[2696] | 1 | SUBROUTINE INTEGRATE( NSENSIT, Y, 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 | C Y - Concentrations and Sensitivities |
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| 11 | KPP_REAL Y(NVAR*(NSENSIT+1)) |
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| 12 | C --- Note: Y contains: (1:NVAR) concentrations, followed by |
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| 13 | C --- (1:NVAR) sensitivities w.r.t. first parameter, followed by |
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| 14 | C --- etc., followed by |
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| 15 | C --- (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
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| 16 | |
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| 17 | INTEGER INFO(5) |
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| 18 | |
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| 19 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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| 20 | |
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| 21 | INFO(1) = Autonomous |
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| 22 | |
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| 23 | CALL ROS4_DDM(NVAR,NSENSIT,TIN,TOUT,STEPMIN,STEPMAX, |
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| 24 | + STEPMIN,Y,ATOL,RTOL, |
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| 25 | + Info,FUNC_CHEM,JAC_CHEM) |
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| 26 | |
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| 27 | |
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| 28 | RETURN |
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| 29 | END |
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| 30 | |
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| 31 | |
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| 32 | |
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| 33 | |
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| 34 | SUBROUTINE ROS4_DDM(N,NSENSIT,T,Tnext,Hmin,Hmax,Hstart, |
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| 35 | + y,AbsTol,RelTol, |
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| 36 | + Info,FUNC_CHEM,JAC_CHEM) |
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| 37 | IMPLICIT NONE |
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| 38 | INCLUDE 'KPP_ROOT_params.h' |
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| 39 | INCLUDE 'KPP_ROOT_global.h' |
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| 40 | INCLUDE 'KPP_ROOT_sparse.h' |
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| 41 | C |
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| 42 | C Four Stages, Fourth Order L-stable Rosenbrock Method, |
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| 43 | C with embedded L-stable, third order method for error control |
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| 44 | C Simplified version of E. Hairer's atmros4; the coefficients are slightly different |
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| 45 | C |
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| 46 | C Direct decoupled computation of sensitivities. |
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| 47 | C The global variable DDMTYPE distinguishes between: |
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| 48 | C DDMTYPE = 0 : sensitivities w.r.t. initial values |
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| 49 | C DDMTYPE = 1 : sensitivities w.r.t. parameters |
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| 50 | C |
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| 51 | C INPUT ARGUMENTS: |
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| 52 | C y = Vector of: (1:NVAR) concentrations, followed by |
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| 53 | C (1:NVAR) sensitivities w.r.t. first parameter, followed by |
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| 54 | C etc., followed by |
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| 55 | C (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
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| 56 | C (y contains initial values at input, final values at output) |
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| 57 | C [T, Tnext] = the integration interval |
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| 58 | C Hmin, Hmax = lower and upper bounds for the selected step-size. |
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| 59 | C Note that for Step = Hmin the current computed |
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| 60 | C solution is unconditionally accepted by the error |
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| 61 | C control mechanism. |
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| 62 | C AbsTol, RelTol = (NVAR) dimensional vectors of |
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| 63 | C componentwise absolute and relative tolerances. |
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| 64 | C FUNC_CHEM = name of routine of derivatives. KPP syntax. |
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| 65 | C See the header below. |
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| 66 | C JAC_CHEM = name of routine that computes the Jacobian, in |
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| 67 | C sparse format. KPP syntax. See the header below. |
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| 68 | C Info(1) = 1 for Autonomous system |
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| 69 | C = 0 for nonAutonomous system |
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| 70 | C |
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| 71 | C OUTPUT ARGUMENTS: |
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| 72 | C y = the values of concentrations and sensitivities at Tend. |
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| 73 | C T = equals TENDon output. |
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| 74 | C Info(2) = # of FUNC_CHEM CALLs. |
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| 75 | C Info(3) = # of JAC_CHEM CALLs. |
