1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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2 | ! RungeKuttaADJ - Adjoint Model of Fully Implicit 3-stage Runge-Kutta: ! |
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3 | ! * Radau-2A quadrature (order 5) ! |
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4 | ! * Radau-1A quadrature (order 5) ! |
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5 | ! * Lobatto-3C quadrature (order 4) ! |
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6 | ! * Gauss quadrature (order 6) ! |
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7 | ! By default the code employs the KPP sparse linear algebra routines ! |
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8 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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9 | ! ! |
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10 | ! (C) Adrian Sandu, August 2005 ! |
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11 | ! Virginia Polytechnic Institute and State University ! |
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12 | ! Contact: sandu@cs.vt.edu ! |
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13 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 ! |
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14 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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15 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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16 | |
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17 | MODULE KPP_ROOT_Integrator |
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18 | |
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19 | USE KPP_ROOT_Precision |
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20 | USE KPP_ROOT_Parameters, ONLY: NVAR, NSPEC, NFIX, LU_NONZERO |
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21 | USE KPP_ROOT_Global, ONLY: FIX, RCONST, TIME |
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22 | USE KPP_ROOT_Jacobian |
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23 | USE KPP_ROOT_LinearAlgebra |
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24 | |
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25 | IMPLICIT NONE |
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26 | PUBLIC |
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27 | SAVE |
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28 | |
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29 | !~~~> Statistics on the work performed by the Runge-Kutta method |
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30 | INTEGER :: Nfun,Njac,Nstp,Nacc,Nrej,Ndec,Nsol,Nsng |
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31 | INTEGER, PARAMETER :: ifun=1, ijac=2, istp=3, iacc=4, & |
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32 | irej=5, idec=6, isol=7, isng=8, itexit=1, ihacc=2, ihnew=3 |
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33 | |
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34 | CONTAINS |
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35 | |
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36 | ! ************************************************************************** |
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37 | |
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38 | SUBROUTINE INTEGRATE_ADJ(NADJ, Y, Lambda, TIN, TOUT, & |
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39 | ATOL_adj, RTOL_adj, & |
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40 | ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U, IERR_U ) |
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41 | |
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42 | USE KPP_ROOT_Parameters, ONLY: NVAR |
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43 | USE KPP_ROOT_Global, ONLY: ATOL,RTOL |
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44 | |
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45 | IMPLICIT NONE |
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46 | |
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47 | !~~~> Y - Concentrations |
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48 | KPP_REAL :: Y(NVAR) |
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49 | !~~~> NADJ - No. of cost functionals for which adjoints |
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50 | ! are evaluated simultaneously |
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51 | ! If single cost functional is considered (like in |
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52 | ! most applications) simply set NADJ = 1 |
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53 | INTEGER NADJ |
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54 | !~~~> Lambda - Sensitivities of concentrations |
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55 | ! Note: Lambda (1:NVAR,j) contains sensitivities of |
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56 | ! the j-th cost functional w.r.t. Y(1:NVAR), j=1...NADJ |
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57 | KPP_REAL :: Lambda(NVAR,NADJ) |
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58 | !~~~> Tolerances for adjoint calculations |
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59 | ! (used for full continuous adjoint, and for controlling |
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60 | ! the convergence of iterations for solving the discrete adjoint) |
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61 | KPP_REAL, INTENT(IN) :: ATOL_adj(NVAR,NADJ), RTOL_adj(NVAR,NADJ) |
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62 | KPP_REAL :: TIN ! TIN - Start Time |
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63 | KPP_REAL :: TOUT ! TOUT - End Time |
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64 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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65 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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66 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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67 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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68 | INTEGER, INTENT(OUT), OPTIONAL :: IERR_U |
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69 | |
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70 | INTEGER :: IERR |
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71 | |
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72 | KPP_REAL :: RCNTRL(20), RSTATUS(20), T1, T2 |
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73 | INTEGER :: ICNTRL(20), ISTATUS(20) |
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74 | INTEGER, SAVE :: Ntotal = 0 |
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75 | |
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76 | |
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77 | ICNTRL(1:20) = 0 |
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78 | RCNTRL(1:20) = 0.0_dp |
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79 | |
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80 | !~~~> fine-tune the integrator: |
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81 | ICNTRL(2) = 0 ! 0=vector tolerances, 1=scalar tolerances |
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82 | ICNTRL(5) = 8 ! Max no. of Newton iterations |
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83 | ICNTRL(6) = 0 ! Starting values for Newton are: 0=interpolated, 1=zero |
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84 | ICNTRL(7) = 2 ! Adj. system solved by: 1=iteration, 2=direct, 3=adaptive |
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85 | ICNTRL(8) = 0 ! Adj. LU decomp: 0=compute, 1=save from fwd |
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86 | ICNTRL(9) = 2 ! Adjoint: 1=none, 2=discrete, 3=full continuous, 4=simplified continuous |
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87 | ICNTRL(10) = 0 ! Error estimator: 0=classic, 1=SDIRK |
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88 | ICNTRL(11) = 1 ! Step controller: 1=Gustaffson, 2=classic |
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89 | |
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90 | |
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91 | !~~~> if optional parameters are given, and if they are >0, |
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92 | ! then use them to overwrite default settings |
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93 | IF (PRESENT(ICNTRL_U)) THEN |
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94 | WHERE(ICNTRL_U(:) > 0) ICNTRL(:) = ICNTRL_U(:) |
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95 | END IF |
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96 | IF (PRESENT(RCNTRL_U)) THEN |
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97 | WHERE(RCNTRL_U(:) > 0) RCNTRL(:) = RCNTRL_U(:) |
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98 | END IF |
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99 | |
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100 | |
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101 | T1 = TIN; T2 = TOUT |
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102 | CALL RungeKuttaADJ(NVAR, Y, NADJ, Lambda, T1, T2, & |
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103 | RTOL, ATOL, ATOL_adj, RTOL_adj, & |
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104 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, IERR ) |
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105 | |
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106 | Ntotal = Ntotal + ISTATUS(istp) |
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107 | ! PRINT*,'NSTEPS=',ISTATUS(istp),' (',Ntotal,')',' O3=', VAR(ind_O3) |
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108 | |
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109 | ! if optional parameters are given for output |
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110 | ! use them to store information in them |
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111 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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112 | IF (PRESENT(RSTATUS_U)) RSTATUS_U(:) = RSTATUS(:) |
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113 | IF (PRESENT(IERR_U)) IERR_U = IERR |
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114 | |
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115 | IF (IERR < 0) THEN |
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116 | PRINT *,'Runge-Kutta-ADJ: Unsuccessful exit at T=', TIN,' (IERR=',IERR,')' |
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117 | ENDIF |
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118 | |
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119 | END SUBROUTINE INTEGRATE_ADJ |
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120 | |
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121 | |
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122 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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123 | SUBROUTINE RungeKuttaADJ( N, Y, NADJ, Lambda,Tstart,Tend, & |
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124 | RelTol, AbsTol, RelTol_adj, AbsTol_adj, & |
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125 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, IERR ) |
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126 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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127 | ! |
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128 | ! This implementation is based on the book and the code Radau5: |
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129 | ! |
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130 | ! E. HAIRER AND G. WANNER |
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131 | ! "SOLVING ORDINARY DIFFERENTIAL EQUATIONS II. |
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132 | ! STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS." |
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133 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS 14, |
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134 | ! SPRINGER-VERLAG (1991) |
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135 | ! |
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136 | ! UNIVERSITE DE GENEVE, DEPT. DE MATHEMATIQUES |
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137 | ! CH-1211 GENEVE 24, SWITZERLAND |
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138 | ! E-MAIL: HAIRER@DIVSUN.UNIGE.CH, WANNER@DIVSUN.UNIGE.CH |
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139 | ! |
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140 | ! Methods: |
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141 | ! * Radau-2A quadrature (order 5) |
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142 | ! * Radau-1A quadrature (order 5) |
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143 | ! * Lobatto-3C quadrature (order 4) |
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144 | ! * Gauss quadrature (order 6) |
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145 | ! |
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146 | ! (C) Adrian Sandu, August 2005 |
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147 | ! Virginia Polytechnic Institute and State University |
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148 | ! Contact: sandu@cs.vt.edu |
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149 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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150 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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151 | ! |
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152 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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153 | ! |
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154 | !~~~> INPUT ARGUMENTS: |
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155 | ! ---------------- |
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156 | ! |
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157 | ! Note: For input parameters equal to zero the default values of the |
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158 | ! corresponding variables are used. |
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159 | ! |
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160 | ! N Dimension of the system |
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161 | ! T Initial time value |
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162 | ! |
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163 | ! Tend Final T value (Tend-T may be positive or negative) |
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164 | ! |
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165 | ! Y(N) Initial values for Y |
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166 | ! |
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167 | ! RelTol,AbsTol Relative and absolute error tolerances. |
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168 | ! for ICNTRL(2) = 0: AbsTol, RelTol are N-dimensional vectors |
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169 | ! = 1: AbsTol, RelTol are scalars |
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170 | ! |
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171 | !~~~> Integer input parameters: |
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172 | ! |
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173 | ! ICNTRL(1) = not used |
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174 | ! |
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175 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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176 | ! = 1: AbsTol, RelTol are scalars |
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177 | ! |
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178 | ! ICNTRL(3) = RK method selection |
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179 | ! = 1: Radau-2A (the default) |
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180 | ! = 2: Lobatto-3C |
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181 | ! = 3: Gauss |
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182 | ! = 4: Radau-1A |
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183 | ! |
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184 | ! ICNTRL(4) -> maximum number of integration steps |
