[2696] | 1 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 2 | ! Discrete adjoints of Rosenbrock, ! |
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| 3 | ! for several Rosenbrock methods: ! |
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| 4 | ! * Ros2 ! |
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| 5 | ! * Ros3 ! |
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| 6 | ! * Ros4 ! |
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| 7 | ! * Rodas3 ! |
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| 8 | ! * Rodas4 ! |
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| 9 | ! By default the code employs the KPP sparse linear algebra routines ! |
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| 10 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 11 | ! ! |
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| 12 | ! (C) Adrian Sandu, August 2004 ! |
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| 13 | ! Virginia Polytechnic Institute and State University ! |
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| 14 | ! Contact: sandu@cs.vt.edu ! |
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| 15 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 ! |
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| 16 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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| 17 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 18 | |
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| 19 | MODULE KPP_ROOT_Integrator |
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| 20 | |
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| 21 | USE KPP_ROOT_Precision |
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| 22 | USE KPP_ROOT_Parameters |
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| 23 | USE KPP_ROOT_Global |
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| 24 | USE KPP_ROOT_LinearAlgebra |
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| 25 | USE KPP_ROOT_Rates |
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| 26 | USE KPP_ROOT_Function |
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| 27 | USE KPP_ROOT_Jacobian |
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| 28 | USE KPP_ROOT_Hessian |
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| 29 | USE KPP_ROOT_Util |
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| 30 | |
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| 31 | IMPLICIT NONE |
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| 32 | PUBLIC |
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| 33 | SAVE |
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| 34 | |
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| 35 | !~~~> Statistics on the work performed by the Rosenbrock method |
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| 36 | INTEGER, PARAMETER :: Nfun=1, Njac=2, Nstp=3, Nacc=4, & |
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| 37 | Nrej=5, Ndec=6, Nsol=7, Nsng=8, & |
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| 38 | Ntexit=1, Nhexit=2, Nhnew = 3 |
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| 39 | |
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| 40 | |
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| 41 | CONTAINS ! Routines in the module KPP_ROOT_Integrator |
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| 42 | |
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| 43 | |
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| 44 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 45 | SUBROUTINE INTEGRATE_ADJ( NADJ, Y, Lambda, TIN, TOUT, & |
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| 46 | ATOL_adj, RTOL_adj, & |
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| 47 | ICNTRL_U, RCNTRL_U, ISTATUS_U, RSTATUS_U ) |
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| 48 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 49 | |
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| 50 | IMPLICIT NONE |
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| 51 | |
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| 52 | !~~~> Y - Concentrations |
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| 53 | KPP_REAL :: Y(NVAR) |
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| 54 | !~~~> NADJ - No. of cost functionals for which adjoints |
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| 55 | ! are evaluated simultaneously |
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| 56 | ! If single cost functional is considered (like in |
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| 57 | ! most applications) simply set NADJ = 1 |
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| 58 | INTEGER NADJ |
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| 59 | !~~~> Lambda - Sensitivities w.r.t. concentrations |
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| 60 | ! Note: Lambda (1:NVAR,j) contains sensitivities of |
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| 61 | ! the j-th cost functional w.r.t. Y(1:NVAR), j=1...NADJ |
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| 62 | KPP_REAL :: Lambda(NVAR,NADJ) |
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| 63 | KPP_REAL, INTENT(IN) :: TIN ! TIN - Start Time |
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| 64 | KPP_REAL, INTENT(IN) :: TOUT ! TOUT - End Time |
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| 65 | !~~~> Tolerances for adjoint calculations |
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| 66 | ! (used only for full continuous adjoint) |
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| 67 | KPP_REAL, INTENT(IN) :: ATOL_adj(NVAR,NADJ), RTOL_adj(NVAR,NADJ) |
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| 68 | !~~~> Optional input parameters and statistics |
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| 69 | INTEGER, INTENT(IN), OPTIONAL :: ICNTRL_U(20) |
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| 70 | KPP_REAL, INTENT(IN), OPTIONAL :: RCNTRL_U(20) |
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| 71 | INTEGER, INTENT(OUT), OPTIONAL :: ISTATUS_U(20) |
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| 72 | KPP_REAL, INTENT(OUT), OPTIONAL :: RSTATUS_U(20) |
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| 73 | |
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| 74 | KPP_REAL :: RCNTRL(20), RSTATUS(20) |
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| 75 | INTEGER :: ICNTRL(20), ISTATUS(20), IERR |
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| 76 | |
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| 77 | INTEGER, SAVE :: Ntotal |
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| 78 | |
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| 79 | |
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| 80 | ICNTRL(1:20) = 0 |
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| 81 | RCNTRL(1:20) = 0.0_dp |
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| 82 | ISTATUS(1:20) = 0 |
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| 83 | RSTATUS(1:20) = 0.0_dp |
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| 84 | |
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| 85 | |
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| 86 | !~~~> fine-tune the integrator: |
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| 87 | ! ICNTRL(1) = 0 ! 0 = non-autonomous, 1 = autonomous |
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| 88 | ! ICNTRL(2) = 1 ! 0 = scalar, 1 = vector tolerances |
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| 89 | ! RCNTRL(3) = STEPMIN ! starting step |
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| 90 | ! ICNTRL(3) = 5 ! choice of the method for forward integration |
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| 91 | ! ICNTRL(6) = 1 ! choice of the method for continuous adjoint |
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| 92 | ! ICNTRL(7) = 2 ! 1=none, 2=discrete, 3=full continuous, 4=simplified continuous adjoint |
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| 93 | ! ICNTRL(8) = 1 ! Save fwd LU factorization: 0 = *don't* save, 1 = save |
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| 94 | |
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| 95 | |
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| 96 | ! if optional parameters are given, and if they are >=0, then they overwrite default settings |
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| 97 | IF (PRESENT(ICNTRL_U)) THEN |
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| 98 | WHERE(ICNTRL_U(:) >= 0) ICNTRL(:) = ICNTRL_U(:) |
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| 99 | END IF |
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| 100 | IF (PRESENT(RCNTRL_U)) THEN |
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| 101 | WHERE(RCNTRL_U(:) >= 0) RCNTRL(:) = RCNTRL_U(:) |
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| 102 | END IF |
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| 103 | |
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| 104 | |
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| 105 | CALL RosenbrockADJ(Y, NADJ, Lambda, & |
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| 106 | TIN, TOUT, & |
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| 107 | ATOL, RTOL, ATOL_adj, RTOL_adj, & |
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| 108 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, IERR) |
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| 109 | |
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| 110 | |
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| 111 | !~~~> Debug option: show number of steps |
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| 112 | ! Ntotal = Ntotal + ISTATUS(Nstp) |
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| 113 | ! WRITE(6,777) ISTATUS(Nstp),Ntotal,VAR(ind_O3),VAR(ind_NO2) |
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| 114 | !777 FORMAT('NSTEPS=',I6,' (',I6,') O3=',E24.14,' NO2=',E24.14) |
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| 115 | |
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| 116 | IF (IERR < 0) THEN |
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| 117 | print *,'RosenbrockADJ: Unsucessful step at T=', & |
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| 118 | TIN,' (IERR=',IERR,')' |
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| 119 | END IF |
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| 120 | |
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| 121 | STEPMIN = RSTATUS(Nhexit) |
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| 122 | ! if optional parameters are given for output |
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| 123 | ! copy to them to return information |
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| 124 | IF (PRESENT(ISTATUS_U)) ISTATUS_U(:) = ISTATUS(:) |
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| 125 | IF (PRESENT(RSTATUS_U)) RSTATUS_U(:) = RSTATUS(:) |
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| 126 | |
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| 127 | END SUBROUTINE INTEGRATE_ADJ |
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| 128 | |
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| 129 | |
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| 130 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 131 | SUBROUTINE RosenbrockADJ( Y, NADJ, Lambda, & |
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| 132 | Tstart, Tend, & |
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| 133 | AbsTol, RelTol, AbsTol_adj, RelTol_adj, & |
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| 134 | RCNTRL, ICNTRL, RSTATUS, ISTATUS, IERR) |
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| 135 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 136 | ! |
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| 137 | ! ADJ = Adjoint of the Tangent Linear Model of a Rosenbrock Method |
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| 138 | ! |
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| 139 | ! Solves the system y'=F(t,y) using a RosenbrockADJ method defined by: |
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| 140 | ! |
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| 141 | ! G = 1/(H*gamma(1)) - Jac(t0,Y0) |
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| 142 | ! T_i = t0 + Alpha(i)*H |
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| 143 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
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| 144 | ! G * K_i = Fun( T_i, Y_i ) + \sum_{j=1}^S C(i,j)/H * K_j + |
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| 145 | ! gamma(i)*dF/dT(t0, Y0) |
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| 146 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
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| 147 | ! |
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| 148 | ! For details on RosenbrockADJ methods and their implementation consult: |
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| 149 | ! E. Hairer and G. Wanner |
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| 150 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 151 | ! Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 152 | ! The codes contained in the book inspired this implementation. |
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| 153 | ! |
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| 154 | ! (C) Adrian Sandu, August 2004 |
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| 155 | ! Virginia Polytechnic Institute and State University |
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| 156 | ! Contact: sandu@cs.vt.edu |
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| 157 | ! Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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| 158 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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| 159 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 160 | ! |
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| 161 | !~~~> INPUT ARGUMENTS: |
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| 162 | ! |
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| 163 | !- Y(NVAR) = vector of initial conditions (at T=Tstart) |
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| 164 | ! NADJ -> dimension of linearized system, |
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| 165 | ! i.e. the number of sensitivity coefficients |
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| 166 | !- Lambda(NVAR,NADJ) -> vector of initial sensitivity conditions (at T=Tstart) |
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| 167 | !- [Tstart,Tend] = time range of integration |
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| 168 | ! (if Tstart>Tend the integration is performed backwards in time) |
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| 169 | !- RelTol, AbsTol = user precribed accuracy |
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| 170 | !- SUBROUTINE Fun( T, Y, Ydot ) = ODE function, |
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| 171 | ! returns Ydot = Y' = F(T,Y) |
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| 172 | !- SUBROUTINE Jac( T, Y, Jcb ) = Jacobian of the ODE function, |
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| 173 | ! returns Jcb = dF/dY |
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| 174 | !- ICNTRL(1:10) = integer inputs parameters |
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| 175 | !- RCNTRL(1:10) = real inputs parameters |
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| 176 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 177 | ! |
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| 178 | !~~~> OUTPUT ARGUMENTS: |
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| 179 | ! |
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| 180 | !- Y(NVAR) -> vector of final states (at T->Tend) |
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| 181 | !- Lambda(NVAR,NADJ) -> vector of final sensitivities (at T=Tend) |
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| 182 | !- ICNTRL(11:20) -> integer output parameters |
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| 183 | !- RCNTRL(11:20) -> real output parameters |
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| 184 | !- IERR -> job status upon return |
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| 185 | ! - succes (positive value) or failure (negative value) - |
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| 186 | ! = 1 : Success |
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| 187 | ! = -1 : Improper value for maximal no of steps |
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| 188 | ! = -2 : Selected RosenbrockADJ method not implemented |
