1 | MODULE KPP_ROOT_Integrator |
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2 | |
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3 | USE KPP_ROOT_Precision |
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4 | USE KPP_ROOT_Parameters |
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5 | USE KPP_ROOT_Global |
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6 | USE KPP_ROOT_Function |
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7 | USE KPP_ROOT_Jacobian |
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8 | USE KPP_ROOT_Hessian |
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9 | USE KPP_ROOT_LinearAlgebra |
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10 | USE KPP_ROOT_Rates |
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11 | |
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12 | IMPLICIT NONE |
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13 | PUBLIC |
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14 | SAVE |
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15 | !~~~> Statistics on the work performed by the Rosenbrock method |
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16 | INTEGER :: Nfun,Njac,Nstp,Nacc,Nrej,Ndec,Nsol,Nsng |
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17 | INTEGER, PARAMETER :: ifun=11, ijac=12, istp=13, & |
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18 | iacc=14, irej=15, idec=16, isol=17, & |
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19 | isng=18, itexit=11,ihexit=12 |
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20 | !~~~> Checkpoints in memory |
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21 | INTEGER, PARAMETER :: bufsize = 1500 |
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22 | INTEGER :: stack_ptr = 0 ! last written entry |
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23 | KPP_REAL, DIMENSION(:), POINTER :: buf_H, buf_T |
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24 | KPP_REAL, DIMENSION(:,:), POINTER :: buf_Y, buf_K |
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25 | KPP_REAL, DIMENSION(:,:), POINTER :: buf_Y_tlm, buf_K_tlm |
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26 | |
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27 | CONTAINS |
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28 | |
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29 | |
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30 | |
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31 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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32 | SUBROUTINE INTEGRATE_SOA( NSOA, Y, Y_tlm, Y_adj, Y_soa, TIN, TOUT, & |
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33 | AtolAdj, RtolAdj, ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U ) |
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34 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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35 | |
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36 | IMPLICIT NONE |
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37 | |
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38 | !~~~> NSOA - No. of vectors to multiply SOA with |
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39 | INTEGER :: NSOA |
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40 | !~~~> Y - Forward model variables |
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41 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
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42 | !~~~> Y_adj - Tangent linear variables |
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43 | KPP_REAL, INTENT(INOUT) :: Y_tlm(NVAR,NSOA) |
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44 | !~~~> Y_adj - First order adjoint |
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45 | KPP_REAL, INTENT(INOUT) :: Y_adj(NVAR) |
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46 | !~~~> Y_soa - Second order adjoint |
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47 | KPP_REAL, INTENT(INOUT) :: Y_soa(NVAR,NSOA) |
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48 | !~~~> |
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49 | KPP_REAL, INTENT(IN) :: TIN ! TIN - Start Time |
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50 | KPP_REAL, INTENT(IN) :: TOUT ! TOUT - End Time |
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51 | !~~~> Optional input parameters and statistics |
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52 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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53 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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54 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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55 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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56 | |
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57 | INTEGER N_stp, N_acc, N_rej, N_sng, IERR |
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58 | SAVE N_stp, N_acc, N_rej, N_sng |
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59 | INTEGER i |
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60 | KPP_REAL :: RCNTRL(20), RSTATUS(20) |
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61 | KPP_REAL :: AtolAdj(NVAR), RtolAdj(NVAR) |
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62 | INTEGER :: ICNTRL(20), ISTATUS(20) |
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63 | |
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64 | ICNTRL(1:20) = 0 |
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65 | RCNTRL(1:20) = 0.0_dp |
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66 | ISTATUS(1:20) = 0 |
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67 | RSTATUS(1:20) = 0.0_dp |
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68 | |
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69 | ICNTRL(1) = 0 ! 0 = non-autonomous, 1 = autonomous |
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70 | ICNTRL(2) = 1 ! 0 = scalar, 1 = vector tolerances |
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71 | RCNTRL(3) = STEPMIN ! starting step |
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72 | ICNTRL(4) = 5 ! choice of the method for forward and adjoint integration |
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73 | |
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74 | ! Tighter tolerances, especially atol, are needed for the full continuous adjoint |
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75 | ! (Atol on sensitivities is different than on concentrations) |
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76 | ! CADJ_ATOL(1:NVAR) = 1.0d-5 |
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77 | ! CADJ_RTOL(1:NVAR) = 1.0d-4 |
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78 | |
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79 | ! if optional parameters are given, and if they are >=0, |
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80 | ! then they overwrite default settings |
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81 | IF (PRESENT(ICNTRL_U)) THEN |
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82 | WHERE(ICNTRL_U(:) >= 0) ICNTRL(:) = ICNTRL_U(:) |
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83 | ENDIF |
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84 | IF (PRESENT(RCNTRL_U)) THEN |
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85 | WHERE(RCNTRL_U(:) >= 0) RCNTRL(:) = RCNTRL_U(:) |
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86 | ENDIF |
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87 | |
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88 | |
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89 | CALL RosenbrockSOA(NSOA, & |
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90 | Y, Y_tlm, Y_adj, Y_soa, & |
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91 | TIN,TOUT, & |
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92 | ATOL,RTOL, & |
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93 | Fun_Template,Jac_Template,Hess_Template, & |
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94 | RCNTRL,ICNTRL,RSTATUS,ISTATUS,IERR) |
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95 | |
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96 | |
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97 | ! N_stp = N_stp + ICNTRL(istp) |
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98 | ! N_acc = N_acc + ICNTRL(iacc) |
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99 | ! N_rej = N_rej + ICNTRL(irej) |
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100 | ! N_sng = N_sng + ICNTRL(isng) |
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101 | ! PRINT*,'Step=',N_stp,' Acc=',N_acc,' Rej=',N_rej, & |
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102 | ! ' Singular=',N_sng |
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103 | |
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104 | IF (IERR < 0) THEN |
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105 | print *,'RosenbrockSOA: Unsucessful step at T=', & |
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106 | TIN,' (IERR=',IERR,')' |
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107 | ENDIF |
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108 | |
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109 | STEPMIN = RCNTRL(ihexit) |
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110 | ! if optional parameters are given for output they to return information |
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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 | |
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114 | END SUBROUTINE INTEGRATE_SOA |
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115 | |
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116 | |
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117 | |
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118 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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119 | SUBROUTINE RosenbrockSOA( NSOA, & |
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120 | Y, Y_tlm, Y_adj, Y_soa, & |
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121 | Tstart,Tend, & |
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122 | AbsTol,RelTol, & |
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123 | ode_Fun,ode_Jac , ode_Hess, & |
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124 | RCNTRL,ICNTRL,RSTATUS,ISTATUS,IERR) |
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125 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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126 | ! |
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127 | ! ADJ = Adjoint of the Tangent Linear Model of a RosenbrockSOA Method |
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128 | ! |
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129 | ! Solves the system y'=F(t,y) using a RosenbrockSOA method defined by: |
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130 | ! |
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131 | ! G = 1/(H*gamma(1)) - ode_Jac(t0,Y0) |
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132 | ! T_i = t0 + Alpha(i)*H |
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133 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
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134 | ! G * K_i = ode_Fun( T_i, Y_i ) + \sum_{j=1}^S C(i,j)/H * K_j + |
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135 | ! gamma(i)*dF/dT(t0, Y0) |
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136 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
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137 | ! |
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138 | ! For details on RosenbrockSOA methods and their implementation consult: |
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139 | ! E. Hairer and G. Wanner |
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140 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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141 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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142 | ! The codes contained in the book inspired this implementation. |
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143 | ! |
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144 | ! (C) Adrian Sandu, August 2004 |
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145 | ! Virginia Polytechnic Institute and State University |
