[2931] | 1 | MODULE chem_gasphase_mod |
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[3228] | 2 | |
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[3280] | 3 | ! Mechanism: phstat |
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| 4 | ! |
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[2931] | 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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[3228] | 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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[2931] | 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 | ! |
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| 49 | ! |
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| 50 | ! Former revisions: |
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| 51 | ! ----------------- |
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| 52 | ! $Id: module_header 2460 2017-09-13 14:47:48Z forkel $ |
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[3487] | 53 | ! forkel June 2018: qvap,fakt added |
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| 54 | ! forkel June 2018: reset case in Initialize,Integrate,Update_rconst |
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| 55 | ! |
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| 56 | ! |
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| 57 | ! 2460 2017-09-13 14:47:48Z forkel |
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[2931] | 58 | ! |
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[3228] | 59 | ! forkel Sept. 2017: Variables for photolyis added |
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[2931] | 60 | ! |
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| 61 | ! |
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| 62 | ! Nov. 2016: Intial version (Klaus Ketelsen) |
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| 63 | ! |
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| 64 | !------------------------------------------------------------------------------! |
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| 65 | ! |
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| 66 | |
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| 67 | |
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| 68 | ! Set kpp Double Precision to PALM Default Precision |
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| 69 | |
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| 70 | USE kinds, ONLY: dp=>wp |
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| 71 | |
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[3228] | 72 | USE pegrid, ONLY: myid, threads_per_task |
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[2931] | 73 | |
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| 74 | IMPLICIT NONE |
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| 75 | PRIVATE |
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[3228] | 76 | !SAVE ! note: occurs again in automatically generated code ... |
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[2931] | 77 | |
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| 78 | ! PUBLIC :: IERR_NAMES |
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| 79 | |
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| 80 | ! PUBLIC :: SPC_NAMES,EQN_NAMES,EQN_TAGS,REQ_HET,REQ_AEROSOL,REQ_PHOTRAT & |
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| 81 | ! ,REQ_MCFCT,IP_MAX,jname |
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| 82 | |
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[3228] | 83 | PUBLIC :: eqn_names, phot_names, spc_names |
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[2931] | 84 | PUBLIC :: nmaxfixsteps |
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[3228] | 85 | PUBLIC :: atol, rtol |
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| 86 | PUBLIC :: nspec, nreact |
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[2931] | 87 | PUBLIC :: temp |
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[3228] | 88 | PUBLIC :: qvap |
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| 89 | PUBLIC :: fakt |
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[2931] | 90 | PUBLIC :: phot |
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| 91 | PUBLIC :: rconst |
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| 92 | PUBLIC :: nvar |
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| 93 | PUBLIC :: nphot |
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[3263] | 94 | PUBLIC :: vl_dim ! PUBLIC to ebable other MODULEs to distiguish between scalar and vec |
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[2931] | 95 | |
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[3228] | 96 | PUBLIC :: initialize, integrate, update_rconst |
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[2931] | 97 | PUBLIC :: chem_gasphase_integrate |
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| 98 | PUBLIC :: initialize_kpp_ctrl |
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| 99 | |
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| 100 | ! END OF MODULE HEADER TEMPLATE |
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| 101 | |
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| 102 | ! Variables used for vector mode |
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| 103 | |
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[3249] | 104 | LOGICAL, PARAMETER :: l_vector = .FALSE. |
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| 105 | INTEGER, PARAMETER :: i_lu_di = 2 |
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| 106 | INTEGER, PARAMETER :: vl_dim = 1 |
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[2931] | 107 | INTEGER :: vl |
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| 108 | |
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| 109 | INTEGER :: vl_glo |
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[3228] | 110 | INTEGER :: is, ie |
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[2931] | 111 | |
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[3228] | 112 | |
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| 113 | INTEGER, DIMENSION(vl_dim) :: kacc, krej |
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[2931] | 114 | INTEGER, DIMENSION(vl_dim) :: ierrv |
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[3228] | 115 | LOGICAL :: data_loaded = .FALSE. |
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[2931] | 116 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 117 | ! |
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| 118 | ! Parameter Module File |
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| 119 | ! |
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| 120 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 121 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 122 | ! KPP is distributed under GPL,the general public licence |
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| 123 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 124 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 125 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 126 | ! With important contributions from: |
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| 127 | ! M. Damian,Villanova University,USA |
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| 128 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 129 | ! |
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| 130 | ! File : chem_gasphase_mod_Parameters.f90 |
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[3280] | 131 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 132 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 133 | ! Equation file : chem_gasphase_mod.kpp |
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| 134 | ! Output root filename : chem_gasphase_mod |
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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 | |
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| 141 | |
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| 142 | |
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| 143 | ! NSPEC - Number of chemical species |
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[3228] | 144 | INTEGER, PARAMETER :: nspec = 3 |
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[2931] | 145 | ! NVAR - Number of Variable species |
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[3228] | 146 | INTEGER, PARAMETER :: nvar = 3 |
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[2931] | 147 | ! NVARACT - Number of Active species |
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[3228] | 148 | INTEGER, PARAMETER :: nvaract = 3 |
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[2931] | 149 | ! NFIX - Number of Fixed species |
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[3228] | 150 | INTEGER, PARAMETER :: nfix = 1 |
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[2931] | 151 | ! NREACT - Number of reactions |
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[3228] | 152 | INTEGER, PARAMETER :: nreact = 2 |
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[2931] | 153 | ! NVARST - Starting of variables in conc. vect. |
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[3228] | 154 | INTEGER, PARAMETER :: nvarst = 1 |
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[2931] | 155 | ! NFIXST - Starting of fixed in conc. vect. |
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[3228] | 156 | INTEGER, PARAMETER :: nfixst = 4 |
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[2931] | 157 | ! NONZERO - Number of nonzero entries in Jacobian |
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[3228] | 158 | INTEGER, PARAMETER :: nonzero = 9 |
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[2931] | 159 | ! LU_NONZERO - Number of nonzero entries in LU factoriz. of Jacobian |
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[3228] | 160 | INTEGER, PARAMETER :: lu_nonzero = 9 |
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[2931] | 161 | ! CNVAR - (NVAR+1) Number of elements in compressed row format |
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[3228] | 162 | INTEGER, PARAMETER :: cnvar = 4 |
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[2931] | 163 | ! CNEQN - (NREACT+1) Number stoicm elements in compressed col format |
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[3228] | 164 | INTEGER, PARAMETER :: cneqn = 3 |
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[2931] | 165 | ! NHESS - Length of Sparse Hessian |
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[3228] | 166 | INTEGER, PARAMETER :: nhess = 3 |
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[2931] | 167 | ! NMASS - Number of atoms to check mass balance |
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[3228] | 168 | INTEGER, PARAMETER :: nmass = 1 |
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[2931] | 169 | |
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| 170 | ! Index declaration for variable species in C and VAR |
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| 171 | ! VAR(ind_spc) = C(ind_spc) |
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| 172 | |
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[3228] | 173 | INTEGER, PARAMETER, PUBLIC :: ind_o3 = 1 |
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| 174 | INTEGER, PARAMETER, PUBLIC :: ind_no = 2 |
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| 175 | INTEGER, PARAMETER, PUBLIC :: ind_no2 = 3 |
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[2931] | 176 | |
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| 177 | ! Index declaration for fixed species in C |
