| 1 | SUBROUTINE INTEGRATE( TIN, TOUT ) |
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| 2 | |
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| 3 | INCLUDE 'KPP_ROOT_params.h' |
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| 4 | INCLUDE 'KPP_ROOT_global.h' |
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| 5 | |
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| 6 | C TIN - Start Time |
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| 7 | KPP_REAL TIN |
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| 8 | C TOUT - End Time |
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| 9 | KPP_REAL TOUT |
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| 10 | |
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| 11 | INTEGER INFO(5) |
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| 12 | |
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| 13 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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| 14 | |
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| 15 | INFO(1) = Autonomous |
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| 16 | |
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| 17 | CALL ROS3(NVAR,TIN,TOUT,STEPMIN,STEPMAX, |
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| 18 | + STEPMIN,VAR,ATOL,RTOL, |
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| 19 | + Info,FUNC_CHEM,JAC_CHEM) |
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| 20 | |
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| 21 | RETURN |
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| 22 | END |
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| 23 | |
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| 24 | |
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| 25 | SUBROUTINE ROS3(N,T,Tnext,Hmin,Hmax,Hstart, |
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| 26 | + y,AbsTol,RelTol, |
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| 27 | + Info,FUNC_CHEM,JAC_CHEM) |
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| 28 | IMPLICIT NONE |
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| 29 | INCLUDE 'KPP_ROOT_params.h' |
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| 30 | INCLUDE 'KPP_ROOT_sparse.h' |
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| 31 | |
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| 32 | C L-stable Rosenbrock 3(2), with |
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| 33 | C strongly A-stable embedded formula for error control. |
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| 34 | C |
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| 35 | C All the arguments aggree with the KPP syntax. |
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| 36 | C |
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| 37 | C INPUT ARGUMENTS: |
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| 38 | C y = Vector of (NVAR) concentrations, contains the |
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| 39 | C initial values on input |
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| 40 | C [T, Tnext] = the integration interval |
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| 41 | C Hmin, Hmax = lower and upper bounds for the selected step-size. |
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| 42 | C Note that for Step = Hmin the current computed |
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| 43 | C solution is unconditionally accepted by the error |
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| 44 | C control mechanism. |
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| 45 | C AbsTol, RelTol = (NVAR) dimensional vectors of |
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| 46 | C componentwise absolute and relative tolerances. |
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| 47 | C FUNC_CHEM = name of routine of derivatives. KPP syntax. |
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| 48 | C See the header below. |
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| 49 | C JAC_CHEM = name of routine that computes the Jacobian, in |
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| 50 | C sparse format. KPP syntax. See the header below. |
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| 51 | C Info(1) = 1 for autonomous system |
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| 52 | C = 0 for nonautonomous system |
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| 53 | C |
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| 54 | C OUTPUT ARGUMENTS: |
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| 55 | C y = the values of concentrations at Tend. |
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| 56 | C T = equals Tend on output. |
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| 57 | C Info(2) = # of FUNC_CHEM calls. |
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| 58 | C Info(3) = # of JAC_CHEM calls. |
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| 59 | C Info(4) = # of accepted steps. |
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| 60 | C Info(5) = # of rejected steps. |
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| 61 | C |
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| 62 | C Adrian Sandu, April 1996 |
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| 63 | C The Center for Global and Regional Environmental Research |
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| 64 | |
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| 65 | KPP_REAL K1(NVAR), K2(NVAR), K3(NVAR) |
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| 66 | KPP_REAL F1(NVAR), JAC(LU_NONZERO) |
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| 67 | KPP_REAL Hmin,Hmax,Hnew,Hstart,ghinv,uround |
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| 68 | KPP_REAL y(NVAR), ynew(NVAR) |
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| 69 | KPP_REAL AbsTol(NVAR), RelTol(NVAR) |
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| 70 | KPP_REAL T, Tnext, Tplus, H, elo |
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| 71 | KPP_REAL ERR, factor, facmax |
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| 72 | KPP_REAL gam, c21, c31, c32, b1, b2, b3 |
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| 73 | KPP_REAL d1, d2, d3, a21, a31, a32 |
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| 74 | KPP_REAL alpha2, alpha3, g1, g2, g3 |
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| 75 | KPP_REAL tau, x1, x2, x3, dround, ytol |
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| 76 | INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier |
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| 77 | INTEGER Info(5) |
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| 78 | LOGICAL IsReject,Autonomous |
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| 79 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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| 80 | |
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| 81 | gam= .43586652150845899941601945119356d+00 |
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| 82 | c21= -.10156171083877702091975600115545d+01 |
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| 83 | c31= .40759956452537699824805835358067d+01 |
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| 84 | c32= .92076794298330791242156818474003d+01 |
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| 85 | b1= .10000000000000000000000000000000d+01 |
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| 86 | b2= .61697947043828245592553615689730d+01 |
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| 87 | b3= -.42772256543218573326238373806514d+00 |
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| 88 | d1= .50000000000000000000000000000000d+00 |
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| 89 | d2= -.29079558716805469821718236208017d+01 |
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| 90 | d3= .22354069897811569627360909276199d+00 |
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| 91 | a21 = 1.d0 |
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| 92 | a31 = 1.d0 |
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| 93 | a32 = 0.d0 |
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| 94 | alpha2 = gam |
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| 95 | alpha3 = gam |