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185 | ! For ICNTRL(4)=0 the default value of 10000 is used |
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186 | ! |
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187 | ! ICNTRL(5) -> maximum number of Newton iterations |
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188 | ! For ICNTRL(5)=0 the default value of 8 is used |
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189 | ! |
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190 | ! ICNTRL(6) -> starting values of Newton iterations: |
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191 | ! ICNTRL(6)=0 : starting values are obtained from |
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192 | ! the extrapolated collocation solution |
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193 | ! (the default) |
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194 | ! ICNTRL(6)=1 : starting values are zero |
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195 | ! |
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196 | ! ICNTRL(7) -> method to solve the linear ADJ equations: |
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197 | ! ICNTRL(7)=0,1 : modified Newton re-using LU (the default) |
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198 | ! with a fixed number of iterations |
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199 | ! ICNTRL(7)=2 : direct solution (additional one LU factorization |
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200 | ! of 3Nx3N matrix per step); good for debugging |
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201 | ! ICNTRL(7)=3 : adaptive solution (if Newton does not converge |
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202 | ! switch to direct) |
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203 | ! |
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204 | ! ICNTRL(8) -> checkpointing the LU factorization at each step: |
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205 | ! ICNTRL(8)=0 : do *not* save LU factorization (the default) |
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206 | ! ICNTRL(8)=1 : save LU factorization |
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207 | ! Note: if ICNTRL(7)=1 the LU factorization is *not* saved |
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208 | ! |
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209 | ! ICNTRL(9) -> Type of adjoint algorithm |
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210 | ! = 0 : default is discrete adjoint ( of method ICNTRL(3) ) |
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211 | ! = 1 : no adjoint |
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212 | ! = 2 : discrete adjoint ( of method ICNTRL(3) ) |
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213 | ! = 3 : fully adaptive continuous adjoint ( with method ICNTRL(6) ) |
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214 | ! = 4 : simplified continuous adjoint ( with method ICNTRL(6) ) |
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215 | ! |
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216 | ! ICNTRL(10) -> switch for error estimation strategy |
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217 | ! ICNTRL(10) = 0: one additional stage at c=0, |
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218 | ! see Hairer (default) |
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219 | ! ICNTRL(10) = 1: two additional stages at c=0 |
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220 | ! and SDIRK at c=1, stiffly accurate |
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221 | ! |
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222 | ! ICNTRL(11) -> switch for step size strategy |
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223 | ! ICNTRL(11)=1: mod. predictive controller (Gustafsson, default) |
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224 | ! ICNTRL(11)=2: classical step size control |
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225 | ! the choice 1 seems to produce safer results; |
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226 | ! for simple problems, the choice 2 produces |
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227 | ! often slightly faster runs |
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228 | ! |
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229 | !~~~> Real input parameters: |
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230 | ! |
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231 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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232 | ! (highly recommended to keep Hmin = ZERO, the default) |
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233 | ! |
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234 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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235 | ! |
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236 | ! RCNTRL(3) -> Hstart, the starting step size |
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237 | ! |
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238 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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239 | ! |
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240 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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241 | ! |
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242 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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243 | ! (default=0.1) |
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244 | ! |
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245 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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246 | ! than the predicted value (default=0.9) |
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247 | ! |
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248 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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249 | ! than ThetaMin the Jacobian is not recomputed; |
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250 | ! (default=0.001) |
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251 | ! |
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252 | ! RCNTRL(9) -> NewtonTol, stopping criterion for Newton's method |
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253 | ! (default=0.03) |
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254 | ! |
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255 | ! RCNTRL(10) -> Qmin |
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256 | ! |
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257 | ! RCNTRL(11) -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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258 | ! step size is kept constant and the LU factorization |
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259 | ! reused (default Qmin=1, Qmax=1.2) |
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260 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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261 | ! |
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262 | ! |
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263 | ! OUTPUT ARGUMENTS: |
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264 | ! ----------------- |
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265 | ! |
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266 | ! T -> T value for which the solution has been computed |
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267 | ! (after successful return T=Tend). |
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268 | ! |
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269 | ! Y(N) -> Numerical solution at T |
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270 | ! |
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271 | ! IERR -> Reports on successfulness upon return: |
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272 | ! = 1 for success |
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273 | ! < 0 for error (value equals error code) |
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274 | ! |
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275 | ! ISTATUS(1) -> No. of function calls |
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276 | ! ISTATUS(2) -> No. of Jacobian calls |
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277 | ! ISTATUS(3) -> No. of steps |
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278 | ! ISTATUS(4) -> No. of accepted steps |
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279 | ! ISTATUS(5) -> No. of rejected steps (except at very beginning) |
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280 | ! ISTATUS(6) -> No. of LU decompositions |
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281 | ! ISTATUS(7) -> No. of forward/backward substitutions |
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282 | ! ISTATUS(8) -> No. of singular matrix decompositions |
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283 | ! |
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284 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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285 | ! computed Y upon return |
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286 | ! RSTATUS(2) -> Hexit, last accepted step before exit |
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287 | ! RSTATUS(3) -> Hnew, last predicted step (not yet taken) |
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288 | ! For multiple restarts, use Hnew as Hstart |
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289 | ! in the subsequent run |
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290 | ! |
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291 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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292 | |
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293 | IMPLICIT NONE |
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294 | |
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295 | INTEGER :: N |
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296 | INTEGER, INTENT(IN) :: NADJ |
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297 | KPP_REAL, INTENT(INOUT) :: Lambda(N,NADJ) |
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298 | KPP_REAL, INTENT(IN) :: AbsTol_adj(N,NADJ), RelTol_adj(N,NADJ) |
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299 | KPP_REAL :: Y(N),AbsTol(N),RelTol(N),RCNTRL(20),RSTATUS(20) |
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300 | INTEGER :: ICNTRL(20), ISTATUS(20) |
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301 | LOGICAL :: StartNewton, Gustafsson, SdirkError, SaveLU |
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302 | INTEGER :: IERR, ITOL |
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303 | KPP_REAL, INTENT(IN):: Tstart,Tend |
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304 | KPP_REAL :: Texit |
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305 | |
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306 | !~~~> Control arguments |
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307 | INTEGER :: Max_no_steps, NewtonMaxit, AdjointType, rkMethod |
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308 | KPP_REAL :: Hmin,Hmax,Hstart,Qmin,Qmax |
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309 | KPP_REAL :: Roundoff, ThetaMin, NewtonTol |
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310 | KPP_REAL :: FacSafe,FacMin,FacMax,FacRej |
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311 | ! Runge-Kutta method parameters |
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312 | INTEGER, PARAMETER :: R2A=1, R1A=2, L3C=3, GAU=4, L3A=5 |
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313 | KPP_REAL :: rkT(3,3), rkTinv(3,3), rkTinvAinv(3,3), rkAinvT(3,3), & |
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314 | rkA(3,3), rkB(3), rkC(3), rkD(0:3), rkE(0:3), & |
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315 | rkBgam(0:4), rkBhat(0:4), rkTheta(0:3), & |
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316 | rkGamma, rkAlpha, rkBeta, rkELO |
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317 | ! ADJ method parameters |
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318 | INTEGER, PARAMETER :: KPP_ROOT_none = 1, KPP_ROOT_discrete = 2, & |
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319 | KPP_ROOT_continuous = 3, KPP_ROOT_simple_continuous = 4 |
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320 | INTEGER :: AdjointSolve |
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321 | INTEGER, PARAMETER :: Solve_direct = 1, Solve_fixed = 2, & |
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322 | Solve_adaptive = 3 |
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323 | INTEGER, PARAMETER :: bufsize = 10000 |
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324 | INTEGER :: stack_ptr = 0 ! last written entry |
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325 | KPP_REAL, DIMENSION(:), POINTER :: chk_H, chk_T |
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326 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_Y, chk_Z, chk_E1 |
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327 | INTEGER, DIMENSION(:), POINTER :: chk_NiT |
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328 | COMPLEX(kind=dp), DIMENSION(:,:), POINTER :: chk_E2 |
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329 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_dY, chk_d2Y |
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330 | !~~~> Local variables |
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331 | INTEGER :: i |
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332 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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333 | |
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334 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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335 | ! SETTING THE PARAMETERS |
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336 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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337 | IERR = 0 |
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338 | ISTATUS(1:20) = 0 |
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339 | RSTATUS(1:20) = ZERO |
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340 | |
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341 | !~~~> ICNTRL(1) - autonomous system - not used |
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342 | !~~~> ITOL: 1 for vector and 0 for scalar AbsTol/RelTol |
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343 | IF (ICNTRL(2) == 0) THEN |
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344 | ITOL = 1 |
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345 | ELSE |
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346 | ITOL = 0 |
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347 | END IF |
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348 | !~~~> Error control selection |
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349 | IF (ICNTRL(10) == 0) THEN |
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350 | SdirkError = .FALSE. |
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351 | ELSE |
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352 | SdirkError = .TRUE. |
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353 | END IF |
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354 | !~~~> Method selection |
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355 | SELECT CASE (ICNTRL(3)) |
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356 | CASE (0,1) |
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357 | CALL Radau2A_Coefficients |
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358 | CASE (2) |
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359 | CALL Lobatto3C_Coefficients |
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360 | CASE (3) |
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361 | CALL Gauss_Coefficients |
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362 | CASE (4) |
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363 | CALL Radau1A_Coefficients |
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364 | CASE DEFAULT |
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365 | WRITE(6,*) 'ICNTRL(3)=',ICNTRL(3) |