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| 178 | ! C(ind_spc) |
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| 179 | |
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| 180 | |
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| 181 | ! Index declaration for fixed species in FIX |
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| 182 | ! FIX(indf_spc) = C(ind_spc) = C(NVAR+indf_spc) |
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| 183 | |
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| 184 | |
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| 185 | ! NJVRP - Length of sparse Jacobian JVRP |
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[3228] | 186 | INTEGER, PARAMETER :: njvrp = 3 |
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[2931] | 187 | |
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| 188 | ! NSTOICM - Length of Sparse Stoichiometric Matrix |
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[3228] | 189 | INTEGER, PARAMETER :: nstoicm = 6 |
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[2931] | 190 | |
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| 191 | |
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| 192 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 193 | ! |
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| 194 | ! Global Data Module File |
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| 195 | ! |
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| 196 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 197 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 198 | ! KPP is distributed under GPL,the general public licence |
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| 199 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 200 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 201 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 202 | ! With important contributions from: |
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| 203 | ! M. Damian,Villanova University,USA |
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| 204 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 205 | ! |
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| 206 | ! File : chem_gasphase_mod_Global.f90 |
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[3280] | 207 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 208 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 209 | ! Equation file : chem_gasphase_mod.kpp |
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| 210 | ! Output root filename : chem_gasphase_mod |
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| 211 | ! |
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| 212 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 213 | |
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| 214 | |
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| 215 | |
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| 216 | |
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| 217 | |
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| 218 | |
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| 219 | ! Declaration of global variables |
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| 220 | |
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| 221 | ! C - Concentration of all species |
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| 222 | REAL(kind=dp):: c(nspec) |
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| 223 | ! VAR - Concentrations of variable species (global) |
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| 224 | REAL(kind=dp):: var(nvar) |
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| 225 | ! FIX - Concentrations of fixed species (global) |
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| 226 | REAL(kind=dp):: fix(nfix) |
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| 227 | ! VAR,FIX are chunks of array C |
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[3228] | 228 | EQUIVALENCE( c(1), var(1)) |
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[2931] | 229 | ! RCONST - Rate constants (global) |
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| 230 | REAL(kind=dp):: rconst(nreact) |
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| 231 | ! TIME - Current integration time |
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| 232 | REAL(kind=dp):: time |
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| 233 | ! TEMP - Temperature |
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[3263] | 234 | REAL(kind=dp):: temp |
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[2931] | 235 | ! TSTART - Integration start time |
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| 236 | REAL(kind=dp):: tstart |
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| 237 | ! ATOL - Absolute tolerance |
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| 238 | REAL(kind=dp):: atol(nvar) |
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| 239 | ! RTOL - Relative tolerance |
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| 240 | REAL(kind=dp):: rtol(nvar) |
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| 241 | ! STEPMIN - Lower bound for integration step |
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| 242 | REAL(kind=dp):: stepmin |
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| 243 | ! CFACTOR - Conversion factor for concentration units |
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| 244 | REAL(kind=dp):: cfactor |
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| 245 | |
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| 246 | ! INLINED global variable declarations |
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| 247 | |
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[3228] | 248 | ! QVAP - Water vapor |
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[3263] | 249 | REAL(kind=dp):: qvap |
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[3228] | 250 | ! FAKT - Conversion factor |
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[3263] | 251 | REAL(kind=dp):: fakt |
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[3228] | 252 | |
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[2931] | 253 | |
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| 254 | ! INLINED global variable declarations |
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| 255 | |
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| 256 | |
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| 257 | |
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| 258 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 259 | ! |
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| 260 | ! Sparse Jacobian Data Structures File |
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| 261 | ! |
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| 262 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 263 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 264 | ! KPP is distributed under GPL,the general public licence |
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| 265 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 266 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 267 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 268 | ! With important contributions from: |
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| 269 | ! M. Damian,Villanova University,USA |
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| 270 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 271 | ! |
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| 272 | ! File : chem_gasphase_mod_JacobianSP.f90 |
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[3280] | 273 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 274 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 275 | ! Equation file : chem_gasphase_mod.kpp |
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| 276 | ! Output root filename : chem_gasphase_mod |
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| 277 | ! |
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| 278 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 279 | |
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| 280 | |
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| 281 | |
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| 282 | |
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| 283 | |
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| 284 | |
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| 285 | ! Sparse Jacobian Data |
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| 286 | |
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| 287 | |
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[3228] | 288 | INTEGER, PARAMETER, DIMENSION(9):: lu_irow = (/ & |
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[2931] | 289 | 1, 1, 1, 2, 2, 2, 3, 3, 3 /) |
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| 290 | |
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[3228] | 291 | INTEGER, PARAMETER, DIMENSION(9):: lu_icol = (/ & |
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[2931] | 292 | 1, 2, 3, 1, 2, 3, 1, 2, 3 /) |
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| 293 | |
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[3228] | 294 | INTEGER, PARAMETER, DIMENSION(4):: lu_crow = (/ & |
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| 295 | 1, 4, 7, 10 /) |
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[2931] | 296 | |
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[3228] | 297 | INTEGER, PARAMETER, DIMENSION(4):: lu_diag = (/ & |
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| 298 | 1, 5, 9, 10 /) |
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[2931] | 299 | |
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| 300 | |
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| 301 | |
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| 302 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 303 | ! |
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| 304 | ! Utility Data Module File |
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| 305 | ! |
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| 306 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 307 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 308 | ! KPP is distributed under GPL,the general public licence |
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| 309 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 310 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 311 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 312 | ! With important contributions from: |
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| 313 | ! M. Damian,Villanova University,USA |
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| 314 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 315 | ! |
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| 316 | ! File : chem_gasphase_mod_Monitor.f90 |
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[3280] | 317 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 318 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 319 | ! Equation file : chem_gasphase_mod.kpp |
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| 320 | ! Output root filename : chem_gasphase_mod |
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| 321 | ! |
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| 322 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 323 | |
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| 324 | |
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| 325 | |
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| 326 | |