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| 76 | C Info(4) = # of accepted steps. |
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| 77 | C Info(5) = # of rejected steps. |
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| 78 | C |
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| 79 | C Adrian Sandu, December 2001 |
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| 80 | C |
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| 81 | |
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| 82 | |
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| 83 | INTEGER NSENSIT |
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| 84 | KPP_REAL y(NVAR*(NSENSIT+1)), ynew(NVAR*(NSENSIT+1)) |
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| 85 | KPP_REAL K1(NVAR*(NSENSIT+1)) |
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| 86 | KPP_REAL K2(NVAR*(NSENSIT+1)) |
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| 87 | KPP_REAL K3(NVAR*(NSENSIT+1)) |
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| 88 | KPP_REAL K4(NVAR*(NSENSIT+1)) |
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| 89 | KPP_REAL Fv(NVAR), Hv(NVAR) |
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| 90 | KPP_REAL DFDT(NVAR*(NSENSIT+1)) |
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| 91 | KPP_REAL DFDP(NVAR*NSENSIT), DFDPDT(NVAR*NSENSIT) |
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| 92 | KPP_REAL DJDP(NVAR*NSENSIT) |
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| 93 | KPP_REAL JAC(LU_NONZERO), AJAC(LU_NONZERO) |
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| 94 | KPP_REAL DJDT(LU_NONZERO) |
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| 95 | KPP_REAL HESS(NHESS) |
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| 96 | KPP_REAL Hmin,Hmax,Hstart,ghinv,uround |
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| 97 | KPP_REAL AbsTol(NVAR), RelTol(NVAR) |
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| 98 | KPP_REAL T, Tnext, Tplus, H, Hnew, elo |
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| 99 | KPP_REAL ERR, factor, facmax, dround, tau |
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| 100 | KPP_REAL w, e, beta1, beta2, beta3, beta4 |
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| 101 | |
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| 102 | INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier |
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| 103 | INTEGER Info(5) |
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| 104 | LOGICAL IsReject, Autonomous |
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| 105 | EXTERNAL FUNC_CHEM, JAC_CHEM, HESS_CHEM |
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| 106 | |
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| 107 | |
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| 108 | C The method coefficients |
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| 109 | C DOUBLE PRECISION gamma, gamma2, gamma3, gamma4 |
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| 110 | C PARAMETER ( gamma = 0.57281606D0 ) |
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| 111 | C PARAMETER ( gamma2 = -1.769177067112013949170520D0 ) |
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| 112 | C PARAMETER ( gamma3 = 0.759293964293209853670967D0 ) |
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| 113 | C PARAMETER ( gamma4 = -0.104894621490955803206743D0 ) |
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| 114 | C DOUBLE PRECISION a21, a31, a32, a41, a42, a43 |
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| 115 | C PARAMETER ( a21 = 2.00000000000000000000000D0 ) |
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| 116 | C PARAMETER ( a31 = 1.86794814949823713234476D0 ) |
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| 117 | C PARAMETER ( a32 = 0.23444556851723885002322D0 ) |
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| 118 | C DOUBLE PRECISION alpha2, alpha3, alpha4 |
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| 119 | C PARAMETER ( alpha2 = 1.145632120D0 ) |
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| 120 | C PARAMETER ( alpha3 = 0.655214975973133829477748D0 ) |
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| 121 | C DOUBLE PRECISION c21, c31, c32, c41, c42, c43 |
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| 122 | C PARAMETER ( c21 = -7.137649943349979830369260D0 ) |
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| 123 | C PARAMETER ( c31 = 2.580923666509657714488050D0 ) |
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| 124 | C PARAMETER ( c32 = 0.651629887302032023387417D0 ) |
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| 125 | C PARAMETER ( c41 = -2.137115266506619116806370D0 ) |
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| 126 | C PARAMETER ( c42 = -0.321469531339951070769241D0 ) |
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| 127 | C PARAMETER ( c43 = -0.694966049282445225157329D0 ) |
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| 128 | C DOUBLE PRECISION m1, m2, m3, m4, mhat1, mhat2, mhat3, mhat4 |
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| 129 | C PARAMETER ( m1 = 2.255566228604565243728840D0 ) |
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| 130 | C PARAMETER ( m2 = 0.287055063194157607662630D0 ) |
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| 131 | C PARAMETER ( m3 = 0.435311963379983213402707D0 ) |
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| 132 | C PARAMETER ( m4 = 1.093507656403247803214820D0 ) |
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| 133 | C PARAMETER ( mhat1 = 2.068399160527583734258670D0 ) |
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| 134 | C PARAMETER ( mhat2 = 0.238681352067532797956493D0 ) |
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| 135 | C PARAMETER ( mhat3 = 0.363373345435391708261747D0 ) |
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| 136 | C PARAMETER ( mhat4 = 0.366557127936155144309163D0 ) |
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| 137 | C DOUBLE PRECISION e1, e2, e3, e4 |