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366 | CALL RK_ErrorMsg(-13,Tstart,ZERO,IERR) |
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367 | END SELECT |
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368 | !~~~> Max_no_steps: the maximal number of time steps |
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369 | IF (ICNTRL(4) == 0) THEN |
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370 | Max_no_steps = 200000 |
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371 | ELSE |
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372 | Max_no_steps=ICNTRL(4) |
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373 | IF (Max_no_steps <= 0) THEN |
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374 | WRITE(6,*) 'ICNTRL(4)=',ICNTRL(4) |
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375 | CALL RK_ErrorMsg(-1,Tstart,ZERO,IERR) |
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376 | END IF |
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377 | END IF |
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378 | !~~~> NewtonMaxit maximal number of Newton iterations |
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379 | IF (ICNTRL(5) == 0) THEN |
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380 | NewtonMaxit = 8 |
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381 | ELSE |
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382 | NewtonMaxit=ICNTRL(5) |
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383 | IF (NewtonMaxit <= 0) THEN |
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384 | WRITE(6,*) 'ICNTRL(5)=',ICNTRL(5) |
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385 | CALL RK_ErrorMsg(-2,Tstart,ZERO,IERR) |
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386 | END IF |
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387 | END IF |
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388 | !~~~> StartNewton: Use extrapolation for starting values of Newton iterations |
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389 | IF (ICNTRL(6) == 0) THEN |
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390 | StartNewton = .TRUE. |
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391 | ELSE |
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392 | StartNewton = .FALSE. |
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393 | END IF |
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394 | !~~~> How to solve the linear adjoint system |
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395 | SELECT CASE (ICNTRL(7)) |
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396 | CASE (0,1) |
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397 | AdjointSolve = Solve_fixed |
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398 | CASE (2) |
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399 | AdjointSolve = Solve_direct |
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400 | CASE (3) |
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401 | AdjointSolve = Solve_adaptive |
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402 | CASE DEFAULT |
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403 | PRINT * , 'User-selected adjoint solution: ICNTRL(7)=', ICNTRL(7) |
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404 | PRINT * , 'Implemented: =(0,1) (fixed), =2 (direct), =3 (adaptive)' |
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405 | CALL rk_ErrorMsg(-9,Tstart,ZERO,IERR) |
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406 | RETURN |
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407 | END SELECT |
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408 | !~~~> Discrete or continuous adjoint formulation |
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409 | SELECT CASE (ICNTRL(9)) |
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410 | CASE (0,2) |
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411 | AdjointType = KPP_ROOT_discrete |
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412 | CASE (1) |
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413 | AdjointType = KPP_ROOT_none |
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414 | CASE DEFAULT |
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415 | PRINT * , 'User-selected adjoint type: ICNTRL(9)=', ICNTRL(9) |
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416 | PRINT * , 'Implemented: =(0,2) (discrete adj) and =1 (no adj)' |
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417 | CALL rk_ErrorMsg(-9,Tstart,ZERO,IERR) |
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418 | RETURN |
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419 | END SELECT |
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420 | !~~~> Save or not the forward LU factorization |
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421 | SaveLU = (ICNTRL(8) /= 0) |
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422 | IF (AdjointSolve == Solve_direct) SaveLU = .FALSE. |
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423 | !~~~> Gustafsson: step size controller |
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424 | IF (ICNTRL(11) == 0) THEN |
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425 | Gustafsson = .TRUE. |
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426 | ELSE |
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427 | Gustafsson = .FALSE. |
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428 | END IF |
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429 | |
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430 | !~~~> Roundoff: smallest number s.t. 1.0 + Roundoff > 1.0 |
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431 | Roundoff = WLAMCH('E'); |
---|
432 | |
---|
433 | !~~~> Hmin = minimal step size |
---|
434 | IF (RCNTRL(1) == ZERO) THEN |
---|
435 | Hmin = ZERO |
---|
436 | ELSE |
---|
437 | Hmin = MIN(ABS(RCNTRL(1)),ABS(Tend-Tstart)) |
---|
438 | END IF |
---|
439 | !~~~> Hmax = maximal step size |
---|
440 | IF (RCNTRL(2) == ZERO) THEN |
---|
441 | Hmax = ABS(Tend-Tstart) |
---|
442 | ELSE |
---|
443 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tend-Tstart)) |
---|
444 | END IF |
---|
445 | !~~~> Hstart = starting step size |
---|
446 | IF (RCNTRL(3) == ZERO) THEN |
---|
447 | Hstart = ZERO |
---|
448 | ELSE |
---|
449 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tend-Tstart)) |
---|
450 | END IF |
---|
451 | !~~~> FacMin: lower bound on step decrease factor |
---|
452 | IF(RCNTRL(4) == ZERO)THEN |
---|
453 | FacMin = 0.2d0 |
---|
454 | ELSE |
---|
455 | FacMin = RCNTRL(4) |
---|
456 | END IF |
---|
457 | !~~~> FacMax: upper bound on step increase factor |
---|
458 | IF(RCNTRL(5) == ZERO)THEN |
---|
459 | FacMax = 8.D0 |
---|
460 | ELSE |
---|
461 | FacMax = RCNTRL(5) |
---|
462 | END IF |
---|
463 | !~~~> FacRej: step decrease factor after 2 consecutive rejections |
---|
464 | IF(RCNTRL(6) == ZERO)THEN |
---|
465 | FacRej = 0.1d0 |
---|
466 | ELSE |
---|
467 | FacRej = RCNTRL(6) |
---|
468 | END IF |
---|
469 | !~~~> FacSafe: by which the new step is slightly smaller |
---|
470 | ! than the predicted value |
---|
471 | IF (RCNTRL(7) == ZERO) THEN |
---|
472 | FacSafe=0.9d0 |
---|
473 | ELSE |
---|
474 | FacSafe=RCNTRL(7) |
---|
475 | END IF |
---|
476 | IF ( (FacMax < ONE) .OR. (FacMin > ONE) .OR. & |
---|
477 | (FacSafe <= 1.0d-3) .OR. (FacSafe >= ONE) ) THEN |
---|
478 | WRITE(6,*)'RCNTRL(4:7)=',RCNTRL(4:7) |
---|
479 | CALL RK_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
480 | END IF |
---|
481 | |
---|
482 | !~~~> ThetaMin: decides whether the Jacobian should be recomputed |
---|
483 | IF (RCNTRL(8) == ZERO) THEN |
---|
484 | ThetaMin = 1.0d-3 |
---|
485 | ELSE |
---|
486 | ThetaMin=RCNTRL(8) |
---|
487 | IF (ThetaMin <= 0.0d0 .OR. ThetaMin >= 1.0d0) THEN |
---|
488 | WRITE(6,*) 'RCNTRL(8)=', RCNTRL(8) |
---|
489 | CALL RK_ErrorMsg(-5,Tstart,ZERO,IERR) |
---|
490 | END IF |
---|
491 | END IF |
---|
492 | !~~~> NewtonTol: stopping crierion for Newton's method |
---|
493 | IF (RCNTRL(9) == ZERO) THEN |
---|
494 | NewtonTol = 3.0d-2 |
---|
495 | ELSE |
---|
496 | NewtonTol = RCNTRL(9) |
---|
497 | IF (NewtonTol <= Roundoff) THEN |
---|
498 | WRITE(6,*) 'RCNTRL(9)=',RCNTRL(9) |
---|
499 | CALL RK_ErrorMsg(-6,Tstart,ZERO,IERR) |
---|
500 | END IF |
---|
501 | END IF |
---|
502 | !~~~> Qmin AND Qmax: IF Qmin < Hnew/Hold < Qmax then step size = const. |
---|
503 | IF (RCNTRL(10) == ZERO) THEN |
---|
504 | Qmin=1.D0 |
---|
505 | ELSE |
---|
506 | Qmin=RCNTRL(10) |
---|
507 | END IF |
---|
508 | IF (RCNTRL(11) == ZERO) THEN |
---|
509 | Qmax=1.2D0 |
---|
510 | ELSE |
---|
511 | Qmax=RCNTRL(11) |
---|
512 | END IF |
---|
513 | IF (Qmin > ONE .OR. Qmax < ONE) THEN |
---|
514 | WRITE(6,*) 'RCNTRL(10:11)=',Qmin,Qmax |
---|
515 | CALL RK_ErrorMsg(-7,Tstart,ZERO,IERR) |
---|
516 | END IF |
---|
517 | !~~~> Check if tolerances are reasonable |
---|
518 | IF (ITOL == 0) THEN |
---|
519 | IF (AbsTol(1) <= ZERO.OR.RelTol(1) <= 10.d0*Roundoff) THEN |
---|
520 | WRITE (6,*) 'AbsTol/RelTol=',AbsTol,RelTol |
---|
521 | CALL RK_ErrorMsg(-8,Tstart,ZERO,IERR) |
---|
522 | END IF |
---|
523 | ELSE |
---|
524 | DO i=1,N |
---|
525 | IF (AbsTol(i) <= ZERO.OR.RelTol(i) <= 10.d0*Roundoff) THEN |
---|
526 | WRITE (6,*) 'AbsTol/RelTol(',i,')=',AbsTol(i),RelTol(i) |
---|
527 | CALL RK_ErrorMsg(-8,Tstart,ZERO,IERR) |
---|
528 | END IF |
---|
529 | END DO |
---|
530 | END IF |
---|
531 | |
---|
532 | !~~~> Parameters are wrong |
---|
533 | IF (IERR < 0) RETURN |
---|
534 | |
---|
535 | !~~~> Allocate checkpoint space or open checkpoint files |
---|
536 | IF (AdjointType == KPP_ROOT_discrete) THEN |
---|
537 | CALL rk_AllocateDBuffers() |
---|
538 | ELSEIF ( (AdjointType == KPP_ROOT_continuous).OR. & |
---|
539 | (AdjointType == KPP_ROOT_simple_continuous) ) THEN |
---|
540 | CALL rk_AllocateCBuffers |
---|
541 | END IF |
---|
542 | |
---|
543 | !~~~> Call the core method |
---|
544 | CALL RK_FwdIntegrator( N,Tstart,Tend,Y,AdjointType,IERR ) |
---|
545 | ! PRINT*,'FORWARD STATISTICS' |
---|
546 | ! PRINT*,'Step=',Istatus(istp),' Acc=',Istatus(iacc), & |
---|
547 | ! ' Rej=',Istatus(irej), ' Singular=',Istatus(isng) |
---|
548 | Nstp = 0 |
---|
549 | Nacc = 0 |
---|
550 | Nrej = 0 |
---|
551 | Nsng = 0 |
---|
552 | |
---|
553 | !~~~> If Forward integration failed return |
---|
554 | IF (IERR<0) RETURN |
---|
555 | |
---|
556 | SELECT CASE (AdjointType) |
---|
557 | CASE (KPP_ROOT_discrete) |
---|
558 | CALL rk_DadjInt ( & |
---|
559 | NADJ, Lambda, & |
---|
560 | Tstart, Tend, Texit, & |
---|
561 | IERR ) |
---|
562 | CASE (KPP_ROOT_continuous) |
---|
563 | CALL rk_CadjInt ( & |
---|
564 | NADJ, Lambda, & |
---|
565 | Tend, Tstart, Texit, & |
---|
566 | IERR ) |
---|
567 | CASE (KPP_ROOT_simple_continuous) |
---|
568 | CALL rk_SimpleCadjInt ( & |
---|
569 | NADJ, Lambda, & |
---|
570 | Tstart, Tend, Texit, & |
---|
571 | IERR ) |
---|
572 | END SELECT ! AdjointType |
---|
573 | ! PRINT*,'ADJOINT STATISTICS' |
---|
574 | ! PRINT*,'Step=',Nstp,' Acc=',Nacc, & |
---|
575 | ! ' Rej=',Nrej, ' Singular=',Nsng |
---|
576 | |
---|
577 | !~~~> Free checkpoint space or close checkpoint files |
---|
578 | IF (AdjointType == KPP_ROOT_discrete) THEN |
---|
579 | CALL rk_FreeDBuffers |
---|
580 | ELSEIF ( (AdjointType == KPP_ROOT_continuous) .OR. & |
---|
581 | (AdjointType == KPP_ROOT_simple_continuous) ) THEN |
---|
582 | CALL rk_FreeCBuffers |
---|
583 | END IF |
---|
584 | |
---|
585 | |
---|
586 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
587 | CONTAINS ! Internal procedures to RungeKuttaADJ |
---|
588 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
589 | |
---|
590 | |
---|
591 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
592 | SUBROUTINE rk_AllocateDBuffers() |
---|
593 | !~~~> Allocate buffer space for discrete adjoint |
---|
594 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
595 | INTEGER :: i |
---|
596 | |
---|
597 | ALLOCATE( chk_H(bufsize), STAT=i ) |
---|
598 | IF (i/=0) THEN |
---|
599 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
600 | END IF |
---|
601 | ALLOCATE( chk_T(bufsize), STAT=i ) |
---|
602 | IF (i/=0) THEN |
---|
603 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
604 | END IF |
---|
605 | ALLOCATE( chk_Y(NVAR,bufsize), STAT=i ) |
---|
606 | IF (i/=0) THEN |
---|
607 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
608 | END IF |
---|
609 | ALLOCATE( chk_Z(NVAR*3,bufsize), STAT=i ) |
---|
610 | IF (i/=0) THEN |
---|
611 | PRINT*,'Failed allocation of buffer Z'; STOP |
---|
612 | END IF |
---|
613 | ALLOCATE( chk_NiT(bufsize), STAT=i ) |
---|
614 | IF (i/=0) THEN |
---|
615 | PRINT*,'Failed allocation of buffer NiT'; STOP |
---|
616 | END IF |
---|
617 | IF (SaveLU) THEN |
---|
618 | #ifdef FULL_ALGEBRA |
---|
619 | ALLOCATE( chk_E1(NVAR*NVAR,bufsize), STAT=i ) |
---|
620 | IF (i/=0) THEN |
---|
621 | PRINT*,'Failed allocation of buffer E1'; STOP |
---|
622 | END IF |
---|
623 | ALLOCATE( chk_E2(NVAR*NVAR,bufsize), STAT=i ) |
---|
624 | IF (i/=0) THEN |
---|
625 | PRINT*,'Failed allocation of buffer E2'; STOP |
---|
626 | END IF |
---|
627 | #else |
---|
628 | ALLOCATE( chk_E1(LU_NONZERO,bufsize), STAT=i ) |
---|
629 | IF (i/=0) THEN |
---|
630 | PRINT*,'Failed allocation of buffer E1'; STOP |
---|
631 | END IF |
---|
632 | ALLOCATE( chk_E2(LU_NONZERO,bufsize), STAT=i ) |
---|
633 | IF (i/=0) THEN |
---|
634 | PRINT*,'Failed allocation of buffer E2'; STOP |
---|
635 | END IF |
---|
636 | #endif |
---|
637 | END IF |
---|
638 | |
---|
639 | |
---|
640 | END SUBROUTINE rk_AllocateDBuffers |
---|
641 | |
---|
642 | |
---|
643 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
644 | SUBROUTINE rk_FreeDBuffers() |
---|
645 | !~~~> Dallocate buffer space for discrete adjoint |
---|
646 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
647 | INTEGER :: i |
---|
648 | |
---|
649 | DEALLOCATE( chk_H, STAT=i ) |
---|
650 | IF (i/=0) THEN |
---|
651 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
652 | END IF |
---|
653 | DEALLOCATE( chk_T, STAT=i ) |
---|
654 | IF (i/=0) THEN |
---|
655 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
656 | END IF |
---|
657 | DEALLOCATE( chk_Y, STAT=i ) |
---|
658 | IF (i/=0) THEN |
---|
659 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
660 | END IF |
---|
661 | DEALLOCATE( chk_Z, STAT=i ) |
---|
662 | IF (i/=0) THEN |
---|
663 | PRINT*,'Failed deallocation of buffer Z'; STOP |
---|
664 | END IF |
---|
665 | DEALLOCATE( chk_NiT, STAT=i ) |
---|
666 | IF (i/=0) THEN |
---|
667 | PRINT*,'Failed deallocation of buffer NiT'; STOP |
---|
668 | END IF |
---|
669 | IF (SaveLU) THEN |
---|
670 | DEALLOCATE( chk_E1, STAT=i ) |
---|
671 | IF (i/=0) THEN |
---|
672 | PRINT*,'Failed allocation of buffer E1'; STOP |
---|
673 | END IF |
---|
674 | DEALLOCATE( chk_E2, STAT=i ) |
---|
675 | IF (i/=0) THEN |
---|
676 | PRINT*,'Failed allocation of buffer E2'; STOP |
---|
677 | END IF |
---|
678 | END IF |
---|
679 | |
---|
680 | END SUBROUTINE rk_FreeDBuffers |
---|
681 | |
---|
682 | |
---|
683 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
684 | SUBROUTINE rk_AllocateCBuffers() |
---|
685 | !~~~> Allocate buffer space for continuous adjoint |
---|
686 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
687 | INTEGER :: i |
---|
688 | |
---|
689 | ALLOCATE( chk_H(bufsize), STAT=i ) |
---|
690 | IF (i/=0) THEN |
---|
691 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
692 | END IF |
---|
693 | ALLOCATE( chk_T(bufsize), STAT=i ) |
---|
694 | IF (i/=0) THEN |
---|
695 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
696 | END IF |
---|
697 | ALLOCATE( chk_Y(NVAR,bufsize), STAT=i ) |
---|
698 | IF (i/=0) THEN |
---|
699 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
700 | END IF |
---|
701 | ALLOCATE( chk_dY(NVAR,bufsize), STAT=i ) |
---|
702 | IF (i/=0) THEN |
---|
703 | PRINT*,'Failed allocation of buffer dY'; STOP |
---|
704 | END IF |
---|
705 | ALLOCATE( chk_d2Y(NVAR,bufsize), STAT=i ) |
---|
706 | IF (i/=0) THEN |
---|
707 | PRINT*,'Failed allocation of buffer d2Y'; STOP |
---|
708 | END IF |
---|
709 | |
---|
710 | END SUBROUTINE rk_AllocateCBuffers |
---|
711 | |
---|
712 | |
---|
713 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
714 | SUBROUTINE rk_FreeCBuffers() |
---|
715 | !~~~> Dallocate buffer space for continuous adjoint |
---|
716 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
717 | INTEGER :: i |
---|
718 | print*,'cbuffers deallocate???' |
---|
719 | DEALLOCATE( chk_H, STAT=i ) |
---|
720 | IF (i/=0) THEN |
---|
721 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
722 | END IF |
---|
723 | DEALLOCATE( chk_T, STAT=i ) |
---|
724 | IF (i/=0) THEN |
---|
725 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
726 | END IF |
---|
727 | DEALLOCATE( chk_Y, STAT=i ) |
---|
728 | IF (i/=0) THEN |