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| 189 | ! = -3 : Hmin/Hmax/Hstart must be positive |
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| 190 | ! = -4 : FacMin/FacMax/FacRej must be positive |
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| 191 | ! = -5 : Improper tolerance values |
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| 192 | ! = -6 : No of steps exceeds maximum bound |
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| 193 | ! = -7 : Step size too small |
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| 194 | ! = -8 : Matrix is repeatedly singular |
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| 195 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 196 | ! |
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| 197 | !~~~> INPUT PARAMETERS: |
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| 198 | ! |
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| 199 | ! Note: For input parameters equal to zero the default values of the |
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| 200 | ! corresponding variables are used. |
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| 201 | ! |
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| 202 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
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| 203 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
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| 204 | ! |
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| 205 | ! ICNTRL(2) = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 206 | ! = 1: AbsTol, RelTol are scalars |
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| 207 | ! |
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| 208 | ! ICNTRL(3) -> selection of a particular Rosenbrock method |
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| 209 | ! = 0 : default method is Rodas3 |
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| 210 | ! = 1 : method is Ros2 |
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| 211 | ! = 2 : method is Ros3 |
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| 212 | ! = 3 : method is Ros4 |
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| 213 | ! = 4 : method is Rodas3 |
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| 214 | ! = 5: method is Rodas4 |
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| 215 | ! |
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| 216 | ! ICNTRL(4) -> maximum number of integration steps |
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| 217 | ! For ICNTRL(4)=0) the default value of BUFSIZE is used |
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| 218 | ! |
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| 219 | ! ICNTRL(6) -> selection of a particular Rosenbrock method for the |
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| 220 | ! continuous adjoint integration - for cts adjoint it |
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| 221 | ! can be different than the forward method ICNTRL(3) |
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| 222 | ! Note 1: to avoid interpolation errors (which can be huge!) |
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| 223 | ! it is recommended to use only ICNTRL(7) = 2 or 4 |
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| 224 | ! Note 2: the performance of the full continuous adjoint |
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| 225 | ! strongly depends on the forward solution accuracy Abs/RelTol |
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| 226 | ! |
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| 227 | ! ICNTRL(7) -> Type of adjoint algorithm |
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| 228 | ! = 0 : default is discrete adjoint ( of method ICNTRL(3) ) |
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| 229 | ! = 1 : no adjoint |
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| 230 | ! = 2 : discrete adjoint ( of method ICNTRL(3) ) |
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| 231 | ! = 3 : fully adaptive continuous adjoint ( with method ICNTRL(6) ) |
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| 232 | ! = 4 : simplified continuous adjoint ( with method ICNTRL(6) ) |
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| 233 | ! |
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| 234 | ! ICNTRL(8) -> checkpointing the LU factorization at each step: |
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| 235 | ! ICNTRL(8)=0 : do *not* save LU factorization (the default) |
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| 236 | ! ICNTRL(8)=1 : save LU factorization |
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| 237 | ! Note: if ICNTRL(7)=1 the LU factorization is *not* saved |
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| 238 | ! |
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| 239 | !~~~> Real input parameters: |
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| 240 | ! |
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| 241 | ! RCNTRL(1) -> Hmin, lower bound for the integration step size |
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| 242 | ! It is strongly recommended to keep Hmin = ZERO |
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| 243 | ! |
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| 244 | ! RCNTRL(2) -> Hmax, upper bound for the integration step size |
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| 245 | ! |
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| 246 | ! RCNTRL(3) -> Hstart, starting value for the integration step size |
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| 247 | ! |
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| 248 | ! RCNTRL(4) -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 249 | ! |
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| 250 | ! RCNTRL(5) -> FacMax, upper bound on step increase factor (default=6) |
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| 251 | ! |
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| 252 | ! RCNTRL(6) -> FacRej, step decrease factor after multiple rejections |
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| 253 | ! (default=0.1) |
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| 254 | ! |
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| 255 | ! RCNTRL(7) -> FacSafe, by which the new step is slightly smaller |
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| 256 | ! than the predicted value (default=0.9) |
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| 257 | ! |
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| 258 | ! RCNTRL(8) -> ThetaMin. If Newton convergence rate smaller |
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| 259 | ! than ThetaMin the Jacobian is not recomputed; |
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| 260 | ! (default=0.001) |
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| 261 | ! |
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| 262 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 263 | ! |
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| 264 | !~~~> OUTPUT PARAMETERS: |
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| 265 | ! |
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| 266 | ! Note: each call to RosenbrockADJ adds the corrent no. of fcn calls |
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| 267 | ! to previous value of ISTATUS(1), and similar for the other params. |
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| 268 | ! Set ISTATUS(1:10) = 0 before call to avoid this accumulation. |
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| 269 | ! |
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| 270 | ! ISTATUS(1) = No. of function calls |
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| 271 | ! ISTATUS(2) = No. of jacobian calls |
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| 272 | ! ISTATUS(3) = No. of steps |
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| 273 | ! ISTATUS(4) = No. of accepted steps |
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| 274 | ! ISTATUS(5) = No. of rejected steps (except at the beginning) |
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| 275 | ! ISTATUS(6) = No. of LU decompositions |
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| 276 | ! ISTATUS(7) = No. of forward/backward substitutions |
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| 277 | ! ISTATUS(8) = No. of singular matrix decompositions |
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| 278 | ! |
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| 279 | ! RSTATUS(1) -> Texit, the time corresponding to the |
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| 280 | ! computed Y upon return |
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| 281 | ! RSTATUS(2) -> Hexit, last accepted step before exit |
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| 282 | ! For multiple restarts, use Hexit as Hstart in the following run |
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| 283 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 284 | |
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| 285 | IMPLICIT NONE |
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| 286 | |
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| 287 | !~~~> Arguments |
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| 288 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
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| 289 | INTEGER, INTENT(IN) :: NADJ |
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| 290 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR,NADJ) |
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| 291 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
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| 292 | KPP_REAL, INTENT(IN) :: AbsTol(NVAR),RelTol(NVAR) |
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| 293 | KPP_REAL, INTENT(IN) :: AbsTol_adj(NVAR,NADJ), RelTol_adj(NVAR,NADJ) |
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| 294 | INTEGER, INTENT(IN) :: ICNTRL(20) |
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| 295 | KPP_REAL, INTENT(IN) :: RCNTRL(20) |
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| 296 | INTEGER, INTENT(INOUT) :: ISTATUS(20) |
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| 297 | KPP_REAL, INTENT(INOUT) :: RSTATUS(20) |
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| 298 | INTEGER, INTENT(OUT) :: IERR |
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| 299 | !~~~> Parameters of the Rosenbrock method, up to 6 stages |
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| 300 | INTEGER :: ros_S, rosMethod |
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| 301 | INTEGER, PARAMETER :: RS2=1, RS3=2, RS4=3, RD3=4, RD4=5 |
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| 302 | KPP_REAL :: ros_A(15), ros_C(15), ros_M(6), ros_E(6), & |
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| 303 | ros_Alpha(6), ros_Gamma(6), ros_ELO |
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| 304 | LOGICAL :: ros_NewF(6) |
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| 305 | CHARACTER(LEN=12) :: ros_Name |
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| 306 | !~~~> Types of Adjoints Implemented |
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| 307 | INTEGER, PARAMETER :: Adj_none = 1, Adj_discrete = 2, & |
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| 308 | Adj_continuous = 3, Adj_simple_continuous = 4 |
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| 309 | !~~~> Checkpoints in memory |
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| 310 | INTEGER, PARAMETER :: bufsize = 200000 |
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| 311 | INTEGER :: stack_ptr = 0 ! last written entry |
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| 312 | KPP_REAL, DIMENSION(:), POINTER :: chk_H, chk_T |
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| 313 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_Y, chk_K, chk_J |
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| 314 | KPP_REAL, DIMENSION(:,:), POINTER :: chk_dY, chk_d2Y |
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| 315 | !~~~> Local variables |
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| 316 | KPP_REAL :: Roundoff, FacMin, FacMax, FacRej, FacSafe |
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| 317 | KPP_REAL :: Hmin, Hmax, Hstart |
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| 318 | KPP_REAL :: Texit |
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| 319 | INTEGER :: i, UplimTol, Max_no_steps |
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| 320 | INTEGER :: AdjointType, CadjMethod |
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| 321 | LOGICAL :: Autonomous, VectorTol, SaveLU |
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| 322 | !~~~> Parameters |
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| 323 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
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| 324 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
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| 325 | |
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| 326 | !~~~> Initialize statistics |
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| 327 | ISTATUS(1:20) = 0 |
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| 328 | RSTATUS(1:20) = ZERO |
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| 329 | |
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| 330 | !~~~> Autonomous or time dependent ODE. Default is time dependent. |
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| 331 | Autonomous = .NOT.(ICNTRL(1) == 0) |
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| 332 | |
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| 333 | !~~~> For Scalar tolerances (ICNTRL(2).NE.0) the code uses AbsTol(1) and RelTol(1) |
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| 334 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:NVAR) and RelTol(1:NVAR) |
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| 335 | IF (ICNTRL(2) == 0) THEN |
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| 336 | VectorTol = .TRUE. |
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| 337 | UplimTol = NVAR |
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| 338 | ELSE |
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| 339 | VectorTol = .FALSE. |
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| 340 | UplimTol = 1 |
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| 341 | END IF |
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| 342 | |
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| 343 | !~~~> Initialize the particular Rosenbrock method selected |
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| 344 | SELECT CASE (ICNTRL(3)) |
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| 345 | CASE (1) |
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| 346 | CALL Ros2 |
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| 347 | CASE (2) |
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| 348 | CALL Ros3 |
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| 349 | CASE (3) |
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| 350 | CALL Ros4 |
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| 351 | CASE (0,4) |
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| 352 | CALL Rodas3 |
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| 353 | CASE (5) |
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| 354 | CALL Rodas4 |
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| 355 | CASE DEFAULT |
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| 356 | PRINT * , 'Unknown Rosenbrock method: ICNTRL(3)=',ICNTRL(3) |
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| 357 | CALL ros_ErrorMsg(-2,Tstart,ZERO,IERR) |
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| 358 | RETURN |
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| 359 | END SELECT |
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| 360 | |
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| 361 | !~~~> The maximum number of steps admitted |
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| 362 | IF (ICNTRL(4) == 0) THEN |
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| 363 | Max_no_steps = bufsize - 1 |
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| 364 | ELSEIF (Max_no_steps > 0) THEN |
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| 365 | Max_no_steps=ICNTRL(4) |
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| 366 | ELSE |
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| 367 | PRINT * ,'User-selected max no. of steps: ICNTRL(4)=',ICNTRL(4) |
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| 368 | CALL ros_ErrorMsg(-1,Tstart,ZERO,IERR) |