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| 138 | c PARAMETER ( e1 = 1.8716706807698191283861888D-01 ) |
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| 139 | c PARAMETER ( e2 = 4.8373711126624835410225955D-02 ) |
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| 140 | c PARAMETER ( e3 = 7.1938617944591554120847832D-02 ) |
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| 141 | c PARAMETER ( e4 = 7.2695052846709262706070831D-01 ) |
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| 142 | C PARAMETER ( e1 = -0.2815431932141155D+00 ) |
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| 143 | C PARAMETER ( e2 = -0.7276199124938920D-01 ) |
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| 144 | C PARAMETER ( e3 = -0.1082196201495311D+00 ) |
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| 145 | C PARAMETER ( e4 = -0.1093502252409163D+01 ) |
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| 146 | C The method coefficients |
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| 147 | DOUBLE PRECISION gamma, gamma2, gamma3, gamma4 |
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| 148 | PARAMETER ( gamma = 0.5728200000000000D+00 ) |
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| 149 | PARAMETER ( gamma2 = -0.1769193891319233D+01 ) |
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| 150 | PARAMETER ( gamma3 = 0.7592633437920482D+00 ) |
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| 151 | PARAMETER ( gamma4 = -0.1049021087100450D+00 ) |
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| 152 | DOUBLE PRECISION a21, a31, a32, a41, a42, a43 |
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| 153 | PARAMETER ( a21 = 0.2000000000000000D+01 ) |
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| 154 | PARAMETER ( a31 = 0.1867943637803922D+01 ) |
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| 155 | PARAMETER ( a32 = 0.2344449711399156D+00 ) |
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| 156 | DOUBLE PRECISION alpha2, alpha3 |
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| 157 | PARAMETER ( alpha2 = 0.1145640000000000D+01 ) |
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| 158 | PARAMETER ( alpha3 = 0.6552168638155900D+00 ) |
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| 159 | DOUBLE PRECISION c21, c31, c32, c41, c42, c43 |
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| 160 | PARAMETER ( c21 = -0.7137615036412310D+01 ) |
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| 161 | PARAMETER ( c31 = 0.2580708087951457D+01 ) |
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| 162 | PARAMETER ( c32 = 0.6515950076447975D+00 ) |
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| 163 | PARAMETER ( c41 = -0.2137148994382534D+01 ) |
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| 164 | PARAMETER ( c42 = -0.3214669691237626D+00 ) |
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| 165 | PARAMETER ( c43 = -0.6949742501781779D+00 ) |
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| 166 | DOUBLE PRECISION b1, b2, b3, b4 |
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| 167 | PARAMETER ( b1 = 0.2255570073418735D+01 ) |
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| 168 | PARAMETER ( b2 = 0.2870493262186792D+00 ) |
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| 169 | PARAMETER ( b3 = 0.4353179431840180D+00 ) |
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| 170 | PARAMETER ( b4 = 0.1093502252409163D+01 ) |
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| 171 | DOUBLE PRECISION d1, d2, d3, d4 |
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| 172 | PARAMETER ( d1 = -0.2815431932141155D+00 ) |
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| 173 | PARAMETER ( d2 = -0.7276199124938920D-01 ) |
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| 174 | PARAMETER ( d3 = -0.1082196201495311D+00 ) |
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| 175 | PARAMETER ( d4 = -0.1093502252409163D+01 ) |
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| 176 | |
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| 177 | |
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| 178 | c Initialization of counters, etc. |
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| 179 | Autonomous = Info(1) .EQ. 1 |
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| 180 | uround = 1.d-15 |
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| 181 | dround = DSQRT(uround) |
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| 182 | IF (Hmax.le.0.D0) THEN |
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| 183 | Hmax = DABS(Tnext-T) |
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| 184 | END IF |
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| 185 | H = DMAX1(1.d-8, Hstart) |
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| 186 | Tplus = T |
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| 187 | IsReject = .false. |
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| 188 | Naccept = 0 |
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| 189 | Nreject = 0 |
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| 190 | Nfcn = 0 |
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| 191 | Njac = 0 |
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| 192 | |
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| 193 | C === Starting the time loop === |
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| 194 | 10 CONTINUE |
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| 195 | |
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| 196 | Tplus = T + H |
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| 197 | IF ( Tplus .gt. Tnext ) THEN |
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| 198 | H = Tnext - T |
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| 199 | Tplus = Tnext |
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| 200 | END IF |
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| 201 | |
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| 202 | C Initial Function, Jacobian, and Hessian Values |
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| 203 | CALL FUNC_CHEM(NVAR, T, y, Fv) |