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| 327 | |
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[3228] | 328 | CHARACTER(len=15), PARAMETER, DIMENSION(3):: spc_names = (/ & |
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[2931] | 329 | 'O3 ','NO ','NO2 ' /) |
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| 330 | |
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[3228] | 331 | CHARACTER(len=100), PARAMETER, DIMENSION(2):: eqn_names = (/ & |
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[2931] | 332 | ' NO2 --> O3 + NO ',& |
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| 333 | 'O3 + NO --> NO2 ' /) |
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| 334 | |
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| 335 | ! INLINED global variables |
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| 336 | |
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| 337 | ! inline f90_data: declaration of global variables for photolysis |
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| 338 | ! REAL(kind=dp):: phot(nphot)must eventually be moved to global later for |
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[3228] | 339 | INTEGER, PARAMETER :: nphot = 1 |
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[2931] | 340 | ! phot photolysis frequencies |
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| 341 | REAL(kind=dp):: phot(nphot) |
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| 342 | |
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[3228] | 343 | INTEGER, PARAMETER, PUBLIC :: j_no2 = 1 |
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[2931] | 344 | |
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[3228] | 345 | CHARACTER(len=15), PARAMETER, DIMENSION(nphot):: phot_names = (/ & |
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[2931] | 346 | 'J_NO2 '/) |
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| 347 | |
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| 348 | ! End INLINED global variables |
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| 349 | |
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| 350 | |
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| 351 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 352 | |
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| 353 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 354 | |
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| 355 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 356 | |
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| 357 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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| 358 | |
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| 359 | |
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| 360 | ! variable definations from individual module headers |
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| 361 | |
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| 362 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 363 | ! |
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| 364 | ! Initialization File |
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| 365 | ! |
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| 366 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 367 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 368 | ! KPP is distributed under GPL,the general public licence |
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| 369 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 370 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 371 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 372 | ! With important contributions from: |
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| 373 | ! M. Damian,Villanova University,USA |
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| 374 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 375 | ! |
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| 376 | ! File : chem_gasphase_mod_Initialize.f90 |
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[3280] | 377 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 378 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 379 | ! Equation file : chem_gasphase_mod.kpp |
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| 380 | ! Output root filename : chem_gasphase_mod |
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| 381 | ! |
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| 382 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 383 | |
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| 384 | |
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| 385 | |
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| 386 | |
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| 387 | |
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| 388 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 389 | ! |
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| 390 | ! Numerical Integrator (Time-Stepping) File |
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| 391 | ! |
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| 392 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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| 393 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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| 394 | ! KPP is distributed under GPL,the general public licence |
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| 395 | ! (http://www.gnu.org/copyleft/gpl.html) |
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| 396 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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| 397 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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| 398 | ! With important contributions from: |
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| 399 | ! M. Damian,Villanova University,USA |
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| 400 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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| 401 | ! |
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| 402 | ! File : chem_gasphase_mod_Integrator.f90 |
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[3280] | 403 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 404 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 405 | ! Equation file : chem_gasphase_mod.kpp |
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| 406 | ! Output root filename : chem_gasphase_mod |
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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 | ! INTEGRATE - Integrator routine |
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| 415 | ! Arguments : |
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| 416 | ! TIN - Start Time for Integration |
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| 417 | ! TOUT - End Time for Integration |
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| 418 | ! |
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| 419 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 420 | |
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| 421 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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| 422 | ! Rosenbrock - Implementation of several Rosenbrock methods: ! |
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| 423 | ! *Ros2 ! |
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| 424 | ! *Ros3 ! |
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| 425 | ! *Ros4 ! |
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| 426 | ! *Rodas3 ! |
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| 427 | ! *Rodas4 ! |
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| 428 | ! By default the code employs the KPP sparse linear algebra routines ! |
---|
| 429 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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| 430 | ! ! |
---|
| 431 | ! (C) Adrian Sandu,August 2004 ! |
---|
| 432 | ! Virginia Polytechnic Institute and State University ! |
---|
| 433 | ! Contact: sandu@cs.vt.edu ! |
---|
| 434 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 ! ! |
---|
| 435 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
---|
| 436 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
---|
| 437 | |
---|
| 438 | |
---|
| 439 | SAVE |
---|
| 440 | |
---|
| 441 | !~~~> statistics on the work performed by the rosenbrock method |
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[3228] | 442 | INTEGER, PARAMETER :: nfun=1, njac=2, nstp=3, nacc=4, & |
---|
| 443 | nrej=5, ndec=6, nsol=7, nsng=8, & |
---|
| 444 | ntexit=1, nhexit=2, nhnew = 3 |
---|
[2931] | 445 | |
---|
| 446 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 447 | ! |
---|
| 448 | ! Linear Algebra Data and Routines File |
---|
| 449 | ! |
---|
| 450 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
| 451 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
| 452 | ! KPP is distributed under GPL,the general public licence |
---|
| 453 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
| 454 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
| 455 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
| 456 | ! With important contributions from: |
---|
| 457 | ! M. Damian,Villanova University,USA |
---|
| 458 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
| 459 | ! |
---|
| 460 | ! File : chem_gasphase_mod_LinearAlgebra.f90 |
---|
[3280] | 461 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 462 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 463 | ! Equation file : chem_gasphase_mod.kpp |
---|
| 464 | ! Output root filename : chem_gasphase_mod |
---|
| 465 | ! |
---|
| 466 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 467 | |
---|
| 468 | |
---|
| 469 | |
---|
| 470 | |
---|
| 471 | |
---|
| 472 | |
---|
| 473 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 474 | ! |
---|
| 475 | ! The ODE Jacobian of Chemical Model File |
---|
| 476 | ! |
---|
| 477 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
| 478 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
| 479 | ! KPP is distributed under GPL,the general public licence |
---|
| 480 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
| 481 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
| 482 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
| 483 | ! With important contributions from: |
---|
| 484 | ! M. Damian,Villanova University,USA |
---|
| 485 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
| 486 | ! |
---|
| 487 | ! File : chem_gasphase_mod_Jacobian.f90 |
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[3280] | 488 | ! Time : Tue Sep 25 18:35:04 2018 |
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| 489 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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[2931] | 490 | ! Equation file : chem_gasphase_mod.kpp |
---|
| 491 | ! Output root filename : chem_gasphase_mod |
---|
| 492 | ! |
---|
| 493 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 494 | |
---|
| 495 | |
---|
| 496 | |
---|
| 497 | |
---|
| 498 | |
---|
| 499 | |
---|
| 500 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 501 | ! |
---|
| 502 | ! The ODE Function of Chemical Model File |
---|
| 503 | ! |
---|
| 504 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
| 505 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
| 506 | ! KPP is distributed under GPL,the general public licence |
---|
| 507 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
| 508 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
