| 1 | MODULE chem_gasphase_mod |
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| 2 | |
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| 3 | ! Mechanism: simplep |
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| 4 | ! |
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| 5 | !------------------------------------------------------------------------------! |
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| 6 | ! |
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| 7 | ! ******Module chem_gasphase_mod is automatically generated by kpp4palm ****** |
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| 8 | ! |
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| 9 | ! *********Please do NOT change this Code,it will be ovewritten ********* |
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| 10 | ! |
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| 11 | !------------------------------------------------------------------------------! |
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| 12 | ! This file was created by KPP (http://people.cs.vt.edu/asandu/Software/Kpp/) |
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| 13 | ! and kpp4palm (created by Klaus Ketelsen). kpp4palm is an adapted version |
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| 14 | ! of KP4 (Jöckel,P.,Kerkweg,A.,Pozzer,A.,Sander,R.,Tost,H.,Riede, |
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| 15 | ! H.,Baumgaertner,A.,Gromov,S.,and Kern,B.,2010: Development cycle 2 of |
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| 16 | ! the Modular Earth Submodel System (MESSy2),Geosci. Model Dev.,3,717-752, |
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| 17 | ! https://doi.org/10.5194/gmd-3-717-2010). KP4 is part of the Modular Earth |
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| 18 | ! Submodel System (MESSy),which is is available under the GNU General Public |
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| 19 | ! License (GPL). |
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| 20 | ! |
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| 21 | ! KPP is free software; you can redistribute it and/or modify it under the terms |
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| 22 | ! of the General Public Licence as published by the Free Software Foundation; |
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| 23 | ! either version 2 of the License,or (at your option) any later version. |
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| 24 | ! KPP is distributed in the hope that it will be useful,but WITHOUT ANY WARRANTY; |
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| 25 | ! without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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| 26 | ! PURPOSE. See the GNU General Public Licence for more details. |
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| 27 | ! |
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| 28 | !------------------------------------------------------------------------------! |
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| 29 | ! This file is part of the PALM model system. |
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| 30 | ! |
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| 31 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 32 | ! terms of the GNU General Public License as published by the Free Software |
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| 33 | ! Foundation,either version 3 of the License,or (at your option) any later |
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| 34 | ! version. |
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| 35 | ! |
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| 36 | ! PALM is distributed in the hope that it will be useful,but WITHOUT ANY |
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| 37 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 38 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 39 | ! |
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| 40 | ! You should have received a copy of the GNU General Public License along with |
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| 41 | ! PALM. If not,see <http://www.gnu.org/licenses/>. |
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| 42 | ! |
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| 43 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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| 44 | !--------------------------------------------------------------------------------! |
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| 45 | ! |
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| 46 | ! Current revisions: |
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| 47 | ! ------------------ |
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| 48 | ! forkel June 2018: qvap,fakt added |
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| 49 | ! forkel June 2018: reset case in Initialize,Integrate,Update_rconst |
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| 50 | ! |
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| 51 | ! |
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| 52 | ! Former revisions: |
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| 53 | ! ----------------- |
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| 54 | ! $Id: module_header 2460 2017-09-13 14:47:48Z forkel $ |
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| 55 | ! |
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| 56 | ! forkel Sept. 2017: Variables for photolyis added |
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| 57 | ! |
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| 58 | ! |
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| 59 | ! Nov. 2016: Intial version (Klaus Ketelsen) |
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| 60 | ! |
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| 61 | !------------------------------------------------------------------------------! |
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| 62 | ! |
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| 63 | |
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| 64 | |
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| 65 | ! Set kpp Double Precision to PALM Default Precision |
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| 66 | |
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| 67 | USE kinds, ONLY: dp=>wp |
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| 68 | |
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| 69 | USE pegrid, ONLY: myid, threads_per_task |
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| 70 | |
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| 71 | IMPLICIT NONE |
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| 72 | PRIVATE |
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| 73 | !SAVE ! note: occurs again in automatically generated code ... |
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| 74 | |
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| 75 | ! PUBLIC :: IERR_NAMES |
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| 76 | |
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| 77 | ! PUBLIC :: SPC_NAMES,EQN_NAMES,EQN_TAGS,REQ_HET,REQ_AEROSOL,REQ_PHOTRAT & |
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| 78 | ! ,REQ_MCFCT,IP_MAX,jname |
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| 79 | |
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| 80 | PUBLIC :: eqn_names, phot_names, spc_names |
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| 81 | PUBLIC :: nmaxfixsteps |
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| 82 | PUBLIC :: atol, rtol |
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| 83 | PUBLIC :: nspec, nreact |
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| 84 | PUBLIC :: temp |
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| 85 | PUBLIC :: qvap |
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| 86 | PUBLIC :: fakt |
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| 87 | PUBLIC :: phot |
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| 88 | PUBLIC :: rconst |
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| 89 | PUBLIC :: nvar |
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| 90 | PUBLIC :: nphot |
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| 91 | PUBLIC :: vl_dim ! PUBLIC to ebable other MODULEs to distiguish between scalar and vec |
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| 92 | |
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| 93 | PUBLIC :: initialize, integrate, update_rconst |
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| 94 | PUBLIC :: chem_gasphase_integrate |
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| 95 | PUBLIC :: initialize_kpp_ctrl |
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| 96 | |
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| 97 | ! END OF MODULE HEADER TEMPLATE |
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| 98 | |
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| 99 | ! Variables used for vector mode |
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| 100 | |
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| 101 | LOGICAL, PARAMETER :: l_vector = .FALSE. |
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| 102 | INTEGER, PARAMETER :: i_lu_di = 2 |
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| 103 | INTEGER, PARAMETER :: vl_dim = 1 |
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| 104 | INTEGER :: vl |
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| 105 | |
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| 106 | INTEGER :: vl_glo |
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| 107 | INTEGER :: is, ie |
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| 108 | |
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| 109 | |
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| 110 | INTEGER, DIMENSION(vl_dim) :: kacc, krej |
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| 111 | INTEGER, DIMENSION(vl_dim) :: ierrv |
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| 112 | LOGICAL :: data_loaded = .FALSE. |
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| 113 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 114 | ! |
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| 115 | ! Parameter Module File |
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| 116 | ! |
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| 117 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 118 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 119 | ! KPP is distributed under GPL,the general public licence |
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| 120 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 121 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 122 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 123 | ! With important contributions from: |
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| 124 | ! M. Damian,Villanova University,USA |
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| 125 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 126 | ! |
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| 127 | ! File : chem_gasphase_mod_Parameters.f90 |
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| 128 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 129 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 130 | ! Equation file : chem_gasphase_mod.kpp |
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| 131 | ! Output root filename : chem_gasphase_mod |
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| 132 | ! |
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| 133 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 134 | |
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| 135 | |
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| 136 | |
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| 137 | |
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| 138 | |
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| 139 | |
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| 140 | ! NSPEC - Number of chemical species |
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| 141 | INTEGER, PARAMETER :: nspec = 12 |
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| 142 | ! NVAR - Number of Variable species |
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| 143 | INTEGER, PARAMETER :: nvar = 10 |
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| 144 | ! NVARACT - Number of Active species |
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| 145 | INTEGER, PARAMETER :: nvaract = 8 |
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| 146 | ! NFIX - Number of Fixed species |
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| 147 | INTEGER, PARAMETER :: nfix = 2 |
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| 148 | ! NREACT - Number of reactions |
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| 149 | INTEGER, PARAMETER :: nreact = 8 |
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| 150 | ! NVARST - Starting of variables in conc. vect. |
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| 151 | INTEGER, PARAMETER :: nvarst = 1 |
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| 152 | ! NFIXST - Starting of fixed in conc. vect. |
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| 153 | INTEGER, PARAMETER :: nfixst = 11 |
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| 154 | ! NONZERO - Number of nonzero entries in Jacobian |
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| 155 | INTEGER, PARAMETER :: nonzero = 36 |
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| 156 | ! LU_NONZERO - Number of nonzero entries in LU factoriz. of Jacobian |
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| 157 | INTEGER, PARAMETER :: lu_nonzero = 38 |
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| 158 | ! CNVAR - (NVAR+1) Number of elements in compressed row format |
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| 159 | INTEGER, PARAMETER :: cnvar = 11 |
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| 160 | ! CNEQN - (NREACT+1) Number stoicm elements in compressed col format |
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| 161 | INTEGER, PARAMETER :: cneqn = 9 |
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| 162 | ! NHESS - Length of Sparse Hessian |
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| 163 | INTEGER, PARAMETER :: nhess = 18 |
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| 164 | ! NMASS - Number of atoms to check mass balance |
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| 165 | INTEGER, PARAMETER :: nmass = 1 |
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| 166 | |
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| 167 | ! Index declaration for variable species in C and VAR |
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| 168 | ! VAR(ind_spc) = C(ind_spc) |
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| 169 | |
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| 170 | INTEGER, PARAMETER, PUBLIC :: ind_pm10 = 1 |
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| 171 | INTEGER, PARAMETER, PUBLIC :: ind_hno3 = 2 |
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| 172 | INTEGER, PARAMETER, PUBLIC :: ind_rcho = 3 |
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| 173 | INTEGER, PARAMETER, PUBLIC :: ind_rh = 4 |
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| 174 | INTEGER, PARAMETER, PUBLIC :: ind_ho2 = 5 |
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| 175 | INTEGER, PARAMETER, PUBLIC :: ind_o3 = 6 |
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| 176 | INTEGER, PARAMETER, PUBLIC :: ind_oh = 7 |
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| 177 | INTEGER, PARAMETER, PUBLIC :: ind_ro2 = 8 |
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| 178 | INTEGER, PARAMETER, PUBLIC :: ind_no = 9 |
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| 179 | INTEGER, PARAMETER, PUBLIC :: ind_no2 = 10 |
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| 180 | |
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| 181 | ! Index declaration for fixed species in C |
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| 182 | ! C(ind_spc) |
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| 183 | |
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| 184 | INTEGER, PARAMETER, PUBLIC :: ind_h2o = 11 |
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| 185 | INTEGER, PARAMETER, PUBLIC :: ind_o2 = 12 |
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| 186 | |
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| 187 | ! Index declaration for fixed species in FIX |
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| 188 | ! FIX(indf_spc) = C(ind_spc) = C(NVAR+indf_spc) |
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| 189 | |
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| 190 | INTEGER, PARAMETER :: indf_h2o = 1 |
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| 191 | INTEGER, PARAMETER :: indf_o2 = 2 |