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| 204 | CALL JAC_CHEM(NVAR, T, y, JAC) |
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| 205 | CALL HESS_CHEM( NVAR, T, y, HESS ) |
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| 206 | IF (DDMTYPE .EQ. 1) THEN |
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| 207 | CALL DFUNDPAR(NVAR, NSENSIT, T, y, DFDP) |
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| 208 | END IF |
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| 209 | |
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| 210 | C The time derivatives for non-Autonomous case |
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| 211 | IF (.not. Autonomous) THEN |
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| 212 | tau = DSIGN(dround*DMAX1( 1.0d0, DABS(T) ), T) |
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| 213 | CALL FUNC_CHEM(NVAR, T+tau, y, K2) |
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| 214 | CALL JAC_CHEM(NVAR, T+tau, y, AJAC) |
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| 215 | nfcn=nfcn+1 |
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| 216 | DO 20 j = 1,NVAR |
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| 217 | DFDT(j) = ( K2(j)-Fv(j) )/tau |
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| 218 | 20 CONTINUE |
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| 219 | DO 30 j = 1,LU_NONZERO |
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| 220 | DJDT(j) = ( AJAC(j)-JAC(j) )/tau |
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| 221 | 30 CONTINUE |
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| 222 | DO 35 i=1,NSENSIT |
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| 223 | CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),DFDT(i*NVAR+1)) |
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| 224 | 35 CONTINUE |
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| 225 | END IF |
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| 226 | |
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| 227 | 11 CONTINUE ! From here we restart after a rejected step |
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| 228 | |
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| 229 | C Form the Prediction matrix and compute its LU factorization |
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| 230 | Njac = Njac+1 |
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| 231 | ghinv = 1.0d0/(gamma*H) |
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| 232 | DO 40 j=1,LU_NONZERO |
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| 233 | AJAC(j) = -JAC(j) |
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| 234 | 40 CONTINUE |
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| 235 | DO 50 j=1,NVAR |
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| 236 | AJAC(LU_DIAG(j)) = AJAC(LU_DIAG(j)) + ghinv |
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| 237 | 50 CONTINUE |
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| 238 | CALL KppDecomp (AJAC, ier) |
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| 239 | C |
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| 240 | IF (ier.ne.0) THEN |
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| 241 | IF ( H.gt.Hmin) THEN |
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| 242 | H = 5.0d-1*H |
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| 243 | GO TO 10 |
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| 244 | ELSE |
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| 245 | PRINT *,'ROS4: Singular factorization at T=',T,'; H=',H |
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| 246 | STOP |
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| 247 | END IF |
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| 248 | END IF |
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| 249 | |
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| 250 | C ------------ STAGE 1------------------------- |
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| 251 | DO 60 j = 1,NVAR |
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| 252 | K1(j) = Fv(j) |
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| 253 | 60 CONTINUE |
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| 254 | IF (.NOT. Autonomous) THEN |
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| 255 | beta1 = H*gamma |
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| 256 | DO 70 j=1,NVAR |
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| 257 | K1(j) = K1(j) + beta1*DFDT(j) |
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| 258 | 70 CONTINUE |
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| 259 | END IF |
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| 260 | CALL KppSolve (AJAC, K1) |
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| 261 | C --- If derivative w.r.t. parameters |
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| 262 | IF (DDMTYPE .EQ. 1) THEN |
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| 263 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K1(1), DJDP) |
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| 264 | END IF |
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| 265 | C --- End of derivative w.r.t. parameters |
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| 266 | |
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| 267 | DO 100 i=1,NSENSIT |
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| 268 | CALL Jac_SP_Vec (JAC,y(i*NVAR+1),K1(i*NVAR+1)) |
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| 269 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K1(1), Hv ) |
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| 270 | DO 80 j=1,NVAR |
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| 271 | K1(i*NVAR+j) = K1(i*NVAR+j) + Hv(j) |
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| 272 | 80 CONTINUE |
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| 273 | IF (.NOT. Autonomous) THEN |
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| 274 | DO 90 j=1,NVAR |
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| 275 | K1(i*NVAR+j) = K1(i*NVAR+j) + beta1*DFDT(i*NVAR+j) |