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| 369 | RETURN |
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| 370 | END IF |
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| 371 | |
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| 372 | !~~~> The particular Rosenbrock method chosen for integrating the cts adjoint |
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| 373 | IF (ICNTRL(6) == 0) THEN |
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| 374 | CadjMethod = 4 |
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| 375 | ELSEIF ( (ICNTRL(6) >= 1).AND.(ICNTRL(6) <= 5) ) THEN |
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| 376 | CadjMethod = ICNTRL(6) |
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| 377 | ELSE |
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| 378 | PRINT * , 'Unknown CADJ Rosenbrock method: ICNTRL(6)=', CadjMethod |
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| 379 | CALL ros_ErrorMsg(-2,Tstart,ZERO,IERR) |
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| 380 | RETURN |
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| 381 | END IF |
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| 382 | |
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| 383 | !~~~> Discrete or continuous adjoint formulation |
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| 384 | IF ( ICNTRL(7) == 0 ) THEN |
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| 385 | AdjointType = Adj_discrete |
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| 386 | ELSEIF ( (ICNTRL(7) >= 1).AND.(ICNTRL(7) <= 4) ) THEN |
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| 387 | AdjointType = ICNTRL(7) |
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| 388 | ELSE |
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| 389 | PRINT * , 'User-selected adjoint type: ICNTRL(7)=', AdjointType |
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| 390 | CALL ros_ErrorMsg(-9,Tstart,ZERO,IERR) |
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| 391 | RETURN |
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| 392 | END IF |
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| 393 | |
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| 394 | !~~~> Save or not the forward LU factorization |
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| 395 | SaveLU = (ICNTRL(8) /= 0) |
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| 396 | |
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| 397 | |
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| 398 | !~~~> Unit roundoff (1+Roundoff>1) |
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| 399 | Roundoff = WLAMCH('E') |
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| 400 | |
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| 401 | !~~~> Lower bound on the step size: (positive value) |
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| 402 | IF (RCNTRL(1) == ZERO) THEN |
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| 403 | Hmin = ZERO |
---|
| 404 | ELSEIF (RCNTRL(1) > ZERO) THEN |
---|
| 405 | Hmin = RCNTRL(1) |
---|
| 406 | ELSE |
---|
| 407 | PRINT * , 'User-selected Hmin: RCNTRL(1)=', RCNTRL(1) |
---|
| 408 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
---|
| 409 | RETURN |
---|
| 410 | END IF |
---|
| 411 | !~~~> Upper bound on the step size: (positive value) |
---|
| 412 | IF (RCNTRL(2) == ZERO) THEN |
---|
| 413 | Hmax = ABS(Tend-Tstart) |
---|
| 414 | ELSEIF (RCNTRL(2) > ZERO) THEN |
---|
| 415 | Hmax = MIN(ABS(RCNTRL(2)),ABS(Tend-Tstart)) |
---|
| 416 | ELSE |
---|
| 417 | PRINT * , 'User-selected Hmax: RCNTRL(2)=', RCNTRL(2) |
---|
| 418 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
---|
| 419 | RETURN |
---|
| 420 | END IF |
---|
| 421 | !~~~> Starting step size: (positive value) |
---|
| 422 | IF (RCNTRL(3) == ZERO) THEN |
---|
| 423 | Hstart = MAX(Hmin,DeltaMin) |
---|
| 424 | ELSEIF (RCNTRL(3) > ZERO) THEN |
---|
| 425 | Hstart = MIN(ABS(RCNTRL(3)),ABS(Tend-Tstart)) |
---|
| 426 | ELSE |
---|
| 427 | PRINT * , 'User-selected Hstart: RCNTRL(3)=', RCNTRL(3) |
---|
| 428 | CALL ros_ErrorMsg(-3,Tstart,ZERO,IERR) |
---|
| 429 | RETURN |
---|
| 430 | END IF |
---|
| 431 | !~~~> Step size can be changed s.t. FacMin < Hnew/Hold < FacMax |
---|
| 432 | IF (RCNTRL(4) == ZERO) THEN |
---|
| 433 | FacMin = 0.2d0 |
---|
| 434 | ELSEIF (RCNTRL(4) > ZERO) THEN |
---|
| 435 | FacMin = RCNTRL(4) |
---|
| 436 | ELSE |
---|
| 437 | PRINT * , 'User-selected FacMin: RCNTRL(4)=', RCNTRL(4) |
---|
| 438 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 439 | RETURN |
---|
| 440 | END IF |
---|
| 441 | IF (RCNTRL(5) == ZERO) THEN |
---|
| 442 | FacMax = 6.0d0 |
---|
| 443 | ELSEIF (RCNTRL(5) > ZERO) THEN |
---|
| 444 | FacMax = RCNTRL(5) |
---|
| 445 | ELSE |
---|
| 446 | PRINT * , 'User-selected FacMax: RCNTRL(5)=', RCNTRL(5) |
---|
| 447 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 448 | RETURN |
---|
| 449 | END IF |
---|
| 450 | !~~~> FacRej: Factor to decrease step after 2 succesive rejections |
---|
| 451 | IF (RCNTRL(6) == ZERO) THEN |
---|
| 452 | FacRej = 0.1d0 |
---|
| 453 | ELSEIF (RCNTRL(6) > ZERO) THEN |
---|
| 454 | FacRej = RCNTRL(6) |
---|
| 455 | ELSE |
---|
| 456 | PRINT * , 'User-selected FacRej: RCNTRL(6)=', RCNTRL(6) |
---|
| 457 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 458 | RETURN |
---|
| 459 | END IF |
---|
| 460 | !~~~> FacSafe: Safety Factor in the computation of new step size |
---|
| 461 | IF (RCNTRL(7) == ZERO) THEN |
---|
| 462 | FacSafe = 0.9d0 |
---|
| 463 | ELSEIF (RCNTRL(7) > ZERO) THEN |
---|
| 464 | FacSafe = RCNTRL(7) |
---|
| 465 | ELSE |
---|
| 466 | PRINT * , 'User-selected FacSafe: RCNTRL(7)=', RCNTRL(7) |
---|
| 467 | CALL ros_ErrorMsg(-4,Tstart,ZERO,IERR) |
---|
| 468 | RETURN |
---|
| 469 | END IF |
---|
| 470 | !~~~> Check if tolerances are reasonable |
---|
| 471 | DO i=1,UplimTol |
---|
| 472 | IF ( (AbsTol(i) <= ZERO) .OR. (RelTol(i) <= 10.d0*Roundoff) & |
---|
| 473 | .OR. (RelTol(i) >= 1.0d0) ) THEN |
---|
| 474 | PRINT * , ' AbsTol(',i,') = ',AbsTol(i) |
---|
| 475 | PRINT * , ' RelTol(',i,') = ',RelTol(i) |
---|
| 476 | CALL ros_ErrorMsg(-5,Tstart,ZERO,IERR) |
---|
| 477 | RETURN |
---|
| 478 | END IF |
---|
| 479 | END DO |
---|
| 480 | |
---|
| 481 | |
---|
| 482 | !~~~> Allocate checkpoint space or open checkpoint files |
---|
| 483 | IF (AdjointType == Adj_discrete) THEN |
---|
| 484 | CALL ros_AllocateDBuffers( ros_S ) |
---|
| 485 | ELSEIF ( (AdjointType == Adj_continuous).OR. & |
---|
| 486 | (AdjointType == Adj_simple_continuous) ) THEN |
---|
| 487 | CALL ros_AllocateCBuffers |
---|
| 488 | END IF |
---|
| 489 | |
---|
| 490 | !~~~> CALL Forward Rosenbrock method |
---|
| 491 | CALL ros_FwdInt(Y,Tstart,Tend,Texit, & |
---|
| 492 | AbsTol, RelTol, & |
---|
| 493 | ! Error indicator |
---|
| 494 | IERR) |
---|
| 495 | |
---|
| 496 | PRINT*,'FORWARD STATISTICS' |
---|
| 497 | PRINT*,'Step=',Nstp,' Acc=',Nacc, & |
---|
| 498 | ' Rej=',Nrej, ' Singular=',Nsng |
---|
| 499 | |
---|
| 500 | !~~~> If Forward integration failed return |
---|
| 501 | IF (IERR<0) RETURN |
---|
| 502 | |
---|
| 503 | !~~~> Initialize the particular Rosenbrock method for continuous adjoint |
---|
| 504 | IF ( (AdjointType == Adj_continuous).OR. & |
---|
| 505 | (AdjointType == Adj_simple_continuous) ) THEN |
---|
| 506 | SELECT CASE (CadjMethod) |
---|
| 507 | CASE (1) |
---|
| 508 | CALL Ros2 |
---|
| 509 | CASE (2) |
---|
| 510 | CALL Ros3 |
---|
| 511 | CASE (3) |
---|
| 512 | CALL Ros4 |
---|
| 513 | CASE (4) |
---|
| 514 | CALL Rodas3 |
---|
| 515 | CASE (5) |
---|
| 516 | CALL Rodas4 |
---|
| 517 | CASE DEFAULT |
---|
| 518 | PRINT * , 'Unknown Rosenbrock method: ICNTRL(3)=', ICNTRL(3) |
---|
| 519 | CALL ros_ErrorMsg(-2,Tstart,ZERO,IERR) |
---|
| 520 | RETURN |
---|
| 521 | END SELECT |
---|
| 522 | END IF |
---|
| 523 | |
---|
| 524 | SELECT CASE (AdjointType) |
---|
| 525 | CASE (Adj_discrete) |
---|
| 526 | CALL ros_DadjInt ( & |
---|
| 527 | NADJ, Lambda, & |
---|
| 528 | Tstart, Tend, Texit, & |
---|
| 529 | IERR ) |
---|
| 530 | CASE (Adj_continuous) |
---|
| 531 | CALL ros_CadjInt ( & |
---|
| 532 | NADJ, Lambda, & |
---|
| 533 | Tend, Tstart, Texit, & |
---|
| 534 | AbsTol_adj, RelTol_adj, & |
---|
| 535 | IERR ) |
---|
| 536 | CASE (Adj_simple_continuous) |
---|
| 537 | CALL ros_SimpleCadjInt ( & |
---|
| 538 | NADJ, Lambda, & |
---|
| 539 | Tstart, Tend, Texit, & |
---|
| 540 | IERR ) |
---|
| 541 | END SELECT ! AdjointType |
---|
| 542 | |
---|
| 543 | PRINT*,'ADJOINT STATISTICS' |
---|
| 544 | PRINT*,'Step=',Nstp,' Acc=',Nacc, & |
---|
| 545 | ' Rej=',Nrej, ' Singular=',Nsng |
---|
| 546 | |
---|
| 547 | !~~~> Free checkpoint space or close checkpoint files |
---|
| 548 | IF (AdjointType == Adj_discrete) THEN |
---|
| 549 | CALL ros_FreeDBuffers |
---|
| 550 | ELSEIF ( (AdjointType == Adj_continuous) .OR. & |
---|
| 551 | (AdjointType == Adj_simple_continuous) ) THEN |
---|
| 552 | CALL ros_FreeCBuffers |
---|
| 553 | END IF |
---|
| 554 | |
---|
| 555 | |
---|
| 556 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 557 | CONTAINS ! Procedures internal to RosenbrockADJ |
---|
| 558 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 559 | |
---|
| 560 | |
---|
| 561 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 562 | SUBROUTINE ros_AllocateDBuffers( S ) |
---|
| 563 | !~~~> Allocate buffer space for discrete adjoint |
---|
| 564 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 565 | INTEGER :: i, S |
---|
| 566 | |
---|
| 567 | ALLOCATE( chk_H(bufsize), STAT=i ) |
---|
| 568 | IF (i/=0) THEN |
---|
| 569 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
| 570 | END IF |
---|
| 571 | ALLOCATE( chk_T(bufsize), STAT=i ) |
---|
| 572 | IF (i/=0) THEN |
---|
| 573 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
| 574 | END IF |
---|
| 575 | ALLOCATE( chk_Y(NVAR*S,bufsize), STAT=i ) |
---|
| 576 | IF (i/=0) THEN |
---|
| 577 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
| 578 | END IF |
---|
| 579 | ALLOCATE( chk_K(NVAR*S,bufsize), STAT=i ) |
---|
| 580 | IF (i/=0) THEN |
---|
| 581 | PRINT*,'Failed allocation of buffer K'; STOP |
---|
| 582 | END IF |
---|
| 583 | IF (SaveLU) THEN |
---|
| 584 | #ifdef FULL_ALGEBRA |
---|
| 585 | ALLOCATE( chk_J(NVAR*NVAR,bufsize), STAT=i ) |
---|
| 586 | #else |
---|
| 587 | ALLOCATE( chk_J(LU_NONZERO,bufsize), STAT=i ) |
---|
| 588 | #endif |
---|
| 589 | IF (i/=0) THEN |
---|
| 590 | PRINT*,'Failed allocation of buffer J'; STOP |
---|
| 591 | END IF |
---|
| 592 | END IF |
---|
| 593 | |
---|
| 594 | END SUBROUTINE ros_AllocateDBuffers |
---|
| 595 | |
---|
| 596 | |
---|
| 597 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 598 | SUBROUTINE ros_FreeDBuffers |
---|
| 599 | !~~~> Dallocate buffer space for discrete adjoint |
---|
| 600 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 601 | INTEGER :: i |
---|
| 602 | |
---|
| 603 | DEALLOCATE( chk_H, STAT=i ) |
---|
| 604 | IF (i/=0) THEN |
---|
| 605 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
| 606 | END IF |
---|
| 607 | DEALLOCATE( chk_T, STAT=i ) |
---|
| 608 | IF (i/=0) THEN |
---|
| 609 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
| 610 | END IF |
---|
| 611 | DEALLOCATE( chk_Y, STAT=i ) |
---|
| 612 | IF (i/=0) THEN |
---|
| 613 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
| 614 | END IF |
---|
| 615 | DEALLOCATE( chk_K, STAT=i ) |
---|
| 616 | IF (i/=0) THEN |
---|
| 617 | PRINT*,'Failed deallocation of buffer K'; STOP |
---|
| 618 | END IF |
---|
| 619 | IF (SaveLU) THEN |
---|
| 620 | DEALLOCATE( chk_J, STAT=i ) |
---|
| 621 | IF (i/=0) THEN |
---|
| 622 | PRINT*,'Failed deallocation of buffer J'; STOP |
---|
| 623 | END IF |
---|
| 624 | END IF |
---|
| 625 | |
---|
| 626 | END SUBROUTINE ros_FreeDBuffers |
---|
| 627 | |
---|
| 628 | |
---|
| 629 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 630 | SUBROUTINE ros_AllocateCBuffers |
---|
| 631 | !~~~> Allocate buffer space for continuous adjoint |
---|
| 632 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 633 | INTEGER :: i |
---|
| 634 | |
---|
| 635 | ALLOCATE( chk_H(bufsize), STAT=i ) |
---|
| 636 | IF (i/=0) THEN |
---|
| 637 | PRINT*,'Failed allocation of buffer H'; STOP |
---|
| 638 | END IF |
---|
| 639 | ALLOCATE( chk_T(bufsize), STAT=i ) |
---|
| 640 | IF (i/=0) THEN |
---|
| 641 | PRINT*,'Failed allocation of buffer T'; STOP |
---|
| 642 | END IF |
---|
| 643 | ALLOCATE( chk_Y(NVAR,bufsize), STAT=i ) |
---|
| 644 | IF (i/=0) THEN |
---|
| 645 | PRINT*,'Failed allocation of buffer Y'; STOP |
---|
| 646 | END IF |
---|
| 647 | ALLOCATE( chk_dY(NVAR,bufsize), STAT=i ) |
---|
| 648 | IF (i/=0) THEN |
---|
| 649 | PRINT*,'Failed allocation of buffer dY'; STOP |
---|
| 650 | END IF |
---|
| 651 | ALLOCATE( chk_d2Y(NVAR,bufsize), STAT=i ) |
---|
| 652 | IF (i/=0) THEN |
---|
| 653 | PRINT*,'Failed allocation of buffer d2Y'; STOP |
---|
| 654 | END IF |
---|
| 655 | |
---|
| 656 | END SUBROUTINE ros_AllocateCBuffers |
---|
| 657 | |
---|
| 658 | |
---|
| 659 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 660 | SUBROUTINE ros_FreeCBuffers |
---|
| 661 | !~~~> Dallocate buffer space for continuous adjoint |
---|
| 662 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 663 | INTEGER :: i |
---|
| 664 | |
---|
| 665 | DEALLOCATE( chk_H, STAT=i ) |
---|
| 666 | IF (i/=0) THEN |
---|
| 667 | PRINT*,'Failed deallocation of buffer H'; STOP |
---|
| 668 | END IF |
---|
| 669 | DEALLOCATE( chk_T, STAT=i ) |
---|
| 670 | IF (i/=0) THEN |
---|
| 671 | PRINT*,'Failed deallocation of buffer T'; STOP |
---|
| 672 | END IF |
---|
| 673 | DEALLOCATE( chk_Y, STAT=i ) |
---|
| 674 | IF (i/=0) THEN |
---|
| 675 | PRINT*,'Failed deallocation of buffer Y'; STOP |
---|
| 676 | END IF |
---|
| 677 | DEALLOCATE( chk_dY, STAT=i ) |
---|
| 678 | IF (i/=0) THEN |
---|
| 679 | PRINT*,'Failed deallocation of buffer dY'; STOP |
---|
| 680 | END IF |
---|
| 681 | DEALLOCATE( chk_d2Y, STAT=i ) |
---|
| 682 | IF (i/=0) THEN |
---|
| 683 | PRINT*,'Failed deallocation of buffer d2Y'; STOP |
---|
| 684 | END IF |
---|
| 685 | |
---|
| 686 | END SUBROUTINE ros_FreeCBuffers |
---|
| 687 | |
---|
| 688 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 689 | SUBROUTINE ros_DPush( S, T, H, Ystage, K, E, P ) |
---|
| 690 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 691 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
| 692 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 693 | INTEGER :: S ! no of stages |
---|
| 694 | KPP_REAL :: T, H, Ystage(NVAR*S), K(NVAR*S) |
---|
| 695 | INTEGER :: P(NVAR) |
---|
| 696 | #ifdef FULL_ALGEBRA |
---|
| 697 | KPP_REAL :: E(NVAR,NVAR) |
---|
| 698 | #else |
---|
| 699 | KPP_REAL :: E(LU_NONZERO) |
---|
| 700 | #endif |
---|
| 701 | |
---|
| 702 | stack_ptr = stack_ptr + 1 |
---|
| 703 | IF ( stack_ptr > bufsize ) THEN |
---|
| 704 | PRINT*,'Push failed: buffer overflow' |
---|
| 705 | STOP |
---|
| 706 | END IF |
---|
| 707 | chk_H( stack_ptr ) = H |
---|
| 708 | chk_T( stack_ptr ) = T |
---|
| 709 | !CALL WCOPY(NVAR*S,Ystage,1,chk_Y(1,stack_ptr),1) |
---|
| 710 | !CALL WCOPY(NVAR*S,K,1,chk_K(1,stack_ptr),1) |
---|
| 711 | chk_Y(1:NVAR*S,stack_ptr) = Ystage(1:NVAR*S) |
---|
| 712 | chk_K(1:NVAR*S,stack_ptr) = K(1:NVAR*S) |
---|
| 713 | IF (SaveLU) THEN |
---|
| 714 | #ifdef FULL_ALGEBRA |
---|
| 715 | chk_J(1:NVAR,1:NVAR,stack_ptr) = E(1:NVAR,1:NVAR) |
---|
| 716 | chk_P(1:NVAR,stack_ptr) = P(1:NVAR) |
---|
| 717 | #else |
---|
| 718 | chk_J(1:LU_NONZERO,stack_ptr) = E(1:LU_NONZERO) |
---|
| 719 | #endif |
---|
| 720 | END IF |
---|
| 721 | |
---|
| 722 | END SUBROUTINE ros_DPush |
---|
| 723 | |
---|
| 724 | |
---|
| 725 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 726 | SUBROUTINE ros_DPop( S, T, H, Ystage, K, E, P ) |
---|
| 727 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 728 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
| 729 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 730 | |
---|
| 731 | INTEGER :: S ! no of stages |
---|
| 732 | KPP_REAL :: T, H, Ystage(NVAR*S), K(NVAR*S) |
---|
| 733 | INTEGER :: P(NVAR) |
---|
| 734 | #ifdef FULL_ALGEBRA |
---|
| 735 | KPP_REAL :: E(NVAR,NVAR) |
---|
| 736 | #else |
---|
| 737 | KPP_REAL :: E(LU_NONZERO) |
---|
| 738 | #endif |
---|
| 739 | |
---|
| 740 | IF ( stack_ptr <= 0 ) THEN |
---|
| 741 | PRINT*,'Pop failed: empty buffer' |
---|
| 742 | STOP |
---|
| 743 | END IF |
---|
| 744 | H = chk_H( stack_ptr ) |
---|
| 745 | T = chk_T( stack_ptr ) |
---|
| 746 | !CALL WCOPY(NVAR*S,chk_Y(1,stack_ptr),1,Ystage,1) |
---|
| 747 | !CALL WCOPY(NVAR*S,chk_K(1,stack_ptr),1,K,1) |
---|
| 748 | Ystage(1:NVAR*S) = chk_Y(1:NVAR*S,stack_ptr) |
---|
| 749 | K(1:NVAR*S) = chk_K(1:NVAR*S,stack_ptr) |
---|
| 750 | !CALL WCOPY(LU_NONZERO,chk_J(1,stack_ptr),1,Jcb,1) |
---|
| 751 | IF (SaveLU) THEN |
---|
| 752 | #ifdef FULL_ALGEBRA |
---|
| 753 | E(1:NVAR,1:NVAR) = chk_J(1:NVAR,1:NVAR,stack_ptr) |
---|
| 754 | P(1:NVAR) = chk_P(1:NVAR,stack_ptr) |
---|
| 755 | #else |
---|