| 509 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
| 510 | ! With important contributions from: |
---|
| 511 | ! M. Damian,Villanova University,USA |
---|
| 512 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
| 513 | ! |
---|
| 514 | ! File : chem_gasphase_mod_Function.f90 |
---|
[3280] | 515 | ! Time : Tue Sep 25 18:35:04 2018 |
---|
| 516 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
[2931] | 517 | ! Equation file : chem_gasphase_mod.kpp |
---|
| 518 | ! Output root filename : chem_gasphase_mod |
---|
| 519 | ! |
---|
| 520 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 521 | |
---|
| 522 | |
---|
| 523 | |
---|
| 524 | |
---|
| 525 | |
---|
| 526 | ! A - Rate for each equation |
---|
| 527 | REAL(kind=dp):: a(nreact) |
---|
| 528 | |
---|
| 529 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 530 | ! |
---|
| 531 | ! The Reaction Rates File |
---|
| 532 | ! |
---|
| 533 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
| 534 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
| 535 | ! KPP is distributed under GPL,the general public licence |
---|
| 536 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
| 537 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
| 538 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
| 539 | ! With important contributions from: |
---|
| 540 | ! M. Damian,Villanova University,USA |
---|
| 541 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
| 542 | ! |
---|
| 543 | ! File : chem_gasphase_mod_Rates.f90 |
---|
[3280] | 544 | ! Time : Tue Sep 25 18:35:04 2018 |
---|
| 545 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
[2931] | 546 | ! Equation file : chem_gasphase_mod.kpp |
---|
| 547 | ! Output root filename : chem_gasphase_mod |
---|
| 548 | ! |
---|
| 549 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 550 | |
---|
| 551 | |
---|
| 552 | |
---|
| 553 | |
---|
| 554 | |
---|
| 555 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 556 | ! |
---|
| 557 | ! Auxiliary Routines File |
---|
| 558 | ! |
---|
| 559 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
| 560 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
| 561 | ! KPP is distributed under GPL,the general public licence |
---|
| 562 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
| 563 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
| 564 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
| 565 | ! With important contributions from: |
---|
| 566 | ! M. Damian,Villanova University,USA |
---|
| 567 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
| 568 | ! |
---|
| 569 | ! File : chem_gasphase_mod_Util.f90 |
---|
[3280] | 570 | ! Time : Tue Sep 25 18:35:04 2018 |
---|
| 571 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
[2931] | 572 | ! Equation file : chem_gasphase_mod.kpp |
---|
| 573 | ! Output root filename : chem_gasphase_mod |
---|
| 574 | ! |
---|
| 575 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 576 | |
---|
| 577 | |
---|
| 578 | |
---|
| 579 | |
---|
| 580 | |
---|
| 581 | |
---|
| 582 | ! header MODULE initialize_kpp_ctrl_template |
---|
| 583 | |
---|
| 584 | ! notes: |
---|
[3228] | 585 | ! - l_vector is automatically defined by kp4 |
---|
| 586 | ! - vl_dim is automatically defined by kp4 |
---|
| 587 | ! - i_lu_di is automatically defined by kp4 |
---|
| 588 | ! - wanted is automatically defined by xmecca |
---|
| 589 | ! - icntrl rcntrl are automatically defined by kpp |
---|
| 590 | ! - "USE messy_main_tools" is in MODULE_header of messy_mecca_kpp.f90 |
---|
| 591 | ! - SAVE will be automatically added by kp4 |
---|
[2931] | 592 | |
---|
| 593 | !SAVE |
---|
| 594 | |
---|
| 595 | ! for fixed time step control |
---|
| 596 | ! ... max. number of fixed time steps (sum must be 1) |
---|
[3228] | 597 | INTEGER, PARAMETER :: nmaxfixsteps = 50 |
---|
[2931] | 598 | ! ... switch for fixed time stepping |
---|
[3228] | 599 | LOGICAL, PUBLIC :: l_fixed_step = .FALSE. |
---|
| 600 | INTEGER, PUBLIC :: nfsteps = 1 |
---|
[2931] | 601 | ! ... number of kpp control PARAMETERs |
---|
[3228] | 602 | INTEGER, PARAMETER, PUBLIC :: nkppctrl = 20 |
---|
[2931] | 603 | ! |
---|
[3228] | 604 | INTEGER, DIMENSION(nkppctrl), PUBLIC :: icntrl = 0 |
---|
| 605 | REAL(dp), DIMENSION(nkppctrl), PUBLIC :: rcntrl = 0.0_dp |
---|
| 606 | REAL(dp), DIMENSION(nmaxfixsteps), PUBLIC :: t_steps = 0.0_dp |
---|
[2931] | 607 | |
---|
| 608 | ! END header MODULE initialize_kpp_ctrl_template |
---|
| 609 | |
---|
| 610 | |
---|
| 611 | ! Interface Block |
---|
| 612 | |
---|
| 613 | INTERFACE initialize |
---|
| 614 | MODULE PROCEDURE initialize |
---|
| 615 | END INTERFACE initialize |
---|
| 616 | |
---|
| 617 | INTERFACE integrate |
---|
| 618 | MODULE PROCEDURE integrate |
---|
| 619 | END INTERFACE integrate |
---|
| 620 | |
---|
| 621 | INTERFACE fun |
---|
| 622 | MODULE PROCEDURE fun |
---|
| 623 | END INTERFACE fun |
---|
| 624 | |
---|
| 625 | INTERFACE kppsolve |
---|
| 626 | MODULE PROCEDURE kppsolve |
---|
| 627 | END INTERFACE kppsolve |
---|
| 628 | |
---|
| 629 | INTERFACE jac_sp |
---|
| 630 | MODULE PROCEDURE jac_sp |
---|
| 631 | END INTERFACE jac_sp |
---|
| 632 | |
---|
| 633 | INTERFACE k_arr |
---|
| 634 | MODULE PROCEDURE k_arr |
---|
| 635 | END INTERFACE k_arr |
---|
| 636 | |
---|
| 637 | INTERFACE update_rconst |
---|
| 638 | MODULE PROCEDURE update_rconst |
---|
| 639 | END INTERFACE update_rconst |
---|
| 640 | |
---|
| 641 | INTERFACE arr2 |
---|
| 642 | MODULE PROCEDURE arr2 |
---|
| 643 | END INTERFACE arr2 |
---|
| 644 | |
---|
| 645 | INTERFACE initialize_kpp_ctrl |
---|
| 646 | MODULE PROCEDURE initialize_kpp_ctrl |
---|
| 647 | END INTERFACE initialize_kpp_ctrl |
---|
| 648 | |
---|
| 649 | INTERFACE error_output |
---|
| 650 | MODULE PROCEDURE error_output |
---|
| 651 | END INTERFACE error_output |
---|
| 652 | |
---|
| 653 | INTERFACE wscal |
---|
| 654 | MODULE PROCEDURE wscal |
---|
| 655 | END INTERFACE wscal |
---|
| 656 | |
---|
[3228] | 657 | !INTERFACE not working INTERFACE waxpy |
---|
| 658 | !INTERFACE not working MODULE PROCEDURE waxpy |
---|
| 659 | !INTERFACE not working END INTERFACE waxpy |
---|
[2931] | 660 | |
---|
| 661 | INTERFACE rosenbrock |
---|
| 662 | MODULE PROCEDURE rosenbrock |
---|
| 663 | END INTERFACE rosenbrock |
---|
| 664 | |
---|
| 665 | INTERFACE funtemplate |
---|
| 666 | MODULE PROCEDURE funtemplate |
---|
| 667 | END INTERFACE funtemplate |
---|
| 668 | |
---|
| 669 | INTERFACE jactemplate |
---|
| 670 | MODULE PROCEDURE jactemplate |
---|
| 671 | END INTERFACE jactemplate |
---|
| 672 | |
---|
[3228] | 673 | INTERFACE kppdecomp |
---|
| 674 | MODULE PROCEDURE kppdecomp |
---|
| 675 | END INTERFACE kppdecomp |
---|
| 676 | |
---|
[2931] | 677 | INTERFACE chem_gasphase_integrate |
---|
| 678 | MODULE PROCEDURE chem_gasphase_integrate |
---|
| 679 | END INTERFACE chem_gasphase_integrate |
---|
| 680 | |
---|
| 681 | |
---|
| 682 | CONTAINS |
---|
| 683 | |
---|
| 684 | SUBROUTINE initialize() |
---|
| 685 | |
---|
| 686 | |
---|
[3249] | 687 | INTEGER :: j, k |
---|
[2931] | 688 | |
---|
| 689 | INTEGER :: i |
---|
| 690 | REAL(kind=dp):: x |
---|
[3249] | 691 | k = is |
---|
[2931] | 692 | cfactor = 1.000000e+00_dp |
---|
| 693 | |
---|
[3228] | 694 | x = (0.) * cfactor |
---|
[3249] | 695 | DO i = 1 , nvar |
---|
[2931] | 696 | ENDDO |
---|
| 697 | |
---|
[3228] | 698 | x = (0.) * cfactor |
---|
[3249] | 699 | DO i = 1 , nfix |
---|
[2931] | 700 | fix(i) = x |
---|
| 701 | ENDDO |
---|
| 702 | |
---|
| 703 | ! constant rate coefficients |
---|
| 704 | ! END constant rate coefficients |
---|
| 705 | |
---|
| 706 | ! INLINED initializations |
---|
| 707 | |
---|
| 708 | ! End INLINED initializations |
---|
| 709 | |
---|
| 710 | |
---|
| 711 | END SUBROUTINE initialize |
---|
| 712 | |
---|
[3228] | 713 | SUBROUTINE integrate( tin, tout, & |
---|
| 714 | icntrl_u, rcntrl_u, istatus_u, rstatus_u, ierr_u) |
---|
[2931] | 715 | |
---|
| 716 | |
---|
[3228] | 717 | REAL(kind=dp), INTENT(IN):: tin ! start time |
---|
| 718 | REAL(kind=dp), INTENT(IN):: tout ! END time |
---|
[2931] | 719 | ! OPTIONAL input PARAMETERs and statistics |
---|
[3228] | 720 | INTEGER, INTENT(IN), OPTIONAL :: icntrl_u(20) |
---|
| 721 | REAL(kind=dp), INTENT(IN), OPTIONAL :: rcntrl_u(20) |
---|
| 722 | INTEGER, INTENT(OUT), OPTIONAL :: istatus_u(20) |
---|
| 723 | REAL(kind=dp), INTENT(OUT), OPTIONAL :: rstatus_u(20) |
---|
| 724 | INTEGER, INTENT(OUT), OPTIONAL :: ierr_u |
---|
[2931] | 725 | |
---|
[3228] | 726 | REAL(kind=dp):: rcntrl(20), rstatus(20) |
---|
| 727 | INTEGER :: icntrl(20), istatus(20), ierr |
---|
[2931] | 728 | |
---|
[3228] | 729 | INTEGER, SAVE :: ntotal = 0 |
---|
[2931] | 730 | |
---|
| 731 | icntrl(:) = 0 |
---|
| 732 | rcntrl(:) = 0.0_dp |
---|
| 733 | istatus(:) = 0 |
---|
| 734 | rstatus(:) = 0.0_dp |
---|
| 735 | |
---|
| 736 | !~~~> fine-tune the integrator: |
---|
[3249] | 737 | icntrl(1) = 0 ! 0 - non- autonomous, 1 - autonomous |
---|
| 738 | icntrl(2) = 0 ! 0 - vector tolerances, 1 - scalars |
---|
[2931] | 739 | |
---|
[3228] | 740 | ! IF OPTIONAL PARAMETERs are given, and IF they are >0, |
---|
[2931] | 741 | ! THEN they overwrite default settings. |
---|
[3228] | 742 | IF (PRESENT(icntrl_u))THEN |
---|
| 743 | WHERE(icntrl_u(:)> 0)icntrl(:) = icntrl_u(:) |
---|
[2931] | 744 | ENDIF |
---|
[3228] | 745 | IF (PRESENT(rcntrl_u))THEN |
---|
| 746 | WHERE(rcntrl_u(:)> 0)rcntrl(:) = rcntrl_u(:) |
---|
[2931] | 747 | ENDIF |
---|
| 748 | |
---|
| 749 | |
---|
[3228] | 750 | CALL rosenbrock(nvar, var, tin, tout, & |
---|
| 751 | atol, rtol, & |
---|
| 752 | rcntrl, icntrl, rstatus, istatus, ierr) |
---|
[2931] | 753 | |
---|
| 754 | !~~~> debug option: show no of steps |
---|
| 755 | ! ntotal = ntotal + istatus(nstp) |
---|
| 756 | ! PRINT*,'NSTEPS=',ISTATUS(Nstp),' (',Ntotal,')',' O3=',VAR(ind_O3) |
---|
| 757 | |
---|
| 758 | stepmin = rstatus(nhexit) |
---|
| 759 | ! IF OPTIONAL PARAMETERs are given for output they |
---|
| 760 | ! are updated with the RETURN information |
---|
[3228] | 761 | IF (PRESENT(istatus_u))istatus_u(:) = istatus(:) |
---|
| 762 | IF (PRESENT(rstatus_u))rstatus_u(:) = rstatus(:) |
---|
| 763 | IF (PRESENT(ierr_u)) ierr_u = ierr |
---|
[2931] | 764 | |
---|
| 765 | END SUBROUTINE integrate |
---|
| 766 | |
---|
[3228] | 767 | SUBROUTINE fun(v, f, rct, vdot) |
---|
[2931] | 768 | |
---|
| 769 | ! V - Concentrations of variable species (local) |
---|
| 770 | REAL(kind=dp):: v(nvar) |
---|
| 771 | ! F - Concentrations of fixed species (local) |
---|
| 772 | REAL(kind=dp):: f(nfix) |
---|
| 773 | ! RCT - Rate constants (local) |
---|
| 774 | REAL(kind=dp):: rct(nreact) |
---|
| 775 | ! Vdot - Time derivative of variable species concentrations |
---|
| 776 | REAL(kind=dp):: vdot(nvar) |
---|
| 777 | |
---|
| 778 | |
---|
| 779 | ! Computation of equation rates |
---|
[3228] | 780 | a(1) = rct(1) * v(3) |
---|
| 781 | a(2) = rct(2) * v(1) * v(2) |
---|
[2931] | 782 | |
---|
| 783 | ! Aggregate function |
---|
[3228] | 784 | vdot(1) = a(1) - a(2) |
---|
| 785 | vdot(2) = a(1) - a(2) |
---|
| 786 | vdot(3) = - a(1) + a(2) |
---|
[2931] | 787 | |
---|
| 788 | END SUBROUTINE fun |
---|
| 789 | |
---|
[3228] | 790 | SUBROUTINE kppsolve(jvs, x) |
---|
[2931] | 791 | |
---|
| 792 | ! JVS - sparse Jacobian of variables |
---|
| 793 | REAL(kind=dp):: jvs(lu_nonzero) |
---|
| 794 | ! X - Vector for variables |
---|
| 795 | REAL(kind=dp):: x(nvar) |
---|
| 796 | |
---|
[3228] | 797 | x(2) = x(2) - jvs(4) * x(1) |
---|
| 798 | x(3) = x(3) - jvs(7) * x(1) - jvs(8) * x(2) |
---|
| 799 | x(3) = x(3) / jvs(9) |
---|
| 800 | x(2) = (x(2) - jvs(6) * x(3)) /(jvs(5)) |
---|
| 801 | x(1) = (x(1) - jvs(2) * x(2) - jvs(3) * x(3)) /(jvs(1)) |
---|
[2931] | 802 | |
---|
| 803 | END SUBROUTINE kppsolve |
---|
| 804 | |
---|
