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 | INTEGER NSENSIT |
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7 | C TIN - Start Time |
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8 | KPP_REAL TIN |
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9 | C TOUT - End Time |
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10 | KPP_REAL TOUT |
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11 | C Y - Concentrations and Sensitivities |
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12 | KPP_REAL Y(NVAR*(NSENSIT+1)) |
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13 | C --- Note: Y contains: (1:NVAR) concentrations, followed by |
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14 | C --- (1:NVAR) sensitivities w.r.t. first parameter, followed by |
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15 | C --- etc., followed by |
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16 | C --- (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
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17 | |
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18 | INTEGER INFO(5) |
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19 | |
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20 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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21 | |
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22 | INFO(1) = Autonomous |
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23 | |
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24 | CALL ROS2_DDM(NVAR,NSENSIT,TIN,TOUT,STEPMIN,STEPMAX, |
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25 | + STEPMIN,Y,ATOL,RTOL, |
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26 | + Info,FUNC_CHEM,JAC_CHEM) |
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27 | |
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28 | |
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29 | RETURN |
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30 | END |
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31 | |
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32 | |
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33 | |
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34 | |
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35 | SUBROUTINE ROS2_DDM(N,NSENSIT,T,Tnext,Hmin,Hmax,Hstart, |
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36 | + y,AbsTol,RelTol, |
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37 | + Info,FUNC_CHEM,JAC_CHEM) |
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38 | IMPLICIT NONE |
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39 | INCLUDE 'KPP_ROOT_params.h' |
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40 | INCLUDE 'KPP_ROOT_global.h' |
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41 | INCLUDE 'KPP_ROOT_sparse.h' |
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42 | C |
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43 | C Ros2 with direct-decoupled calculation of sensitivities |
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44 | C |
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45 | C The global variable DDMTYPE distinguishes between: |
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46 | C DDMTYPE = 0 : sensitivities w.r.t. initial values |
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47 | C DDMTYPE = 1 : sensitivities w.r.t. parameters |
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48 | C |
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49 | C INPUT ARGUMENTS: |
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50 | C y = Vector of: (1:NVAR) concentrations, followed by |
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51 | C (1:NVAR) sensitivities w.r.t. first parameter, followed by |
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52 | C etc., followed by |
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53 | C (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
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54 | C (y contains initial values at input, final values at output) |
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55 | C [T, Tnext] = the integration interval |
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56 | C Hmin, Hmax = lower and upper bounds for the selected step-size. |
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57 | C Note that for Step = Hmin the current computed |
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58 | C solution is unconditionally accepted by the error |
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59 | C control mechanism. |
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60 | C AbsTol, RelTol = (NVAR) dimensional vectors of |
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61 | C componentwise absolute and relative tolerances. |
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62 | C FUNC_CHEM = name of routine of derivatives. KPP syntax. |
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63 | C See the header below. |
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64 | C JAC_CHEM = name of routine that computes the Jacobian, in |
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65 | C sparse format. KPP syntax. See the header below. |
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66 | C Info(1) = 1 for autonomous system |
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67 | C = 0 for nonautonomous system |
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68 | C |
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69 | C OUTPUT ARGUMENTS: |
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70 | C y = the values of concentrations at TEND. |
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71 | C T = equals TEND on output. |
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72 | C Info(2) = # of FUNC_CHEM calls. |
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73 | C Info(3) = # of JAC_CHEM calls. |
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74 | C Info(4) = # of accepted steps. |
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75 | C Info(5) = # of rejected steps. |
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76 | C |
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77 | C Adrian Sandu, December 2001 |
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78 | |
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79 | |
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80 | INTEGER NSENSIT |
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81 | KPP_REAL y(NVAR*(NSENSIT+1)), ynew(NVAR*(NSENSIT+1)) |
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82 | KPP_REAL K1(NVAR*(NSENSIT+1)) |
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83 | KPP_REAL K2(NVAR*(NSENSIT+1)) |
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84 | KPP_REAL K3(NVAR) |
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85 | KPP_REAL DFDT(NVAR*(NSENSIT+1)) |
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86 | KPP_REAL DFDP(NVAR*NSENSIT+1), DFDPDT(NVAR*NSENSIT+1) |
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87 | KPP_REAL DJDP(NVAR*NSENSIT+1) |
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88 | KPP_REAL F1(NVAR), F2(NVAR) |
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89 | KPP_REAL JAC(LU_NONZERO), AJAC(LU_NONZERO) |
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90 | KPP_REAL DJDT(LU_NONZERO) |
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91 | KPP_REAL HESS(NHESS) |
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92 | KPP_REAL Hmin,Hmax,Hnew,Hstart,ghinv,uround |
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93 | KPP_REAL AbsTol(NVAR), RelTol(NVAR) |
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94 | KPP_REAL T, Tnext, H, Hold, Tplus, e |
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95 | KPP_REAL ERR, factor, facmax, dround, elo, tau, gam |