| 756 | E(1:LU_NONZERO) = chk_J(1:LU_NONZERO,stack_ptr) |
---|
| 757 | #endif |
---|
| 758 | END IF |
---|
| 759 | |
---|
| 760 | stack_ptr = stack_ptr - 1 |
---|
| 761 | |
---|
| 762 | END SUBROUTINE ros_DPop |
---|
| 763 | |
---|
| 764 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 765 | SUBROUTINE ros_CPush( T, H, Y, dY, d2Y ) |
---|
| 766 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 767 | !~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
| 768 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 769 | |
---|
| 770 | KPP_REAL :: T, H, Y(NVAR), dY(NVAR), d2Y(NVAR) |
---|
| 771 | |
---|
| 772 | stack_ptr = stack_ptr + 1 |
---|
| 773 | IF ( stack_ptr > bufsize ) THEN |
---|
| 774 | PRINT*,'Push failed: buffer overflow' |
---|
| 775 | STOP |
---|
| 776 | END IF |
---|
| 777 | chk_H( stack_ptr ) = H |
---|
| 778 | chk_T( stack_ptr ) = T |
---|
| 779 | !CALL WCOPY(NVAR,Y,1,chk_Y(1,stack_ptr),1) |
---|
| 780 | !CALL WCOPY(NVAR,dY,1,chk_dY(1,stack_ptr),1) |
---|
| 781 | !CALL WCOPY(NVAR,d2Y,1,chk_d2Y(1,stack_ptr),1) |
---|
| 782 | chk_Y(1:NVAR,stack_ptr) = Y(1:NVAR) |
---|
| 783 | chk_dY(1:NVAR,stack_ptr) = dY(1:NVAR) |
---|
| 784 | chk_d2Y(1:NVAR,stack_ptr) = d2Y(1:NVAR) |
---|
| 785 | END SUBROUTINE ros_CPush |
---|
| 786 | |
---|
| 787 | |
---|
| 788 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 789 | SUBROUTINE ros_CPop( T, H, Y, dY, d2Y ) |
---|
| 790 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 791 | !~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
| 792 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 793 | |
---|
| 794 | KPP_REAL :: T, H, Y(NVAR), dY(NVAR), d2Y(NVAR) |
---|
| 795 | |
---|
| 796 | IF ( stack_ptr <= 0 ) THEN |
---|
| 797 | PRINT*,'Pop failed: empty buffer' |
---|
| 798 | STOP |
---|
| 799 | END IF |
---|
| 800 | H = chk_H( stack_ptr ) |
---|
| 801 | T = chk_T( stack_ptr ) |
---|
| 802 | !CALL WCOPY(NVAR,chk_Y(1,stack_ptr),1,Y,1) |
---|
| 803 | !CALL WCOPY(NVAR,chk_dY(1,stack_ptr),1,dY,1) |
---|
| 804 | !CALL WCOPY(NVAR,chk_d2Y(1,stack_ptr),1,d2Y,1) |
---|
| 805 | Y(1:NVAR) = chk_Y(1:NVAR,stack_ptr) |
---|
| 806 | dY(1:NVAR) = chk_dY(1:NVAR,stack_ptr) |
---|
| 807 | d2Y(1:NVAR) = chk_d2Y(1:NVAR,stack_ptr) |
---|
| 808 | |
---|
| 809 | stack_ptr = stack_ptr - 1 |
---|
| 810 | |
---|
| 811 | END SUBROUTINE ros_CPop |
---|
| 812 | |
---|
| 813 | |
---|
| 814 | |
---|
| 815 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 816 | SUBROUTINE ros_ErrorMsg(Code,T,H,IERR) |
---|
| 817 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 818 | ! Handles all error messages |
---|
| 819 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 820 | |
---|
| 821 | KPP_REAL, INTENT(IN) :: T, H |
---|
| 822 | INTEGER, INTENT(IN) :: Code |
---|
| 823 | INTEGER, INTENT(OUT) :: IERR |
---|
| 824 | |
---|
| 825 | IERR = Code |
---|
| 826 | PRINT * , & |
---|
| 827 | 'Forced exit from RosenbrockADJ due to the following error:' |
---|
| 828 | |
---|
| 829 | SELECT CASE (Code) |
---|
| 830 | CASE (-1) |
---|
| 831 | PRINT * , '--> Improper value for maximal no of steps' |
---|
| 832 | CASE (-2) |
---|
| 833 | PRINT * , '--> Selected RosenbrockADJ method not implemented' |
---|
| 834 | CASE (-3) |
---|
| 835 | PRINT * , '--> Hmin/Hmax/Hstart must be positive' |
---|
| 836 | CASE (-4) |
---|
| 837 | PRINT * , '--> FacMin/FacMax/FacRej must be positive' |
---|
| 838 | CASE (-5) |
---|
| 839 | PRINT * , '--> Improper tolerance values' |
---|
| 840 | CASE (-6) |
---|
| 841 | PRINT * , '--> No of steps exceeds maximum buffer bound' |
---|
| 842 | CASE (-7) |
---|
| 843 | PRINT * , '--> Step size too small: T + 10*H = T', & |
---|
| 844 | ' or H < Roundoff' |
---|
| 845 | CASE (-8) |
---|
| 846 | PRINT * , '--> Matrix is repeatedly singular' |
---|
| 847 | CASE (-9) |
---|
| 848 | PRINT * , '--> Improper type of adjoint selected' |
---|
| 849 | CASE DEFAULT |
---|
| 850 | PRINT *, 'Unknown Error code: ', Code |
---|
| 851 | END SELECT |
---|
| 852 | |
---|
| 853 | PRINT *, "T=", T, "and H=", H |
---|
| 854 | |
---|
| 855 | END SUBROUTINE ros_ErrorMsg |
---|
| 856 | |
---|
| 857 | |
---|
| 858 | |
---|
| 859 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 860 | SUBROUTINE ros_FwdInt (Y, & |
---|
| 861 | Tstart, Tend, T, & |
---|
| 862 | AbsTol, RelTol, & |
---|
| 863 | !~~~> Error indicator |
---|
| 864 | IERR ) |
---|
| 865 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 866 | ! Template for the implementation of a generic RosenbrockADJ method |
---|
| 867 | ! defined by ros_S (no of stages) |
---|
| 868 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
| 869 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 870 | |
---|
| 871 | IMPLICIT NONE |
---|
| 872 | |
---|
| 873 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
| 874 | KPP_REAL, INTENT(INOUT) :: Y(NVAR) |
---|
| 875 | !~~~> Input: integration interval |
---|
| 876 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
| 877 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
| 878 | KPP_REAL, INTENT(OUT) :: T |
---|
| 879 | !~~~> Input: tolerances |
---|
| 880 | KPP_REAL, INTENT(IN) :: AbsTol(NVAR), RelTol(NVAR) |
---|
| 881 | !~~~> Output: Error indicator |
---|
| 882 | INTEGER, INTENT(OUT) :: IERR |
---|
| 883 | ! ~~~~ Local variables |
---|
| 884 | KPP_REAL :: Ynew(NVAR), Fcn0(NVAR), Fcn(NVAR) |
---|
| 885 | KPP_REAL :: K(NVAR*ros_S), dFdT(NVAR) |
---|
| 886 | KPP_REAL, DIMENSION(:), POINTER :: Ystage |
---|
| 887 | #ifdef FULL_ALGEBRA |
---|
| 888 | KPP_REAL :: Jac0(NVAR,NVAR), Ghimj(NVAR,NVAR) |
---|
| 889 | #else |
---|
| 890 | KPP_REAL :: Jac0(LU_NONZERO), Ghimj(LU_NONZERO) |
---|
| 891 | #endif |
---|
| 892 | KPP_REAL :: H, Hnew, HC, HG, Fac, Tau |
---|
| 893 | KPP_REAL :: Err, Yerr(NVAR) |
---|
| 894 | INTEGER :: Pivot(NVAR), Direction, ioffset, i, j, istage |
---|
| 895 | LOGICAL :: RejectLastH, RejectMoreH, Singular |
---|
| 896 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 897 | |
---|
| 898 | !~~~> Allocate stage vector buffer if needed |
---|
| 899 | IF (AdjointType == Adj_discrete) THEN |
---|
| 900 | ALLOCATE(Ystage(NVAR*ros_S), STAT=i) |
---|
| 901 | ! Uninitialized Ystage may lead to NaN on some compilers |
---|
| 902 | Ystage = 0.0d0 |
---|
| 903 | IF (i/=0) THEN |
---|
| 904 | PRINT*,'Allocation of Ystage failed' |
---|
| 905 | STOP |
---|
| 906 | END IF |
---|
| 907 | END IF |
---|
| 908 | |
---|
| 909 | !~~~> Initial preparations |
---|
| 910 | T = Tstart |
---|
| 911 | RSTATUS(Nhexit) = ZERO |
---|
| 912 | H = MIN( MAX(ABS(Hmin),ABS(Hstart)) , ABS(Hmax) ) |
---|
| 913 | IF (ABS(H) <= 10.0_dp*Roundoff) H = DeltaMin |
---|
| 914 | |
---|
| 915 | IF (Tend >= Tstart) THEN |
---|
| 916 | Direction = +1 |
---|
| 917 | ELSE |
---|
| 918 | Direction = -1 |
---|
| 919 | END IF |
---|
| 920 | H = Direction*H |
---|
| 921 | |
---|
| 922 | RejectLastH=.FALSE. |
---|
| 923 | RejectMoreH=.FALSE. |
---|
| 924 | |
---|
| 925 | !~~~> Time loop begins below |
---|
| 926 | |
---|
| 927 | TimeLoop: DO WHILE ( (Direction > 0).AND.((T-Tend)+Roundoff <= ZERO) & |
---|
| 928 | .OR. (Direction < 0).AND.((Tend-T)+Roundoff <= ZERO) ) |
---|
| 929 | |
---|
| 930 | IF ( ISTATUS(Nstp) > Max_no_steps ) THEN ! Too many steps |
---|
| 931 | CALL ros_ErrorMsg(-6,T,H,IERR) |
---|
| 932 | RETURN |
---|
| 933 | END IF |
---|
| 934 | IF ( ((T+0.1d0*H) == T).OR.(H <= Roundoff) ) THEN ! Step size too small |
---|
| 935 | CALL ros_ErrorMsg(-7,T,H,IERR) |
---|
| 936 | RETURN |
---|
| 937 | END IF |
---|
| 938 | |
---|
| 939 | !~~~> Limit H if necessary to avoid going beyond Tend |
---|
| 940 | RSTATUS(Nhexit) = H |
---|
| 941 | H = MIN(H,ABS(Tend-T)) |
---|
| 942 | |
---|
| 943 | !~~~> Compute the function at current time |
---|
| 944 | CALL FunTemplate(T,Y,Fcn0) |
---|
| 945 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 946 | |
---|
| 947 | !~~~> Compute the function derivative with respect to T |
---|
| 948 | IF (.NOT.Autonomous) THEN |
---|
| 949 | CALL ros_FunTimeDerivative ( T, Roundoff, Y, & |
---|
| 950 | Fcn0, dFdT ) |
---|
| 951 | END IF |
---|
| 952 | |
---|
| 953 | !~~~> Compute the Jacobian at current time |
---|
| 954 | CALL JacTemplate(T,Y,Jac0) |
---|
| 955 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 956 | |
---|
| 957 | !~~~> Repeat step calculation until current step accepted |
---|
| 958 | UntilAccepted: DO |
---|
| 959 | |
---|
| 960 | CALL ros_PrepareMatrix(H,Direction,ros_Gamma(1), & |
---|
| 961 | Jac0,Ghimj,Pivot,Singular) |
---|
| 962 | IF (Singular) THEN ! More than 5 consecutive failed decompositions |
---|
| 963 | CALL ros_ErrorMsg(-8,T,H,IERR) |
---|
| 964 | RETURN |
---|
| 965 | END IF |
---|
| 966 | |
---|
| 967 | !~~~> Compute the stages |
---|
| 968 | Stage: DO istage = 1, ros_S |
---|
| 969 | |
---|
| 970 | ! Current istage offset. Current istage vector is K(ioffset+1:ioffset+NVAR) |
---|
| 971 | ioffset = NVAR*(istage-1) |
---|
| 972 | |
---|
| 973 | ! For the 1st istage the function has been computed previously |
---|
| 974 | IF ( istage == 1 ) THEN |
---|
| 975 | CALL WCOPY(NVAR,Fcn0,1,Fcn,1) |
---|
| 976 | IF (AdjointType == Adj_discrete) THEN ! Save stage solution |
---|
| 977 | ! CALL WCOPY(NVAR,Y,1,Ystage(1),1) |
---|
| 978 | Ystage(1:NVAR) = Y(1:NVAR) |
---|
| 979 | CALL WCOPY(NVAR,Y,1,Ynew,1) |
---|
| 980 | END IF |
---|
| 981 | ! istage>1 and a new function evaluation is needed at the current istage |
---|
| 982 | ELSEIF ( ros_NewF(istage) ) THEN |
---|
| 983 | CALL WCOPY(NVAR,Y,1,Ynew,1) |
---|
| 984 | DO j = 1, istage-1 |
---|
| 985 | CALL WAXPY(NVAR,ros_A((istage-1)*(istage-2)/2+j), & |
---|
| 986 | K(NVAR*(j-1)+1),1,Ynew,1) |
---|
| 987 | END DO |
---|
| 988 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
| 989 | CALL FunTemplate(Tau,Ynew,Fcn) |
---|
| 990 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 991 | END IF ! if istage == 1 elseif ros_NewF(istage) |
---|
| 992 | ! save stage solution every time even if ynew is not updated |
---|
| 993 | IF ( ( istage > 1 ).AND.(AdjointType == Adj_discrete) ) THEN |
---|
| 994 | ! CALL WCOPY(NVAR,Ynew,1,Ystage(ioffset+1),1) |
---|
| 995 | Ystage(ioffset+1:ioffset+NVAR) = Ynew(1:NVAR) |
---|
| 996 | END IF |
---|
| 997 | CALL WCOPY(NVAR,Fcn,1,K(ioffset+1),1) |
---|
| 998 | DO j = 1, istage-1 |
---|
| 999 | HC = ros_C((istage-1)*(istage-2)/2+j)/(Direction*H) |
---|
| 1000 | CALL WAXPY(NVAR,HC,K(NVAR*(j-1)+1),1,K(ioffset+1),1) |
---|
| 1001 | END DO |
---|
| 1002 | IF ((.NOT. Autonomous).AND.(ros_Gamma(istage).NE.ZERO)) THEN |
---|
| 1003 | HG = Direction*H*ros_Gamma(istage) |
---|
| 1004 | CALL WAXPY(NVAR,HG,dFdT,1,K(ioffset+1),1) |
---|
| 1005 | END IF |
---|
| 1006 | CALL ros_Solve('N', Ghimj, Pivot, K(ioffset+1)) |
---|
| 1007 | |
---|
| 1008 | END DO Stage |
---|
| 1009 | |
---|
| 1010 | |
---|
| 1011 | !~~~> Compute the new solution |
---|
| 1012 | CALL WCOPY(NVAR,Y,1,Ynew,1) |
---|
| 1013 | DO j=1,ros_S |
---|
| 1014 | CALL WAXPY(NVAR,ros_M(j),K(NVAR*(j-1)+1),1,Ynew,1) |
---|
| 1015 | END DO |
---|
| 1016 | |
---|
| 1017 | !~~~> Compute the error estimation |
---|
| 1018 | CALL WSCAL(NVAR,ZERO,Yerr,1) |
---|
| 1019 | DO j=1,ros_S |
---|
| 1020 | CALL WAXPY(NVAR,ros_E(j),K(NVAR*(j-1)+1),1,Yerr,1) |
---|
| 1021 | END DO |
---|
| 1022 | Err = ros_ErrorNorm ( Y, Ynew, Yerr, AbsTol, RelTol, VectorTol ) |
---|
| 1023 | |
---|
| 1024 | !~~~> New step size is bounded by FacMin <= Hnew/H <= FacMax |
---|
| 1025 | Fac = MIN(FacMax,MAX(FacMin,FacSafe/Err**(ONE/ros_ELO))) |
---|
| 1026 | Hnew = H*Fac |
---|
| 1027 | |
---|
| 1028 | !~~~> Check the error magnitude and adjust step size |
---|
| 1029 | ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
| 1030 | IF ( (Err <= ONE).OR.(H <= Hmin) ) THEN !~~~> Accept step |
---|
| 1031 | ISTATUS(Nacc) = ISTATUS(Nacc) + 1 |
---|
| 1032 | IF (AdjointType == Adj_discrete) THEN ! Save current state |
---|
| 1033 | CALL ros_DPush( ros_S, T, H, Ystage, K, Ghimj, Pivot ) |
---|
| 1034 | ELSEIF ( (AdjointType == Adj_continuous) .OR. & |
---|
| 1035 | (AdjointType == Adj_simple_continuous) ) THEN |
---|
| 1036 | #ifdef FULL_ALGEBRA |
---|
| 1037 | K = MATMUL(Jac0,Fcn0) |
---|
| 1038 | #else |
---|
| 1039 | CALL Jac_SP_Vec( Jac0, Fcn0, K(1) ) |
---|
| 1040 | #endif |
---|
| 1041 | IF (.NOT. Autonomous) THEN |
---|
| 1042 | CALL WAXPY(NVAR,ONE,dFdT,1,K(1),1) |
---|
| 1043 | END IF |
---|
| 1044 | CALL ros_CPush( T, H, Y, Fcn0, K(1) ) |
---|
| 1045 | END IF |
---|
| 1046 | CALL WCOPY(NVAR,Ynew,1,Y,1) |
---|
| 1047 | T = T + Direction*H |
---|
| 1048 | Hnew = MAX(Hmin,MIN(Hnew,Hmax)) |
---|
| 1049 | IF (RejectLastH) THEN ! No step size increase after a rejected step |
---|
| 1050 | Hnew = MIN(Hnew,H) |
---|
| 1051 | END IF |
---|
| 1052 | RSTATUS(Nhexit) = H |
---|
| 1053 | RSTATUS(Nhnew) = Hnew |
---|
| 1054 | RSTATUS(Ntexit) = T |
---|
| 1055 | RejectLastH = .FALSE. |
---|
| 1056 | RejectMoreH = .FALSE. |
---|
| 1057 | H = Hnew |
---|
| 1058 | EXIT UntilAccepted ! EXIT THE LOOP: WHILE STEP NOT ACCEPTED |
---|
| 1059 | ELSE !~~~> Reject step |
---|
| 1060 | IF (RejectMoreH) THEN |
---|
| 1061 | Hnew = H*FacRej |
---|
| 1062 | END IF |
---|
| 1063 | RejectMoreH = RejectLastH |
---|
| 1064 | RejectLastH = .TRUE. |
---|
| 1065 | H = Hnew |
---|
| 1066 | IF (ISTATUS(Nacc) >= 1) THEN |
---|
| 1067 | ISTATUS(Nrej) = ISTATUS(Nrej) + 1 |
---|
| 1068 | END IF |
---|
| 1069 | END IF ! Err <= 1 |
---|
| 1070 | |
---|
| 1071 | END DO UntilAccepted |
---|
| 1072 | |
---|
| 1073 | END DO TimeLoop |
---|
| 1074 | |
---|
| 1075 | !~~~> Save last state: only needed for continuous adjoint |
---|
| 1076 | IF ( (AdjointType == Adj_continuous) .OR. & |
---|
| 1077 | (AdjointType == Adj_simple_continuous) ) THEN |
---|
| 1078 | CALL FunTemplate(T,Y,Fcn0) |
---|
| 1079 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 1080 | CALL JacTemplate(T,Y,Jac0) |
---|
| 1081 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1082 | #ifdef FULL_ALGEBRA |
---|
| 1083 | K = MATMUL(Jac0,Fcn0) |
---|
| 1084 | #else |
---|
| 1085 | CALL Jac_SP_Vec( Jac0, Fcn0, K(1) ) |
---|
| 1086 | #endif |
---|
| 1087 | IF (.NOT. Autonomous) THEN |
---|
| 1088 | CALL ros_FunTimeDerivative ( T, Roundoff, Y, & |
---|
| 1089 | Fcn0, dFdT ) |
---|
| 1090 | CALL WAXPY(NVAR,ONE,dFdT,1,K(1),1) |
---|
| 1091 | END IF |
---|
| 1092 | CALL ros_CPush( T, H, Y, Fcn0, K(1) ) |
---|
| 1093 | !~~~> Deallocate stage buffer: only needed for discrete adjoint |
---|
| 1094 | ELSEIF (AdjointType == Adj_discrete) THEN |
---|
| 1095 | DEALLOCATE(Ystage, STAT=i) |
---|
| 1096 | IF (i/=0) THEN |
---|
| 1097 | PRINT*,'Deallocation of Ystage failed' |
---|
| 1098 | STOP |
---|
| 1099 | END IF |
---|
| 1100 | END IF |
---|
| 1101 | |
---|
| 1102 | !~~~> Succesful exit |
---|
| 1103 | IERR = 1 !~~~> The integration was successful |
---|
| 1104 | |
---|
| 1105 | END SUBROUTINE ros_FwdInt |
---|
| 1106 | |
---|
| 1107 | |
---|
| 1108 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1109 | SUBROUTINE ros_DadjInt ( & |
---|
| 1110 | NADJ, Lambda, & |
---|
| 1111 | Tstart, Tend, T, & |
---|
| 1112 | !~~~> Error indicator |
---|
| 1113 | IERR ) |
---|
| 1114 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1115 | ! Template for the implementation of a generic RosenbrockSOA method |
---|
| 1116 | ! defined by ros_S (no of stages) |
---|
| 1117 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
| 1118 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1119 | |
---|
| 1120 | IMPLICIT NONE |
---|
| 1121 | |
---|
| 1122 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
| 1123 | INTEGER, INTENT(IN) :: NADJ |
---|
| 1124 | !~~~> First order adjoint |
---|
| 1125 | KPP_REAL, INTENT(INOUT) :: Lambda(NVAR,NADJ) |
---|
| 1126 | !!~~~> Input: integration interval |
---|
| 1127 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
| 1128 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
| 1129 | KPP_REAL, INTENT(OUT) :: T |
---|
| 1130 | !~~~> Output: Error indicator |
---|
| 1131 | INTEGER, INTENT(OUT) :: IERR |
---|
| 1132 | ! ~~~~ Local variables |
---|
| 1133 | KPP_REAL :: Ystage(NVAR*ros_S), K(NVAR*ros_S) |
---|
| 1134 | KPP_REAL :: U(NVAR*ros_S,NADJ), V(NVAR*ros_S,NADJ) |
---|
| 1135 | #ifdef FULL_ALGEBRA |
---|
| 1136 | KPP_REAL, DIMENSION(NVAR,NVAR) :: Jac, dJdT, Ghimj |
---|
| 1137 | #else |
---|
| 1138 | KPP_REAL, DIMENSION(LU_NONZERO) :: Jac, dJdT, Ghimj |
---|
| 1139 | #endif |
---|
| 1140 | KPP_REAL :: Hes0(NHESS) |
---|
| 1141 | KPP_REAL :: Tmp(NVAR), Tmp2(NVAR) |
---|
| 1142 | KPP_REAL :: H, HC, HA, Tau |
---|
| 1143 | INTEGER :: Pivot(NVAR), Direction |
---|
| 1144 | INTEGER :: i, j, m, istage, istart, jstart |
---|
| 1145 | !~~~> Local parameters |
---|
| 1146 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
| 1147 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
---|
| 1148 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1149 | |
---|
| 1150 | |
---|
| 1151 | |
---|
| 1152 | IF (Tend >= Tstart) THEN |
---|
| 1153 | Direction = +1 |
---|
| 1154 | ELSE |
---|
| 1155 | Direction = -1 |
---|
| 1156 | END IF |
---|
| 1157 | |
---|
| 1158 | !~~~> Time loop begins below |
---|
| 1159 | TimeLoop: DO WHILE ( stack_ptr > 0 ) |
---|
| 1160 | |
---|
| 1161 | !~~~> Recover checkpoints for stage values and vectors |
---|