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| 192 | |
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| 193 | ! NJVRP - Length of sparse Jacobian JVRP |
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| 194 | INTEGER, PARAMETER :: njvrp = 13 |
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| 195 | |
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| 196 | ! NSTOICM - Length of Sparse Stoichiometric Matrix |
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| 197 | INTEGER, PARAMETER :: nstoicm = 23 |
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| 198 | |
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| 199 | |
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| 200 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 201 | ! |
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| 202 | ! Global Data Module File |
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| 203 | ! |
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| 204 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 205 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 206 | ! KPP is distributed under GPL,the general public licence |
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| 207 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 208 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 209 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 210 | ! With important contributions from: |
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| 211 | ! M. Damian,Villanova University,USA |
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| 212 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 213 | ! |
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| 214 | ! File : chem_gasphase_mod_Global.f90 |
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| 215 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 216 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 217 | ! Equation file : chem_gasphase_mod.kpp |
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| 218 | ! Output root filename : chem_gasphase_mod |
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| 219 | ! |
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| 220 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 221 | |
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| 222 | |
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| 223 | |
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| 224 | |
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| 225 | |
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| 226 | |
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| 227 | ! Declaration of global variables |
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| 228 | |
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| 229 | ! C - Concentration of all species |
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| 230 | REAL(kind=dp):: c(nspec) |
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| 231 | ! VAR - Concentrations of variable species (global) |
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| 232 | REAL(kind=dp):: var(nvar) |
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| 233 | ! FIX - Concentrations of fixed species (global) |
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| 234 | REAL(kind=dp):: fix(nfix) |
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| 235 | ! VAR,FIX are chunks of array C |
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| 236 | EQUIVALENCE( c(1), var(1)) |
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| 237 | EQUIVALENCE( c(11), fix(1)) |
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| 238 | ! RCONST - Rate constants (global) |
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| 239 | REAL(kind=dp):: rconst(nreact) |
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| 240 | ! TIME - Current integration time |
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| 241 | REAL(kind=dp):: time |
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| 242 | ! TEMP - Temperature |
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| 243 | REAL(kind=dp):: temp |
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| 244 | ! TSTART - Integration start time |
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| 245 | REAL(kind=dp):: tstart |
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| 246 | ! ATOL - Absolute tolerance |
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| 247 | REAL(kind=dp):: atol(nvar) |
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| 248 | ! RTOL - Relative tolerance |
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| 249 | REAL(kind=dp):: rtol(nvar) |
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| 250 | ! STEPMIN - Lower bound for integration step |
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| 251 | REAL(kind=dp):: stepmin |
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| 252 | ! CFACTOR - Conversion factor for concentration units |
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| 253 | REAL(kind=dp):: cfactor |
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| 254 | |
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| 255 | ! INLINED global variable declarations |
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| 256 | |
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| 257 | ! QVAP - Water vapor |
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| 258 | REAL(kind=dp):: qvap |
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| 259 | ! FAKT - Conversion factor |
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| 260 | REAL(kind=dp):: fakt |
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| 261 | |
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| 262 | |
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| 263 | ! INLINED global variable declarations |
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| 264 | |
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| 265 | |
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| 266 | |
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| 267 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 268 | ! |
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| 269 | ! Sparse Jacobian Data Structures File |
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| 270 | ! |
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| 271 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 272 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 273 | ! KPP is distributed under GPL,the general public licence |
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| 274 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 275 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 276 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 277 | ! With important contributions from: |
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| 278 | ! M. Damian,Villanova University,USA |
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| 279 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 280 | ! |
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| 281 | ! File : chem_gasphase_mod_JacobianSP.f90 |
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| 282 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 283 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 284 | ! Equation file : chem_gasphase_mod.kpp |
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| 285 | ! Output root filename : chem_gasphase_mod |
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| 286 | ! |
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| 287 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 288 | |
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| 289 | |
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| 290 | |
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| 291 | |
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| 292 | |
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| 293 | |
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| 294 | ! Sparse Jacobian Data |
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| 295 | |
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| 296 | |
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| 297 | INTEGER, PARAMETER, DIMENSION(38):: lu_irow = (/ & |
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| 298 | 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, & |
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| 299 | 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, & |
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| 300 | 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, & |
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| 301 | 10, 10 /) |
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| 302 | |
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| 303 | INTEGER, PARAMETER, DIMENSION(38):: lu_icol = (/ & |
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| 304 | 1, 2, 7, 10, 3, 8, 9, 4, 7, 5, 8, 9, & |
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| 305 | 6, 9, 10, 4, 5, 6, 7, 8, 9, 10, 4, 7, & |
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| 306 | 8, 9, 10, 5, 6, 8, 9, 10, 5, 6, 7, 8, & |
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| 307 | 9, 10 /) |
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| 308 | |
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| 309 | INTEGER, PARAMETER, DIMENSION(11):: lu_crow = (/ & |
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| 310 | 1, 2, 5, 8, 10, 13, 16, 23, 28, 33, 39 /) |
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| 311 | |
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| 312 | INTEGER, PARAMETER, DIMENSION(11):: lu_diag = (/ & |
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| 313 | 1, 2, 5, 8, 10, 13, 19, 25, 31, 38, 39 /) |
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| 314 | |
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| 315 | |
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| 316 | |
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| 317 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 318 | ! |
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| 319 | ! Utility Data Module File |
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| 320 | ! |
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| 321 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 322 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 323 | ! KPP is distributed under GPL,the general public licence |
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| 324 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 325 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 326 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 327 | ! With important contributions from: |
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| 328 | ! M. Damian,Villanova University,USA |
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| 329 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 330 | ! |
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| 331 | ! File : chem_gasphase_mod_Monitor.f90 |
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| 332 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 333 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 334 | ! Equation file : chem_gasphase_mod.kpp |
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| 335 | ! Output root filename : chem_gasphase_mod |
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| 336 | ! |
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| 337 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 338 | |
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| 339 | |
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| 340 | |
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| 341 | |
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| 342 | |
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| 343 | CHARACTER(len=15), PARAMETER, DIMENSION(12):: spc_names = (/ & |
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| 344 | 'PM10 ','HNO3 ','RCHO ',& |
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| 345 | 'RH ','HO2 ','O3 ',& |
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| 346 | 'OH ','RO2 ','NO ',& |
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| 347 | 'NO2 ','H2O ','O2 ' /) |
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| 348 | |
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| 349 | CHARACTER(len=100), PARAMETER, DIMENSION(8):: eqn_names = (/ & |
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| 350 | ' NO2 --> O3 + NO ',& |
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| 351 | ' O3 --> 2 OH + O2 ',& |
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| 352 | ' O3 + NO --> NO2 ',& |
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| 353 | ' RH + OH --> RO2 + H2O ',& |
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| 354 | 'RO2 + NO --> RCHO + HO2 + NO2 ',& |
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| 355 | 'HO2 + NO --> OH + NO2 ',& |
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| 356 | 'OH + NO2 --> HNO3 ',& |
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| 357 | ' PM10 --> PM10 ' /) |
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| 358 | |
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| 359 | ! INLINED global variables |
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| 360 | |
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| 361 | ! inline f90_data: declaration of global variables for photolysis |
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| 362 | ! REAL(kind=dp):: phot(nphot)must eventually be moved to global later for |
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| 363 | INTEGER, PARAMETER :: nphot = 2 |
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| 364 | ! phot photolysis frequencies |
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| 365 | REAL(kind=dp):: phot(nphot) |
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| 366 | |
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| 367 | INTEGER, PARAMETER, PUBLIC :: j_no2 = 1 |
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| 368 | INTEGER, PARAMETER, PUBLIC :: j_o31d = 2 |
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| 369 | |
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| 370 | CHARACTER(len=15), PARAMETER, DIMENSION(nphot):: phot_names = (/ & |
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| 371 | 'J_NO2 ','J_O31D '/) |
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| 372 | |
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| 373 | ! End INLINED global variables |
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| 374 | |
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| 375 | |
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| 376 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 377 | |
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| 378 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 379 | |
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| 380 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 381 | |
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| 382 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 383 | |
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| 384 | |
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| 385 | ! variable definations from individual module headers |
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| 386 | |
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| 387 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 388 | ! |
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| 389 | ! Initialization File |
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| 390 | ! |
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| 391 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 392 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 393 | ! KPP is distributed under GPL,the general public licence |
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| 394 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 395 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 396 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 397 | ! With important contributions from: |
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| 398 | ! M. Damian,Villanova University,USA |
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| 399 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 400 | ! |
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| 401 | ! File : chem_gasphase_mod_Initialize.f90 |
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| 402 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 403 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 404 | ! Equation file : chem_gasphase_mod.kpp |
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| 405 | ! Output root filename : chem_gasphase_mod |
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| 406 | ! |
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| 407 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 408 | |
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| 409 | |