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96 | |
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97 | INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier |
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98 | INTEGER Info(5) |
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99 | LOGICAL IsReject,Autonomous,Embed3 |
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100 | EXTERNAL FUNC_CHEM, JAC_CHEM, HESS_CHEM |
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101 | |
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102 | LOGICAL negative |
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103 | KPP_REAL gamma, m1, m2, alpha, beta, delta, theta, w |
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104 | KPP_REAL gamma3, d1, d2, d3, beta1, beta2 |
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105 | KPP_REAL c31, c32, c34 |
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106 | |
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107 | c Initialization of counters, etc. |
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108 | Autonomous = Info(1) .EQ. 1 |
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109 | Embed3 = Info(2) .EQ. 1 |
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110 | uround = 1.d-15 |
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111 | dround = 1.0d-7 ! DSQRT(uround) |
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112 | H = DMAX1(1.d-8, Hstart) |
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113 | Tplus = T |
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114 | IsReject = .false. |
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115 | Naccept = 0 |
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116 | Nreject = 0 |
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117 | Nfcn = 0 |
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118 | Njac = 0 |
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119 | gamma = 1.d0 + 1.d0/DSQRT(2.0d0) |
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120 | c31 = -1.0D0/gamma**2*(1.0D0-7.0D0*gamma+9.0D0*gamma**2) |
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121 | & /(-1.0D0+2.0D0*gamma) |
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122 | c32 = -1.0D0/gamma**2*(1.0D0-6.0D0*gamma+6.0D0*gamma**2) |
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123 | & /(-1.0D0+2.0D0*gamma)/2 |
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124 | gamma3 = 0.5D0 - 2*gamma |
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125 | d1 = ((-9.0D0*gamma+8.0D0*gamma**2+2.0D0)/gamma**2/ |
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126 | & (-1.0D0+2*gamma))/6.0D0 |
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127 | d2 = ((-1.0D0+3.0D0*gamma)/gamma**2/ |
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128 | & (-1.0D0+2.0D0*gamma))/6.0D0 |
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129 | d3 = -1.0D0/(3.0D0*gamma) |
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130 | m1 = -3.d0/(2.d0*gamma) |
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131 | m2 = -1.d0/(2.d0*gamma) |
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132 | |
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133 | |
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134 | C === Starting the time loop === |
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135 | 10 CONTINUE |
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136 | Tplus = T + H |
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137 | IF ( Tplus .gt. Tnext ) THEN |
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138 | H = Tnext - T |
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139 | Tplus = Tnext |
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140 | END IF |
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141 | |
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142 | C Initial Function, Jacobian, and Hessian Values |
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143 | CALL FUNC_CHEM(NVAR, T, y, F1) |
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144 | CALL JAC_CHEM(NVAR, T, y, JAC) |
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145 | CALL HESS_CHEM( NVAR, T, y, HESS ) |
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146 | IF (DDMTYPE .EQ. 1) THEN |
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147 | CALL DFUNDPAR(NVAR, NSENSIT, T, y, DFDP) |
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148 | END IF |
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149 | |
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150 | C Estimate the time derivatives in non-autonomous case |
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151 | IF (.not. Autonomous) THEN |
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152 | tau = DSIGN(dround*DMAX1( 1.0d0, DABS(T) ), T) |
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153 | CALL FUNC_CHEM(NVAR, T+tau, y, K2) |
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154 | nfcn=nfcn+1 |
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155 | CALL JAC_CHEM(NVAR, T+tau, y, AJAC) |
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156 | njac=njac+1 |
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157 | DO 20 j = 1,NVAR |
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158 | DFDT(j) = ( K2(j)-F1(j) )/tau |
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159 | 20 CONTINUE |
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160 | DO 30 j = 1,LU_NONZERO |
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161 | DJDT(j) = ( AJAC(j)-JAC(j) )/tau |
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162 | 30 CONTINUE |
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163 | DO 40 i=1,NSENSIT |
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164 | CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),DFDT(i*NVAR+1)) |
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165 | 40 CONTINUE |
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166 | END IF ! .not. Autonomous |
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167 | |
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168 | Njac = Njac+1 |
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169 | ghinv = - 1.0d0/(gamma*H) |
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170 | DO 50 j=1,LU_NONZERO |
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171 | AJAC(j) = JAC(j) |
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172 | 50 CONTINUE |
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173 | DO 60 j=1,NVAR |
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174 | AJAC(LU_DIAG(j)) = JAC(LU_DIAG(j)) + ghinv |
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175 | 60 CONTINUE |
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176 | CALL KppDecomp (AJAC, ier) |
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177 | |
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178 | IF (ier.ne.0) THEN |
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179 | IF ( H.gt.Hmin) THEN |
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180 | H = 5.0d-1*H |
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181 | go to 10 |
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182 | ELSE |
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183 | print *,'IER <> 0, H=',H |
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184 | stop |
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185 | END IF |
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186 | END IF |
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187 | |
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188 | |
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189 | |
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190 | |
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191 | C ----- STAGE 1 ----- |
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192 | delta = gamma*H |