| 1162 | CALL ros_DPop( ros_S, T, H, Ystage, K, Ghimj, Pivot ) |
---|
| 1163 | |
---|
| 1164 | ! ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
| 1165 | |
---|
| 1166 | !~~~> Compute LU decomposition |
---|
| 1167 | IF (.NOT.SaveLU) THEN |
---|
| 1168 | CALL JacTemplate(T,Ystage(1),Ghimj) |
---|
| 1169 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1170 | Tau = ONE/(Direction*H*ros_Gamma(1)) |
---|
| 1171 | #ifdef FULL_ALGEBRA |
---|
| 1172 | Ghimj(1:NVAR,1:NVAR) = -Ghimj(1:NVAR,1:NVAR) |
---|
| 1173 | DO i=1,NVAR |
---|
| 1174 | Ghimj(i,i) = Ghimj(i,i)+Tau |
---|
| 1175 | END DO |
---|
| 1176 | #else |
---|
| 1177 | CALL WSCAL(LU_NONZERO,(-ONE),Ghimj,1) |
---|
| 1178 | DO i=1,NVAR |
---|
| 1179 | Ghimj(LU_DIAG(i)) = Ghimj(LU_DIAG(i))+Tau |
---|
| 1180 | END DO |
---|
| 1181 | #endif |
---|
| 1182 | CALL ros_Decomp( Ghimj, Pivot, j ) |
---|
| 1183 | END IF |
---|
| 1184 | |
---|
| 1185 | !~~~> Compute Hessian at the beginning of the interval |
---|
| 1186 | CALL HessTemplate(T,Ystage(1),Hes0) |
---|
| 1187 | |
---|
| 1188 | !~~~> Compute the stages |
---|
| 1189 | Stage: DO istage = ros_S, 1, -1 |
---|
| 1190 | |
---|
| 1191 | !~~~> Current istage first entry |
---|
| 1192 | istart = NVAR*(istage-1) + 1 |
---|
| 1193 | |
---|
| 1194 | !~~~> Compute U |
---|
| 1195 | DO m = 1,NADJ |
---|
| 1196 | CALL WCOPY(NVAR,Lambda(1,m),1,U(istart,m),1) |
---|
| 1197 | CALL WSCAL(NVAR,ros_M(istage),U(istart,m),1) |
---|
| 1198 | END DO ! m=1:NADJ |
---|
| 1199 | DO j = istage+1, ros_S |
---|
| 1200 | jstart = NVAR*(j-1) + 1 |
---|
| 1201 | HA = ros_A((j-1)*(j-2)/2+istage) |
---|
| 1202 | HC = ros_C((j-1)*(j-2)/2+istage)/(Direction*H) |
---|
| 1203 | DO m = 1,NADJ |
---|
| 1204 | CALL WAXPY(NVAR,HA,V(jstart,m),1,U(istart,m),1) |
---|
| 1205 | CALL WAXPY(NVAR,HC,U(jstart,m),1,U(istart,m),1) |
---|
| 1206 | END DO ! m=1:NADJ |
---|
| 1207 | END DO |
---|
| 1208 | DO m = 1,NADJ |
---|
| 1209 | CALL ros_Solve('T', Ghimj, Pivot, U(istart,m)) |
---|
| 1210 | END DO ! m=1:NADJ |
---|
| 1211 | !~~~> Compute V |
---|
| 1212 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
| 1213 | CALL JacTemplate(Tau,Ystage(istart),Jac) |
---|
| 1214 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1215 | DO m = 1,NADJ |
---|
| 1216 | #ifdef FULL_ALGEBRA |
---|
| 1217 | V(istart:istart+NVAR-1,m) = MATMUL(TRANSPOSE(Jac),U(istart:istart+NVAR-1,m)) |
---|
| 1218 | #else |
---|
| 1219 | CALL JacTR_SP_Vec(Jac,U(istart,m),V(istart,m)) |
---|
| 1220 | #endif |
---|
| 1221 | END DO ! m=1:NADJ |
---|
| 1222 | |
---|
| 1223 | END DO Stage |
---|
| 1224 | |
---|
| 1225 | IF (.NOT.Autonomous) THEN |
---|
| 1226 | !~~~> Compute the Jacobian derivative with respect to T. |
---|
| 1227 | ! Last "Jac" computed for stage 1 |
---|
| 1228 | CALL ros_JacTimeDerivative ( T, Roundoff, Ystage(1), Jac, dJdT ) |
---|
| 1229 | END IF |
---|
| 1230 | |
---|
| 1231 | !~~~> Compute the new solution |
---|
| 1232 | |
---|
| 1233 | !~~~> Compute Lambda |
---|
| 1234 | DO istage=1,ros_S |
---|
| 1235 | istart = NVAR*(istage-1) + 1 |
---|
| 1236 | DO m = 1,NADJ |
---|
| 1237 | ! Add V_i |
---|
| 1238 | CALL WAXPY(NVAR,ONE,V(istart,m),1,Lambda(1,m),1) |
---|
| 1239 | ! Add (H0xK_i)^T * U_i |
---|
| 1240 | CALL HessTR_Vec ( Hes0, U(istart,m), K(istart), Tmp ) |
---|
| 1241 | CALL WAXPY(NVAR,ONE,Tmp,1,Lambda(1,m),1) |
---|
| 1242 | END DO ! m=1:NADJ |
---|
| 1243 | END DO |
---|
| 1244 | ! Add H * dJac_dT_0^T * \sum(gamma_i U_i) |
---|
| 1245 | ! Tmp holds sum gamma_i U_i |
---|
| 1246 | IF (.NOT.Autonomous) THEN |
---|
| 1247 | DO m = 1,NADJ |
---|
| 1248 | Tmp(1:NVAR) = ZERO |
---|
| 1249 | DO istage = 1, ros_S |
---|
| 1250 | istart = NVAR*(istage-1) + 1 |
---|
| 1251 | CALL WAXPY(NVAR,ros_Gamma(istage),U(istart,m),1,Tmp,1) |
---|
| 1252 | END DO |
---|
| 1253 | #ifdef FULL_ALGEBRA |
---|
| 1254 | Tmp2 = MATMUL(TRANSPOSE(dJdT),Tmp) |
---|
| 1255 | #else |
---|
| 1256 | CALL JacTR_SP_Vec(dJdT,Tmp,Tmp2) |
---|
| 1257 | #endif |
---|
| 1258 | CALL WAXPY(NVAR,H,Tmp2,1,Lambda(1,m),1) |
---|
| 1259 | END DO ! m=1:NADJ |
---|
| 1260 | END IF ! .NOT.Autonomous |
---|
| 1261 | |
---|
| 1262 | |
---|
| 1263 | END DO TimeLoop |
---|
| 1264 | |
---|
| 1265 | !~~~> Save last state |
---|
| 1266 | |
---|
| 1267 | !~~~> Succesful exit |
---|
| 1268 | IERR = 1 !~~~> The integration was successful |
---|
| 1269 | |
---|
| 1270 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1271 | END SUBROUTINE ros_DadjInt |
---|
| 1272 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1273 | |
---|
| 1274 | |
---|
| 1275 | |
---|
| 1276 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1277 | SUBROUTINE ros_CadjInt ( & |
---|
| 1278 | NADJ, Y, & |
---|
| 1279 | Tstart, Tend, T, & |
---|
| 1280 | AbsTol_adj, RelTol_adj, & |
---|
| 1281 | !~~~> Error indicator |
---|
| 1282 | IERR ) |
---|
| 1283 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1284 | ! Template for the implementation of a generic RosenbrockADJ method |
---|
| 1285 | ! defined by ros_S (no of stages) |
---|
| 1286 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
| 1287 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1288 | |
---|
| 1289 | IMPLICIT NONE |
---|
| 1290 | |
---|
| 1291 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
| 1292 | INTEGER, INTENT(IN) :: NADJ |
---|
| 1293 | KPP_REAL, INTENT(INOUT) :: Y(NVAR,NADJ) |
---|
| 1294 | !~~~> Input: integration interval |
---|
| 1295 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
| 1296 | !~~~> Input: adjoint tolerances |
---|
| 1297 | KPP_REAL, INTENT(IN) :: AbsTol_adj(NVAR,NADJ), RelTol_adj(NVAR,NADJ) |
---|
| 1298 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
| 1299 | KPP_REAL, INTENT(OUT) :: T |
---|
| 1300 | !~~~> Output: Error indicator |
---|
| 1301 | INTEGER, INTENT(OUT) :: IERR |
---|
| 1302 | ! ~~~~ Local variables |
---|
| 1303 | KPP_REAL :: Y0(NVAR) |
---|
| 1304 | KPP_REAL :: Ynew(NVAR,NADJ), Fcn0(NVAR,NADJ), Fcn(NVAR,NADJ) |
---|
| 1305 | KPP_REAL :: K(NVAR*ros_S,NADJ), dFdT(NVAR,NADJ) |
---|
| 1306 | #ifdef FULL_ALGEBRA |
---|
| 1307 | KPP_REAL, DIMENSION(NVAR,NVAR) :: Jac0, Ghimj, Jac, dJdT |
---|
| 1308 | #else |
---|
| 1309 | KPP_REAL, DIMENSION(LU_NONZERO) :: Jac0, Ghimj, Jac, dJdT |
---|
| 1310 | #endif |
---|
| 1311 | KPP_REAL :: H, Hnew, HC, HG, Fac, Tau |
---|
| 1312 | KPP_REAL :: Err, Yerr(NVAR,NADJ) |
---|
| 1313 | INTEGER :: Pivot(NVAR), Direction, ioffset, j, istage, iadj |
---|
| 1314 | LOGICAL :: RejectLastH, RejectMoreH, Singular |
---|
| 1315 | !~~~> Local parameters |
---|
| 1316 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
| 1317 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
---|
| 1318 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1319 | |
---|
| 1320 | |
---|
| 1321 | !~~~> Initial preparations |
---|
| 1322 | T = Tstart |
---|
| 1323 | RSTATUS(Nhexit) = 0.0_dp |
---|
| 1324 | H = MIN( MAX(ABS(Hmin),ABS(Hstart)) , ABS(Hmax) ) |
---|
| 1325 | IF (ABS(H) <= 10.0_dp*Roundoff) H = DeltaMin |
---|
| 1326 | |
---|
| 1327 | IF (Tend >= Tstart) THEN |
---|
| 1328 | Direction = +1 |
---|
| 1329 | ELSE |
---|
| 1330 | Direction = -1 |
---|
| 1331 | END IF |
---|
| 1332 | H = Direction*H |
---|
| 1333 | |
---|
| 1334 | RejectLastH=.FALSE. |
---|
| 1335 | RejectMoreH=.FALSE. |
---|
| 1336 | |
---|
| 1337 | !~~~> Time loop begins below |
---|
| 1338 | |
---|
| 1339 | TimeLoop: DO WHILE ( (Direction > 0).AND.((T-Tend)+Roundoff <= ZERO) & |
---|
| 1340 | .OR. (Direction < 0).AND.((Tend-T)+Roundoff <= ZERO) ) |
---|
| 1341 | |
---|
| 1342 | IF ( ISTATUS(Nstp) > Max_no_steps ) THEN ! Too many steps |
---|
| 1343 | CALL ros_ErrorMsg(-6,T,H,IERR) |
---|
| 1344 | RETURN |
---|
| 1345 | END IF |
---|
| 1346 | IF ( ((T+0.1d0*H) == T).OR.(H <= Roundoff) ) THEN ! Step size too small |
---|
| 1347 | CALL ros_ErrorMsg(-7,T,H,IERR) |
---|
| 1348 | RETURN |
---|
| 1349 | END IF |
---|
| 1350 | |
---|
| 1351 | !~~~> Limit H if necessary to avoid going beyond Tend |
---|
| 1352 | RSTATUS(Nhexit) = H |
---|
| 1353 | H = MIN(H,ABS(Tend-T)) |
---|
| 1354 | |
---|
| 1355 | !~~~> Interpolate forward solution |
---|
| 1356 | CALL ros_cadj_Y( T, Y0 ) |
---|
| 1357 | !~~~> Compute the Jacobian at current time |
---|
| 1358 | CALL JacTemplate(T, Y0, Jac0) |
---|
| 1359 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1360 | |
---|
| 1361 | !~~~> Compute the function derivative with respect to T |
---|
| 1362 | IF (.NOT.Autonomous) THEN |
---|
| 1363 | CALL ros_JacTimeDerivative ( T, Roundoff, Y0, & |
---|
| 1364 | Jac0, dJdT ) |
---|
| 1365 | DO iadj = 1, NADJ |
---|
| 1366 | #ifdef FULL_ALGEBRA |
---|
| 1367 | dFdT(1:NVAR,iadj) = MATMUL(TRANSPOSE(dJdT),Y(1:NVAR,iadj)) |
---|
| 1368 | #else |
---|
| 1369 | CALL JacTR_SP_Vec(dJdT,Y(1,iadj),dFdT(1,iadj)) |
---|
| 1370 | #endif |
---|
| 1371 | CALL WSCAL(NVAR,(-ONE),dFdT(1,iadj),1) |
---|
| 1372 | END DO |
---|
| 1373 | END IF |
---|
| 1374 | |
---|
| 1375 | !~~~> Ydot = -J^T*Y |
---|
| 1376 | #ifdef FULL_ALGEBRA |
---|
| 1377 | Jac0(1:NVAR,1:NVAR) = -Jac0(1:NVAR,1:NVAR) |
---|
| 1378 | #else |
---|
| 1379 | CALL WSCAL(LU_NONZERO,(-ONE),Jac0,1) |
---|
| 1380 | #endif |
---|
| 1381 | DO iadj = 1, NADJ |
---|
| 1382 | #ifdef FULL_ALGEBRA |
---|
| 1383 | Fcn0(1:NVAR,iadj) = MATMUL(TRANSPOSE(Jac0),Y(1:NVAR,iadj)) |
---|
| 1384 | #else |
---|
| 1385 | CALL JacTR_SP_Vec(Jac0,Y(1,iadj),Fcn0(1,iadj)) |
---|
| 1386 | #endif |
---|
| 1387 | END DO |
---|
| 1388 | |
---|
| 1389 | !~~~> Repeat step calculation until current step accepted |
---|
| 1390 | UntilAccepted: DO |
---|
| 1391 | |
---|
| 1392 | CALL ros_PrepareMatrix(H,Direction,ros_Gamma(1), & |
---|
| 1393 | Jac0,Ghimj,Pivot,Singular) |
---|
| 1394 | IF (Singular) THEN ! More than 5 consecutive failed decompositions |
---|
| 1395 | CALL ros_ErrorMsg(-8,T,H,IERR) |
---|
| 1396 | RETURN |
---|
| 1397 | END IF |
---|
| 1398 | |
---|
| 1399 | !~~~> Compute the stages |
---|
| 1400 | Stage: DO istage = 1, ros_S |
---|
| 1401 | |
---|
| 1402 | ! Current istage offset. Current istage vector is K(ioffset+1:ioffset+NVAR) |
---|
| 1403 | ioffset = NVAR*(istage-1) |
---|
| 1404 | |
---|
| 1405 | ! For the 1st istage the function has been computed previously |
---|
| 1406 | IF ( istage == 1 ) THEN |
---|
| 1407 | DO iadj = 1, NADJ |
---|
| 1408 | CALL WCOPY(NVAR,Fcn0(1,iadj),1,Fcn(1,iadj),1) |
---|
| 1409 | END DO |
---|
| 1410 | ! istage>1 and a new function evaluation is needed at the current istage |
---|
| 1411 | ELSEIF ( ros_NewF(istage) ) THEN |
---|
| 1412 | CALL WCOPY(NVAR*NADJ,Y,1,Ynew,1) |
---|
| 1413 | DO j = 1, istage-1 |
---|
| 1414 | DO iadj = 1, NADJ |
---|
| 1415 | CALL WAXPY(NVAR,ros_A((istage-1)*(istage-2)/2+j), & |
---|
| 1416 | K(NVAR*(j-1)+1,iadj),1,Ynew(1,iadj),1) |
---|
| 1417 | END DO |
---|
| 1418 | END DO |
---|
| 1419 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
| 1420 | ! CALL FunTemplate(Tau,Ynew,Fcn) |
---|
| 1421 | ! ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 1422 | CALL ros_cadj_Y( Tau, Y0 ) |
---|
| 1423 | CALL JacTemplate(Tau, Y0, Jac) |
---|
| 1424 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1425 | #ifdef FULL_ALGEBRA |
---|
| 1426 | Jac(1:NVAR,1:NVAR) = -Jac(1:NVAR,1:NVAR) |
---|
| 1427 | #else |
---|
| 1428 | CALL WSCAL(LU_NONZERO,(-ONE),Jac,1) |
---|
| 1429 | #endif |
---|
| 1430 | DO iadj = 1, NADJ |
---|
| 1431 | #ifdef FULL_ALGEBRA |
---|
| 1432 | Fcn(1:NVAR,iadj) = MATMUL(TRANSPOSE(Jac),Ynew(1:NVAR,iadj)) |
---|
| 1433 | #else |
---|
| 1434 | CALL JacTR_SP_Vec(Jac,Ynew(1,iadj),Fcn(1,iadj)) |
---|
| 1435 | #endif |
---|
| 1436 | !CALL WSCAL(NVAR,(-ONE),Fcn(1,iadj),1) |
---|
| 1437 | END DO |
---|
| 1438 | END IF ! if istage == 1 elseif ros_NewF(istage) |
---|
| 1439 | |
---|
| 1440 | DO iadj = 1, NADJ |
---|
| 1441 | CALL WCOPY(NVAR,Fcn(1,iadj),1,K(ioffset+1,iadj),1) |
---|
| 1442 | END DO |
---|
| 1443 | DO j = 1, istage-1 |
---|
| 1444 | HC = ros_C((istage-1)*(istage-2)/2+j)/(Direction*H) |
---|
| 1445 | DO iadj = 1, NADJ |
---|
| 1446 | CALL WAXPY(NVAR,HC,K(NVAR*(j-1)+1,iadj),1, & |
---|
| 1447 | K(ioffset+1,iadj),1) |
---|
| 1448 | END DO |
---|
| 1449 | END DO |
---|
| 1450 | IF ((.NOT. Autonomous).AND.(ros_Gamma(istage).NE.ZERO)) THEN |
---|
| 1451 | HG = Direction*H*ros_Gamma(istage) |
---|
| 1452 | DO iadj = 1, NADJ |
---|
| 1453 | CALL WAXPY(NVAR,HG,dFdT(1,iadj),1,K(ioffset+1,iadj),1) |
---|
| 1454 | END DO |
---|
| 1455 | END IF |
---|
| 1456 | DO iadj = 1, NADJ |
---|
| 1457 | CALL ros_Solve('T', Ghimj, Pivot, K(ioffset+1,iadj)) |
---|
| 1458 | END DO |
---|
| 1459 | |
---|
| 1460 | END DO Stage |
---|
| 1461 | |
---|
| 1462 | |
---|
| 1463 | !~~~> Compute the new solution |
---|
| 1464 | DO iadj = 1, NADJ |
---|
| 1465 | CALL WCOPY(NVAR,Y(1,iadj),1,Ynew(1,iadj),1) |
---|
| 1466 | DO j=1,ros_S |
---|
| 1467 | CALL WAXPY(NVAR,ros_M(j),K(NVAR*(j-1)+1,iadj),1,Ynew(1,iadj),1) |
---|
| 1468 | END DO |
---|
| 1469 | END DO |
---|
| 1470 | |
---|
| 1471 | !~~~> Compute the error estimation |
---|
| 1472 | CALL WSCAL(NVAR*NADJ,ZERO,Yerr,1) |
---|
| 1473 | DO j=1,ros_S |
---|
| 1474 | DO iadj = 1, NADJ |
---|
| 1475 | CALL WAXPY(NVAR,ros_E(j),K(NVAR*(j-1)+1,iadj),1,Yerr(1,iadj),1) |
---|
| 1476 | END DO |
---|
| 1477 | END DO |
---|
| 1478 | !~~~> Max error among all adjoint components |
---|
| 1479 | iadj = 1 |
---|
| 1480 | Err = ros_ErrorNorm ( Y(1,iadj), Ynew(1,iadj), Yerr(1,iadj), & |
---|
| 1481 | AbsTol_adj(1,iadj), RelTol_adj(1,iadj), VectorTol ) |
---|
| 1482 | |
---|
| 1483 | !~~~> New step size is bounded by FacMin <= Hnew/H <= FacMax |
---|
| 1484 | Fac = MIN(FacMax,MAX(FacMin,FacSafe/Err**(ONE/ros_ELO))) |
---|
| 1485 | Hnew = H*Fac |
---|
| 1486 | |
---|
| 1487 | !~~~> Check the error magnitude and adjust step size |
---|
| 1488 | ! ISTATUS(Nstp) = ISTATUS(Nstp) + 1 |
---|
| 1489 | IF ( (Err <= ONE).OR.(H <= Hmin) ) THEN !~~~> Accept step |
---|
| 1490 | ISTATUS(Nacc) = ISTATUS(Nacc) + 1 |
---|
| 1491 | CALL WCOPY(NVAR*NADJ,Ynew,1,Y,1) |
---|
| 1492 | T = T + Direction*H |
---|
| 1493 | Hnew = MAX(Hmin,MIN(Hnew,Hmax)) |
---|
| 1494 | IF (RejectLastH) THEN ! No step size increase after a rejected step |
---|
| 1495 | Hnew = MIN(Hnew,H) |
---|
| 1496 | END IF |
---|
| 1497 | RSTATUS(Nhexit) = H |
---|
| 1498 | RSTATUS(Nhnew) = Hnew |
---|
| 1499 | RSTATUS(Ntexit) = T |
---|
| 1500 | RejectLastH = .FALSE. |
---|
| 1501 | RejectMoreH = .FALSE. |
---|
| 1502 | H = Hnew |
---|
| 1503 | EXIT UntilAccepted ! EXIT THE LOOP: WHILE STEP NOT ACCEPTED |
---|
| 1504 | ELSE !~~~> Reject step |
---|
| 1505 | IF (RejectMoreH) THEN |
---|
| 1506 | Hnew = H*FacRej |
---|
| 1507 | END IF |
---|
| 1508 | RejectMoreH = RejectLastH |
---|
| 1509 | RejectLastH = .TRUE. |
---|
| 1510 | H = Hnew |
---|
| 1511 | IF (ISTATUS(Nacc) >= 1) THEN |
---|
| 1512 | ISTATUS(Nrej) = ISTATUS(Nrej) + 1 |
---|
| 1513 | END IF |
---|
| 1514 | END IF ! Err <= 1 |
---|
| 1515 | |
---|
| 1516 | END DO UntilAccepted |
---|
| 1517 | |
---|
| 1518 | END DO TimeLoop |
---|
| 1519 | |
---|
| 1520 | !~~~> Succesful exit |
---|
| 1521 | IERR = 1 !~~~> The integration was successful |
---|
| 1522 | |
---|
| 1523 | END SUBROUTINE ros_CadjInt |
---|
| 1524 | |
---|
| 1525 | |
---|
| 1526 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1527 | SUBROUTINE ros_SimpleCadjInt ( & |
---|
| 1528 | NADJ, Y, & |
---|
| 1529 | Tstart, Tend, T, & |
---|
| 1530 | !~~~> Error indicator |
---|
| 1531 | IERR ) |
---|
| 1532 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1533 | ! Template for the implementation of a generic RosenbrockADJ method |
---|
| 1534 | ! defined by ros_S (no of stages) |
---|
| 1535 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
| 1536 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1537 | |
---|
| 1538 | IMPLICIT NONE |
---|
| 1539 | |
---|
| 1540 | !~~~> Input: the initial condition at Tstart; Output: the solution at T |
---|
| 1541 | INTEGER, INTENT(IN) :: NADJ |
---|
| 1542 | KPP_REAL, INTENT(INOUT) :: Y(NVAR,NADJ) |
---|
| 1543 | !~~~> Input: integration interval |
---|
| 1544 | KPP_REAL, INTENT(IN) :: Tstart,Tend |
---|
| 1545 | !~~~> Output: time at which the solution is returned (T=Tend if success) |
---|
| 1546 | KPP_REAL, INTENT(OUT) :: T |
---|
| 1547 | !~~~> Output: Error indicator |
---|
| 1548 | INTEGER, INTENT(OUT) :: IERR |
---|
| 1549 | ! ~~~~ Local variables |
---|
| 1550 | KPP_REAL :: Y0(NVAR) |
---|
| 1551 | KPP_REAL :: Ynew(NVAR,NADJ), Fcn0(NVAR,NADJ), Fcn(NVAR,NADJ) |
---|
| 1552 | KPP_REAL :: K(NVAR*ros_S,NADJ), dFdT(NVAR,NADJ) |
---|
| 1553 | #ifdef FULL_ALGEBRA |
---|
| 1554 | KPP_REAL,DIMENSION(NVAR,NVAR) :: Jac0, Ghimj, Jac, dJdT |
---|
| 1555 | #else |
---|
| 1556 | KPP_REAL,DIMENSION(LU_NONZERO) :: Jac0, Ghimj, Jac, dJdT |
---|
| 1557 | #endif |
---|
| 1558 | KPP_REAL :: H, HC, HG, Tau |
---|
| 1559 | KPP_REAL :: ghinv |
---|
| 1560 | INTEGER :: Pivot(NVAR), Direction, ioffset, i, j, istage, iadj |
---|
| 1561 | INTEGER :: istack |
---|
| 1562 | !~~~> Local parameters |
---|
| 1563 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, ONE = 1.0d0 |
---|
| 1564 | KPP_REAL, PARAMETER :: DeltaMin = 1.0d-5 |
---|
| 1565 | !~~~> Locally called functions |
---|
| 1566 | ! KPP_REAL WLAMCH |
---|
| 1567 | ! EXTERNAL WLAMCH |
---|
| 1568 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1569 | |