---|
729 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
730 | END IF |
---|
731 | DEALLOCATE( chk_dY, STAT=i ) |
---|
732 | IF (i/=0) THEN |
---|
733 | PRINT*,'Failed deallocation of buffer dY'; STOP |
---|
734 | END IF |
---|
735 | DEALLOCATE( chk_d2Y, STAT=i ) |
---|
736 | IF (i/=0) THEN |
---|
737 | PRINT*,'Failed deallocation of buffer d2Y'; STOP |
---|
738 | END IF |
---|
739 | |
---|
740 | END SUBROUTINE rk_FreeCBuffers |
---|
741 | |
---|
742 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
743 | SUBROUTINE rk_DPush( T, H, Y, Zstage, NewIt, E1, E2 )!, Jcb ) |
---|
744 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
745 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
746 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
747 | KPP_REAL :: T, H, Y(NVAR), Zstage(NVAR*3) |
---|
748 | INTEGER :: NewIt |
---|
749 | #ifdef FULL_ALGEBRA |
---|
750 | KPP_REAL :: E1(NVAR,NVAR) |
---|
751 | COMPLEX(kind=dp) :: E2(NVAR,NVAR) |
---|
752 | INTEGER :: i, j |
---|
753 | #else |
---|
754 | KPP_REAL :: E1(LU_NONZERO) |
---|
755 | COMPLEX(kind=dp) :: E2(LU_NONZERO) |
---|
756 | #endif |
---|
757 | |
---|
758 | stack_ptr = stack_ptr + 1 |
---|
759 | IF ( stack_ptr > bufsize ) THEN |
---|
760 | PRINT*,'Push failed: buffer overflow' |
---|
761 | STOP |
---|
762 | END IF |
---|
763 | chk_H( stack_ptr ) = H |
---|
764 | chk_T( stack_ptr ) = T |
---|
765 | ! CALL WCOPY(NVAR,Y,1,chk_Y(1,stack_ptr),1) |
---|
766 | ! CALL WCOPY(NVAR*3,Zstage,1,chk_Z(1,stack_ptr),1) |
---|
767 | chk_Y(1:N,stack_ptr) = Y(1:N) |
---|
768 | chk_Z(1:3*N,stack_ptr) = Zstage(1:3*N) |
---|
769 | chk_NiT( stack_ptr ) = NewIt |
---|
770 | IF (SaveLU) THEN |
---|
771 | #ifdef FULL_ALGEBRA |
---|
772 | ! CALL WCOPY(NVAR*NVAR, E1,1,chk_E1(1,stack_ptr),1) |
---|
773 | ! CALL WCOPYCmplx(NVAR*NVAR, E2,1,chk_E2(1,stack_ptr),1) |
---|
774 | DO j=1,NVAR |
---|
775 | DO i=1,NVAR |
---|
776 | chk_E1(NVAR*(j-1)+i,stack_ptr) = E1(i,j) |
---|
777 | chk_E2(NVAR*(j-1)+i,stack_ptr) = E2(i,j) |
---|
778 | END DO |
---|
779 | END DO |
---|
780 | #else |
---|
781 | ! CALL WCOPY(LU_NONZERO, E1,1,chk_E1(1,stack_ptr),1) |
---|
782 | ! CALL WCOPYCmplx(LU_NONZERO, E2,1,chk_E2(1,stack_ptr),1) |
---|
783 | chk_E1(1:LU_NONZERO,stack_ptr) = E1(1:LU_NONZERO) |
---|
784 | chk_E2(1:LU_NONZERO,stack_ptr) = E2(1:LU_NONZERO) |
---|
785 | #endif |
---|
786 | END IF |
---|
787 | !CALL WCOPY(LU_NONZERO,Jcb,1,chk_J(1,stack_ptr),1) |
---|
788 | |
---|
789 | END SUBROUTINE rk_DPush |
---|
790 | |
---|
791 | |
---|
792 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
793 | SUBROUTINE rk_DPop( T, H, Y, Zstage, NewIt, E1, E2 ) !, Jcb ) |
---|
794 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
795 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
796 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
797 | |
---|
798 | KPP_REAL :: T, H, Y(NVAR), Zstage(NVAR*3) ! , Jcb(LU_NONZERO) |
---|
799 | INTEGER :: NewIt |
---|
800 | #ifdef FULL_ALGEBRA |
---|
801 | KPP_REAL :: E1(NVAR,NVAR) |
---|
802 | COMPLEX(kind=dp) :: E2(NVAR,NVAR) |
---|
803 | INTEGER :: i, j |
---|
804 | #else |
---|
805 | KPP_REAL :: E1(LU_NONZERO) |
---|
806 | COMPLEX(kind=dp) :: E2(LU_NONZERO) |
---|
807 | #endif |
---|
808 | |
---|
809 | IF ( stack_ptr <= 0 ) THEN |
---|
810 | PRINT*,'Pop failed: empty buffer' |
---|
811 | STOP |
---|
812 | END IF |
---|
813 | H = chk_H( stack_ptr ) |
---|
814 | T = chk_T( stack_ptr ) |
---|
815 | ! CALL WCOPY(NVAR,chk_Y(1,stack_ptr),1,Y,1) |
---|
816 | Y(1:NVAR) = chk_Y(1:NVAR,stack_ptr) |
---|
817 | ! CALL WCOPY(NVAR*3,chk_Z(1,stack_ptr),1,Zstage,1) |
---|
818 | Zstage(1:3*NVAR) = chk_Z(1:3*NVAR,stack_ptr) |
---|
819 | NewIt = chk_NiT( stack_ptr ) |
---|
820 | IF (SaveLU) THEN |
---|
821 | #ifdef FULL_ALGEBRA |
---|
822 | ! CALL WCOPY(NVAR*NVAR,chk_E1(1,stack_ptr),1, E1,1) |
---|
823 | ! CALL WCOPYCmplx(NVAR*NVAR,chk_E2(1,stack_ptr),1, E2,1) |
---|
824 | DO j=1,NVAR |
---|
825 | DO i=1,NVAR |
---|
826 | E1(i,j) = chk_E1(NVAR*(j-1)+i,stack_ptr) |
---|
827 | E2(i,j) = chk_E2(NVAR*(j-1)+i,stack_ptr) |
---|
828 | END DO |
---|
829 | END DO |
---|
830 | #else |
---|
831 | ! CALL WCOPY(LU_NONZERO,chk_E1(1,stack_ptr),1, E1,1) |
---|
832 | ! CALL WCOPYCmplx(LU_NONZERO,chk_E2(1,stack_ptr),1, E2,1) |
---|
833 | E1(1:LU_NONZERO) = chk_E1(1:LU_NONZERO,stack_ptr) |
---|
834 | E2(1:LU_NONZERO) = chk_E2(1:LU_NONZERO,stack_ptr) |
---|
835 | #endif |
---|
836 | END IF |
---|
837 | !CALL WCOPY(LU_NONZERO,chk_J(1,stack_ptr),1,Jcb,1) |
---|
838 | |
---|
839 | stack_ptr = stack_ptr - 1 |
---|
840 | |
---|
841 | END SUBROUTINE rk_DPop |
---|
842 | |
---|
843 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
844 | SUBROUTINE rk_CPush(T, H, Y, dY, d2Y ) |
---|
845 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
846 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
847 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
848 | |
---|
849 | KPP_REAL :: T, H, Y(NVAR), dY(NVAR), d2Y(NVAR) |
---|
850 | |
---|
851 | stack_ptr = stack_ptr + 1 |
---|
852 | IF ( stack_ptr > bufsize ) THEN |
---|
853 | PRINT*,'Push failed: buffer overflow' |
---|
854 | STOP |
---|
855 | END IF |
---|
856 | chk_H( stack_ptr ) = H |
---|
857 | chk_T( stack_ptr ) = T |
---|
858 | ! CALL WCOPY(NVAR,Y,1,chk_Y(1,stack_ptr),1) |
---|
859 | ! CALL WCOPY(NVAR,dY,1,chk_dY(1,stack_ptr),1) |
---|
860 | ! CALL WCOPY(NVAR,d2Y,1,chk_d2Y(1,stack_ptr),1) |
---|
861 | chk_Y(1:NVAR,stack_ptr) = Y(1:NVAR) |
---|
862 | chk_dY(1:NVAR,stack_ptr) = dY(1:NVAR) |
---|
863 | chk_d2Y(1:NVAR,stack_ptr)= d2Y(1:NVAR) |
---|
864 | |
---|
865 | END SUBROUTINE rk_CPush |
---|
866 | |
---|
867 | |
---|
868 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
869 | SUBROUTINE rk_CPop( T, H, Y, dY, d2Y ) |
---|
870 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
871 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
872 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
873 | |
---|
874 | KPP_REAL :: T, H, Y(NVAR), dY(NVAR), d2Y(NVAR) |
---|
875 | |
---|
876 | IF ( stack_ptr <= 0 ) THEN |
---|
877 | PRINT*,'Pop failed: empty buffer' |
---|
878 | STOP |
---|
879 | END IF |
---|
880 | H = chk_H( stack_ptr ) |
---|
881 | T = chk_T( stack_ptr ) |
---|
882 | ! CALL WCOPY(NVAR,chk_Y(1,stack_ptr),1,Y,1) |
---|
883 | ! CALL WCOPY(NVAR,chk_dY(1,stack_ptr),1,dY,1) |
---|
884 | ! CALL WCOPY(NVAR,chk_d2Y(1,stack_ptr),1,d2Y,1) |
---|
885 | Y(1:NVAR) = chk_Y(1:NVAR,stack_ptr) |
---|
886 | dY(1:NVAR) = chk_dY(1:NVAR,stack_ptr) |
---|
887 | d2Y(1:NVAR) = chk_d2Y(1:NVAR,stack_ptr) |
---|
888 | |
---|
889 | stack_ptr = stack_ptr - 1 |
---|
890 | |
---|
891 | END SUBROUTINE rk_CPop |
---|
892 | |
---|
893 | |
---|
894 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
895 | SUBROUTINE RK_FwdIntegrator( N,Tstart,Tend,Y,AdjointType,IERR ) |
---|
896 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
897 | |
---|
898 | IMPLICIT NONE |
---|
899 | !~~~> Arguments |
---|
900 | INTEGER, INTENT(IN) :: N |
---|
901 | KPP_REAL, INTENT(IN) :: Tend, Tstart |
---|
902 | KPP_REAL, INTENT(INOUT) :: Y(N) |
---|
903 | INTEGER, INTENT(OUT) :: IERR |
---|
904 | INTEGER, INTENT(IN) :: AdjointType |
---|
905 | |
---|
906 | !~~~> Local variables |
---|
907 | #ifdef FULL_ALGEBRA |
---|
908 | KPP_REAL :: FJAC(N,N), E1(N,N) |
---|
909 | COMPLEX(kind=dp) :: E2(N,N) |
---|
910 | #else |
---|
911 | KPP_REAL :: FJAC(LU_NONZERO), E1(LU_NONZERO) |
---|
912 | COMPLEX(kind=dp) :: E2(LU_NONZERO) |
---|
913 | #endif |
---|
914 | KPP_REAL, DIMENSION(N) :: Z1,Z2,Z3,Z4,SCAL,DZ1,DZ2,DZ3,DZ4,G,TMP,FCN0 |
---|
915 | KPP_REAL :: CONT(N,3), Tdirection, H, T, Hacc, Hnew, Hold, Fac, & |
---|
916 | FacGus, Theta, Err, ErrOld, NewtonRate, NewtonIncrement, & |
---|
917 | Hratio, Qnewton, NewtonPredictedErr,NewtonIncrementOld, ThetaSD |
---|
918 | INTEGER :: IP1(N),IP2(N),NewtonIter, ISING, Nconsecutive, NewIt |
---|
919 | LOGICAL :: Reject, FirstStep, SkipJac, NewtonDone, SkipLU |
---|
920 | |
---|
921 | KPP_REAL, DIMENSION(:), POINTER :: Zstage |
---|
922 | |
---|
923 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
924 | !~~~> Initial setting |
---|
925 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
926 | IF (AdjointType == KPP_ROOT_discrete) THEN ! Save stage solution |
---|
927 | ALLOCATE(Zstage(N*3), STAT=i) |
---|
928 | IF (i/=0) THEN |
---|
929 | PRINT*,'Allocation of Zstage failed' |
---|
930 | STOP |
---|
931 | END IF |
---|
932 | END IF |
---|
933 | T=Tstart |
---|
934 | |
---|
935 | Tdirection = SIGN(ONE,Tend-Tstart) |
---|
936 | H = MIN( MAX(ABS(Hmin),ABS(Hstart)) , Hmax ) |
---|
937 | IF (ABS(H) <= 10.d0*Roundoff) H = 1.0d-6 |
---|
938 | H = SIGN(H,Tdirection) |
---|
939 | Hold = H |
---|
940 | Reject = .FALSE. |
---|
941 | FirstStep = .TRUE. |
---|
942 | SkipJac = .FALSE. |
---|
943 | SkipLU = .FALSE. |
---|
944 | IF ((T+H*1.0001D0-Tend)*Tdirection >= ZERO) THEN |
---|
945 | H = Tend-T |
---|
946 | END IF |
---|
947 | Nconsecutive = 0 |
---|
948 | CALL RK_ErrorScale(N,ITOL,AbsTol,RelTol,Y,SCAL) |
---|
949 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
950 | !~~~> Time loop begins |
---|
951 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
952 | Tloop: DO WHILE ( (Tend-T)*Tdirection - Roundoff > ZERO ) |
---|
953 | |
---|
954 | IF ( .NOT.SkipLU ) THEN ! This time around skip the Jac update and LU |
---|
955 | !~~~> Compute the Jacobian matrix |
---|
956 | IF ( .NOT.SkipJac ) THEN |
---|
957 | CALL JAC_CHEM(T,Y,FJAC) |
---|
958 | ISTATUS(ijac) = ISTATUS(ijac) + 1 |
---|
959 | END IF |
---|
960 | !~~~> Compute the matrices E1 and E2 and their decompositions |
---|
961 | CALL RK_Decomp(N,H,FJAC,E1,IP1,E2,IP2,ISING) |
---|
962 | IF (ISING /= 0) THEN |
---|
963 | ISTATUS(isng) = ISTATUS(isng) + 1; Nconsecutive = Nconsecutive + 1 |
---|
964 | IF (Nconsecutive >= 5) THEN |
---|
965 | CALL RK_ErrorMsg(-12,T,H,IERR); RETURN |
---|
966 | END IF |
---|
967 | H=H*0.5d0; Reject=.TRUE.; SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
968 | CYCLE Tloop |
---|
969 | ELSE |
---|
970 | Nconsecutive = 0 |
---|
971 | END IF |
---|
972 | END IF ! SkipLU |
---|
973 | |
---|
974 | ISTATUS(istp) = ISTATUS(istp) + 1 |
---|
975 | IF (ISTATUS(istp) > Max_no_steps) THEN |
---|
976 | PRINT*,'Max number of time steps is ',Max_no_steps |
---|
977 | CALL RK_ErrorMsg(-9,T,H,IERR); RETURN |
---|
978 | END IF |
---|
979 | IF (0.1D0*ABS(H) <= ABS(T)*Roundoff) THEN |
---|
980 | CALL RK_ErrorMsg(-10,T,H,IERR); RETURN |
---|
981 | END IF |
---|
982 | |
---|
983 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
984 | !~~~> Loop for the simplified Newton iterations |
---|
985 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
986 | |
---|
987 | !~~~> Starting values for Newton iteration |
---|
988 | IF ( FirstStep .OR. (.NOT.StartNewton) ) THEN |
---|
989 | CALL Set2zero(N,Z1) |
---|
990 | CALL Set2zero(N,Z2) |
---|
991 | CALL Set2zero(N,Z3) |
---|
992 | ELSE |
---|
993 | ! Evaluate quadratic polynomial |
---|
994 | CALL RK_Interpolate('eval',N,H,Hold,Z1,Z2,Z3,CONT) |
---|
995 | END IF |
---|
996 | |
---|
997 | !~~~> Initializations for Newton iteration |
---|
998 | NewtonDone = .FALSE. |
---|
999 | Fac = 0.5d0 ! Step reduction if too many iterations |
---|
1000 | |
---|
1001 | NewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
1002 | |
---|
1003 | !~~~> Prepare the right-hand side |
---|
1004 | CALL RK_PrepareRHS(N,T,H,Y,Z1,Z2,Z3,DZ1,DZ2,DZ3) |
---|
1005 | |
---|
1006 | !~~~> Solve the linear systems |
---|
1007 | CALL RK_Solve( N,H,E1,IP1,E2,IP2,DZ1,DZ2,DZ3,ISING ) |
---|
1008 | |
---|
1009 | |
---|
1010 | NewtonIncrement = SQRT( ( RK_ErrorNorm(N,SCAL,DZ1)**2 + & |
---|
1011 | RK_ErrorNorm(N,SCAL,DZ2)**2 + & |
---|
1012 | RK_ErrorNorm(N,SCAL,DZ3)**2 )/3.0d0 ) |
---|
1013 | |
---|
1014 | IF ( NewtonIter == 1 ) THEN |
---|
1015 | Theta = ABS(ThetaMin) |
---|
1016 | NewtonRate = 2.0d0 |
---|
1017 | ELSE |
---|
1018 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
1019 | IF (Theta < 0.99d0) THEN |
---|
1020 | NewtonRate = Theta/(ONE-Theta) |
---|
1021 | ELSE ! Non-convergence of Newton: Theta too large |
---|
1022 | EXIT NewtonLoop |
---|
1023 | END IF |
---|
1024 | IF ( NewtonIter < NewtonMaxit ) THEN |
---|
1025 | ! Predict error at the end of Newton process |
---|
1026 | NewtonPredictedErr = NewtonIncrement & |
---|
1027 | *Theta**(NewtonMaxit-NewtonIter)/(ONE-Theta) |
---|
1028 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
1029 | ! Non-convergence of Newton: predicted error too large |
---|
1030 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
1031 | Fac=0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIter)) |
---|
1032 | EXIT NewtonLoop |
---|
1033 | END IF |
---|
1034 | END IF |
---|
1035 | END IF |
---|
1036 | |
---|
1037 | NewtonIncrementOld = MAX(NewtonIncrement,Roundoff) |
---|
1038 | ! Update solution |
---|
1039 | CALL WAXPY(N,-ONE,DZ1,1,Z1,1) ! Z1 <- Z1 - DZ1 |
---|
1040 | CALL WAXPY(N,-ONE,DZ2,1,Z2,1) ! Z2 <- Z2 - DZ2 |
---|
1041 | CALL WAXPY(N,-ONE,DZ3,1,Z3,1) ! Z3 <- Z3 - DZ3 |
---|
1042 | |
---|
1043 | ! Check error in Newton iterations |
---|
1044 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
1045 | IF (NewtonDone) THEN |
---|
1046 | NewIt = NewtonIter |
---|
1047 | EXIT NewtonLoop |
---|
1048 | END IF |
---|
1049 | IF (NewtonIter == NewtonMaxit) THEN |
---|
1050 | PRINT*, 'Slow or no convergence in Newton Iteration: Max no. of', & |
---|
1051 | 'Newton iterations reached' |
---|
1052 | END IF |
---|
1053 | |
---|
1054 | END DO NewtonLoop |
---|
1055 | |
---|
1056 | |
---|
1057 | IF (.NOT.NewtonDone) THEN |
---|
1058 | !CALL RK_ErrorMsg(-12,T,H,IERR); |
---|
1059 | H = Fac*H; Reject=.TRUE.; SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
1060 | ISTATUS(irej) = ISTATUS(irej) + 1 |
---|
1061 | CYCLE Tloop |
---|
1062 | END IF |
---|
1063 | |
---|
1064 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1065 | !~~~> SDIRK Stage |
---|
1066 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1067 | IF (SdirkError) THEN |
---|
1068 | |
---|
1069 | !~~~> Starting values for Newton iterations |
---|
1070 | Z4(1:N) = Z3(1:N) |
---|
1071 | |
---|
1072 | !~~~> Prepare the loop-independent part of the right-hand side |
---|
1073 | CALL FUN_CHEM(T,Y,DZ4) |
---|
1074 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
1075 | |
---|
1076 | ! G = H*rkBgam(0)*DZ4 + rkTheta(1)*Z1 + rkTheta(2)*Z2 + rkTheta(3)*Z3 |
---|
1077 | CALL Set2Zero(N, G) |
---|
1078 | CALL WAXPY(N,rkBgam(0)*H, DZ4,1,G,1) |
---|
1079 | CALL WAXPY(N,rkTheta(1),Z1,1,G,1) |
---|
1080 | CALL WAXPY(N,rkTheta(2),Z2,1,G,1) |
---|
1081 | CALL WAXPY(N,rkTheta(3),Z3,1,G,1) |
---|
1082 | |
---|
1083 | !~~~> Initializations for Newton iteration |
---|
1084 | NewtonDone = .FALSE. |
---|
1085 | Fac = 0.5d0 ! Step reduction factor if too many iterations |
---|
1086 | |
---|
1087 | SDNewtonLoop:DO NewtonIter = 1, NewtonMaxit |
---|
1088 | |
---|
1089 | !~~~> Prepare the loop-dependent part of the right-hand side |
---|
1090 | CALL WADD(N,Y,Z4,TMP) ! TMP <- Y + Z4 |
---|
1091 | CALL FUN_CHEM(T+H,TMP,DZ4) ! DZ4 <- Fun(Y+Z4) |
---|
1092 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
1093 | ! DZ4(1:N) = (G(1:N)-Z4(1:N))*(rkGamma/H) + DZ4(1:N) |
---|
1094 | CALL WAXPY (N, -ONE*rkGamma/H, Z4, 1, DZ4, 1) |
---|
1095 | CALL WAXPY (N, rkGamma/H, G,1, DZ4,1) |
---|
1096 | |
---|
1097 | !~~~> Solve the linear system |
---|
1098 | #ifdef FULL_ALGEBRA |
---|
1099 | CALL DGETRS( 'N', N, 1, E1, N, IP1, DZ4, N, ISING ) |
---|
1100 | #else |
---|
1101 | CALL KppSolve(E1, DZ4) |
---|
1102 | #endif |
---|
1103 | |
---|
1104 | !~~~> Check convergence of Newton iterations |
---|
1105 | NewtonIncrement = RK_ErrorNorm(N,SCAL,DZ4) |
---|
1106 | IF ( NewtonIter == 1 ) THEN |
---|
1107 | ThetaSD = ABS(ThetaMin) |
---|
1108 | NewtonRate = 2.0d0 |
---|
1109 | ELSE |
---|
1110 | ThetaSD = NewtonIncrement/NewtonIncrementOld |
---|
1111 | IF (ThetaSD < 0.99d0) THEN |
---|
1112 | NewtonRate = ThetaSD/(ONE-ThetaSD) |
---|
1113 | ! Predict error at the end of Newton process |
---|
1114 | NewtonPredictedErr = NewtonIncrement & |
---|
1115 | *ThetaSD**(NewtonMaxit-NewtonIter)/(ONE-ThetaSD) |
---|
1116 | IF (NewtonPredictedErr >= NewtonTol) THEN |
---|
1117 | ! Non-convergence of Newton: predicted error too large |
---|
1118 | !print*,'Error too large: ', NewtonPredictedErr |
---|
1119 | Qnewton = MIN(10.0d0,NewtonPredictedErr/NewtonTol) |
---|
1120 | Fac = 0.8d0*Qnewton**(-ONE/(1+NewtonMaxit-NewtonIter)) |
---|
1121 | EXIT SDNewtonLoop |
---|
1122 | END IF |
---|
1123 | ELSE ! Non-convergence of Newton: ThetaSD too large |
---|
1124 | !print*,'Theta too large: ',ThetaSD |
---|
1125 | EXIT SDNewtonLoop |
---|
1126 | END IF |
---|
1127 | END IF |
---|
1128 | NewtonIncrementOld = NewtonIncrement |
---|
1129 | ! Update solution: Z4 <-- Z4 + DZ4 |
---|
1130 | CALL WAXPY(N,ONE,DZ4,1,Z4,1) |
---|
1131 | |
---|
1132 | ! Check error in Newton iterations |
---|
1133 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
1134 | IF (NewtonDone) EXIT SDNewtonLoop |