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| 410 | |
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| 411 | |
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| 412 | |
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| 413 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 414 | ! |
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| 415 | ! Numerical Integrator (Time-Stepping) File |
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| 416 | ! |
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| 417 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 418 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 419 | ! KPP is distributed under GPL,the general public licence |
|---|
| 420 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 421 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 422 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 423 | ! With important contributions from: |
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| 424 | ! M. Damian,Villanova University,USA |
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| 425 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 426 | ! |
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| 427 | ! File : chem_gasphase_mod_Integrator.f90 |
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| 428 | ! Time : Tue Sep 25 18:35:48 2018 |
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| 429 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 430 | ! Equation file : chem_gasphase_mod.kpp |
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| 431 | ! Output root filename : chem_gasphase_mod |
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| 432 | ! |
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| 433 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 434 | |
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| 435 | |
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| 436 | |
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| 437 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 438 | ! |
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| 439 | ! INTEGRATE - Integrator routine |
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| 440 | ! Arguments : |
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| 441 | ! TIN - Start Time for Integration |
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| 442 | ! TOUT - End Time for Integration |
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| 443 | ! |
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| 444 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 445 | |
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| 446 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 447 | ! Rosenbrock - Implementation of several Rosenbrock methods: ! |
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| 448 | ! *Ros2 ! |
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| 449 | ! *Ros3 ! |
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| 450 | ! *Ros4 ! |
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| 451 | ! *Rodas3 ! |
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| 452 | ! *Rodas4 ! |
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| 453 | ! By default the code employs the KPP sparse linear algebra routines ! |
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| 454 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 455 | ! ! |
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| 456 | ! (C) Adrian Sandu,August 2004 ! |
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| 457 | ! Virginia Polytechnic Institute and State University ! |
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| 458 | ! Contact: sandu@cs.vt.edu ! |
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| 459 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 ! ! |
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| 460 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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| 461 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 462 | |
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| 463 | |
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| 464 | SAVE |
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| 465 | |
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| 466 | !~~~> statistics on the work performed by the rosenbrock method |
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| 467 | INTEGER, PARAMETER :: nfun=1, njac=2, nstp=3, nacc=4, & |
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| 468 | nrej=5, ndec=6, nsol=7, nsng=8, & |
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| 469 | ntexit=1, nhexit=2, nhnew = 3 |
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| 470 | |
|---|
| 471 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 472 | ! |
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| 473 | ! Linear Algebra Data and Routines File |
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| 474 | ! |
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| 475 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 476 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 477 | ! KPP is distributed under GPL,the general public licence |
|---|
| 478 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 479 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 480 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 481 | ! With important contributions from: |
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| 482 | ! M. Damian,Villanova University,USA |
|---|
| 483 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 484 | ! |
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| 485 | ! File : chem_gasphase_mod_LinearAlgebra.f90 |
|---|
| 486 | ! Time : Tue Sep 25 18:35:48 2018 |
|---|
| 487 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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| 488 | ! Equation file : chem_gasphase_mod.kpp |
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| 489 | ! Output root filename : chem_gasphase_mod |
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| 490 | ! |
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| 491 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 492 | |
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| 493 | |
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| 494 | |
|---|
| 495 | |
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| 496 | |
|---|
| 497 | |
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| 498 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 499 | ! |
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| 500 | ! The ODE Jacobian of Chemical Model File |
|---|
| 501 | ! |
|---|
| 502 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 503 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 504 | ! KPP is distributed under GPL,the general public licence |
|---|
| 505 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 506 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 507 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 508 | ! With important contributions from: |
|---|
| 509 | ! M. Damian,Villanova University,USA |
|---|
| 510 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 511 | ! |
|---|
| 512 | ! File : chem_gasphase_mod_Jacobian.f90 |
|---|
| 513 | ! Time : Tue Sep 25 18:35:48 2018 |
|---|
| 514 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
|---|
| 515 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 516 | ! Output root filename : chem_gasphase_mod |
|---|
| 517 | ! |
|---|
| 518 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 519 | |
|---|
| 520 | |
|---|
| 521 | |
|---|
| 522 | |
|---|
| 523 | |
|---|
| 524 | |
|---|
| 525 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 526 | ! |
|---|
| 527 | ! The ODE Function of Chemical Model File |
|---|
| 528 | ! |
|---|
| 529 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 530 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 531 | ! KPP is distributed under GPL,the general public licence |
|---|
| 532 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 533 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 534 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 535 | ! With important contributions from: |
|---|
| 536 | ! M. Damian,Villanova University,USA |
|---|
| 537 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 538 | ! |
|---|
| 539 | ! File : chem_gasphase_mod_Function.f90 |
|---|
| 540 | ! Time : Tue Sep 25 18:35:48 2018 |
|---|
| 541 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
|---|
| 542 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 543 | ! Output root filename : chem_gasphase_mod |
|---|
| 544 | ! |
|---|
| 545 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 546 | |
|---|
| 547 | |
|---|
| 548 | |
|---|
| 549 | |
|---|
| 550 | |
|---|
| 551 | ! A - Rate for each equation |
|---|
| 552 | REAL(kind=dp):: a(nreact) |
|---|
| 553 | |
|---|
| 554 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 555 | ! |
|---|
| 556 | ! The Reaction Rates File |
|---|
| 557 | ! |
|---|
| 558 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 559 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 560 | ! KPP is distributed under GPL,the general public licence |
|---|
| 561 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 562 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 563 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 564 | ! With important contributions from: |
|---|
| 565 | ! M. Damian,Villanova University,USA |
|---|
| 566 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 567 | ! |
|---|
| 568 | ! File : chem_gasphase_mod_Rates.f90 |
|---|
| 569 | ! Time : Tue Sep 25 18:35:48 2018 |
|---|
| 570 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
|---|
| 571 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 572 | ! Output root filename : chem_gasphase_mod |
|---|
| 573 | ! |
|---|
| 574 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 575 | |
|---|
| 576 | |
|---|
| 577 | |
|---|
| 578 | |
|---|
| 579 | |
|---|
| 580 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 581 | ! |
|---|
| 582 | ! Auxiliary Routines File |
|---|
| 583 | ! |
|---|
| 584 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
|---|
| 585 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
|---|
| 586 | ! KPP is distributed under GPL,the general public licence |
|---|
| 587 | ! (http://www.gnu.org/copyleft/gpl.html) |
|---|
| 588 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
|---|
| 589 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
|---|
| 590 | ! With important contributions from: |
|---|
| 591 | ! M. Damian,Villanova University,USA |
|---|
| 592 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
|---|
| 593 | ! |
|---|
| 594 | ! File : chem_gasphase_mod_Util.f90 |
|---|
| 595 | ! Time : Tue Sep 25 18:35:48 2018 |
|---|
| 596 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
|---|
| 597 | ! Equation file : chem_gasphase_mod.kpp |
|---|
| 598 | ! Output root filename : chem_gasphase_mod |
|---|
| 599 | ! |
|---|
| 600 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 601 | |
|---|
| 602 | |
|---|
| 603 | |
|---|
| 604 | |
|---|
| 605 | |
|---|
| 606 | |
|---|
| 607 | ! header MODULE initialize_kpp_ctrl_template |
|---|
| 608 | |
|---|
| 609 | ! notes: |
|---|
| 610 | ! - l_vector is automatically defined by kp4 |
|---|
| 611 | ! - vl_dim is automatically defined by kp4 |
|---|
| 612 | ! - i_lu_di is automatically defined by kp4 |
|---|
| 613 | ! - wanted is automatically defined by xmecca |
|---|
| 614 | ! - icntrl rcntrl are automatically defined by kpp |
|---|
| 615 | ! - "USE messy_main_tools" is in MODULE_header of messy_mecca_kpp.f90 |
|---|
| 616 | ! - SAVE will be automatically added by kp4 |
|---|
| 617 | |
|---|
| 618 | !SAVE |
|---|
| 619 | |
|---|
| 620 | ! for fixed time step control |
|---|
| 621 | ! ... max. number of fixed time steps (sum must be 1) |
|---|
| 622 | INTEGER, PARAMETER :: nmaxfixsteps = 50 |
|---|
| 623 | ! ... switch for fixed time stepping |
|---|
| 624 | LOGICAL, PUBLIC :: l_fixed_step = .FALSE. |
|---|
| 625 | INTEGER, PUBLIC :: nfsteps = 1 |
|---|
| 626 | ! ... number of kpp control PARAMETERs |
|---|
| 627 | INTEGER, PARAMETER, PUBLIC :: nkppctrl = 20 |
|---|
| 628 | ! |
|---|
| 629 | INTEGER, DIMENSION(nkppctrl), PUBLIC :: icntrl = 0 |
|---|
| 630 | REAL(dp), DIMENSION(nkppctrl), PUBLIC :: rcntrl = 0.0_dp |
|---|
| 631 | REAL(dp), DIMENSION(nmaxfixsteps), PUBLIC :: t_steps = 0.0_dp |
|---|
| 632 | |
|---|
| 633 | ! END header MODULE initialize_kpp_ctrl_template |
|---|
| 634 | |
|---|
| 635 | |
|---|
| 636 | ! Interface Block |
|---|
| 637 | |
|---|
| 638 | INTERFACE initialize |
|---|
| 639 | MODULE PROCEDURE initialize |
|---|
| 640 | END INTERFACE initialize |
|---|
| 641 | |
|---|
| 642 | INTERFACE integrate |
|---|
| 643 | MODULE PROCEDURE integrate |
|---|
| 644 | END INTERFACE integrate |
|---|
| 645 | |
|---|
| 646 | INTERFACE fun |
|---|
| 647 | MODULE PROCEDURE fun |
|---|
| 648 | END INTERFACE fun |
|---|
| 649 | |
|---|
| 650 | INTERFACE kppsolve |
|---|
| 651 | MODULE PROCEDURE kppsolve |
|---|
| 652 | END INTERFACE kppsolve |
|---|
| 653 | |
|---|
| 654 | INTERFACE jac_sp |
|---|
| 655 | MODULE PROCEDURE jac_sp |
|---|
| 656 | END INTERFACE jac_sp |
|---|
| 657 | |
|---|
| 658 | INTERFACE k_arr |
|---|
| 659 | MODULE PROCEDURE k_arr |
|---|
| 660 | END INTERFACE k_arr |
|---|
| 661 | |
|---|
| 662 | INTERFACE update_rconst |
|---|
| 663 | MODULE PROCEDURE update_rconst |
|---|
| 664 | END INTERFACE update_rconst |
|---|
| 665 | |
|---|
| 666 | INTERFACE arr2 |
|---|
| 667 | MODULE PROCEDURE arr2 |
|---|
| 668 | END INTERFACE arr2 |
|---|
| 669 | |
|---|
| 670 | INTERFACE initialize_kpp_ctrl |
|---|
| 671 | MODULE PROCEDURE initialize_kpp_ctrl |
|---|
| 672 | END INTERFACE initialize_kpp_ctrl |
|---|
| 673 | |
|---|
| 674 | INTERFACE error_output |
|---|
| 675 | MODULE PROCEDURE error_output |
|---|
| 676 | END INTERFACE error_output |
|---|
| 677 | |
|---|
| 678 | INTERFACE wscal |
|---|
| 679 | MODULE PROCEDURE wscal |
|---|
| 680 | END INTERFACE wscal |
|---|
| 681 | |
|---|
| 682 | !INTERFACE not working INTERFACE waxpy |
|---|
| 683 | !INTERFACE not working MODULE PROCEDURE waxpy |
|---|
| 684 | !INTERFACE not working END INTERFACE waxpy |
|---|
| 685 | |
|---|
| 686 | INTERFACE rosenbrock |
|---|
| 687 | MODULE PROCEDURE rosenbrock |
|---|
| 688 | END INTERFACE rosenbrock |
|---|
| 689 | |
|---|
| 690 | INTERFACE funtemplate |
|---|
| 691 | MODULE PROCEDURE funtemplate |
|---|
| 692 | END INTERFACE funtemplate |
|---|
| 693 | |
|---|
| 694 | INTERFACE jactemplate |
|---|
| 695 | MODULE PROCEDURE jactemplate |
|---|
| 696 | END INTERFACE jactemplate |
|---|
| 697 | |
|---|
| 698 | INTERFACE kppdecomp |
|---|
| 699 | MODULE PROCEDURE kppdecomp |
|---|
| 700 | END INTERFACE kppdecomp |
|---|
| 701 | |
|---|
| 702 | INTERFACE chem_gasphase_integrate |
|---|
| 703 | MODULE PROCEDURE chem_gasphase_integrate |
|---|
| 704 | END INTERFACE chem_gasphase_integrate |
|---|
| 705 | |
|---|
| 706 | |
|---|
| 707 | CONTAINS |
|---|
| 708 | |
|---|
| 709 | SUBROUTINE initialize() |
|---|
| 710 | |
|---|
| 711 | |
|---|
| 712 | INTEGER :: j, k |
|---|
| 713 | |
|---|
| 714 | INTEGER :: i |
|---|
| 715 | REAL(kind=dp):: x |
|---|
| 716 | k = is |
|---|
| 717 | cfactor = 1.000000e+00_dp |
|---|
| 718 | |
|---|
| 719 | x = (0.) * cfactor |
|---|
| 720 | DO i = 1 , nvar |
|---|
| 721 | ENDDO |
|---|
| 722 | |
|---|
| 723 | x = (0.) * cfactor |
|---|
| 724 | DO i = 1 , nfix |
|---|
| 725 | fix(i) = x |
|---|
| 726 | ENDDO |
|---|
| 727 | |
|---|
| 728 | ! constant rate coefficients |
|---|
| 729 | ! END constant rate coefficients |
|---|
| 730 | |
|---|
| 731 | ! INLINED initializations |
|---|
| 732 | |
|---|
| 733 | ! End INLINED initializations |
|---|
| 734 | |
|---|
| 735 | |
|---|
| 736 | END SUBROUTINE initialize |
|---|
| 737 | |
|---|
| 738 | SUBROUTINE integrate( tin, tout, & |
|---|
| 739 | icntrl_u, rcntrl_u, istatus_u, rstatus_u, ierr_u) |
|---|
| 740 | |
|---|
| 741 | |
|---|
| 742 | REAL(kind=dp), INTENT(IN):: tin ! start time |
|---|
| 743 | REAL(kind=dp), INTENT(IN):: tout ! END time |
|---|
| 744 | ! OPTIONAL input PARAMETERs and statistics |
|---|
| 745 | INTEGER, INTENT(IN), OPTIONAL :: icntrl_u(20) |
|---|
| 746 | REAL(kind=dp), INTENT(IN), OPTIONAL :: rcntrl_u(20) |
|---|
| 747 | INTEGER, INTENT(OUT), OPTIONAL :: istatus_u(20) |
|---|
| 748 | REAL(kind=dp), INTENT(OUT), OPTIONAL :: rstatus_u(20) |
|---|
| 749 | INTEGER, INTENT(OUT), OPTIONAL :: ierr_u |
|---|
| 750 | |
|---|
| 751 | REAL(kind=dp):: rcntrl(20), rstatus(20) |
|---|
| 752 | INTEGER :: icntrl(20), istatus(20), ierr |
|---|
| 753 | |
|---|
| 754 | INTEGER, SAVE :: ntotal = 0 |
|---|
| 755 | |
|---|
| 756 | icntrl(:) = 0 |
|---|
| 757 | rcntrl(:) = 0.0_dp |
|---|
| 758 | istatus(:) = 0 |
|---|
| 759 | rstatus(:) = 0.0_dp |
|---|
| 760 | |
|---|
| 761 | !~~~> fine-tune the integrator: |
|---|
| 762 | icntrl(1) = 0 ! 0 - non- autonomous, 1 - autonomous |
|---|
| 763 | icntrl(2) = 0 ! 0 - vector tolerances, 1 - scalars |
|---|
| 764 | |
|---|
| 765 | ! IF OPTIONAL PARAMETERs are given, and IF they are >0, |
|---|
| 766 | ! THEN they overwrite default settings. |
|---|
| 767 | IF (PRESENT(icntrl_u))THEN |