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146 | ! Contact: sandu@cs.vt.edu |
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147 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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148 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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149 | ! |
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150 | !~~~> INPUT ARGUMENTS: |
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151 | ! |
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152 | !- Y(NVAR) -> vector of initial conditions (at T=Tstart) |
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153 | ! NSOA -> dimension of linearized system, |
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154 | ! i.e. the number of sensitivity coefficients |
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155 | !- Y_adj(NVAR) -> vector of initial sensitivity conditions (at T=Tstart) |
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156 | !- [Tstart,Tend] = time range of integration |
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157 | ! (if Tstart>Tend the integration is performed backwards in time) |
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158 | !- RelTol, AbsTol = user precribed accuracy |
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159 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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160 | ! returns Ydot = Y' = F(T,Y) |
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161 | !- SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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162 | ! returns Jcb = dF/dY |
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163 | !- ICNTRL(1:10) = integer inputs parameters |
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164 | !- RCNTRL(1:10) = real inputs parameters |
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165 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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166 | ! |
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167 | !~~~> OUTPUT ARGUMENTS: |
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168 | ! |
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169 | !- Y(NVAR) -> vector of final states (at T->Tend) |
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170 | !- Y_adj(NVAR) -> vector of final sensitivities (at T=Tend) |
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171 | !- ICNTRL(11:20) -> integer output parameters |
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172 | !- RCNTRL(11:20) -> real output parameters |
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173 | !- IERR -> job status upon return |
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174 | ! - succes (positive value) or failure (negative value) - |
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175 | ! = 1 : Success |
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176 | ! = -1 : Improper value for maximal no of steps |
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177 | ! = -2 : Selected RosenbrockSOA method not implemented |
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178 | ! = -3 : Hmin/Hmax/Hstart must be positive |
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179 | ! = -4 : FacMin/FacMax/FacRej must be positive |
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180 | ! = -5 : Improper tolerance values |
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181 | ! = -6 : No of steps exceeds maximum bound |
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182 | ! = -7 : Step size too small |
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183 | ! = -8 : Matrix is repeatedly singular |
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184 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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185 | ! |
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186 | !~~~> INPUT PARAMETERS: |
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187 | ! |
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188 | ! Note: For input parameters equal to zero the default values of the |
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189 | ! corresponding variables are used. |
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190 | ! |
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191 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
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192 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
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193 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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194 | ! = 1: AbsTol, RelTol are scalars |
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195 | ! ICNTRL(3) -> maximum number of integration steps |
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196 | ! For ICNTRL(3)=0) the default value of 100000 is used |
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197 | ! |
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198 | ! ICNTRL(4) -> selection of a particular Rosenbrock method |
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199 | ! = 0 : default method is Rodas3 |
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200 | ! = 1 : method is Ros2 |
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201 | ! = 2 : method is Ros3 |
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202 | ! = 3 : method is Ros4 |
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203 | ! = 4 : method is Rodas3 |
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204 | ! = 5: method is Rodas4 |
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205 | ! |
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206 | ! ICNTRL(5) -> Type of adjoint algorithm |
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207 | ! = 0 : default is discrete adjoint ( of method ICNTRL(4) ) |
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208 | ! = 1 : no adjoint |
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209 | ! = 2 : discrete adjoint ( of method ICNTRL(4) ) |
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210 | ! = 3 : fully adaptive continuous adjoint ( with method ICNTRL(6) ) |
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211 | ! = 4 : simplified continuous adjoint ( with method ICNTRL(6) ) |
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212 | ! |
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213 | ! ICNTRL(6) -> selection of a particular Rosenbrock method for the |
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214 | ! continuous adjoint integration - for cts adjoint it |
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215 | ! can be different than the forward method ICNTRL(4) |
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216 | ! Note 1: to avoid interpolation errors (which can be huge!) |
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217 | ! it is recommended to use only ICNTRL(6) = 1 or 4 |
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218 | ! Note 2: the performance of the full continuous adjoint |
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219 | ! strongly depends on the forward solution accuracy Abs/RelTol |
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220 | ! |
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221 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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222 | ! It is strongly recommended to keep Hmin = ZERO |
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223 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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224 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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225 | ! |
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226 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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227 | ! RCNTRL(5) -> FacMin,upper bound on step increase factor (default=6) |
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228 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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229 | ! (default=0.1) |
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230 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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231 | ! than the predicted value (default=0.9) |
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232 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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233 | ! |
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234 | !~~~> OUTPUT PARAMETERS: |
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235 | ! |
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236 | ! Note: each call to RosenbrockSOA adds the corrent no. of fcn calls |
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237 | ! to previous value of ISTATUS(1), and similar for the other params. |
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238 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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239 | ! |
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240 | ! ISTATUS(1) = No. of function calls |
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241 | ! ISTATUS(2) = No. of jacobian calls |
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242 | ! ISTATUS(3) = No. of steps |
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243 | ! ISTATUS(4) = No. of accepted steps |
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244 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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245 | ! ISTATUS(6) = No. of LU decompositions |
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246 | ! ISTATUS(7) = No. of forward/backward substitutions |
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247 | ! ISTATUS(8) = No. of singular matrix decompositions |
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248 | ! |
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249 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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250 | ! computed Y upon return |
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251 | ! RSTATUS(2) -> Hexit, last accepted step before exit |
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252 | ! For multiple restarts, use Hexit as Hstart in the following run |
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253 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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254 | |
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255 | IMPLICIT NONE |
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256 | |
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257 | !~~~> Arguments |
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258 | INTEGER, INTENT(IN) :: NSOA |
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259 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
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260 | KPP_REAL, INTENT(INOUT) :: Y_tlm(NVAR,NSOA) |
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261 | KPP_REAL, INTENT(INOUT) :: Y_adj(NVAR) |
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262 | KPP_REAL, INTENT(INOUT) :: Y_soa(NVAR,NSOA) |
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263 | KPP_REAL, INTENT(IN) :: Tstart, Tend |
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264 | KPP_REAL, INTENT(IN) :: AbsTol(NVAR),RelTol(NVAR) |
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265 | INTEGER, INTENT(IN) :: ICNTRL(20) |
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266 | KPP_REAL, INTENT(IN) :: RCNTRL(20) |
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267 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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268 | KPP_REAL, INTENT(INOUT) :: RSTATUS(20) |
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269 | INTEGER, INTENT(OUT) :: IERR |
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270 | !~~~> The method parameters |
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271 | INTEGER, PARAMETER :: Smax = 6 |
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272 | INTEGER :: Method, ros_S |
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273 | KPP_REAL, DIMENSION(Smax) :: ros_M, ros_E, ros_Alpha, ros_Gamma |
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274 | KPP_REAL, DIMENSION(Smax*(Smax-1)/2) :: ros_A, ros_C |
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275 | KPP_REAL :: ros_ELO |
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276 | LOGICAL, DIMENSION(Smax) :: ros_NewF |