---|
1135 | |
---|
1136 | END DO SDNewtonLoop |
---|
1137 | |
---|
1138 | IF (.NOT.NewtonDone) THEN |
---|
1139 | H = Fac*H; Reject=.TRUE.; SkipJac = .TRUE.; SkipLU = .FALSE. |
---|
1140 | CYCLE Tloop |
---|
1141 | END IF |
---|
1142 | END IF |
---|
1143 | !~~~> End of implified SDIRK Newton iterations |
---|
1144 | |
---|
1145 | |
---|
1146 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1147 | !~~~> Error estimation |
---|
1148 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1149 | IF (SdirkError) THEN |
---|
1150 | ! DZ4(1:N) = rkD(1)*Z1 + rkD(2)*Z2 + rkD(3)*Z3 - Z4 |
---|
1151 | CALL Set2Zero(N, DZ4) |
---|
1152 | IF (rkD(1) /= ZERO) CALL WAXPY(N, rkD(1), Z1, 1, DZ4, 1) |
---|
1153 | IF (rkD(2) /= ZERO) CALL WAXPY(N, rkD(2), Z2, 1, DZ4, 1) |
---|
1154 | IF (rkD(3) /= ZERO) CALL WAXPY(N, rkD(3), Z3, 1, DZ4, 1) |
---|
1155 | CALL WAXPY(N, -ONE, Z4, 1, DZ4, 1) |
---|
1156 | Err = RK_ErrorNorm(N,SCAL,DZ4) |
---|
1157 | ELSE |
---|
1158 | CALL RK_ErrorEstimate(N,H,Y,T, & |
---|
1159 | E1,IP1,Z1,Z2,Z3,SCAL,Err,FirstStep,Reject) |
---|
1160 | END IF |
---|
1161 | !~~~> Computation of new step size Hnew |
---|
1162 | Fac = Err**(-ONE/rkELO)* & |
---|
1163 | MIN(FacSafe,(ONE+2*NewtonMaxit)/(NewtonIter+2*NewtonMaxit)) |
---|
1164 | Fac = MIN(FacMax,MAX(FacMin,Fac)) |
---|
1165 | Hnew = Fac*H |
---|
1166 | |
---|
1167 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1168 | !~~~> Accept/reject step |
---|
1169 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1170 | accept:IF (Err < ONE) THEN !~~~> STEP IS ACCEPTED |
---|
1171 | IF (AdjointType == KPP_ROOT_discrete) THEN ! Save stage solution |
---|
1172 | ! CALL WCOPY(N,Z1,1,Zstage(1),1) |
---|
1173 | ! CALL WCOPY(N,Z2,1,Zstage(N+1),1) |
---|
1174 | ! CALL WCOPY(N,Z3,1,Zstage(2*N+1),1) |
---|
1175 | Zstage(1:N) = Z1(1:N) |
---|
1176 | Zstage(N+1:2*N) = Z2(1:N) |
---|
1177 | Zstage(2*N+1:3*N) = Z3(1:N) |
---|
1178 | ! Push old Y - Y at the beginning of the stage |
---|
1179 | CALL rk_DPush(T, H, Y, Zstage, NewIt, E1, E2) |
---|
1180 | END IF |
---|
1181 | |
---|
1182 | FirstStep=.FALSE. |
---|
1183 | ISTATUS(iacc) = ISTATUS(iacc) + 1 |
---|
1184 | IF (Gustafsson) THEN |
---|
1185 | !~~~> Predictive controller of Gustafsson |
---|
1186 | IF (ISTATUS(iacc) > 1) THEN |
---|
1187 | FacGus=FacSafe*(H/Hacc)*(Err**2/ErrOld)**(-0.25d0) |
---|
1188 | FacGus=MIN(FacMax,MAX(FacMin,FacGus)) |
---|
1189 | Fac=MIN(Fac,FacGus) |
---|
1190 | Hnew = Fac*H |
---|
1191 | END IF |
---|
1192 | Hacc=H |
---|
1193 | ErrOld=MAX(1.0d-2,Err) |
---|
1194 | END IF |
---|
1195 | Hold = H |
---|
1196 | T = T+H |
---|
1197 | ! Update solution: Y <- Y + sum (d_i Z_i) |
---|
1198 | IF (rkD(1) /= ZERO) CALL WAXPY(N,rkD(1),Z1,1,Y,1) |
---|
1199 | IF (rkD(2) /= ZERO) CALL WAXPY(N,rkD(2),Z2,1,Y,1) |
---|
1200 | IF (rkD(3) /= ZERO) CALL WAXPY(N,rkD(3),Z3,1,Y,1) |
---|
1201 | ! Construct the solution quadratic interpolant Q(c_i) = Z_i, i=1:3 |
---|
1202 | IF (StartNewton) CALL RK_Interpolate('make',N,H,Hold,Z1,Z2,Z3,CONT) |
---|
1203 | CALL RK_ErrorScale(N,ITOL,AbsTol,RelTol,Y,SCAL) |
---|
1204 | RSTATUS(itexit) = T |
---|
1205 | RSTATUS(ihnew) = Hnew |
---|
1206 | RSTATUS(ihacc) = H |
---|
1207 | Hnew = Tdirection*MIN( MAX(ABS(Hnew),Hmin) , Hmax ) |
---|
1208 | IF (Reject) Hnew = Tdirection*MIN(ABS(Hnew),ABS(H)) |
---|
1209 | Reject = .FALSE. |
---|
1210 | IF ((T+Hnew/Qmin-Tend)*Tdirection >= ZERO) THEN |
---|
1211 | H = Tend-T |
---|
1212 | ELSE |
---|
1213 | Hratio=Hnew/H |
---|
1214 | ! Reuse the LU decomposition |
---|
1215 | SkipLU = (Theta<=ThetaMin) .AND. (Hratio>=Qmin) .AND. (Hratio<=Qmax) |
---|
1216 | SkipLU = .false. |
---|
1217 | IF (.NOT.SkipLU) H=Hnew |
---|
1218 | END IF |
---|
1219 | ! If convergence is fast enough, do not update Jacobian |
---|
1220 | ! SkipJac = (Theta <= ThetaMin) |
---|
1221 | SkipJac = .FALSE. |
---|
1222 | |
---|
1223 | ELSE accept !~~~> Step is rejected |
---|
1224 | IF (FirstStep .OR. Reject) THEN |
---|
1225 | H = FacRej*H |
---|
1226 | ELSE |
---|
1227 | H = Hnew |
---|
1228 | END IF |
---|
1229 | Reject = .TRUE. |
---|
1230 | SkipJac = .TRUE. |
---|
1231 | SkipLU = .FALSE. |
---|
1232 | IF (ISTATUS(iacc) >= 1) ISTATUS(irej) = ISTATUS(irej) + 1 |
---|
1233 | END IF accept |
---|
1234 | |
---|
1235 | END DO Tloop |
---|
1236 | |
---|
1237 | !~~~> Save last state: only needed for continuous adjoint |
---|
1238 | IF ( (AdjointType == KPP_ROOT_continuous) .OR. & |
---|
1239 | (AdjointType == KPP_ROOT_simple_continuous) ) THEN |
---|
1240 | CALL Fun_Chem(T,Y,Fcn0) |
---|
1241 | CALL rk_CPush( T, H, Y, Fcn0, DZ3) |
---|
1242 | !~~~> Deallocate stage buffer: only needed for discrete adjoint |
---|
1243 | ELSEIF (AdjointType == KPP_ROOT_discrete) THEN |
---|
1244 | DEALLOCATE(Zstage, STAT=i) |
---|
1245 | IF (i/=0) THEN |
---|
1246 | PRINT*,'Deallocation of Zstage failed' |
---|
1247 | STOP |
---|
1248 | END IF |
---|
1249 | END IF |
---|
1250 | |
---|
1251 | ! Successful exit |
---|
1252 | IERR = 1 |
---|
1253 | |
---|
1254 | END SUBROUTINE RK_FwdIntegrator |
---|
1255 | |
---|
1256 | |
---|
1257 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1258 | SUBROUTINE rk_DadjInt( NADJ,Lambda,Tstart,Tend,T,IERR ) |
---|
1259 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1260 | |
---|
1261 | IMPLICIT NONE |
---|
1262 | !~~~> Arguments |
---|
1263 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
1264 | INTEGER, INTENT(IN) :: NADJ |
---|
1265 | !~~~> First order adjoint |
---|
1266 | KPP_REAL, INTENT(INOUT) :: Lambda(N,NADJ) |
---|
1267 | KPP_REAL, INTENT(IN) :: Tstart, Tend |
---|
1268 | KPP_REAL, INTENT(INOUT) :: T |
---|
1269 | INTEGER, INTENT(OUT) :: IERR |
---|
1270 | |
---|
1271 | !~~~> Local variables |
---|
1272 | #ifdef FULL_ALGEBRA |
---|
1273 | KPP_REAL :: Jac0(N,N), Jac1(N,N),Jac2(N,N),Jac3(N,N), E1(N,N) |
---|
1274 | COMPLEX(kind=dp) :: E2(N,N) |
---|
1275 | KPP_REAL :: Jbig(3*N,3*N), X(3*N) |
---|
1276 | INTEGER :: IPbig(3*N), ISING |
---|
1277 | #else |
---|
1278 | KPP_REAL, DIMENSION(LU_NONZERO) :: Jac0, Jac1, Jac2, Jac3, E1 |
---|
1279 | COMPLEX(kind=dp), DIMENSION(LU_NONZERO) :: E2 |
---|
1280 | ! Next two lines for sparse big algebra: |
---|
1281 | ! KPP_REAL :: Jbig(3,3,LU_NONZERO), X(3,N) |
---|
1282 | ! INTEGER :: IPbig(3,N) |
---|
1283 | KPP_REAL :: Jbig(3*N,3*N), X(3*N) |
---|
1284 | INTEGER :: IPbig(3*N) |
---|
1285 | #endif |
---|
1286 | KPP_REAL, DIMENSION(N,NADJ) :: U1,U2,U3 |
---|
1287 | KPP_REAL, DIMENSION(N) :: SCAL,DU1,DU2,DU3 |
---|
1288 | KPP_REAL :: Y(N), Zstage(3*N) |
---|
1289 | KPP_REAL :: H, NewtonRate, NewtonIncrement, NewtonIncrementOld |
---|
1290 | INTEGER :: IP1(N),IP2(N),NewtonIter, ISING, iadj, NewIt |
---|
1291 | LOGICAL :: Reject, NewtonDone, NewtonConverge |
---|
1292 | KPP_REAL :: T1, Theta |
---|
1293 | KPP_REAL, DIMENSION(N) :: TMP, G1, G2, G3 |
---|
1294 | INTEGER :: i, j |
---|
1295 | |
---|
1296 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1297 | !~~~> Initial setting |
---|
1298 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1299 | T1 = Tend |
---|
1300 | ! Tdirection = SIGN(ONE,Tend-Tstart) |
---|
1301 | NewtonConverge = .TRUE. |
---|
1302 | Reject = .FALSE. |
---|
1303 | |
---|
1304 | !~~~> Time loop begins below |
---|
1305 | TimeLoop:DO WHILE ( stack_ptr > 0 ) |
---|
1306 | |
---|
1307 | IF (.not.Reject) THEN |
---|
1308 | |
---|
1309 | !~~~> Recover checkpoints for stage values and vectors |
---|
1310 | CALL rk_DPop(T, H, Y, Zstage, NewIt, E1, E2) |
---|
1311 | |
---|
1312 | !~~~> Compute LU decomposition |
---|
1313 | IF (.NOT.SaveLU) THEN |
---|
1314 | !~~~> Compute the Jacobian matrix |
---|
1315 | CALL JAC_CHEM(T,Y,Jac0) |
---|
1316 | ISTATUS(ijac) = ISTATUS(ijac) + 1 |
---|
1317 | !~~~> Compute the matrices E1 and E2 and their decompositions |
---|
1318 | CALL RK_Decomp(N,H,Jac0,E1,IP1,E2,IP2,ISING) |
---|
1319 | END IF |
---|
1320 | |
---|
1321 | !~~~> Jacobian values at stage vectors |
---|
1322 | CALL WADD(N,Y,Zstage(1),TMP) ! TMP <- Y + Z1 |
---|
1323 | CALL JAC_CHEM(T+rkC(1)*H,TMP,Jac1) ! Jac1 <- Jac(Y+Z1) |
---|
1324 | CALL WADD(N,Y,Zstage(1+N),TMP) ! TMP <- Y + Z2 |
---|
1325 | CALL JAC_CHEM(T+rkC(2)*H,TMP,Jac2) ! Jac2 <- Jac(Y+Z2) |
---|
1326 | CALL WADD(N,Y,Zstage(1+2*N),TMP) ! TMP <- Y + Z3 |
---|
1327 | CALL JAC_CHEM(T+rkC(3)*H,TMP,Jac3) ! Jac3 <- Jac(Y+Z3) |
---|
1328 | |
---|
1329 | END IF ! .not.Reject |
---|
1330 | |
---|
1331 | 111 CONTINUE |
---|
1332 | |
---|
1333 | IF ( (AdjointSolve == Solve_adaptive .and. .not.NewtonConverge) & |
---|
1334 | .or. (AdjointSolve == Solve_direct) ) THEN |
---|
1335 | #ifdef FULL_ALGEBRA |
---|
1336 | DO j=1,N |
---|
1337 | DO i=1,N |
---|
1338 | Jbig(i,j) = -H*rkA(1,1)*Jac1(i,j) |
---|
1339 | Jbig(N+i,j) = -H*rkA(2,1)*Jac1(i,j) |
---|
1340 | Jbig(2*N+i,j) = -H*rkA(3,1)*Jac1(i,j) |
---|
1341 | Jbig(i,N+j) = -H*rkA(1,2)*Jac2(i,j) |
---|
1342 | Jbig(N+i,N+j) = -H*rkA(2,2)*Jac2(i,j) |
---|
1343 | Jbig(2*N+i,N+j) = -H*rkA(3,2)*Jac2(i,j) |
---|
1344 | Jbig(i,2*N+j) = -H*rkA(1,3)*Jac3(i,j) |
---|
1345 | Jbig(N+i,2*N+j) = -H*rkA(2,3)*Jac3(i,j) |
---|
1346 | Jbig(2*N+i,2*N+j) = -H*rkA(3,3)*Jac3(i,j) |
---|
1347 | END DO |
---|
1348 | END DO |
---|
1349 | DO i=1,3*N |
---|
1350 | Jbig(i,i) = Jbig(i,i) + ONE |
---|
1351 | END DO |
---|
1352 | CALL DGETRF(3*N,3*N,Jbig,3*N,IPbig,ISING) |
---|
1353 | ! CALL WGEFA(3*N,Jbig,IPbig,ISING) |
---|
1354 | IF (ISING /= 0) THEN |
---|
1355 | PRINT*,'Big guy is singular'; STOP |
---|
1356 | END IF |
---|
1357 | #else |
---|
1358 | ! Commented lines for sparse big algebra: |
---|
1359 | ! !~~~> Construct the big Jacobian |
---|
1360 | ! DO j=1,LU_NONZERO |
---|
1361 | ! DO i=1,3 |
---|
1362 | ! Jbig(i,1,j) = -H*rkA(i,1)*Jac1(j) |
---|
1363 | ! Jbig(i,2,j) = -H*rkA(i,2)*Jac2(j) |
---|
1364 | ! Jbig(i,3,j) = -H*rkA(i,3)*Jac3(j) |
---|
1365 | ! END DO |
---|
1366 | ! END DO |
---|
1367 | ! DO j=1,NVAR |
---|
1368 | ! DO i=1,3 |
---|
1369 | ! Jbig(i,i,LU_DIAG(j)) = ONE + Jbig(i,i,LU_DIAG(j)) |
---|
1370 | ! END DO |
---|
1371 | ! END DO |
---|
1372 | ! !~~~> Solve the big system |
---|
1373 | ! CALL KppDecompBig( Jbig, IPbig, ISING ) |
---|
1374 | ! Use full big algebra: |
---|
1375 | Jbig(1:3*N,1:3*N) = 0.0d0 |
---|
1376 | DO i=1,LU_NONZERO |
---|
1377 | Jbig(LU_irow(i),LU_icol(i)) = -H*rkA(1,1)*Jac1(i) |
---|
1378 | Jbig(LU_irow(i),N+LU_icol(i)) = -H*rkA(1,2)*Jac2(i) |
---|
1379 | Jbig(LU_irow(i),2*N+LU_icol(i)) = -H*rkA(1,3)*Jac3(i) |
---|
1380 | Jbig(N+LU_irow(i),LU_icol(i)) = -H*rkA(2,1)*Jac1(i) |
---|
1381 | Jbig(N+LU_irow(i),N+LU_icol(i)) = -H*rkA(2,2)*Jac2(i) |
---|
1382 | Jbig(N+LU_irow(i),2*N+LU_icol(i)) = -H*rkA(2,3)*Jac3(i) |
---|
1383 | Jbig(2*N+LU_irow(i),LU_icol(i)) = -H*rkA(3,1)*Jac1(i) |
---|
1384 | Jbig(2*N+LU_irow(i),N+LU_icol(i)) = -H*rkA(3,2)*Jac2(i) |
---|
1385 | Jbig(2*N+LU_irow(i),2*N+LU_icol(i)) = -H*rkA(3,3)*Jac3(i) |
---|
1386 | END DO |
---|
1387 | DO i=1, 3*N |
---|
1388 | Jbig(i,i) = ONE + Jbig(i,i) |
---|
1389 | END DO |
---|
1390 | ! CALL DGETRF(3*N,3*N,Jbig,3*N,IPbig,ISING) |
---|
1391 | CALL WGEFA(3*N,Jbig,IPbig,ISING) |
---|
1392 | IF (ISING /= 0) THEN |
---|
1393 | PRINT*,'Big guy is singular'; STOP |
---|
1394 | END IF |
---|
1395 | #endif |
---|
1396 | END IF |
---|
1397 | |
---|
1398 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1399 | !~~~> Loop for the simplified Newton iterations |
---|
1400 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1401 | Adj:DO iadj = 1, NADJ |
---|
1402 | !~~~> Starting values for Newton iteration |
---|
1403 | ! CALL WCOPY(N,Lambda(1,iadj),1,U1(1,iadj),1) |
---|
1404 | ! CALL WCOPY(N,Lambda(1,iadj),1,U2(1,iadj),1) |
---|
1405 | ! CALL WCOPY(N,Lambda(1,iadj),1,U3(1,iadj),1) |
---|
1406 | CALL Set2Zero(N,U1(1,iadj)) |
---|
1407 | CALL Set2Zero(N,U2(1,iadj)) |
---|
1408 | CALL Set2Zero(N,U3(1,iadj)) |
---|
1409 | |
---|
1410 | !~~~> Initializations for Newton iteration |
---|
1411 | NewtonDone = .FALSE. |
---|
1412 | !~~~> Right Hand Side - part G for all Newton iterations |
---|
1413 | CALL RK_PrepareRHS_G(N,H,Jac1,Jac2,Jac3,Lambda(1,iadj), & |
---|
1414 | G1, G2, G3) |
---|
1415 | |
---|
1416 | IF ( (AdjointSolve == Solve_adaptive .and. NewtonConverge) & |
---|
1417 | .or. (AdjointSolve == Solve_fixed) ) THEN |
---|
1418 | |
---|
1419 | NewtonLoopAdj:DO NewtonIter = 1, NewtonMaxit |
---|
1420 | |
---|
1421 | !~~~> Prepare the right-hand side |
---|
1422 | CALL RK_PrepareRHS_Adj(N,H,Jac1,Jac2,Jac3,Lambda(1,iadj), & |
---|
1423 | U1(1,iadj),U2(1,iadj),U3(1,iadj), & |
---|
1424 | G1, G2, G3, DU1,DU2,DU3) |
---|
1425 | |
---|
1426 | !~~~> Solve the linear systems |
---|
1427 | CALL RK_SolveTR( N,H,E1,IP1,E2,IP2,DU1,DU2,DU3,ISING ) |
---|
1428 | |
---|
1429 | !~~~> The following code performs an adaptive number of Newton |
---|
1430 | ! iterations for solving adjoint system |
---|
1431 | IF (AdjointSolve == Solve_adaptive) THEN |
---|
1432 | |
---|
1433 | CALL RK_ErrorScale(N,ITOL, & |
---|
1434 | AbsTol_adj(1:N,iadj),RelTol_adj(1:N,iadj), & |
---|
1435 | Lambda(1:N,iadj),SCAL) |
---|
1436 | |
---|
1437 | ! SCAL(1:N) = 1.0d0 |
---|
1438 | NewtonIncrement = SQRT( ( RK_ErrorNorm(N,SCAL,DU1)**2 + & |
---|
1439 | RK_ErrorNorm(N,SCAL,DU2)**2 + & |
---|
1440 | RK_ErrorNorm(N,SCAL,DU3)**2 )/3.0d0 ) |
---|
1441 | |
---|
1442 | |
---|
1443 | IF ( NewtonIter == 1 ) THEN |
---|
1444 | Theta = ABS(ThetaMin) |
---|
1445 | NewtonRate = 2.0d0 |
---|
1446 | ELSE |
---|
1447 | Theta = NewtonIncrement/NewtonIncrementOld |
---|
1448 | IF (Theta < 0.99d0) THEN |
---|
1449 | NewtonRate = Theta/(ONE-Theta) |
---|
1450 | ELSE ! Non-convergence of Newton: Theta too large |
---|
1451 | Reject = .TRUE. |
---|
1452 | NewtonDone = .FALSE. |
---|
1453 | EXIT NewtonLoopAdj |
---|
1454 | END IF |
---|
1455 | |
---|
1456 | END IF |
---|
1457 | |
---|
1458 | NewtonIncrementOld = MAX(NewtonIncrement,Roundoff) |
---|
1459 | |
---|
1460 | END IF ! (AdjointSolve == Solve_adaptive) |
---|
1461 | |
---|
1462 | ! Update solution |
---|
1463 | CALL WAXPY(N,-ONE,DU1,1,U1(1,iadj),1) ! U1 <- U1 - DU1 |
---|
1464 | CALL WAXPY(N,-ONE,DU2,1,U2(1,iadj),1) ! U2 <- U2 - DU2 |
---|
1465 | CALL WAXPY(N,-ONE,DU3,1,U3(1,iadj),1) ! U3 <- U3 - DU3 |
---|
1466 | |
---|
1467 | IF (AdjointSolve == Solve_adaptive) THEN |
---|
1468 | ! When performing an adaptive number of iterations |
---|
1469 | ! check the error in Newton iterations |
---|
1470 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol) |
---|
1471 | IF ((NewtonDone).and.(NewtonIter>NewIt+1)) EXIT NewtonLoopAdj |
---|
1472 | ELSE IF (AdjointSolve == Solve_fixed) THEN |
---|
1473 | IF (NewtonIter>MAX(NewIt+1,6)) EXIT NewtonLoopAdj |
---|
1474 | END IF |
---|
1475 | |
---|
1476 | END DO NewtonLoopAdj |
---|
1477 | |
---|
1478 | IF ((AdjointSolve==Solve_adaptive).AND.(.NOT.NewtonDone)) THEN |
---|
1479 | ! print*,'Newton iterations do not converge, switching to full system.' |
---|
1480 | NewtonConverge = .FALSE. |
---|
1481 | Reject = .TRUE. |
---|
1482 | GOTO 111 |
---|
1483 | END IF |
---|
1484 | |
---|
1485 | ! Update adjoint solution: Y_adj <- Y_adj + sum (U_i) |
---|
1486 | CALL WAXPY(N,ONE,U1(1,iadj),1,Lambda(1,iadj),1) |
---|
1487 | CALL WAXPY(N,ONE,U2(1,iadj),1,Lambda(1,iadj),1) |
---|
1488 | CALL WAXPY(N,ONE,U3(1,iadj),1,Lambda(1,iadj),1) |
---|
1489 | |
---|
1490 | ELSE ! NewtonConverge = .false. |
---|
1491 | |
---|
1492 | #ifdef FULL_ALGEBRA |
---|
1493 | X(1:N) = -G1(1:N) |
---|
1494 | X(N+1:2*N) = -G2(1:N) |
---|
1495 | X(2*N+1:3*N) = -G3(1:N) |
---|
1496 | CALL DGETRS('T',3*N,1,Jbig,3*N,IPbig,X,3*N,ISING) |
---|
1497 | ! CALL WGESL('T',3*N,Jbig,IPbig,X) |
---|
1498 | Lambda(1:N,iadj) = Lambda(1:N,iadj)+X(1:N)+X(N+1:2*N)+X(2*N+1:3*N) |
---|
1499 | #else |
---|
1500 | ! Commented lines for sparse big algebra: |
---|
1501 | ! X(1,1:N) = -G1(1:N) |
---|
1502 | ! X(2,1:N) = -G2(1:N) |
---|
1503 | ! X(3,1:N) = -G3(1:N) |
---|
1504 | ! CALL KppSolveBigTR( Jbig, IPbig, X ) |
---|
1505 | ! Lambda(1:N,iadj) = Lambda(1:N,iadj)+X(1,1:N)+X(2,1:N)+X(3,1:N) |
---|
1506 | ! Use fill big algebra: |
---|
1507 | X(1:N) = -G1(1:N) |
---|
1508 | X(N+1:2*N) = -G2(1:N) |
---|
1509 | X(2*N+1:3*N) = -G3(1:N) |
---|
1510 | ! CALL DGETRS('T',3*N,1,Jbig,3*N,IPbig,X,3*N,ISING) |
---|
1511 | CALL WGESL('T',3*N,Jbig,IPbig,X) |
---|
1512 | Lambda(1:N,iadj) = Lambda(1:N,iadj)+X(1:N)+X(N+1:2*N)+X(2*N+1:3*N) |
---|
1513 | #endif |
---|
1514 | IF ((AdjointSolve==Solve_adaptive).AND.(iadj>=NADJ)) THEN |
---|
1515 | NewtonConverge = .TRUE. |
---|
1516 | Reject = .FALSE. |
---|
1517 | END IF |
---|
1518 | |
---|
1519 | END IF ! NewtonConverge |
---|
1520 | |
---|
1521 | END DO Adj |
---|
1522 | |
---|
1523 | T1 = T1-H |
---|
1524 | |
---|
1525 | END DO TimeLoop |
---|
1526 | |
---|
1527 | ! Successful exit |
---|
1528 | IERR = 1 |
---|
1529 | |
---|
1530 | END SUBROUTINE RK_DadjInt |
---|
1531 | |
---|
1532 | |
---|
1533 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1534 | SUBROUTINE rk_CadjInt ( & |
---|
1535 | NADJ, Y, & |
---|
1536 | Tstart, Tend, T, IERR) |
---|