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193 | DO 70 j = 1,NVAR |
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194 | K1(j) = F1(j) |
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195 | 70 CONTINUE |
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196 | IF (.NOT. Autonomous) THEN |
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197 | DO 80 j = 1,NVAR |
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198 | K1(j) = K1(j) + delta*DFDT(j) |
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199 | 80 CONTINUE |
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200 | END IF |
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201 | CALL KppSolve (AJAC, K1) |
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202 | C --- If derivative w.r.t. parameters |
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203 | IF (DDMTYPE .EQ. 1) THEN |
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204 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K1(1), DJDP) |
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205 | END IF |
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206 | C --- End of derivative w.r.t. parameters |
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207 | DO 120 i=1,NSENSIT |
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208 | CALL Jac_SP_Vec (JAC,y(i*NVAR+1),K1(i*NVAR+1)) |
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209 | CALL Hess_Vec ( HESS, K1(1), y(i*NVAR+1), F2 ) |
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210 | DO 90 j=1,NVAR |
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211 | K1(i*NVAR+j) = K1(i*NVAR+j) + gHinv*F2(j) |
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212 | 90 CONTINUE |
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213 | IF (.NOT. Autonomous) THEN |
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214 | DO 100 j = 1,NVAR |
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215 | K1(i*NVAR+j) = K1(i*NVAR+j) + delta*DFDT(i*NVAR+j) |
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216 | 100 CONTINUE |
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217 | END IF |
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218 | C --- If derivative w.r.t. parameters |
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219 | IF (DDMTYPE .EQ. 1) THEN |
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220 | DO 110 j = 1,NVAR |
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221 | K1(i*NVAR+j) = K1(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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222 | & + DJDP((i-1)*NVAR+j) |
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223 | 110 CONTINUE |
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224 | END IF |
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225 | C --- End of derivative w.r.t. parameters |
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226 | CALL KppSolve (AJAC, K1(i*NVAR+1)) |
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227 | 120 CONTINUE |
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228 | |
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229 | C ----- STAGE 2 ----- |
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230 | alpha = - 1.d0/gamma |
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231 | DO 130 j = 1,NVAR*(NSENSIT+1) |
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232 | ynew(j) = y(j) + alpha*K1(j) |
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233 | 130 CONTINUE |
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234 | CALL FUNC_CHEM(NVAR, T+H, ynew, F1) |
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235 | IF (DDMTYPE.EQ.1) THEN |
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236 | CALL DFUNDPAR(NVAR, NSENSIT, T+H, ynew, DFDP) |
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237 | END IF |
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238 | nfcn=nfcn+1 |
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239 | beta1 = 2.d0/(gamma*H) |
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240 | delta = -gamma*H |
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241 | DO 140 j = 1,NVAR |
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242 | K2(j) = F1(j) + beta1*K1(j) |
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243 | 140 CONTINUE |
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244 | IF (.NOT. Autonomous) THEN |
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245 | DO 150 j = 1,NVAR |
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246 | K2(j) = K2(j) + delta*DFDT(j) |
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247 | 150 CONTINUE |
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248 | END IF |
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249 | CALL KppSolve (AJAC, K2) |
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250 | C --- If derivative w.r.t. parameters |
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251 | IF (DDMTYPE .EQ. 1) THEN |
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252 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K2(1), DJDP) |
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253 | END IF |
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254 | C --- End of derivative w.r.t. parameters |
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255 | |
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256 | CALL JAC_CHEM(NVAR, T+H, Ynew, JAC) |
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257 | njac=njac+1 |
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258 | DO 190 i=1,NSENSIT |
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259 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K2(i*NVAR+1)) |
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260 | CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),F1) |
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261 | CALL Hess_Vec ( HESS, K2(1), y(i*NVAR+1), F2 ) |
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262 | DO 160 j = 1,NVAR |
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263 | K2(i*NVAR+j) = K2(i*NVAR+j) + beta1*K1(i*NVAR+j) |
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264 | & + gHinv*F2(j) |
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265 | 160 CONTINUE |
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266 | IF (.NOT. Autonomous) THEN |
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267 | DO 170 j = 1,NVAR |
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268 | K2(i*NVAR+j) = K2(i*NVAR+j) + delta*DFDT(i*NVAR+j) |
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269 | 170 CONTINUE |
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270 | END IF |
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271 | C --- If derivative w.r.t. parameters |
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272 | IF (DDMTYPE .EQ. 1) THEN |
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273 | DO 180 j = 1,NVAR |
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274 | K2(i*NVAR+j) = K2(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
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275 | & + DJDP((i-1)*NVAR+j) |
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276 | 180 CONTINUE |
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277 | END IF |
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278 | C --- End of derivative w.r.t. parameters |
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279 | CALL KppSolve (AJAC, K2(i*NVAR+1)) |
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280 | 190 CONTINUE |
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281 | |
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282 | C ----- STAGE 3 for error control only ----- |
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283 | IF (Embed3) THEN |
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284 | beta1 = -c31/H |
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285 | beta2 = -c32/H |