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| 276 | 90 CONTINUE |
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| 277 | END IF |
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| 278 | C --- If derivative w.r.t. parameters |
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| 279 | IF (DDMTYPE .EQ. 1) THEN |
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| 280 | DO 95 j = 1,NVAR |
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| 281 | K1(i*NVAR+j) = K1(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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| 282 | & + DJDP((i-1)*NVAR+j) |
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| 283 | 95 CONTINUE |
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| 284 | END IF |
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| 285 | C --- End of derivative w.r.t. parameters |
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| 286 | CALL KppSolve (AJAC, K1(i*NVAR+1)) |
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| 287 | 100 CONTINUE |
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| 288 | |
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| 289 | C ----------- STAGE 2 ------------------------- |
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| 290 | DO 110 j = 1,NVAR*(NSENSIT+1) |
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| 291 | ynew(j) = y(j) + a21*K1(j) |
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| 292 | 110 CONTINUE |
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| 293 | CALL FUNC_CHEM(NVAR, T+alpha2*H, ynew, Fv) |
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| 294 | IF (DDMTYPE .EQ. 1) THEN |
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| 295 | CALL DFUNDPAR(NVAR, NSENSIT, T+alpha2*H, ynew, DFDP) |
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| 296 | END IF |
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| 297 | nfcn=nfcn+1 |
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| 298 | beta1 = c21/H |
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| 299 | DO 120 j = 1,NVAR |
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| 300 | K2(j) = Fv(j) + beta1*K1(j) |
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| 301 | 120 CONTINUE |
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| 302 | IF (.NOT. Autonomous) THEN |
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| 303 | beta2 = H*gamma2 |
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| 304 | DO 130 j=1,NVAR |
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| 305 | K2(j) = K2(j) + beta2*DFDT(j) |
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| 306 | 130 CONTINUE |
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| 307 | END IF |
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| 308 | CALL KppSolve (AJAC, K2) |
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| 309 | C --- If derivative w.r.t. parameters |
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| 310 | IF (DDMTYPE .EQ. 1) THEN |
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| 311 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K2(1), DJDP) |
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| 312 | END IF |
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| 313 | C --- End of derivative w.r.t. parameters |
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| 314 | |
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| 315 | CALL JAC_CHEM(NVAR, T+alpha2*H, ynew, JAC) |
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| 316 | njac=njac+1 |
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| 317 | DO 160 i=1,NSENSIT |
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| 318 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K2(i*NVAR+1)) |
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| 319 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K2(1), Hv ) |
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| 320 | DO 140 j = 1,NVAR |
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| 321 | K2(i*NVAR+j) = K2(i*NVAR+j) + beta1*K1(i*NVAR+j) |
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| 322 | & + Hv(j) |
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| 323 | 140 CONTINUE |
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| 324 | IF (.NOT. Autonomous) THEN |
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| 325 | DO 150 j=1,NVAR |
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| 326 | K2(i*NVAR+j) = K2(i*NVAR+j) + beta2*DFDT(i*NVAR+j) |
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| 327 | 150 CONTINUE |
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| 328 | END IF |
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| 329 | C --- If derivative w.r.t. parameters |
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| 330 | IF (DDMTYPE .EQ. 1) THEN |
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| 331 | DO 155 j = 1,NVAR |
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| 332 | K2(i*NVAR+j) = K2(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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| 333 | & + DJDP((i-1)*NVAR+j) |
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| 334 | 155 CONTINUE |
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| 335 | END IF |
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| 336 | C --- End of derivative w.r.t. parameters |
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| 337 | CALL KppSolve (AJAC, K2(i*NVAR+1)) |
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| 338 | 160 CONTINUE |
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| 339 | |
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| 340 | |
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| 341 | C ------------ STAGE 3 ------------------------- |
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| 342 | DO 170 j = 1,NVAR*(NSENSIT+1) |
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| 343 | ynew(j) = y(j) + a31*K1(j) + a32*K2(j) |
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| 344 | 170 CONTINUE |
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| 345 | CALL FUNC_CHEM(NVAR, T+alpha3*H, ynew, Fv) |