[3228] | 805 | SUBROUTINE jac_sp(v, f, rct, jvs) |
---|
[2931] | 806 | |
---|
| 807 | ! V - Concentrations of variable species (local) |
---|
| 808 | REAL(kind=dp):: v(nvar) |
---|
| 809 | ! F - Concentrations of fixed species (local) |
---|
| 810 | REAL(kind=dp):: f(nfix) |
---|
| 811 | ! RCT - Rate constants (local) |
---|
| 812 | REAL(kind=dp):: rct(nreact) |
---|
| 813 | ! JVS - sparse Jacobian of variables |
---|
| 814 | REAL(kind=dp):: jvs(lu_nonzero) |
---|
| 815 | |
---|
| 816 | |
---|
| 817 | ! Local variables |
---|
| 818 | ! B - Temporary array |
---|
| 819 | REAL(kind=dp):: b(3) |
---|
| 820 | |
---|
| 821 | ! B(1) = dA(1)/dV(3) |
---|
| 822 | b(1) = rct(1) |
---|
| 823 | ! B(2) = dA(2)/dV(1) |
---|
[3228] | 824 | b(2) = rct(2) * v(2) |
---|
[2931] | 825 | ! B(3) = dA(2)/dV(2) |
---|
[3228] | 826 | b(3) = rct(2) * v(1) |
---|
[2931] | 827 | |
---|
| 828 | ! Construct the Jacobian terms from B's |
---|
| 829 | ! JVS(1) = Jac_FULL(1,1) |
---|
| 830 | jvs(1) = - b(2) |
---|
| 831 | ! JVS(2) = Jac_FULL(1,2) |
---|
| 832 | jvs(2) = - b(3) |
---|
| 833 | ! JVS(3) = Jac_FULL(1,3) |
---|
| 834 | jvs(3) = b(1) |
---|
| 835 | ! JVS(4) = Jac_FULL(2,1) |
---|
| 836 | jvs(4) = - b(2) |
---|
| 837 | ! JVS(5) = Jac_FULL(2,2) |
---|
| 838 | jvs(5) = - b(3) |
---|
| 839 | ! JVS(6) = Jac_FULL(2,3) |
---|
| 840 | jvs(6) = b(1) |
---|
| 841 | ! JVS(7) = Jac_FULL(3,1) |
---|
| 842 | jvs(7) = b(2) |
---|
| 843 | ! JVS(8) = Jac_FULL(3,2) |
---|
| 844 | jvs(8) = b(3) |
---|
| 845 | ! JVS(9) = Jac_FULL(3,3) |
---|
| 846 | jvs(9) = - b(1) |
---|
| 847 | |
---|
| 848 | END SUBROUTINE jac_sp |
---|
| 849 | |
---|
[3228] | 850 | elemental REAL(kind=dp)FUNCTION k_arr (k_298, tdep, temp) |
---|
[2931] | 851 | ! arrhenius FUNCTION |
---|
| 852 | |
---|
[3228] | 853 | REAL, INTENT(IN):: k_298 ! k at t = 298.15k |
---|
| 854 | REAL, INTENT(IN):: tdep ! temperature dependence |
---|
| 855 | REAL(kind=dp), INTENT(IN):: temp ! temperature |
---|
[2931] | 856 | |
---|
| 857 | intrinsic exp |
---|
| 858 | |
---|
[3228] | 859 | k_arr = k_298 * exp(tdep* (1._dp/temp- 3.3540e-3_dp))! 1/298.15=3.3540e-3 |
---|
[2931] | 860 | |
---|
| 861 | END FUNCTION k_arr |
---|
| 862 | |
---|
| 863 | SUBROUTINE update_rconst() |
---|
[3249] | 864 | INTEGER :: k |
---|
[2931] | 865 | |
---|
| 866 | k = is |
---|
| 867 | |
---|
| 868 | ! Begin INLINED RCONST |
---|
| 869 | |
---|
| 870 | |
---|
| 871 | ! End INLINED RCONST |
---|
| 872 | |
---|
| 873 | rconst(1) = (phot(j_no2)) |
---|
[3263] | 874 | rconst(2) = (arr2(1.8e-12_dp , 1370.0_dp , temp)) |
---|
[2931] | 875 | |
---|
| 876 | END SUBROUTINE update_rconst |
---|
| 877 | |
---|
[3228] | 878 | ! END FUNCTION ARR2 |
---|
| 879 | REAL(kind=dp)FUNCTION arr2( a0, b0, temp) |
---|
[2931] | 880 | REAL(kind=dp):: temp |
---|
[3228] | 881 | REAL(kind=dp):: a0, b0 |
---|
| 882 | arr2 = a0 * exp( - b0 / temp) |
---|
[2931] | 883 | END FUNCTION arr2 |
---|
| 884 | |
---|
[3249] | 885 | SUBROUTINE initialize_kpp_ctrl(status) |
---|
[2931] | 886 | |
---|
| 887 | |
---|
| 888 | ! i/o |
---|
[3228] | 889 | INTEGER, INTENT(OUT):: status |
---|
[2931] | 890 | |
---|
| 891 | ! local |
---|
| 892 | REAL(dp):: tsum |
---|
| 893 | INTEGER :: i |
---|
| 894 | |
---|
| 895 | ! check fixed time steps |
---|
| 896 | tsum = 0.0_dp |
---|
[3228] | 897 | DO i=1, nmaxfixsteps |
---|
[2931] | 898 | IF (t_steps(i)< tiny(0.0_dp))exit |
---|
| 899 | tsum = tsum + t_steps(i) |
---|
| 900 | ENDDO |
---|
| 901 | |
---|
| 902 | nfsteps = i- 1 |
---|
| 903 | |
---|
| 904 | l_fixed_step = (nfsteps > 0).and.((tsum - 1.0)< tiny(0.0_dp)) |
---|
| 905 | |
---|
| 906 | IF (l_vector)THEN |
---|
| 907 | WRITE(*,*) ' MODE : VECTOR (LENGTH=',VL_DIM,')' |
---|
| 908 | ELSE |
---|
| 909 | WRITE(*,*) ' MODE : SCALAR' |
---|
| 910 | ENDIF |
---|
| 911 | ! |
---|
| 912 | WRITE(*,*) ' DE-INDEXING MODE :',I_LU_DI |
---|
| 913 | ! |
---|
| 914 | WRITE(*,*) ' ICNTRL : ',icntrl |
---|
| 915 | WRITE(*,*) ' RCNTRL : ',rcntrl |
---|
| 916 | ! |
---|
[3228] | 917 | ! note: this is ONLY meaningful for vectorized (kp4)rosenbrock- methods |
---|
[2931] | 918 | IF (l_vector)THEN |
---|
| 919 | IF (l_fixed_step)THEN |
---|
| 920 | WRITE(*,*) ' TIME STEPS : FIXED (',t_steps(1:nfsteps),')' |
---|
| 921 | ELSE |
---|
| 922 | WRITE(*,*) ' TIME STEPS : AUTOMATIC' |
---|
| 923 | ENDIF |
---|
| 924 | ELSE |
---|
| 925 | WRITE(*,*) ' TIME STEPS : AUTOMATIC '//& |
---|
| 926 | &'(t_steps (CTRL_KPP) ignored in SCALAR MODE)' |
---|
| 927 | ENDIF |
---|
| 928 | ! mz_pj_20070531- |
---|
| 929 | |
---|
| 930 | status = 0 |
---|
| 931 | |
---|
| 932 | |
---|
| 933 | END SUBROUTINE initialize_kpp_ctrl |
---|
| 934 | |
---|
[3228] | 935 | SUBROUTINE error_output(c, ierr, pe) |
---|
[2931] | 936 | |
---|
| 937 | |
---|
[3228] | 938 | INTEGER, INTENT(IN):: ierr |
---|
| 939 | INTEGER, INTENT(IN):: pe |
---|
| 940 | REAL(dp), DIMENSION(:), INTENT(IN):: c |
---|
[2931] | 941 | |
---|
| 942 | write(6,*) 'ERROR in chem_gasphase_mod ',ierr,C(1) |
---|
| 943 | |
---|
| 944 | |
---|
| 945 | END SUBROUTINE error_output |
---|
| 946 | |
---|
[3228] | 947 | SUBROUTINE wscal(n, alpha, x, incx) |
---|
[2931] | 948 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
| 949 | ! constant times a vector: x(1:N) <- Alpha*x(1:N) |
---|
| 950 | ! only for incX=incY=1 |
---|
| 951 | ! after BLAS |
---|
| 952 | ! replace this by the function from the optimized BLAS implementation: |
---|
| 953 | ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) |
---|
| 954 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
| 955 | |
---|
[3228] | 956 | INTEGER :: i, incx, m, mp1, n |
---|
| 957 | REAL(kind=dp) :: x(n), alpha |
---|
| 958 | REAL(kind=dp), PARAMETER :: zero=0.0_dp, one=1.0_dp |
---|
[2931] | 959 | |
---|
| 960 | IF (alpha .eq. one)RETURN |
---|
| 961 | IF (n .le. 0)RETURN |
---|
| 962 | |
---|
[3228] | 963 | m = mod(n, 5) |
---|
| 964 | IF ( m .ne. 0)THEN |
---|
[2931] | 965 | IF (alpha .eq. (- one))THEN |
---|
[3228] | 966 | DO i = 1, m |
---|
[2931] | 967 | x(i) = - x(i) |
---|
| 968 | ENDDO |
---|
| 969 | ELSEIF (alpha .eq. zero)THEN |
---|
[3228] | 970 | DO i = 1, m |
---|
[2931] | 971 | x(i) = zero |
---|
| 972 | ENDDO |
---|
| 973 | ELSE |
---|
[3228] | 974 | DO i = 1, m |
---|
| 975 | x(i) = alpha* x(i) |
---|
[2931] | 976 | ENDDO |
---|
| 977 | ENDIF |
---|
[3228] | 978 | IF ( n .lt. 5)RETURN |
---|
[2931] | 979 | ENDIF |
---|
| 980 | mp1 = m + 1 |
---|
| 981 | IF (alpha .eq. (- one))THEN |
---|
[3228] | 982 | DO i = mp1, n, 5 |
---|
| 983 | x(i) = - x(i) |
---|
[2931] | 984 | x(i + 1) = - x(i + 1) |
---|
| 985 | x(i + 2) = - x(i + 2) |
---|
| 986 | x(i + 3) = - x(i + 3) |
---|
| 987 | x(i + 4) = - x(i + 4) |
---|
| 988 | ENDDO |
---|
| 989 | ELSEIF (alpha .eq. zero)THEN |
---|
[3228] | 990 | DO i = mp1, n, 5 |
---|
| 991 | x(i) = zero |
---|
[2931] | 992 | x(i + 1) = zero |
---|
| 993 | x(i + 2) = zero |
---|
| 994 | x(i + 3) = zero |
---|
| 995 | x(i + 4) = zero |
---|
| 996 | ENDDO |
---|
| 997 | ELSE |
---|
[3228] | 998 | DO i = mp1, n, 5 |
---|
| 999 | x(i) = alpha* x(i) |
---|
| 1000 | x(i + 1) = alpha* x(i + 1) |
---|
| 1001 | x(i + 2) = alpha* x(i + 2) |
---|
| 1002 | x(i + 3) = alpha* x(i + 3) |
---|
| 1003 | x(i + 4) = alpha* x(i + 4) |
---|
[2931] | 1004 | ENDDO |
---|
| 1005 | ENDIF |
---|
| 1006 | |
---|
| 1007 | END SUBROUTINE wscal |
---|
| 1008 | |
---|
[3228] | 1009 | SUBROUTINE waxpy(n, alpha, x, incx, y, incy) |
---|
[2931] | 1010 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
| 1011 | ! constant times a vector plus a vector: y <- y + Alpha*x |
---|
| 1012 | ! only for incX=incY=1 |
---|
| 1013 | ! after BLAS |
---|
| 1014 | ! replace this by the function from the optimized BLAS implementation: |
---|
| 1015 | ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) |
---|
| 1016 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
| 1017 | |
---|
[3228] | 1018 | INTEGER :: i, incx, incy, m, mp1, n |
---|
| 1019 | REAL(kind=dp):: x(n), y(n), alpha |
---|
| 1020 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
---|
[2931] | 1021 | |
---|
| 1022 | IF (alpha .eq. zero)RETURN |
---|
| 1023 | IF (n .le. 0)RETURN |
---|
| 1024 | |
---|
[3228] | 1025 | m = mod(n, 4) |
---|
| 1026 | IF ( m .ne. 0)THEN |
---|
| 1027 | DO i = 1, m |
---|
| 1028 | y(i) = y(i) + alpha* x(i) |
---|
[2931] | 1029 | ENDDO |
---|
[3228] | 1030 | IF ( n .lt. 4)RETURN |
---|
[2931] | 1031 | ENDIF |
---|
| 1032 | mp1 = m + 1 |
---|
[3228] | 1033 | DO i = mp1, n, 4 |
---|
| 1034 | y(i) = y(i) + alpha* x(i) |
---|
| 1035 | y(i + 1) = y(i + 1) + alpha* x(i + 1) |
---|
| 1036 | y(i + 2) = y(i + 2) + alpha* x(i + 2) |
---|
| 1037 | y(i + 3) = y(i + 3) + alpha* x(i + 3) |
---|
[2931] | 1038 | ENDDO |
---|
| 1039 | |
---|
| 1040 | END SUBROUTINE waxpy |
---|
| 1041 | |
---|
[3228] | 1042 | SUBROUTINE rosenbrock(n, y, tstart, tend, & |
---|
| 1043 | abstol, reltol, & |
---|
| 1044 | rcntrl, icntrl, rstatus, istatus, ierr) |
---|
[2931] | 1045 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1046 | ! |
---|
| 1047 | ! Solves the system y'=F(t,y) using a Rosenbrock method defined by: |
---|
| 1048 | ! |
---|
| 1049 | ! G = 1/(H*gamma(1)) - Jac(t0,Y0) |
---|
| 1050 | ! T_i = t0 + Alpha(i)*H |
---|
| 1051 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
---|
| 1052 | ! G *K_i = Fun( T_i,Y_i)+ \sum_{j=1}^S C(i,j)/H *K_j + |
---|
| 1053 | ! gamma(i)*dF/dT(t0,Y0) |
---|
| 1054 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
---|
| 1055 | ! |
---|
| 1056 | ! For details on Rosenbrock methods and their implementation consult: |
---|
| 1057 | ! E. Hairer and G. Wanner |
---|
| 1058 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
---|
| 1059 | ! Springer series in computational mathematics,Springer-Verlag,1996. |
---|
| 1060 | ! The codes contained in the book inspired this implementation. |
---|
| 1061 | ! |
---|
| 1062 | ! (C) Adrian Sandu,August 2004 |
---|
| 1063 | ! Virginia Polytechnic Institute and State University |
---|
| 1064 | ! Contact: sandu@cs.vt.edu |
---|
| 1065 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 |
---|
| 1066 | ! This implementation is part of KPP - the Kinetic PreProcessor |
---|
| 1067 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1068 | ! |
---|
| 1069 | !~~~> input arguments: |
---|
| 1070 | ! |
---|
[3228] | 1071 | !- y(n) = vector of initial conditions (at t=tstart) |
---|
| 1072 | !- [tstart, tend] = time range of integration |
---|
[2931] | 1073 | ! (if Tstart>Tend the integration is performed backwards in time) |
---|
[3228] | 1074 | !- reltol, abstol = user precribed accuracy |
---|
| 1075 | !- SUBROUTINE fun( t, y, ydot) = ode FUNCTION, |
---|
[2931] | 1076 | ! returns Ydot = Y' = F(T,Y) |
---|
[3228] | 1077 | !- SUBROUTINE jac( t, y, jcb) = jacobian of the ode FUNCTION, |
---|
[2931] | 1078 | ! returns Jcb = dFun/dY |
---|
[3228] | 1079 | !- icntrl(1:20) = INTEGER inputs PARAMETERs |
---|
| 1080 | !- rcntrl(1:20) = REAL inputs PARAMETERs |
---|
[2931] | 1081 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1082 | ! |
---|
| 1083 | !~~~> output arguments: |
---|
| 1084 | ! |
---|
[3228] | 1085 | !- y(n) - > vector of final states (at t- >tend) |
---|
| 1086 | !- istatus(1:20) - > INTEGER output PARAMETERs |
---|
| 1087 | !- rstatus(1:20) - > REAL output PARAMETERs |
---|
| 1088 | !- ierr - > job status upon RETURN |
---|
[2931] | 1089 | ! success (positive value) or |
---|
| 1090 | ! failure (negative value) |
---|
| 1091 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1092 | ! |
---|
| 1093 | !~~~> input PARAMETERs: |
---|
| 1094 | ! |
---|
| 1095 | ! Note: For input parameters equal to zero the default values of the |
---|
| 1096 | ! corresponding variables are used. |
---|
| 1097 | ! |
---|
| 1098 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
---|
| 1099 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