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286 | delta = gamma3*H |
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287 | DO 195 j = 1,NVAR |
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288 | K3(j) = F1(j) + beta1*K1(j) + beta2*K2(j) |
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289 | 195 CONTINUE |
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290 | IF (.NOT. Autonomous) THEN |
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291 | DO 196 j = 1,NVAR |
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292 | K3(j) = K3(j) + delta*DFDT(j) |
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293 | 196 CONTINUE |
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294 | END IF |
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295 | CALL KppSolve (AJAC, K3) |
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296 | END IF |
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297 | |
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298 | C ---- The Solution --- |
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299 | DO 200 j = 1,NVAR*(NSENSIT+1) |
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300 | ynew(j) = y(j) + m1*K1(j) + m2*K2(j) |
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301 | 200 CONTINUE |
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302 | |
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303 | |
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304 | C ====== Error estimation for concentrations only; this can be easily adapted to |
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305 | C estimate the sensitivity error too ======== |
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306 | |
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307 | ERR=0.d0 |
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308 | DO 210 i=1,NVAR |
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309 | w = AbsTol(i) + RelTol(i)*DMAX1(DABS(y(i)),DABS(ynew(i))) |
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310 | IF (Embed3) THEN |
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311 | e = d1*K1(i) + d2*K2(i) + d3*K3(i) |
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312 | ELSE |
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313 | e = (1.d0/(2.d0*gamma))*(K1(i)+K2(i)) |
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314 | END IF |
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315 | ERR = ERR + ( e/w )**2 |
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316 | 210 CONTINUE |
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317 | ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) |
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318 | |
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319 | C ======= Choose the stepsize =============================== |
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320 | |
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321 | IF (Embed3) THEN |
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322 | elo = 3.0D0 ! estimator local order |
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323 | ELSE |
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324 | elo = 2.0D0 |
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325 | END IF |
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326 | factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) |
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327 | Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) |
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328 | |
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329 | C ======= Rejected/Accepted Step ============================ |
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330 | |
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331 | IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN |
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332 | IsReject = .true. |
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333 | H = DMIN1(H/10,Hnew) |
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334 | Nreject = Nreject+1 |
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335 | ELSE |
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336 | DO 300 i=1,NVAR*(NSENSIT+1) |
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337 | y(i) = ynew(i) |
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338 | 300 CONTINUE |
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339 | T = Tplus |
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340 | IF (.NOT.IsReject) THEN |
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341 | H = Hnew ! Do not increase stepsize if previous step was rejected |
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342 | END IF |
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343 | IsReject = .false. |
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344 | Naccept = Naccept+1 |
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345 | END IF |
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346 | |
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347 | C ======= End of the time loop =============================== |
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348 | IF ( T .lt. Tnext ) GO TO 10 |
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349 | |
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350 | |
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351 | |
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352 | C ======= Output Information ================================= |
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353 | Info(2) = Nfcn |
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354 | Info(3) = Njac |
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355 | Info(4) = Naccept |
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356 | Info(5) = Nreject |
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357 | |
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358 | RETURN |
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359 | END |
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360 | |
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361 | |
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362 | |
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363 | SUBROUTINE FUNC_CHEM(N, T, Y, P) |
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364 | INCLUDE 'KPP_ROOT_params.h' |
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365 | INCLUDE 'KPP_ROOT_global.h' |
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366 | KPP_REAL T, Told |
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367 | KPP_REAL Y(NVAR), P(NVAR) |
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368 | Told = TIME |
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369 | TIME = T |
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370 | CALL Update_SUN() |
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371 | CALL Update_RCONST() |
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372 | CALL Fun( Y, FIX, RCONST, P ) |
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373 | TIME = Told |
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374 | RETURN |
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375 | END |
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376 | |
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377 | |
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378 | SUBROUTINE DFUNDPAR(N, NSENSIT, T, Y, P) |
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379 | C --- Computes the partial derivatives of FUNC_CHEM w.r.t. parameters |
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380 | INCLUDE 'KPP_ROOT_params.h' |
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381 | INCLUDE 'KPP_ROOT_global.h' |
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382 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