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277 | CHARACTER(LEN=12) :: ros_Name |
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278 | !~~~> Local variables |
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279 | KPP_REAL :: Roundoff, FacMin, FacMax, FacRej, FacSafe |
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280 | KPP_REAL :: Hmin, Hmax, Hstart, Hexit |
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281 | KPP_REAL :: T |
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282 | INTEGER :: i, UplimTol, Max_no_steps |
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283 | LOGICAL :: Autonomous, VectorTol |
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284 | !~~~> Parameters |
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285 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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286 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
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287 | !~~~> Functions |
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288 | EXTERNAL ode_Fun, ode_Jac, ode_Hess |
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289 | |
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290 | !~~~> Initialize statistics |
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291 | Nfun = ISTATUS(ifun) |
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292 | Njac = ISTATUS(ijac) |
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293 | Nstp = ISTATUS(istp) |
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294 | Nacc = ISTATUS(iacc) |
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295 | Nrej = ISTATUS(irej) |
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296 | Ndec = ISTATUS(idec) |
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297 | Nsol = ISTATUS(isol) |
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298 | Nsng = ISTATUS(isng) |
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299 | |
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300 | !~~~> Autonomous or time dependent ODE. Default is time dependent. |
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301 | Autonomous = .NOT.(ICNTRL(1) == 0) |
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302 | |
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303 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) |
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304 | ! the code uses AbsTol(1) and RelTol(1) |
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305 | ! For Vector tolerances (ICNTRL(2) == 0) |
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306 | ! the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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307 | IF (ICNTRL(2) == 0) THEN |
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308 | VectorTol = .TRUE. |
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309 | UplimTol = NVAR |
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310 | ELSE |
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311 | VectorTol = .FALSE. |
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312 | UplimTol = 1 |
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313 | END IF |
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314 | |
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315 | !~~~> The maximum number of steps admitted |
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316 | IF (ICNTRL(3) == 0) THEN |
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317 | Max_no_steps = bufsize - 1 |
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318 | ELSEIF (Max_no_steps > 0) THEN |
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319 | Max_no_steps=ICNTRL(3) |
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320 | ELSE |
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321 | PRINT * ,'User-selected max no. of steps: ICNTRL(3)=',ICNTRL(3) |
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322 | CALL ros_ErrorMsg(-1,Tstart,ZERO,IERR) |
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323 | RETURN |
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324 | END IF |
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325 | |
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326 | !~~~> The particular Rosenbrock method chosen |
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327 | IF (ICNTRL(4) == 0) THEN |
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328 | Method = 5 |
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329 | ELSEIF ( (ICNTRL(4) >= 1).AND.(ICNTRL(4) <= 5) ) THEN |
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330 | Method = ICNTRL(4) |
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331 | ELSE |
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332 | PRINT * , 'User-selected Rosenbrock method: ICNTRL(4)=', Method |
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333 | CALL ros_ErrorMsg(-2,Tstart,ZERO,IERR) |
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334 | RETURN |
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335 | END IF |
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336 | |
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337 | |
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338 | !~~~> Unit roundoff (1+Roundoff>1) |
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339 | Roundoff = WLAMCH('E') |
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340 | |
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341 | !~~~> Lower bound on the step size: (positive value) |
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342 | IF (RCNTRL(1) == ZERO) THEN |
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343 | Hmin = ZERO |
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344 | ELSEIF (RCNTRL(1) > ZERO) THEN |
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345 | Hmin = RCNTRL(1) |
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346 | ELSE |
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347 | PRINT * , 'User-selected Hmin: RCNTRL(1)=', RCNTRL(1) |
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348 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
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349 | RETURN |
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350 | END IF |
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351 | !~~~> Upper bound on the step size: (positive value) |
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352 | IF (RCNTRL(2) == ZERO) THEN |
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353 | Hmax = ABS(Tend-Tstart) |
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354 | ELSEIF (RCNTRL(2) > ZERO) THEN |
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355 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tend-Tstart)) |
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356 | ELSE |
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357 | PRINT * , 'User-selected Hmax: RCNTRL(2)=', RCNTRL(2) |
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358 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
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359 | RETURN |
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360 | END IF |
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361 | !~~~> Starting step size: (positive value) |
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362 | IF (RCNTRL(3) == ZERO) THEN |
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363 | Hstart = MAX(Hmin,DeltaMin) |
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364 | ELSEIF (RCNTRL(3) > ZERO) THEN |
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365 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tend-Tstart)) |
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366 | ELSE |
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367 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
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368 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
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369 | RETURN |
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370 | END IF |
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371 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax |
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372 | IF (RCNTRL(4) == ZERO) THEN |
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373 | FacMin = 0.2d0 |
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374 | ELSEIF (RCNTRL(4) > ZERO) THEN |
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375 | FacMin = RCNTRL(4) |
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376 | ELSE |
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377 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
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378 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
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379 | RETURN |
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380 | END IF |
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381 | IF (RCNTRL(5) == ZERO) THEN |
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382 | FacMax = 6.0d0 |
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383 | ELSEIF (RCNTRL(5) > ZERO) THEN |
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384 | FacMax = RCNTRL(5) |
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385 | ELSE |
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386 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
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387 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
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388 | RETURN |
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389 | END IF |
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390 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
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391 | IF (RCNTRL(6) == ZERO) THEN |
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392 | FacRej = 0.1d0 |
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393 | ELSEIF (RCNTRL(6) > ZERO) THEN |
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394 | FacRej = RCNTRL(6) |
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395 | ELSE |
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396 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
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397 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
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398 | RETURN |
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399 | END IF |
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400 | !~~~> FacSafe: Safety Factor in the computation of new step size |
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401 | IF (RCNTRL(7) == ZERO) THEN |
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402 | FacSafe = 0.9d0 |
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403 | ELSEIF (RCNTRL(7) > ZERO) THEN |
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404 | FacSafe = RCNTRL(7) |
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405 | ELSE |
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406 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
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407 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
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408 | RETURN |
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409 | END IF |
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410 | !~~~> Check if tolerances are reasonable |
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411 | DO i=1,UplimTol |
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412 | IF ( (AbsTol(i) <= ZERO) .OR. (RelTol(i) <= 10.d0*Roundoff) & |
---|
413 | .OR. (RelTol(i) >= 1.0d0) ) THEN |
---|
414 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
---|
415 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
---|
416 | CALL ros_ErrorMsg(-5,Tstart,ZERO,IERR) |
---|
417 | RETURN |
---|
418 | END IF |
---|
419 | END DO |
---|
420 | |
---|
421 | |
---|
422 | !~~~> Initialize the particular RosenbrockSOA method |
---|
423 | SELECT CASE (Method) |
---|
424 | CASE (1) |
---|
425 | CALL Ros2(ros_S, ros_A, ros_C, ros_M, ros_E, & |
---|
426 | ros_Alpha, ros_Gamma, ros_NewF, ros_ELO, ros_Name) |
---|
427 | CASE (2) |
---|
428 | CALL Ros3(ros_S, ros_A, ros_C, ros_M, ros_E, & |
---|
429 | ros_Alpha, ros_Gamma, ros_NewF, ros_ELO, ros_Name) |
---|
430 | CASE (3) |
---|
431 | CALL Ros4(ros_S, ros_A, ros_C, ros_M, ros_E, & |
---|
432 | ros_Alpha, ros_Gamma, ros_NewF, ros_ELO, ros_Name) |
---|
433 | CASE (4) |
---|
434 | CALL Rodas3(ros_S, ros_A, ros_C, ros_M, ros_E, & |
---|
435 | ros_Alpha, ros_Gamma, ros_NewF, ros_ELO, ros_Name) |
