[2696] | 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 |
---|
| 394 | FacRej = RCNTRL(6) |
---|
| 395 | ELSE |
---|
| 396 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
---|
| 397 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 398 | RETURN |
---|
| 399 | END IF |
---|
| 400 | !~~~> FacSafe: Safety Factor in the computation of new step size |
---|
| 401 | IF (RCNTRL(7) == ZERO) THEN |
---|
| 402 | FacSafe = 0.9d0 |
---|
| 403 | ELSEIF (RCNTRL(7) > ZERO) THEN |
---|
| 404 | FacSafe = RCNTRL(7) |
---|
| 405 | ELSE |
---|
| 406 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
---|
| 407 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 408 | RETURN |
---|
| 409 | END IF |
---|
| 410 | !~~~> Check if tolerances are reasonable |
---|
| 411 | DO i=1,UplimTol |
---|
| 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 ) |
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| 1876 | IF (i/=0) THEN |
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| 1877 | PRINT*,'Failed deallocation of buffer K_tlm'; STOP |
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| 1878 | END IF |
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| 1879 | |
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| 1880 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1881 | END SUBROUTINE ros_FreeDBuffers |
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| 1882 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1883 | |
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| 1884 | |
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| 1885 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1886 | SUBROUTINE ros_DPush( S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
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| 1887 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1888 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
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| 1889 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1890 | |
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| 1891 | INTEGER, INTENT(IN) :: S ! no of stages |
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| 1892 | INTEGER, INTENT(IN) :: NSOA ! no of second order adjoints |
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| 1893 | KPP_REAL :: T, H, Ystage(NVAR*S), K(NVAR*S) |
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| 1894 | KPP_REAL :: Ystage_tlm(NVAR*S,NSOA), K_tlm(NVAR*S,NSOA) |
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| 1895 | |
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| 1896 | stack_ptr = stack_ptr + 1 |
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| 1897 | IF ( stack_ptr > bufsize ) THEN |
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| 1898 | PRINT*,'Push failed: buffer overflow' |
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| 1899 | STOP |
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| 1900 | END IF |
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| 1901 | buf_H( stack_ptr ) = H |
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| 1902 | buf_T( stack_ptr ) = T |
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| 1903 | CALL WCOPY(NVAR*S,Ystage,1,buf_Y(1:NVAR*S,stack_ptr),1) |
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| 1904 | CALL WCOPY(NVAR*S,K,1,buf_K(1:NVAR*S,stack_ptr),1) |
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| 1905 | CALL WCOPY(NVAR*S*NSOA,Ystage_tlm,1,buf_Y_tlm(1:NVAR*S*NSOA,stack_ptr),1) |
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| 1906 | CALL WCOPY(NVAR*S*NSOA,K_tlm,1,buf_K_tlm(1:NVAR*S*NSOA,stack_ptr),1) |
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| 1907 | |
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| 1908 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1909 | END SUBROUTINE ros_DPush |
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| 1910 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1911 | |
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| 1912 | |
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| 1913 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1914 | SUBROUTINE ros_DPop( S, NSOA, T, H, Ystage, K, Ystage_tlm, K_tlm ) |
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| 1915 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1916 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
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| 1917 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1918 | |
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| 1919 | INTEGER, INTENT(IN) :: S ! no of stages |
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| 1920 | INTEGER, INTENT(IN) :: NSOA ! no of second order adjoints |
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| 1921 | KPP_REAL, INTENT(OUT) :: T, H, Ystage(NVAR*S), K(NVAR*S) |
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| 1922 | KPP_REAL, INTENT(OUT) :: Ystage_tlm(NVAR*S,NSOA), K_tlm(NVAR*S,NSOA) |
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| 1923 | |
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| 1924 | IF ( stack_ptr <= 0 ) THEN |
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| 1925 | PRINT*,'Pop failed: empty buffer' |
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| 1926 | STOP |
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| 1927 | END IF |
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| 1928 | H = buf_H( stack_ptr ) |
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| 1929 | T = buf_T( stack_ptr ) |
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| 1930 | CALL WCOPY(NVAR*S,buf_Y(1:NVAR*S,stack_ptr),1,Ystage,1) |
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| 1931 | CALL WCOPY(NVAR*S,buf_K(1:NVAR*S,stack_ptr),1,K,1) |
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| 1932 | CALL WCOPY(NVAR*S*NSOA,buf_Y_tlm(1:NVAR*S*NSOA,stack_ptr),1,Ystage_tlm,1) |
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| 1933 | CALL WCOPY(NVAR*S*NSOA,buf_K_tlm(1:NVAR*S*NSOA,stack_ptr),1,K_tlm,1) |
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| 1934 | |
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| 1935 | stack_ptr = stack_ptr - 1 |
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| 1936 | |
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| 1937 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1938 | END SUBROUTINE ros_DPop |
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| 1939 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1940 | |
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| 1941 | END MODULE KPP_ROOT_Integrator |
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| 1942 | |
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