|---|
| 768 | WHERE(icntrl_u(:)> 0)icntrl(:) = icntrl_u(:) |
|---|
| 769 | ENDIF |
|---|
| 770 | IF (PRESENT(rcntrl_u))THEN |
|---|
| 771 | WHERE(rcntrl_u(:)> 0)rcntrl(:) = rcntrl_u(:) |
|---|
| 772 | ENDIF |
|---|
| 773 | |
|---|
| 774 | |
|---|
| 775 | CALL rosenbrock(nvar, var, tin, tout, & |
|---|
| 776 | atol, rtol, & |
|---|
| 777 | rcntrl, icntrl, rstatus, istatus, ierr) |
|---|
| 778 | |
|---|
| 779 | !~~~> debug option: show no of steps |
|---|
| 780 | ! ntotal = ntotal + istatus(nstp) |
|---|
| 781 | ! PRINT*,'NSTEPS=',ISTATUS(Nstp),' (',Ntotal,')',' O3=',VAR(ind_O3) |
|---|
| 782 | |
|---|
| 783 | stepmin = rstatus(nhexit) |
|---|
| 784 | ! IF OPTIONAL PARAMETERs are given for output they |
|---|
| 785 | ! are updated with the RETURN information |
|---|
| 786 | IF (PRESENT(istatus_u))istatus_u(:) = istatus(:) |
|---|
| 787 | IF (PRESENT(rstatus_u))rstatus_u(:) = rstatus(:) |
|---|
| 788 | IF (PRESENT(ierr_u)) ierr_u = ierr |
|---|
| 789 | |
|---|
| 790 | END SUBROUTINE integrate |
|---|
| 791 | |
|---|
| 792 | SUBROUTINE fun(v, f, rct, vdot) |
|---|
| 793 | |
|---|
| 794 | ! V - Concentrations of variable species (local) |
|---|
| 795 | REAL(kind=dp):: v(nvar) |
|---|
| 796 | ! F - Concentrations of fixed species (local) |
|---|
| 797 | REAL(kind=dp):: f(nfix) |
|---|
| 798 | ! RCT - Rate constants (local) |
|---|
| 799 | REAL(kind=dp):: rct(nreact) |
|---|
| 800 | ! Vdot - Time derivative of variable species concentrations |
|---|
| 801 | REAL(kind=dp):: vdot(nvar) |
|---|
| 802 | |
|---|
| 803 | |
|---|
| 804 | ! Computation of equation rates |
|---|
| 805 | a(1) = rct(1) * v(10) |
|---|
| 806 | a(2) = rct(2) * v(6) |
|---|
| 807 | a(3) = rct(3) * v(6) * v(9) |
|---|
| 808 | a(4) = rct(4) * v(4) * v(7) |
|---|
| 809 | a(5) = rct(5) * v(8) * v(9) |
|---|
| 810 | a(6) = rct(6) * v(5) * v(9) |
|---|
| 811 | a(7) = rct(7) * v(7) * v(10) |
|---|
| 812 | |
|---|
| 813 | ! Aggregate function |
|---|
| 814 | vdot(1) = 0 |
|---|
| 815 | vdot(2) = a(7) |
|---|
| 816 | vdot(3) = a(5) |
|---|
| 817 | vdot(4) = - a(4) |
|---|
| 818 | vdot(5) = a(5) - a(6) |
|---|
| 819 | vdot(6) = a(1) - a(2) - a(3) |
|---|
| 820 | vdot(7) = 2* a(2) - a(4) + a(6) - a(7) |
|---|
| 821 | vdot(8) = a(4) - a(5) |
|---|
| 822 | vdot(9) = a(1) - a(3) - a(5) - a(6) |
|---|
| 823 | vdot(10) = - a(1) + a(3) + a(5) + a(6) - a(7) |
|---|
| 824 | |
|---|
| 825 | END SUBROUTINE fun |
|---|
| 826 | |
|---|
| 827 | SUBROUTINE kppsolve(jvs, x) |
|---|
| 828 | |
|---|
| 829 | ! JVS - sparse Jacobian of variables |
|---|
| 830 | REAL(kind=dp):: jvs(lu_nonzero) |
|---|
| 831 | ! X - Vector for variables |
|---|
| 832 | REAL(kind=dp):: x(nvar) |
|---|
| 833 | |
|---|
| 834 | x(7) = x(7) - jvs(16) * x(4) - jvs(17) * x(5) - jvs(18) * x(6) |
|---|
| 835 | x(8) = x(8) - jvs(23) * x(4) - jvs(24) * x(7) |
|---|
| 836 | x(9) = x(9) - jvs(28) * x(5) - jvs(29) * x(6) - jvs(30) * x(8) |
|---|
| 837 | x(10) = x(10) - jvs(33) * x(5) - jvs(34) * x(6) - jvs(35) * x(7) - jvs(36) * x(8) - jvs(37) * x(9) |
|---|
| 838 | x(10) = x(10) / jvs(38) |
|---|
| 839 | x(9) = (x(9) - jvs(32) * x(10)) /(jvs(31)) |
|---|
| 840 | x(8) = (x(8) - jvs(26) * x(9) - jvs(27) * x(10)) /(jvs(25)) |
|---|
| 841 | x(7) = (x(7) - jvs(20) * x(8) - jvs(21) * x(9) - jvs(22) * x(10)) /(jvs(19)) |
|---|
| 842 | x(6) = (x(6) - jvs(14) * x(9) - jvs(15) * x(10)) /(jvs(13)) |
|---|
| 843 | x(5) = (x(5) - jvs(11) * x(8) - jvs(12) * x(9)) /(jvs(10)) |
|---|
| 844 | x(4) = (x(4) - jvs(9) * x(7)) /(jvs(8)) |
|---|
| 845 | x(3) = (x(3) - jvs(6) * x(8) - jvs(7) * x(9)) /(jvs(5)) |
|---|
| 846 | x(2) = (x(2) - jvs(3) * x(7) - jvs(4) * x(10)) /(jvs(2)) |
|---|
| 847 | x(1) = x(1) / jvs(1) |
|---|
| 848 | |
|---|
| 849 | END SUBROUTINE kppsolve |
|---|
| 850 | |
|---|
| 851 | SUBROUTINE jac_sp(v, f, rct, jvs) |
|---|
| 852 | |
|---|
| 853 | ! V - Concentrations of variable species (local) |
|---|
| 854 | REAL(kind=dp):: v(nvar) |
|---|
| 855 | ! F - Concentrations of fixed species (local) |
|---|
| 856 | REAL(kind=dp):: f(nfix) |
|---|
| 857 | ! RCT - Rate constants (local) |
|---|
| 858 | REAL(kind=dp):: rct(nreact) |
|---|
| 859 | ! JVS - sparse Jacobian of variables |
|---|
| 860 | REAL(kind=dp):: jvs(lu_nonzero) |
|---|
| 861 | |
|---|
| 862 | |
|---|
| 863 | ! Local variables |
|---|
| 864 | ! B - Temporary array |
|---|
| 865 | REAL(kind=dp):: b(13) |
|---|
| 866 | |
|---|
| 867 | ! B(1) = dA(1)/dV(10) |
|---|
| 868 | b(1) = rct(1) |
|---|
| 869 | ! B(2) = dA(2)/dV(6) |
|---|
| 870 | b(2) = rct(2) |
|---|
| 871 | ! B(3) = dA(3)/dV(6) |
|---|
| 872 | b(3) = rct(3) * v(9) |
|---|
| 873 | ! B(4) = dA(3)/dV(9) |
|---|
| 874 | b(4) = rct(3) * v(6) |
|---|
| 875 | ! B(5) = dA(4)/dV(4) |
|---|
| 876 | b(5) = rct(4) * v(7) |
|---|
| 877 | ! B(6) = dA(4)/dV(7) |
|---|
| 878 | b(6) = rct(4) * v(4) |
|---|
| 879 | ! B(7) = dA(5)/dV(8) |
|---|
| 880 | b(7) = rct(5) * v(9) |
|---|
| 881 | ! B(8) = dA(5)/dV(9) |
|---|
| 882 | b(8) = rct(5) * v(8) |
|---|
| 883 | ! B(9) = dA(6)/dV(5) |
|---|
| 884 | b(9) = rct(6) * v(9) |
|---|
| 885 | ! B(10) = dA(6)/dV(9) |
|---|
| 886 | b(10) = rct(6) * v(5) |
|---|
| 887 | ! B(11) = dA(7)/dV(7) |
|---|
| 888 | b(11) = rct(7) * v(10) |
|---|
| 889 | ! B(12) = dA(7)/dV(10) |
|---|
| 890 | b(12) = rct(7) * v(7) |
|---|
| 891 | ! B(13) = dA(8)/dV(1) |
|---|
| 892 | b(13) = rct(8) |
|---|
| 893 | |
|---|
| 894 | ! Construct the Jacobian terms from B's |
|---|
| 895 | ! JVS(1) = Jac_FULL(1,1) |
|---|
| 896 | jvs(1) = 0 |
|---|
| 897 | ! JVS(2) = Jac_FULL(2,2) |
|---|
| 898 | jvs(2) = 0 |
|---|
| 899 | ! JVS(3) = Jac_FULL(2,7) |
|---|
| 900 | jvs(3) = b(11) |
|---|
| 901 | ! JVS(4) = Jac_FULL(2,10) |
|---|
| 902 | jvs(4) = b(12) |
|---|
| 903 | ! JVS(5) = Jac_FULL(3,3) |
|---|
| 904 | jvs(5) = 0 |
|---|
| 905 | ! JVS(6) = Jac_FULL(3,8) |
|---|
| 906 | jvs(6) = b(7) |
|---|
| 907 | ! JVS(7) = Jac_FULL(3,9) |
|---|
| 908 | jvs(7) = b(8) |
|---|
| 909 | ! JVS(8) = Jac_FULL(4,4) |
|---|
| 910 | jvs(8) = - b(5) |
|---|
| 911 | ! JVS(9) = Jac_FULL(4,7) |
|---|
| 912 | jvs(9) = - b(6) |
|---|
| 913 | ! JVS(10) = Jac_FULL(5,5) |
|---|
| 914 | jvs(10) = - b(9) |
|---|
| 915 | ! JVS(11) = Jac_FULL(5,8) |
|---|
| 916 | jvs(11) = b(7) |
|---|
| 917 | ! JVS(12) = Jac_FULL(5,9) |
|---|
| 918 | jvs(12) = b(8) - b(10) |
|---|
| 919 | ! JVS(13) = Jac_FULL(6,6) |
|---|
| 920 | jvs(13) = - b(2) - b(3) |
|---|
| 921 | ! JVS(14) = Jac_FULL(6,9) |
|---|
| 922 | jvs(14) = - b(4) |
|---|
| 923 | ! JVS(15) = Jac_FULL(6,10) |
|---|
| 924 | jvs(15) = b(1) |
|---|
| 925 | ! JVS(16) = Jac_FULL(7,4) |
|---|
| 926 | jvs(16) = - b(5) |
|---|
| 927 | ! JVS(17) = Jac_FULL(7,5) |
|---|
| 928 | jvs(17) = b(9) |
|---|
| 929 | ! JVS(18) = Jac_FULL(7,6) |
|---|
| 930 | jvs(18) = 2* b(2) |
|---|
| 931 | ! JVS(19) = Jac_FULL(7,7) |
|---|
| 932 | jvs(19) = - b(6) - b(11) |
|---|
| 933 | ! JVS(20) = Jac_FULL(7,8) |
|---|
| 934 | jvs(20) = 0 |
|---|
| 935 | ! JVS(21) = Jac_FULL(7,9) |
|---|
| 936 | jvs(21) = b(10) |
|---|
| 937 | ! JVS(22) = Jac_FULL(7,10) |
|---|
| 938 | jvs(22) = - b(12) |
|---|
| 939 | ! JVS(23) = Jac_FULL(8,4) |
|---|
| 940 | jvs(23) = b(5) |
|---|
| 941 | ! JVS(24) = Jac_FULL(8,7) |
|---|
| 942 | jvs(24) = b(6) |
|---|
| 943 | ! JVS(25) = Jac_FULL(8,8) |
|---|
| 944 | jvs(25) = - b(7) |
|---|
| 945 | ! JVS(26) = Jac_FULL(8,9) |
|---|
| 946 | jvs(26) = - b(8) |
|---|
| 947 | ! JVS(27) = Jac_FULL(8,10) |
|---|
| 948 | jvs(27) = 0 |
|---|
| 949 | ! JVS(28) = Jac_FULL(9,5) |
|---|
| 950 | jvs(28) = - b(9) |
|---|
| 951 | ! JVS(29) = Jac_FULL(9,6) |
|---|
| 952 | jvs(29) = - b(3) |
|---|
| 953 | ! JVS(30) = Jac_FULL(9,8) |
|---|
| 954 | jvs(30) = - b(7) |
|---|
| 955 | ! JVS(31) = Jac_FULL(9,9) |
|---|
| 956 | jvs(31) = - b(4) - b(8) - b(10) |
|---|
| 957 | ! JVS(32) = Jac_FULL(9,10) |
|---|
| 958 | jvs(32) = b(1) |
|---|
| 959 | ! JVS(33) = Jac_FULL(10,5) |
|---|
| 960 | jvs(33) = b(9) |
|---|
| 961 | ! JVS(34) = Jac_FULL(10,6) |
|---|
| 962 | jvs(34) = b(3) |
|---|
| 963 | ! JVS(35) = Jac_FULL(10,7) |
|---|
| 964 | jvs(35) = - b(11) |
|---|
| 965 | ! JVS(36) = Jac_FULL(10,8) |
|---|
| 966 | jvs(36) = b(7) |
|---|
| 967 | ! JVS(37) = Jac_FULL(10,9) |
|---|
| 968 | jvs(37) = b(4) + b(8) + b(10) |
|---|
| 969 | ! JVS(38) = Jac_FULL(10,10) |
|---|
| 970 | jvs(38) = - b(1) - b(12) |
|---|
| 971 | |
|---|
| 972 | END SUBROUTINE jac_sp |
|---|
| 973 | |
|---|
| 974 | elemental REAL(kind=dp)FUNCTION k_arr (k_298, tdep, temp) |
|---|
| 975 | ! arrhenius FUNCTION |
|---|
| 976 | |
|---|
| 977 | REAL, INTENT(IN):: k_298 ! k at t = 298.15k |
|---|
| 978 | REAL, INTENT(IN):: tdep ! temperature dependence |
|---|
| 979 | REAL(kind=dp), INTENT(IN):: temp ! temperature |
|---|
| 980 | |
|---|
| 981 | intrinsic exp |
|---|
| 982 | |
|---|
| 983 | k_arr = k_298 * exp(tdep* (1._dp/temp- 3.3540e-3_dp))! 1/298.15=3.3540e-3 |
|---|
| 984 | |
|---|
| 985 | END FUNCTION k_arr |
|---|
| 986 | |
|---|
| 987 | SUBROUTINE update_rconst() |
|---|
| 988 | INTEGER :: k |
|---|
| 989 | |
|---|
| 990 | k = is |
|---|
| 991 | |
|---|
| 992 | ! Begin INLINED RCONST |
|---|
| 993 | |
|---|
| 994 | |
|---|
| 995 | ! End INLINED RCONST |
|---|
| 996 | |
|---|
| 997 | rconst(1) = (phot(j_no2)) |
|---|
| 998 | rconst(2) = (phot(j_o31d)) |
|---|
| 999 | rconst(3) = (arr2(1.8e-12_dp , 1370.0_dp , temp)) |
|---|
| 1000 | rconst(4) = (arr2(2.e-11_dp , 500.0_dp , temp)) |
|---|
| 1001 | rconst(5) = (arr2(4.2e-12_dp , -180.0_dp , temp)) |
|---|
| 1002 | rconst(6) = (arr2(3.7e-12_dp , -240.0_dp , temp)) |
|---|
| 1003 | rconst(7) = (arr2(1.15e-11_dp , 0.0_dp , temp)) |
|---|
| 1004 | rconst(8) = (1.0_dp) |
|---|
| 1005 | |
|---|
| 1006 | END SUBROUTINE update_rconst |
|---|
| 1007 | |
|---|
| 1008 | ! END FUNCTION ARR2 |
|---|
| 1009 | REAL(kind=dp)FUNCTION arr2( a0, b0, temp) |
|---|
| 1010 | REAL(kind=dp):: temp |
|---|
| 1011 | REAL(kind=dp):: a0, b0 |
|---|
| 1012 | arr2 = a0 * exp( - b0 / temp) |
|---|
| 1013 | END FUNCTION arr2 |
|---|
| 1014 | |
|---|
| 1015 | SUBROUTINE initialize_kpp_ctrl(status) |
|---|
| 1016 | |
|---|
| 1017 | |
|---|
| 1018 | ! i/o |
|---|
| 1019 | INTEGER, INTENT(OUT):: status |
|---|
| 1020 | |
|---|
| 1021 | ! local |
|---|
| 1022 | REAL(dp):: tsum |
|---|
| 1023 | INTEGER :: i |
|---|
| 1024 | |
|---|
| 1025 | ! check fixed time steps |
|---|
| 1026 | tsum = 0.0_dp |
|---|
| 1027 | DO i=1, nmaxfixsteps |
|---|
| 1028 | IF (t_steps(i)< tiny(0.0_dp))exit |
|---|
| 1029 | tsum = tsum + t_steps(i) |
|---|
| 1030 | ENDDO |
|---|
| 1031 | |
|---|
| 1032 | nfsteps = i- 1 |
|---|
| 1033 | |
|---|
| 1034 | l_fixed_step = (nfsteps > 0).and.((tsum - 1.0)< tiny(0.0_dp)) |
|---|
| 1035 | |
|---|
| 1036 | IF (l_vector)THEN |
|---|
| 1037 | WRITE(*,*) ' MODE : VECTOR (LENGTH=',VL_DIM,')' |
|---|
| 1038 | ELSE |
|---|
| 1039 | WRITE(*,*) ' MODE : SCALAR' |
|---|
| 1040 | ENDIF |
|---|
| 1041 | ! |
|---|
| 1042 | WRITE(*,*) ' DE-INDEXING MODE :',I_LU_DI |
|---|
| 1043 | ! |
|---|
| 1044 | WRITE(*,*) ' ICNTRL : ',icntrl |
|---|
| 1045 | WRITE(*,*) ' RCNTRL : ',rcntrl |
|---|
| 1046 | ! |
|---|
| 1047 | ! note: this is ONLY meaningful for vectorized (kp4)rosenbrock- methods |
|---|
| 1048 | IF (l_vector)THEN |
|---|
| 1049 | IF (l_fixed_step)THEN |
|---|
| 1050 | WRITE(*,*) ' TIME STEPS : FIXED (',t_steps(1:nfsteps),')' |
|---|
| 1051 | ELSE |
|---|
| 1052 | WRITE(*,*) ' TIME STEPS : AUTOMATIC' |
|---|
| 1053 | ENDIF |
|---|
| 1054 | ELSE |
|---|
| 1055 | WRITE(*,*) ' TIME STEPS : AUTOMATIC '//& |
|---|
| 1056 | &'(t_steps (CTRL_KPP) ignored in SCALAR MODE)' |
|---|
| 1057 | ENDIF |
|---|
| 1058 | ! mz_pj_20070531- |
|---|
| 1059 | |
|---|
| 1060 | status = 0 |
|---|
| 1061 | |
|---|
| 1062 | |
|---|
| 1063 | END SUBROUTINE initialize_kpp_ctrl |
|---|
| 1064 | |
|---|
| 1065 | SUBROUTINE error_output(c, ierr, pe) |
|---|
| 1066 | |
|---|
| 1067 | |
|---|
| 1068 | INTEGER, INTENT(IN):: ierr |
|---|
| 1069 | INTEGER, INTENT(IN):: pe |
|---|
| 1070 | REAL(dp), DIMENSION(:), INTENT(IN):: c |
|---|
| 1071 | |
|---|
| 1072 | write(6,*) 'ERROR in chem_gasphase_mod ',ierr,C(1) |
|---|
| 1073 | |
|---|
| 1074 | |
|---|
| 1075 | END SUBROUTINE error_output |
|---|
| 1076 | |
|---|
| 1077 | SUBROUTINE wscal(n, alpha, x, incx) |
|---|
| 1078 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1079 | ! constant times a vector: x(1:N) <- Alpha*x(1:N) |
|---|
| 1080 | ! only for incX=incY=1 |
|---|
| 1081 | ! after BLAS |
|---|
| 1082 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 1083 | ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) |
|---|
| 1084 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1085 | |
|---|
| 1086 | INTEGER :: i, incx, m, mp1, n |
|---|
| 1087 | REAL(kind=dp) :: x(n), alpha |
|---|
| 1088 | REAL(kind=dp), PARAMETER :: zero=0.0_dp, one=1.0_dp |
|---|
| 1089 | |
|---|
| 1090 | IF (alpha .eq. one)RETURN |
|---|
| 1091 | IF (n .le. 0)RETURN |
|---|
| 1092 | |
|---|
| 1093 | m = mod(n, 5) |
|---|
| 1094 | IF ( m .ne. 0)THEN |
|---|
| 1095 | IF (alpha .eq. (- one))THEN |
|---|
| 1096 | DO i = 1, m |
|---|
| 1097 | x(i) = - x(i) |
|---|
| 1098 | ENDDO |
|---|
| 1099 | ELSEIF (alpha .eq. zero)THEN |
|---|
| 1100 | DO i = 1, m |
|---|
| 1101 | x(i) = zero |
|---|
| 1102 | ENDDO |
|---|
| 1103 | ELSE |
|---|
| 1104 | DO i = 1, m |
|---|
| 1105 | x(i) = alpha* x(i) |
|---|
| 1106 | ENDDO |
|---|
| 1107 | ENDIF |
|---|
| 1108 | IF ( n .lt. 5)RETURN |
|---|
| 1109 | ENDIF |
|---|
| 1110 | mp1 = m + 1 |
|---|
| 1111 | IF (alpha .eq. (- one))THEN |
|---|
| 1112 | DO i = mp1, n, 5 |
|---|
| 1113 | x(i) = - x(i) |
|---|
| 1114 | x(i + 1) = - x(i + 1) |
|---|
| 1115 | x(i + 2) = - x(i + 2) |
|---|
| 1116 | x(i + 3) = - x(i + 3) |
|---|
| 1117 | x(i + 4) = - x(i + 4) |
|---|
| 1118 | ENDDO |
|---|
| 1119 | ELSEIF (alpha .eq. zero)THEN |
|---|
| 1120 | DO i = mp1, n, 5 |
|---|
| 1121 | x(i) = zero |
|---|
| 1122 | x(i + 1) = zero |
|---|
| 1123 | x(i + 2) = zero |
|---|
| 1124 | x(i + 3) = zero |
|---|
| 1125 | x(i + 4) = zero |
|---|
| 1126 | ENDDO |
|---|
| 1127 | ELSE |
|---|
| 1128 | DO i = mp1, n, 5 |
|---|
| 1129 | x(i) = alpha* x(i) |
|---|
| 1130 | x(i + 1) = alpha* x(i + 1) |
|---|
| 1131 | x(i + 2) = alpha* x(i + 2) |
|---|
| 1132 | x(i + 3) = alpha* x(i + 3) |
|---|
| 1133 | x(i + 4) = alpha* x(i + 4) |
|---|
| 1134 | ENDDO |
|---|
| 1135 | ENDIF |
|---|
| 1136 | |
|---|
| 1137 | END SUBROUTINE wscal |
|---|
| 1138 | |
|---|
| 1139 | SUBROUTINE waxpy(n, alpha, x, incx, y, incy) |
|---|
| 1140 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1141 | ! constant times a vector plus a vector: y <- y + Alpha*x |
|---|
| 1142 | ! only for incX=incY=1 |
|---|
| 1143 | ! after BLAS |
|---|
| 1144 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 1145 | ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) |
|---|
| 1146 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|---|
| 1147 | |
|---|
| 1148 | INTEGER :: i, incx, incy, m, mp1, n |
|---|
| 1149 | REAL(kind=dp):: x(n), y(n), alpha |
|---|
| 1150 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
|---|
| 1151 | |
|---|
| 1152 | IF (alpha .eq. zero)RETURN |
|---|
| 1153 | IF (n .le. 0)RETURN |
|---|
| 1154 | |
|---|
| 1155 | m = mod(n, 4) |
|---|
| 1156 | IF ( m .ne. 0)THEN |
|---|
| 1157 | DO i = 1, m |
|---|
| 1158 | y(i) = y(i) + alpha* x(i) |
|---|
| 1159 | ENDDO |
|---|
| 1160 | IF ( n .lt. 4)RETURN |
|---|
| 1161 | ENDIF |
|---|
| 1162 | mp1 = m + 1 |
|---|
| 1163 | DO i = mp1, n, 4 |
|---|
| 1164 | y(i) = y(i) + alpha* x(i) |
|---|
| 1165 | y(i + 1) = y(i + 1) + alpha* x(i + 1) |
|---|
| 1166 | y(i + 2) = y(i + 2) + alpha* x(i + 2) |
|---|
| 1167 | y(i + 3) = y(i + 3) + alpha* x(i + 3) |
|---|
| 1168 | ENDDO |
|---|
| 1169 | |
|---|
| 1170 | END SUBROUTINE waxpy |
|---|
| 1171 | |
|---|
| 1172 | SUBROUTINE rosenbrock(n, y, tstart, tend, & |
|---|
| 1173 | abstol, reltol, & |
|---|
| 1174 | rcntrl, icntrl, rstatus, istatus, ierr) |
|---|
| 1175 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1176 | ! |
|---|
| 1177 | ! Solves the system y'=F(t,y) using a Rosenbrock method defined by: |
|---|
| 1178 | ! |
|---|
| 1179 | ! G = 1/(H*gamma(1)) - Jac(t0,Y0) |
|---|
| 1180 | ! T_i = t0 + Alpha(i)*H |
|---|
| 1181 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
|---|
| 1182 | ! G *K_i = Fun( T_i,Y_i)+ \sum_{j=1}^S C(i,j)/H *K_j + |
|---|
| 1183 | ! gamma(i)*dF/dT(t0,Y0) |
|---|
| 1184 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
|---|
| 1185 | ! |
|---|
| 1186 | ! For details on Rosenbrock methods and their implementation consult: |
|---|
| 1187 | ! E. Hairer and G. Wanner |
|---|
| 1188 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
|---|
| 1189 | ! Springer series in computational mathematics,Springer-Verlag,1996. |
|---|
| 1190 | ! The codes contained in the book inspired this implementation. |
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| 1191 | ! |
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| 1192 | ! (C) Adrian Sandu,August 2004 |
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| 1193 | ! Virginia Polytechnic Institute and State University |
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| 1194 | ! Contact: sandu@cs.vt.edu |
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| 1195 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 |
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| 1196 | ! This implementation is part of KPP - the Kinetic PreProcessor |
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| 1197 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1198 | ! |