---|
| 1570 | |
---|
| 1571 | !~~~> INITIAL PREPARATIONS |
---|
| 1572 | |
---|
| 1573 | IF (Tend >= Tstart) THEN |
---|
| 1574 | Direction = -1 |
---|
| 1575 | ELSE |
---|
| 1576 | Direction = +1 |
---|
| 1577 | END IF |
---|
| 1578 | |
---|
| 1579 | !~~~> Time loop begins below |
---|
| 1580 | TimeLoop: DO istack = stack_ptr,2,-1 |
---|
| 1581 | |
---|
| 1582 | T = chk_T(istack) |
---|
| 1583 | H = chk_H(istack-1) |
---|
| 1584 | !CALL WCOPY(NVAR,chk_Y(1,istack),1,Y0,1) |
---|
| 1585 | Y0(1:NVAR) = chk_Y(1:NVAR,istack) |
---|
| 1586 | |
---|
| 1587 | !~~~> Compute the Jacobian at current time |
---|
| 1588 | CALL JacTemplate(T, Y0, Jac0) |
---|
| 1589 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1590 | |
---|
| 1591 | !~~~> Compute the function derivative with respect to T |
---|
| 1592 | IF (.NOT.Autonomous) THEN |
---|
| 1593 | CALL ros_JacTimeDerivative ( T, Roundoff, Y0, & |
---|
| 1594 | Jac0, dJdT ) |
---|
| 1595 | DO iadj = 1, NADJ |
---|
| 1596 | #ifdef FULL_ALGEBRA |
---|
| 1597 | dFdT(1:NVAR,iadj) = MATMUL(TRANSPOSE(dJdT),Y(1:NVAR,iadj)) |
---|
| 1598 | #else |
---|
| 1599 | CALL JacTR_SP_Vec(dJdT,Y(1,iadj),dFdT(1,iadj)) |
---|
| 1600 | #endif |
---|
| 1601 | CALL WSCAL(NVAR,(-ONE),dFdT(1,iadj),1) |
---|
| 1602 | END DO |
---|
| 1603 | END IF |
---|
| 1604 | |
---|
| 1605 | !~~~> Ydot = -J^T*Y |
---|
| 1606 | #ifdef FULL_ALGEBRA |
---|
| 1607 | Jac0(1:NVAR,1:NVAR) = -Jac0(1:NVAR,1:NVAR) |
---|
| 1608 | #else |
---|
| 1609 | CALL WSCAL(LU_NONZERO,(-ONE),Jac0,1) |
---|
| 1610 | #endif |
---|
| 1611 | DO iadj = 1, NADJ |
---|
| 1612 | #ifdef FULL_ALGEBRA |
---|
| 1613 | Fcn0(1:NVAR,iadj) = MATMUL(TRANSPOSE(Jac0),Y(1:NVAR,iadj)) |
---|
| 1614 | #else |
---|
| 1615 | CALL JacTR_SP_Vec(Jac0,Y(1,iadj),Fcn0(1,iadj)) |
---|
| 1616 | #endif |
---|
| 1617 | END DO |
---|
| 1618 | |
---|
| 1619 | !~~~> Construct Ghimj = 1/(H*ham) - Jac0 |
---|
| 1620 | ghinv = ONE/(Direction*H*ros_Gamma(1)) |
---|
| 1621 | #ifdef FULL_ALGEBRA |
---|
| 1622 | Ghimj(1:NVAR,1:NVAR) = -Jac0(1:NVAR,1:NVAR) |
---|
| 1623 | DO i=1,NVAR |
---|
| 1624 | Ghimj(i,i) = Ghimj(i,i)+ghinv |
---|
| 1625 | END DO |
---|
| 1626 | #else |
---|
| 1627 | CALL WCOPY(LU_NONZERO,Jac0,1,Ghimj,1) |
---|
| 1628 | CALL WSCAL(LU_NONZERO,(-ONE),Ghimj,1) |
---|
| 1629 | DO i=1,NVAR |
---|
| 1630 | Ghimj(LU_DIAG(i)) = Ghimj(LU_DIAG(i))+ghinv |
---|
| 1631 | END DO |
---|
| 1632 | #endif |
---|
| 1633 | !~~~> Compute LU decomposition |
---|
| 1634 | CALL ros_Decomp( Ghimj, Pivot, j ) |
---|
| 1635 | IF (j /= 0) THEN |
---|
| 1636 | CALL ros_ErrorMsg(-8,T,H,IERR) |
---|
| 1637 | PRINT*,' The matrix is singular !' |
---|
| 1638 | STOP |
---|
| 1639 | END IF |
---|
| 1640 | |
---|
| 1641 | !~~~> Compute the stages |
---|
| 1642 | Stage: DO istage = 1, ros_S |
---|
| 1643 | |
---|
| 1644 | ! Current istage offset. Current istage vector is K(ioffset+1:ioffset+NVAR) |
---|
| 1645 | ioffset = NVAR*(istage-1) |
---|
| 1646 | |
---|
| 1647 | ! For the 1st istage the function has been computed previously |
---|
| 1648 | IF ( istage == 1 ) THEN |
---|
| 1649 | DO iadj = 1, NADJ |
---|
| 1650 | CALL WCOPY(NVAR,Fcn0(1,iadj),1,Fcn(1,iadj),1) |
---|
| 1651 | END DO |
---|
| 1652 | ! istage>1 and a new function evaluation is needed at the current istage |
---|
| 1653 | ELSEIF ( ros_NewF(istage) ) THEN |
---|
| 1654 | CALL WCOPY(NVAR*NADJ,Y,1,Ynew,1) |
---|
| 1655 | DO j = 1, istage-1 |
---|
| 1656 | DO iadj = 1, NADJ |
---|
| 1657 | CALL WAXPY(NVAR,ros_A((istage-1)*(istage-2)/2+j), & |
---|
| 1658 | K(NVAR*(j-1)+1,iadj),1,Ynew(1,iadj),1) |
---|
| 1659 | END DO |
---|
| 1660 | END DO |
---|
| 1661 | Tau = T + ros_Alpha(istage)*Direction*H |
---|
| 1662 | CALL ros_Hermite3( chk_T(istack-1), chk_T(istack), Tau, & |
---|
| 1663 | chk_Y(1:NVAR,istack-1), chk_Y(1:NVAR,istack), & |
---|
| 1664 | chk_dY(1:NVAR,istack-1), chk_dY(1:NVAR,istack), Y0 ) |
---|
| 1665 | CALL JacTemplate(Tau, Y0, Jac) |
---|
| 1666 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1667 | #ifdef FULL_ALGEBRA |
---|
| 1668 | Jac(1:NVAR,1:NVAR) = -Jac(1:NVAR,1:NVAR) |
---|
| 1669 | #else |
---|
| 1670 | CALL WSCAL(LU_NONZERO,(-ONE),Jac,1) |
---|
| 1671 | #endif |
---|
| 1672 | DO iadj = 1, NADJ |
---|
| 1673 | #ifdef FULL_ALGEBRA |
---|
| 1674 | Fcn(1:NVAR,iadj) = MATMUL(TRANSPOSE(Jac),Ynew(1:NVAR,iadj)) |
---|
| 1675 | #else |
---|
| 1676 | CALL JacTR_SP_Vec(Jac,Ynew(1,iadj),Fcn(1,iadj)) |
---|
| 1677 | #endif |
---|
| 1678 | END DO |
---|
| 1679 | END IF ! if istage == 1 elseif ros_NewF(istage) |
---|
| 1680 | |
---|
| 1681 | DO iadj = 1, NADJ |
---|
| 1682 | CALL WCOPY(NVAR,Fcn(1,iadj),1,K(ioffset+1,iadj),1) |
---|
| 1683 | END DO |
---|
| 1684 | DO j = 1, istage-1 |
---|
| 1685 | HC = ros_C((istage-1)*(istage-2)/2+j)/(Direction*H) |
---|
| 1686 | DO iadj = 1, NADJ |
---|
| 1687 | CALL WAXPY(NVAR,HC,K(NVAR*(j-1)+1,iadj),1, & |
---|
| 1688 | K(ioffset+1,iadj),1) |
---|
| 1689 | END DO |
---|
| 1690 | END DO |
---|
| 1691 | IF ((.NOT. Autonomous).AND.(ros_Gamma(istage).NE.ZERO)) THEN |
---|
| 1692 | HG = Direction*H*ros_Gamma(istage) |
---|
| 1693 | DO iadj = 1, NADJ |
---|
| 1694 | CALL WAXPY(NVAR,HG,dFdT(1,iadj),1,K(ioffset+1,iadj),1) |
---|
| 1695 | END DO |
---|
| 1696 | END IF |
---|
| 1697 | DO iadj = 1, NADJ |
---|
| 1698 | CALL ros_Solve('T', Ghimj, Pivot, K(ioffset+1,iadj)) |
---|
| 1699 | END DO |
---|
| 1700 | |
---|
| 1701 | END DO Stage |
---|
| 1702 | |
---|
| 1703 | |
---|
| 1704 | !~~~> Compute the new solution |
---|
| 1705 | DO iadj = 1, NADJ |
---|
| 1706 | DO j=1,ros_S |
---|
| 1707 | CALL WAXPY(NVAR,ros_M(j),K(NVAR*(j-1)+1,iadj),1,Y(1,iadj),1) |
---|
| 1708 | END DO |
---|
| 1709 | END DO |
---|
| 1710 | |
---|
| 1711 | END DO TimeLoop |
---|
| 1712 | |
---|
| 1713 | !~~~> Succesful exit |
---|
| 1714 | IERR = 1 !~~~> The integration was successful |
---|
| 1715 | |
---|
| 1716 | END SUBROUTINE ros_SimpleCadjInt |
---|
| 1717 | |
---|
| 1718 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1719 | KPP_REAL FUNCTION ros_ErrorNorm ( Y, Ynew, Yerr, & |
---|
| 1720 | AbsTol, RelTol, VectorTol ) |
---|
| 1721 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1722 | !~~~> Computes the "scaled norm" of the error vector Yerr |
---|
| 1723 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1724 | IMPLICIT NONE |
---|
| 1725 | |
---|
| 1726 | ! Input arguments |
---|
| 1727 | KPP_REAL, INTENT(IN) :: Y(NVAR), Ynew(NVAR), & |
---|
| 1728 | Yerr(NVAR), AbsTol(NVAR), RelTol(NVAR) |
---|
| 1729 | LOGICAL, INTENT(IN) :: VectorTol |
---|
| 1730 | ! Local variables |
---|
| 1731 | KPP_REAL :: Err, Scale, Ymax |
---|
| 1732 | INTEGER :: i |
---|
| 1733 | |
---|
| 1734 | Err = ZERO |
---|
| 1735 | DO i=1,NVAR |
---|
| 1736 | Ymax = MAX(ABS(Y(i)),ABS(Ynew(i))) |
---|
| 1737 | IF (VectorTol) THEN |
---|
| 1738 | Scale = AbsTol(i)+RelTol(i)*Ymax |
---|
| 1739 | ELSE |
---|
| 1740 | Scale = AbsTol(1)+RelTol(1)*Ymax |
---|
| 1741 | END IF |
---|
| 1742 | Err = Err+(Yerr(i)/Scale)**2 |
---|
| 1743 | END DO |
---|
| 1744 | Err = SQRT(Err/NVAR) |
---|
| 1745 | |
---|
| 1746 | ros_ErrorNorm = MAX(Err,1.0d-10) |
---|
| 1747 | |
---|
| 1748 | END FUNCTION ros_ErrorNorm |
---|
| 1749 | |
---|
| 1750 | |
---|
| 1751 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1752 | SUBROUTINE ros_FunTimeDerivative ( T, Roundoff, Y, Fcn0, dFdT ) |
---|
| 1753 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1754 | !~~~> The time partial derivative of the function by finite differences |
---|
| 1755 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1756 | IMPLICIT NONE |
---|
| 1757 | |
---|
| 1758 | !~~~> Input arguments |
---|
| 1759 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR), Fcn0(NVAR) |
---|
| 1760 | !~~~> Output arguments |
---|
| 1761 | KPP_REAL, INTENT(OUT) :: dFdT(NVAR) |
---|
| 1762 | !~~~> Local variables |
---|
| 1763 | KPP_REAL :: Delta |
---|
| 1764 | KPP_REAL, PARAMETER :: ONE = 1.0d0, DeltaMin = 1.0d-6 |
---|
| 1765 | |
---|
| 1766 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
| 1767 | CALL FunTemplate(T+Delta,Y,dFdT) |
---|
| 1768 | ISTATUS(Nfun) = ISTATUS(Nfun) + 1 |
---|
| 1769 | CALL WAXPY(NVAR,(-ONE),Fcn0,1,dFdT,1) |
---|
| 1770 | CALL WSCAL(NVAR,(ONE/Delta),dFdT,1) |
---|
| 1771 | |
---|
| 1772 | END SUBROUTINE ros_FunTimeDerivative |
---|
| 1773 | |
---|
| 1774 | |
---|
| 1775 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1776 | SUBROUTINE ros_JacTimeDerivative ( T, Roundoff, Y, & |
---|
| 1777 | Jac0, dJdT ) |
---|
| 1778 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1779 | !~~~> The time partial derivative of the Jacobian by finite differences |
---|
| 1780 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1781 | IMPLICIT NONE |
---|
| 1782 | |
---|
| 1783 | !~~~> Arguments |
---|
| 1784 | KPP_REAL, INTENT(IN) :: T, Roundoff, Y(NVAR) |
---|
| 1785 | #ifdef FULL_ALGEBRA |
---|
| 1786 | KPP_REAL, INTENT(IN) :: Jac0(NVAR,NVAR) |
---|
| 1787 | KPP_REAL, INTENT(OUT) :: dJdT(NVAR,NVAR) |
---|
| 1788 | #else |
---|
| 1789 | KPP_REAL, INTENT(IN) :: Jac0(LU_NONZERO) |
---|
| 1790 | KPP_REAL, INTENT(OUT) :: dJdT(LU_NONZERO) |
---|
| 1791 | #endif |
---|
| 1792 | !~~~> Local variables |
---|
| 1793 | KPP_REAL :: Delta |
---|
| 1794 | |
---|
| 1795 | Delta = SQRT(Roundoff)*MAX(DeltaMin,ABS(T)) |
---|
| 1796 | CALL JacTemplate(T+Delta,Y,dJdT) |
---|
| 1797 | ISTATUS(Njac) = ISTATUS(Njac) + 1 |
---|
| 1798 | #ifdef FULL_ALGEBRA |
---|
| 1799 | CALL WAXPY(NVAR*NVAR,(-ONE),Jac0,1,dJdT,1) |
---|
| 1800 | CALL WSCAL(NVAR*NVAR,(ONE/Delta),dJdT,1) |
---|
| 1801 | #else |
---|
| 1802 | CALL WAXPY(LU_NONZERO,(-ONE),Jac0,1,dJdT,1) |
---|
| 1803 | CALL WSCAL(LU_NONZERO,(ONE/Delta),dJdT,1) |
---|
| 1804 | #endif |
---|
| 1805 | |
---|
| 1806 | END SUBROUTINE ros_JacTimeDerivative |
---|
| 1807 | |
---|
| 1808 | |
---|
| 1809 | |
---|
| 1810 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1811 | SUBROUTINE ros_PrepareMatrix ( H, Direction, gam, & |
---|
| 1812 | Jac0, Ghimj, Pivot, Singular ) |
---|
| 1813 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
| 1814 | ! Prepares the LHS matrix for stage calculations |
---|
| 1815 | ! 1. Construct Ghimj = 1/(H*gam) - Jac0 |
---|
| 1816 | ! "(Gamma H) Inverse Minus Jacobian" |
---|
| 1817 | ! 2. Repeat LU decomposition of Ghimj until successful. |
---|
| 1818 | ! -half the step size if LU decomposition fails and retry |
---|
| 1819 | ! -exit after 5 consecutive fails |
---|
| 1820 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
| 1821 | IMPLICIT NONE |
---|
| 1822 | |
---|
| 1823 | !~~~> Input arguments |
---|
| 1824 | #ifdef FULL_ALGEBRA |
---|
| 1825 | KPP_REAL, INTENT(IN) :: Jac0(NVAR,NVAR) |
---|
| 1826 | #else |
---|
| 1827 | KPP_REAL, INTENT(IN) :: Jac0(LU_NONZERO) |
---|
| 1828 | #endif |
---|
| 1829 | KPP_REAL, INTENT(IN) :: gam |
---|
| 1830 | INTEGER, INTENT(IN) :: Direction |
---|
| 1831 | !~~~> Output arguments |
---|
| 1832 | #ifdef FULL_ALGEBRA |
---|
| 1833 | KPP_REAL, INTENT(OUT) :: Ghimj(NVAR,NVAR) |
---|
| 1834 | #else |
---|
| 1835 | KPP_REAL, INTENT(OUT) :: Ghimj(LU_NONZERO) |
---|
| 1836 | #endif |
---|
| 1837 | LOGICAL, INTENT(OUT) :: Singular |
---|
| 1838 | INTEGER, INTENT(OUT) :: Pivot(NVAR) |
---|
| 1839 | !~~~> Inout arguments |
---|
| 1840 | KPP_REAL, INTENT(INOUT) :: H ! step size is decreased when LU fails |
---|
| 1841 | !~~~> Local variables |
---|
| 1842 | INTEGER :: i, ISING, Nconsecutive |
---|
| 1843 | KPP_REAL :: ghinv |
---|
| 1844 | KPP_REAL, PARAMETER :: ONE = 1.0_dp, HALF = 0.5_dp |
---|
| 1845 | |
---|
| 1846 | Nconsecutive = 0 |
---|
| 1847 | Singular = .TRUE. |
---|
| 1848 | |
---|
| 1849 | DO WHILE (Singular) |
---|
| 1850 | |
---|
| 1851 | !~~~> Construct Ghimj = 1/(H*gam) - Jac0 |
---|
| 1852 | #ifdef FULL_ALGEBRA |
---|
| 1853 | CALL WCOPY(NVAR*NVAR,Jac0,1,Ghimj,1) |
---|
| 1854 | CALL WSCAL(NVAR*NVAR,(-ONE),Ghimj,1) |
---|
| 1855 | ghinv = ONE/(Direction*H*gam) |
---|
| 1856 | DO i=1,NVAR |
---|
| 1857 | Ghimj(i,i) = Ghimj(i,i)+ghinv |
---|
| 1858 | END DO |
---|
| 1859 | #else |
---|
| 1860 | CALL WCOPY(LU_NONZERO,Jac0,1,Ghimj,1) |
---|
| 1861 | CALL WSCAL(LU_NONZERO,(-ONE),Ghimj,1) |
---|
| 1862 | ghinv = ONE/(Direction*H*gam) |
---|
| 1863 | DO i=1,NVAR |
---|
| 1864 | Ghimj(LU_DIAG(i)) = Ghimj(LU_DIAG(i))+ghinv |
---|
| 1865 | END DO |
---|
| 1866 | #endif |
---|
| 1867 | !~~~> Compute LU decomposition |
---|
| 1868 | CALL ros_Decomp( Ghimj, Pivot, ISING ) |
---|
| 1869 | IF (ISING == 0) THEN |
---|
| 1870 | !~~~> If successful done |
---|
| 1871 | Singular = .FALSE. |
---|
| 1872 | ELSE ! ISING .ne. 0 |
---|
| 1873 | !~~~> If unsuccessful half the step size; if 5 consecutive fails then return |
---|
| 1874 | ISTATUS(Nsng) = ISTATUS(Nsng) + 1 |
---|
| 1875 | Nconsecutive = Nconsecutive+1 |
---|
| 1876 | Singular = .TRUE. |
---|
| 1877 | PRINT*,'Warning: LU Decomposition returned ISING = ',ISING |
---|
| 1878 | IF (Nconsecutive <= 5) THEN ! Less than 5 consecutive failed decompositions |
---|
| 1879 | H = H*HALF |
---|
| 1880 | ELSE ! More than 5 consecutive failed decompositions |
---|
| 1881 | RETURN |
---|
| 1882 | END IF ! Nconsecutive |
---|
| 1883 | END IF ! ISING |
---|
| 1884 | |
---|
| 1885 | END DO ! WHILE Singular |
---|
| 1886 | |
---|
| 1887 | END SUBROUTINE ros_PrepareMatrix |
---|
| 1888 | |
---|
| 1889 | |
---|
| 1890 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1891 | SUBROUTINE ros_Decomp( A, Pivot, ISING ) |
---|
| 1892 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1893 | ! Template for the LU decomposition |
---|
| 1894 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1895 | IMPLICIT NONE |
---|
| 1896 | !~~~> Inout variables |
---|
| 1897 | #ifdef FULL_ALGEBRA |
---|
| 1898 | KPP_REAL, INTENT(INOUT) :: A(NVAR,NVAR) |
---|
| 1899 | #else |
---|
| 1900 | KPP_REAL, INTENT(INOUT) :: A(LU_NONZERO) |
---|
| 1901 | #endif |
---|
| 1902 | !~~~> Output variables |
---|
| 1903 | INTEGER, INTENT(OUT) :: Pivot(NVAR), ISING |
---|
| 1904 | |
---|
| 1905 | #ifdef FULL_ALGEBRA |
---|
| 1906 | CALL DGETRF( NVAR, NVAR, A, NVAR, Pivot, ISING ) |
---|
| 1907 | #else |
---|
| 1908 | CALL KppDecomp ( A, ISING ) |
---|
| 1909 | Pivot(1) = 1 |
---|
| 1910 | #endif |
---|
| 1911 | ISTATUS(Ndec) = ISTATUS(Ndec) + 1 |
---|
| 1912 | |
---|
| 1913 | END SUBROUTINE ros_Decomp |
---|
| 1914 | |
---|
| 1915 | |
---|
| 1916 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1917 | SUBROUTINE ros_Solve( How, A, Pivot, b ) |
---|
| 1918 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1919 | ! Template for the forward/backward substitution (using pre-computed LU decomposition) |
---|
| 1920 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1921 | IMPLICIT NONE |
---|
| 1922 | !~~~> Input variables |
---|
| 1923 | CHARACTER, INTENT(IN) :: How |
---|
| 1924 | #ifdef FULL_ALGEBRA |
---|
| 1925 | KPP_REAL, INTENT(IN) :: A(NVAR,NVAR) |
---|
| 1926 | INTEGER :: ISING |
---|
| 1927 | #else |
---|
| 1928 | KPP_REAL, INTENT(IN) :: A(LU_NONZERO) |
---|
| 1929 | #endif |
---|
| 1930 | INTEGER, INTENT(IN) :: Pivot(NVAR) |
---|
| 1931 | !~~~> InOut variables |
---|
| 1932 | KPP_REAL, INTENT(INOUT) :: b(NVAR) |
---|
| 1933 | |
---|
| 1934 | SELECT CASE (How) |
---|
| 1935 | CASE ('N') |
---|
| 1936 | #ifdef FULL_ALGEBRA |
---|
| 1937 | CALL DGETRS( 'N', NVAR , 1, A, NVAR, Pivot, b, NVAR, ISING ) |
---|
| 1938 | #else |
---|
| 1939 | CALL KppSolve( A, b ) |
---|
| 1940 | #endif |
---|
| 1941 | CASE ('T') |
---|
| 1942 | #ifdef FULL_ALGEBRA |
---|
| 1943 | CALL DGETRS( 'T', NVAR , 1, A, NVAR, Pivot, b, NVAR, ISING ) |
---|
| 1944 | #else |
---|
| 1945 | CALL KppSolveTR( A, b, b ) |
---|
| 1946 | #endif |
---|
| 1947 | CASE DEFAULT |
---|
| 1948 | PRINT*,'Error: unknown argument in ros_Solve: How=',How |
---|
| 1949 | STOP |
---|
| 1950 | END SELECT |
---|
| 1951 | ISTATUS(Nsol) = ISTATUS(Nsol) + 1 |
---|
| 1952 | |
---|
| 1953 | END SUBROUTINE ros_Solve |
---|
| 1954 | |
---|
| 1955 | |
---|
| 1956 | |
---|
| 1957 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1958 | SUBROUTINE ros_cadj_Y( T, Y ) |
---|
| 1959 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1960 | ! Finds the solution Y at T by interpolating the stored forward trajectory |
---|
| 1961 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1962 | IMPLICIT NONE |
---|
| 1963 | !~~~> Input variables |
---|
| 1964 | KPP_REAL, INTENT(IN) :: T |
---|
| 1965 | !~~~> Output variables |
---|
| 1966 | KPP_REAL, INTENT(OUT) :: Y(NVAR) |
---|
| 1967 | !~~~> Local variables |
---|
| 1968 | INTEGER :: i |
---|
| 1969 | KPP_REAL, PARAMETER :: ONE = 1.0d0 |
---|
| 1970 | |
---|
| 1971 | ! chk_H, chk_T, chk_Y, chk_dY, chk_d2Y |
---|
| 1972 | |
---|
| 1973 | IF( (T < chk_T(1)).OR.(T> chk_T(stack_ptr)) ) THEN |
---|
| 1974 | PRINT*,'Cannot locate solution at T = ',T |
---|
| 1975 | PRINT*,'Stored trajectory is between Tstart = ',chk_T(1) |
---|
| 1976 | PRINT*,' and Tend = ',chk_T(stack_ptr) |
---|
| 1977 | STOP |
---|
| 1978 | END IF |
---|
| 1979 | DO i = 1, stack_ptr-1 |
---|
| 1980 | IF( (T>= chk_T(i)).AND.(T<= chk_T(i+1)) ) EXIT |
---|
| 1981 | END DO |
---|
| 1982 | |
---|
| 1983 | |
---|
| 1984 | ! IF (.FALSE.) THEN |
---|
| 1985 | ! |
---|