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383 | INTEGER NCOEFF, JCOEFF(NREACT) |
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384 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
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385 | |
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386 | KPP_REAL T, Told |
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387 | KPP_REAL Y(NVAR), P(NVAR*NSENSIT) |
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388 | Told = TIME |
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389 | TIME = T |
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390 | CALL Update_SUN() |
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391 | CALL Update_RCONST() |
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392 | C |
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393 | IF (DDMTYPE .EQ. 0) THEN |
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394 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
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395 | C --- they may have to be changed for other applications |
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396 | DO j=1,NSENSIT |
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397 | DO i=1,NVAR |
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398 | P(i+NVAR*(j-1)) = 0.0D0 |
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399 | END DO |
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400 | END DO |
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401 | ELSE |
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402 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
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403 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
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404 | C --- w.r.t. which one differentiates |
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405 | CALL dFun_dRcoeff( Y, FIX, NCOEFF, JCOEFF, P ) |
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406 | END IF |
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407 | TIME = Told |
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408 | RETURN |
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409 | END |
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410 | |
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411 | SUBROUTINE DJACDPAR(N, NSENSIT, T, Y, U, P) |
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412 | C --- Computes the partial derivatives of JAC w.r.t. parameters times user vector U |
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413 | INCLUDE 'KPP_ROOT_params.h' |
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414 | INCLUDE 'KPP_ROOT_global.h' |
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415 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
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416 | INTEGER NCOEFF, JCOEFF(NREACT) |
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417 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
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418 | |
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419 | KPP_REAL T, Told |
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420 | KPP_REAL Y(NVAR), U(NVAR) |
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421 | KPP_REAL P(NVAR*NSENSIT) |
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422 | Told = TIME |
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423 | TIME = T |
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424 | CALL Update_SUN() |
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425 | CALL Update_RCONST() |
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426 | C |
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427 | IF (DDMTYPE .EQ. 0) THEN |
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428 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
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429 | C --- they may have to be changed for other applications |
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430 | DO j=1,NSENSIT |
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431 | DO i=1,NVAR |
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432 | P(i+NVAR*(j-1)) = 0.0D0 |
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433 | END DO |
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434 | END DO |
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435 | ELSE |
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436 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
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437 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
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438 | C --- w.r.t. which one differentiates |
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439 | CALL dJac_dRcoeff( Y, FIX, U, NCOEFF, JCOEFF, P ) |
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440 | END IF |
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441 | TIME = Told |
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442 | RETURN |
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443 | END |
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444 | |
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445 | SUBROUTINE JAC_CHEM(N, T, Y, J) |
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446 | INCLUDE 'KPP_ROOT_params.h' |
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447 | INCLUDE 'KPP_ROOT_global.h' |
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448 | INTEGER N |
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449 | KPP_REAL Told, T |
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450 | KPP_REAL Y(NVAR), J(LU_NONZERO) |
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451 | Told = TIME |
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452 | TIME = T |
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453 | CALL Update_SUN() |
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454 | CALL Update_RCONST() |
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455 | CALL Jac_SP( Y, FIX, RCONST, J ) |
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456 | TIME = Told |
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457 | RETURN |
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458 | END |
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459 | |
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460 | |
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461 | SUBROUTINE HESS_CHEM(N, T, Y, HESS) |
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462 | INCLUDE 'KPP_ROOT_params.h' |
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463 | INCLUDE 'KPP_ROOT_global.h' |
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464 | INTEGER N |
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465 | KPP_REAL Told, T |
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466 | KPP_REAL Y(NVAR), HESS(NHESS) |
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467 | Told = TIME |
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468 | TIME = T |
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469 | CALL Update_SUN() |
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470 | CALL Update_RCONST() |
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471 | CALL Hessian( Y, FIX, RCONST, HESS ) |
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472 | TIME = Told |
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473 | RETURN |
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474 | END |
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475 | |
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476 | |
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477 | |
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478 | |
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479 | |
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480 | |
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