1537 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1538 | IMPLICIT NONE |
---|
1539 | !~~~> Arguments |
---|
1540 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
1541 | INTEGER, INTENT(IN) :: NADJ |
---|
1542 | !~~~> First order adjoint |
---|
1543 | KPP_REAL, INTENT(INOUT) :: Y(N,NADJ) |
---|
1544 | KPP_REAL, INTENT(IN) :: Tstart, Tend |
---|
1545 | KPP_REAL, INTENT(INOUT) :: T |
---|
1546 | INTEGER, INTENT(OUT) :: IERR |
---|
1547 | |
---|
1548 | END SUBROUTINE rk_CadjInt |
---|
1549 | |
---|
1550 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1551 | SUBROUTINE rk_SimpleCadjInt ( & |
---|
1552 | NADJ, Y, & |
---|
1553 | Tstart, Tend, T, & |
---|
1554 | IERR ) |
---|
1555 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1556 | IMPLICIT NONE |
---|
1557 | !~~~> Arguments |
---|
1558 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
1559 | INTEGER, INTENT(IN) :: NADJ |
---|
1560 | !~~~> First order adjoint |
---|
1561 | KPP_REAL, INTENT(INOUT) :: Y(N,NADJ) |
---|
1562 | KPP_REAL, INTENT(IN) :: Tstart, Tend |
---|
1563 | KPP_REAL, INTENT(INOUT) :: T |
---|
1564 | INTEGER, INTENT(OUT) :: IERR |
---|
1565 | |
---|
1566 | END SUBROUTINE rk_SimpleCadjInt |
---|
1567 | |
---|
1568 | |
---|
1569 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1570 | SUBROUTINE RK_ErrorMsg(Code,T,H,IERR) |
---|
1571 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1572 | ! Handles all error messages |
---|
1573 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1574 | |
---|
1575 | IMPLICIT NONE |
---|
1576 | KPP_REAL, INTENT(IN) :: T, H |
---|
1577 | INTEGER, INTENT(IN) :: Code |
---|
1578 | INTEGER, INTENT(OUT) :: IERR |
---|
1579 | |
---|
1580 | IERR = Code |
---|
1581 | PRINT * , & |
---|
1582 | 'Forced exit from RungeKutta due to the following error:' |
---|
1583 | |
---|
1584 | |
---|
1585 | SELECT CASE (Code) |
---|
1586 | CASE (-1) |
---|
1587 | PRINT * , '--> Improper value for maximal no of steps' |
---|
1588 | CASE (-2) |
---|
1589 | PRINT * , '--> Improper value for maximal no of Newton iterations' |
---|
1590 | CASE (-3) |
---|
1591 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
1592 | CASE (-4) |
---|
1593 | PRINT * , '--> Improper values for FacMin/FacMax/FacSafe/FacRej' |
---|
1594 | CASE (-5) |
---|
1595 | PRINT * , '--> Improper value for ThetaMin' |
---|
1596 | CASE (-6) |
---|
1597 | PRINT * , '--> Newton stopping tolerance too small' |
---|
1598 | CASE (-7) |
---|
1599 | PRINT * , '--> Improper values for Qmin, Qmax' |
---|
1600 | CASE (-8) |
---|
1601 | PRINT * , '--> Tolerances are too small' |
---|
1602 | CASE (-9) |
---|
1603 | PRINT * , '--> No of steps exceeds maximum bound' |
---|
1604 | CASE (-10) |
---|
1605 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
1606 | ' or H < Roundoff' |
---|
1607 | CASE (-11) |
---|
1608 | PRINT * , '--> Matrix is repeatedly singular' |
---|
1609 | CASE (-12) |
---|
1610 | PRINT * , '--> Non-convergence of Newton iterations' |
---|
1611 | CASE (-13) |
---|
1612 | PRINT * , '--> Requested RK method not implemented' |
---|
1613 | CASE DEFAULT |
---|
1614 | PRINT *, 'Unknown Error code: ', Code |
---|
1615 | END SELECT |
---|
1616 | |
---|
1617 | WRITE(6,FMT="(5X,'T=',E12.5,' H=',E12.5)") T, H |
---|
1618 | |
---|
1619 | END SUBROUTINE RK_ErrorMsg |
---|
1620 | |
---|
1621 | |
---|
1622 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1623 | SUBROUTINE RK_ErrorScale(N,ITOL,AbsTol,RelTol,Y,SCAL) |
---|
1624 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1625 | ! Handles all error messages |
---|
1626 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1627 | IMPLICIT NONE |
---|
1628 | INTEGER, INTENT(IN) :: N, ITOL |
---|
1629 | KPP_REAL, INTENT(IN) :: AbsTol(*), RelTol(*), Y(N) |
---|
1630 | KPP_REAL, INTENT(OUT) :: SCAL(N) |
---|
1631 | INTEGER :: i |
---|
1632 | |
---|
1633 | IF (ITOL==0) THEN |
---|
1634 | DO i=1,N |
---|
1635 | SCAL(i)= ONE/(AbsTol(1)+RelTol(1)*ABS(Y(i))) |
---|
1636 | END DO |
---|
1637 | ELSE |
---|
1638 | DO i=1,N |
---|
1639 | SCAL(i)=ONE/(AbsTol(i)+RelTol(i)*ABS(Y(i))) |
---|
1640 | END DO |
---|
1641 | END IF |
---|
1642 | |
---|
1643 | END SUBROUTINE RK_ErrorScale |
---|
1644 | |
---|
1645 | |
---|
1646 | !!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1647 | ! SUBROUTINE RK_Transform(N,Tr,Z1,Z2,Z3,W1,W2,W3) |
---|
1648 | !!~~~> W <-- Tr x Z |
---|
1649 | !!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1650 | ! IMPLICIT NONE |
---|
1651 | ! INTEGER :: N, i |
---|
1652 | ! KPP_REAL :: Tr(3,3),Z1(N),Z2(N),Z3(N),W1(N),W2(N),W3(N) |
---|
1653 | ! KPP_REAL :: x1, x2, x3 |
---|
1654 | ! DO i=1,N |
---|
1655 | ! x1 = Z1(i); x2 = Z2(i); x3 = Z3(i) |
---|
1656 | ! W1(i) = Tr(1,1)*x1 + Tr(1,2)*x2 + Tr(1,3)*x3 |
---|
1657 | ! W2(i) = Tr(2,1)*x1 + Tr(2,2)*x2 + Tr(2,3)*x3 |
---|
1658 | ! W3(i) = Tr(3,1)*x1 + Tr(3,2)*x2 + Tr(3,3)*x3 |
---|
1659 | ! END DO |
---|
1660 | ! END SUBROUTINE RK_Transform |
---|
1661 | |
---|
1662 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1663 | SUBROUTINE RK_Interpolate(action,N,H,Hold,Z1,Z2,Z3,CONT) |
---|
1664 | !~~~> Constructs or evaluates a quadratic polynomial |
---|
1665 | ! that interpolates the Z solution at current step |
---|
1666 | ! and provides starting values for the next step |
---|
1667 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1668 | INTEGER :: N, i |
---|
1669 | KPP_REAL :: H,Hold,Z1(N),Z2(N),Z3(N),CONT(N,3) |
---|
1670 | KPP_REAL :: r, x1, x2, x3, den |
---|
1671 | CHARACTER(LEN=4) :: action |
---|
1672 | |
---|
1673 | SELECT CASE (action) |
---|
1674 | CASE ('make') |
---|
1675 | ! Construct the solution quadratic interpolant Q(c_i) = Z_i, i=1:3 |
---|
1676 | den = (rkC(3)-rkC(2))*(rkC(2)-rkC(1))*(rkC(1)-rkC(3)) |
---|
1677 | DO i=1,N |
---|
1678 | CONT(i,1)=(-rkC(3)**2*rkC(2)*Z1(i)+Z3(i)*rkC(2)*rkC(1)**2 & |
---|
1679 | +rkC(2)**2*rkC(3)*Z1(i)-rkC(2)**2*rkC(1)*Z3(i) & |
---|
1680 | +rkC(3)**2*rkC(1)*Z2(i)-Z2(i)*rkC(3)*rkC(1)**2)& |
---|
1681 | /den-Z3(i) |
---|
1682 | CONT(i,2)= -( rkC(1)**2*(Z3(i)-Z2(i)) + rkC(2)**2*(Z1(i) & |
---|
1683 | -Z3(i)) +rkC(3)**2*(Z2(i)-Z1(i)) )/den |
---|
1684 | CONT(i,3)= ( rkC(1)*(Z3(i)-Z2(i)) + rkC(2)*(Z1(i)-Z3(i)) & |
---|
1685 | +rkC(3)*(Z2(i)-Z1(i)) )/den |
---|
1686 | END DO |
---|
1687 | CASE ('eval') |
---|
1688 | ! Evaluate quadratic polynomial |
---|
1689 | r = H/Hold |
---|
1690 | x1 = ONE + rkC(1)*r |
---|
1691 | x2 = ONE + rkC(2)*r |
---|
1692 | x3 = ONE + rkC(3)*r |
---|
1693 | DO i=1,N |
---|
1694 | Z1(i) = CONT(i,1)+x1*(CONT(i,2)+x1*CONT(i,3)) |
---|
1695 | Z2(i) = CONT(i,1)+x2*(CONT(i,2)+x2*CONT(i,3)) |
---|
1696 | Z3(i) = CONT(i,1)+x3*(CONT(i,2)+x3*CONT(i,3)) |
---|
1697 | END DO |
---|
1698 | END SELECT |
---|
1699 | END SUBROUTINE RK_Interpolate |
---|
1700 | |
---|
1701 | |
---|
1702 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1703 | SUBROUTINE RK_PrepareRHS(N,T,H,Y,Z1,Z2,Z3,R1,R2,R3) |
---|
1704 | !~~~> Prepare the right-hand side for Newton iterations |
---|
1705 | ! R = Z - hA x F |
---|
1706 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1707 | IMPLICIT NONE |
---|
1708 | |
---|
1709 | INTEGER :: N |
---|
1710 | KPP_REAL :: T,H |
---|
1711 | KPP_REAL, DIMENSION(N) :: Y,Z1,Z2,Z3,F,R1,R2,R3,TMP |
---|
1712 | |
---|
1713 | CALL WCOPY(N,Z1,1,R1,1) ! R1 <- Z1 |
---|
1714 | CALL WCOPY(N,Z2,1,R2,1) ! R2 <- Z2 |
---|
1715 | CALL WCOPY(N,Z3,1,R3,1) ! R3 <- Z3 |
---|
1716 | |
---|
1717 | CALL WADD(N,Y,Z1,TMP) ! TMP <- Y + Z1 |
---|
1718 | CALL FUN_CHEM(T+rkC(1)*H,TMP,F) ! F1 <- Fun(Y+Z1) |
---|
1719 | CALL WAXPY(N,-H*rkA(1,1),F,1,R1,1) ! R1 <- R1 - h*A_11*F1 |
---|
1720 | CALL WAXPY(N,-H*rkA(2,1),F,1,R2,1) ! R2 <- R2 - h*A_21*F1 |
---|
1721 | CALL WAXPY(N,-H*rkA(3,1),F,1,R3,1) ! R3 <- R3 - h*A_31*F1 |
---|
1722 | |
---|
1723 | CALL WADD(N,Y,Z2,TMP) ! TMP <- Y + Z2 |
---|
1724 | CALL FUN_CHEM(T+rkC(2)*H,TMP,F) ! F2 <- Fun(Y+Z2) |
---|
1725 | CALL WAXPY(N,-H*rkA(1,2),F,1,R1,1) ! R1 <- R1 - h*A_12*F2 |
---|
1726 | CALL WAXPY(N,-H*rkA(2,2),F,1,R2,1) ! R2 <- R2 - h*A_22*F2 |
---|
1727 | CALL WAXPY(N,-H*rkA(3,2),F,1,R3,1) ! R3 <- R3 - h*A_32*F2 |
---|
1728 | |
---|
1729 | CALL WADD(N,Y,Z3,TMP) ! TMP <- Y + Z3 |
---|
1730 | CALL FUN_CHEM(T+rkC(3)*H,TMP,F) ! F3 <- Fun(Y+Z3) |
---|
1731 | CALL WAXPY(N,-H*rkA(1,3),F,1,R1,1) ! R1 <- R1 - h*A_13*F3 |
---|
1732 | CALL WAXPY(N,-H*rkA(2,3),F,1,R2,1) ! R2 <- R2 - h*A_23*F3 |
---|
1733 | CALL WAXPY(N,-H*rkA(3,3),F,1,R3,1) ! R3 <- R3 - h*A_33*F3 |
---|
1734 | |
---|
1735 | END SUBROUTINE RK_PrepareRHS |
---|
1736 | |
---|
1737 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1738 | SUBROUTINE RK_PrepareRHS_Adj(N,H,Jac1,Jac2,Jac3,Lambda, & |
---|
1739 | U1,U2,U3,G1,G2,G3,R1,R2,R3) |
---|
1740 | !~~~> Prepare the right-hand side for Newton iterations |
---|
1741 | ! R = Z_adj - hA x Jac*Z_adj - h J^t b lambda |
---|
1742 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1743 | IMPLICIT NONE |
---|
1744 | |
---|
1745 | INTEGER, INTENT(IN) :: N |
---|
1746 | KPP_REAL, INTENT(IN) :: H |
---|
1747 | KPP_REAL, DIMENSION(N), INTENT(IN) :: U1,U2,U3,Lambda,G1,G2,G3 |
---|
1748 | KPP_REAL, DIMENSION(N), INTENT(OUT) :: R1,R2,R3 |
---|
1749 | #ifdef FULL_ALGEBRA |
---|
1750 | KPP_REAL, DIMENSION(N,N), INTENT(IN) :: Jac1, Jac2, Jac3 |
---|
1751 | #else |
---|
1752 | KPP_REAL, DIMENSION(LU_NONZERO),INTENT(IN) :: Jac1, Jac2, Jac3 |
---|
1753 | #endif |
---|
1754 | KPP_REAL, DIMENSION(N) :: F,TMP |
---|
1755 | |
---|
1756 | |
---|
1757 | CALL WCOPY(N,G1,1,R1,1) ! R1 <- G1 |
---|
1758 | CALL WCOPY(N,G2,1,R2,1) ! R2 <- G2 |
---|
1759 | CALL WCOPY(N,G3,1,R3,1) ! R3 <- G3 |
---|
1760 | |
---|
1761 | CALL SET2ZERO(N,F) |
---|
1762 | CALL WAXPY(N,-H*rkA(1,1),U1,1,F,1) ! F1 <- -h*A_11*U1 |
---|
1763 | CALL WAXPY(N,-H*rkA(2,1),U2,1,F,1) ! F1 <- F1 - h*A_21*U2 |
---|
1764 | CALL WAXPY(N,-H*rkA(3,1),U3,1,F,1) ! F1 <- F1 - h*A_31*U3 |
---|
1765 | #ifdef FULL_ALGEBRA |
---|
1766 | TMP = MATMUL(TRANSPOSE(Jac1),F) |
---|
1767 | #else |
---|
1768 | CALL JacTR_SP_Vec ( Jac1, F, TMP ) ! R1 <- -Jac(Y+Z1)^t*h*sum(A_j1*U_j) |
---|
1769 | #endif |
---|
1770 | CALL WAXPY(N,ONE,U1,1,TMP,1) ! R1 <- U1 -Jac(Y+Z1)^t*h*sum(A_j1*U_j) |
---|
1771 | CALL WAXPY(N,ONE,TMP,1,R1,1) ! R1 <- U1 -Jac(Y+Z1)^t*h*sum(A_j1*U_j) |
---|
1772 | |
---|
1773 | CALL SET2ZERO(N,F) |
---|
1774 | CALL WAXPY(N,-H*rkA(1,2),U1,1,F,1) ! F2 <- -h*A_11*U1 |
---|
1775 | CALL WAXPY(N,-H*rkA(2,2),U2,1,F,1) ! F2 <- F2 - h*A_21*U2 |
---|
1776 | CALL WAXPY(N,-H*rkA(3,2),U3,1,F,1) ! F2 <- F2 - h*A_31*U3 |
---|
1777 | #ifdef FULL_ALGEBRA |
---|
1778 | TMP = MATMUL(TRANSPOSE(Jac2),F) |
---|
1779 | #else |
---|
1780 | CALL JacTR_SP_Vec ( Jac2, F, TMP ) ! R2 <- -Jac(Y+Z2)^t*h*sum(A_j2*U_j) |
---|
1781 | #endif |
---|
1782 | CALL WAXPY(N,ONE,U2,1,TMP,1) ! R2 <- U2 -Jac(Y+Z2)^t*h*sum(A_j2*U_j) |
---|
1783 | CALL WAXPY(N,ONE,TMP,1,R2,1) ! R2 <- U2 -Jac(Y+Z2)^t*h*sum(A_j2*U_j) |
---|
1784 | |
---|
1785 | CALL SET2ZERO(N,F) |
---|
1786 | CALL WAXPY(N,-H*rkA(1,3),U1,1,F,1) ! F3 <- -h*A_11*U1 |
---|
1787 | CALL WAXPY(N,-H*rkA(2,3),U2,1,F,1) ! F3 <- F3 - h*A_21*U2 |
---|
1788 | CALL WAXPY(N,-H*rkA(3,3),U3,1,F,1) ! F3 <- F3 - h*A_31*U3 |
---|
1789 | #ifdef FULL_ALGEBRA |
---|
1790 | TMP = MATMUL(TRANSPOSE(Jac3),F) |
---|
1791 | #else |
---|
1792 | CALL JacTR_SP_Vec ( Jac3, F, TMP ) ! R3 <- -Jac(Y+Z3)^t*h*sum(A_j3*U_j) |
---|
1793 | #endif |
---|
1794 | CALL WAXPY(N,ONE,U3,1,TMP,1) ! R3 <- U3 -Jac(Y+Z3)^t*h*sum(A_j3*U_j) |
---|
1795 | CALL WAXPY(N,ONE,TMP,1,R3,1) ! R3 <- U3 -Jac(Y+Z3)^t*h*sum(A_j3*U_j) |
---|
1796 | |
---|
1797 | |
---|
1798 | END SUBROUTINE RK_PrepareRHS_Adj |
---|
1799 | |
---|
1800 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1801 | SUBROUTINE RK_PrepareRHS_G(N,H,Jac1,Jac2,Jac3,Lambda, & |
---|
1802 | G1,G2,G3) |
---|
1803 | !~~~> Prepare the right-hand side for Newton iterations |
---|
1804 | ! R = Z_adj - hA x Jac*Z_adj - h J^t b lambda |
---|
1805 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1806 | IMPLICIT NONE |
---|
1807 | |
---|
1808 | INTEGER, INTENT(IN) :: N |
---|
1809 | KPP_REAL, INTENT(IN) :: H |
---|
1810 | KPP_REAL, DIMENSION(N), INTENT(IN) :: Lambda |
---|
1811 | KPP_REAL, DIMENSION(N), INTENT(OUT) :: G1,G2,G3 |
---|
1812 | #ifdef FULL_ALGEBRA |
---|
1813 | KPP_REAL, DIMENSION(N,N), INTENT(IN) :: Jac1, Jac2, Jac3 |
---|
1814 | #else |
---|
1815 | KPP_REAL, DIMENSION(LU_NONZERO),INTENT(IN) :: Jac1, Jac2, Jac3 |
---|
1816 | #endif |
---|
1817 | KPP_REAL, DIMENSION(N) :: F |
---|
1818 | |
---|
1819 | CALL SET2ZERO(N,G1) |
---|
1820 | CALL SET2ZERO(N,G2) |
---|
1821 | CALL SET2ZERO(N,G3) |
---|
1822 | #ifdef FULL_ALGEBRA |
---|
1823 | F = MATMUL(TRANSPOSE(Jac1),Lambda) |
---|
1824 | #else |
---|
1825 | CALL JacTR_SP_Vec ( Jac1, Lambda, F ) ! F1 <- Jac(Y+Z1)^t*Lambda |
---|
1826 | #endif |
---|
1827 | CALL WAXPY(N,-H*rkB(1),F,1,G1,1) ! R1 <- R1 - h*B_1*F1 |
---|
1828 | |
---|
1829 | #ifdef FULL_ALGEBRA |
---|
1830 | F = MATMUL(TRANSPOSE(Jac2),Lambda) |
---|
1831 | #else |
---|
1832 | CALL JacTR_SP_Vec ( Jac2, Lambda, F ) ! F2 <- Jac(Y+Z2)^t*Lambda |
---|
1833 | #endif |
---|
1834 | CALL WAXPY(N,-H*rkB(2),F,1,G2,1) ! R2 <- R2 - h*B_2*F2 |
---|
1835 | |
---|
1836 | #ifdef FULL_ALGEBRA |
---|
1837 | F = MATMUL(TRANSPOSE(Jac3),Lambda) |
---|
1838 | #else |
---|
1839 | CALL JacTR_SP_Vec ( Jac3, Lambda, F ) ! F3 <- Jac(Y+Z3)^t*Lambda |
---|
1840 | #endif |
---|
1841 | CALL WAXPY(N,-H*rkB(3),F,1,G3,1) ! R3 <- R3 - h*B_3*F3 |
---|
1842 | |
---|
1843 | |
---|
1844 | END SUBROUTINE RK_PrepareRHS_G |
---|
1845 | |
---|
1846 | |
---|
1847 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1848 | SUBROUTINE RK_Decomp(N,H,FJAC,E1,IP1,E2,IP2,ISING) |
---|
1849 | !~~~> Compute the matrices E1 and E2 and their decompositions |
---|
1850 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1851 | IMPLICIT NONE |
---|
1852 | |
---|
1853 | INTEGER :: N, ISING |
---|
1854 | KPP_REAL :: H, Alpha, Beta, Gamma |
---|
1855 | #ifdef FULL_ALGEBRA |
---|
1856 | KPP_REAL :: FJAC(N,N),E1(N,N) |
---|
1857 | COMPLEX(kind=dp) :: E2(N,N) |
---|
1858 | #else |
---|
1859 | KPP_REAL :: FJAC(LU_NONZERO),E1(LU_NONZERO) |
---|
1860 | COMPLEX(kind=dp) :: E2(LU_NONZERO) |
---|
1861 | #endif |
---|
1862 | INTEGER :: IP1(N), IP2(N), i, j |
---|
1863 | |
---|
1864 | Gamma = rkGamma/H |
---|
1865 | Alpha = rkAlpha/H |
---|
1866 | Beta = rkBeta /H |
---|
1867 | |
---|
1868 | #ifdef FULL_ALGEBRA |
---|
1869 | DO j=1,N |
---|
1870 | DO i=1,N |
---|
1871 | E1(i,j)=-FJAC(i,j) |
---|
1872 | END DO |
---|
1873 | E1(j,j)=E1(j,j)+Gamma |
---|
1874 | END DO |
---|
1875 | CALL DGETRF(N,N,E1,N,IP1,ISING) |
---|
1876 | #else |
---|
1877 | DO i=1,LU_NONZERO |
---|
1878 | E1(i)=-FJAC(i) |
---|
1879 | END DO |
---|
1880 | DO i=1,N |
---|
1881 | j=LU_DIAG(i); E1(j)=E1(j)+Gamma |
---|
1882 | END DO |
---|
1883 | CALL KppDecomp(E1,ISING) |
---|
1884 | #endif |
---|
1885 | |
---|
1886 | IF (ISING /= 0) THEN |
---|
1887 | ISTATUS(idec) = ISTATUS(idec) + 1 |
---|
1888 | RETURN |
---|
1889 | END IF |
---|
1890 | |
---|
1891 | #ifdef FULL_ALGEBRA |
---|
1892 | DO j=1,N |
---|
1893 | DO i=1,N |
---|
1894 | E2(i,j) = DCMPLX( -FJAC(i,j), ZERO ) |
---|
1895 | END DO |
---|
1896 | E2(j,j) = E2(j,j) + CMPLX( Alpha, Beta ) |
---|
1897 | END DO |
---|
1898 | CALL ZGETRF(N,N,E2,N,IP2,ISING) |
---|
1899 | #else |
---|
1900 | DO i=1,LU_NONZERO |
---|
1901 | E2(i) = DCMPLX( -FJAC(i), ZERO ) |
---|
1902 | END DO |
---|
1903 | DO i=1,N |
---|
1904 | j = LU_DIAG(i); E2(j)=E2(j) + CMPLX( Alpha, Beta ) |
---|
1905 | END DO |
---|
1906 | CALL KppDecompCmplx(E2,ISING) |
---|
1907 | #endif |
---|
1908 | ISTATUS(idec) = ISTATUS(idec) + 1 |
---|
1909 | |
---|
1910 | END SUBROUTINE RK_Decomp |
---|
1911 | |
---|
1912 | |
---|
1913 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1914 | SUBROUTINE RK_Solve(N,H,E1,IP1,E2,IP2,R1,R2,R3,ISING) |
---|
1915 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1916 | IMPLICIT NONE |
---|
1917 | INTEGER :: N,IP1(N),IP2(N),ISING |
---|
1918 | #ifdef FULL_ALGEBRA |
---|
1919 | KPP_REAL :: E1(N,N) |
---|
1920 | COMPLEX(kind=dp) :: E2(N,N) |
---|
1921 | #else |
---|
1922 | KPP_REAL :: E1(LU_NONZERO) |
---|
1923 | COMPLEX(kind=dp) :: E2(LU_NONZERO) |
---|
1924 | #endif |
---|
1925 | KPP_REAL :: R1(N),R2(N),R3(N) |
---|
1926 | KPP_REAL :: H, x1, x2, x3 |
---|
1927 | COMPLEX(kind=dp) :: BC(N) |
---|
1928 | INTEGER :: i |
---|
1929 | ! |
---|
1930 | ! Z <- h^{-1) T^{-1) A^{-1) x Z |
---|
1931 | DO i=1,N |
---|
1932 | x1 = R1(i)/H; x2 = R2(i)/H; x3 = R3(i)/H |
---|
1933 | R1(i) = rkTinvAinv(1,1)*x1 + rkTinvAinv(1,2)*x2 + rkTinvAinv(1,3)*x3 |
---|
1934 | R2(i) = rkTinvAinv(2,1)*x1 + rkTinvAinv(2,2)*x2 + rkTinvAinv(2,3)*x3 |
---|
1935 | R3(i) = rkTinvAinv(3,1)*x1 + rkTinvAinv(3,2)*x2 + rkTinvAinv(3,3)*x3 |
---|
1936 | END DO |
---|
1937 | |
---|
1938 | #ifdef FULL_ALGEBRA |
---|
1939 | CALL DGETRS ('N',N,1,E1,N,IP1,R1,N,ISING) |
---|
1940 | #else |
---|
1941 | CALL KppSolve (E1,R1) |
---|
1942 | #endif |
---|
1943 | ! |
---|
1944 | DO i=1,N |
---|
1945 | BC(i) = DCMPLX(R2(i),R3(i)) |