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| 1199 | !~~~> input arguments: |
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| 1200 | ! |
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| 1201 | !- y(n) = vector of initial conditions (at t=tstart) |
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| 1202 | !- [tstart, tend] = time range of integration |
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| 1203 | ! (if Tstart>Tend the integration is performed backwards in time) |
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| 1204 | !- reltol, abstol = user precribed accuracy |
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| 1205 | !- SUBROUTINE fun( t, y, ydot) = ode FUNCTION, |
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| 1206 | ! returns Ydot = Y' = F(T,Y) |
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| 1207 | !- SUBROUTINE jac( t, y, jcb) = jacobian of the ode FUNCTION, |
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| 1208 | ! returns Jcb = dFun/dY |
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| 1209 | !- icntrl(1:20) = INTEGER inputs PARAMETERs |
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| 1210 | !- rcntrl(1:20) = REAL inputs PARAMETERs |
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| 1211 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1212 | ! |
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| 1213 | !~~~> output arguments: |
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| 1214 | ! |
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| 1215 | !- y(n) - > vector of final states (at t- >tend) |
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| 1216 | !- istatus(1:20) - > INTEGER output PARAMETERs |
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| 1217 | !- rstatus(1:20) - > REAL output PARAMETERs |
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| 1218 | !- ierr - > job status upon RETURN |
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| 1219 | ! success (positive value) or |
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| 1220 | ! failure (negative value) |
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| 1221 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1222 | ! |
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| 1223 | !~~~> input PARAMETERs: |
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| 1224 | ! |
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| 1225 | ! Note: For input parameters equal to zero the default values of the |
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| 1226 | ! corresponding variables are used. |
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| 1227 | ! |
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| 1228 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
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| 1229 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
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| 1230 | ! |
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| 1231 | ! ICNTRL(2) = 0: AbsTol,RelTol are N-dimensional vectors |
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| 1232 | ! = 1: AbsTol,RelTol are scalars |
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| 1233 | ! |
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| 1234 | ! ICNTRL(3) -> selection of a particular Rosenbrock method |
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| 1235 | ! = 0 : Rodas3 (default) |
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| 1236 | ! = 1 : Ros2 |
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| 1237 | ! = 2 : Ros3 |
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| 1238 | ! = 3 : Ros4 |
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| 1239 | ! = 4 : Rodas3 |
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| 1240 | ! = 5 : Rodas4 |
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| 1241 | ! |
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| 1242 | ! ICNTRL(4) -> maximum number of integration steps |
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| 1243 | ! For ICNTRL(4) =0) the default value of 100000 is used |
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| 1244 | ! |
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| 1245 | ! RCNTRL(1) -> Hmin,lower bound for the integration step size |
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| 1246 | ! It is strongly recommended to keep Hmin = ZERO |
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| 1247 | ! RCNTRL(2) -> Hmax,upper bound for the integration step size |
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| 1248 | ! RCNTRL(3) -> Hstart,starting value for the integration step size |
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| 1249 | ! |
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| 1250 | ! RCNTRL(4) -> FacMin,lower bound on step decrease factor (default=0.2) |
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| 1251 | ! RCNTRL(5) -> FacMax,upper bound on step increase factor (default=6) |
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| 1252 | ! RCNTRL(6) -> FacRej,step decrease factor after multiple rejections |
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| 1253 | ! (default=0.1) |
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| 1254 | ! RCNTRL(7) -> FacSafe,by which the new step is slightly smaller |
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| 1255 | ! than the predicted value (default=0.9) |
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| 1256 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1257 | ! |
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| 1258 | ! |
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| 1259 | ! OUTPUT ARGUMENTS: |
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| 1260 | ! ----------------- |
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| 1261 | ! |
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| 1262 | ! T -> T value for which the solution has been computed |
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| 1263 | ! (after successful return T=Tend). |
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| 1264 | ! |
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| 1265 | ! Y(N) -> Numerical solution at T |
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| 1266 | ! |
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| 1267 | ! IDID -> Reports on successfulness upon return: |
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| 1268 | ! = 1 for success |
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| 1269 | ! < 0 for error (value equals error code) |
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| 1270 | ! |
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| 1271 | ! ISTATUS(1) -> No. of function calls |
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| 1272 | ! ISTATUS(2) -> No. of jacobian calls |
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| 1273 | ! ISTATUS(3) -> No. of steps |
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| 1274 | ! ISTATUS(4) -> No. of accepted steps |
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| 1275 | ! ISTATUS(5) -> No. of rejected steps (except at very beginning) |
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| 1276 | ! ISTATUS(6) -> No. of LU decompositions |
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| 1277 | ! ISTATUS(7) -> No. of forward/backward substitutions |
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| 1278 | ! ISTATUS(8) -> No. of singular matrix decompositions |
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| 1279 | ! |
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| 1280 | ! RSTATUS(1) -> Texit,the time corresponding to the |
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| 1281 | ! computed Y upon return |
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| 1282 | ! RSTATUS(2) -> Hexit,last accepted step before exit |
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| 1283 | ! RSTATUS(3) -> Hnew,last predicted step (not yet taken) |
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| 1284 | ! For multiple restarts,use Hnew as Hstart |
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| 1285 | ! in the subsequent run |
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| 1286 | ! |
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| 1287 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1288 | |
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| 1289 | |
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| 1290 | !~~~> arguments |
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| 1291 | INTEGER, INTENT(IN) :: n |
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| 1292 | REAL(kind=dp), INTENT(INOUT):: y(n) |
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| 1293 | REAL(kind=dp), INTENT(IN) :: tstart, tend |
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| 1294 | REAL(kind=dp), INTENT(IN) :: abstol(n), reltol(n) |
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| 1295 | INTEGER, INTENT(IN) :: icntrl(20) |
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| 1296 | REAL(kind=dp), INTENT(IN) :: rcntrl(20) |
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| 1297 | INTEGER, INTENT(INOUT):: istatus(20) |
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| 1298 | REAL(kind=dp), INTENT(INOUT):: rstatus(20) |
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| 1299 | INTEGER, INTENT(OUT) :: ierr |
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| 1300 | !~~~> PARAMETERs of the rosenbrock method, up to 6 stages |
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| 1301 | INTEGER :: ros_s, rosmethod |
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| 1302 | INTEGER, PARAMETER :: rs2=1, rs3=2, rs4=3, rd3=4, rd4=5, rg3=6 |
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| 1303 | REAL(kind=dp):: ros_a(15), ros_c(15), ros_m(6), ros_e(6), & |
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| 1304 | ros_alpha(6), ros_gamma(6), ros_elo |
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| 1305 | LOGICAL :: ros_newf(6) |
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| 1306 | CHARACTER(len=12):: ros_name |
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| 1307 | !~~~> local variables |
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| 1308 | REAL(kind=dp):: roundoff, facmin, facmax, facrej, facsafe |
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| 1309 | REAL(kind=dp):: hmin, hmax, hstart |
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| 1310 | REAL(kind=dp):: texit |
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| 1311 | INTEGER :: i, uplimtol, max_no_steps |
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| 1312 | LOGICAL :: autonomous, vectortol |
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| 1313 | !~~~> PARAMETERs |
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| 1314 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
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| 1315 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
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| 1316 | |
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| 1317 | !~~~> initialize statistics |
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| 1318 | istatus(1:8) = 0 |
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| 1319 | rstatus(1:3) = zero |
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| 1320 | |
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| 1321 | !~~~> autonomous or time dependent ode. default is time dependent. |
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| 1322 | autonomous = .not.(icntrl(1) == 0) |
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| 1323 | |
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| 1324 | !~~~> for scalar tolerances (icntrl(2).ne.0) the code uses abstol(1)and reltol(1) |
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| 1325 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:N) and RelTol(1:N) |
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| 1326 | IF (icntrl(2) == 0)THEN |
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| 1327 | vectortol = .TRUE. |
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| 1328 | uplimtol = n |
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| 1329 | ELSE |
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| 1330 | vectortol = .FALSE. |
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| 1331 | uplimtol = 1 |
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| 1332 | ENDIF |
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| 1333 | |
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| 1334 | !~~~> initialize the particular rosenbrock method selected |
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| 1335 | select CASE (icntrl(3)) |
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| 1336 | CASE (1) |
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| 1337 | CALL ros2 |
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| 1338 | CASE (2) |
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| 1339 | CALL ros3 |
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| 1340 | CASE (3) |
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| 1341 | CALL ros4 |
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| 1342 | CASE (0, 4) |
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| 1343 | CALL rodas3 |
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| 1344 | CASE (5) |
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| 1345 | CALL rodas4 |
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| 1346 | CASE (6) |
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| 1347 | CALL rang3 |
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| 1348 | CASE default |
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| 1349 | PRINT *,'Unknown Rosenbrock method: ICNTRL(3) =',ICNTRL(3) |
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| 1350 | CALL ros_errormsg(- 2, tstart, zero, ierr) |
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| 1351 | RETURN |
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| 1352 | END select |
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| 1353 | |
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| 1354 | !~~~> the maximum number of steps admitted |
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| 1355 | IF (icntrl(4) == 0)THEN |
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| 1356 | max_no_steps = 200000 |
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| 1357 | ELSEIF (icntrl(4)> 0)THEN |
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| 1358 | max_no_steps=icntrl(4) |
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| 1359 | ELSE |
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| 1360 | PRINT *,'User-selected max no. of steps: ICNTRL(4) =',ICNTRL(4) |
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| 1361 | CALL ros_errormsg(- 1, tstart, zero, ierr) |
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| 1362 | RETURN |
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| 1363 | ENDIF |
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| 1364 | |
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| 1365 | !~~~> unit roundoff (1+ roundoff>1) |
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| 1366 | roundoff = epsilon(one) |
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| 1367 | |
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| 1368 | !~~~> lower bound on the step size: (positive value) |
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| 1369 | IF (rcntrl(1) == zero)THEN |
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| 1370 | hmin = zero |
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| 1371 | ELSEIF (rcntrl(1)> zero)THEN |
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| 1372 | hmin = rcntrl(1) |
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| 1373 | ELSE |
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| 1374 | PRINT *,'User-selected Hmin: RCNTRL(1) =',RCNTRL(1) |
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| 1375 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
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| 1376 | RETURN |
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| 1377 | ENDIF |
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| 1378 | !~~~> upper bound on the step size: (positive value) |
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| 1379 | IF (rcntrl(2) == zero)THEN |
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| 1380 | hmax = abs(tend-tstart) |
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| 1381 | ELSEIF (rcntrl(2)> zero)THEN |
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| 1382 | hmax = min(abs(rcntrl(2)), abs(tend-tstart)) |
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| 1383 | ELSE |
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| 1384 | PRINT *,'User-selected Hmax: RCNTRL(2) =',RCNTRL(2) |
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| 1385 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