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| 346 | IF (DDMTYPE .EQ. 1) THEN |
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| 347 | CALL DFUNDPAR(NVAR, NSENSIT, T+alpha3*H, ynew, DFDP) |
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| 348 | END IF |
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| 349 | nfcn=nfcn+1 |
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| 350 | beta1 = c31/H |
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| 351 | beta2 = c32/H |
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| 352 | DO 180 j = 1,NVAR |
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| 353 | K3(j) = Fv(j) + beta1*K1(j) + beta2*K2(j) |
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| 354 | 180 CONTINUE |
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| 355 | IF (.NOT. Autonomous) THEN |
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| 356 | beta3 = H*gamma3 |
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| 357 | DO 190 j=1,NVAR |
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| 358 | K3(j) = K3(j) + beta3*DFDT(j) |
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| 359 | 190 CONTINUE |
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| 360 | END IF |
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| 361 | CALL KppSolve (AJAC, K3) |
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| 362 | C --- If derivative w.r.t. parameters |
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| 363 | IF (DDMTYPE .EQ. 1) THEN |
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| 364 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K3(1), DJDP) |
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| 365 | END IF |
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| 366 | C --- End of derivative w.r.t. parameters |
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| 367 | |
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| 368 | CALL JAC_CHEM(NVAR, T+alpha3*H, ynew, JAC) |
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| 369 | njac=njac+1 |
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| 370 | DO 220 i=1,NSENSIT |
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| 371 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K3(i*NVAR+1)) |
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| 372 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K3(1), Hv ) |
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| 373 | DO 200 j = 1,NVAR |
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| 374 | K3(i*NVAR+j) = K3(i*NVAR+j) + beta1*K1(i*NVAR+j) |
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| 375 | & + beta2*K2(i*NVAR+j) + Hv(j) |
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| 376 | 200 CONTINUE |
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| 377 | IF (.NOT. Autonomous) THEN |
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| 378 | DO 210 j=1,NVAR |
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| 379 | K3(i*NVAR+j) = K3(i*NVAR+j) + beta3*DFDT(i*NVAR+j) |
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| 380 | 210 CONTINUE |
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| 381 | END IF |
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| 382 | C --- If derivative w.r.t. parameters |
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| 383 | IF (DDMTYPE .EQ. 1) THEN |
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| 384 | DO 215 j = 1,NVAR |
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| 385 | K3(i*NVAR+j) = K3(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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| 386 | & + DJDP((i-1)*NVAR+j) |
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| 387 | 215 CONTINUE |
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| 388 | END IF |
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| 389 | C --- End of derivative w.r.t. parameters |
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| 390 | CALL KppSolve (AJAC, K3(i*NVAR+1)) |
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| 391 | 220 CONTINUE |
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| 392 | |
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| 393 | C ------------ STAGE 4 ------------------------- |
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| 394 | C Note: uses the same function values as stage 3 |
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| 395 | beta1 = c41/H |
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| 396 | beta2 = c42/H |
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| 397 | beta3 = c43/H |
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| 398 | DO 230 j = 1,NVAR |
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| 399 | K4(j) = Fv(j) + beta1*K1(j) + beta2*K2(j) + beta3*K3(j) |
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| 400 | 230 CONTINUE |
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| 401 | IF (.NOT. Autonomous) THEN |
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| 402 | beta4 = H*gamma4 |
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| 403 | DO 240 j=1,NVAR |
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| 404 | K4(j) = K4(j) + beta4*DFDT(j) |
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| 405 | 240 CONTINUE |
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| 406 | END IF |
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| 407 | CALL KppSolve (AJAC, K4) |
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| 408 | C --- If derivative w.r.t. parameters |
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| 409 | IF (DDMTYPE .EQ. 1) THEN |
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| 410 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K4(1), DJDP) |
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| 411 | END IF |
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| 412 | C --- End of derivative w.r.t. parameters |
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| 413 | |
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| 414 | njac=njac+1 |
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| 415 | DO 270 i=1,NSENSIT |