---|
436 | CASE (5) |
---|
437 | CALL Rodas4(ros_S, ros_A, ros_C, ros_M, ros_E, & |
---|
438 | ros_Alpha, ros_Gamma, ros_NewF, ros_ELO, ros_Name) |
---|
439 | CASE DEFAULT |
---|
440 | PRINT * , 'Unknown Rosenbrock method: ICNTRL(4)=', Method |
---|
441 | CALL ros_ErrorMsg(-2,Tstart,ZERO,IERR) |
---|
442 | RETURN |
---|
443 | END SELECT |
---|
444 | |
---|
445 | !~~~> Allocate checkpoint space or open checkpoint files |
---|
446 | CALL ros_AllocateDBuffers( ros_S ) |
---|
447 | |
---|
448 | !~~~> Forward Rosenbrock and TLM integration |
---|
449 | CALL ros_TlmInt (NSOA, Y, Y_tlm, & |
---|
450 | Tstart, Tend, T, & |
---|
451 | AbsTol, RelTol, & |
---|
452 | ode_Fun, ode_Jac, ode_Hess, & |
---|
453 | !~~~> Rosenbrock method coefficients |
---|
454 | ros_S, ros_M, ros_E, ros_A, ros_C, & |
---|
455 | ros_Alpha, ros_Gamma, ros_ELO, ros_NewF, & |
---|
456 | !~~~> Integration parameters |
---|
457 | Autonomous, VectorTol, Max_no_steps, & |
---|
458 | Roundoff, Hmin, Hmax, Hstart, Hexit, & |
---|
459 | FacMin, FacMax, FacRej, FacSafe, & |
---|
460 | !~~~> Error indicator |
---|
461 | IERR ) |
---|
462 | |
---|
463 | PRINT*,'FORWARD STATISTICS' |
---|
464 | PRINT*,'Step=',Nstp,' Acc=',Nacc, & |
---|
465 | ' Rej=',Nrej, ' Singular=',Nsng |
---|
466 | Nstp = 0 |
---|
467 | Nacc = 0 |
---|
468 | Nrej = 0 |
---|
469 | Nsng = 0 |
---|
470 | |
---|
471 | !~~~> If Forward integration failed return |
---|
472 | IF (IERR<0) RETURN |
---|
473 | |
---|
474 | !~~~> Backward ADJ and SOADJ Rosenbrock integration |
---|
475 | CALL ros_SoaInt ( & |
---|
476 | NSOA, Y_adj, Y_soa, & |
---|
477 | Tstart, Tend, T, & |
---|
478 | AbsTol, RelTol, & |
---|
479 | ode_Fun, ode_Jac, ode_Hess, & |
---|
480 | !~~~> RosenbrockSOA method coefficients |
---|
481 | ros_S, ros_M, ros_E, ros_A, ros_C, & |
---|
482 | ros_Alpha, ros_Gamma, ros_ELO, ros_NewF, & |
---|
483 | !~~~> Integration parameters |
---|
484 | Autonomous, VectorTol, Max_no_steps, & |
---|
485 | Roundoff, Hmin, Hmax, Hstart, & |
---|
486 | FacMin, FacMax, FacRej, FacSafe, & |
---|
487 | !~~~> Error indicator |
---|
488 | IERR ) |
---|
489 | |
---|
490 | |
---|
491 | PRINT*,'ADJOINT STATISTICS' |
---|
492 | PRINT*,'Step=',Nstp,' Acc=',Nacc, & |
---|
493 | ' Rej=',Nrej, ' Singular=',Nsng |
---|
494 | |
---|
495 | !~~~> Free checkpoint space or close checkpoint files |
---|
496 | CALL ros_FreeDBuffers |
---|
497 | |
---|
498 | !~~~> Collect run statistics |
---|
499 | ISTATUS(ifun) = Nfun |
---|
500 | ISTATUS(ijac) = Njac |
---|
501 | ISTATUS(istp) = Nstp |
---|
502 | ISTATUS(iacc) = Nacc |
---|
503 | ISTATUS(irej) = Nrej |
---|
504 | ISTATUS(idec) = Ndec |
---|
505 | ISTATUS(isol) = Nsol |
---|
506 | ISTATUS(isng) = Nsng |
---|
507 | !~~~> Last T and H |
---|
508 | RSTATUS(itexit) = T |
---|
509 | RSTATUS(ihexit) = Hexit |
---|
510 | |
---|
511 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
512 | END SUBROUTINE RosenbrockSOA |
---|
513 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
514 | |
---|
515 | |
---|
516 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
517 | SUBROUTINE ros_ErrorMsg(Code,T,H,IERR) |
---|
518 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
519 | ! Handles all error messages |
---|
520 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
521 | |
---|
522 | KPP_REAL, INTENT(IN) :: T, H |
---|
523 | INTEGER, INTENT(IN) :: Code |
---|
524 | INTEGER, INTENT(OUT) :: IERR |
---|
525 | |
---|
526 | IERR = Code |
---|
527 | PRINT * , & |
---|
528 | 'Forced exit from RosenbrockSOA due to the following error:' |
---|
529 | |
---|
530 | SELECT CASE (Code) |
---|
531 | CASE (-1) |
---|
532 | PRINT * , '--> Improper value for maximal no of steps' |
---|
533 | CASE (-2) |
---|
534 | PRINT * , '--> Selected RosenbrockSOA method not implemented' |
---|
535 | CASE (-3) |
---|
536 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
537 | CASE (-4) |
---|
538 | PRINT * , '--> FacMin/FacMax/FacRej must be positive' |
---|
539 | CASE (-5) |
---|
540 | PRINT * , '--> Improper tolerance values' |
---|
541 | CASE (-6) |
---|
542 | PRINT * , '--> No of steps exceeds maximum bound' |
---|
543 | CASE (-7) |
---|
544 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
545 | ' or H < Roundoff' |
---|
546 | CASE (-8) |
---|
547 | PRINT * , '--> Matrix is repeatedly singular' |
---|
548 | CASE (-9) |
---|
549 | PRINT * , '--> Improper type of adjoint selected' |
---|
550 | CASE DEFAULT |
---|
551 | PRINT *, 'Unknown Error code: ', Code |
---|
552 | END SELECT |
---|
553 | |
---|
554 | PRINT *, "T=", T, "and H=", H |
---|
555 | |
---|
556 | END SUBROUTINE ros_ErrorMsg |
---|
557 | |
---|
558 | |
---|
559 | |
---|
560 | |
---|
561 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
562 | SUBROUTINE ros_TlmInt (NSOA, Y, Y_tlm, & |
---|
563 | Tstart, Tend, T, & |
---|
564 | AbsTol, RelTol, & |
---|
565 | ode_Fun, ode_Jac, ode_Hess, & |
---|
566 | !~~~> Rosenbrock method coefficients |
---|
567 | ros_S, ros_M, ros_E, ros_A, ros_C, & |
---|
568 | ros_Alpha, ros_Gamma, ros_ELO, ros_NewF, & |
---|
569 | !~~~> Integration parameters |
---|
570 | Autonomous, VectorTol, Max_no_steps, & |
---|
571 | Roundoff, Hmin, Hmax, Hstart, Hexit, & |
---|
572 | FacMin, FacMax, FacRej, FacSafe, & |
---|
573 | !~~~> Error indicator |
---|
574 | IERR ) |
---|
575 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
576 | ! Template for the implementation of a generic Rosenbrock method |
---|
577 | ! defined by ros_S (no of stages) |
---|
578 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
579 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
580 | |
---|
581 | IMPLICIT NONE |
---|
582 | |
---|
583 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
584 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
---|
585 | !~~~> Input: Number of sensitivity coefficients |
---|
586 | INTEGER, INTENT(IN) :: NSOA |
---|
587 | !~~~> Input: the initial sensitivites at Tstart; Output: the sensitivities at T |
---|
588 | KPP_REAL, INTENT(INOUT) :: Y_tlm(NVAR,NSOA) |
---|
589 | !~~~> Input: integration interval |
---|
590 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
591 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
592 | KPP_REAL, INTENT(OUT) :: T |
---|
593 | !~~~> Input: tolerances |
---|
594 | KPP_REAL, INTENT(IN) :: AbsTol(NVAR), RelTol(NVAR) |
---|
595 | !~~~> Input: ode function and its Jacobian |
---|
596 | EXTERNAL ode_Fun, ode_Jac, ode_Hess |
---|
597 | !~~~> Input: The Rosenbrock method parameters |
---|
598 | INTEGER, INTENT(IN) :: ros_S |
---|
599 | KPP_REAL, INTENT(IN) :: ros_M(ros_S), ros_E(ros_S), & |
---|
600 | ros_Alpha(ros_S), ros_A(ros_S*(ros_S-1)/2), & |
---|
601 | ros_Gamma(ros_S), ros_C(ros_S*(ros_S-1)/2), ros_ELO |
---|
602 | LOGICAL, INTENT(IN) :: ros_NewF(ros_S) |
---|
603 | !~~~> Input: integration parameters |
---|
604 | LOGICAL, INTENT(IN) :: Autonomous, VectorTol |
---|
605 | KPP_REAL, INTENT(IN) :: Hstart, Hmin, Hmax |
---|
606 | INTEGER, INTENT(IN) :: Max_no_steps |
---|
607 | KPP_REAL, INTENT(IN) :: Roundoff, FacMin, FacMax, FacRej, FacSafe |
---|
608 | !~~~> Output: last accepted step |
---|
609 | KPP_REAL, INTENT(OUT) :: Hexit |
---|
610 | !~~~> Output: Error indicator |
---|
611 | INTEGER, INTENT(OUT) :: IERR |
---|
612 | ! ~~~~ Local variables |
---|
613 | KPP_REAL :: Ystage(NVAR*ros_S), Fcn0(NVAR), Fcn(NVAR) |
---|
614 | KPP_REAL :: K(NVAR*ros_S), Tmp(NVAR) |
---|
615 | KPP_REAL :: Ystage_tlm(NVAR*ros_S,NSOA), Fcn0_tlm(NVAR,NSOA), Fcn_tlm(NVAR,NSOA) |
---|
616 | KPP_REAL :: K_tlm(NVAR*ros_S,NSOA) |
---|
617 | KPP_REAL :: Hes0(NHESS) |
---|
618 | KPP_REAL :: dFdT(NVAR), dJdT(LU_NONZERO) |
---|
619 | KPP_REAL :: Jac0(LU_NONZERO), Jac(LU_NONZERO), Ghimj(LU_NONZERO) |
---|
620 | KPP_REAL :: H, Hnew, HC, HG, Fac, Tau |
---|
621 | KPP_REAL :: Err, Yerr(NVAR), Ynew(NVAR), Ynew_tlm(NVAR,NSOA) |
---|
622 | INTEGER :: Pivot(NVAR), Direction, ioffset, joffset, j, istage, mtlm |
---|
623 | LOGICAL :: RejectLastH, RejectMoreH, Singular |
---|
624 | !~~~> Local parameters |
---|
625 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
626 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
---|
627 | !~~~> Locally called functions |
---|
628 | ! KPP_REAL WLAMCH |
---|
629 | ! EXTERNAL WLAMCH |
---|
630 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
631 | |
---|
632 | |
---|
633 | !~~~> Initial preparations |
---|
634 | T = Tstart |
---|
635 | Hexit = 0.0_dp |
---|
636 | H = MIN(Hstart,Hmax) |
---|
637 | IF (ABS(H) <= 10.D0*Roundoff) H = DeltaMin |
---|
638 | |
---|
639 | IF (Tend >= Tstart) THEN |
---|
640 | Direction = +1 |
---|
641 | ELSE |
---|
642 | Direction = -1 |
---|
643 | END IF |
---|
644 | |
---|
645 | RejectLastH=.FALSE. |
---|
646 | RejectMoreH=.FALSE. |
---|
647 | |
---|
648 | !~~~> Time loop begins below |
---|
649 | |
---|
650 | TimeLoop: DO WHILE ( (Direction > 0).AND.((T-Tend)+Roundoff <= ZERO) & |
---|
651 | .OR. (Direction < 0).AND.((Tend-T)+Roundoff <= ZERO) ) |
---|
652 | |
---|
653 | IF ( Nstp > Max_no_steps ) THEN ! Too many steps |
---|
654 | CALL ros_ErrorMsg(-6,T,H,IERR) |
---|
655 | RETURN |
---|
656 | END IF |
---|
657 | IF ( ((T+0.1d0*H) == T).OR.(H <= Roundoff) ) THEN ! Step size too small |
---|
658 | CALL ros_ErrorMsg(-7,T,H,IERR) |
---|
659 | RETURN |
---|
660 | END IF |
---|
661 | |
---|
662 | !~~~> Limit H if necessary to avoid going beyond Tend |
---|
663 | Hexit = H |
---|
664 | H = MIN(H,ABS(Tend-T)) |
---|
665 | |
---|
666 | !~~~> Compute the function at current time |
---|
667 | CALL ode_Fun(T,Y,Fcn0) |
---|
668 | |
---|
669 | !~~~> Compute the Jacobian at current time |
---|
670 | CALL ode_Jac(T,Y,Jac0) |
---|
671 | |
---|
672 | !~~~> Compute the Hessian at current time |
---|
673 | CALL ode_Hess(T,Y,Hes0) |
---|
674 | |
---|
675 | !~~~> Compute the TLM function at current time |
---|
676 | DO mtlm = 1, NSOA |
---|
677 | CALL Jac_SP_Vec ( Jac0, Y_tlm(1:NVAR,mtlm), Fcn0_tlm(1:NVAR,mtlm) ) |
---|
678 | END DO |
---|
679 | |
---|
680 | !~~~> Compute the function and Jacobian derivatives with respect to T |
---|
681 | IF (.NOT.Autonomous) THEN |
---|
682 | CALL ros_FunTimeDerivative ( T, Roundoff, Y, & |
---|
683 | Fcn0, ode_Fun, dFdT ) |
---|
684 | CALL ros_JacTimeDerivative ( T, Roundoff, Y, & |
---|
685 | Jac0, ode_Jac, dJdT ) |
---|
686 | END IF |
---|
687 | |
---|
688 | !~~~> Repeat step calculation until current step accepted |
---|
689 | UntilAccepted: DO |
---|
690 | |
---|
691 | CALL ros_PrepareMatrix(H,Direction,ros_Gamma(1),& |
---|
692 | Jac0,Ghimj,Pivot,Singular) |
---|
693 | IF (Singular) THEN ! More than 5 consecutive failed decompositions |
---|
694 | CALL ros_ErrorMsg(-8,T,H,IERR) |
---|
695 | RETURN |
---|
696 | END IF |
---|
697 | |
---|
698 | !~~~> Compute the stages |
---|
699 | Stage: DO istage = 1, ros_S |
---|
700 | |
---|
701 | ! Current istage vector is K(ioffset+1:ioffset+NVAR:ioffset+1+NVAR-1) |
---|
702 | ioffset = NVAR*(istage-1) |
---|
703 | |
---|
704 | ! For the 1st istage the function has been computed previously |
---|
705 | IF ( istage == 1 ) THEN |
---|
706 | CALL WCOPY(NVAR,Y,1,Ystage(ioffset+1:ioffset+NVAR),1) |
---|
707 | DO mtlm=1,NSOA |
---|
708 | CALL WCOPY(NVAR,Y_tlm(1:NVAR,mtlm),1,Ystage_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
709 | END DO |
---|
710 | CALL WCOPY(NVAR,Fcn0,1,Fcn,1) |
---|
711 | CALL WCOPY(NVAR*NSOA,Fcn0_tlm,1,Fcn_tlm,1) |
---|
712 | ! istage>1 and a new function evaluation is needed at the current istage |
---|
713 | ELSEIF ( ros_NewF(istage) ) THEN |
---|
714 | CALL WCOPY(NVAR,Y,1,Ystage(ioffset+1:ioffset+NVAR),1) |
---|
715 | DO mtlm=1,NSOA |
---|
716 | CALL WCOPY(NVAR,Y_tlm(1:NVAR,mtlm),1,Ystage_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
717 | END DO |
---|
718 | DO j = 1, istage-1 |
---|
719 | joffset = NVAR*(j-1) |
---|
720 | CALL WAXPY(NVAR,ros_A((istage-1)*(istage-2)/2+j), & |
---|
721 | K(joffset+1:joffset+NVAR),1,Ystage(ioffset+1:ioffset+NVAR),1) |
---|
722 | DO mtlm=1,NSOA |
---|
723 | CALL WAXPY(NVAR,ros_A((istage-1)*(istage-2)/2+j), & |
---|
724 | K_tlm(joffset+1:joffset+NVAR,mtlm),1,Ystage_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
725 | END DO |
---|
726 | END DO |
---|
727 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
728 | CALL ode_Fun(Tau,Ystage(ioffset+1:ioffset+NVAR),Fcn) |
---|
729 | CALL ode_Jac(Tau,Ystage(ioffset+1:ioffset+NVAR),Jac) |
---|
730 | DO mtlm=1,NSOA |
---|
731 | CALL Jac_SP_Vec ( Jac, Ystage_tlm(ioffset+1:ioffset+NVAR,mtlm), Fcn_tlm(1:NVAR,mtlm) ) |
---|
732 | END DO |
---|
733 | END IF ! if istage == 1 elseif ros_NewF(istage) |
---|
734 | |
---|
735 | CALL WCOPY(NVAR,Fcn,1,K(ioffset+1:ioffset+NVAR),1) |
---|
736 | DO mtlm=1,NSOA |
---|
737 | CALL WCOPY(NVAR,Fcn_tlm(1:NVAR,mtlm),1,K_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
738 | END DO |
---|
739 | DO j = 1, istage-1 |
---|
740 | HC = ros_C((istage-1)*(istage-2)/2+j)/(Direction*H) |
---|
741 | CALL WAXPY(NVAR,HC,K(NVAR*(j-1)+1:NVAR*j),1,K(ioffset+1:ioffset+NVAR),1) |