---|
1946 | END DO |
---|
1947 | #ifdef FULL_ALGEBRA |
---|
1948 | CALL ZGETRS ('N',N,1,E2,N,IP2,BC,N,ISING) |
---|
1949 | #else |
---|
1950 | CALL KppSolveCmplx (E2,BC) |
---|
1951 | #endif |
---|
1952 | DO i=1,N |
---|
1953 | R2(i) = DBLE( BC(i) ) |
---|
1954 | R3(i) = AIMAG( BC(i) ) |
---|
1955 | END DO |
---|
1956 | |
---|
1957 | ! Z <- T x Z |
---|
1958 | DO i=1,N |
---|
1959 | x1 = R1(i); x2 = R2(i); x3 = R3(i) |
---|
1960 | R1(i) = rkT(1,1)*x1 + rkT(1,2)*x2 + rkT(1,3)*x3 |
---|
1961 | R2(i) = rkT(2,1)*x1 + rkT(2,2)*x2 + rkT(2,3)*x3 |
---|
1962 | R3(i) = rkT(3,1)*x1 + rkT(3,2)*x2 + rkT(3,3)*x3 |
---|
1963 | END DO |
---|
1964 | |
---|
1965 | ISTATUS(isol) = ISTATUS(isol) + 1 |
---|
1966 | |
---|
1967 | END SUBROUTINE RK_Solve |
---|
1968 | |
---|
1969 | |
---|
1970 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1971 | SUBROUTINE RK_SolveTR(N,H,E1,IP1,E2,IP2,R1,R2,R3,ISING) |
---|
1972 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1973 | IMPLICIT NONE |
---|
1974 | INTEGER, INTENT(IN) :: N,IP1(N),IP2(N) |
---|
1975 | INTEGER, INTENT(OUT) :: ISING |
---|
1976 | #ifdef FULL_ALGEBRA |
---|
1977 | KPP_REAL, INTENT(IN) :: E1(N,N) |
---|
1978 | COMPLEX(kind=dp), INTENT(IN) :: E2(N,N) |
---|
1979 | #else |
---|
1980 | KPP_REAL, INTENT(IN) :: E1(LU_NONZERO) |
---|
1981 | COMPLEX(kind=dp), INTENT(IN) :: E2(LU_NONZERO) |
---|
1982 | #endif |
---|
1983 | KPP_REAL, INTENT(INOUT) :: R1(N),R2(N),R3(N) |
---|
1984 | KPP_REAL :: H, x1, x2, x3 |
---|
1985 | COMPLEX(kind=dp) :: BC(N) |
---|
1986 | INTEGER :: i |
---|
1987 | ! |
---|
1988 | ! RHS <- h^{-1) (A^{-1) T^{-1))^t x RHS |
---|
1989 | DO i=1,N |
---|
1990 | x1 = R1(i)/H; x2 = R2(i)/H; x3 = R3(i)/H |
---|
1991 | R1(i) = rkAinvT(1,1)*x1 + rkAinvT(2,1)*x2 + rkAinvT(3,1)*x3 |
---|
1992 | R2(i) = rkAinvT(1,2)*x1 + rkAinvT(2,2)*x2 + rkAinvT(3,2)*x3 |
---|
1993 | R3(i) = rkAinvT(1,3)*x1 + rkAinvT(2,3)*x2 + rkAinvT(3,3)*x3 |
---|
1994 | END DO |
---|
1995 | |
---|
1996 | #ifdef FULL_ALGEBRA |
---|
1997 | CALL DGETRS ('T',N,1,E1,N,IP1,R1,N,ISING) |
---|
1998 | #else |
---|
1999 | CALL KppSolveTR (E1,R1,R1) |
---|
2000 | #endif |
---|
2001 | ! |
---|
2002 | DO i=1,N |
---|
2003 | BC(i) = DCMPLX(R2(i),-R3(i)) |
---|
2004 | END DO |
---|
2005 | #ifdef FULL_ALGEBRA |
---|
2006 | CALL ZGETRS ('T',N,1,E2,N,IP2,BC,N,ISING) |
---|
2007 | #else |
---|
2008 | CALL KppSolveTRCmplx (E2,BC) |
---|
2009 | #endif |
---|
2010 | DO i=1,N |
---|
2011 | R2(i) = DBLE( BC(i) ) |
---|
2012 | R3(i) = -AIMAG( BC(i) ) |
---|
2013 | END DO |
---|
2014 | |
---|
2015 | ! X <- (T^{-1})^t x X |
---|
2016 | DO i=1,N |
---|
2017 | x1 = R1(i); x2 = R2(i); x3 = R3(i) |
---|
2018 | R1(i) = rkTinv(1,1)*x1 + rkTinv(2,1)*x2 + rkTinv(3,1)*x3 |
---|
2019 | R2(i) = rkTinv(1,2)*x1 + rkTinv(2,2)*x2 + rkTinv(3,2)*x3 |
---|
2020 | R3(i) = rkTinv(1,3)*x1 + rkTinv(2,3)*x2 + rkTinv(3,3)*x3 |
---|
2021 | END DO |
---|
2022 | |
---|
2023 | ISTATUS(isol) = ISTATUS(isol) + 1 |
---|
2024 | |
---|
2025 | END SUBROUTINE RK_SolveTR |
---|
2026 | |
---|
2027 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2028 | SUBROUTINE RK_ErrorEstimate(N,H,Y,T, & |
---|
2029 | E1,IP1,Z1,Z2,Z3,SCAL,Err, & |
---|
2030 | FirstStep,Reject) |
---|
2031 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2032 | IMPLICIT NONE |
---|
2033 | |
---|
2034 | INTEGER :: N |
---|
2035 | #ifdef FULL_ALGEBRA |
---|
2036 | KPP_REAL :: E1(N,N) |
---|
2037 | INTEGER :: ISING |
---|
2038 | #else |
---|
2039 | KPP_REAL :: E1(LU_NONZERO) |
---|
2040 | #endif |
---|
2041 | KPP_REAL :: SCAL(N),Z1(N),Z2(N),Z3(N),F1(N),F2(N), & |
---|
2042 | F0(N),Y(N),TMP(N),T,H |
---|
2043 | INTEGER :: IP1(N), i |
---|
2044 | LOGICAL FirstStep,Reject |
---|
2045 | KPP_REAL :: HEE1,HEE2,HEE3,Err |
---|
2046 | |
---|
2047 | HEE1 = rkE(1)/H |
---|
2048 | HEE2 = rkE(2)/H |
---|
2049 | HEE3 = rkE(3)/H |
---|
2050 | |
---|
2051 | CALL FUN_CHEM(T,Y,F0) |
---|
2052 | ISTATUS(ifun) = ISTATUS(ifun) + 1 |
---|
2053 | |
---|
2054 | DO i=1,N |
---|
2055 | F2(i) = HEE1*Z1(i)+HEE2*Z2(i)+HEE3*Z3(i) |
---|
2056 | TMP(i) = rkE(0)*F0(i) + F2(i) |
---|
2057 | END DO |
---|
2058 | |
---|
2059 | #ifdef FULL_ALGEBRA |
---|
2060 | CALL DGETRS ('N',N,1,E1,N,IP1,TMP,N,ISING) |
---|
2061 | IF ((rkMethod==R1A).OR.(rkMethod==GAU).OR.(rkMethod==L3A)) THEN |
---|
2062 | CALL DGETRS('N',N,1,E1,N,IP1,TMP,N,ISING) |
---|
2063 | END IF |
---|
2064 | IF (rkMethod==GAU) THEN |
---|
2065 | CALL DGETRS ('N',N,1,E1,N,IP1,TMP,N,ISING) |
---|
2066 | END IF |
---|
2067 | #else |
---|
2068 | CALL KppSolve (E1, TMP) |
---|
2069 | IF ((rkMethod==R1A).OR.(rkMethod==GAU).OR.(rkMethod==L3A)) THEN |
---|
2070 | CALL KppSolve (E1,TMP) |
---|
2071 | END IF |
---|
2072 | IF (rkMethod==GAU) THEN |
---|
2073 | CALL KppSolve (E1,TMP) |
---|
2074 | END IF |
---|
2075 | #endif |
---|
2076 | |
---|
2077 | Err = RK_ErrorNorm(N,SCAL,TMP) |
---|
2078 | ! |
---|
2079 | IF (Err < ONE) RETURN |
---|
2080 | firej:IF (FirstStep.OR.Reject) THEN |
---|
2081 | DO i=1,N |
---|
2082 | TMP(i)=Y(i)+TMP(i) |
---|
2083 | END DO |
---|
2084 | CALL FUN_CHEM(T,TMP,F1) |
---|
2085 | ISTATUS(ifun) = ISTATUS(ifun) + 1 |
---|
2086 | DO i=1,N |
---|
2087 | TMP(i)=F1(i)+F2(i) |
---|
2088 | END DO |
---|
2089 | |
---|
2090 | #ifdef FULL_ALGEBRA |
---|
2091 | CALL DGETRS ('N',N,1,E1,N,IP1,TMP,N,ISING) |
---|
2092 | #else |
---|
2093 | CALL KppSolve (E1, TMP) |
---|
2094 | #endif |
---|
2095 | Err = RK_ErrorNorm(N,SCAL,TMP) |
---|
2096 | END IF firej |
---|
2097 | |
---|
2098 | END SUBROUTINE RK_ErrorEstimate |
---|
2099 | |
---|
2100 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2101 | KPP_REAL FUNCTION RK_ErrorNorm(N,SCAL,DY) |
---|
2102 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2103 | IMPLICIT NONE |
---|
2104 | |
---|
2105 | INTEGER :: N |
---|
2106 | KPP_REAL :: SCAL(N),DY(N) |
---|
2107 | INTEGER :: i |
---|
2108 | |
---|
2109 | RK_ErrorNorm = ZERO |
---|
2110 | DO i=1,N |
---|
2111 | RK_ErrorNorm = RK_ErrorNorm + (DY(i)*SCAL(i))**2 |
---|
2112 | END DO |
---|
2113 | RK_ErrorNorm = MAX( SQRT(RK_ErrorNorm/N), 1.0d-10 ) |
---|
2114 | |
---|
2115 | END FUNCTION RK_ErrorNorm |
---|
2116 | |
---|
2117 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2118 | SUBROUTINE Radau2A_Coefficients |
---|
2119 | ! The coefficients of the 3-stage Radau-2A method |
---|
2120 | ! (given to ~30 accurate digits) |
---|
2121 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2122 | IMPLICIT NONE |
---|
2123 | ! The coefficients of the Radau2A method |
---|
2124 | KPP_REAL :: b0 |
---|
2125 | |
---|
2126 | ! b0 = 1.0d0 |
---|
2127 | IF (SdirkError) THEN |
---|
2128 | b0 = 0.2d-1 |
---|
2129 | ELSE |
---|
2130 | b0 = 0.5d-1 |
---|
2131 | END IF |
---|
2132 | |
---|
2133 | ! The coefficients of the Radau2A method |
---|
2134 | rkMethod = R2A |
---|
2135 | |
---|
2136 | rkA(1,1) = 1.968154772236604258683861429918299d-1 |
---|
2137 | rkA(1,2) = -6.55354258501983881085227825696087d-2 |
---|
2138 | rkA(1,3) = 2.377097434822015242040823210718965d-2 |
---|
2139 | rkA(2,1) = 3.944243147390872769974116714584975d-1 |
---|
2140 | rkA(2,2) = 2.920734116652284630205027458970589d-1 |
---|
2141 | rkA(2,3) = -4.154875212599793019818600988496743d-2 |
---|
2142 | rkA(3,1) = 3.764030627004672750500754423692808d-1 |
---|
2143 | rkA(3,2) = 5.124858261884216138388134465196080d-1 |
---|
2144 | rkA(3,3) = 1.111111111111111111111111111111111d-1 |
---|
2145 | |
---|
2146 | rkB(1) = 3.764030627004672750500754423692808d-1 |
---|
2147 | rkB(2) = 5.124858261884216138388134465196080d-1 |
---|
2148 | rkB(3) = 1.111111111111111111111111111111111d-1 |
---|
2149 | |
---|
2150 | rkC(1) = 1.550510257216821901802715925294109d-1 |
---|
2151 | rkC(2) = 6.449489742783178098197284074705891d-1 |
---|
2152 | rkC(3) = 1.0d0 |
---|
2153 | |
---|
2154 | ! New solution: H* Sum B_j*f(Z_j) = Sum D_j*Z_j |
---|
2155 | rkD(1) = 0.0d0 |
---|
2156 | rkD(2) = 0.0d0 |
---|
2157 | rkD(3) = 1.0d0 |
---|
2158 | |
---|
2159 | ! Classical error estimator: |
---|
2160 | ! H* Sum (B_j-Bhat_j)*f(Z_j) = H*E(0)*f(0) + Sum E_j*Z_j |
---|
2161 | rkE(0) = 1.0d0*b0 |
---|
2162 | rkE(1) = -10.04880939982741556246032950764708d0*b0 |
---|
2163 | rkE(2) = 1.382142733160748895793662840980412d0*b0 |
---|
2164 | rkE(3) = -.3333333333333333333333333333333333d0*b0 |
---|
2165 | |
---|
2166 | ! Sdirk error estimator |
---|
2167 | rkBgam(0) = b0 |
---|
2168 | rkBgam(1) = .3764030627004672750500754423692807d0-1.558078204724922382431975370686279d0*b0 |
---|
2169 | rkBgam(2) = .8914115380582557157653087040196118d0*b0+.5124858261884216138388134465196077d0 |
---|
2170 | rkBgam(3) = -.1637777184845662566367174924883037d0-.3333333333333333333333333333333333d0*b0 |
---|
2171 | rkBgam(4) = .2748888295956773677478286035994148d0 |
---|
2172 | |
---|
2173 | ! H* Sum Bgam_j*f(Z_j) = H*Bgam(0)*f(0) + Sum Theta_j*Z_j |
---|
2174 | rkTheta(1) = -1.520677486405081647234271944611547d0-10.04880939982741556246032950764708d0*b0 |
---|
2175 | rkTheta(2) = 2.070455145596436382729929151810376d0+1.382142733160748895793662840980413d0*b0 |
---|
2176 | rkTheta(3) = -.3333333333333333333333333333333333d0*b0-.3744441479783868387391430179970741d0 |
---|
2177 | |
---|
2178 | ! Local order of error estimator |
---|
2179 | IF (b0==0.0d0) THEN |
---|
2180 | rkELO = 6.0d0 |
---|
2181 | ELSE |
---|
2182 | rkELO = 4.0d0 |
---|
2183 | END IF |
---|
2184 | |
---|
2185 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2186 | !~~~> Diagonalize the RK matrix: |
---|
2187 | ! rkTinv * inv(rkA) * rkT = |
---|
2188 | ! | rkGamma 0 0 | |
---|
2189 | ! | 0 rkAlpha -rkBeta | |
---|
2190 | ! | 0 rkBeta rkAlpha | |
---|
2191 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2192 | |
---|
2193 | rkGamma = 3.637834252744495732208418513577775d0 |
---|
2194 | rkAlpha = 2.681082873627752133895790743211112d0 |
---|
2195 | rkBeta = 3.050430199247410569426377624787569d0 |
---|
2196 | |
---|
2197 | rkT(1,1) = 9.443876248897524148749007950641664d-2 |
---|
2198 | rkT(1,2) = -1.412552950209542084279903838077973d-1 |
---|
2199 | rkT(1,3) = -3.00291941051474244918611170890539d-2 |
---|
2200 | rkT(2,1) = 2.502131229653333113765090675125018d-1 |
---|
2201 | rkT(2,2) = 2.041293522937999319959908102983381d-1 |
---|
2202 | rkT(2,3) = 3.829421127572619377954382335998733d-1 |
---|
2203 | rkT(3,1) = 1.0d0 |
---|
2204 | rkT(3,2) = 1.0d0 |
---|
2205 | rkT(3,3) = 0.0d0 |
---|
2206 | |
---|
2207 | rkTinv(1,1) = 4.178718591551904727346462658512057d0 |
---|
2208 | rkTinv(1,2) = 3.27682820761062387082533272429617d-1 |
---|
2209 | rkTinv(1,3) = 5.233764454994495480399309159089876d-1 |
---|
2210 | rkTinv(2,1) = -4.178718591551904727346462658512057d0 |
---|
2211 | rkTinv(2,2) = -3.27682820761062387082533272429617d-1 |
---|
2212 | rkTinv(2,3) = 4.766235545005504519600690840910124d-1 |
---|
2213 | rkTinv(3,1) = -5.02872634945786875951247343139544d-1 |
---|
2214 | rkTinv(3,2) = 2.571926949855605429186785353601676d0 |
---|
2215 | rkTinv(3,3) = -5.960392048282249249688219110993024d-1 |
---|
2216 | |
---|
2217 | rkTinvAinv(1,1) = 1.520148562492775501049204957366528d+1 |
---|
2218 | rkTinvAinv(1,2) = 1.192055789400527921212348994770778d0 |
---|
2219 | rkTinvAinv(1,3) = 1.903956760517560343018332287285119d0 |
---|
2220 | rkTinvAinv(2,1) = -9.669512977505946748632625374449567d0 |
---|
2221 | rkTinvAinv(2,2) = -8.724028436822336183071773193986487d0 |
---|
2222 | rkTinvAinv(2,3) = 3.096043239482439656981667712714881d0 |
---|
2223 | rkTinvAinv(3,1) = -1.409513259499574544876303981551774d+1 |
---|
2224 | rkTinvAinv(3,2) = 5.895975725255405108079130152868952d0 |
---|
2225 | rkTinvAinv(3,3) = -1.441236197545344702389881889085515d-1 |
---|
2226 | |
---|
2227 | rkAinvT(1,1) = .3435525649691961614912493915818282d0 |
---|
2228 | rkAinvT(1,2) = -.4703191128473198422370558694426832d0 |
---|
2229 | rkAinvT(1,3) = .3503786597113668965366406634269080d0 |
---|
2230 | rkAinvT(2,1) = .9102338692094599309122768354288852d0 |
---|
2231 | rkAinvT(2,2) = 1.715425895757991796035292755937326d0 |
---|
2232 | rkAinvT(2,3) = .4040171993145015239277111187301784d0 |
---|
2233 | rkAinvT(3,1) = 3.637834252744495732208418513577775d0 |
---|
2234 | rkAinvT(3,2) = 2.681082873627752133895790743211112d0 |
---|
2235 | rkAinvT(3,3) = -3.050430199247410569426377624787569d0 |
---|
2236 | |
---|
2237 | END SUBROUTINE Radau2A_Coefficients |
---|
2238 | |
---|
2239 | |
---|
2240 | |
---|
2241 | |
---|
2242 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2243 | SUBROUTINE Lobatto3C_Coefficients |
---|
2244 | ! The coefficients of the 3-stage Lobatto-3C method |
---|
2245 | ! (given to ~30 accurate digits) |
---|
2246 | ! The parameter b0 can be chosen to tune the error estimator |
---|
2247 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2248 | IMPLICIT NONE |
---|
2249 | KPP_REAL :: b0 |
---|
2250 | |
---|
2251 | rkMethod = L3C |
---|
2252 | |
---|
2253 | ! b0 = 1.0d0 |
---|
2254 | IF (SdirkError) THEN |
---|
2255 | b0 = 0.2d0 |
---|
2256 | ELSE |
---|
2257 | b0 = 0.5d0 |
---|
2258 | END IF |
---|
2259 | ! The coefficients of the Lobatto3C method |
---|
2260 | |
---|
2261 | rkA(1,1) = .1666666666666666666666666666666667d0 |
---|
2262 | rkA(1,2) = -.3333333333333333333333333333333333d0 |
---|
2263 | rkA(1,3) = .1666666666666666666666666666666667d0 |
---|
2264 | rkA(2,1) = .1666666666666666666666666666666667d0 |
---|
2265 | rkA(2,2) = .4166666666666666666666666666666667d0 |
---|
2266 | rkA(2,3) = -.8333333333333333333333333333333333d-1 |
---|
2267 | rkA(3,1) = .1666666666666666666666666666666667d0 |
---|
2268 | rkA(3,2) = .6666666666666666666666666666666667d0 |
---|
2269 | rkA(3,3) = .1666666666666666666666666666666667d0 |
---|
2270 | |
---|
2271 | rkB(1) = .1666666666666666666666666666666667d0 |
---|
2272 | rkB(2) = .6666666666666666666666666666666667d0 |
---|
2273 | rkB(3) = .1666666666666666666666666666666667d0 |
---|
2274 | |
---|
2275 | rkC(1) = 0.0d0 |
---|
2276 | rkC(2) = 0.5d0 |
---|
2277 | rkC(3) = 1.0d0 |
---|
2278 | |
---|
2279 | ! Classical error estimator, embedded solution: |
---|
2280 | rkBhat(0) = b0 |
---|
2281 | rkBhat(1) = .16666666666666666666666666666666667d0-b0 |
---|
2282 | rkBhat(2) = .66666666666666666666666666666666667d0 |
---|
2283 | rkBhat(3) = .16666666666666666666666666666666667d0 |
---|
2284 | |
---|
2285 | ! New solution: h Sum_j b_j f(Z_j) = sum d_j Z_j |
---|
2286 | rkD(1) = 0.0d0 |
---|
2287 | rkD(2) = 0.0d0 |
---|
2288 | rkD(3) = 1.0d0 |
---|
2289 | |
---|
2290 | ! Classical error estimator: |
---|
2291 | ! H* Sum (B_j-Bhat_j)*f(Z_j) = H*E(0)*f(0) + Sum E_j*Z_j |
---|
2292 | rkE(0) = .3808338772072650364017425226487022*b0 |
---|
2293 | rkE(1) = -1.142501631621795109205227567946107*b0 |
---|
2294 | rkE(2) = -1.523335508829060145606970090594809*b0 |
---|
2295 | rkE(3) = .3808338772072650364017425226487022*b0 |
---|
2296 | |
---|
2297 | ! Sdirk error estimator |
---|
2298 | rkBgam(0) = b0 |
---|
2299 | rkBgam(1) = .1666666666666666666666666666666667d0-1.d0*b0 |
---|
2300 | rkBgam(2) = .6666666666666666666666666666666667d0 |
---|
2301 | rkBgam(3) = -.2141672105405983697350758559820354d0 |
---|
2302 | rkBgam(4) = .3808338772072650364017425226487021d0 |
---|
2303 | |
---|
2304 | ! H* Sum Bgam_j*f(Z_j) = H*Bgam(0)*f(0) + Sum Theta_j*Z_j |
---|
2305 | rkTheta(1) = -3.d0*b0-.3808338772072650364017425226487021d0 |
---|
2306 | rkTheta(2) = -4.d0*b0+1.523335508829060145606970090594808d0 |
---|
2307 | rkTheta(3) = -.142501631621795109205227567946106d0+b0 |
---|
2308 | |
---|
2309 | ! Local order of error estimator |
---|
2310 | IF (b0==0.0d0) THEN |
---|
2311 | rkELO = 5.0d0 |
---|
2312 | ELSE |
---|
2313 | rkELO = 4.0d0 |
---|
2314 | END IF |
---|
2315 | |
---|
2316 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2317 | !~~~> Diagonalize the RK matrix: |
---|
2318 | ! rkTinv * inv(rkA) * rkT = |
---|
2319 | ! | rkGamma 0 0 | |
---|
2320 | ! | 0 rkAlpha -rkBeta | |
---|
2321 | ! | 0 rkBeta rkAlpha | |
---|
2322 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2323 | |
---|
2324 | rkGamma = 2.625816818958466716011888933765284d0 |
---|
2325 | rkAlpha = 1.687091590520766641994055533117359d0 |
---|
2326 | rkBeta = 2.508731754924880510838743672432351d0 |
---|
2327 | |
---|
2328 | rkT(1,1) = 1.d0 |
---|
2329 | rkT(1,2) = 1.d0 |
---|
2330 | rkT(1,3) = 0.d0 |
---|
2331 | rkT(2,1) = .4554100411010284672111720348287483d0 |
---|
2332 | rkT(2,2) = -.6027050205505142336055860174143743d0 |
---|
2333 | rkT(2,3) = -.4309321229203225731070721341350346d0 |
---|
2334 | rkT(3,1) = 2.195823345445647152832799205549709d0 |
---|
2335 | rkT(3,2) = -1.097911672722823576416399602774855d0 |
---|
2336 | rkT(3,3) = .7850032632435902184104551358922130d0 |
---|
2337 | |
---|
2338 | rkTinv(1,1) = .4205559181381766909344950150991349d0 |
---|
2339 | rkTinv(1,2) = .3488903392193734304046467270632057d0 |
---|
2340 | rkTinv(1,3) = .1915253879645878102698098373933487d0 |
---|
2341 | rkTinv(2,1) = .5794440818618233090655049849008650d0 |
---|
2342 | rkTinv(2,2) = -.3488903392193734304046467270632057d0 |