| 1986 | ! CALL ros_Hermite5( chk_T(i), chk_T(i+1), T, & |
---|
| 1987 | ! chk_Y(1,i), chk_Y(1,i+1), & |
---|
| 1988 | ! chk_dY(1,i), chk_dY(1,i+1), & |
---|
| 1989 | ! chk_d2Y(1,i), chk_d2Y(1,i+1), Y ) |
---|
| 1990 | ! |
---|
| 1991 | ! ELSE |
---|
| 1992 | |
---|
| 1993 | CALL ros_Hermite3( chk_T(i), chk_T(i+1), T, & |
---|
| 1994 | chk_Y(1:NVAR,i), chk_Y(1:NVAR,i+1), & |
---|
| 1995 | chk_dY(1:NVAR,i), chk_dY(1:NVAR,i+1), & |
---|
| 1996 | Y ) |
---|
| 1997 | |
---|
| 1998 | ! |
---|
| 1999 | ! END IF |
---|
| 2000 | |
---|
| 2001 | END SUBROUTINE ros_cadj_Y |
---|
| 2002 | |
---|
| 2003 | |
---|
| 2004 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2005 | SUBROUTINE ros_Hermite3( a, b, T, Ya, Yb, Ja, Jb, Y ) |
---|
| 2006 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2007 | ! Template for Hermite interpolation of order 5 on the interval [a,b] |
---|
| 2008 | ! P = c(1) + c(2)*(x-a) + ... + c(4)*(x-a)^3 |
---|
| 2009 | ! P[a,b] = [Ya,Yb], P'[a,b] = [Ja,Jb] |
---|
| 2010 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2011 | IMPLICIT NONE |
---|
| 2012 | !~~~> Input variables |
---|
| 2013 | KPP_REAL, INTENT(IN) :: a, b, T, Ya(NVAR), Yb(NVAR) |
---|
| 2014 | KPP_REAL, INTENT(IN) :: Ja(NVAR), Jb(NVAR) |
---|
| 2015 | !~~~> Output variables |
---|
| 2016 | KPP_REAL, INTENT(OUT) :: Y(NVAR) |
---|
| 2017 | !~~~> Local variables |
---|
| 2018 | KPP_REAL :: Tau, amb(3), C(NVAR,4) |
---|
| 2019 | KPP_REAL, PARAMETER :: ZERO = 0.0d0 |
---|
| 2020 | INTEGER :: i, j |
---|
| 2021 | |
---|
| 2022 | amb(1) = 1.0d0/(a-b) |
---|
| 2023 | DO i=2,3 |
---|
| 2024 | amb(i) = amb(i-1)*amb(1) |
---|
| 2025 | END DO |
---|
| 2026 | |
---|
| 2027 | |
---|
| 2028 | ! c(1) = ya; |
---|
| 2029 | CALL WCOPY(NVAR,Ya,1,C(1,1),1) |
---|
| 2030 | ! c(2) = ja; |
---|
| 2031 | CALL WCOPY(NVAR,Ja,1,C(1,2),1) |
---|
| 2032 | ! c(3) = 2/(a-b)*ja + 1/(a-b)*jb - 3/(a - b)^2*ya + 3/(a - b)^2*yb ; |
---|
| 2033 | CALL WCOPY(NVAR,Ya,1,C(1,3),1) |
---|
| 2034 | CALL WSCAL(NVAR,-3.0*amb(2),C(1,3),1) |
---|
| 2035 | CALL WAXPY(NVAR,3.0*amb(2),Yb,1,C(1,3),1) |
---|
| 2036 | CALL WAXPY(NVAR,2.0*amb(1),Ja,1,C(1,3),1) |
---|
| 2037 | CALL WAXPY(NVAR,amb(1),Jb,1,C(1,3),1) |
---|
| 2038 | ! c(4) = 1/(a-b)^2*ja + 1/(a-b)^2*jb - 2/(a-b)^3*ya + 2/(a-b)^3*yb ; |
---|
| 2039 | CALL WCOPY(NVAR,Ya,1,C(1,4),1) |
---|
| 2040 | CALL WSCAL(NVAR,-2.0*amb(3),C(1,4),1) |
---|
| 2041 | CALL WAXPY(NVAR,2.0*amb(3),Yb,1,C(1,4),1) |
---|
| 2042 | CALL WAXPY(NVAR,amb(2),Ja,1,C(1,4),1) |
---|
| 2043 | CALL WAXPY(NVAR,amb(2),Jb,1,C(1,4),1) |
---|
| 2044 | |
---|
| 2045 | Tau = T - a |
---|
| 2046 | CALL WCOPY(NVAR,C(1,4),1,Y,1) |
---|
| 2047 | CALL WSCAL(NVAR,Tau**3,Y,1) |
---|
| 2048 | DO j = 3,1,-1 |
---|
| 2049 | CALL WAXPY(NVAR,TAU**(j-1),C(1,j),1,Y,1) |
---|
| 2050 | END DO |
---|
| 2051 | |
---|
| 2052 | END SUBROUTINE ros_Hermite3 |
---|
| 2053 | |
---|
| 2054 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2055 | SUBROUTINE ros_Hermite5( a, b, T, Ya, Yb, Ja, Jb, Ha, Hb, Y ) |
---|
| 2056 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2057 | ! Template for Hermite interpolation of order 5 on the interval [a,b] |
---|
| 2058 | ! P = c(1) + c(2)*(x-a) + ... + c(6)*(x-a)^5 |
---|
| 2059 | ! P[a,b] = [Ya,Yb], P'[a,b] = [Ja,Jb], P"[a,b] = [Ha,Hb] |
---|
| 2060 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2061 | IMPLICIT NONE |
---|
| 2062 | !~~~> Input variables |
---|
| 2063 | KPP_REAL, INTENT(IN) :: a, b, T, Ya(NVAR), Yb(NVAR) |
---|
| 2064 | KPP_REAL, INTENT(IN) :: Ja(NVAR), Jb(NVAR), Ha(NVAR), Hb(NVAR) |
---|
| 2065 | !~~~> Output variables |
---|
| 2066 | KPP_REAL, INTENT(OUT) :: Y(NVAR) |
---|
| 2067 | !~~~> Local variables |
---|
| 2068 | KPP_REAL :: Tau, amb(5), C(NVAR,6) |
---|
| 2069 | KPP_REAL, PARAMETER :: ZERO = 0.0d0, HALF = 0.5d0 |
---|
| 2070 | INTEGER :: i, j |
---|
| 2071 | |
---|
| 2072 | amb(1) = 1.0d0/(a-b) |
---|
| 2073 | DO i=2,5 |
---|
| 2074 | amb(i) = amb(i-1)*amb(1) |
---|
| 2075 | END DO |
---|
| 2076 | |
---|
| 2077 | ! c(1) = ya; |
---|
| 2078 | CALL WCOPY(NVAR,Ya,1,C(1,1),1) |
---|
| 2079 | ! c(2) = ja; |
---|
| 2080 | CALL WCOPY(NVAR,Ja,1,C(1,2),1) |
---|
| 2081 | ! c(3) = ha/2; |
---|
| 2082 | CALL WCOPY(NVAR,Ha,1,C(1,3),1) |
---|
| 2083 | CALL WSCAL(NVAR,HALF,C(1,3),1) |
---|
| 2084 | |
---|
| 2085 | ! c(4) = 10*amb(3)*ya - 10*amb(3)*yb - 6*amb(2)*ja - 4*amb(2)*jb + 1.5*amb(1)*ha - 0.5*amb(1)*hb ; |
---|
| 2086 | CALL WCOPY(NVAR,Ya,1,C(1,4),1) |
---|
| 2087 | CALL WSCAL(NVAR,10.0*amb(3),C(1,4),1) |
---|
| 2088 | CALL WAXPY(NVAR,-10.0*amb(3),Yb,1,C(1,4),1) |
---|
| 2089 | CALL WAXPY(NVAR,-6.0*amb(2),Ja,1,C(1,4),1) |
---|
| 2090 | CALL WAXPY(NVAR,-4.0*amb(2),Jb,1,C(1,4),1) |
---|
| 2091 | CALL WAXPY(NVAR, 1.5*amb(1),Ha,1,C(1,4),1) |
---|
| 2092 | CALL WAXPY(NVAR,-0.5*amb(1),Hb,1,C(1,4),1) |
---|
| 2093 | |
---|
| 2094 | ! c(5) = 15*amb(4)*ya - 15*amb(4)*yb - 8.*amb(3)*ja - 7*amb(3)*jb + 1.5*amb(2)*ha - 1*amb(2)*hb ; |
---|
| 2095 | CALL WCOPY(NVAR,Ya,1,C(1,5),1) |
---|
| 2096 | CALL WSCAL(NVAR, 15.0*amb(4),C(1,5),1) |
---|
| 2097 | CALL WAXPY(NVAR,-15.0*amb(4),Yb,1,C(1,5),1) |
---|
| 2098 | CALL WAXPY(NVAR,-8.0*amb(3),Ja,1,C(1,5),1) |
---|
| 2099 | CALL WAXPY(NVAR,-7.0*amb(3),Jb,1,C(1,5),1) |
---|
| 2100 | CALL WAXPY(NVAR,1.5*amb(2),Ha,1,C(1,5),1) |
---|
| 2101 | CALL WAXPY(NVAR,-amb(2),Hb,1,C(1,5),1) |
---|
| 2102 | |
---|
| 2103 | ! c(6) = 6*amb(5)*ya - 6*amb(5)*yb - 3.*amb(4)*ja - 3.*amb(4)*jb + 0.5*amb(3)*ha -0.5*amb(3)*hb ; |
---|
| 2104 | CALL WCOPY(NVAR,Ya,1,C(1,6),1) |
---|
| 2105 | CALL WSCAL(NVAR, 6.0*amb(5),C(1,6),1) |
---|
| 2106 | CALL WAXPY(NVAR,-6.0*amb(5),Yb,1,C(1,6),1) |
---|
| 2107 | CALL WAXPY(NVAR,-3.0*amb(4),Ja,1,C(1,6),1) |
---|
| 2108 | CALL WAXPY(NVAR,-3.0*amb(4),Jb,1,C(1,6),1) |
---|
| 2109 | CALL WAXPY(NVAR, 0.5*amb(3),Ha,1,C(1,6),1) |
---|
| 2110 | CALL WAXPY(NVAR,-0.5*amb(3),Hb,1,C(1,6),1) |
---|
| 2111 | |
---|
| 2112 | Tau = T - a |
---|
| 2113 | CALL WCOPY(NVAR,C(1,6),1,Y,1) |
---|
| 2114 | DO j = 5,1,-1 |
---|
| 2115 | CALL WSCAL(NVAR,Tau,Y,1) |
---|
| 2116 | CALL WAXPY(NVAR,ONE,C(1,j),1,Y,1) |
---|
| 2117 | END DO |
---|
| 2118 | |
---|
| 2119 | END SUBROUTINE ros_Hermite5 |
---|
| 2120 | |
---|
| 2121 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2122 | SUBROUTINE Ros2 |
---|
| 2123 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2124 | ! --- AN L-STABLE METHOD, 2 stages, order 2 |
---|
| 2125 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2126 | |
---|
| 2127 | IMPLICIT NONE |
---|
| 2128 | DOUBLE PRECISION g |
---|
| 2129 | |
---|
| 2130 | g = 1.0d0 + 1.0d0/SQRT(2.0d0) |
---|
| 2131 | |
---|
| 2132 | rosMethod = RS2 |
---|
| 2133 | !~~~> Name of the method |
---|
| 2134 | ros_Name = 'ROS-2' |
---|
| 2135 | !~~~> Number of stages |
---|
| 2136 | ros_S = 2 |
---|
| 2137 | |
---|
| 2138 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
| 2139 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 2140 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
| 2141 | ! The general mapping formula is: |
---|
| 2142 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
| 2143 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
| 2144 | |
---|
| 2145 | ros_A(1) = (1.d0)/g |
---|
| 2146 | ros_C(1) = (-2.d0)/g |
---|
| 2147 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
| 2148 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
| 2149 | ros_NewF(1) = .TRUE. |
---|
| 2150 | ros_NewF(2) = .TRUE. |
---|
| 2151 | !~~~> M_i = Coefficients for new step solution |
---|
| 2152 | ros_M(1)= (3.d0)/(2.d0*g) |
---|
| 2153 | ros_M(2)= (1.d0)/(2.d0*g) |
---|
| 2154 | ! E_i = Coefficients for error estimator |
---|
| 2155 | ros_E(1) = 1.d0/(2.d0*g) |
---|
| 2156 | ros_E(2) = 1.d0/(2.d0*g) |
---|
| 2157 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
| 2158 | ! main and the embedded scheme orders plus one |
---|
| 2159 | ros_ELO = 2.0d0 |
---|
| 2160 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
| 2161 | ros_Alpha(1) = 0.0d0 |
---|
| 2162 | ros_Alpha(2) = 1.0d0 |
---|
| 2163 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
| 2164 | ros_Gamma(1) = g |
---|
| 2165 | ros_Gamma(2) =-g |
---|
| 2166 | |
---|
| 2167 | END SUBROUTINE Ros2 |
---|
| 2168 | |
---|
| 2169 | |
---|
| 2170 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2171 | SUBROUTINE Ros3 |
---|
| 2172 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2173 | ! --- AN L-STABLE METHOD, 3 stages, order 3, 2 function evaluations |
---|
| 2174 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2175 | |
---|
| 2176 | IMPLICIT NONE |
---|
| 2177 | |
---|
| 2178 | rosMethod = RS3 |
---|
| 2179 | !~~~> Name of the method |
---|
| 2180 | ros_Name = 'ROS-3' |
---|
| 2181 | !~~~> Number of stages |
---|
| 2182 | ros_S = 3 |
---|
| 2183 | |
---|
| 2184 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
| 2185 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 2186 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
| 2187 | ! The general mapping formula is: |
---|
| 2188 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
| 2189 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
| 2190 | |
---|
| 2191 | ros_A(1)= 1.d0 |
---|
| 2192 | ros_A(2)= 1.d0 |
---|
| 2193 | ros_A(3)= 0.d0 |
---|
| 2194 | |
---|
| 2195 | ros_C(1) = -0.10156171083877702091975600115545d+01 |
---|
| 2196 | ros_C(2) = 0.40759956452537699824805835358067d+01 |
---|
| 2197 | ros_C(3) = 0.92076794298330791242156818474003d+01 |
---|
| 2198 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
| 2199 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
| 2200 | ros_NewF(1) = .TRUE. |
---|
| 2201 | ros_NewF(2) = .TRUE. |
---|
| 2202 | ros_NewF(3) = .FALSE. |
---|
| 2203 | !~~~> M_i = Coefficients for new step solution |
---|
| 2204 | ros_M(1) = 0.1d+01 |
---|
| 2205 | ros_M(2) = 0.61697947043828245592553615689730d+01 |
---|
| 2206 | ros_M(3) = -0.42772256543218573326238373806514d+00 |
---|
| 2207 | ! E_i = Coefficients for error estimator |
---|
| 2208 | ros_E(1) = 0.5d+00 |
---|
| 2209 | ros_E(2) = -0.29079558716805469821718236208017d+01 |
---|
| 2210 | ros_E(3) = 0.22354069897811569627360909276199d+00 |
---|
| 2211 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
| 2212 | ! main and the embedded scheme orders plus 1 |
---|
| 2213 | ros_ELO = 3.0d0 |
---|
| 2214 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
| 2215 | ros_Alpha(1)= 0.0d+00 |
---|
| 2216 | ros_Alpha(2)= 0.43586652150845899941601945119356d+00 |
---|
| 2217 | ros_Alpha(3)= 0.43586652150845899941601945119356d+00 |
---|
| 2218 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
| 2219 | ros_Gamma(1)= 0.43586652150845899941601945119356d+00 |
---|
| 2220 | ros_Gamma(2)= 0.24291996454816804366592249683314d+00 |
---|
| 2221 | ros_Gamma(3)= 0.21851380027664058511513169485832d+01 |
---|
| 2222 | |
---|
| 2223 | END SUBROUTINE Ros3 |
---|
| 2224 | |
---|
| 2225 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2226 | |
---|
| 2227 | |
---|
| 2228 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2229 | SUBROUTINE Ros4 |
---|
| 2230 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2231 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4, WITH 4 STAGES |
---|
| 2232 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
---|
| 2233 | ! |
---|
| 2234 | ! E. HAIRER AND G. WANNER, SOLVING ORDINARY DIFFERENTIAL |
---|
| 2235 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
| 2236 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
| 2237 | ! SPRINGER-VERLAG (1990) |
---|
| 2238 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2239 | |
---|
| 2240 | IMPLICIT NONE |
---|
| 2241 | |
---|
| 2242 | rosMethod = RS4 |
---|
| 2243 | !~~~> Name of the method |
---|
| 2244 | ros_Name = 'ROS-4' |
---|
| 2245 | !~~~> Number of stages |
---|
| 2246 | ros_S = 4 |
---|
| 2247 | |
---|
| 2248 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
| 2249 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 2250 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
| 2251 | ! The general mapping formula is: |
---|
| 2252 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
| 2253 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
| 2254 | |
---|
| 2255 | ros_A(1) = 0.2000000000000000d+01 |
---|
| 2256 | ros_A(2) = 0.1867943637803922d+01 |
---|
| 2257 | ros_A(3) = 0.2344449711399156d+00 |
---|
| 2258 | ros_A(4) = ros_A(2) |
---|
| 2259 | ros_A(5) = ros_A(3) |
---|
| 2260 | ros_A(6) = 0.0D0 |
---|
| 2261 | |
---|
| 2262 | ros_C(1) =-0.7137615036412310d+01 |
---|
| 2263 | ros_C(2) = 0.2580708087951457d+01 |
---|
| 2264 | ros_C(3) = 0.6515950076447975d+00 |
---|
| 2265 | ros_C(4) =-0.2137148994382534d+01 |
---|
| 2266 | ros_C(5) =-0.3214669691237626d+00 |
---|
| 2267 | ros_C(6) =-0.6949742501781779d+00 |
---|
| 2268 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
| 2269 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
| 2270 | ros_NewF(1) = .TRUE. |
---|
| 2271 | ros_NewF(2) = .TRUE. |
---|
| 2272 | ros_NewF(3) = .TRUE. |
---|
| 2273 | ros_NewF(4) = .FALSE. |
---|
| 2274 | !~~~> M_i = Coefficients for new step solution |
---|
| 2275 | ros_M(1) = 0.2255570073418735d+01 |
---|
| 2276 | ros_M(2) = 0.2870493262186792d+00 |
---|
| 2277 | ros_M(3) = 0.4353179431840180d+00 |
---|
| 2278 | ros_M(4) = 0.1093502252409163d+01 |
---|
| 2279 | !~~~> E_i = Coefficients for error estimator |
---|
| 2280 | ros_E(1) =-0.2815431932141155d+00 |
---|
| 2281 | ros_E(2) =-0.7276199124938920d-01 |
---|
| 2282 | ros_E(3) =-0.1082196201495311d+00 |
---|
| 2283 | ros_E(4) =-0.1093502252409163d+01 |
---|
| 2284 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
| 2285 | ! main and the embedded scheme orders plus 1 |
---|
| 2286 | ros_ELO = 4.0d0 |
---|
| 2287 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
| 2288 | ros_Alpha(1) = 0.D0 |
---|
| 2289 | ros_Alpha(2) = 0.1145640000000000d+01 |
---|
| 2290 | ros_Alpha(3) = 0.6552168638155900d+00 |
---|
| 2291 | ros_Alpha(4) = ros_Alpha(3) |
---|
| 2292 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
| 2293 | ros_Gamma(1) = 0.5728200000000000d+00 |
---|
| 2294 | ros_Gamma(2) =-0.1769193891319233d+01 |
---|
| 2295 | ros_Gamma(3) = 0.7592633437920482d+00 |
---|
| 2296 | ros_Gamma(4) =-0.1049021087100450d+00 |
---|
| 2297 | |
---|
| 2298 | END SUBROUTINE Ros4 |
---|
| 2299 | |
---|
| 2300 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2301 | SUBROUTINE Rodas3 |
---|
| 2302 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2303 | ! --- A STIFFLY-STABLE METHOD, 4 stages, order 3 |
---|
| 2304 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2305 | |
---|
| 2306 | IMPLICIT NONE |
---|
| 2307 | |
---|
| 2308 | rosMethod = RD3 |
---|
| 2309 | !~~~> Name of the method |
---|
| 2310 | ros_Name = 'RODAS-3' |
---|
| 2311 | !~~~> Number of stages |
---|
| 2312 | ros_S = 4 |
---|
| 2313 | |
---|
| 2314 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
---|
| 2315 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 2316 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
---|
| 2317 | ! The general mapping formula is: |
---|
| 2318 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
---|
| 2319 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
---|
| 2320 | |
---|
| 2321 | ros_A(1) = 0.0d+00 |
---|
| 2322 | ros_A(2) = 2.0d+00 |
---|
| 2323 | ros_A(3) = 0.0d+00 |
---|
| 2324 | ros_A(4) = 2.0d+00 |
---|
| 2325 | ros_A(5) = 0.0d+00 |
---|
| 2326 | ros_A(6) = 1.0d+00 |
---|
| 2327 | |
---|
| 2328 | ros_C(1) = 4.0d+00 |
---|
| 2329 | ros_C(2) = 1.0d+00 |
---|
| 2330 | ros_C(3) =-1.0d+00 |
---|
| 2331 | ros_C(4) = 1.0d+00 |
---|
| 2332 | ros_C(5) =-1.0d+00 |
---|
| 2333 | ros_C(6) =-(8.0d+00/3.0d+00) |
---|
| 2334 | |
---|
| 2335 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
---|
| 2336 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
---|
| 2337 | ros_NewF(1) = .TRUE. |
---|
| 2338 | ros_NewF(2) = .FALSE. |
---|
| 2339 | ros_NewF(3) = .TRUE. |
---|
| 2340 | ros_NewF(4) = .TRUE. |
---|
| 2341 | !~~~> M_i = Coefficients for new step solution |
---|
| 2342 | ros_M(1) = 2.0d+00 |
---|
| 2343 | ros_M(2) = 0.0d+00 |
---|
| 2344 | ros_M(3) = 1.0d+00 |
---|
| 2345 | ros_M(4) = 1.0d+00 |
---|
| 2346 | !~~~> E_i = Coefficients for error estimator |
---|
| 2347 | ros_E(1) = 0.0d+00 |
---|
| 2348 | ros_E(2) = 0.0d+00 |
---|
| 2349 | ros_E(3) = 0.0d+00 |
---|
| 2350 | ros_E(4) = 1.0d+00 |
---|
| 2351 | !~~~> ros_ELO = estimator of local order - the minimum between the |
---|
| 2352 | ! main and the embedded scheme orders plus 1 |
---|
| 2353 | ros_ELO = 3.0d+00 |
---|
| 2354 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
---|
| 2355 | ros_Alpha(1) = 0.0d+00 |
---|
| 2356 | ros_Alpha(2) = 0.0d+00 |
---|
| 2357 | ros_Alpha(3) = 1.0d+00 |
---|
| 2358 | ros_Alpha(4) = 1.0d+00 |
---|
| 2359 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
---|
| 2360 | ros_Gamma(1) = 0.5d+00 |
---|
| 2361 | ros_Gamma(2) = 1.5d+00 |
---|
| 2362 | ros_Gamma(3) = 0.0d+00 |
---|
| 2363 | ros_Gamma(4) = 0.0d+00 |
---|
| 2364 | |
---|
| 2365 | END SUBROUTINE Rodas3 |
---|
| 2366 | |
---|
| 2367 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2368 | SUBROUTINE Rodas4 |
---|
| 2369 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2370 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4, WITH 6 STAGES |