---|
| 1100 | ! |
---|
| 1101 | ! ICNTRL(2) = 0: AbsTol,RelTol are N-dimensional vectors |
---|
| 1102 | ! = 1: AbsTol,RelTol are scalars |
---|
| 1103 | ! |
---|
| 1104 | ! ICNTRL(3) -> selection of a particular Rosenbrock method |
---|
| 1105 | ! = 0 : Rodas3 (default) |
---|
| 1106 | ! = 1 : Ros2 |
---|
| 1107 | ! = 2 : Ros3 |
---|
| 1108 | ! = 3 : Ros4 |
---|
| 1109 | ! = 4 : Rodas3 |
---|
| 1110 | ! = 5 : Rodas4 |
---|
| 1111 | ! |
---|
| 1112 | ! ICNTRL(4) -> maximum number of integration steps |
---|
| 1113 | ! For ICNTRL(4) =0) the default value of 100000 is used |
---|
| 1114 | ! |
---|
| 1115 | ! RCNTRL(1) -> Hmin,lower bound for the integration step size |
---|
| 1116 | ! It is strongly recommended to keep Hmin = ZERO |
---|
| 1117 | ! RCNTRL(2) -> Hmax,upper bound for the integration step size |
---|
| 1118 | ! RCNTRL(3) -> Hstart,starting value for the integration step size |
---|
| 1119 | ! |
---|
| 1120 | ! RCNTRL(4) -> FacMin,lower bound on step decrease factor (default=0.2) |
---|
| 1121 | ! RCNTRL(5) -> FacMax,upper bound on step increase factor (default=6) |
---|
| 1122 | ! RCNTRL(6) -> FacRej,step decrease factor after multiple rejections |
---|
| 1123 | ! (default=0.1) |
---|
| 1124 | ! RCNTRL(7) -> FacSafe,by which the new step is slightly smaller |
---|
| 1125 | ! than the predicted value (default=0.9) |
---|
| 1126 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1127 | ! |
---|
| 1128 | ! |
---|
| 1129 | ! OUTPUT ARGUMENTS: |
---|
| 1130 | ! ----------------- |
---|
| 1131 | ! |
---|
| 1132 | ! T -> T value for which the solution has been computed |
---|
| 1133 | ! (after successful return T=Tend). |
---|
| 1134 | ! |
---|
| 1135 | ! Y(N) -> Numerical solution at T |
---|
| 1136 | ! |
---|
| 1137 | ! IDID -> Reports on successfulness upon return: |
---|
| 1138 | ! = 1 for success |
---|
| 1139 | ! < 0 for error (value equals error code) |
---|
| 1140 | ! |
---|
| 1141 | ! ISTATUS(1) -> No. of function calls |
---|
| 1142 | ! ISTATUS(2) -> No. of jacobian calls |
---|
| 1143 | ! ISTATUS(3) -> No. of steps |
---|
| 1144 | ! ISTATUS(4) -> No. of accepted steps |
---|
| 1145 | ! ISTATUS(5) -> No. of rejected steps (except at very beginning) |
---|
| 1146 | ! ISTATUS(6) -> No. of LU decompositions |
---|
| 1147 | ! ISTATUS(7) -> No. of forward/backward substitutions |
---|
| 1148 | ! ISTATUS(8) -> No. of singular matrix decompositions |
---|
| 1149 | ! |
---|
| 1150 | ! RSTATUS(1) -> Texit,the time corresponding to the |
---|
| 1151 | ! computed Y upon return |
---|
| 1152 | ! RSTATUS(2) -> Hexit,last accepted step before exit |
---|
| 1153 | ! RSTATUS(3) -> Hnew,last predicted step (not yet taken) |
---|
| 1154 | ! For multiple restarts,use Hnew as Hstart |
---|
| 1155 | ! in the subsequent run |
---|
| 1156 | ! |
---|
| 1157 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1158 | |
---|
| 1159 | |
---|
| 1160 | !~~~> arguments |
---|
[3228] | 1161 | INTEGER, INTENT(IN) :: n |
---|
| 1162 | REAL(kind=dp), INTENT(INOUT):: y(n) |
---|
| 1163 | REAL(kind=dp), INTENT(IN) :: tstart, tend |
---|
| 1164 | REAL(kind=dp), INTENT(IN) :: abstol(n), reltol(n) |
---|
| 1165 | INTEGER, INTENT(IN) :: icntrl(20) |
---|
| 1166 | REAL(kind=dp), INTENT(IN) :: rcntrl(20) |
---|
| 1167 | INTEGER, INTENT(INOUT):: istatus(20) |
---|
| 1168 | REAL(kind=dp), INTENT(INOUT):: rstatus(20) |
---|
| 1169 | INTEGER, INTENT(OUT) :: ierr |
---|
| 1170 | !~~~> PARAMETERs of the rosenbrock method, up to 6 stages |
---|
| 1171 | INTEGER :: ros_s, rosmethod |
---|
| 1172 | INTEGER, PARAMETER :: rs2=1, rs3=2, rs4=3, rd3=4, rd4=5, rg3=6 |
---|
| 1173 | REAL(kind=dp):: ros_a(15), ros_c(15), ros_m(6), ros_e(6), & |
---|
| 1174 | ros_alpha(6), ros_gamma(6), ros_elo |
---|
[2931] | 1175 | LOGICAL :: ros_newf(6) |
---|
| 1176 | CHARACTER(len=12):: ros_name |
---|
| 1177 | !~~~> local variables |
---|
[3228] | 1178 | REAL(kind=dp):: roundoff, facmin, facmax, facrej, facsafe |
---|
| 1179 | REAL(kind=dp):: hmin, hmax, hstart |
---|
[2931] | 1180 | REAL(kind=dp):: texit |
---|
[3228] | 1181 | INTEGER :: i, uplimtol, max_no_steps |
---|
| 1182 | LOGICAL :: autonomous, vectortol |
---|
[2931] | 1183 | !~~~> PARAMETERs |
---|
[3228] | 1184 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
---|
| 1185 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
---|
[2931] | 1186 | |
---|
| 1187 | !~~~> initialize statistics |
---|
| 1188 | istatus(1:8) = 0 |
---|
| 1189 | rstatus(1:3) = zero |
---|
| 1190 | |
---|
| 1191 | !~~~> autonomous or time dependent ode. default is time dependent. |
---|
| 1192 | autonomous = .not.(icntrl(1) == 0) |
---|
| 1193 | |
---|
| 1194 | !~~~> for scalar tolerances (icntrl(2).ne.0) the code uses abstol(1)and reltol(1) |
---|
| 1195 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:N) and RelTol(1:N) |
---|
| 1196 | IF (icntrl(2) == 0)THEN |
---|
[3228] | 1197 | vectortol = .TRUE. |
---|
[2931] | 1198 | uplimtol = n |
---|
| 1199 | ELSE |
---|
[3228] | 1200 | vectortol = .FALSE. |
---|
[2931] | 1201 | uplimtol = 1 |
---|
| 1202 | ENDIF |
---|
| 1203 | |
---|
| 1204 | !~~~> initialize the particular rosenbrock method selected |
---|
| 1205 | select CASE (icntrl(3)) |
---|
| 1206 | CASE (1) |
---|
| 1207 | CALL ros2 |
---|
| 1208 | CASE (2) |
---|
| 1209 | CALL ros3 |
---|
| 1210 | CASE (3) |
---|
| 1211 | CALL ros4 |
---|
[3228] | 1212 | CASE (0, 4) |
---|
[2931] | 1213 | CALL rodas3 |
---|
| 1214 | CASE (5) |
---|
| 1215 | CALL rodas4 |
---|
| 1216 | CASE (6) |
---|
| 1217 | CALL rang3 |
---|
| 1218 | CASE default |
---|
| 1219 | PRINT *,'Unknown Rosenbrock method: ICNTRL(3) =',ICNTRL(3) |
---|
[3228] | 1220 | CALL ros_errormsg(- 2, tstart, zero, ierr) |
---|
[2931] | 1221 | RETURN |
---|
| 1222 | END select |
---|
| 1223 | |
---|
| 1224 | !~~~> the maximum number of steps admitted |
---|
| 1225 | IF (icntrl(4) == 0)THEN |
---|
| 1226 | max_no_steps = 200000 |
---|
| 1227 | ELSEIF (icntrl(4)> 0)THEN |
---|
| 1228 | max_no_steps=icntrl(4) |
---|
| 1229 | ELSE |
---|
| 1230 | PRINT *,'User-selected max no. of steps: ICNTRL(4) =',ICNTRL(4) |
---|
[3228] | 1231 | CALL ros_errormsg(- 1, tstart, zero, ierr) |
---|
[2931] | 1232 | RETURN |
---|
| 1233 | ENDIF |
---|
| 1234 | |
---|
| 1235 | !~~~> unit roundoff (1+ roundoff>1) |
---|
[3228] | 1236 | roundoff = epsilon(one) |
---|
[2931] | 1237 | |
---|
| 1238 | !~~~> lower bound on the step size: (positive value) |
---|
| 1239 | IF (rcntrl(1) == zero)THEN |
---|
| 1240 | hmin = zero |
---|
| 1241 | ELSEIF (rcntrl(1)> zero)THEN |
---|
| 1242 | hmin = rcntrl(1) |
---|
| 1243 | ELSE |
---|
| 1244 | PRINT *,'User-selected Hmin: RCNTRL(1) =',RCNTRL(1) |
---|
[3228] | 1245 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
[2931] | 1246 | RETURN |
---|
| 1247 | ENDIF |
---|
| 1248 | !~~~> upper bound on the step size: (positive value) |
---|
| 1249 | IF (rcntrl(2) == zero)THEN |
---|
| 1250 | hmax = abs(tend-tstart) |
---|
| 1251 | ELSEIF (rcntrl(2)> zero)THEN |
---|
[3228] | 1252 | hmax = min(abs(rcntrl(2)), abs(tend-tstart)) |
---|
[2931] | 1253 | ELSE |
---|
| 1254 | PRINT *,'User-selected Hmax: RCNTRL(2) =',RCNTRL(2) |
---|
[3228] | 1255 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
[2931] | 1256 | RETURN |
---|
| 1257 | ENDIF |
---|
| 1258 | !~~~> starting step size: (positive value) |
---|
| 1259 | IF (rcntrl(3) == zero)THEN |
---|
[3228] | 1260 | hstart = max(hmin, deltamin) |
---|
[2931] | 1261 | ELSEIF (rcntrl(3)> zero)THEN |
---|
[3228] | 1262 | hstart = min(abs(rcntrl(3)), abs(tend-tstart)) |
---|
[2931] | 1263 | ELSE |
---|
| 1264 | PRINT *,'User-selected Hstart: RCNTRL(3) =',RCNTRL(3) |
---|
[3228] | 1265 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
[2931] | 1266 | RETURN |
---|
| 1267 | ENDIF |
---|
| 1268 | !~~~> step size can be changed s.t. facmin < hnew/hold < facmax |
---|
| 1269 | IF (rcntrl(4) == zero)THEN |
---|
| 1270 | facmin = 0.2_dp |
---|
| 1271 | ELSEIF (rcntrl(4)> zero)THEN |
---|
| 1272 | facmin = rcntrl(4) |
---|
| 1273 | ELSE |
---|
| 1274 | PRINT *,'User-selected FacMin: RCNTRL(4) =',RCNTRL(4) |
---|
[3228] | 1275 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
[2931] | 1276 | RETURN |
---|
| 1277 | ENDIF |
---|
| 1278 | IF (rcntrl(5) == zero)THEN |
---|
| 1279 | facmax = 6.0_dp |
---|
| 1280 | ELSEIF (rcntrl(5)> zero)THEN |
---|
| 1281 | facmax = rcntrl(5) |
---|
| 1282 | ELSE |
---|
| 1283 | PRINT *,'User-selected FacMax: RCNTRL(5) =',RCNTRL(5) |
---|
[3228] | 1284 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
[2931] | 1285 | RETURN |
---|
| 1286 | ENDIF |
---|
| 1287 | !~~~> facrej: factor to decrease step after 2 succesive rejections |
---|
| 1288 | IF (rcntrl(6) == zero)THEN |
---|
| 1289 | facrej = 0.1_dp |
---|
| 1290 | ELSEIF (rcntrl(6)> zero)THEN |
---|
| 1291 | facrej = rcntrl(6) |
---|
| 1292 | ELSE |
---|
| 1293 | PRINT *,'User-selected FacRej: RCNTRL(6) =',RCNTRL(6) |
---|
[3228] | 1294 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
[2931] | 1295 | RETURN |
---|
| 1296 | ENDIF |
---|
| 1297 | !~~~> facsafe: safety factor in the computation of new step size |
---|
| 1298 | IF (rcntrl(7) == zero)THEN |
---|
| 1299 | facsafe = 0.9_dp |
---|
| 1300 | ELSEIF (rcntrl(7)> zero)THEN |
---|
| 1301 | facsafe = rcntrl(7) |
---|
| 1302 | ELSE |
---|
| 1303 | PRINT *,'User-selected FacSafe: RCNTRL(7) =',RCNTRL(7) |
---|
[3228] | 1304 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
[2931] | 1305 | RETURN |
---|
| 1306 | ENDIF |
---|
| 1307 | !~~~> check IF tolerances are reasonable |
---|
[3228] | 1308 | DO i=1, uplimtol |
---|
| 1309 | IF ((abstol(i)<= zero).or. (reltol(i)<= 10.0_dp* roundoff)& |
---|
[2931] | 1310 | .or. (reltol(i)>= 1.0_dp))THEN |
---|
| 1311 | PRINT *,' AbsTol(',i,') = ',AbsTol(i) |
---|
| 1312 | PRINT *,' RelTol(',i,') = ',RelTol(i) |
---|
[3228] | 1313 | CALL ros_errormsg(- 5, tstart, zero, ierr) |
---|
[2931] | 1314 | RETURN |
---|
| 1315 | ENDIF |
---|
| 1316 | ENDDO |
---|
| 1317 | |
---|
| 1318 | |
---|
| 1319 | !~~~> CALL rosenbrock method |
---|
[3228] | 1320 | CALL ros_integrator(y, tstart, tend, texit, & |
---|
| 1321 | abstol, reltol, & |
---|
[2931] | 1322 | ! Integration parameters |
---|
[3228] | 1323 | autonomous, vectortol, max_no_steps, & |
---|
| 1324 | roundoff, hmin, hmax, hstart, & |
---|
| 1325 | facmin, facmax, facrej, facsafe, & |
---|
[2931] | 1326 | ! Error indicator |
---|
| 1327 | ierr) |
---|
| 1328 | |
---|
| 1329 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1330 | CONTAINS ! SUBROUTINEs internal to rosenbrock |
---|
| 1331 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1332 | |
---|
| 1333 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1334 | SUBROUTINE ros_errormsg(code, t, h, ierr) |
---|
[2931] | 1335 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1336 | ! Handles all error messages |
---|
| 1337 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1338 | |
---|
[3228] | 1339 | REAL(kind=dp), INTENT(IN):: t, h |
---|
| 1340 | INTEGER, INTENT(IN) :: code |
---|
| 1341 | INTEGER, INTENT(OUT):: ierr |
---|
[2931] | 1342 | |
---|
| 1343 | ierr = code |
---|
[3228] | 1344 | print * , & |
---|
[2931] | 1345 | 'Forced exit from Rosenbrock due to the following error:' |
---|
| 1346 | |
---|
| 1347 | select CASE (code) |
---|
[3228] | 1348 | CASE (- 1) |
---|
[2931] | 1349 | PRINT *,'--> Improper value for maximal no of steps' |
---|
[3228] | 1350 | CASE (- 2) |
---|
[2931] | 1351 | PRINT *,'--> Selected Rosenbrock method not implemented' |
---|
[3228] | 1352 | CASE (- 3) |
---|
[2931] | 1353 | PRINT *,'--> Hmin/Hmax/Hstart must be positive' |
---|
[3228] | 1354 | CASE (- 4) |
---|
[2931] | 1355 | PRINT *,'--> FacMin/FacMax/FacRej must be positive' |
---|
| 1356 | CASE (- 5) |
---|
| 1357 | PRINT *,'--> Improper tolerance values' |
---|
| 1358 | CASE (- 6) |
---|