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| 1386 | RETURN |
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| 1387 | ENDIF |
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| 1388 | !~~~> starting step size: (positive value) |
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| 1389 | IF (rcntrl(3) == zero)THEN |
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| 1390 | hstart = max(hmin, deltamin) |
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| 1391 | ELSEIF (rcntrl(3)> zero)THEN |
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| 1392 | hstart = min(abs(rcntrl(3)), abs(tend-tstart)) |
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| 1393 | ELSE |
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| 1394 | PRINT *,'User-selected Hstart: RCNTRL(3) =',RCNTRL(3) |
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| 1395 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
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| 1396 | RETURN |
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| 1397 | ENDIF |
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| 1398 | !~~~> step size can be changed s.t. facmin < hnew/hold < facmax |
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| 1399 | IF (rcntrl(4) == zero)THEN |
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| 1400 | facmin = 0.2_dp |
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| 1401 | ELSEIF (rcntrl(4)> zero)THEN |
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| 1402 | facmin = rcntrl(4) |
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| 1403 | ELSE |
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| 1404 | PRINT *,'User-selected FacMin: RCNTRL(4) =',RCNTRL(4) |
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| 1405 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
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| 1406 | RETURN |
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| 1407 | ENDIF |
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| 1408 | IF (rcntrl(5) == zero)THEN |
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| 1409 | facmax = 6.0_dp |
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| 1410 | ELSEIF (rcntrl(5)> zero)THEN |
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| 1411 | facmax = rcntrl(5) |
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| 1412 | ELSE |
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| 1413 | PRINT *,'User-selected FacMax: RCNTRL(5) =',RCNTRL(5) |
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| 1414 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
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| 1415 | RETURN |
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| 1416 | ENDIF |
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| 1417 | !~~~> facrej: factor to decrease step after 2 succesive rejections |
|---|
| 1418 | IF (rcntrl(6) == zero)THEN |
|---|
| 1419 | facrej = 0.1_dp |
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| 1420 | ELSEIF (rcntrl(6)> zero)THEN |
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| 1421 | facrej = rcntrl(6) |
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| 1422 | ELSE |
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| 1423 | PRINT *,'User-selected FacRej: RCNTRL(6) =',RCNTRL(6) |
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| 1424 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
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| 1425 | RETURN |
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| 1426 | ENDIF |
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| 1427 | !~~~> facsafe: safety factor in the computation of new step size |
|---|
| 1428 | IF (rcntrl(7) == zero)THEN |
|---|
| 1429 | facsafe = 0.9_dp |
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| 1430 | ELSEIF (rcntrl(7)> zero)THEN |
|---|
| 1431 | facsafe = rcntrl(7) |
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| 1432 | ELSE |
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| 1433 | PRINT *,'User-selected FacSafe: RCNTRL(7) =',RCNTRL(7) |
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| 1434 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
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| 1435 | RETURN |
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| 1436 | ENDIF |
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| 1437 | !~~~> check IF tolerances are reasonable |
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| 1438 | DO i=1, uplimtol |
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| 1439 | IF ((abstol(i)<= zero).or. (reltol(i)<= 10.0_dp* roundoff)& |
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| 1440 | .or. (reltol(i)>= 1.0_dp))THEN |
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| 1441 | PRINT *,' AbsTol(',i,') = ',AbsTol(i) |
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| 1442 | PRINT *,' RelTol(',i,') = ',RelTol(i) |
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| 1443 | CALL ros_errormsg(- 5, tstart, zero, ierr) |
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| 1444 | RETURN |
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| 1445 | ENDIF |
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| 1446 | ENDDO |
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| 1447 | |
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| 1448 | |
|---|
| 1449 | !~~~> CALL rosenbrock method |
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| 1450 | CALL ros_integrator(y, tstart, tend, texit, & |
|---|
| 1451 | abstol, reltol, & |
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| 1452 | ! Integration parameters |
|---|
| 1453 | autonomous, vectortol, max_no_steps, & |
|---|
| 1454 | roundoff, hmin, hmax, hstart, & |
|---|
| 1455 | facmin, facmax, facrej, facsafe, & |
|---|
| 1456 | ! Error indicator |
|---|
| 1457 | ierr) |
|---|
| 1458 | |
|---|
| 1459 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 1460 | CONTAINS ! SUBROUTINEs internal to rosenbrock |
|---|
| 1461 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1462 | |
|---|
| 1463 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1464 | SUBROUTINE ros_errormsg(code, t, h, ierr) |
|---|
| 1465 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1466 | ! Handles all error messages |
|---|
| 1467 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1468 | |
|---|
| 1469 | REAL(kind=dp), INTENT(IN):: t, h |
|---|
| 1470 | INTEGER, INTENT(IN) :: code |
|---|
| 1471 | INTEGER, INTENT(OUT):: ierr |
|---|
| 1472 | |
|---|
| 1473 | ierr = code |
|---|
| 1474 | print * , & |
|---|
| 1475 | 'Forced exit from Rosenbrock due to the following error:' |
|---|
| 1476 | |
|---|
| 1477 | select CASE (code) |
|---|
| 1478 | CASE (- 1) |
|---|
| 1479 | PRINT *,'--> Improper value for maximal no of steps' |
|---|
| 1480 | CASE (- 2) |
|---|
| 1481 | PRINT *,'--> Selected Rosenbrock method not implemented' |
|---|
| 1482 | CASE (- 3) |
|---|
| 1483 | PRINT *,'--> Hmin/Hmax/Hstart must be positive' |
|---|
| 1484 | CASE (- 4) |
|---|
| 1485 | PRINT *,'--> FacMin/FacMax/FacRej must be positive' |
|---|
| 1486 | CASE (- 5) |
|---|
| 1487 | PRINT *,'--> Improper tolerance values' |
|---|
| 1488 | CASE (- 6) |
|---|
| 1489 | PRINT *,'--> No of steps exceeds maximum bound' |
|---|
| 1490 | CASE (- 7) |
|---|
| 1491 | PRINT *,'--> Step size too small: T + 10*H = T',& |
|---|
| 1492 | ' or H < Roundoff' |
|---|
| 1493 | CASE (- 8) |
|---|
| 1494 | PRINT *,'--> Matrix is repeatedly singular' |
|---|
| 1495 | CASE default |
|---|
| 1496 | PRINT *,'Unknown Error code: ',Code |
|---|
| 1497 | END select |
|---|
| 1498 | |
|---|
| 1499 | print * , "t=", t, "and h=", h |
|---|
| 1500 | |
|---|
| 1501 | END SUBROUTINE ros_errormsg |
|---|
| 1502 | |
|---|
| 1503 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1504 | SUBROUTINE ros_integrator (y, tstart, tend, t, & |
|---|
| 1505 | abstol, reltol, & |
|---|
| 1506 | !~~~> integration PARAMETERs |
|---|
| 1507 | autonomous, vectortol, max_no_steps, & |
|---|
| 1508 | roundoff, hmin, hmax, hstart, & |
|---|
| 1509 | facmin, facmax, facrej, facsafe, & |
|---|
| 1510 | !~~~> error indicator |
|---|
| 1511 | ierr) |
|---|
| 1512 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1513 | ! Template for the implementation of a generic Rosenbrock method |
|---|
| 1514 | ! defined by ros_S (no of stages) |
|---|
| 1515 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
|---|
| 1516 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1517 | |
|---|
| 1518 | |
|---|
| 1519 | !~~~> input: the initial condition at tstart; output: the solution at t |
|---|
| 1520 | REAL(kind=dp), INTENT(INOUT):: y(n) |
|---|
| 1521 | !~~~> input: integration interval |
|---|
| 1522 | REAL(kind=dp), INTENT(IN):: tstart, tend |
|---|
| 1523 | !~~~> output: time at which the solution is RETURNed (t=tendIF success) |
|---|
| 1524 | REAL(kind=dp), INTENT(OUT):: t |
|---|
| 1525 | !~~~> input: tolerances |
|---|
| 1526 | REAL(kind=dp), INTENT(IN):: abstol(n), reltol(n) |
|---|
| 1527 | !~~~> input: integration PARAMETERs |
|---|
| 1528 | LOGICAL, INTENT(IN):: autonomous, vectortol |
|---|
| 1529 | REAL(kind=dp), INTENT(IN):: hstart, hmin, hmax |
|---|
| 1530 | INTEGER, INTENT(IN):: max_no_steps |
|---|
| 1531 | REAL(kind=dp), INTENT(IN):: roundoff, facmin, facmax, facrej, facsafe |
|---|
| 1532 | !~~~> output: error indicator |
|---|
| 1533 | INTEGER, INTENT(OUT):: ierr |
|---|
| 1534 | ! ~~~~ Local variables |
|---|
| 1535 | REAL(kind=dp):: ynew(n), fcn0(n), fcn(n) |
|---|
| 1536 | REAL(kind=dp):: k(n* ros_s), dfdt(n) |
|---|
| 1537 | #ifdef full_algebra |
|---|
| 1538 | REAL(kind=dp):: jac0(n, n), ghimj(n, n) |
|---|
| 1539 | #else |
|---|
| 1540 | REAL(kind=dp):: jac0(lu_nonzero), ghimj(lu_nonzero) |
|---|
| 1541 | #endif |
|---|
| 1542 | REAL(kind=dp):: h, hnew, hc, hg, fac, tau |
|---|
| 1543 | REAL(kind=dp):: err, yerr(n) |
|---|
| 1544 | INTEGER :: pivot(n), direction, ioffset, j, istage |
|---|
| 1545 | LOGICAL :: rejectlasth, rejectmoreh, singular |
|---|
| 1546 | !~~~> local PARAMETERs |
|---|
| 1547 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
|---|
| 1548 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
|---|
| 1549 | !~~~> locally called FUNCTIONs |
|---|
| 1550 | ! REAL(kind=dp) WLAMCH |
|---|
| 1551 | ! EXTERNAL WLAMCH |
|---|
| 1552 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1553 | |
|---|
| 1554 | |
|---|
| 1555 | !~~~> initial preparations |
|---|
| 1556 | t = tstart |
|---|
| 1557 | rstatus(nhexit) = zero |
|---|
| 1558 | h = min( max(abs(hmin), abs(hstart)), abs(hmax)) |
|---|
| 1559 | IF (abs(h)<= 10.0_dp* roundoff)h = deltamin |
|---|
| 1560 | |
|---|
| 1561 | IF (tend >= tstart)THEN |
|---|
| 1562 | direction = + 1 |
|---|
| 1563 | ELSE |
|---|
| 1564 | direction = - 1 |
|---|
| 1565 | ENDIF |
|---|
| 1566 | h = direction* h |
|---|
| 1567 | |
|---|
| 1568 | rejectlasth=.FALSE. |
|---|
| 1569 | rejectmoreh=.FALSE. |
|---|
| 1570 | |
|---|
| 1571 | !~~~> time loop begins below |
|---|
| 1572 | |
|---|
| 1573 | timeloop: DO WHILE((direction > 0).and.((t- tend) + roundoff <= zero)& |
|---|
| 1574 | .or. (direction < 0).and.((tend-t) + roundoff <= zero)) |
|---|
| 1575 | |
|---|
| 1576 | IF (istatus(nstp)> max_no_steps)THEN ! too many steps |
|---|
| 1577 | CALL ros_errormsg(- 6, t, h, ierr) |
|---|
| 1578 | RETURN |
|---|
| 1579 | ENDIF |
|---|
| 1580 | IF (((t+ 0.1_dp* h) == t).or.(h <= roundoff))THEN ! step size too small |
|---|
| 1581 | CALL ros_errormsg(- 7, t, h, ierr) |
|---|
| 1582 | RETURN |
|---|
| 1583 | ENDIF |
|---|
| 1584 | |
|---|
| 1585 | !~~~> limit h IF necessary to avoid going beyond tend |
|---|
| 1586 | h = min(h, abs(tend-t)) |
|---|
| 1587 | |
|---|
| 1588 | !~~~> compute the FUNCTION at current time |
|---|
| 1589 | CALL funtemplate(t, y, fcn0) |
|---|
| 1590 | istatus(nfun) = istatus(nfun) + 1 |
|---|
| 1591 | |
|---|
| 1592 | !~~~> compute the FUNCTION derivative with respect to t |
|---|
| 1593 | IF (.not.autonomous)THEN |
|---|
| 1594 | CALL ros_funtimederivative(t, roundoff, y, & |
|---|
| 1595 | fcn0, dfdt) |
|---|
| 1596 | ENDIF |
|---|
| 1597 | |
|---|
| 1598 | !~~~> compute the jacobian at current time |
|---|
| 1599 | CALL jactemplate(t, y, jac0) |
|---|
| 1600 | istatus(njac) = istatus(njac) + 1 |
|---|
| 1601 | |
|---|
| 1602 | !~~~> repeat step calculation until current step accepted |
|---|
| 1603 | untilaccepted: do |
|---|
| 1604 | |
|---|
| 1605 | CALL ros_preparematrix(h, direction, ros_gamma(1), & |
|---|
| 1606 | jac0, ghimj, pivot, singular) |
|---|
| 1607 | IF (singular)THEN ! more than 5 consecutive failed decompositions |
|---|
| 1608 | CALL ros_errormsg(- 8, t, h, ierr) |
|---|
| 1609 | RETURN |
|---|
| 1610 | ENDIF |
|---|
| 1611 | |
|---|
| 1612 | !~~~> compute the stages |
|---|
| 1613 | stage: DO istage = 1, ros_s |
|---|
| 1614 | |
|---|
| 1615 | ! current istage offset. current istage vector is k(ioffset+ 1:ioffset+ n) |
|---|
| 1616 | ioffset = n* (istage-1) |
|---|
| 1617 | |
|---|
| 1618 | ! for the 1st istage the FUNCTION has been computed previously |
|---|
| 1619 | IF (istage == 1)THEN |
|---|
| 1620 | !slim: CALL wcopy(n, fcn0, 1, fcn, 1) |
|---|
| 1621 | fcn(1:n) = fcn0(1:n) |
|---|
| 1622 | ! istage>1 and a new FUNCTION evaluation is needed at the current istage |
|---|
| 1623 | ELSEIF(ros_newf(istage))THEN |
|---|
| 1624 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
|---|
| 1625 | ynew(1:n) = y(1:n) |
|---|
| 1626 | DO j = 1, istage-1 |
|---|
| 1627 | CALL waxpy(n, ros_a((istage-1) * (istage-2) /2+ j), & |
|---|
| 1628 | k(n* (j- 1) + 1), 1, ynew, 1) |
|---|
| 1629 | ENDDO |
|---|
| 1630 | tau = t + ros_alpha(istage) * direction* h |
|---|
| 1631 | CALL funtemplate(tau, ynew, fcn) |
|---|
| 1632 | istatus(nfun) = istatus(nfun) + 1 |
|---|
| 1633 | ENDIF ! IF istage == 1 ELSEIF ros_newf(istage) |
|---|
| 1634 | !slim: CALL wcopy(n, fcn, 1, k(ioffset+ 1), 1) |
|---|
| 1635 | k(ioffset+ 1:ioffset+ n) = fcn(1:n) |
|---|
| 1636 | DO j = 1, istage-1 |
|---|
| 1637 | hc = ros_c((istage-1) * (istage-2) /2+ j) /(direction* h) |
|---|
| 1638 | CALL waxpy(n, hc, k(n* (j- 1) + 1), 1, k(ioffset+ 1), 1) |
|---|
| 1639 | ENDDO |
|---|
| 1640 | IF ((.not. autonomous).and.(ros_gamma(istage).ne.zero))THEN |
|---|
| 1641 | hg = direction* h* ros_gamma(istage) |
|---|
| 1642 | CALL waxpy(n, hg, dfdt, 1, k(ioffset+ 1), 1) |
|---|
| 1643 | ENDIF |
|---|
| 1644 | CALL ros_solve(ghimj, pivot, k(ioffset+ 1)) |
|---|
| 1645 | |
|---|
| 1646 | END DO stage |
|---|
| 1647 | |
|---|
| 1648 | |
|---|
| 1649 | !~~~> compute the new solution |
|---|
| 1650 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
|---|
| 1651 | ynew(1:n) = y(1:n) |
|---|
| 1652 | DO j=1, ros_s |
|---|
| 1653 | CALL waxpy(n, ros_m(j), k(n* (j- 1) + 1), 1, ynew, 1) |
|---|
| 1654 | ENDDO |
|---|
| 1655 | |
|---|
| 1656 | !~~~> compute the error estimation |
|---|
| 1657 | !slim: CALL wscal(n, zero, yerr, 1) |
|---|
| 1658 | yerr(1:n) = zero |
|---|
| 1659 | DO j=1, ros_s |
|---|
| 1660 | CALL waxpy(n, ros_e(j), k(n* (j- 1) + 1), 1, yerr, 1) |
|---|
| 1661 | ENDDO |
|---|
| 1662 | err = ros_errornorm(y, ynew, yerr, abstol, reltol, vectortol) |
|---|
| 1663 | |
|---|
| 1664 | !~~~> new step size is bounded by facmin <= hnew/h <= facmax |
|---|
| 1665 | fac = min(facmax, max(facmin, facsafe/err** (one/ros_elo))) |
|---|
| 1666 | hnew = h* fac |
|---|
| 1667 | |
|---|
| 1668 | !~~~> check the error magnitude and adjust step size |
|---|
| 1669 | istatus(nstp) = istatus(nstp) + 1 |
|---|
| 1670 | IF ((err <= one).or.(h <= hmin))THEN !~~~> accept step |
|---|
| 1671 | istatus(nacc) = istatus(nacc) + 1 |
|---|
| 1672 | !slim: CALL wcopy(n, ynew, 1, y, 1) |
|---|
| 1673 | y(1:n) = ynew(1:n) |
|---|
| 1674 | t = t + direction* h |
|---|
| 1675 | hnew = max(hmin, min(hnew, hmax)) |
|---|
| 1676 | IF (rejectlasth)THEN ! no step size increase after a rejected step |
|---|
| 1677 | hnew = min(hnew, h) |
|---|
| 1678 | ENDIF |
|---|
| 1679 | rstatus(nhexit) = h |
|---|
| 1680 | rstatus(nhnew) = hnew |
|---|
| 1681 | rstatus(ntexit) = t |
|---|
| 1682 | rejectlasth = .FALSE. |
|---|
| 1683 | rejectmoreh = .FALSE. |
|---|
| 1684 | h = hnew |
|---|
| 1685 | exit untilaccepted ! exit the loop: WHILE step not accepted |
|---|
| 1686 | ELSE !~~~> reject step |
|---|
| 1687 | IF (rejectmoreh)THEN |
|---|
| 1688 | hnew = h* facrej |
|---|
| 1689 | ENDIF |
|---|
| 1690 | rejectmoreh = rejectlasth |
|---|
| 1691 | rejectlasth = .TRUE. |
|---|
| 1692 | h = hnew |
|---|
| 1693 | IF (istatus(nacc)>= 1) istatus(nrej) = istatus(nrej) + 1 |
|---|
| 1694 | ENDIF ! err <= 1 |
|---|
| 1695 | |
|---|
| 1696 | END DO untilaccepted |
|---|
| 1697 | |
|---|
| 1698 | END DO timeloop |
|---|
| 1699 | |
|---|
| 1700 | !~~~> succesful exit |
|---|
| 1701 | ierr = 1 !~~~> the integration was successful |
|---|
| 1702 | |
|---|
| 1703 | END SUBROUTINE ros_integrator |
|---|
| 1704 | |
|---|
| 1705 | |
|---|
| 1706 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1707 | REAL(kind=dp)FUNCTION ros_errornorm(y, ynew, yerr, & |
|---|
| 1708 | abstol, reltol, vectortol) |
|---|
| 1709 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1710 | !~~~> computes the "scaled norm" of the error vector yerr |
|---|
| 1711 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1712 | |