---|
2343 | rkTinv(2,3) = -.1915253879645878102698098373933487d0 |
---|
2344 | rkTinv(3,1) = -.3659705575742745254721332009249516d0 |
---|
2345 | rkTinv(3,2) = -1.463882230297098101888532803699806d0 |
---|
2346 | rkTinv(3,3) = .4702733607340189781407813565524989d0 |
---|
2347 | |
---|
2348 | rkTinvAinv(1,1) = 1.104302803159744452668648155627548d0 |
---|
2349 | rkTinvAinv(1,2) = .916122120694355522658740710823143d0 |
---|
2350 | rkTinvAinv(1,3) = .5029105849749601702795812241441172d0 |
---|
2351 | rkTinvAinv(2,1) = 1.895697196840255547331351844372453d0 |
---|
2352 | rkTinvAinv(2,2) = 3.083877879305644477341259289176857d0 |
---|
2353 | rkTinvAinv(2,3) = -1.502910584974960170279581224144117d0 |
---|
2354 | rkTinvAinv(3,1) = .8362439183082935036129145574774502d0 |
---|
2355 | rkTinvAinv(3,2) = -3.344975673233174014451658229909802d0 |
---|
2356 | rkTinvAinv(3,3) = .312908409479233358005944466882642d0 |
---|
2357 | |
---|
2358 | rkAinvT(1,1) = 2.625816818958466716011888933765282d0 |
---|
2359 | rkAinvT(1,2) = 1.687091590520766641994055533117358d0 |
---|
2360 | rkAinvT(1,3) = -2.508731754924880510838743672432351d0 |
---|
2361 | rkAinvT(2,1) = 1.195823345445647152832799205549710d0 |
---|
2362 | rkAinvT(2,2) = -2.097911672722823576416399602774855d0 |
---|
2363 | rkAinvT(2,3) = .7850032632435902184104551358922130d0 |
---|
2364 | rkAinvT(3,1) = 5.765829871932827589653709477334136d0 |
---|
2365 | rkAinvT(3,2) = .1170850640335862051731452613329320d0 |
---|
2366 | rkAinvT(3,3) = 4.078738281412060947659653944216779d0 |
---|
2367 | |
---|
2368 | END SUBROUTINE Lobatto3C_Coefficients |
---|
2369 | |
---|
2370 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2371 | SUBROUTINE Gauss_Coefficients |
---|
2372 | ! The coefficients of the 3-stage Gauss method |
---|
2373 | ! (given to ~30 accurate digits) |
---|
2374 | ! The parameter b3 can be chosen by the user |
---|
2375 | ! to tune the error estimator |
---|
2376 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2377 | IMPLICIT NONE |
---|
2378 | KPP_REAL :: b0 |
---|
2379 | ! The coefficients of the Gauss method |
---|
2380 | |
---|
2381 | |
---|
2382 | rkMethod = GAU |
---|
2383 | |
---|
2384 | ! b0 = 4.0d0 |
---|
2385 | b0 = 0.1d0 |
---|
2386 | |
---|
2387 | ! The coefficients of the Gauss method |
---|
2388 | |
---|
2389 | rkA(1,1) = .1388888888888888888888888888888889d0 |
---|
2390 | rkA(1,2) = -.359766675249389034563954710966045d-1 |
---|
2391 | rkA(1,3) = .97894440153083260495800422294756d-2 |
---|
2392 | rkA(2,1) = .3002631949808645924380249472131556d0 |
---|
2393 | rkA(2,2) = .2222222222222222222222222222222222d0 |
---|
2394 | rkA(2,3) = -.224854172030868146602471694353778d-1 |
---|
2395 | rkA(3,1) = .2679883337624694517281977355483022d0 |
---|
2396 | rkA(3,2) = .4804211119693833479008399155410489d0 |
---|
2397 | rkA(3,3) = .1388888888888888888888888888888889d0 |
---|
2398 | |
---|
2399 | rkB(1) = .2777777777777777777777777777777778d0 |
---|
2400 | rkB(2) = .4444444444444444444444444444444444d0 |
---|
2401 | rkB(3) = .2777777777777777777777777777777778d0 |
---|
2402 | |
---|
2403 | rkC(1) = .1127016653792583114820734600217600d0 |
---|
2404 | rkC(2) = .5000000000000000000000000000000000d0 |
---|
2405 | rkC(3) = .8872983346207416885179265399782400d0 |
---|
2406 | |
---|
2407 | ! Classical error estimator, embedded solution: |
---|
2408 | rkBhat(0) = b0 |
---|
2409 | rkBhat(1) =-1.4788305577012361475298775666303999d0*b0 & |
---|
2410 | +.27777777777777777777777777777777778d0 |
---|
2411 | rkBhat(2) = .44444444444444444444444444444444444d0 & |
---|
2412 | +.66666666666666666666666666666666667d0*b0 |
---|
2413 | rkBhat(3) = -.18783610896543051913678910003626672d0*b0 & |
---|
2414 | +.27777777777777777777777777777777778d0 |
---|
2415 | |
---|
2416 | ! New solution: h Sum_j b_j f(Z_j) = sum d_j Z_j |
---|
2417 | rkD(1) = .1666666666666666666666666666666667d1 |
---|
2418 | rkD(2) = -.1333333333333333333333333333333333d1 |
---|
2419 | rkD(3) = .1666666666666666666666666666666667d1 |
---|
2420 | |
---|
2421 | ! Classical error estimator: |
---|
2422 | ! H* Sum (B_j-Bhat_j)*f(Z_j) = H*E(0)*f(0) + Sum E_j*Z_j |
---|
2423 | rkE(0) = .2153144231161121782447335303806954d0*b0 |
---|
2424 | rkE(1) = -2.825278112319014084275808340593191d0*b0 |
---|
2425 | rkE(2) = .2870858974881495709929780405075939d0*b0 |
---|
2426 | rkE(3) = -.4558086256248162565397206448274867d-1*b0 |
---|
2427 | |
---|
2428 | ! Sdirk error estimator |
---|
2429 | rkBgam(0) = 0.d0 |
---|
2430 | rkBgam(1) = .2373339543355109188382583162660537d0 |
---|
2431 | rkBgam(2) = .5879873931885192299409334646982414d0 |
---|
2432 | rkBgam(3) = -.4063577064014232702392531134499046d-1 |
---|
2433 | rkBgam(4) = .2153144231161121782447335303806955d0 |
---|
2434 | |
---|
2435 | ! H* Sum Bgam_j*f(Z_j) = H*Bgam(0)*f(0) + Sum Theta_j*Z_j |
---|
2436 | rkTheta(1) = -2.594040933093095272574031876464493d0 |
---|
2437 | rkTheta(2) = 1.824611539036311947589425112250199d0 |
---|
2438 | rkTheta(3) = .1856563166634371860478043996459493d0 |
---|
2439 | |
---|
2440 | ! ELO = local order of classical error estimator |
---|
2441 | rkELO = 4.0d0 |
---|
2442 | |
---|
2443 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2444 | !~~~> Diagonalize the RK matrix: |
---|
2445 | ! rkTinv * inv(rkA) * rkT = |
---|
2446 | ! | rkGamma 0 0 | |
---|
2447 | ! | 0 rkAlpha -rkBeta | |
---|
2448 | ! | 0 rkBeta rkAlpha | |
---|
2449 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2450 | |
---|
2451 | rkGamma = 4.644370709252171185822941421408064d0 |
---|
2452 | rkAlpha = 3.677814645373914407088529289295970d0 |
---|
2453 | rkBeta = 3.508761919567443321903661209182446d0 |
---|
2454 | |
---|
2455 | rkT(1,1) = .7215185205520017032081769924397664d-1 |
---|
2456 | rkT(1,2) = -.8224123057363067064866206597516454d-1 |
---|
2457 | rkT(1,3) = -.6012073861930850173085948921439054d-1 |
---|
2458 | rkT(2,1) = .1188325787412778070708888193730294d0 |
---|
2459 | rkT(2,2) = .5306509074206139504614411373957448d-1 |
---|
2460 | rkT(2,3) = .3162050511322915732224862926182701d0 |
---|
2461 | rkT(3,1) = 1.d0 |
---|
2462 | rkT(3,2) = 1.d0 |
---|
2463 | rkT(3,3) = 0.d0 |
---|
2464 | |
---|
2465 | rkTinv(1,1) = 5.991698084937800775649580743981285d0 |
---|
2466 | rkTinv(1,2) = 1.139214295155735444567002236934009d0 |
---|
2467 | rkTinv(1,3) = .4323121137838583855696375901180497d0 |
---|
2468 | rkTinv(2,1) = -5.991698084937800775649580743981285d0 |
---|
2469 | rkTinv(2,2) = -1.139214295155735444567002236934009d0 |
---|
2470 | rkTinv(2,3) = .5676878862161416144303624098819503d0 |
---|
2471 | rkTinv(3,1) = -1.246213273586231410815571640493082d0 |
---|
2472 | rkTinv(3,2) = 2.925559646192313662599230367054972d0 |
---|
2473 | rkTinv(3,3) = -.2577352012734324923468722836888244d0 |
---|
2474 | |
---|
2475 | rkTinvAinv(1,1) = 27.82766708436744962047620566703329d0 |
---|
2476 | rkTinvAinv(1,2) = 5.290933503982655311815946575100597d0 |
---|
2477 | rkTinvAinv(1,3) = 2.007817718512643701322151051660114d0 |
---|
2478 | rkTinvAinv(2,1) = -17.66368928942422710690385180065675d0 |
---|
2479 | rkTinvAinv(2,2) = -14.45491129892587782538830044147713d0 |
---|
2480 | rkTinvAinv(2,3) = 2.992182281487356298677848948339886d0 |
---|
2481 | rkTinvAinv(3,1) = -25.60678350282974256072419392007303d0 |
---|
2482 | rkTinvAinv(3,2) = 6.762434375611708328910623303779923d0 |
---|
2483 | rkTinvAinv(3,3) = 1.043979339483109825041215970036771d0 |
---|
2484 | |
---|
2485 | rkAinvT(1,1) = .3350999483034677402618981153470483d0 |
---|
2486 | rkAinvT(1,2) = -.5134173605009692329246186488441294d0 |
---|
2487 | rkAinvT(1,3) = .6745196507033116204327635673208923d-1 |
---|
2488 | rkAinvT(2,1) = .5519025480108928886873752035738885d0 |
---|
2489 | rkAinvT(2,2) = 1.304651810077110066076640761092008d0 |
---|
2490 | rkAinvT(2,3) = .9767507983414134987545585703726984d0 |
---|
2491 | rkAinvT(3,1) = 4.644370709252171185822941421408064d0 |
---|
2492 | rkAinvT(3,2) = 3.677814645373914407088529289295970d0 |
---|
2493 | rkAinvT(3,3) = -3.508761919567443321903661209182446d0 |
---|
2494 | |
---|
2495 | END SUBROUTINE Gauss_Coefficients |
---|
2496 | |
---|
2497 | |
---|
2498 | |
---|
2499 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2500 | SUBROUTINE Radau1A_Coefficients |
---|
2501 | ! The coefficients of the 3-stage Gauss method |
---|
2502 | ! (given to ~30 accurate digits) |
---|
2503 | ! The parameter b3 can be chosen by the user |
---|
2504 | ! to tune the error estimator |
---|
2505 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2506 | IMPLICIT NONE |
---|
2507 | ! KPP_REAL :: b0 = 0.3d0 |
---|
2508 | KPP_REAL :: b0 = 0.1d0 |
---|
2509 | |
---|
2510 | ! The coefficients of the Radau1A method |
---|
2511 | |
---|
2512 | rkMethod = R1A |
---|
2513 | |
---|
2514 | rkA(1,1) = .1111111111111111111111111111111111d0 |
---|
2515 | rkA(1,2) = -.1916383190435098943442935597058829d0 |
---|
2516 | rkA(1,3) = .8052720793239878323318244859477174d-1 |
---|
2517 | rkA(2,1) = .1111111111111111111111111111111111d0 |
---|
2518 | rkA(2,2) = .2920734116652284630205027458970589d0 |
---|
2519 | rkA(2,3) = -.481334970546573839513422644787591d-1 |
---|
2520 | rkA(3,1) = .1111111111111111111111111111111111d0 |
---|
2521 | rkA(3,2) = .5370223859435462728402311533676479d0 |
---|
2522 | rkA(3,3) = .1968154772236604258683861429918299d0 |
---|
2523 | |
---|
2524 | rkB(1) = .1111111111111111111111111111111111d0 |
---|
2525 | rkB(2) = .5124858261884216138388134465196080d0 |
---|
2526 | rkB(3) = .3764030627004672750500754423692808d0 |
---|
2527 | |
---|
2528 | rkC(1) = 0.d0 |
---|
2529 | rkC(2) = .3550510257216821901802715925294109d0 |
---|
2530 | rkC(3) = .8449489742783178098197284074705891d0 |
---|
2531 | |
---|
2532 | ! Classical error estimator, embedded solution: |
---|
2533 | rkBhat(0) = b0 |
---|
2534 | rkBhat(1) = .11111111111111111111111111111111111d0-b0 |
---|
2535 | rkBhat(2) = .51248582618842161383881344651960810d0 |
---|
2536 | rkBhat(3) = .37640306270046727505007544236928079d0 |
---|
2537 | |
---|
2538 | ! New solution: H* Sum B_j*f(Z_j) = Sum D_j*Z_j |
---|
2539 | rkD(1) = .3333333333333333333333333333333333d0 |
---|
2540 | rkD(2) = -.8914115380582557157653087040196127d0 |
---|
2541 | rkD(3) = .1558078204724922382431975370686279d1 |
---|
2542 | |
---|
2543 | ! Classical error estimator: |
---|
2544 | ! H* Sum (b_j-bhat_j) f(Z_j) = H*E(0)*F(0) + Sum E_j Z_j |
---|
2545 | rkE(0) = .2748888295956773677478286035994148d0*b0 |
---|
2546 | rkE(1) = -1.374444147978386838739143017997074d0*b0 |
---|
2547 | rkE(2) = -1.335337922441686804550326197041126d0*b0 |
---|
2548 | rkE(3) = .235782604058977333559011782643466d0*b0 |
---|
2549 | |
---|
2550 | ! Sdirk error estimator |
---|
2551 | rkBgam(0) = 0.0d0 |
---|
2552 | rkBgam(1) = .1948150124588532186183490991130616d-1 |
---|
2553 | rkBgam(2) = .7575249005733381398986810981093584d0 |
---|
2554 | rkBgam(3) = -.518952314149008295083446116200793d-1 |
---|
2555 | rkBgam(4) = .2748888295956773677478286035994148d0 |
---|
2556 | |
---|
2557 | ! H* Sum Bgam_j*f(Z_j) = H*Bgam(0)*f(0) + Sum Theta_j*Z_j |
---|
2558 | rkTheta(1) = -1.224370034375505083904362087063351d0 |
---|
2559 | rkTheta(2) = .9340045331532641409047527962010133d0 |
---|
2560 | rkTheta(3) = .4656990124352088397561234800640929d0 |
---|
2561 | |
---|
2562 | ! ELO = local order of classical error estimator |
---|
2563 | rkELO = 4.0d0 |
---|
2564 | |
---|
2565 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2566 | !~~~> Diagonalize the RK matrix: |
---|
2567 | ! rkTinv * inv(rkA) * rkT = |
---|
2568 | ! | rkGamma 0 0 | |
---|
2569 | ! | 0 rkAlpha -rkBeta | |
---|
2570 | ! | 0 rkBeta rkAlpha | |
---|
2571 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2572 | |
---|
2573 | rkGamma = 3.637834252744495732208418513577775d0 |
---|
2574 | rkAlpha = 2.681082873627752133895790743211112d0 |
---|
2575 | rkBeta = 3.050430199247410569426377624787569d0 |
---|
2576 | |
---|
2577 | rkT(1,1) = .424293819848497965354371036408369d0 |
---|
2578 | rkT(1,2) = -.3235571519651980681202894497035503d0 |
---|
2579 | rkT(1,3) = -.522137786846287839586599927945048d0 |
---|
2580 | rkT(2,1) = .57594609499806128896291585429339d-1 |
---|
2581 | rkT(2,2) = .3148663231849760131614374283783d-2 |
---|
2582 | rkT(2,3) = .452429247674359778577728510381731d0 |
---|
2583 | rkT(3,1) = 1.d0 |
---|
2584 | rkT(3,2) = 1.d0 |
---|
2585 | rkT(3,3) = 0.d0 |
---|
2586 | |
---|
2587 | rkTinv(1,1) = 1.233523612685027760114769983066164d0 |
---|
2588 | rkTinv(1,2) = 1.423580134265707095505388133369554d0 |
---|
2589 | rkTinv(1,3) = .3946330125758354736049045150429624d0 |
---|
2590 | rkTinv(2,1) = -1.233523612685027760114769983066164d0 |
---|
2591 | rkTinv(2,2) = -1.423580134265707095505388133369554d0 |
---|
2592 | rkTinv(2,3) = .6053669874241645263950954849570376d0 |
---|
2593 | rkTinv(3,1) = -.1484438963257383124456490049673414d0 |
---|
2594 | rkTinv(3,2) = 2.038974794939896109682070471785315d0 |
---|
2595 | rkTinv(3,3) = -.544501292892686735299355831692542d-1 |
---|
2596 | |
---|
2597 | rkTinvAinv(1,1) = 4.487354449794728738538663081025420d0 |
---|
2598 | rkTinvAinv(1,2) = 5.178748573958397475446442544234494d0 |
---|
2599 | rkTinvAinv(1,3) = 1.435609490412123627047824222335563d0 |
---|
2600 | rkTinvAinv(2,1) = -2.854361287939276673073807031221493d0 |
---|
2601 | rkTinvAinv(2,2) = -1.003648660720543859000994063139137d+1 |
---|
2602 | rkTinvAinv(2,3) = 1.789135380979465422050817815017383d0 |
---|
2603 | rkTinvAinv(3,1) = -4.160768067752685525282947313530352d0 |
---|
2604 | rkTinvAinv(3,2) = 1.124128569859216916690209918405860d0 |
---|
2605 | rkTinvAinv(3,3) = 1.700644430961823796581896350418417d0 |
---|
2606 | |
---|
2607 | rkAinvT(1,1) = 1.543510591072668287198054583233180d0 |
---|
2608 | rkAinvT(1,2) = -2.460228411937788329157493833295004d0 |
---|
2609 | rkAinvT(1,3) = -.412906170450356277003910443520499d0 |
---|
2610 | rkAinvT(2,1) = .209519643211838264029272585946993d0 |
---|
2611 | rkAinvT(2,2) = 1.388545667194387164417459732995766d0 |
---|
2612 | rkAinvT(2,3) = 1.20339553005832004974976023130002d0 |
---|
2613 | rkAinvT(3,1) = 3.637834252744495732208418513577775d0 |
---|
2614 | rkAinvT(3,2) = 2.681082873627752133895790743211112d0 |
---|
2615 | rkAinvT(3,3) = -3.050430199247410569426377624787569d0 |
---|
2616 | |
---|
2617 | END SUBROUTINE Radau1A_Coefficients |
---|
2618 | |
---|
2619 | |
---|
2620 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2621 | END SUBROUTINE RungeKuttaADJ ! and all its internal procedures |
---|
2622 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2623 | |
---|
2624 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2625 | SUBROUTINE FUN_CHEM(T, V, FCT) |
---|
2626 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2627 | |
---|
2628 | USE KPP_ROOT_Parameters |
---|
2629 | USE KPP_ROOT_Global |
---|
2630 | USE KPP_ROOT_Function, ONLY: Fun |
---|
2631 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
2632 | |
---|
2633 | IMPLICIT NONE |
---|
2634 | |
---|
2635 | KPP_REAL :: V(NVAR), FCT(NVAR) |
---|
2636 | KPP_REAL :: T, Told |
---|
2637 | |
---|
2638 | Told = TIME |
---|
2639 | TIME = T |
---|
2640 | CALL Update_SUN() |
---|
2641 | CALL Update_RCONST() |
---|
2642 | CALL Update_PHOTO() |
---|
2643 | TIME = Told |
---|
2644 | |
---|
2645 | CALL Fun(V, FIX, RCONST, FCT) |
---|
2646 | |
---|
2647 | END SUBROUTINE FUN_CHEM |
---|
2648 | |
---|
2649 | |
---|
2650 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2651 | SUBROUTINE JAC_CHEM (T, V, JF) |
---|
2652 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2653 | |
---|
2654 | USE KPP_ROOT_Parameters |
---|
2655 | USE KPP_ROOT_Global |
---|
2656 | USE KPP_ROOT_JacobianSP |
---|
2657 | USE KPP_ROOT_Jacobian, ONLY: Jac_SP |
---|
2658 | USE KPP_ROOT_Rates, ONLY: Update_SUN, Update_RCONST, Update_PHOTO |
---|
2659 | |
---|
2660 | IMPLICIT NONE |
---|
2661 | |
---|
2662 | KPP_REAL :: V(NVAR), T , Told |
---|
2663 | #ifdef FULL_ALGEBRA |
---|
2664 | KPP_REAL :: JV(LU_NONZERO), JF(NVAR,NVAR) |
---|
2665 | INTEGER :: i, j |
---|
2666 | #else |
---|
2667 | KPP_REAL :: JF(LU_NONZERO) |
---|
2668 | #endif |
---|
2669 | |
---|
2670 | Told = TIME |
---|
2671 | TIME = T |
---|
2672 | CALL Update_SUN() |
---|
2673 | CALL Update_RCONST() |
---|
2674 | CALL Update_PHOTO() |
---|
2675 | TIME = Told |
---|
2676 | |
---|
2677 | #ifdef FULL_ALGEBRA |
---|
2678 | CALL Jac_SP(V, FIX, RCONST, JV) |
---|
2679 | DO j=1,NVAR |
---|
2680 | DO i=1,NVAR |
---|
2681 | JF(i,j) = 0.0d0 |
---|
2682 | END DO |
---|
2683 | END DO |
---|
2684 | DO i=1,LU_NONZERO |
---|
2685 | JF(LU_IROW(i),LU_ICOL(i)) = JV(i) |
---|
2686 | END DO |
---|
2687 | #else |
---|
2688 | CALL Jac_SP(V, FIX, RCONST, JF) |
---|
2689 | #endif |
---|
2690 | |
---|
2691 | END SUBROUTINE JAC_CHEM |
---|
2692 | |
---|
2693 | |
---|
2694 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2695 | |
---|
2696 | END MODULE KPP_ROOT_Integrator |
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