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| 2371 | ! |
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| 2372 | ! E. HAIRER AND G. WANNER, SOLVING ORDINARY DIFFERENTIAL |
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| 2373 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
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| 2374 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
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| 2375 | ! SPRINGER-VERLAG (1996) |
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| 2376 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2377 | |
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| 2378 | IMPLICIT NONE |
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| 2379 | |
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| 2380 | rosMethod = RD4 |
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| 2381 | !~~~> Name of the method |
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| 2382 | ros_Name = 'RODAS-4' |
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| 2383 | !~~~> Number of stages |
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| 2384 | ros_S = 6 |
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| 2385 | |
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| 2386 | !~~~> Y_stage_i ~ Y( T + H*Alpha_i ) |
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| 2387 | ros_Alpha(1) = 0.000d0 |
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| 2388 | ros_Alpha(2) = 0.386d0 |
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| 2389 | ros_Alpha(3) = 0.210d0 |
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| 2390 | ros_Alpha(4) = 0.630d0 |
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| 2391 | ros_Alpha(5) = 1.000d0 |
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| 2392 | ros_Alpha(6) = 1.000d0 |
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| 2393 | |
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| 2394 | !~~~> Gamma_i = \sum_j gamma_{i,j} |
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| 2395 | ros_Gamma(1) = 0.2500000000000000d+00 |
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| 2396 | ros_Gamma(2) =-0.1043000000000000d+00 |
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| 2397 | ros_Gamma(3) = 0.1035000000000000d+00 |
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| 2398 | ros_Gamma(4) =-0.3620000000000023d-01 |
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| 2399 | ros_Gamma(5) = 0.0d0 |
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| 2400 | ros_Gamma(6) = 0.0d0 |
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| 2401 | |
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| 2402 | !~~~> The coefficient matrices A and C are strictly lower triangular. |
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| 2403 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
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| 2404 | ! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc. |
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| 2405 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j ) |
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| 2406 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j ) |
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| 2407 | |
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| 2408 | ros_A(1) = 0.1544000000000000d+01 |
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| 2409 | ros_A(2) = 0.9466785280815826d+00 |
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| 2410 | ros_A(3) = 0.2557011698983284d+00 |
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| 2411 | ros_A(4) = 0.3314825187068521d+01 |
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| 2412 | ros_A(5) = 0.2896124015972201d+01 |
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| 2413 | ros_A(6) = 0.9986419139977817d+00 |
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| 2414 | ros_A(7) = 0.1221224509226641d+01 |
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| 2415 | ros_A(8) = 0.6019134481288629d+01 |
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| 2416 | ros_A(9) = 0.1253708332932087d+02 |
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| 2417 | ros_A(10) =-0.6878860361058950d+00 |
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| 2418 | ros_A(11) = ros_A(7) |
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| 2419 | ros_A(12) = ros_A(8) |
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| 2420 | ros_A(13) = ros_A(9) |
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| 2421 | ros_A(14) = ros_A(10) |
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| 2422 | ros_A(15) = 1.0d+00 |
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| 2423 | |
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| 2424 | ros_C(1) =-0.5668800000000000d+01 |
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| 2425 | ros_C(2) =-0.2430093356833875d+01 |
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| 2426 | ros_C(3) =-0.2063599157091915d+00 |
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| 2427 | ros_C(4) =-0.1073529058151375d+00 |
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| 2428 | ros_C(5) =-0.9594562251023355d+01 |
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| 2429 | ros_C(6) =-0.2047028614809616d+02 |
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| 2430 | ros_C(7) = 0.7496443313967647d+01 |
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| 2431 | ros_C(8) =-0.1024680431464352d+02 |
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| 2432 | ros_C(9) =-0.3399990352819905d+02 |
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| 2433 | ros_C(10) = 0.1170890893206160d+02 |
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| 2434 | ros_C(11) = 0.8083246795921522d+01 |
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| 2435 | ros_C(12) =-0.7981132988064893d+01 |
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| 2436 | ros_C(13) =-0.3152159432874371d+02 |
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| 2437 | ros_C(14) = 0.1631930543123136d+02 |
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| 2438 | ros_C(15) =-0.6058818238834054d+01 |
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| 2439 | |
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| 2440 | !~~~> M_i = Coefficients for new step solution |
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| 2441 | ros_M(1) = ros_A(7) |
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| 2442 | ros_M(2) = ros_A(8) |
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| 2443 | ros_M(3) = ros_A(9) |
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| 2444 | ros_M(4) = ros_A(10) |
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| 2445 | ros_M(5) = 1.0d+00 |
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| 2446 | ros_M(6) = 1.0d+00 |
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| 2447 | |
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| 2448 | !~~~> E_i = Coefficients for error estimator |
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| 2449 | ros_E(1) = 0.0d+00 |
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| 2450 | ros_E(2) = 0.0d+00 |
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| 2451 | ros_E(3) = 0.0d+00 |
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| 2452 | ros_E(4) = 0.0d+00 |
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| 2453 | ros_E(5) = 0.0d+00 |
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| 2454 | ros_E(6) = 1.0d+00 |
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| 2455 | |
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| 2456 | !~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE) |
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| 2457 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) |
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| 2458 | ros_NewF(1) = .TRUE. |
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| 2459 | ros_NewF(2) = .TRUE. |
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| 2460 | ros_NewF(3) = .TRUE. |
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| 2461 | ros_NewF(4) = .TRUE. |
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| 2462 | ros_NewF(5) = .TRUE. |
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| 2463 | ros_NewF(6) = .TRUE. |
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| 2464 | |
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| 2465 | !~~~> ros_ELO = estimator of local order - the minimum between the |
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| 2466 | ! main and the embedded scheme orders plus 1 |
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| 2467 | ros_ELO = 4.0d0 |
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| 2468 | |
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| 2469 | END SUBROUTINE Rodas4 |
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| 2470 | |
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| 2471 | |
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| 2472 | END SUBROUTINE RosenbrockADJ ! and its internal procedures |
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| 2473 | |
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| 2474 | |
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| 2475 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2476 | SUBROUTINE FunTemplate( T, Y, Ydot ) |
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| 2477 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2478 | ! Template for the ODE function call. |
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| 2479 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
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| 2480 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2481 | |
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| 2482 | !~~~> Input variables |
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| 2483 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
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| 2484 | !~~~> Output variables |
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| 2485 | KPP_REAL, INTENT(OUT) :: Ydot(NVAR) |
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| 2486 | !~~~> Local variables |
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| 2487 | KPP_REAL :: Told |
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| 2488 | |
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| 2489 | Told = TIME |
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| 2490 | TIME = T |
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| 2491 | CALL Update_SUN() |
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| 2492 | CALL Update_RCONST() |
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| 2493 | CALL Fun( Y, FIX, RCONST, Ydot ) |
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| 2494 | TIME = Told |
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| 2495 | |
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| 2496 | END SUBROUTINE FunTemplate |
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| 2497 | |
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| 2498 | |
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| 2499 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2500 | SUBROUTINE JacTemplate( T, Y, Jcb ) |
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| 2501 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2502 | ! Template for the ODE Jacobian call. |
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| 2503 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
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| 2504 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2505 | |
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| 2506 | !~~~> Input variables |
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| 2507 | KPP_REAL :: T, Y(NVAR) |
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| 2508 | !~~~> Output variables |
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| 2509 | #ifdef FULL_ALGEBRA |
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| 2510 | KPP_REAL :: JV(LU_NONZERO), Jcb(NVAR,NVAR) |
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| 2511 | #else |
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| 2512 | KPP_REAL :: Jcb(LU_NONZERO) |
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| 2513 | #endif |
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| 2514 | !~~~> Local variables |
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| 2515 | KPP_REAL :: Told |
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| 2516 | #ifdef FULL_ALGEBRA |
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| 2517 | INTEGER :: i, j |
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| 2518 | #endif |
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| 2519 | |
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| 2520 | Told = TIME |
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| 2521 | TIME = T |
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| 2522 | CALL Update_SUN() |
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| 2523 | CALL Update_RCONST() |
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| 2524 | #ifdef FULL_ALGEBRA |
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| 2525 | CALL Jac_SP(Y, FIX, RCONST, JV) |
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| 2526 | DO j=1,NVAR |
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| 2527 | DO i=1,NVAR |
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| 2528 | Jcb(i,j) = 0.0_dp |
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| 2529 | END DO |
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| 2530 | END DO |
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| 2531 | DO i=1,LU_NONZERO |
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| 2532 | Jcb(LU_IROW(i),LU_ICOL(i)) = JV(i) |
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| 2533 | END DO |
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| 2534 | #else |
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| 2535 | CALL Jac_SP( Y, FIX, RCONST, Jcb ) |
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| 2536 | #endif |
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| 2537 | TIME = Told |
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| 2538 | |
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| 2539 | END SUBROUTINE JacTemplate |
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| 2540 | |
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| 2541 | |
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| 2542 | |
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| 2543 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2544 | SUBROUTINE HessTemplate( T, Y, Hes ) |
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| 2545 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2546 | ! Template for the ODE Hessian call. |
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| 2547 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
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| 2548 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 2549 | |
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| 2550 | !~~~> Input variables |
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| 2551 | KPP_REAL, INTENT(IN) :: T, Y(NVAR) |
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| 2552 | !~~~> Output variables |
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| 2553 | KPP_REAL, INTENT(OUT) :: Hes(NHESS) |
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| 2554 | !~~~> Local variables |
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| 2555 | KPP_REAL :: Told |
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| 2556 | |
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| 2557 | Told = TIME |
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| 2558 | TIME = T |
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| 2559 | CALL Update_SUN() |
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| 2560 | CALL Update_RCONST() |
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| 2561 | CALL Hessian( Y, FIX, RCONST, Hes ) |
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| 2562 | TIME = Told |
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| 2563 | |
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| 2564 | END SUBROUTINE HessTemplate |
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| 2565 | |
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| 2566 | END MODULE KPP_ROOT_Integrator |
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| 2567 | |
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| 2568 | |
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| 2569 | |
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| 2570 | |
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