---|
742 | DO mtlm=1,NSOA |
---|
743 | CALL WAXPY(NVAR,HC,K_tlm(NVAR*(j-1)+1:NVAR*j,mtlm),1,K_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
744 | END DO |
---|
745 | END DO |
---|
746 | IF ((.NOT. Autonomous).AND.(ros_Gamma(istage).NE.ZERO)) THEN |
---|
747 | HG = Direction*H*ros_Gamma(istage) |
---|
748 | CALL WAXPY(NVAR,HG,dFdT,1,K(ioffset+1:ioffset+NVAR),1) |
---|
749 | DO mtlm=1,NSOA |
---|
750 | CALL Jac_SP_Vec ( dJdT, Ystage_tlm(ioffset+1:ioffset+NVAR,mtlm), Fcn_tlm(1:NVAR,mtlm) ) |
---|
751 | CALL WAXPY(NVAR,HG,Fcn_tlm(1:NVAR,mtlm),1,K_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
752 | END DO |
---|
753 | END IF |
---|
754 | CALL ros_Solve('N', Ghimj, Pivot, K(ioffset+1:ioffset+NVAR)) |
---|
755 | DO mtlm=1,NSOA |
---|
756 | CALL Hess_Vec ( Hes0, K(ioffset+1:ioffset+NVAR), Y_tlm(1:NVAR,mtlm), Tmp ) |
---|
757 | CALL WAXPY(NVAR,ONE,Tmp,1,K_tlm(ioffset+1:ioffset+NVAR,mtlm),1) |
---|
758 | CALL ros_Solve('N', Ghimj, Pivot, K_tlm(ioffset+1:ioffset+NVAR,mtlm)) |
---|
759 | END DO |
---|
760 | |
---|
761 | END DO Stage |
---|
762 | |
---|
763 | |
---|
764 | !~~~> Compute the new solution |
---|
765 | CALL WCOPY(NVAR,Y,1,Ynew,1) |
---|
766 | DO j=1,ros_S |
---|
767 | CALL WAXPY(NVAR,ros_M(j),K(NVAR*(j-1)+1:NVAR*j),1,Ynew,1) |
---|
768 | END DO |
---|
769 | DO mtlm=1,NSOA |
---|
770 | CALL WCOPY(NVAR,Y_tlm(1:NVAR,mtlm),1,Ynew_tlm(1:NVAR,mtlm),1) |
---|
771 | DO j=1,ros_S |
---|
772 | joffset = NVAR*(j-1) |
---|
773 | CALL WAXPY(NVAR,ros_M(j),K_tlm(joffset+1:joffset+NVAR,mtlm),1,Ynew_tlm(1:NVAR,mtlm),1) |
---|
774 | END DO |
---|
775 | END DO |
---|
776 | |
---|
777 | !~~~> Compute the error estimation |
---|
778 | CALL WSCAL(NVAR,ZERO,Yerr,1) |
---|
779 | DO j=1,ros_S |
---|
780 | CALL WAXPY(NVAR,ros_E(j),K(NVAR*(j-1)+1:NVAR*j),1,Yerr,1) |
---|
781 | END DO |
---|
782 | Err = ros_ErrorNorm ( Y, Ynew, Yerr, AbsTol, RelTol, VectorTol ) |
---|
783 | |
---|
784 | !~~~> New step size is bounded by FacMin <= Hnew/H <= FacMax |
---|
785 | Fac = MIN(FacMax,MAX(FacMin,FacSafe/Err**(ONE/ros_ELO))) |
---|
786 | Hnew = H*Fac |
---|
787 | |
---|
788 | !~~~> Check the error magnitude and adjust step size |
---|
789 | Nstp = Nstp+1 |
---|
790 | IF ( (Err <= ONE).OR.(H <= Hmin) ) THEN !~~~> Accept step |
---|
791 | Nacc = Nacc+1 |
---|
792 | !~~~> Checkpoints for stage values and vectors |
---|
793 | CALL ros_DPush( ros_S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
---|
794 | !~~~> Accept new solution, etc. |
---|
795 | CALL WCOPY(NVAR,Ynew,1,Y,1) |
---|
796 | CALL WCOPY(NVAR*NSOA,Ynew_tlm,1,Y_tlm,1) |
---|
797 | T = T + Direction*H |
---|
798 | Hnew = MAX(Hmin,MIN(Hnew,Hmax)) |
---|
799 | IF (RejectLastH) THEN ! No step size increase after a rejected step |
---|
800 | Hnew = MIN(Hnew,H) |
---|
801 | END IF |
---|
802 | RejectLastH = .FALSE. |
---|
803 | RejectMoreH = .FALSE. |
---|
804 | H = Hnew |
---|
805 | EXIT UntilAccepted ! EXIT THE LOOP: WHILE STEP NOT ACCEPTED |
---|
806 | ELSE !~~~> Reject step |
---|
807 | IF (RejectMoreH) THEN |
---|
808 | Hnew = H*FacRej |
---|
809 | END IF |
---|
810 | RejectMoreH = RejectLastH |
---|
811 | RejectLastH = .TRUE. |
---|
812 | H = Hnew |
---|
813 | IF (Nacc >= 1) THEN |
---|
814 | Nrej = Nrej+1 |
---|
815 | END IF |
---|
816 | END IF ! Err <= 1 |
---|
817 | |
---|
818 | END DO UntilAccepted |
---|
819 | |
---|
820 | END DO TimeLoop |
---|
821 | |
---|
822 | !~~~> Succesful exit |
---|
823 | IERR = 1 !~~~> The integration was successful |
---|
824 | |
---|
825 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
826 | END SUBROUTINE ros_TlmInt |
---|
827 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
828 | |
---|
829 | |
---|
830 | |
---|
831 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
832 | SUBROUTINE ros_SoaInt ( & |
---|
833 | NSOA, Lambda, Sigma, & |
---|
834 | Tstart, Tend, T, & |
---|
835 | AbsTol, RelTol, & |
---|
836 | ode_Fun, ode_Jac, ode_Hess, & |
---|
837 | !~~~> RosenbrockSOA method coefficients |
---|
838 | ros_S, ros_M, ros_E, ros_A, ros_C, & |
---|
839 | ros_Alpha, ros_Gamma, ros_ELO, ros_NewF, & |
---|
840 | !~~~> Integration parameters |
---|
841 | Autonomous, VectorTol, Max_no_steps, & |
---|
842 | Roundoff, Hmin, Hmax, Hstart, & |
---|
843 | FacMin, FacMax, FacRej, FacSafe, & |
---|
844 | !~~~> Error indicator |
---|
845 | IERR ) |
---|
846 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
847 | ! Template for the implementation of a generic RosenbrockSOA method |
---|
848 | ! defined by ros_S (no of stages) |
---|
849 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
850 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
851 | |
---|
852 | IMPLICIT NONE |
---|
853 | |
---|
854 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
855 | INTEGER, INTENT(IN) :: NSOA |
---|
856 | !~~~> First order adjoint |
---|
857 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR) |
---|
858 | !~~~> Second order adjoint |
---|
859 | KPP_REAL, INTENT(INOUT) :: Sigma(NVAR,NSOA) |
---|
860 | !~~~> Input: integration interval |
---|
861 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
862 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
863 | KPP_REAL, INTENT(OUT) :: T |
---|
864 | !~~~> Input: tolerances |
---|
865 | KPP_REAL, INTENT(IN) :: AbsTol(NVAR), RelTol(NVAR) |
---|
866 | !~~~> Input: ode function and its Jacobian |
---|
867 | EXTERNAL ode_Fun, ode_Jac, ode_Hess |
---|
868 | !~~~> Input: The RosenbrockSOA method parameters |
---|
869 | INTEGER, INTENT(IN) :: ros_S |
---|
870 | KPP_REAL, INTENT(IN) :: ros_M(ros_S), ros_E(ros_S), & |
---|
871 | ros_Alpha(ros_S), ros_A(ros_S*(ros_S-1)/2), & |
---|
872 | ros_Gamma(ros_S), ros_C(ros_S*(ros_S-1)/2), ros_ELO |
---|
873 | LOGICAL, INTENT(IN) :: ros_NewF(ros_S) |
---|
874 | !~~~> Input: integration parameters |
---|
875 | LOGICAL, INTENT(IN) :: Autonomous, VectorTol |
---|
876 | KPP_REAL, INTENT(IN) :: Hstart, Hmin, Hmax |
---|
877 | INTEGER, INTENT(IN) :: Max_no_steps |
---|
878 | KPP_REAL, INTENT(IN) :: Roundoff, FacMin, FacMax, FacRej, FacSafe |
---|
879 | !~~~> Output: Error indicator |
---|
880 | INTEGER, INTENT(OUT) :: IERR |
---|
881 | ! ~~~~ Local variables |
---|
882 | !KPP_REAL :: Ystage_adj(NVAR,NSOA) |
---|
883 | !KPP_REAL :: dFdT(NVAR) |
---|
884 | KPP_REAL :: Ystage(NVAR*ros_S), K(NVAR*ros_S) |
---|
885 | KPP_REAL :: Ystage_tlm(NVAR*ros_S,NSOA), K_tlm(NVAR*ros_S,NSOA) |
---|
886 | KPP_REAL :: U(NVAR*ros_S), V(NVAR*ros_S) |
---|
887 | KPP_REAL :: W(NVAR*ros_S,NSOA), Z(NVAR*ros_S,NSOA) |
---|
888 | KPP_REAL :: Jac(LU_NONZERO), dJdT(LU_NONZERO), Ghimj(LU_NONZERO) |
---|
889 | KPP_REAL :: Hes0(NHESS), Hes1(NHESS), dHdT(NHESS) |
---|
890 | KPP_REAL :: Tmp(NVAR), Tmp2(NVAR) |
---|
891 | KPP_REAL :: H, HC, HA, Tau |
---|
892 | INTEGER :: Pivot(NVAR), Direction, i, ioffset, joffset |
---|
893 | INTEGER :: msoa, j, istage |
---|
894 | !~~~> Local parameters |
---|
895 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
896 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
---|
897 | !~~~> Locally called functions |
---|
898 | ! KPP_REAL WLAMCH |
---|
899 | ! EXTERNAL WLAMCH |
---|
900 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
901 | |
---|
902 | |
---|
903 | |
---|
904 | IF (Tend >= Tstart) THEN |
---|
905 | Direction = +1 |
---|
906 | ELSE |
---|
907 | Direction = -1 |
---|
908 | END IF |
---|
909 | |
---|
910 | !~~~> Time loop begins below |
---|
911 | TimeLoop: DO WHILE ( stack_ptr > 0 ) |
---|
912 | |
---|
913 | !~~~> Recover checkpoints for stage values and vectors |
---|
914 | CALL ros_DPop( ros_S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
---|
915 | |
---|
916 | Nstp = Nstp+1 |
---|
917 | |
---|
918 | !~~~> Compute LU decomposition |
---|
919 | CALL ode_Jac(T,Ystage(1:NVAR),Ghimj) |
---|
920 | CALL WSCAL(LU_NONZERO,(-ONE),Ghimj,1) |
---|
921 | Tau = ONE/(Direction*H*ros_Gamma(1)) |
---|
922 | DO i=1,NVAR |
---|
923 | Ghimj(LU_DIAG(i)) = Ghimj(LU_DIAG(i))+Tau |
---|
924 | END DO |
---|
925 | CALL ros_Decomp( Ghimj, Pivot, j ) |
---|
926 | |
---|
927 | !~~~> Compute Hessian at the beginning of the interval |
---|
928 | CALL ode_Hess(T,Ystage(1),Hes0) |
---|
929 | |
---|
930 | !~~~> Compute the stages |
---|
931 | Stage: DO istage = ros_S, 1, -1 |
---|
932 | |
---|
933 | !~~~> Current istage offset. |
---|
934 | ioffset = NVAR*(istage-1) |
---|
935 | |
---|
936 | !~~~> Compute U |
---|
937 | CALL WCOPY(NVAR,Lambda,1,U(ioffset+1:ioffset+NVAR),1) |
---|
938 | CALL WSCAL(NVAR,ros_M(istage),U(ioffset+1:ioffset+NVAR),1) |
---|
939 | DO j = istage+1, ros_S |
---|
940 | joffset = NVAR*(j-1) |
---|
941 | HA = ros_A((j-1)*(j-2)/2+istage) |
---|
942 | HC = ros_C((j-1)*(j-2)/2+istage)/(Direction*H) |
---|
943 | CALL WAXPY(NVAR,HA,V(joffset+1:joffset+NVAR),1,U(ioffset+1:ioffset+NVAR),1) |
---|
944 | CALL WAXPY(NVAR,HC,U(joffset+1:joffset+NVAR),1,U(ioffset+1:ioffset+NVAR),1) |
---|
945 | END DO |
---|
946 | CALL ros_Solve('T', Ghimj, Pivot, U(ioffset+1:ioffset+NVAR)) |
---|
947 | !~~~> Compute W |
---|
948 | DO msoa = 1, NSOA |
---|
949 | CALL WCOPY(NVAR,Sigma(1:NVAR,msoa),1,W(ioffset+1:ioffset+NVAR,msoa),1) |
---|
950 | CALL WSCAL(NVAR,ros_M(istage),W(ioffset+1:ioffset+NVAR,msoa),1) |
---|
951 | END DO |
---|
952 | DO j = istage+1, ros_S |
---|
953 | joffset = NVAR*(j-1) |
---|
954 | HA = ros_A((j-1)*(j-2)/2+istage) |
---|
955 | HC = ros_C((j-1)*(j-2)/2+istage)/(Direction*H) |
---|
956 | DO msoa = 1, NSOA |
---|
957 | CALL WAXPY(NVAR,HA, & |
---|
958 | Z(joffset+1:joffset+NVAR,msoa),1,W(ioffset+1:ioffset+NVAR,msoa),1) |
---|
959 | CALL WAXPY(NVAR,HC, & |
---|
960 | W(joffset+1:joffset+NVAR,msoa),1,W(ioffset+1:ioffset+NVAR,msoa),1) |
---|
961 | END DO |
---|
962 | END DO |
---|
963 | DO msoa = 1, NSOA |
---|
964 | CALL HessTR_Vec( Hes0, U(ioffset+1:ioffset+NVAR), Ystage_tlm(ioffset+1:ioffset+NVAR,msoa), Tmp ) |
---|
965 | CALL WAXPY(NVAR,ONE,Tmp,1,W(ioffset+1:ioffset+NVAR,msoa),1) |
---|
966 | CALL ros_Solve('T', Ghimj, Pivot, W(ioffset+1:ioffset+NVAR,msoa)) |
---|
967 | END DO |
---|
968 | !~~~> Compute V |
---|
969 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
970 | CALL ode_Jac(Tau,Ystage(ioffset+1:ioffset+NVAR),Jac) |
---|
971 | CALL JacTR_SP_Vec(Jac,U(ioffset+1:ioffset+NVAR),V(ioffset+1:ioffset+NVAR)) |
---|
972 | !~~~> Compute Z |
---|
973 | CALL ode_Hess(T,Ystage(ioffset+1:ioffset+NVAR),Hes1) |
---|
974 | DO msoa = 1, NSOA |
---|
975 | CALL JacTR_SP_Vec(Jac,W(ioffset+1:ioffset+NVAR,msoa),Z(ioffset+1:ioffset+NVAR,msoa)) |
---|
976 | CALL HessTR_Vec( Hes1, U(ioffset+1:ioffset+NVAR), Ystage_tlm(ioffset+1:ioffset+NVAR,msoa), Tmp ) |
---|
977 | CALL WAXPY(NVAR,ONE,Tmp,1,Z(ioffset+1:ioffset+NVAR,msoa),1) |
---|
978 | END DO |
---|
979 | |
---|
980 | END DO Stage |
---|
981 | |
---|
982 | IF (.NOT.Autonomous) THEN |
---|
983 | !~~~> Compute the Jacobian derivative with respect to T. |
---|
984 | ! Last "Jac" computed for stage 1 |
---|
985 | CALL ros_JacTimeDerivative ( T, Roundoff, Ystage(1), & |
---|
986 | Jac, ode_Jac, dJdT ) |
---|
987 | !~~~> Compute the Hessian derivative with respect to T. |
---|
988 | ! Last "Jac" computed for stage 1 |
---|
989 | CALL ros_HesTimeDerivative ( T, Roundoff, Ystage(1), & |
---|
990 | Hes0, ode_Hess, dHdT ) |
---|
991 | END IF |
---|
992 | |
---|
993 | !~~~> Compute the new solution |
---|
994 | |
---|
995 | !~~~> Compute Lambda |
---|
996 | DO istage=1,ros_S |
---|
997 | ioffset = NVAR*(istage-1) |
---|
998 | ! Add V_i |
---|
999 | CALL WAXPY(NVAR,ONE,V(ioffset+1:ioffset+NVAR),1,Lambda,1) |
---|
1000 | ! Add (H0xK_i)^T * U_i |
---|
1001 | CALL HessTR_Vec ( Hes0, U(ioffset+1:ioffset+NVAR), K(ioffset+1:ioffset+NVAR), Tmp ) |
---|
1002 | CALL WAXPY(NVAR,ONE,Tmp,1,Lambda,1) |
---|
1003 | END DO |
---|
1004 | ! Add H * dJac_dT_0^T * \sum(gamma_i U_i) |
---|
1005 | ! Tmp holds sum gamma_i U_i |
---|
1006 | IF (.NOT.Autonomous) THEN |
---|
1007 | Tmp(1:NVAR) = ZERO |
---|
1008 | DO istage = 1, ros_S |
---|
1009 | ioffset = NVAR*(istage-1) |
---|
1010 | CALL WAXPY(NVAR,ros_Gamma(istage),U(ioffset+1:ioffset+NVAR),1,Tmp,1) |
---|
1011 | END DO |
---|
1012 | CALL JacTR_SP_Vec(dJdT,Tmp,Tmp2) |
---|
1013 | CALL WAXPY(NVAR,H,Tmp2,1,Lambda,1) |
---|
1014 | END IF ! .NOT.Autonomous |
---|
1015 | |
---|
1016 | !~~~> Compute Sigma |
---|
1017 | DO msoa = 1, NSOA |
---|
1018 | |
---|
1019 | DO istage=1,ros_S |
---|
1020 | ioffset = NVAR*(istage-1) |
---|
1021 | ! Add Z_i |
---|
1022 | CALL WAXPY(NVAR,ONE,Z(ioffset+1:ioffset+NVAR,msoa),1,Sigma(1:NVAR,msoa),1) |
---|
1023 | ! Add (Hess_0 x K_i)^T * W_i |
---|
1024 | CALL HessTR_Vec ( Hes0, W(ioffset+1:ioffset+NVAR,msoa), K(ioffset+1:ioffset+NVAR), Tmp ) |
---|
1025 | CALL WAXPY(NVAR,ONE,Tmp,1,Sigma(1:NVAR,msoa),1) |
---|
1026 | ! Add (Hess_0 x K_tlm_i)^T * U_i |
---|
1027 | CALL HessTR_Vec ( Hes0, U(ioffset+1:ioffset+NVAR), K_tlm(ioffset+1:ioffset+NVAR,msoa), Tmp ) |
---|
1028 | CALL WAXPY(NVAR,ONE,Tmp,1,Sigma(1:NVAR,msoa),1) |
---|
1029 | END DO |
---|
1030 | |
---|