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| 416 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K4(i*NVAR+1)) |
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| 417 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K4(1), Hv ) |
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| 418 | DO 250 j = 1,NVAR |
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| 419 | K4(i*NVAR+j) = K4(i*NVAR+j) + beta1*K1(i*NVAR+j) |
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| 420 | & + beta2*K2(i*NVAR+j) + beta3*K3(i*NVAR+j) |
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| 421 | & + Hv(j) |
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| 422 | 250 CONTINUE |
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| 423 | IF (.NOT. Autonomous) THEN |
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| 424 | DO 260 j=1,NVAR |
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| 425 | K4(i*NVAR+j) = K4(i*NVAR+j) + beta4*DFDT(i*NVAR+j) |
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| 426 | 260 CONTINUE |
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| 427 | END IF |
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| 428 | C --- If derivative w.r.t. parameters |
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| 429 | IF (DDMTYPE .EQ. 1) THEN |
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| 430 | DO 265 j = 1,NVAR |
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| 431 | K4(i*NVAR+j) = K4(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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| 432 | & + DJDP((i-1)*NVAR+j) |
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| 433 | 265 CONTINUE |
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| 434 | END IF |
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| 435 | CALL KppSolve (AJAC, K4(i*NVAR+1)) |
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| 436 | 270 CONTINUE |
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| 437 | |
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| 438 | |
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| 439 | C ---- The Solution --- |
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| 440 | DO 280 j = 1,NVAR*(NSENSIT+1) |
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| 441 | ynew(j) = y(j) + b1*K1(j) + b2*K2(j) + b3*K3(j) + b4*K4(j) |
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| 442 | 280 CONTINUE |
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| 443 | |
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| 444 | |
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| 445 | C ====== Error estimation -- can be extended to control sensitivities too ======== |
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| 446 | |
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| 447 | ERR = 0.d0 |
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| 448 | DO 290 i=1,NVAR |
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| 449 | w = AbsTol(i) + RelTol(i)*DMAX1(DABS(ynew(i)),DABS(y(i))) |
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| 450 | e = d1*K1(i) + d2*K2(i) + d3*K3(i) + d4*K4(i) |
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| 451 | ERR = ERR + ( e/w )**2 |
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| 452 | 290 CONTINUE |
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| 453 | ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) |
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| 454 | |
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| 455 | C ======= Choose the stepsize =============================== |
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| 456 | |
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| 457 | elo = 4.0D0 ! estimator local order |
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| 458 | factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) |
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| 459 | Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) |
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| 460 | |
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| 461 | C ======= Rejected/Accepted Step ============================ |
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| 462 | |
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| 463 | IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN |
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| 464 | IsReject = .true. |
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| 465 | H = DMIN1(H/10,Hnew) |
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| 466 | Nreject = Nreject+1 |
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| 467 | ELSE |
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| 468 | DO 300 i=1,NVAR*(NSENSIT+1) |
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| 469 | y(i) = ynew(i) |
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| 470 | 300 CONTINUE |
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| 471 | T = Tplus |
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| 472 | IF (.NOT.IsReject) THEN |
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| 473 | H = Hnew ! Do not increase stepsize if previos step was rejected |
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| 474 | END IF |
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| 475 | IsReject = .false. |
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| 476 | Naccept = Naccept+1 |
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| 477 | END IF |
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| 478 | |
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| 479 | C ======= End of the time loop =============================== |
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| 480 | IF ( T .lt. Tnext ) GO TO 10 |
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| 481 | |
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| 482 | |
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| 483 | |
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| 484 | C ======= Output Information ================================= |
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| 485 | Info(2) = Nfcn |
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| 486 | Info(3) = Njac |