|---|
| 1713 | ! Input arguments |
|---|
| 1714 | REAL(kind=dp), INTENT(IN):: y(n), ynew(n), & |
|---|
| 1715 | yerr(n), abstol(n), reltol(n) |
|---|
| 1716 | LOGICAL, INTENT(IN):: vectortol |
|---|
| 1717 | ! Local variables |
|---|
| 1718 | REAL(kind=dp):: err, scale, ymax |
|---|
| 1719 | INTEGER :: i |
|---|
| 1720 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
|---|
| 1721 | |
|---|
| 1722 | err = zero |
|---|
| 1723 | DO i=1, n |
|---|
| 1724 | ymax = max(abs(y(i)), abs(ynew(i))) |
|---|
| 1725 | IF (vectortol)THEN |
|---|
| 1726 | scale = abstol(i) + reltol(i) * ymax |
|---|
| 1727 | ELSE |
|---|
| 1728 | scale = abstol(1) + reltol(1) * ymax |
|---|
| 1729 | ENDIF |
|---|
| 1730 | err = err+ (yerr(i) /scale) ** 2 |
|---|
| 1731 | ENDDO |
|---|
| 1732 | err = sqrt(err/n) |
|---|
| 1733 | |
|---|
| 1734 | ros_errornorm = max(err, 1.0d-10) |
|---|
| 1735 | |
|---|
| 1736 | END FUNCTION ros_errornorm |
|---|
| 1737 | |
|---|
| 1738 | |
|---|
| 1739 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1740 | SUBROUTINE ros_funtimederivative(t, roundoff, y, & |
|---|
| 1741 | fcn0, dfdt) |
|---|
| 1742 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1743 | !~~~> the time partial derivative of the FUNCTION by finite differences |
|---|
| 1744 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1745 | |
|---|
| 1746 | !~~~> input arguments |
|---|
| 1747 | REAL(kind=dp), INTENT(IN):: t, roundoff, y(n), fcn0(n) |
|---|
| 1748 | !~~~> output arguments |
|---|
| 1749 | REAL(kind=dp), INTENT(OUT):: dfdt(n) |
|---|
| 1750 | !~~~> local variables |
|---|
| 1751 | REAL(kind=dp):: delta |
|---|
| 1752 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, deltamin = 1.0e-6_dp |
|---|
| 1753 | |
|---|
| 1754 | delta = sqrt(roundoff) * max(deltamin, abs(t)) |
|---|
| 1755 | CALL funtemplate(t+ delta, y, dfdt) |
|---|
| 1756 | istatus(nfun) = istatus(nfun) + 1 |
|---|
| 1757 | CALL waxpy(n, (- one), fcn0, 1, dfdt, 1) |
|---|
| 1758 | CALL wscal(n, (one/delta), dfdt, 1) |
|---|
| 1759 | |
|---|
| 1760 | END SUBROUTINE ros_funtimederivative |
|---|
| 1761 | |
|---|
| 1762 | |
|---|
| 1763 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1764 | SUBROUTINE ros_preparematrix(h, direction, gam, & |
|---|
| 1765 | jac0, ghimj, pivot, singular) |
|---|
| 1766 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
|---|
| 1767 | ! Prepares the LHS matrix for stage calculations |
|---|
| 1768 | ! 1. Construct Ghimj = 1/(H*ham) - Jac0 |
|---|
| 1769 | ! "(Gamma H) Inverse Minus Jacobian" |
|---|
| 1770 | ! 2. Repeat LU decomposition of Ghimj until successful. |
|---|
| 1771 | ! -half the step size if LU decomposition fails and retry |
|---|
| 1772 | ! -exit after 5 consecutive fails |
|---|
| 1773 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
|---|
| 1774 | |
|---|
| 1775 | !~~~> input arguments |
|---|
| 1776 | #ifdef full_algebra |
|---|
| 1777 | REAL(kind=dp), INTENT(IN):: jac0(n, n) |
|---|
| 1778 | #else |
|---|
| 1779 | REAL(kind=dp), INTENT(IN):: jac0(lu_nonzero) |
|---|
| 1780 | #endif |
|---|
| 1781 | REAL(kind=dp), INTENT(IN):: gam |
|---|
| 1782 | INTEGER, INTENT(IN):: direction |
|---|
| 1783 | !~~~> output arguments |
|---|
| 1784 | #ifdef full_algebra |
|---|
| 1785 | REAL(kind=dp), INTENT(OUT):: ghimj(n, n) |
|---|
| 1786 | #else |
|---|
| 1787 | REAL(kind=dp), INTENT(OUT):: ghimj(lu_nonzero) |
|---|
| 1788 | #endif |
|---|
| 1789 | LOGICAL, INTENT(OUT):: singular |
|---|
| 1790 | INTEGER, INTENT(OUT):: pivot(n) |
|---|
| 1791 | !~~~> inout arguments |
|---|
| 1792 | REAL(kind=dp), INTENT(INOUT):: h ! step size is decreased when lu fails |
|---|
| 1793 | !~~~> local variables |
|---|
| 1794 | INTEGER :: i, ising, nconsecutive |
|---|
| 1795 | REAL(kind=dp):: ghinv |
|---|
| 1796 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, half = 0.5_dp |
|---|
| 1797 | |
|---|
| 1798 | nconsecutive = 0 |
|---|
| 1799 | singular = .TRUE. |
|---|
| 1800 | |
|---|
| 1801 | DO WHILE (singular) |
|---|
| 1802 | |
|---|
| 1803 | !~~~> construct ghimj = 1/(h* gam) - jac0 |
|---|
| 1804 | #ifdef full_algebra |
|---|
| 1805 | !slim: CALL wcopy(n* n, jac0, 1, ghimj, 1) |
|---|
| 1806 | !slim: CALL wscal(n* n, (- one), ghimj, 1) |
|---|
| 1807 | ghimj = - jac0 |
|---|
| 1808 | ghinv = one/(direction* h* gam) |
|---|
| 1809 | DO i=1, n |
|---|
| 1810 | ghimj(i, i) = ghimj(i, i) + ghinv |
|---|
| 1811 | ENDDO |
|---|
| 1812 | #else |
|---|
| 1813 | !slim: CALL wcopy(lu_nonzero, jac0, 1, ghimj, 1) |
|---|
| 1814 | !slim: CALL wscal(lu_nonzero, (- one), ghimj, 1) |
|---|
| 1815 | ghimj(1:lu_nonzero) = - jac0(1:lu_nonzero) |
|---|
| 1816 | ghinv = one/(direction* h* gam) |
|---|
| 1817 | DO i=1, n |
|---|
| 1818 | ghimj(lu_diag(i)) = ghimj(lu_diag(i)) + ghinv |
|---|
| 1819 | ENDDO |
|---|
| 1820 | #endif |
|---|
| 1821 | !~~~> compute lu decomposition |
|---|
| 1822 | CALL ros_decomp( ghimj, pivot, ising) |
|---|
| 1823 | IF (ising == 0)THEN |
|---|
| 1824 | !~~~> IF successful done |
|---|
| 1825 | singular = .FALSE. |
|---|
| 1826 | ELSE ! ising .ne. 0 |
|---|
| 1827 | !~~~> IF unsuccessful half the step size; IF 5 consecutive fails THEN RETURN |
|---|
| 1828 | istatus(nsng) = istatus(nsng) + 1 |
|---|
| 1829 | nconsecutive = nconsecutive+1 |
|---|
| 1830 | singular = .TRUE. |
|---|
| 1831 | PRINT*,'Warning: LU Decomposition returned ISING = ',ISING |
|---|
| 1832 | IF (nconsecutive <= 5)THEN ! less than 5 consecutive failed decompositions |
|---|
| 1833 | h = h* half |
|---|
| 1834 | ELSE ! more than 5 consecutive failed decompositions |
|---|
| 1835 | RETURN |
|---|
| 1836 | ENDIF ! nconsecutive |
|---|
| 1837 | ENDIF ! ising |
|---|
| 1838 | |
|---|
| 1839 | END DO ! WHILE singular |
|---|
| 1840 | |
|---|
| 1841 | END SUBROUTINE ros_preparematrix |
|---|
| 1842 | |
|---|
| 1843 | |
|---|
| 1844 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1845 | SUBROUTINE ros_decomp( a, pivot, ising) |
|---|
| 1846 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1847 | ! Template for the LU decomposition |
|---|
| 1848 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1849 | !~~~> inout variables |
|---|
| 1850 | #ifdef full_algebra |
|---|
| 1851 | REAL(kind=dp), INTENT(INOUT):: a(n, n) |
|---|
| 1852 | #else |
|---|
| 1853 | REAL(kind=dp), INTENT(INOUT):: a(lu_nonzero) |
|---|
| 1854 | #endif |
|---|
| 1855 | !~~~> output variables |
|---|
| 1856 | INTEGER, INTENT(OUT):: pivot(n), ising |
|---|
| 1857 | |
|---|
| 1858 | #ifdef full_algebra |
|---|
| 1859 | CALL dgetrf( n, n, a, n, pivot, ising) |
|---|
| 1860 | #else |
|---|
| 1861 | CALL kppdecomp(a, ising) |
|---|
| 1862 | pivot(1) = 1 |
|---|
| 1863 | #endif |
|---|
| 1864 | istatus(ndec) = istatus(ndec) + 1 |
|---|
| 1865 | |
|---|
| 1866 | END SUBROUTINE ros_decomp |
|---|
| 1867 | |
|---|
| 1868 | |
|---|
| 1869 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1870 | SUBROUTINE ros_solve( a, pivot, b) |
|---|
| 1871 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1872 | ! Template for the forward/backward substitution (using pre-computed LU decomposition) |
|---|
| 1873 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1874 | !~~~> input variables |
|---|
| 1875 | #ifdef full_algebra |
|---|
| 1876 | REAL(kind=dp), INTENT(IN):: a(n, n) |
|---|
| 1877 | INTEGER :: ising |
|---|
| 1878 | #else |
|---|
| 1879 | REAL(kind=dp), INTENT(IN):: a(lu_nonzero) |
|---|
| 1880 | #endif |
|---|
| 1881 | INTEGER, INTENT(IN):: pivot(n) |
|---|
| 1882 | !~~~> inout variables |
|---|
| 1883 | REAL(kind=dp), INTENT(INOUT):: b(n) |
|---|
| 1884 | |
|---|
| 1885 | #ifdef full_algebra |
|---|
| 1886 | CALL DGETRS( 'N',N ,1,A,N,Pivot,b,N,ISING) |
|---|
| 1887 | IF (info < 0)THEN |
|---|
| 1888 | print* , "error in dgetrs. ising=", ising |
|---|
| 1889 | ENDIF |
|---|
| 1890 | #else |
|---|
| 1891 | CALL kppsolve( a, b) |
|---|
| 1892 | #endif |
|---|
| 1893 | |
|---|
| 1894 | istatus(nsol) = istatus(nsol) + 1 |
|---|
| 1895 | |
|---|
| 1896 | END SUBROUTINE ros_solve |
|---|
| 1897 | |
|---|
| 1898 | |
|---|
| 1899 | |
|---|
| 1900 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1901 | SUBROUTINE ros2 |
|---|
| 1902 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1903 | ! --- AN L-STABLE METHOD,2 stages,order 2 |
|---|
| 1904 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1905 | |
|---|
| 1906 | double precision g |
|---|
| 1907 | |
|---|
| 1908 | g = 1.0_dp + 1.0_dp/sqrt(2.0_dp) |
|---|
| 1909 | rosmethod = rs2 |
|---|
| 1910 | !~~~> name of the method |
|---|
| 1911 | ros_Name = 'ROS-2' |
|---|
| 1912 | !~~~> number of stages |
|---|
| 1913 | ros_s = 2 |
|---|
| 1914 | |
|---|
| 1915 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 1916 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 1917 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 1918 | ! The general mapping formula is: |
|---|
| 1919 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 1920 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 1921 | |
|---|
| 1922 | ros_a(1) = (1.0_dp) /g |
|---|
| 1923 | ros_c(1) = (- 2.0_dp) /g |
|---|
| 1924 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 1925 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 1926 | ros_newf(1) = .TRUE. |
|---|
| 1927 | ros_newf(2) = .TRUE. |
|---|
| 1928 | !~~~> m_i = coefficients for new step solution |
|---|
| 1929 | ros_m(1) = (3.0_dp) /(2.0_dp* g) |
|---|
| 1930 | ros_m(2) = (1.0_dp) /(2.0_dp* g) |
|---|
| 1931 | ! E_i = Coefficients for error estimator |
|---|
| 1932 | ros_e(1) = 1.0_dp/(2.0_dp* g) |
|---|
| 1933 | ros_e(2) = 1.0_dp/(2.0_dp* g) |
|---|
| 1934 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 1935 | ! main and the embedded scheme orders plus one |
|---|
| 1936 | ros_elo = 2.0_dp |
|---|
| 1937 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
|---|
| 1938 | ros_alpha(1) = 0.0_dp |
|---|
| 1939 | ros_alpha(2) = 1.0_dp |
|---|
| 1940 | !~~~> gamma_i = \sum_j gamma_{i, j} |
|---|
| 1941 | ros_gamma(1) = g |
|---|
| 1942 | ros_gamma(2) = -g |
|---|
| 1943 | |
|---|
| 1944 | END SUBROUTINE ros2 |
|---|
| 1945 | |
|---|
| 1946 | |
|---|
| 1947 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1948 | SUBROUTINE ros3 |
|---|
| 1949 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1950 | ! --- AN L-STABLE METHOD,3 stages,order 3,2 function evaluations |
|---|
| 1951 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 1952 | |
|---|
| 1953 | rosmethod = rs3 |
|---|
| 1954 | !~~~> name of the method |
|---|
| 1955 | ros_Name = 'ROS-3' |
|---|
| 1956 | !~~~> number of stages |
|---|
| 1957 | ros_s = 3 |
|---|
| 1958 | |
|---|
| 1959 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 1960 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 1961 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 1962 | ! The general mapping formula is: |
|---|
| 1963 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 1964 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 1965 | |
|---|
| 1966 | ros_a(1) = 1.0_dp |
|---|
| 1967 | ros_a(2) = 1.0_dp |
|---|
| 1968 | ros_a(3) = 0.0_dp |
|---|
| 1969 | |
|---|
| 1970 | ros_c(1) = - 0.10156171083877702091975600115545e+01_dp |
|---|
| 1971 | ros_c(2) = 0.40759956452537699824805835358067e+01_dp |
|---|
| 1972 | ros_c(3) = 0.92076794298330791242156818474003e+01_dp |
|---|
| 1973 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 1974 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 1975 | ros_newf(1) = .TRUE. |
|---|
| 1976 | ros_newf(2) = .TRUE. |
|---|
| 1977 | ros_newf(3) = .FALSE. |
|---|
| 1978 | !~~~> m_i = coefficients for new step solution |
|---|
| 1979 | ros_m(1) = 0.1e+01_dp |
|---|
| 1980 | ros_m(2) = 0.61697947043828245592553615689730e+01_dp |
|---|
| 1981 | ros_m(3) = - 0.42772256543218573326238373806514_dp |
|---|
| 1982 | ! E_i = Coefficients for error estimator |
|---|
| 1983 | ros_e(1) = 0.5_dp |
|---|
| 1984 | ros_e(2) = - 0.29079558716805469821718236208017e+01_dp |
|---|
| 1985 | ros_e(3) = 0.22354069897811569627360909276199_dp |
|---|
| 1986 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 1987 | ! main and the embedded scheme orders plus 1 |
|---|
| 1988 | ros_elo = 3.0_dp |
|---|
| 1989 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
|---|
| 1990 | ros_alpha(1) = 0.0_dp |
|---|
| 1991 | ros_alpha(2) = 0.43586652150845899941601945119356_dp |
|---|
| 1992 | ros_alpha(3) = 0.43586652150845899941601945119356_dp |
|---|
| 1993 | !~~~> gamma_i = \sum_j gamma_{i, j} |
|---|
| 1994 | ros_gamma(1) = 0.43586652150845899941601945119356_dp |
|---|
| 1995 | ros_gamma(2) = 0.24291996454816804366592249683314_dp |
|---|
| 1996 | ros_gamma(3) = 0.21851380027664058511513169485832e+01_dp |
|---|
| 1997 | |
|---|
| 1998 | END SUBROUTINE ros3 |
|---|
| 1999 | |
|---|
| 2000 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2001 | |
|---|
| 2002 | |
|---|
| 2003 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2004 | SUBROUTINE ros4 |
|---|
| 2005 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2006 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 4 STAGES |
|---|
| 2007 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
|---|
| 2008 | ! |
|---|
| 2009 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
|---|
| 2010 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
|---|
| 2011 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
|---|
| 2012 | ! SPRINGER-VERLAG (1990) |
|---|
| 2013 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2014 | |
|---|
| 2015 | |
|---|
| 2016 | rosmethod = rs4 |
|---|
| 2017 | !~~~> name of the method |
|---|
| 2018 | ros_Name = 'ROS-4' |
|---|
| 2019 | !~~~> number of stages |
|---|
| 2020 | ros_s = 4 |
|---|
| 2021 | |
|---|
| 2022 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 2023 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 2024 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 2025 | ! The general mapping formula is: |
|---|
| 2026 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2027 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2028 | |
|---|
| 2029 | ros_a(1) = 0.2000000000000000e+01_dp |
|---|
| 2030 | ros_a(2) = 0.1867943637803922e+01_dp |
|---|
| 2031 | ros_a(3) = 0.2344449711399156_dp |
|---|
| 2032 | ros_a(4) = ros_a(2) |
|---|
| 2033 | ros_a(5) = ros_a(3) |
|---|
| 2034 | ros_a(6) = 0.0_dp |
|---|
| 2035 | |
|---|
| 2036 | ros_c(1) = -0.7137615036412310e+01_dp |
|---|
| 2037 | ros_c(2) = 0.2580708087951457e+01_dp |
|---|
| 2038 | ros_c(3) = 0.6515950076447975_dp |
|---|
| 2039 | ros_c(4) = -0.2137148994382534e+01_dp |
|---|
| 2040 | ros_c(5) = -0.3214669691237626_dp |
|---|
| 2041 | ros_c(6) = -0.6949742501781779_dp |
|---|
| 2042 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2043 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2044 | ros_newf(1) = .TRUE. |
|---|
| 2045 | ros_newf(2) = .TRUE. |
|---|
| 2046 | ros_newf(3) = .TRUE. |
|---|
| 2047 | ros_newf(4) = .FALSE. |
|---|
| 2048 | !~~~> m_i = coefficients for new step solution |
|---|
| 2049 | ros_m(1) = 0.2255570073418735e+01_dp |
|---|
| 2050 | ros_m(2) = 0.2870493262186792_dp |
|---|
| 2051 | ros_m(3) = 0.4353179431840180_dp |
|---|
| 2052 | ros_m(4) = 0.1093502252409163e+01_dp |
|---|
| 2053 | !~~~> e_i = coefficients for error estimator |
|---|
| 2054 | ros_e(1) = -0.2815431932141155_dp |
|---|
| 2055 | ros_e(2) = -0.7276199124938920e-01_dp |
|---|
| 2056 | ros_e(3) = -0.1082196201495311_dp |
|---|
| 2057 | ros_e(4) = -0.1093502252409163e+01_dp |
|---|
| 2058 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2059 | ! main and the embedded scheme orders plus 1 |
|---|
| 2060 | ros_elo = 4.0_dp |
|---|
| 2061 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
|---|
| 2062 | ros_alpha(1) = 0.0_dp |
|---|
| 2063 | ros_alpha(2) = 0.1145640000000000e+01_dp |
|---|
| 2064 | ros_alpha(3) = 0.6552168638155900_dp |
|---|
| 2065 | ros_alpha(4) = ros_alpha(3) |
|---|
| 2066 | !~~~> gamma_i = \sum_j gamma_{i, j} |
|---|
| 2067 | ros_gamma(1) = 0.5728200000000000_dp |
|---|
| 2068 | ros_gamma(2) = -0.1769193891319233e+01_dp |
|---|
| 2069 | ros_gamma(3) = 0.7592633437920482_dp |
|---|
| 2070 | ros_gamma(4) = -0.1049021087100450_dp |
|---|
| 2071 | |
|---|
| 2072 | END SUBROUTINE ros4 |
|---|
| 2073 | |
|---|
| 2074 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2075 | SUBROUTINE rodas3 |
|---|
| 2076 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2077 | ! --- A STIFFLY-STABLE METHOD,4 stages,order 3 |
|---|
| 2078 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2079 | |
|---|
| 2080 | |
|---|
| 2081 | rosmethod = rd3 |
|---|
| 2082 | !~~~> name of the method |
|---|
| 2083 | ros_Name = 'RODAS-3' |
|---|
| 2084 | !~~~> number of stages |
|---|
| 2085 | ros_s = 4 |
|---|
| 2086 | |
|---|
| 2087 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 2088 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 2089 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 2090 | ! The general mapping formula is: |
|---|
| 2091 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2092 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2093 | |
|---|
| 2094 | ros_a(1) = 0.0_dp |
|---|
| 2095 | ros_a(2) = 2.0_dp |
|---|
| 2096 | ros_a(3) = 0.0_dp |
|---|
| 2097 | ros_a(4) = 2.0_dp |
|---|
| 2098 | ros_a(5) = 0.0_dp |
|---|
| 2099 | ros_a(6) = 1.0_dp |
|---|
| 2100 | |
|---|
| 2101 | ros_c(1) = 4.0_dp |
|---|
| 2102 | ros_c(2) = 1.0_dp |
|---|
| 2103 | ros_c(3) = -1.0_dp |