1031 | !~~~> Add high derivative terms |
---|
1032 | DO istage=1,ros_S |
---|
1033 | ioffset = NVAR*(istage-1) |
---|
1034 | CALL ros_HighDerivative ( T, Roundoff, Ystage(1), Hes0, K(ioffset+1:ioffset+NVAR), & |
---|
1035 | U(ioffset+1:ioffset+NVAR), Ystage_tlm(1:NVAR,msoa), ode_Hess, Tmp) |
---|
1036 | CALL WAXPY(NVAR,ONE,Tmp,1,Sigma(1:NVAR,msoa),1) |
---|
1037 | END DO |
---|
1038 | |
---|
1039 | IF (.NOT.Autonomous) THEN |
---|
1040 | ! Add H * dJac_dT_0^T * \sum(gamma_i W_i) |
---|
1041 | ! Tmp holds sum gamma_i W_i |
---|
1042 | Tmp(1:NVAR) = ZERO |
---|
1043 | DO istage = 1, ros_S |
---|
1044 | ioffset = NVAR*(istage-1) |
---|
1045 | CALL WAXPY(NVAR,ros_Gamma(istage),W(ioffset+1:ioffset+NVAR,msoa),1,Tmp,1) |
---|
1046 | END DO |
---|
1047 | CALL JacTR_SP_Vec(dJdT,Tmp,Tmp2) |
---|
1048 | CALL WAXPY(NVAR,H,Tmp2,1,Sigma(1:NVAR,msoa),1) |
---|
1049 | ! Add H * ( dHess_dT_0 x Y_tlm_0)^T * \sum(gamma_i U_i) |
---|
1050 | ! Tmp holds sum gamma_i U_i |
---|
1051 | Tmp(1:NVAR) = ZERO |
---|
1052 | DO istage = 1, ros_S |
---|
1053 | ioffset = NVAR*(istage-1) |
---|
1054 | CALL WAXPY(NVAR,ros_Gamma(istage),U(ioffset+1:ioffset+NVAR),1,Tmp,1) |
---|
1055 | END DO |
---|
1056 | CALL HessTR_Vec ( dHdT, Tmp, Ystage_tlm(ioffset+1:ioffset+NVAR,msoa), Tmp2 ) |
---|
1057 | CALL WAXPY(NVAR,H,Tmp2,1,Sigma(1:NVAR,msoa),1) |
---|
1058 | END IF ! .NOT.Autonomous |
---|
1059 | |
---|
1060 | END DO ! msoa |
---|
1061 | |
---|
1062 | |
---|
1063 | END DO TimeLoop |
---|
1064 | |
---|
1065 | !~~~> Save last state |
---|
1066 | |
---|
1067 | !~~~> Succesful exit |
---|
1068 | IERR = 1 !~~~> The integration was successful |
---|
1069 | |
---|
1070 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1071 | END SUBROUTINE ros_SoaInt |
---|
1072 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1073 | |
---|
1074 | |
---|
1075 | |
---|
1076 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1077 | KPP_REAL FUNCTION ros_ErrorNorm ( Y, Ynew, Yerr, & |
---|
1078 | AbsTol, RelTol, VectorTol ) |
---|
1079 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1080 | !~~~> Computes the "scaled norm" of the error vector Yerr |
---|
1081 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1082 | IMPLICIT NONE |
---|
1083 | |
---|
1084 | ! Input arguments |
---|
1085 | KPP_REAL, INTENT(IN) :: Y(NVAR), Ynew(NVAR), & |
---|
1086 | Yerr(NVAR), AbsTol(NVAR), RelTol(NVAR) |
---|
1087 | LOGICAL, INTENT(IN) :: VectorTol |
---|
1088 | ! Local variables |
---|
1089 | KPP_REAL :: Err, Scale, Ymax |
---|
1090 | INTEGER :: i |
---|
1091 | KPP_REAL, PARAMETER :: ZERO = 0.0d0 |
---|
1092 | |
---|
1093 | Err = ZERO |
---|
1094 | DO i=1,NVAR |
---|
1095 | Ymax = MAX(ABS(Y(i)),ABS(Ynew(i))) |
---|
1096 | IF (VectorTol) THEN |
---|
1097 | Scale = AbsTol(i)+RelTol(i)*Ymax |
---|
1098 | ELSE |
---|
1099 | Scale = AbsTol(1)+RelTol(1)*Ymax |
---|
1100 | END IF |
---|
1101 | Err = Err+(Yerr(i)/Scale)**2 |
---|
1102 | END DO |
---|
1103 | Err = SQRT(Err/NVAR) |
---|
1104 | |
---|
1105 | ros_ErrorNorm = MAX(Err,1.0d-10) |
---|
1106 | |
---|
1107 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1108 | END FUNCTION ros_ErrorNorm |
---|
1109 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1110 | |
---|
1111 | |
---|
1112 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1113 | SUBROUTINE ros_FunTimeDerivative ( T, Roundoff, Y, & |
---|
1114 | Fcn0, ode_Fun, dFdT ) |
---|
1115 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1116 | !~~~> The time partial derivative of the function by finite differences |
---|
1117 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1118 | IMPLICIT NONE |
---|
1119 | |
---|
1120 | !~~~> Input arguments |
---|
1121 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR), Fcn0(NVAR) |
---|
1122 | EXTERNAL ode_Fun |
---|
1123 | !~~~> Output arguments |
---|
1124 | KPP_REAL, INTENT(OUT) :: dFdT(NVAR) |
---|
1125 | !~~~> Local variables |
---|
1126 | KPP_REAL :: Delta |
---|
1127 | KPP_REAL, PARAMETER :: ONE = 1.0d0, DeltaMin = 1.0d-6 |
---|
1128 | |
---|
1129 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
1130 | CALL ode_Fun(T+Delta,Y,dFdT) |
---|
1131 | CALL WAXPY(NVAR,(-ONE),Fcn0,1,dFdT,1) |
---|
1132 | CALL WSCAL(NVAR,(ONE/Delta),dFdT,1) |
---|
1133 | |
---|
1134 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1135 | END SUBROUTINE ros_FunTimeDerivative |
---|
1136 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1137 | |
---|
1138 | |
---|
1139 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1140 | SUBROUTINE ros_JacTimeDerivative ( T, Roundoff, Y, & |
---|
1141 | Jac0, ode_Jac, dJdT ) |
---|
1142 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1143 | !~~~> The time partial derivative of the Jacobian by finite differences |
---|
1144 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1145 | IMPLICIT NONE |
---|
1146 | |
---|
1147 | !~~~> Input arguments |
---|
1148 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR), Jac0(LU_NONZERO) |
---|
1149 | EXTERNAL ode_Jac |
---|
1150 | !~~~> Output arguments |
---|
1151 | KPP_REAL, INTENT(OUT) :: dJdT(LU_NONZERO) |
---|
1152 | !~~~> Local variables |
---|
1153 | KPP_REAL Delta |
---|
1154 | KPP_REAL, PARAMETER :: ONE = 1.0d0, DeltaMin = 1.0d-6 |
---|
1155 | |
---|
1156 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
1157 | CALL ode_Jac( T+Delta, Y, dJdT ) |
---|
1158 | CALL WAXPY(LU_NONZERO,(-ONE),Jac0,1,dJdT,1) |
---|
1159 | CALL WSCAL(LU_NONZERO,(ONE/Delta),dJdT,1) |
---|
1160 | |
---|
1161 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1162 | END SUBROUTINE ros_JacTimeDerivative |
---|
1163 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1164 | |
---|
1165 | |
---|
1166 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1167 | SUBROUTINE ros_HesTimeDerivative ( T, Roundoff, Y, Hes0, ode_Hess, dHdT ) |
---|
1168 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1169 | !~~~> The time partial derivative of the Hessian by finite differences |
---|
1170 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1171 | IMPLICIT NONE |
---|
1172 | |
---|
1173 | !~~~> Input arguments |
---|
1174 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR), Hes0(NHESS) |
---|
1175 | EXTERNAL ode_Hess |
---|
1176 | !~~~> Output arguments |
---|
1177 | KPP_REAL, INTENT(OUT) :: dHdT(NHESS) |
---|
1178 | !~~~> Local variables |
---|
1179 | KPP_REAL Delta |
---|
1180 | KPP_REAL, PARAMETER :: ONE = 1.0d0, DeltaMin = 1.0d-6 |
---|
1181 | |
---|
1182 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
1183 | CALL ode_Hess( T+Delta, Y, dHdT ) |
---|
1184 | CALL WAXPY(NHESS,(-ONE),Hes0,1,dHdT,1) |
---|
1185 | CALL WSCAL(NHESS,(ONE/Delta),dHdT,1) |
---|
1186 | |
---|
1187 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1188 | END SUBROUTINE ros_HesTimeDerivative |
---|
1189 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1190 | |
---|
1191 | |
---|
1192 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1193 | SUBROUTINE ros_HighDerivative ( T, Roundoff, Y, Hes0, K, U, Y_tlm, & |
---|
1194 | ode_Hess, Term) |
---|
1195 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1196 | !~~~> High order derivative by finite differences: |
---|
1197 | ! d/dy { (Hes0 x K_i)^T * U_i } * Y_tlm |
---|
1198 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1199 | IMPLICIT NONE |
---|
1200 | |
---|
1201 | !~~~> Input arguments |
---|
1202 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR), Hes0(NHESS) |
---|
1203 | KPP_REAL, INTENT(IN) :: K(NVAR), U(NVAR), Y_tlm(NVAR) |
---|
1204 | EXTERNAL ode_Hess |
---|
1205 | !~~~> Output arguments |
---|
1206 | KPP_REAL, INTENT(OUT) :: Term(NVAR) |
---|
1207 | !~~~> Local variables |
---|
1208 | KPP_REAL :: Delta, Y1(NVAR), Hes1(NHESS), Tmp(NVAR) |
---|
1209 | KPP_REAL, PARAMETER :: ONE = 1.0d0, DeltaMin = 1.0d-6 |
---|
1210 | |
---|
1211 | CALL HessTR_Vec ( Hes0, U, K, Tmp ) |
---|
1212 | |
---|
1213 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
1214 | Y1(1:NVAR) = Y(1:NVAR) + Delta*Y_tlm(1:NVAR) |
---|
1215 | CALL ode_Hess( T, Y1, Hes1 ) |
---|
1216 | ! Add (Hess_0 x K_i)^T * U_i |
---|
1217 | CALL HessTR_Vec ( Hes1, U, K, Term ) |
---|
1218 | |
---|
1219 | CALL WAXPY(NVAR,(-ONE),Tmp,1,Term,1) |
---|
1220 | CALL WSCAL(NVAR,(ONE/Delta),Term,1) |
---|
1221 | |
---|
1222 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1223 | END SUBROUTINE ros_HighDerivative |
---|
1224 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1225 | |
---|
1226 | |
---|
1227 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1228 | SUBROUTINE ros_PrepareMatrix ( H, Direction, gam, & |
---|
1229 | Jac0, Ghimj, Pivot, Singular ) |
---|
1230 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
1231 | ! Prepares the LHS matrix for stage calculations |
---|
1232 | ! 1. Construct Ghimj = 1/(H*ham) - Jac0 |
---|
1233 | ! "(Gamma H) Inverse Minus Jacobian" |
---|
1234 | ! 2. Repeat LU decomposition of Ghimj until successful. |
---|
1235 | ! -half the step size if LU decomposition fails and retry |
---|
1236 | ! -exit after 5 consecutive fails |
---|
1237 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
1238 | IMPLICIT NONE |
---|
1239 | |
---|
1240 | !~~~> Input arguments |
---|
1241 | KPP_REAL, INTENT(IN) :: gam, Jac0(LU_NONZERO) |
---|
1242 | INTEGER, INTENT(IN) :: Direction |
---|
1243 | !~~~> Output arguments |
---|
1244 | KPP_REAL, INTENT(OUT) :: Ghimj(LU_NONZERO) |
---|
1245 | LOGICAL, INTENT(OUT) :: Singular |
---|
1246 | INTEGER, INTENT(OUT) :: Pivot(NVAR) |
---|
1247 | !~~~> Inout arguments |
---|
1248 | KPP_REAL, INTENT(INOUT) :: H ! step size is decreased when LU fails |
---|
1249 | !~~~> Local variables |
---|
1250 | INTEGER :: i, ising, Nconsecutive |
---|
1251 | KPP_REAL :: ghinv |
---|
1252 | KPP_REAL, PARAMETER :: ONE = 1.0d0, HALF = 0.5d0 |
---|
1253 | |
---|
1254 | Nconsecutive = 0 |
---|
1255 | Singular = .TRUE. |
---|
1256 | |
---|
1257 | DO WHILE (Singular) |
---|
1258 | |
---|
1259 | !~~~> Construct Ghimj = 1/(H*ham) - Jac0 |
---|
1260 | CALL WCOPY(LU_NONZERO,Jac0,1,Ghimj,1) |
---|
1261 | CALL WSCAL(LU_NONZERO,(-ONE),Ghimj,1) |
---|
1262 | ghinv = ONE/(Direction*H*gam) |
---|
1263 | DO i=1,NVAR |
---|
1264 | Ghimj(LU_DIAG(i)) = Ghimj(LU_DIAG(i))+ghinv |
---|
1265 | END DO |
---|
1266 | !~~~> Compute LU decomposition |
---|
1267 | CALL ros_Decomp( Ghimj, Pivot, ising ) |
---|
1268 | IF (ising == 0) THEN |
---|
1269 | !~~~> If successful done |
---|
1270 | Singular = .FALSE. |
---|
1271 | ELSE ! ising .ne. 0 |
---|
1272 | !~~~> If unsuccessful half the step size; if 5 consecutive fails then return |
---|
1273 | Nsng = Nsng+1 |
---|
1274 | Nconsecutive = Nconsecutive+1 |
---|
1275 | Singular = .TRUE. |
---|
1276 | PRINT*,'Warning: LU Decomposition returned ising = ',ising |
---|
1277 | IF (Nconsecutive <= 5) THEN ! Less than 5 consecutive failed decomps |
---|
1278 | H = H*HALF |
---|
1279 | ELSE ! More than 5 consecutive failed decompositions |
---|
1280 | RETURN |
---|
1281 | END IF ! Nconsecutive |
---|
1282 | END IF ! ising |
---|
1283 | |
---|
1284 | END DO ! WHILE Singular |
---|
1285 | |
---|
1286 | END SUBROUTINE ros_PrepareMatrix |
---|
1287 | |
---|
1288 | |
---|
1289 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1290 | SUBROUTINE ros_Decomp( A, Pivot, ising ) |
---|
1291 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1292 | ! Template for the LU decomposition |
---|
1293 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1294 | IMPLICIT NONE |
---|
1295 | !~~~> Inout variables |
---|
1296 | KPP_REAL, INTENT(INOUT) :: A(LU_NONZERO) |
---|
1297 | !~~~> Output variables |
---|
1298 | INTEGER, INTENT(OUT) :: Pivot(NVAR), ising |
---|
1299 | |
---|
1300 | CALL KppDecomp ( A, ising ) |
---|
1301 | !~~~> Note: for a full matrix use Lapack: |
---|
1302 | ! CALL DGETRF( NVAR, NVAR, A, NVAR, Pivot, ising ) |
---|
1303 | Pivot(1) = 1 |
---|
1304 | |
---|
1305 | Ndec = Ndec + 1 |
---|
1306 | |
---|
1307 | END SUBROUTINE ros_Decomp |
---|
1308 | |
---|
1309 | |
---|
1310 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1311 | SUBROUTINE ros_Solve( C, A, Pivot, b ) |
---|
1312 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1313 | ! Template for the forward/backward substitution (using pre-computed LU decomp) |
---|
1314 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1315 | IMPLICIT NONE |
---|
1316 | !~~~> Input variables |
---|
1317 | CHARACTER, INTENT(IN) :: C |
---|
1318 | KPP_REAL, INTENT(IN) :: A(LU_NONZERO) |
---|
1319 | INTEGER, INTENT(IN) :: Pivot(NVAR) |
---|
1320 | !~~~> InOut variables |
---|
1321 | KPP_REAL, INTENT(INOUT) :: b(NVAR) |
---|
1322 | |
---|
1323 | SELECT CASE (C) |
---|
1324 | CASE ('N') |
---|
1325 | CALL KppSolve( A, b ) |
---|
1326 | CASE ('T') |
---|
1327 | CALL KppSolveTR( A, b, b ) |
---|
1328 | CASE DEFAULT |
---|
1329 | PRINT*,'Unknown C = (',C,') in ros_Solve' |
---|
1330 | STOP |
---|
1331 | END SELECT |
---|
1332 | !~~~> Note: for a full matrix use Lapack: |
---|
1333 | ! NRHS = 1 |
---|