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| 487 | Info(4) = Naccept |
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| 488 | Info(5) = Nreject |
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| 489 | Hstart = H |
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| 490 | |
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| 491 | RETURN |
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| 492 | END |
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| 493 | |
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| 494 | |
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| 495 | |
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| 496 | SUBROUTINE FUNC_CHEM(N, T, Y, P) |
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| 497 | INCLUDE 'KPP_ROOT_params.h' |
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| 498 | INCLUDE 'KPP_ROOT_global.h' |
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| 499 | KPP_REAL T, Told |
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| 500 | KPP_REAL Y(NVAR), P(NVAR) |
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| 501 | Told = TIME |
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| 502 | TIME = T |
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| 503 | CALL Update_SUN() |
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| 504 | CALL Update_RCONST() |
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| 505 | CALL Fun( Y, FIX, RCONST, P ) |
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| 506 | TIME = Told |
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| 507 | RETURN |
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| 508 | END |
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| 509 | |
---|
| 510 | |
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| 511 | SUBROUTINE DFUNDPAR(N, NSENSIT, T, Y, P) |
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| 512 | C --- Computes the partial derivatives of FUNC_CHEM w.r.t. parameters |
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| 513 | INCLUDE 'KPP_ROOT_params.h' |
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| 514 | INCLUDE 'KPP_ROOT_global.h' |
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| 515 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
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| 516 | INTEGER NCOEFF, JCOEFF(NREACT) |
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| 517 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
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| 518 | |
---|
| 519 | KPP_REAL T, Told |
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| 520 | KPP_REAL Y(NVAR), P(NVAR*NSENSIT) |
---|
| 521 | Told = TIME |
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| 522 | TIME = T |
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| 523 | CALL Update_SUN() |
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| 524 | CALL Update_RCONST() |
---|
| 525 | C |
---|
| 526 | IF (DDMTYPE .EQ. 0) THEN |
---|
| 527 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
---|
| 528 | C --- they may have to be changed for other applications |
---|
| 529 | DO j=1,NSENSIT |
---|
| 530 | DO i=1,NVAR |
---|
| 531 | P(i+NVAR*(j-1)) = 0.0D0 |
---|
| 532 | END DO |
---|
| 533 | END DO |
---|
| 534 | ELSE |
---|
| 535 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
---|
| 536 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
---|
| 537 | C --- w.r.t. which one differentiates |
---|
| 538 | CALL dFun_dRcoeff( Y, FIX, NCOEFF, JCOEFF, P ) |
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| 539 | END IF |
---|
| 540 | TIME = Told |
---|
| 541 | RETURN |
---|
| 542 | END |
---|
| 543 | |
---|
| 544 | SUBROUTINE JAC_CHEM(N, T, Y, J) |
---|
| 545 | INCLUDE 'KPP_ROOT_params.h' |
---|
| 546 | INCLUDE 'KPP_ROOT_global.h' |
---|
| 547 | INTEGER N |
---|
| 548 | KPP_REAL Told, T |
---|
| 549 | KPP_REAL Y(NVAR), J(LU_NONZERO) |
---|
| 550 | Told = TIME |
---|
| 551 | TIME = T |
---|
| 552 | CALL Update_SUN() |
---|
| 553 | CALL Update_RCONST() |
---|
| 554 | CALL Jac_SP( Y, FIX, RCONST, J ) |
---|
| 555 | TIME = Told |
---|
| 556 | RETURN |
---|
| 557 | END |
---|
| 558 | |
---|
| 559 | |
---|
| 560 | SUBROUTINE DJACDPAR(N, NSENSIT, T, Y, U, P) |
---|
| 561 | C --- Computes the partial derivatives of JAC w.r.t. parameters times user vector U |
---|
| 562 | INCLUDE 'KPP_ROOT_params.h' |
---|
| 563 | INCLUDE 'KPP_ROOT_global.h' |
---|
| 564 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
---|
| 565 | INTEGER N |
---|
| 566 | INTEGER NCOEFF, JCOEFF(NREACT) |
---|
| 567 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
---|
| 568 | |
---|
| 569 | KPP_REAL T, Told |
---|
| 570 | KPP_REAL Y(NVAR), U(NVAR) |
---|
| 571 | KPP_REAL P(NVAR*NSENSIT) |
---|
| 572 | Told = TIME |
---|
| 573 | TIME = T |
---|
| 574 | CALL Update_SUN() |
---|
| 575 | CALL Update_RCONST() |
---|
| 576 | C |
---|
| 577 | IF (DDMTYPE .EQ. 0) THEN |
---|
| 578 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
---|
| 579 | C --- they may have to be changed for other applications |
---|
| 580 | DO j=1,NSENSIT |
---|
| 581 | DO i=1,NVAR |
---|
| 582 | P(i+NVAR*(j-1)) = 0.0D0 |
---|
| 583 | END DO |
---|
| 584 | END DO |
---|
| 585 | ELSE |
---|
| 586 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
---|
| 587 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
---|
| 588 | C --- w.r.t. which one differentiates |
---|
| 589 | CALL dJac_dRcoeff( Y, FIX, U, NCOEFF, JCOEFF, P ) |
---|
| 590 | END IF |
---|
| 591 | TIME = Told |
---|
| 592 | RETURN |
---|
| 593 | END |
---|
| 594 | |
---|
| 595 | |
---|
| 596 | SUBROUTINE HESS_CHEM(N, T, Y, HESS) |
---|
| 597 | INCLUDE 'KPP_ROOT_params.h' |
---|
| 598 | INCLUDE 'KPP_ROOT_global.h' |
---|
| 599 | INTEGER N |
---|
| 600 | KPP_REAL Told, T |
---|
| 601 | KPP_REAL Y(NVAR), HESS(NHESS) |
---|
| 602 | Told = TIME |
---|
| 603 | TIME = T |
---|
| 604 | CALL Update_SUN() |
---|
| 605 | CALL Update_RCONST() |
---|
| 606 | CALL Hessian( Y, FIX, RCONST, HESS ) |
---|
| 607 | TIME = Told |
---|
| 608 | RETURN |
---|
| 609 | END |
---|
| 610 | |
---|
| 611 | |
---|
| 612 | |
---|
| 613 | |
---|
| 614 | |
---|
| 615 | |
---|