|---|
| 2104 | ros_c(4) = 1.0_dp |
|---|
| 2105 | ros_c(5) = -1.0_dp |
|---|
| 2106 | ros_c(6) = -(8.0_dp/3.0_dp) |
|---|
| 2107 | |
|---|
| 2108 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2109 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2110 | ros_newf(1) = .TRUE. |
|---|
| 2111 | ros_newf(2) = .FALSE. |
|---|
| 2112 | ros_newf(3) = .TRUE. |
|---|
| 2113 | ros_newf(4) = .TRUE. |
|---|
| 2114 | !~~~> m_i = coefficients for new step solution |
|---|
| 2115 | ros_m(1) = 2.0_dp |
|---|
| 2116 | ros_m(2) = 0.0_dp |
|---|
| 2117 | ros_m(3) = 1.0_dp |
|---|
| 2118 | ros_m(4) = 1.0_dp |
|---|
| 2119 | !~~~> e_i = coefficients for error estimator |
|---|
| 2120 | ros_e(1) = 0.0_dp |
|---|
| 2121 | ros_e(2) = 0.0_dp |
|---|
| 2122 | ros_e(3) = 0.0_dp |
|---|
| 2123 | ros_e(4) = 1.0_dp |
|---|
| 2124 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2125 | ! main and the embedded scheme orders plus 1 |
|---|
| 2126 | ros_elo = 3.0_dp |
|---|
| 2127 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
|---|
| 2128 | ros_alpha(1) = 0.0_dp |
|---|
| 2129 | ros_alpha(2) = 0.0_dp |
|---|
| 2130 | ros_alpha(3) = 1.0_dp |
|---|
| 2131 | ros_alpha(4) = 1.0_dp |
|---|
| 2132 | !~~~> gamma_i = \sum_j gamma_{i, j} |
|---|
| 2133 | ros_gamma(1) = 0.5_dp |
|---|
| 2134 | ros_gamma(2) = 1.5_dp |
|---|
| 2135 | ros_gamma(3) = 0.0_dp |
|---|
| 2136 | ros_gamma(4) = 0.0_dp |
|---|
| 2137 | |
|---|
| 2138 | END SUBROUTINE rodas3 |
|---|
| 2139 | |
|---|
| 2140 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2141 | SUBROUTINE rodas4 |
|---|
| 2142 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2143 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 6 STAGES |
|---|
| 2144 | ! |
|---|
| 2145 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
|---|
| 2146 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
|---|
| 2147 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
|---|
| 2148 | ! SPRINGER-VERLAG (1996) |
|---|
| 2149 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2150 | |
|---|
| 2151 | |
|---|
| 2152 | rosmethod = rd4 |
|---|
| 2153 | !~~~> name of the method |
|---|
| 2154 | ros_Name = 'RODAS-4' |
|---|
| 2155 | !~~~> number of stages |
|---|
| 2156 | ros_s = 6 |
|---|
| 2157 | |
|---|
| 2158 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
|---|
| 2159 | ros_alpha(1) = 0.000_dp |
|---|
| 2160 | ros_alpha(2) = 0.386_dp |
|---|
| 2161 | ros_alpha(3) = 0.210_dp |
|---|
| 2162 | ros_alpha(4) = 0.630_dp |
|---|
| 2163 | ros_alpha(5) = 1.000_dp |
|---|
| 2164 | ros_alpha(6) = 1.000_dp |
|---|
| 2165 | |
|---|
| 2166 | !~~~> gamma_i = \sum_j gamma_{i, j} |
|---|
| 2167 | ros_gamma(1) = 0.2500000000000000_dp |
|---|
| 2168 | ros_gamma(2) = -0.1043000000000000_dp |
|---|
| 2169 | ros_gamma(3) = 0.1035000000000000_dp |
|---|
| 2170 | ros_gamma(4) = -0.3620000000000023e-01_dp |
|---|
| 2171 | ros_gamma(5) = 0.0_dp |
|---|
| 2172 | ros_gamma(6) = 0.0_dp |
|---|
| 2173 | |
|---|
| 2174 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
|---|
| 2175 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
|---|
| 2176 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
|---|
| 2177 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
|---|
| 2178 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
|---|
| 2179 | |
|---|
| 2180 | ros_a(1) = 0.1544000000000000e+01_dp |
|---|
| 2181 | ros_a(2) = 0.9466785280815826_dp |
|---|
| 2182 | ros_a(3) = 0.2557011698983284_dp |
|---|
| 2183 | ros_a(4) = 0.3314825187068521e+01_dp |
|---|
| 2184 | ros_a(5) = 0.2896124015972201e+01_dp |
|---|
| 2185 | ros_a(6) = 0.9986419139977817_dp |
|---|
| 2186 | ros_a(7) = 0.1221224509226641e+01_dp |
|---|
| 2187 | ros_a(8) = 0.6019134481288629e+01_dp |
|---|
| 2188 | ros_a(9) = 0.1253708332932087e+02_dp |
|---|
| 2189 | ros_a(10) = -0.6878860361058950_dp |
|---|
| 2190 | ros_a(11) = ros_a(7) |
|---|
| 2191 | ros_a(12) = ros_a(8) |
|---|
| 2192 | ros_a(13) = ros_a(9) |
|---|
| 2193 | ros_a(14) = ros_a(10) |
|---|
| 2194 | ros_a(15) = 1.0_dp |
|---|
| 2195 | |
|---|
| 2196 | ros_c(1) = -0.5668800000000000e+01_dp |
|---|
| 2197 | ros_c(2) = -0.2430093356833875e+01_dp |
|---|
| 2198 | ros_c(3) = -0.2063599157091915_dp |
|---|
| 2199 | ros_c(4) = -0.1073529058151375_dp |
|---|
| 2200 | ros_c(5) = -0.9594562251023355e+01_dp |
|---|
| 2201 | ros_c(6) = -0.2047028614809616e+02_dp |
|---|
| 2202 | ros_c(7) = 0.7496443313967647e+01_dp |
|---|
| 2203 | ros_c(8) = -0.1024680431464352e+02_dp |
|---|
| 2204 | ros_c(9) = -0.3399990352819905e+02_dp |
|---|
| 2205 | ros_c(10) = 0.1170890893206160e+02_dp |
|---|
| 2206 | ros_c(11) = 0.8083246795921522e+01_dp |
|---|
| 2207 | ros_c(12) = -0.7981132988064893e+01_dp |
|---|
| 2208 | ros_c(13) = -0.3152159432874371e+02_dp |
|---|
| 2209 | ros_c(14) = 0.1631930543123136e+02_dp |
|---|
| 2210 | ros_c(15) = -0.6058818238834054e+01_dp |
|---|
| 2211 | |
|---|
| 2212 | !~~~> m_i = coefficients for new step solution |
|---|
| 2213 | ros_m(1) = ros_a(7) |
|---|
| 2214 | ros_m(2) = ros_a(8) |
|---|
| 2215 | ros_m(3) = ros_a(9) |
|---|
| 2216 | ros_m(4) = ros_a(10) |
|---|
| 2217 | ros_m(5) = 1.0_dp |
|---|
| 2218 | ros_m(6) = 1.0_dp |
|---|
| 2219 | |
|---|
| 2220 | !~~~> e_i = coefficients for error estimator |
|---|
| 2221 | ros_e(1) = 0.0_dp |
|---|
| 2222 | ros_e(2) = 0.0_dp |
|---|
| 2223 | ros_e(3) = 0.0_dp |
|---|
| 2224 | ros_e(4) = 0.0_dp |
|---|
| 2225 | ros_e(5) = 0.0_dp |
|---|
| 2226 | ros_e(6) = 1.0_dp |
|---|
| 2227 | |
|---|
| 2228 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2229 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2230 | ros_newf(1) = .TRUE. |
|---|
| 2231 | ros_newf(2) = .TRUE. |
|---|
| 2232 | ros_newf(3) = .TRUE. |
|---|
| 2233 | ros_newf(4) = .TRUE. |
|---|
| 2234 | ros_newf(5) = .TRUE. |
|---|
| 2235 | ros_newf(6) = .TRUE. |
|---|
| 2236 | |
|---|
| 2237 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2238 | ! main and the embedded scheme orders plus 1 |
|---|
| 2239 | ros_elo = 4.0_dp |
|---|
| 2240 | |
|---|
| 2241 | END SUBROUTINE rodas4 |
|---|
| 2242 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2243 | SUBROUTINE rang3 |
|---|
| 2244 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2245 | ! STIFFLY-STABLE W METHOD OF ORDER 3,WITH 4 STAGES |
|---|
| 2246 | ! |
|---|
| 2247 | ! J. RANG and L. ANGERMANN |
|---|
| 2248 | ! NEW ROSENBROCK W-METHODS OF ORDER 3 |
|---|
| 2249 | ! FOR PARTIAL DIFFERENTIAL ALGEBRAIC |
|---|
| 2250 | ! EQUATIONS OF INDEX 1 |
|---|
| 2251 | ! BIT Numerical Mathematics (2005) 45: 761-787 |
|---|
| 2252 | ! DOI: 10.1007/s10543-005-0035-y |
|---|
| 2253 | ! Table 4.1-4.2 |
|---|
| 2254 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2255 | |
|---|
| 2256 | |
|---|
| 2257 | rosmethod = rg3 |
|---|
| 2258 | !~~~> name of the method |
|---|
| 2259 | ros_Name = 'RANG-3' |
|---|
| 2260 | !~~~> number of stages |
|---|
| 2261 | ros_s = 4 |
|---|
| 2262 | |
|---|
| 2263 | ros_a(1) = 5.09052051067020d+00; |
|---|
| 2264 | ros_a(2) = 5.09052051067020d+00; |
|---|
| 2265 | ros_a(3) = 0.0d0; |
|---|
| 2266 | ros_a(4) = 4.97628111010787d+00; |
|---|
| 2267 | ros_a(5) = 2.77268164715849d-02; |
|---|
| 2268 | ros_a(6) = 2.29428036027904d-01; |
|---|
| 2269 | |
|---|
| 2270 | ros_c(1) = - 1.16790812312283d+01; |
|---|
| 2271 | ros_c(2) = - 1.64057326467367d+01; |
|---|
| 2272 | ros_c(3) = - 2.77268164715850d-01; |
|---|
| 2273 | ros_c(4) = - 8.38103960500476d+00; |
|---|
| 2274 | ros_c(5) = - 8.48328409199343d-01; |
|---|
| 2275 | ros_c(6) = 2.87009860433106d-01; |
|---|
| 2276 | |
|---|
| 2277 | ros_m(1) = 5.22582761233094d+00; |
|---|
| 2278 | ros_m(2) = - 5.56971148154165d-01; |
|---|
| 2279 | ros_m(3) = 3.57979469353645d-01; |
|---|
| 2280 | ros_m(4) = 1.72337398521064d+00; |
|---|
| 2281 | |
|---|
| 2282 | ros_e(1) = - 5.16845212784040d+00; |
|---|
| 2283 | ros_e(2) = - 1.26351942603842d+00; |
|---|
| 2284 | ros_e(3) = - 1.11022302462516d-16; |
|---|
| 2285 | ros_e(4) = 2.22044604925031d-16; |
|---|
| 2286 | |
|---|
| 2287 | ros_alpha(1) = 0.0d00; |
|---|
| 2288 | ros_alpha(2) = 2.21878746765329d+00; |
|---|
| 2289 | ros_alpha(3) = 2.21878746765329d+00; |
|---|
| 2290 | ros_alpha(4) = 1.55392337535788d+00; |
|---|
| 2291 | |
|---|
| 2292 | ros_gamma(1) = 4.35866521508459d-01; |
|---|
| 2293 | ros_gamma(2) = - 1.78292094614483d+00; |
|---|
| 2294 | ros_gamma(3) = - 2.46541900496934d+00; |
|---|
| 2295 | ros_gamma(4) = - 8.05529997906370d-01; |
|---|
| 2296 | |
|---|
| 2297 | |
|---|
| 2298 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
|---|
| 2299 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
|---|
| 2300 | ros_newf(1) = .TRUE. |
|---|
| 2301 | ros_newf(2) = .TRUE. |
|---|
| 2302 | ros_newf(3) = .TRUE. |
|---|
| 2303 | ros_newf(4) = .TRUE. |
|---|
| 2304 | |
|---|
| 2305 | !~~~> ros_elo = estimator of local order - the minimum between the |
|---|
| 2306 | ! main and the embedded scheme orders plus 1 |
|---|
| 2307 | ros_elo = 3.0_dp |
|---|
| 2308 | |
|---|
| 2309 | END SUBROUTINE rang3 |
|---|
| 2310 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2311 | |
|---|
| 2312 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2313 | ! End of the set of internal Rosenbrock subroutines |
|---|
| 2314 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2315 | END SUBROUTINE rosenbrock |
|---|
| 2316 | |
|---|
| 2317 | SUBROUTINE funtemplate( t, y, ydot) |
|---|
| 2318 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2319 | ! Template for the ODE function call. |
|---|
| 2320 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
|---|
| 2321 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2322 | !~~~> input variables |
|---|
| 2323 | REAL(kind=dp):: t, y(nvar) |
|---|
| 2324 | !~~~> output variables |
|---|
| 2325 | REAL(kind=dp):: ydot(nvar) |
|---|
| 2326 | !~~~> local variables |
|---|
| 2327 | REAL(kind=dp):: told |
|---|
| 2328 | |
|---|
| 2329 | told = time |
|---|
| 2330 | time = t |
|---|
| 2331 | CALL fun( y, fix, rconst, ydot) |
|---|
| 2332 | time = told |
|---|
| 2333 | |
|---|
| 2334 | END SUBROUTINE funtemplate |
|---|
| 2335 | |
|---|
| 2336 | SUBROUTINE jactemplate( t, y, jcb) |
|---|
| 2337 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2338 | ! Template for the ODE Jacobian call. |
|---|
| 2339 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
|---|
| 2340 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2341 | !~~~> input variables |
|---|
| 2342 | REAL(kind=dp):: t, y(nvar) |
|---|
| 2343 | !~~~> output variables |
|---|
| 2344 | #ifdef full_algebra |
|---|
| 2345 | REAL(kind=dp):: jv(lu_nonzero), jcb(nvar, nvar) |
|---|
| 2346 | #else |
|---|
| 2347 | REAL(kind=dp):: jcb(lu_nonzero) |
|---|
| 2348 | #endif |
|---|
| 2349 | !~~~> local variables |
|---|
| 2350 | REAL(kind=dp):: told |
|---|
| 2351 | #ifdef full_algebra |
|---|
| 2352 | INTEGER :: i, j |
|---|
| 2353 | #endif |
|---|
| 2354 | |
|---|
| 2355 | told = time |
|---|
| 2356 | time = t |
|---|
| 2357 | #ifdef full_algebra |
|---|
| 2358 | CALL jac_sp(y, fix, rconst, jv) |
|---|
| 2359 | DO j=1, nvar |
|---|
| 2360 | DO i=1, nvar |
|---|
| 2361 | jcb(i, j) = 0.0_dp |
|---|
| 2362 | ENDDO |
|---|
| 2363 | ENDDO |
|---|
| 2364 | DO i=1, lu_nonzero |
|---|
| 2365 | jcb(lu_irow(i), lu_icol(i)) = jv(i) |
|---|
| 2366 | ENDDO |
|---|
| 2367 | #else |
|---|
| 2368 | CALL jac_sp( y, fix, rconst, jcb) |
|---|
| 2369 | #endif |
|---|
| 2370 | time = told |
|---|
| 2371 | |
|---|
| 2372 | END SUBROUTINE jactemplate |
|---|
| 2373 | |
|---|
| 2374 | SUBROUTINE kppdecomp( jvs, ier) |
|---|
| 2375 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2376 | ! sparse lu factorization |
|---|
| 2377 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 2378 | ! loop expansion generated by kp4 |
|---|
| 2379 | |
|---|
| 2380 | INTEGER :: ier |
|---|
| 2381 | REAL(kind=dp):: jvs(lu_nonzero), w(nvar), a |
|---|
| 2382 | INTEGER :: k, kk, j, jj |
|---|
| 2383 | |
|---|
| 2384 | a = 0. |
|---|
| 2385 | ier = 0 |
|---|
| 2386 | |
|---|
| 2387 | ! i = 1 |
|---|
| 2388 | ! i = 2 |
|---|
| 2389 | ! i = 3 |
|---|
| 2390 | ! i = 4 |
|---|
| 2391 | ! i = 5 |
|---|
| 2392 | ! i = 6 |
|---|
| 2393 | ! i = 7 |
|---|
| 2394 | jvs(16) = (jvs(16)) / jvs(8) |
|---|
| 2395 | jvs(17) = (jvs(17)) / jvs(10) |
|---|
| 2396 | jvs(18) = (jvs(18)) / jvs(13) |
|---|
| 2397 | jvs(19) = jvs(19) - jvs(9) * jvs(16) |
|---|
| 2398 | jvs(20) = jvs(20) - jvs(11) * jvs(17) |
|---|
| 2399 | jvs(21) = jvs(21) - jvs(12) * jvs(17) - jvs(14) * jvs(18) |
|---|
| 2400 | jvs(22) = jvs(22) - jvs(15) * jvs(18) |
|---|
| 2401 | ! i = 8 |
|---|
| 2402 | jvs(23) = (jvs(23)) / jvs(8) |
|---|
| 2403 | a = 0.0; a = a - jvs(9) * jvs(23) |
|---|
| 2404 | jvs(24) = (jvs(24) + a) / jvs(19) |
|---|
| 2405 | jvs(25) = jvs(25) - jvs(20) * jvs(24) |
|---|
| 2406 | jvs(26) = jvs(26) - jvs(21) * jvs(24) |
|---|
| 2407 | jvs(27) = jvs(27) - jvs(22) * jvs(24) |
|---|
| 2408 | ! i = 9 |
|---|
| 2409 | jvs(28) = (jvs(28)) / jvs(10) |
|---|
| 2410 | jvs(29) = (jvs(29)) / jvs(13) |
|---|
| 2411 | a = 0.0; a = a - jvs(11) * jvs(28) |
|---|
| 2412 | jvs(30) = (jvs(30) + a) / jvs(25) |
|---|
| 2413 | jvs(31) = jvs(31) - jvs(12) * jvs(28) - jvs(14) * jvs(29) - jvs(26) * jvs(30) |
|---|
| 2414 | jvs(32) = jvs(32) - jvs(15) * jvs(29) - jvs(27) * jvs(30) |
|---|
| 2415 | ! i = 10 |
|---|
| 2416 | jvs(33) = (jvs(33)) / jvs(10) |
|---|
| 2417 | jvs(34) = (jvs(34)) / jvs(13) |
|---|
| 2418 | jvs(35) = (jvs(35)) / jvs(19) |
|---|
| 2419 | a = 0.0; a = a - jvs(11) * jvs(33) - jvs(20) * jvs(35) |
|---|
| 2420 | jvs(36) = (jvs(36) + a) / jvs(25) |
|---|
| 2421 | a = 0.0; a = a - jvs(12) * jvs(33) - jvs(14) * jvs(34) - jvs(21) * jvs(35) - jvs(26) * jvs(36) |
|---|
| 2422 | jvs(37) = (jvs(37) + a) / jvs(31) |
|---|
| 2423 | jvs(38) = jvs(38) - jvs(15) * jvs(34) - jvs(22) * jvs(35) - jvs(27) * jvs(36) - jvs(32) * jvs(37) |
|---|
| 2424 | RETURN |
|---|
| 2425 | |
|---|
| 2426 | END SUBROUTINE kppdecomp |
|---|
| 2427 | |
|---|
| 2428 | SUBROUTINE chem_gasphase_integrate (time_step_len, conc, tempi, qvapi, fakti, photo, ierrf, xnacc, xnrej, istatus, l_debug, pe, & |
|---|
| 2429 | icntrl_i, rcntrl_i) |
|---|
| 2430 | |
|---|
| 2431 | IMPLICIT NONE |
|---|
| 2432 | |
|---|
| 2433 | REAL(dp), INTENT(IN) :: time_step_len |
|---|
| 2434 | REAL(dp), DIMENSION(:, :), INTENT(INOUT) :: conc |
|---|
| 2435 | REAL(dp), DIMENSION(:, :), INTENT(IN) :: photo |
|---|
| 2436 | REAL(dp), DIMENSION(:), INTENT(IN) :: tempi |
|---|
| 2437 | REAL(dp), DIMENSION(:), INTENT(IN) :: qvapi |
|---|
| 2438 | REAL(dp), DIMENSION(:), INTENT(IN) :: fakti |
|---|
| 2439 | INTEGER, INTENT(OUT), OPTIONAL :: ierrf(:) |
|---|
| 2440 | INTEGER, INTENT(OUT), OPTIONAL :: xnacc(:) |
|---|
| 2441 | INTEGER, INTENT(OUT), OPTIONAL :: xnrej(:) |
|---|
| 2442 | INTEGER, INTENT(INOUT), OPTIONAL :: istatus(:) |
|---|
| 2443 | INTEGER, INTENT(IN), OPTIONAL :: pe |
|---|
| 2444 | LOGICAL, INTENT(IN), OPTIONAL :: l_debug |
|---|
| 2445 | INTEGER, DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: icntrl_i |
|---|
| 2446 | REAL(dp), DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: rcntrl_i |
|---|
| 2447 | |
|---|
| 2448 | INTEGER :: k ! loop variable |
|---|
| 2449 | REAL(dp) :: dt |
|---|
| 2450 | INTEGER, DIMENSION(20) :: istatus_u |
|---|
| 2451 | INTEGER :: ierr_u |
|---|
| 2452 | INTEGER :: istatf |
|---|
| 2453 | INTEGER :: vl_dim_lo |
|---|
| 2454 | |
|---|
| 2455 | |
|---|
| 2456 | IF (PRESENT (istatus)) istatus = 0 |
|---|
| 2457 | IF (PRESENT (icntrl_i)) icntrl = icntrl_i |
|---|
| 2458 | IF (PRESENT (rcntrl_i)) rcntrl = rcntrl_i |
|---|
| 2459 | |
|---|
| 2460 | vl_glo = size(tempi, 1) |
|---|
| 2461 | |
|---|
| 2462 | vl_dim_lo = vl_dim |
|---|
| 2463 | DO k=1, vl_glo, vl_dim_lo |
|---|
| 2464 | is = k |
|---|
| 2465 | ie = min(k+ vl_dim_lo-1, vl_glo) |
|---|
| 2466 | vl = ie-is+ 1 |
|---|
| 2467 | |
|---|
| 2468 | c(:) = conc(is, :) |
|---|
| 2469 | |
|---|
| 2470 | temp = tempi(is) |
|---|
| 2471 | |
|---|
| 2472 | qvap = qvapi(is) |
|---|
| 2473 | |
|---|
| 2474 | fakt = fakti(is) |
|---|
| 2475 | |
|---|
| 2476 | CALL initialize |
|---|
| 2477 | |
|---|
| 2478 | phot(:) = photo(is, :) |
|---|
| 2479 | |
|---|
| 2480 | CALL update_rconst |
|---|
| 2481 | |
|---|
| 2482 | dt = time_step_len |
|---|
| 2483 | |
|---|
| 2484 | ! integrate from t=0 to t=dt |
|---|
| 2485 | CALL integrate(0._dp, dt, icntrl, rcntrl, istatus_u = istatus_u, ierr_u=ierr_u) |
|---|
| 2486 | |
|---|
| 2487 | |
|---|
| 2488 | IF (PRESENT(l_debug) .AND. PRESENT(pe)) THEN |
|---|
| 2489 | IF (l_debug) CALL error_output(conc(is, :), ierr_u, pe) |
|---|
| 2490 | ENDIF |
|---|
| 2491 | |
|---|
| 2492 | conc(is, :) = c(:) |
|---|
| 2493 | |
|---|
| 2494 | ! RETURN diagnostic information |
|---|
| 2495 | |
|---|
| 2496 | IF (PRESENT(ierrf)) ierrf(is) = ierr_u |
|---|
| 2497 | IF (PRESENT(xnacc)) xnacc(is) = istatus_u(4) |
|---|
| 2498 | IF (PRESENT(xnrej)) xnrej(is) = istatus_u(5) |
|---|
| 2499 | |
|---|
| 2500 | IF (PRESENT (istatus)) THEN |
|---|
| 2501 | istatus(1:8) = istatus(1:8) + istatus_u(1:8) |
|---|
| 2502 | ENDIF |
|---|
| 2503 | |
|---|
| 2504 | END DO |
|---|
| 2505 | |
|---|
| 2506 | |
|---|
| 2507 | ! Deallocate input arrays |
|---|
| 2508 | |
|---|
| 2509 | |
|---|
| 2510 | data_loaded = .FALSE. |
|---|
| 2511 | |
|---|
| 2512 | RETURN |
|---|
| 2513 | END SUBROUTINE chem_gasphase_integrate |
|---|
| 2514 | |
|---|
| 2515 | END MODULE chem_gasphase_mod |
|---|
| 2516 | |
|---|