1334 | ! CALL DGETRS( C, NVAR , NRHS, A, NVAR, Pivot, b, NVAR, INFO ) |
---|
1335 | |
---|
1336 | Nsol = Nsol+1 |
---|
1337 | |
---|
1338 | END SUBROUTINE ros_Solve |
---|
1339 | |
---|
1340 | |
---|
1341 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1342 | SUBROUTINE Ros2 (ros_S,ros_A,ros_C,ros_M,ros_E,ros_Alpha,& |
---|
1343 | ros_Gamma,ros_NewF,ros_ELO,ros_Name) |
---|
1344 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1345 | ! --- AN L-STABLE METHOD, 2 stages, order 2 |
---|
1346 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1347 | |
---|
1348 | IMPLICIT NONE |
---|
1349 | |
---|
1350 | INTEGER, PARAMETER :: S = 2 |
---|
1351 | INTEGER, INTENT(OUT) :: ros_S |
---|
1352 | KPP_REAL, DIMENSION(S), INTENT(OUT) :: ros_M,ros_E,ros_Alpha,ros_Gamma |
---|
1353 | KPP_REAL, DIMENSION(S*(S-1)/2), INTENT(OUT) :: ros_A, ros_C |
---|
1354 | KPP_REAL, INTENT(OUT) :: ros_ELO |
---|
1355 | LOGICAL, DIMENSION(S), INTENT(OUT) :: ros_NewF |
---|
1356 | CHARACTER(LEN=12), INTENT(OUT) :: ros_Name |
---|
1357 | KPP_REAL :: g |
---|
1358 | |
---|
1359 | g = 1.0d0 + 1.0d0/SQRT(2.0d0) |
---|
1360 | |
---|
1361 | !~~~> Name of the method |
---|
1362 | ros_Name = 'ROS-2' |
---|
1363 | !~~~> Number of stages |
---|
1364 | ros_S = S |
---|
1365 | |
---|
1366 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
1367 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1368 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
1369 | ! The general mapping formula is: |
---|
1370 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
1371 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
1372 | |
---|
1373 | ros_A(1) = (1.d0)/g |
---|
1374 | ros_C(1) = (-2.d0)/g |
---|
1375 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
1376 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
1377 | ros_NewF(1) = .TRUE. |
---|
1378 | ros_NewF(2) = .TRUE. |
---|
1379 | !~~~> M_i = Coefficients for new step solution |
---|
1380 | ros_M(1)= (3.d0)/(2.d0*g) |
---|
1381 | ros_M(2)= (1.d0)/(2.d0*g) |
---|
1382 | ! E_i = Coefficients for error estimator |
---|
1383 | ros_E(1) = 1.d0/(2.d0*g) |
---|
1384 | ros_E(2) = 1.d0/(2.d0*g) |
---|
1385 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
1386 | ! main and the embedded scheme orders plus one |
---|
1387 | ros_ELO = 2.0d0 |
---|
1388 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
1389 | ros_Alpha(1) = 0.0d0 |
---|
1390 | ros_Alpha(2) = 1.0d0 |
---|
1391 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
1392 | ros_Gamma(1) = g |
---|
1393 | ros_Gamma(2) =-g |
---|
1394 | |
---|
1395 | END SUBROUTINE Ros2 |
---|
1396 | |
---|
1397 | |
---|
1398 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1399 | SUBROUTINE Ros3 (ros_S,ros_A,ros_C,ros_M,ros_E,ros_Alpha,& |
---|
1400 | ros_Gamma,ros_NewF,ros_ELO,ros_Name) |
---|
1401 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1402 | ! --- AN L-STABLE METHOD, 3 stages, order 3, 2 function evaluations |
---|
1403 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1404 | |
---|
1405 | IMPLICIT NONE |
---|
1406 | |
---|
1407 | INTEGER, PARAMETER :: S = 3 |
---|
1408 | INTEGER, INTENT(OUT) :: ros_S |
---|
1409 | KPP_REAL, DIMENSION(S), INTENT(OUT) :: ros_M,ros_E,ros_Alpha,ros_Gamma |
---|
1410 | KPP_REAL, DIMENSION(S*(S-1)/2), INTENT(OUT) :: ros_A, ros_C |
---|
1411 | KPP_REAL, INTENT(OUT) :: ros_ELO |
---|
1412 | LOGICAL, DIMENSION(S), INTENT(OUT) :: ros_NewF |
---|
1413 | CHARACTER(LEN=12), INTENT(OUT) :: ros_Name |
---|
1414 | |
---|
1415 | !~~~> Name of the method |
---|
1416 | ros_Name = 'ROS-3' |
---|
1417 | !~~~> Number of stages |
---|
1418 | ros_S = S |
---|
1419 | |
---|
1420 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
1421 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1422 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
1423 | ! The general mapping formula is: |
---|
1424 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
1425 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
1426 | |
---|
1427 | ros_A(1)= 1.d0 |
---|
1428 | ros_A(2)= 1.d0 |
---|
1429 | ros_A(3)= 0.d0 |
---|
1430 | |
---|
1431 | ros_C(1) = -0.10156171083877702091975600115545d+01 |
---|
1432 | ros_C(2) = 0.40759956452537699824805835358067d+01 |
---|
1433 | ros_C(3) = 0.92076794298330791242156818474003d+01 |
---|
1434 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
1435 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
1436 | ros_NewF(1) = .TRUE. |
---|
1437 | ros_NewF(2) = .TRUE. |
---|
1438 | ros_NewF(3) = .FALSE. |
---|
1439 | !~~~> M_i = Coefficients for new step solution |
---|
1440 | ros_M(1) = 0.1d+01 |
---|
1441 | ros_M(2) = 0.61697947043828245592553615689730d+01 |
---|
1442 | ros_M(3) = -0.42772256543218573326238373806514d+00 |
---|
1443 | ! E_i = Coefficients for error estimator |
---|
1444 | ros_E(1) = 0.5d+00 |
---|
1445 | ros_E(2) = -0.29079558716805469821718236208017d+01 |
---|
1446 | ros_E(3) = 0.22354069897811569627360909276199d+00 |
---|
1447 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
1448 | ! main and the embedded scheme orders plus 1 |
---|
1449 | ros_ELO = 3.0d0 |
---|
1450 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
1451 | ros_Alpha(1)= 0.0d+00 |
---|
1452 | ros_Alpha(2)= 0.43586652150845899941601945119356d+00 |
---|
1453 | ros_Alpha(3)= 0.43586652150845899941601945119356d+00 |
---|
1454 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
1455 | ros_Gamma(1)= 0.43586652150845899941601945119356d+00 |
---|
1456 | ros_Gamma(2)= 0.24291996454816804366592249683314d+00 |
---|
1457 | ros_Gamma(3)= 0.21851380027664058511513169485832d+01 |
---|
1458 | |
---|
1459 | END SUBROUTINE Ros3 |
---|
1460 | |
---|
1461 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1462 | |
---|
1463 | |
---|
1464 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1465 | SUBROUTINE Ros4 (ros_S,ros_A,ros_C,ros_M,ros_E,ros_Alpha,& |
---|
1466 | ros_Gamma,ros_NewF,ros_ELO,ros_Name) |
---|
1467 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1468 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4, WITH 4 STAGES |
---|
1469 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
---|
1470 | ! |
---|
1471 | ! E. HAIRER AND G. WANNER, SOLVING ORDINARY DIFFERENTIAL |
---|
1472 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
1473 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
1474 | ! SPRINGER-VERLAG (1990) |
---|
1475 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1476 | |
---|
1477 | IMPLICIT NONE |
---|
1478 | |
---|
1479 | INTEGER, PARAMETER :: S=4 |
---|
1480 | INTEGER, INTENT(OUT) :: ros_S |
---|
1481 | KPP_REAL, DIMENSION(S), INTENT(OUT) :: ros_M,ros_E,ros_Alpha,ros_Gamma |
---|
1482 | KPP_REAL, DIMENSION(S*(S-1)/2), INTENT(OUT) :: ros_A, ros_C |
---|
1483 | KPP_REAL, INTENT(OUT) :: ros_ELO |
---|
1484 | LOGICAL, DIMENSION(S), INTENT(OUT) :: ros_NewF |
---|
1485 | CHARACTER(LEN=12), INTENT(OUT) :: ros_Name |
---|
1486 | |
---|
1487 | |
---|
1488 | !~~~> Name of the method |
---|
1489 | ros_Name = 'ROS-4' |
---|
1490 | !~~~> Number of stages |
---|
1491 | ros_S = S |
---|
1492 | |
---|
1493 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
1494 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1495 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
1496 | ! The general mapping formula is: |
---|
1497 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
1498 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
1499 | |
---|
1500 | ros_A(1) = 0.2000000000000000d+01 |
---|
1501 | ros_A(2) = 0.1867943637803922d+01 |
---|
1502 | ros_A(3) = 0.2344449711399156d+00 |
---|
1503 | ros_A(4) = ros_A(2) |
---|
1504 | ros_A(5) = ros_A(3) |
---|
1505 | ros_A(6) = 0.0D0 |
---|
1506 | |
---|
1507 | ros_C(1) =-0.7137615036412310d+01 |
---|
1508 | ros_C(2) = 0.2580708087951457d+01 |
---|
1509 | ros_C(3) = 0.6515950076447975d+00 |
---|
1510 | ros_C(4) =-0.2137148994382534d+01 |
---|
1511 | ros_C(5) =-0.3214669691237626d+00 |
---|
1512 | ros_C(6) =-0.6949742501781779d+00 |
---|
1513 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
1514 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
1515 | ros_NewF(1) = .TRUE. |
---|
1516 | ros_NewF(2) = .TRUE. |
---|
1517 | ros_NewF(3) = .TRUE. |
---|
1518 | ros_NewF(4) = .FALSE. |
---|
1519 | !~~~> M_i = Coefficients for new step solution |
---|
1520 | ros_M(1) = 0.2255570073418735d+01 |
---|
1521 | ros_M(2) = 0.2870493262186792d+00 |
---|
1522 | ros_M(3) = 0.4353179431840180d+00 |
---|
1523 | ros_M(4) = 0.1093502252409163d+01 |
---|
1524 | !~~~> E_i = Coefficients for error estimator |
---|
1525 | ros_E(1) =-0.2815431932141155d+00 |
---|
1526 | ros_E(2) =-0.7276199124938920d-01 |
---|
1527 | ros_E(3) =-0.1082196201495311d+00 |
---|
1528 | ros_E(4) =-0.1093502252409163d+01 |
---|
1529 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
1530 | ! main and the embedded scheme orders plus 1 |
---|
1531 | ros_ELO = 4.0d0 |
---|
1532 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
1533 | ros_Alpha(1) = 0.D0 |
---|
1534 | ros_Alpha(2) = 0.1145640000000000d+01 |
---|
1535 | ros_Alpha(3) = 0.6552168638155900d+00 |
---|
1536 | ros_Alpha(4) = ros_Alpha(3) |
---|
1537 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
1538 | ros_Gamma(1) = 0.5728200000000000d+00 |
---|
1539 | ros_Gamma(2) =-0.1769193891319233d+01 |
---|
1540 | ros_Gamma(3) = 0.7592633437920482d+00 |
---|
1541 | ros_Gamma(4) =-0.1049021087100450d+00 |
---|
1542 | |
---|
1543 | END SUBROUTINE Ros4 |
---|
1544 | |
---|
1545 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1546 | SUBROUTINE Rodas3 (ros_S,ros_A,ros_C,ros_M,ros_E,ros_Alpha,& |
---|
1547 | ros_Gamma,ros_NewF,ros_ELO,ros_Name) |
---|
1548 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1549 | ! --- A STIFFLY-STABLE METHOD, 4 stages, order 3 |
---|
1550 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1551 | |
---|
1552 | IMPLICIT NONE |
---|
1553 | |
---|
1554 | INTEGER, PARAMETER :: S=4 |
---|
1555 | INTEGER, INTENT(OUT) :: ros_S |
---|
1556 | KPP_REAL, DIMENSION(S), INTENT(OUT) :: ros_M,ros_E,ros_Alpha,ros_Gamma |
---|
1557 | KPP_REAL, DIMENSION(S*(S-1)/2), INTENT(OUT) :: ros_A, ros_C |
---|
1558 | KPP_REAL, INTENT(OUT) :: ros_ELO |
---|
1559 | LOGICAL, DIMENSION(S), INTENT(OUT) :: ros_NewF |
---|
1560 | CHARACTER(LEN=12), INTENT(OUT) :: ros_Name |
---|
1561 | |
---|
1562 | |
---|
1563 | !~~~> Name of the method |
---|
1564 | ros_Name = 'RODAS-3' |
---|
1565 | !~~~> Number of stages |
---|
1566 | ros_S = S |
---|
1567 | |
---|
1568 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
1569 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1570 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
1571 | ! The general mapping formula is: |
---|
1572 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
1573 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
1574 | |
---|
1575 | ros_A(1) = 0.0d+00 |
---|
1576 | ros_A(2) = 2.0d+00 |
---|
1577 | ros_A(3) = 0.0d+00 |
---|
1578 | ros_A(4) = 2.0d+00 |
---|
1579 | ros_A(5) = 0.0d+00 |
---|
1580 | ros_A(6) = 1.0d+00 |
---|
1581 | |
---|
1582 | ros_C(1) = 4.0d+00 |
---|
1583 | ros_C(2) = 1.0d+00 |
---|
1584 | ros_C(3) =-1.0d+00 |
---|
1585 | ros_C(4) = 1.0d+00 |
---|
1586 | ros_C(5) =-1.0d+00 |
---|
1587 | ros_C(6) =-(8.0d+00/3.0d+00) |
---|
1588 | |
---|
1589 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
1590 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
1591 | ros_NewF(1) = .TRUE. |
---|
1592 | ros_NewF(2) = .FALSE. |
---|
1593 | ros_NewF(3) = .TRUE. |
---|
1594 | ros_NewF(4) = .TRUE. |
---|
1595 | !~~~> M_i = Coefficients for new step solution |
---|
1596 | ros_M(1) = 2.0d+00 |
---|
1597 | ros_M(2) = 0.0d+00 |
---|
1598 | ros_M(3) = 1.0d+00 |
---|
1599 | ros_M(4) = 1.0d+00 |
---|
1600 | !~~~> E_i = Coefficients for error estimator |
---|
1601 | ros_E(1) = 0.0d+00 |
---|
1602 | ros_E(2) = 0.0d+00 |
---|
1603 | ros_E(3) = 0.0d+00 |
---|
1604 | ros_E(4) = 1.0d+00 |
---|
1605 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
1606 | ! main and the embedded scheme orders plus 1 |
---|
1607 | ros_ELO = 3.0d+00 |
---|
1608 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
1609 | ros_Alpha(1) = 0.0d+00 |
---|
1610 | ros_Alpha(2) = 0.0d+00 |
---|
1611 | ros_Alpha(3) = 1.0d+00 |
---|
1612 | ros_Alpha(4) = 1.0d+00 |
---|
1613 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
1614 | ros_Gamma(1) = 0.5d+00 |
---|
1615 | ros_Gamma(2) = 1.5d+00 |
---|
1616 | ros_Gamma(3) = 0.0d+00 |
---|
1617 | ros_Gamma(4) = 0.0d+00 |
---|
1618 | |
---|
1619 | END SUBROUTINE Rodas3 |
---|
1620 | |
---|
1621 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1622 | SUBROUTINE Rodas4 (ros_S,ros_A,ros_C,ros_M,ros_E,ros_Alpha,& |
---|
1623 | ros_Gamma,ros_NewF,ros_ELO,ros_Name) |
---|
1624 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1625 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4, WITH 6 STAGES |
---|
1626 | ! |
---|
1627 | ! E. HAIRER AND G. WANNER, SOLVING ORDINARY DIFFERENTIAL |
---|