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| 96 | g1= .43586652150845899941601945119356d+00 |
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| 97 | g2= .24291996454816804366592249683314d+00 |
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| 98 | g3= .21851380027664058511513169485832d+01 |
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| 99 | |
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| 100 | |
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| 101 | c Initialization of counters, etc. |
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| 102 | Autonomous = Info(1) .EQ. 1 |
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| 103 | uround = 1.d-15 |
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| 104 | dround = DSQRT(uround) |
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| 105 | IF (Hmax.le.0.D0) THEN |
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| 106 | Hmax = DABS(Tnext-T) |
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| 107 | END IF |
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| 108 | H = DMAX1(1.d-8, Hstart) |
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| 109 | Tplus = T |
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| 110 | IsReject = .false. |
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| 111 | Naccept = 0 |
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| 112 | Nreject = 0 |
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| 113 | Nfcn = 0 |
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| 114 | Njac = 0 |
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| 115 | |
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| 116 | C === Starting the time loop === |
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| 117 | 10 continue |
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| 118 | |
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| 119 | Tplus = T + H |
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| 120 | if ( Tplus .gt. Tnext ) then |
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| 121 | H = Tnext - T |
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| 122 | Tplus = Tnext |
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| 123 | end if |
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| 124 | |
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| 125 | CALL JAC_CHEM(NVAR, T, y, JAC) |
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| 126 | Njac = Njac+1 |
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| 127 | gHinv = -1.0d0/(gam*H) |
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| 128 | do 15 j=1,LU_NONZERO |
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| 129 | JAC(j) = -JAC(j) |
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| 130 | 15 continue |
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| 131 | do 20 j=1,NVAR |
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| 132 | JAC(LU_DIAG(j)) = JAC(LU_DIAG(j)) - gHinv |
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| 133 | 20 continue |
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| 134 | CALL KppDecomp (JAC, ier) |
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| 135 | |
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| 136 | if (ier.ne.0) then |
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| 137 | if ( H.gt.Hmin) then |
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| 138 | H = 5.0d-1*H |
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| 139 | go to 10 |
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| 140 | else |
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| 141 | print *,'IER <> 0, H=',H |
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| 142 | stop |
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| 143 | end if |
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| 144 | end if |
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| 145 | |
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| 146 | CALL FUNC_CHEM(NVAR, T, y, F1) |
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| 147 | |
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| 148 | C ====== NONAUTONOMOUS CASE =============== |
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| 149 | IF (.not. Autonomous) THEN |
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| 150 | tau = DSIGN(dround*DMAX1( 1.0d-6, DABS(T) ), T) |
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| 151 | CALL FUNC_CHEM(NVAR, T+tau, y, K2) |
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| 152 | nfcn=nfcn+1 |
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| 153 | do 30 j = 1,NVAR |
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| 154 | K3(j) = ( K2(j)-F1(j) )/tau |
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| 155 | 30 continue |
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| 156 | |
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| 157 | C ----- STAGE 1 (NONAUTONOMOUS) ----- |
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| 158 | x1 = g1*H |
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| 159 | do 35 j = 1,NVAR |
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| 160 | K1(j) = F1(j) + x1*K3(j) |
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| 161 | 35 continue |
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| 162 | CALL KppSolve (JAC, K1) |
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| 163 | |
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| 164 | C ----- STAGE 2 (NONAUTONOMOUS) ----- |
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| 165 | do 40 j = 1,NVAR |
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| 166 | ynew(j) = y(j) + K1(j) |
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| 167 | 40 continue |
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| 168 | CALL FUNC_CHEM(NVAR, T+gam*H, ynew, F1) |
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| 169 | nfcn=nfcn+1 |
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| 170 | x1 = c21/H |
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| 171 | x2 = g2*H |
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| 172 | do 45 j = 1,NVAR |
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| 173 | K2(j) = F1(j) + x1*K1(j) + x2*K3(j) |
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| 174 | 45 continue |
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| 175 | CALL KppSolve (JAC, K2) |
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| 176 | |
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| 177 | C ----- STAGE 3 (NONAUTONOMOUS) ----- |
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| 178 | x1 = c31/H |
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| 179 | x2 = c32/H |
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| 180 | x3 = g3*H |
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| 181 | do 50 j = 1,NVAR |
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| 182 | K3(j) = F1(j) + x1*K1(j) + x2*K2(j) + x3*K3(j) |
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| 183 | 50 continue |
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| 184 | CALL KppSolve (JAC, K3) |
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| 185 | |
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| 186 | |
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| 187 | C ====== AUTONOMOUS CASE =============== |
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| 188 | ELSE |
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| 189 | |
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| 190 | C ----- STAGE 1 (AUTONOMOUS) ----- |
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| 191 | do 60 j = 1,NVAR |
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| 192 | K1(j) = F1(j) |
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| 193 | 60 continue |
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| 194 | CALL KppSolve (JAC, K1) |
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| 195 | |
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| 196 | C ----- STAGE 2 (AUTONOMOUS) ----- |
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| 197 | do 65 j = 1,NVAR |
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| 198 | ynew(j) = y(j) + K1(j) |
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| 199 | 65 continue |
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| 200 | CALL FUNC_CHEM(NVAR, T + gam*H, ynew, F1) |