| 1359 | PRINT *,'--> No of steps exceeds maximum bound' |
---|
| 1360 | CASE (- 7) |
---|
| 1361 | PRINT *,'--> Step size too small: T + 10*H = T',& |
---|
| 1362 | ' or H < Roundoff' |
---|
[3228] | 1363 | CASE (- 8) |
---|
[2931] | 1364 | PRINT *,'--> Matrix is repeatedly singular' |
---|
| 1365 | CASE default |
---|
| 1366 | PRINT *,'Unknown Error code: ',Code |
---|
| 1367 | END select |
---|
| 1368 | |
---|
[3228] | 1369 | print * , "t=", t, "and h=", h |
---|
[2931] | 1370 | |
---|
| 1371 | END SUBROUTINE ros_errormsg |
---|
| 1372 | |
---|
| 1373 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1374 | SUBROUTINE ros_integrator (y, tstart, tend, t, & |
---|
| 1375 | abstol, reltol, & |
---|
[2931] | 1376 | !~~~> integration PARAMETERs |
---|
[3228] | 1377 | autonomous, vectortol, max_no_steps, & |
---|
| 1378 | roundoff, hmin, hmax, hstart, & |
---|
| 1379 | facmin, facmax, facrej, facsafe, & |
---|
[2931] | 1380 | !~~~> error indicator |
---|
| 1381 | ierr) |
---|
| 1382 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1383 | ! Template for the implementation of a generic Rosenbrock method |
---|
| 1384 | ! defined by ros_S (no of stages) |
---|
| 1385 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
| 1386 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1387 | |
---|
| 1388 | |
---|
| 1389 | !~~~> input: the initial condition at tstart; output: the solution at t |
---|
[3228] | 1390 | REAL(kind=dp), INTENT(INOUT):: y(n) |
---|
[2931] | 1391 | !~~~> input: integration interval |
---|
[3228] | 1392 | REAL(kind=dp), INTENT(IN):: tstart, tend |
---|
| 1393 | !~~~> output: time at which the solution is RETURNed (t=tendIF success) |
---|
| 1394 | REAL(kind=dp), INTENT(OUT):: t |
---|
[2931] | 1395 | !~~~> input: tolerances |
---|
[3228] | 1396 | REAL(kind=dp), INTENT(IN):: abstol(n), reltol(n) |
---|
[2931] | 1397 | !~~~> input: integration PARAMETERs |
---|
[3228] | 1398 | LOGICAL, INTENT(IN):: autonomous, vectortol |
---|
| 1399 | REAL(kind=dp), INTENT(IN):: hstart, hmin, hmax |
---|
| 1400 | INTEGER, INTENT(IN):: max_no_steps |
---|
| 1401 | REAL(kind=dp), INTENT(IN):: roundoff, facmin, facmax, facrej, facsafe |
---|
[2931] | 1402 | !~~~> output: error indicator |
---|
[3228] | 1403 | INTEGER, INTENT(OUT):: ierr |
---|
[2931] | 1404 | ! ~~~~ Local variables |
---|
[3228] | 1405 | REAL(kind=dp):: ynew(n), fcn0(n), fcn(n) |
---|
| 1406 | REAL(kind=dp):: k(n* ros_s), dfdt(n) |
---|
[2931] | 1407 | #ifdef full_algebra |
---|
[3228] | 1408 | REAL(kind=dp):: jac0(n, n), ghimj(n, n) |
---|
[2931] | 1409 | #else |
---|
[3228] | 1410 | REAL(kind=dp):: jac0(lu_nonzero), ghimj(lu_nonzero) |
---|
[2931] | 1411 | #endif |
---|
[3228] | 1412 | REAL(kind=dp):: h, hnew, hc, hg, fac, tau |
---|
| 1413 | REAL(kind=dp):: err, yerr(n) |
---|
| 1414 | INTEGER :: pivot(n), direction, ioffset, j, istage |
---|
| 1415 | LOGICAL :: rejectlasth, rejectmoreh, singular |
---|
[2931] | 1416 | !~~~> local PARAMETERs |
---|
[3228] | 1417 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
---|
| 1418 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
---|
[2931] | 1419 | !~~~> locally called FUNCTIONs |
---|
| 1420 | ! REAL(kind=dp) WLAMCH |
---|
| 1421 | ! EXTERNAL WLAMCH |
---|
| 1422 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1423 | |
---|
| 1424 | |
---|
| 1425 | !~~~> initial preparations |
---|
| 1426 | t = tstart |
---|
| 1427 | rstatus(nhexit) = zero |
---|
[3228] | 1428 | h = min( max(abs(hmin), abs(hstart)), abs(hmax)) |
---|
| 1429 | IF (abs(h)<= 10.0_dp* roundoff)h = deltamin |
---|
[2931] | 1430 | |
---|
[3228] | 1431 | IF (tend >= tstart)THEN |
---|
[2931] | 1432 | direction = + 1 |
---|
| 1433 | ELSE |
---|
| 1434 | direction = - 1 |
---|
| 1435 | ENDIF |
---|
[3228] | 1436 | h = direction* h |
---|
[2931] | 1437 | |
---|
[3228] | 1438 | rejectlasth=.FALSE. |
---|
| 1439 | rejectmoreh=.FALSE. |
---|
[2931] | 1440 | |
---|
| 1441 | !~~~> time loop begins below |
---|
| 1442 | |
---|
[3228] | 1443 | timeloop: DO WHILE((direction > 0).and.((t- tend) + roundoff <= zero)& |
---|
| 1444 | .or. (direction < 0).and.((tend-t) + roundoff <= zero)) |
---|
[2931] | 1445 | |
---|
[3228] | 1446 | IF (istatus(nstp)> max_no_steps)THEN ! too many steps |
---|
| 1447 | CALL ros_errormsg(- 6, t, h, ierr) |
---|
[2931] | 1448 | RETURN |
---|
| 1449 | ENDIF |
---|
[3228] | 1450 | IF (((t+ 0.1_dp* h) == t).or.(h <= roundoff))THEN ! step size too small |
---|
| 1451 | CALL ros_errormsg(- 7, t, h, ierr) |
---|
[2931] | 1452 | RETURN |
---|
| 1453 | ENDIF |
---|
| 1454 | |
---|
| 1455 | !~~~> limit h IF necessary to avoid going beyond tend |
---|
[3228] | 1456 | h = min(h, abs(tend-t)) |
---|
[2931] | 1457 | |
---|
| 1458 | !~~~> compute the FUNCTION at current time |
---|
[3228] | 1459 | CALL funtemplate(t, y, fcn0) |
---|
| 1460 | istatus(nfun) = istatus(nfun) + 1 |
---|
[2931] | 1461 | |
---|
| 1462 | !~~~> compute the FUNCTION derivative with respect to t |
---|
| 1463 | IF (.not.autonomous)THEN |
---|
[3228] | 1464 | CALL ros_funtimederivative(t, roundoff, y, & |
---|
| 1465 | fcn0, dfdt) |
---|
[2931] | 1466 | ENDIF |
---|
| 1467 | |
---|
| 1468 | !~~~> compute the jacobian at current time |
---|
[3228] | 1469 | CALL jactemplate(t, y, jac0) |
---|
| 1470 | istatus(njac) = istatus(njac) + 1 |
---|
[2931] | 1471 | |
---|
| 1472 | !~~~> repeat step calculation until current step accepted |
---|
| 1473 | untilaccepted: do |
---|
| 1474 | |
---|
[3228] | 1475 | CALL ros_preparematrix(h, direction, ros_gamma(1), & |
---|
| 1476 | jac0, ghimj, pivot, singular) |
---|
[2931] | 1477 | IF (singular)THEN ! more than 5 consecutive failed decompositions |
---|
[3228] | 1478 | CALL ros_errormsg(- 8, t, h, ierr) |
---|
[2931] | 1479 | RETURN |
---|
| 1480 | ENDIF |
---|
| 1481 | |
---|
| 1482 | !~~~> compute the stages |
---|
[3228] | 1483 | stage: DO istage = 1, ros_s |
---|
[2931] | 1484 | |
---|
| 1485 | ! current istage offset. current istage vector is k(ioffset+ 1:ioffset+ n) |
---|
[3228] | 1486 | ioffset = n* (istage-1) |
---|
[2931] | 1487 | |
---|
| 1488 | ! for the 1st istage the FUNCTION has been computed previously |
---|
[3228] | 1489 | IF (istage == 1)THEN |
---|
| 1490 | !slim: CALL wcopy(n, fcn0, 1, fcn, 1) |
---|
[3249] | 1491 | fcn(1:n) = fcn0(1:n) |
---|
[2931] | 1492 | ! istage>1 and a new FUNCTION evaluation is needed at the current istage |
---|
| 1493 | ELSEIF(ros_newf(istage))THEN |
---|
[3228] | 1494 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
---|
[3249] | 1495 | ynew(1:n) = y(1:n) |
---|
[3228] | 1496 | DO j = 1, istage-1 |
---|
| 1497 | CALL waxpy(n, ros_a((istage-1) * (istage-2) /2+ j), & |
---|
| 1498 | k(n* (j- 1) + 1), 1, ynew, 1) |
---|
[2931] | 1499 | ENDDO |
---|
[3228] | 1500 | tau = t + ros_alpha(istage) * direction* h |
---|
| 1501 | CALL funtemplate(tau, ynew, fcn) |
---|
| 1502 | istatus(nfun) = istatus(nfun) + 1 |
---|
[2931] | 1503 | ENDIF ! IF istage == 1 ELSEIF ros_newf(istage) |
---|
[3228] | 1504 | !slim: CALL wcopy(n, fcn, 1, k(ioffset+ 1), 1) |
---|
[2931] | 1505 | k(ioffset+ 1:ioffset+ n) = fcn(1:n) |
---|
[3228] | 1506 | DO j = 1, istage-1 |
---|
| 1507 | hc = ros_c((istage-1) * (istage-2) /2+ j) /(direction* h) |
---|
| 1508 | CALL waxpy(n, hc, k(n* (j- 1) + 1), 1, k(ioffset+ 1), 1) |
---|
[2931] | 1509 | ENDDO |
---|
| 1510 | IF ((.not. autonomous).and.(ros_gamma(istage).ne.zero))THEN |
---|
[3228] | 1511 | hg = direction* h* ros_gamma(istage) |
---|
| 1512 | CALL waxpy(n, hg, dfdt, 1, k(ioffset+ 1), 1) |
---|
[2931] | 1513 | ENDIF |
---|
[3228] | 1514 | CALL ros_solve(ghimj, pivot, k(ioffset+ 1)) |
---|
[2931] | 1515 | |
---|
| 1516 | END DO stage |
---|
| 1517 | |
---|
| 1518 | |
---|
| 1519 | !~~~> compute the new solution |
---|
[3228] | 1520 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
---|
[2931] | 1521 | ynew(1:n) = y(1:n) |
---|
[3228] | 1522 | DO j=1, ros_s |
---|
| 1523 | CALL waxpy(n, ros_m(j), k(n* (j- 1) + 1), 1, ynew, 1) |
---|
[2931] | 1524 | ENDDO |
---|
| 1525 | |
---|
| 1526 | !~~~> compute the error estimation |
---|
[3228] | 1527 | !slim: CALL wscal(n, zero, yerr, 1) |
---|
[2931] | 1528 | yerr(1:n) = zero |
---|
[3228] | 1529 | DO j=1, ros_s |
---|
| 1530 | CALL waxpy(n, ros_e(j), k(n* (j- 1) + 1), 1, yerr, 1) |
---|
[2931] | 1531 | ENDDO |
---|
[3228] | 1532 | err = ros_errornorm(y, ynew, yerr, abstol, reltol, vectortol) |
---|
[2931] | 1533 | |
---|
| 1534 | !~~~> new step size is bounded by facmin <= hnew/h <= facmax |
---|
[3228] | 1535 | fac = min(facmax, max(facmin, facsafe/err** (one/ros_elo))) |
---|
| 1536 | hnew = h* fac |
---|
[2931] | 1537 | |
---|
| 1538 | !~~~> check the error magnitude and adjust step size |
---|
[3228] | 1539 | istatus(nstp) = istatus(nstp) + 1 |
---|
| 1540 | IF ((err <= one).or.(h <= hmin))THEN !~~~> accept step |
---|
| 1541 | istatus(nacc) = istatus(nacc) + 1 |
---|
| 1542 | !slim: CALL wcopy(n, ynew, 1, y, 1) |
---|
[2931] | 1543 | y(1:n) = ynew(1:n) |
---|
[3228] | 1544 | t = t + direction* h |
---|
| 1545 | hnew = max(hmin, min(hnew, hmax)) |
---|
[2931] | 1546 | IF (rejectlasth)THEN ! no step size increase after a rejected step |
---|
[3228] | 1547 | hnew = min(hnew, h) |
---|
[2931] | 1548 | ENDIF |
---|
| 1549 | rstatus(nhexit) = h |
---|
| 1550 | rstatus(nhnew) = hnew |
---|
| 1551 | rstatus(ntexit) = t |
---|
[3228] | 1552 | rejectlasth = .FALSE. |
---|
| 1553 | rejectmoreh = .FALSE. |
---|
[2931] | 1554 | h = hnew |
---|
| 1555 | exit untilaccepted ! exit the loop: WHILE step not accepted |
---|
| 1556 | ELSE !~~~> reject step |
---|
| 1557 | IF (rejectmoreh)THEN |
---|
[3228] | 1558 | hnew = h* facrej |
---|
[2931] | 1559 | ENDIF |
---|
| 1560 | rejectmoreh = rejectlasth |
---|
[3228] | 1561 | rejectlasth = .TRUE. |
---|
[2931] | 1562 | h = hnew |
---|
[3228] | 1563 | IF (istatus(nacc)>= 1) istatus(nrej) = istatus(nrej) + 1 |
---|
[2931] | 1564 | ENDIF ! err <= 1 |
---|
| 1565 | |
---|
| 1566 | END DO untilaccepted |
---|
| 1567 | |
---|
| 1568 | END DO timeloop |
---|
| 1569 | |
---|
| 1570 | !~~~> succesful exit |
---|
| 1571 | ierr = 1 !~~~> the integration was successful |
---|
| 1572 | |
---|
| 1573 | END SUBROUTINE ros_integrator |
---|
| 1574 | |
---|
| 1575 | |
---|
| 1576 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1577 | REAL(kind=dp)FUNCTION ros_errornorm(y, ynew, yerr, & |
---|
| 1578 | abstol, reltol, vectortol) |
---|
[2931] | 1579 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1580 | !~~~> computes the "scaled norm" of the error vector yerr |
---|
| 1581 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1582 | |
---|
| 1583 | ! Input arguments |
---|
[3228] | 1584 | REAL(kind=dp), INTENT(IN):: y(n), ynew(n), & |
---|
| 1585 | yerr(n), abstol(n), reltol(n) |
---|
| 1586 | LOGICAL, INTENT(IN):: vectortol |
---|
[2931] | 1587 | ! Local variables |
---|
[3228] | 1588 | REAL(kind=dp):: err, scale, ymax |
---|
[2931] | 1589 | INTEGER :: i |
---|
[3228] | 1590 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
---|
[2931] | 1591 | |
---|
| 1592 | err = zero |
---|
[3228] | 1593 | DO i=1, n |
---|
| 1594 | ymax = max(abs(y(i)), abs(ynew(i))) |
---|
[2931] | 1595 | IF (vectortol)THEN |
---|
[3228] | 1596 | scale = abstol(i) + reltol(i) * ymax |
---|
[2931] | 1597 | ELSE |
---|
[3228] | 1598 | scale = abstol(1) + reltol(1) * ymax |
---|
[2931] | 1599 | ENDIF |
---|
[3228] | 1600 | err = err+ (yerr(i) /scale) ** 2 |
---|
[2931] | 1601 | ENDDO |
---|
| 1602 | err = sqrt(err/n) |
---|
| 1603 | |
---|
[3228] | 1604 | ros_errornorm = max(err, 1.0d-10) |
---|
[2931] | 1605 | |
---|
| 1606 | END FUNCTION ros_errornorm |
---|
| 1607 | |
---|
| 1608 | |
---|
| 1609 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1610 | SUBROUTINE ros_funtimederivative(t, roundoff, y, & |
---|
| 1611 | fcn0, dfdt) |
---|