1628 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
1629 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
1630 | ! SPRINGER-VERLAG (1996) |
---|
1631 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1632 | |
---|
1633 | IMPLICIT NONE |
---|
1634 | |
---|
1635 | INTEGER, PARAMETER :: S=6 |
---|
1636 | INTEGER, INTENT(OUT) :: ros_S |
---|
1637 | KPP_REAL, DIMENSION(S), INTENT(OUT) :: ros_M,ros_E,ros_Alpha,ros_Gamma |
---|
1638 | KPP_REAL, DIMENSION(S*(S-1)/2), INTENT(OUT) :: ros_A, ros_C |
---|
1639 | KPP_REAL, INTENT(OUT) :: ros_ELO |
---|
1640 | LOGICAL, DIMENSION(S), INTENT(OUT) :: ros_NewF |
---|
1641 | CHARACTER(LEN=12), INTENT(OUT) :: ros_Name |
---|
1642 | |
---|
1643 | |
---|
1644 | !~~~> Name of the method |
---|
1645 | ros_Name = 'RODAS-4' |
---|
1646 | !~~~> Number of stages |
---|
1647 | ros_S = S |
---|
1648 | |
---|
1649 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
1650 | ros_Alpha(1) = 0.000d0 |
---|
1651 | ros_Alpha(2) = 0.386d0 |
---|
1652 | ros_Alpha(3) = 0.210d0 |
---|
1653 | ros_Alpha(4) = 0.630d0 |
---|
1654 | ros_Alpha(5) = 1.000d0 |
---|
1655 | ros_Alpha(6) = 1.000d0 |
---|
1656 | |
---|
1657 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
1658 | ros_Gamma(1) = 0.2500000000000000d+00 |
---|
1659 | ros_Gamma(2) =-0.1043000000000000d+00 |
---|
1660 | ros_Gamma(3) = 0.1035000000000000d+00 |
---|
1661 | ros_Gamma(4) =-0.3620000000000023d-01 |
---|
1662 | ros_Gamma(5) = 0.0d0 |
---|
1663 | ros_Gamma(6) = 0.0d0 |
---|
1664 | |
---|
1665 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
1666 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1667 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
1668 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
1669 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
1670 | |
---|
1671 | ros_A(1) = 0.1544000000000000d+01 |
---|
1672 | ros_A(2) = 0.9466785280815826d+00 |
---|
1673 | ros_A(3) = 0.2557011698983284d+00 |
---|
1674 | ros_A(4) = 0.3314825187068521d+01 |
---|
1675 | ros_A(5) = 0.2896124015972201d+01 |
---|
1676 | ros_A(6) = 0.9986419139977817d+00 |
---|
1677 | ros_A(7) = 0.1221224509226641d+01 |
---|
1678 | ros_A(8) = 0.6019134481288629d+01 |
---|
1679 | ros_A(9) = 0.1253708332932087d+02 |
---|
1680 | ros_A(10) =-0.6878860361058950d+00 |
---|
1681 | ros_A(11) = ros_A(7) |
---|
1682 | ros_A(12) = ros_A(8) |
---|
1683 | ros_A(13) = ros_A(9) |
---|
1684 | ros_A(14) = ros_A(10) |
---|
1685 | ros_A(15) = 1.0d+00 |
---|
1686 | |
---|
1687 | ros_C(1) =-0.5668800000000000d+01 |
---|
1688 | ros_C(2) =-0.2430093356833875d+01 |
---|
1689 | ros_C(3) =-0.2063599157091915d+00 |
---|
1690 | ros_C(4) =-0.1073529058151375d+00 |
---|
1691 | ros_C(5) =-0.9594562251023355d+01 |
---|
1692 | ros_C(6) =-0.2047028614809616d+02 |
---|
1693 | ros_C(7) = 0.7496443313967647d+01 |
---|
1694 | ros_C(8) =-0.1024680431464352d+02 |
---|
1695 | ros_C(9) =-0.3399990352819905d+02 |
---|
1696 | ros_C(10) = 0.1170890893206160d+02 |
---|
1697 | ros_C(11) = 0.8083246795921522d+01 |
---|
1698 | ros_C(12) =-0.7981132988064893d+01 |
---|
1699 | ros_C(13) =-0.3152159432874371d+02 |
---|
1700 | ros_C(14) = 0.1631930543123136d+02 |
---|
1701 | ros_C(15) =-0.6058818238834054d+01 |
---|
1702 | |
---|
1703 | !~~~> M_i = Coefficients for new step solution |
---|
1704 | ros_M(1) = ros_A(7) |
---|
1705 | ros_M(2) = ros_A(8) |
---|
1706 | ros_M(3) = ros_A(9) |
---|
1707 | ros_M(4) = ros_A(10) |
---|
1708 | ros_M(5) = 1.0d+00 |
---|
1709 | ros_M(6) = 1.0d+00 |
---|
1710 | |
---|
1711 | !~~~> E_i = Coefficients for error estimator |
---|
1712 | ros_E(1) = 0.0d+00 |
---|
1713 | ros_E(2) = 0.0d+00 |
---|
1714 | ros_E(3) = 0.0d+00 |
---|
1715 | ros_E(4) = 0.0d+00 |
---|
1716 | ros_E(5) = 0.0d+00 |
---|
1717 | ros_E(6) = 1.0d+00 |
---|
1718 | |
---|
1719 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
1720 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
1721 | ros_NewF(1) = .TRUE. |
---|
1722 | ros_NewF(2) = .TRUE. |
---|
1723 | ros_NewF(3) = .TRUE. |
---|
1724 | ros_NewF(4) = .TRUE. |
---|
1725 | ros_NewF(5) = .TRUE. |
---|
1726 | ros_NewF(6) = .TRUE. |
---|
1727 | |
---|
1728 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
1729 | ! main and the embedded scheme orders plus 1 |
---|
1730 | ros_ELO = 4.0d0 |
---|
1731 | |
---|
1732 | END SUBROUTINE Rodas4 |
---|
1733 | |
---|
1734 | |
---|
1735 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1736 | SUBROUTINE Fun_Template( T, Y, Ydot ) |
---|
1737 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1738 | ! Template for the ODE function call. |
---|
1739 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
1740 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1741 | !~~~> Input variables |
---|
1742 | KPP_REAL T, Y(NVAR) |
---|
1743 | !~~~> Output variables |
---|
1744 | KPP_REAL Ydot(NVAR) |
---|
1745 | !~~~> Local variables |
---|
1746 | KPP_REAL Told |
---|
1747 | |
---|
1748 | Told = TIME |
---|
1749 | TIME = T |
---|
1750 | CALL Update_SUN() |
---|
1751 | CALL Update_RCONST() |
---|
1752 | CALL Fun( Y, FIX, RCONST, Ydot ) |
---|
1753 | TIME = Told |
---|
1754 | |
---|
1755 | Nfun = Nfun+1 |
---|
1756 | |
---|
1757 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1758 | END SUBROUTINE Fun_Template |
---|
1759 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1760 | |
---|
1761 | |
---|
1762 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1763 | SUBROUTINE Jac_Template( T, Y, Jcb ) |
---|
1764 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1765 | ! Template for the ODE Jacobian call. |
---|
1766 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
1767 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1768 | |
---|
1769 | !~~~> Input variables |
---|
1770 | KPP_REAL T, Y(NVAR) |
---|
1771 | !~~~> Output variables |
---|
1772 | KPP_REAL Jcb(LU_NONZERO) |
---|
1773 | !~~~> Local variables |
---|
1774 | KPP_REAL Told |
---|
1775 | |
---|
1776 | Told = TIME |
---|
1777 | TIME = T |
---|
1778 | CALL Update_SUN() |
---|
1779 | CALL Update_RCONST() |
---|
1780 | CALL Jac_SP( Y, FIX, RCONST, Jcb ) |
---|
1781 | TIME = Told |
---|
1782 | |
---|
1783 | Njac = Njac+1 |
---|
1784 | |
---|
1785 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1786 | END SUBROUTINE Jac_Template |
---|
1787 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1788 | |
---|
1789 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1790 | SUBROUTINE Hess_Template( T, Y, Hes ) |
---|
1791 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1792 | ! Template for the ODE Hessian call. |
---|
1793 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
1794 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1795 | !~~~> Input variables |
---|
1796 | KPP_REAL T, Y(NVAR) |
---|
1797 | !~~~> Output variables |
---|
1798 | KPP_REAL Hes(NHESS) |
---|
1799 | !~~~> Local variables |
---|
1800 | KPP_REAL Told |
---|
1801 | |
---|
1802 | Told = TIME |
---|
1803 | TIME = T |
---|
1804 | CALL Update_SUN() |
---|
1805 | CALL Update_RCONST() |
---|
1806 | CALL Hessian( Y, FIX, RCONST, Hes ) |
---|
1807 | TIME = Told |
---|
1808 | |
---|
1809 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1810 | END SUBROUTINE Hess_Template |
---|
1811 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1812 | |
---|
1813 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1814 | SUBROUTINE ros_AllocateDBuffers( S ) |
---|
1815 | !~~~> Allocate buffer space for discrete adjoint |
---|
1816 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1817 | INTEGER :: i, S |
---|
1818 | |
---|
1819 | ALLOCATE( buf_H(bufsize), STAT=i ) |
---|
1820 | IF (i/=0) THEN |
---|
1821 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
1822 | END IF |
---|
1823 | ALLOCATE( buf_T(bufsize), STAT=i ) |
---|
1824 | IF (i/=0) THEN |
---|
1825 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
1826 | END IF |
---|
1827 | ALLOCATE( buf_Y(NVAR*S,bufsize), STAT=i ) |
---|
1828 | IF (i/=0) THEN |
---|
1829 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
1830 | END IF |
---|
1831 | ALLOCATE( buf_K(NVAR*S,bufsize), STAT=i ) |
---|
1832 | IF (i/=0) THEN |
---|
1833 | PRINT*,'Failed allocation of buffer K'; STOP |
---|
1834 | END IF |
---|
1835 | ALLOCATE( buf_Y_tlm(NVAR*S,bufsize), STAT=i ) |
---|
1836 | IF (i/=0) THEN |
---|
1837 | PRINT*,'Failed allocation of buffer Y_tlm'; STOP |
---|
1838 | END IF |
---|
1839 | ALLOCATE( buf_K_tlm(NVAR*S,bufsize), STAT=i ) |
---|
1840 | IF (i/=0) THEN |
---|
1841 | PRINT*,'Failed allocation of buffer K_tlm'; STOP |
---|
1842 | END IF |
---|
1843 | |
---|
1844 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1845 | END SUBROUTINE ros_AllocateDBuffers |
---|
1846 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1847 | |
---|
1848 | |
---|
1849 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1850 | SUBROUTINE ros_FreeDBuffers |
---|
1851 | !~~~> Dallocate buffer space for discrete adjoint |
---|
1852 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1853 | INTEGER :: i |
---|
1854 | |
---|
1855 | DEALLOCATE( buf_H, STAT=i ) |
---|
1856 | IF (i/=0) THEN |
---|
1857 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
1858 | END IF |
---|
1859 | DEALLOCATE( buf_T, STAT=i ) |
---|
1860 | IF (i/=0) THEN |
---|
1861 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
1862 | END IF |
---|
1863 | DEALLOCATE( buf_Y, STAT=i ) |
---|
1864 | IF (i/=0) THEN |
---|
1865 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
1866 | END IF |
---|
1867 | DEALLOCATE( buf_K, STAT=i ) |
---|
1868 | IF (i/=0) THEN |
---|
1869 | PRINT*,'Failed deallocation of buffer K'; STOP |
---|
1870 | END IF |
---|
1871 | DEALLOCATE( buf_Y_tlm, STAT=i ) |
---|
1872 | IF (i/=0) THEN |
---|
1873 | PRINT*,'Failed deallocation of buffer Y_tlm'; STOP |
---|
1874 | END IF |
---|
1875 | DEALLOCATE( buf_K_tlm, STAT=i ) |
---|
1876 | IF (i/=0) THEN |
---|
1877 | PRINT*,'Failed deallocation of buffer K_tlm'; STOP |
---|
1878 | END IF |
---|
1879 | |
---|
1880 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1881 | END SUBROUTINE ros_FreeDBuffers |
---|
1882 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1883 | |
---|
1884 | |
---|
1885 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1886 | SUBROUTINE ros_DPush( S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
---|
1887 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1888 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
1889 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1890 | |
---|
1891 | INTEGER, INTENT(IN) :: S ! no of stages |
---|
1892 | INTEGER, INTENT(IN) :: NSOA ! no of second order adjoints |
---|
1893 | KPP_REAL :: T, H, Ystage(NVAR*S), K(NVAR*S) |
---|
1894 | KPP_REAL :: Ystage_tlm(NVAR*S,NSOA), K_tlm(NVAR*S,NSOA) |
---|
1895 | |
---|
1896 | stack_ptr = stack_ptr + 1 |
---|
1897 | IF ( stack_ptr > bufsize ) THEN |
---|
1898 | PRINT*,'Push failed: buffer overflow' |
---|
1899 | STOP |
---|
1900 | END IF |
---|
1901 | buf_H( stack_ptr ) = H |
---|
1902 | buf_T( stack_ptr ) = T |
---|
1903 | CALL WCOPY(NVAR*S,Ystage,1,buf_Y(1:NVAR*S,stack_ptr),1) |
---|
1904 | CALL WCOPY(NVAR*S,K,1,buf_K(1:NVAR*S,stack_ptr),1) |
---|
1905 | CALL WCOPY(NVAR*S*NSOA,Ystage_tlm,1,buf_Y_tlm(1:NVAR*S*NSOA,stack_ptr),1) |
---|
1906 | CALL WCOPY(NVAR*S*NSOA,K_tlm,1,buf_K_tlm(1:NVAR*S*NSOA,stack_ptr),1) |
---|
1907 | |
---|
1908 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1909 | END SUBROUTINE ros_DPush |
---|
1910 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1911 | |
---|
1912 | |
---|
1913 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1914 | SUBROUTINE ros_DPop( S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
---|
1915 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1916 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
1917 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1918 | |
---|
1919 | INTEGER, INTENT(IN) :: S ! no of stages |
---|
1920 | INTEGER, INTENT(IN) :: NSOA ! no of second order adjoints |
---|
1921 | KPP_REAL, INTENT(OUT) :: T, H, Ystage(NVAR*S), K(NVAR*S) |
---|
1922 | KPP_REAL, INTENT(OUT) :: Ystage_tlm(NVAR*S,NSOA), K_tlm(NVAR*S,NSOA) |
---|
1923 | |
---|
1924 | IF ( stack_ptr <= 0 ) THEN |
---|
1925 | PRINT*,'Pop failed: empty buffer' |
---|
1926 | STOP |
---|
1927 | END IF |
---|
1928 | H = buf_H( stack_ptr ) |
---|
1929 | T = buf_T( stack_ptr ) |
---|
1930 | CALL WCOPY(NVAR*S,buf_Y(1:NVAR*S,stack_ptr),1,Ystage,1) |
---|
1931 | CALL WCOPY(NVAR*S,buf_K(1:NVAR*S,stack_ptr),1,K,1) |
---|
1932 | CALL WCOPY(NVAR*S*NSOA,buf_Y_tlm(1:NVAR*S*NSOA,stack_ptr),1,Ystage_tlm,1) |
---|
1933 | CALL WCOPY(NVAR*S*NSOA,buf_K_tlm(1:NVAR*S*NSOA,stack_ptr),1,K_tlm,1) |
---|
1934 | |
---|
1935 | stack_ptr = stack_ptr - 1 |
---|
1936 | |
---|
1937 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1938 | END SUBROUTINE ros_DPop |
---|
1939 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1940 | |
---|
1941 | END MODULE KPP_ROOT_Integrator |
---|
1942 | |
---|