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| 201 | nfcn=nfcn+1 |
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| 202 | x1 = c21/H |
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| 203 | do 70 j = 1,NVAR |
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| 204 | K2(j) = F1(j) + x1*K1(j) |
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| 205 | 70 continue |
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| 206 | CALL KppSolve (JAC, K2) |
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| 207 | |
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| 208 | C ----- STAGE 3 (AUTONOMOUS) ----- |
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| 209 | x1 = c31/H |
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| 210 | x2 = c32/H |
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| 211 | do 90 j = 1,NVAR |
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| 212 | K3(j) = F1(j) + x1*K1(j) + x2*K2(j) |
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| 213 | 90 continue |
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| 214 | CALL KppSolve (JAC, K3) |
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| 215 | |
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| 216 | END IF ! Autonomousous |
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| 217 | |
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| 218 | C ---- The Solution --- |
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| 219 | |
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| 220 | do 120 j = 1,NVAR |
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| 221 | ynew(j) = y(j) + b1*K1(j) + b2*K2(j) + b3*K3(j) |
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| 222 | 120 continue |
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| 223 | |
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| 224 | |
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| 225 | C ====== Error estimation ======== |
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| 226 | |
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| 227 | ERR=0.d0 |
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| 228 | do 130 i=1,NVAR |
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| 229 | ytol = AbsTol(i) + RelTol(i)*DMAX1(DABS(y(i)),DABS(ynew(i))) |
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| 230 | ERR=ERR+((d1*K1(i)+d2*K2(i)+d3*K3(i))/ytol)**2 |
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| 231 | 130 continue |
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| 232 | ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) |
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| 233 | |
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| 234 | C ======= Choose the stepsize =============================== |
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| 235 | |
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| 236 | elo = 3.0D0 ! estimator local order |
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| 237 | factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) |
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| 238 | Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) |
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| 239 | |
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| 240 | C ======= Rejected/Accepted Step ============================ |
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| 241 | |
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| 242 | IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN |
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| 243 | IsReject = .true. |
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| 244 | H = DMIN1(H/10,Hnew) |
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| 245 | Nreject = Nreject+1 |
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| 246 | ELSE |
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| 247 | DO 140 i=1,NVAR |
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| 248 | y(i) = ynew(i) |
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| 249 | 140 CONTINUE |
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| 250 | T = Tplus |
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| 251 | IF (.NOT.IsReject) THEN |
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| 252 | H = Hnew ! Do not increase stepsize if previos step was rejected |
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| 253 | END IF |
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| 254 | IsReject = .false. |
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| 255 | Naccept = Naccept+1 |
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| 256 | END IF |
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| 257 | |
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| 258 | |
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| 259 | C ======= End of the time loop =============================== |
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| 260 | if ( T .lt. Tnext ) go to 10 |
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| 261 | |
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| 262 | |
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| 263 | C ======= Output Information ================================= |
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| 264 | Info(2) = Nfcn |
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| 265 | Info(3) = Njac |
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| 266 | Info(4) = Naccept |
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| 267 | Info(5) = Nreject |
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| 268 | Hstart = H |
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| 269 | |
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| 270 | RETURN |
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| 271 | END |
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| 272 | |
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| 273 | |
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| 274 | |
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| 275 | SUBROUTINE FUNC_CHEM(N, T, Y, P) |
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| 276 | INCLUDE 'KPP_ROOT_params.h' |
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| 277 | INCLUDE 'KPP_ROOT_global.h' |
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| 278 | INTEGER N |
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| 279 | KPP_REAL T, Told |
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| 280 | KPP_REAL Y(NVAR), P(NVAR) |
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| 281 | Told = TIME |
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| 282 | TIME = T |
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| 283 | CALL Update_SUN() |
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| 284 | CALL Update_RCONST() |
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| 285 | CALL Fun( Y, FIX, RCONST, P ) |
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| 286 | TIME = Told |
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| 287 | RETURN |
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| 288 | END |
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| 289 | |
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| 290 | SUBROUTINE JAC_CHEM(N, T, Y, J) |
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| 291 | INCLUDE 'KPP_ROOT_params.h' |
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| 292 | INCLUDE 'KPP_ROOT_global.h' |
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| 293 | INTEGER N |
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| 294 | KPP_REAL Told, T |
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| 295 | KPP_REAL Y(NVAR), J(LU_NONZERO) |
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| 296 | Told = TIME |
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| 297 | TIME = T |
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| 298 | CALL Update_SUN() |
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| 299 | CALL Update_RCONST() |
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| 300 | CALL Jac_SP( Y, FIX, RCONST, J ) |
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| 301 | TIME = Told |
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| 302 | RETURN |
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| 303 | END |
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| 304 | |
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