX POSITIONS FILLED AFTER MAT. PROCESSES
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C IRMA,B,C = SPECIES # OF EACH REACTANT
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C ISCHAN = ORIGINAL ORDER OF MATRIX
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C KTLOOP = NUMBER OF GRID-CELLS IN A GRID-BLOCK
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C NONDIAG1 = 1 + # OF FINAL MATRIX POSITIONS, EXCLUDING DIAGONAL TERMS,
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C FILLED AFTER ALL MATRIX PROCESSES.
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C NPDERIV = COUNTER OF NUMBER OF TIMES THIS ROUTINE IS CALLED
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C R1DELT = -ASET(NQQ,1) * TIME STEP = -COEFFICIENT OF METHOD * DT
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C RRATE = REACTION RATE COEFFICIENT
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C
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C EXAMPLE OF HOW PARTIAL DERIVATIVES ARE PLACED IN AN ARRAY:
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C ---------------------------------------------------------
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C
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C SPECIES: A, B, C
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C CONCENTRATIONS: [A], [B], [C]
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C
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C REACTIONS: 1) A --> B J
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C 2) A + B --> C K1
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C 3 A + B + C --> D K2
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C
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C FIRST d[A] / dt = -J[A] - K1[A][B] - K2[A][B][C]
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C DERIVATIVES: d[B] / dt = +J[A] - K1[A][B] - K2[A][B][C]
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C d[C] / dt = + K1[A][B] - K2[A][B][C]
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C d[D] / dt = + K2[A][B][C]
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C
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C PREDICTOR MATRIX (P) = I - h * b * J:
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C J = JACOBIAN MATRIX OF PARTIAL DERIVATES
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C I = IDENTITY MATRIX
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C h = TIME-STEP
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C b = COEFFICIENT OF METHOD
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C R = h * b = -R1DELT
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C
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C A B C D
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C ___________________________________________________________________
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C |
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C A | 1-R(-J-K1[B]-K2[B][C]) -R(-K1[A]-K2[A][C]) -R(-K2[A][B]) 0
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C |
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C B | -R(+J-K1[B]-K2[B][C]) 1-R(-K1[A]-K2[A][C]) -R(-K2[A][B]) 0
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C |
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C C | -R( +K1[B]-K2[B][C]) -R(+K1[A]-K2[A][C]) 1-R(-K2[A][B]) 0
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C |
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C D | -R( +K2[B][C]) -R( +K2[A][C]) -R(+K2[A][B]) 1
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C
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C
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C *********************************************************************
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C ********* CALCULATE PARTIAL DERIVATIVES **********
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C ********* AND SUM UP PARTIAL DERIVATIVE LOSS TERMS **********
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C *********************************************************************
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C
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INTEGER IARRY,NONDIAG,NONDIAG1,NPDL,NPDH,NKN,JA,JB,JC,K,IAR,N
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INTEGER IAL
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REAL*8 FRACR1
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NPDERIV = NPDERIV + 1
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IARRY = IARRAY(NCSP)
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NONDIAG = IARRY - ISCHAN
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NONDIAG1 = NONDIAG + 1
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NFDH1 = NFDH2 + IONER(NCSP)
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NPDL = NPDLO(NCSP)
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NPDH = NPDHI(NCSP)
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C
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C *********************************************************************
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C * PARTIAL DERIVATIVES FOR RATES WITH THREE ACTIVE LOSS TERMS *
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C *********************************************************************
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C
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DO 105 NKN = 1, NFDH3
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JA = IRMA(NKN)
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JB = IRMB(NKN)
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JC = IRMC(NKN)
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DO 100 K = 1, KTLOOP
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URATE(K,NKN,1) = RRATE(K,NKN) * CNEW(K,JB) * CNEW(K,JC)
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URATE(K,NKN,2) = RRATE(K,NKN) * CNEW(K,JA) * CNEW(K,JC)
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URATE(K,NKN,3) = RRATE(K,NKN) * CNEW(K,JA) * CNEW(K,JB)
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100 CONTINUE
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105 CONTINUE
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C
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C *********************************************************************
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C * PARTIAL DERIVATIVES FOR RATES WITH TWO ACTIVE LOSS TERMS *
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C *********************************************************************
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C
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DO 155 NKN = NFDL2, NFDH2
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JA = IRMA(NKN)
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JB = IRMB(NKN)
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DO 150 K = 1, KTLOOP
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URATE(K,NKN,1) = RRATE(K,NKN) * CNEW(K,JB)
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URATE(K,NKN,2) = RRATE(K,NKN) * CNEW(K,JA)
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150 CONTINUE
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155 CONTINUE
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C
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C *********************************************************************
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C * PARTIAL DERIVATIVES FOR RATES WITH ONE ACTIVE LOSS TERM *
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C *********************************************************************
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C
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DO 205 NKN = NFDL1, NFDH1
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DO 200 K = 1, KTLOOP
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URATE(K,NKN,1) = RRATE(K,NKN)
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200 CONTINUE
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205 CONTINUE
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C
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C *********************************************************************
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C * PUT PARTIAL DERIVATIVES PRODUCTION AND LOSS TERMS IN MATRIX ARRAY *
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C *********************************************************************
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C FRACPL = -1. FOR ALL REACTANTS
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C = +1. OR +FRACTION FOR ALL PRODUCTS
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C
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DO 255 IAR = 1, NONDIAG
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DO 250 K = 1, KTLOOP
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CC2(K,IAR) = 0.d0
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250 CONTINUE
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255 CONTINUE
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C
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DO 305 IAR = NONDIAG1, IARRY
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DO 300 K = 1, KTLOOP
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CC2(K,IAR) = 1.d0
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300 CONTINUE
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305 CONTINUE
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C
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DO 405 N = NPDL, NPDH
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NKN = NKPDTERM(N)
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IAR = IPOSPD( N)
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IAL = IIALPD( N)
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FRACR1 = FRACPL( N) * R1DELT
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DO 400 K = 1, KTLOOP
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CC2(K,IAR) = CC2(K,IAR) + FRACR1 * URATE(K,NKN,IAL)
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400 CONTINUE
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405 CONTINUE
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C
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C *********************************************************************
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C ********************* END OF SUBROUTINE PDERIV **********************
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C *********************************************************************
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C
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RETURN
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END SUBROUTINE PDERIV
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