[2931] | 1612 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1613 | !~~~> the time partial derivative of the FUNCTION by finite differences |
---|
| 1614 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1615 | |
---|
| 1616 | !~~~> input arguments |
---|
[3228] | 1617 | REAL(kind=dp), INTENT(IN):: t, roundoff, y(n), fcn0(n) |
---|
[2931] | 1618 | !~~~> output arguments |
---|
[3228] | 1619 | REAL(kind=dp), INTENT(OUT):: dfdt(n) |
---|
[2931] | 1620 | !~~~> local variables |
---|
| 1621 | REAL(kind=dp):: delta |
---|
[3228] | 1622 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, deltamin = 1.0e-6_dp |
---|
[2931] | 1623 | |
---|
[3228] | 1624 | delta = sqrt(roundoff) * max(deltamin, abs(t)) |
---|
| 1625 | CALL funtemplate(t+ delta, y, dfdt) |
---|
| 1626 | istatus(nfun) = istatus(nfun) + 1 |
---|
| 1627 | CALL waxpy(n, (- one), fcn0, 1, dfdt, 1) |
---|
| 1628 | CALL wscal(n, (one/delta), dfdt, 1) |
---|
[2931] | 1629 | |
---|
| 1630 | END SUBROUTINE ros_funtimederivative |
---|
| 1631 | |
---|
| 1632 | |
---|
| 1633 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1634 | SUBROUTINE ros_preparematrix(h, direction, gam, & |
---|
| 1635 | jac0, ghimj, pivot, singular) |
---|
[2931] | 1636 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
| 1637 | ! Prepares the LHS matrix for stage calculations |
---|
| 1638 | ! 1. Construct Ghimj = 1/(H*ham) - Jac0 |
---|
| 1639 | ! "(Gamma H) Inverse Minus Jacobian" |
---|
| 1640 | ! 2. Repeat LU decomposition of Ghimj until successful. |
---|
| 1641 | ! -half the step size if LU decomposition fails and retry |
---|
| 1642 | ! -exit after 5 consecutive fails |
---|
| 1643 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
| 1644 | |
---|
| 1645 | !~~~> input arguments |
---|
| 1646 | #ifdef full_algebra |
---|
[3228] | 1647 | REAL(kind=dp), INTENT(IN):: jac0(n, n) |
---|
[2931] | 1648 | #else |
---|
[3228] | 1649 | REAL(kind=dp), INTENT(IN):: jac0(lu_nonzero) |
---|
[2931] | 1650 | #endif |
---|
[3228] | 1651 | REAL(kind=dp), INTENT(IN):: gam |
---|
| 1652 | INTEGER, INTENT(IN):: direction |
---|
[2931] | 1653 | !~~~> output arguments |
---|
| 1654 | #ifdef full_algebra |
---|
[3228] | 1655 | REAL(kind=dp), INTENT(OUT):: ghimj(n, n) |
---|
[2931] | 1656 | #else |
---|
[3228] | 1657 | REAL(kind=dp), INTENT(OUT):: ghimj(lu_nonzero) |
---|
[2931] | 1658 | #endif |
---|
[3228] | 1659 | LOGICAL, INTENT(OUT):: singular |
---|
| 1660 | INTEGER, INTENT(OUT):: pivot(n) |
---|
[2931] | 1661 | !~~~> inout arguments |
---|
[3228] | 1662 | REAL(kind=dp), INTENT(INOUT):: h ! step size is decreased when lu fails |
---|
[2931] | 1663 | !~~~> local variables |
---|
[3228] | 1664 | INTEGER :: i, ising, nconsecutive |
---|
[2931] | 1665 | REAL(kind=dp):: ghinv |
---|
[3228] | 1666 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, half = 0.5_dp |
---|
[2931] | 1667 | |
---|
| 1668 | nconsecutive = 0 |
---|
[3228] | 1669 | singular = .TRUE. |
---|
[2931] | 1670 | |
---|
| 1671 | DO WHILE (singular) |
---|
| 1672 | |
---|
[3228] | 1673 | !~~~> construct ghimj = 1/(h* gam) - jac0 |
---|
[2931] | 1674 | #ifdef full_algebra |
---|
[3228] | 1675 | !slim: CALL wcopy(n* n, jac0, 1, ghimj, 1) |
---|
| 1676 | !slim: CALL wscal(n* n, (- one), ghimj, 1) |
---|
[2931] | 1677 | ghimj = - jac0 |
---|
[3228] | 1678 | ghinv = one/(direction* h* gam) |
---|
| 1679 | DO i=1, n |
---|
| 1680 | ghimj(i, i) = ghimj(i, i) + ghinv |
---|
[2931] | 1681 | ENDDO |
---|
| 1682 | #else |
---|
[3228] | 1683 | !slim: CALL wcopy(lu_nonzero, jac0, 1, ghimj, 1) |
---|
| 1684 | !slim: CALL wscal(lu_nonzero, (- one), ghimj, 1) |
---|
[2931] | 1685 | ghimj(1:lu_nonzero) = - jac0(1:lu_nonzero) |
---|
[3228] | 1686 | ghinv = one/(direction* h* gam) |
---|
| 1687 | DO i=1, n |
---|
| 1688 | ghimj(lu_diag(i)) = ghimj(lu_diag(i)) + ghinv |
---|
[2931] | 1689 | ENDDO |
---|
| 1690 | #endif |
---|
| 1691 | !~~~> compute lu decomposition |
---|
[3228] | 1692 | CALL ros_decomp( ghimj, pivot, ising) |
---|
[2931] | 1693 | IF (ising == 0)THEN |
---|
| 1694 | !~~~> IF successful done |
---|
[3228] | 1695 | singular = .FALSE. |
---|
[2931] | 1696 | ELSE ! ising .ne. 0 |
---|
| 1697 | !~~~> IF unsuccessful half the step size; IF 5 consecutive fails THEN RETURN |
---|
[3228] | 1698 | istatus(nsng) = istatus(nsng) + 1 |
---|
[2931] | 1699 | nconsecutive = nconsecutive+1 |
---|
[3228] | 1700 | singular = .TRUE. |
---|
[2931] | 1701 | PRINT*,'Warning: LU Decomposition returned ISING = ',ISING |
---|
| 1702 | IF (nconsecutive <= 5)THEN ! less than 5 consecutive failed decompositions |
---|
[3228] | 1703 | h = h* half |
---|
[2931] | 1704 | ELSE ! more than 5 consecutive failed decompositions |
---|
| 1705 | RETURN |
---|
| 1706 | ENDIF ! nconsecutive |
---|
| 1707 | ENDIF ! ising |
---|
| 1708 | |
---|
| 1709 | END DO ! WHILE singular |
---|
| 1710 | |
---|
| 1711 | END SUBROUTINE ros_preparematrix |
---|
| 1712 | |
---|
| 1713 | |
---|
| 1714 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1715 | SUBROUTINE ros_decomp( a, pivot, ising) |
---|
[2931] | 1716 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1717 | ! Template for the LU decomposition |
---|
| 1718 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1719 | !~~~> inout variables |
---|
| 1720 | #ifdef full_algebra |
---|
[3228] | 1721 | REAL(kind=dp), INTENT(INOUT):: a(n, n) |
---|
[2931] | 1722 | #else |
---|
[3228] | 1723 | REAL(kind=dp), INTENT(INOUT):: a(lu_nonzero) |
---|
[2931] | 1724 | #endif |
---|
| 1725 | !~~~> output variables |
---|
[3228] | 1726 | INTEGER, INTENT(OUT):: pivot(n), ising |
---|
[2931] | 1727 | |
---|
| 1728 | #ifdef full_algebra |
---|
[3228] | 1729 | CALL dgetrf( n, n, a, n, pivot, ising) |
---|
[2931] | 1730 | #else |
---|
[3228] | 1731 | CALL kppdecomp(a, ising) |
---|
[2931] | 1732 | pivot(1) = 1 |
---|
| 1733 | #endif |
---|
[3228] | 1734 | istatus(ndec) = istatus(ndec) + 1 |
---|
[2931] | 1735 | |
---|
| 1736 | END SUBROUTINE ros_decomp |
---|
| 1737 | |
---|
| 1738 | |
---|
| 1739 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
[3228] | 1740 | SUBROUTINE ros_solve( a, pivot, b) |
---|
[2931] | 1741 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1742 | ! Template for the forward/backward substitution (using pre-computed LU decomposition) |
---|
| 1743 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1744 | !~~~> input variables |
---|
| 1745 | #ifdef full_algebra |
---|
[3228] | 1746 | REAL(kind=dp), INTENT(IN):: a(n, n) |
---|
[2931] | 1747 | INTEGER :: ising |
---|
| 1748 | #else |
---|
[3228] | 1749 | REAL(kind=dp), INTENT(IN):: a(lu_nonzero) |
---|
[2931] | 1750 | #endif |
---|
[3228] | 1751 | INTEGER, INTENT(IN):: pivot(n) |
---|
[2931] | 1752 | !~~~> inout variables |
---|
[3228] | 1753 | REAL(kind=dp), INTENT(INOUT):: b(n) |
---|
[2931] | 1754 | |
---|
| 1755 | #ifdef full_algebra |
---|
| 1756 | CALL DGETRS( 'N',N ,1,A,N,Pivot,b,N,ISING) |
---|
[3228] | 1757 | IF (info < 0)THEN |
---|
| 1758 | print* , "error in dgetrs. ising=", ising |
---|
[2931] | 1759 | ENDIF |
---|
| 1760 | #else |
---|
[3228] | 1761 | CALL kppsolve( a, b) |
---|
[2931] | 1762 | #endif |
---|
| 1763 | |
---|
[3228] | 1764 | istatus(nsol) = istatus(nsol) + 1 |
---|
[2931] | 1765 | |
---|
| 1766 | END SUBROUTINE ros_solve |
---|
| 1767 | |
---|
| 1768 | |
---|
| 1769 | |
---|
| 1770 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1771 | SUBROUTINE ros2 |
---|
| 1772 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1773 | ! --- AN L-STABLE METHOD,2 stages,order 2 |
---|
| 1774 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1775 | |
---|
| 1776 | double precision g |
---|
| 1777 | |
---|
| 1778 | g = 1.0_dp + 1.0_dp/sqrt(2.0_dp) |
---|
| 1779 | rosmethod = rs2 |
---|
| 1780 | !~~~> name of the method |
---|
| 1781 | ros_Name = 'ROS-2' |
---|
| 1782 | !~~~> number of stages |
---|
| 1783 | ros_s = 2 |
---|
| 1784 | |
---|
| 1785 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
| 1786 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 1787 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
| 1788 | ! The general mapping formula is: |
---|
| 1789 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
| 1790 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
| 1791 | |
---|
[3228] | 1792 | ros_a(1) = (1.0_dp) /g |
---|
| 1793 | ros_c(1) = (- 2.0_dp) /g |
---|
[2931] | 1794 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 1795 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 1796 | ros_newf(1) = .TRUE. |
---|
| 1797 | ros_newf(2) = .TRUE. |
---|
[2931] | 1798 | !~~~> m_i = coefficients for new step solution |
---|
[3228] | 1799 | ros_m(1) = (3.0_dp) /(2.0_dp* g) |
---|
| 1800 | ros_m(2) = (1.0_dp) /(2.0_dp* g) |
---|
[2931] | 1801 | ! E_i = Coefficients for error estimator |
---|
[3228] | 1802 | ros_e(1) = 1.0_dp/(2.0_dp* g) |
---|
| 1803 | ros_e(2) = 1.0_dp/(2.0_dp* g) |
---|
| 1804 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 1805 | ! main and the embedded scheme orders plus one |
---|
| 1806 | ros_elo = 2.0_dp |
---|
[3228] | 1807 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
[2931] | 1808 | ros_alpha(1) = 0.0_dp |
---|
| 1809 | ros_alpha(2) = 1.0_dp |
---|
[3228] | 1810 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
[2931] | 1811 | ros_gamma(1) = g |
---|
[3228] | 1812 | ros_gamma(2) = -g |
---|
[2931] | 1813 | |
---|
| 1814 | END SUBROUTINE ros2 |
---|
| 1815 | |
---|
| 1816 | |
---|
| 1817 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1818 | SUBROUTINE ros3 |
---|
| 1819 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1820 | ! --- AN L-STABLE METHOD,3 stages,order 3,2 function evaluations |
---|
| 1821 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1822 | |
---|
| 1823 | rosmethod = rs3 |
---|
| 1824 | !~~~> name of the method |
---|
| 1825 | ros_Name = 'ROS-3' |
---|
| 1826 | !~~~> number of stages |
---|
| 1827 | ros_s = 3 |
---|
| 1828 | |
---|
| 1829 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
| 1830 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 1831 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
| 1832 | ! The general mapping formula is: |
---|
| 1833 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
| 1834 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
| 1835 | |
---|
| 1836 | ros_a(1) = 1.0_dp |
---|
| 1837 | ros_a(2) = 1.0_dp |
---|
| 1838 | ros_a(3) = 0.0_dp |
---|
| 1839 | |
---|
| 1840 | ros_c(1) = - 0.10156171083877702091975600115545e+01_dp |
---|
| 1841 | ros_c(2) = 0.40759956452537699824805835358067e+01_dp |
---|
| 1842 | ros_c(3) = 0.92076794298330791242156818474003e+01_dp |
---|
| 1843 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 1844 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 1845 | ros_newf(1) = .TRUE. |
---|
| 1846 | ros_newf(2) = .TRUE. |
---|
| 1847 | ros_newf(3) = .FALSE. |
---|
[2931] | 1848 | !~~~> m_i = coefficients for new step solution |
---|
| 1849 | ros_m(1) = 0.1e+01_dp |
---|
| 1850 | ros_m(2) = 0.61697947043828245592553615689730e+01_dp |
---|
| 1851 | ros_m(3) = - 0.42772256543218573326238373806514_dp |
---|
| 1852 | ! E_i = Coefficients for error estimator |
---|
| 1853 | ros_e(1) = 0.5_dp |
---|
| 1854 | ros_e(2) = - 0.29079558716805469821718236208017e+01_dp |
---|
| 1855 | ros_e(3) = 0.22354069897811569627360909276199_dp |
---|
[3228] | 1856 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 1857 | ! main and the embedded scheme orders plus 1 |
---|
| 1858 | ros_elo = 3.0_dp |
---|
[3228] | 1859 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
[2931] | 1860 | ros_alpha(1) = 0.0_dp |
---|
| 1861 | ros_alpha(2) = 0.43586652150845899941601945119356_dp |
---|
| 1862 | ros_alpha(3) = 0.43586652150845899941601945119356_dp |
---|
[3228] | 1863 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
[2931] | 1864 | ros_gamma(1) = 0.43586652150845899941601945119356_dp |
---|
| 1865 | ros_gamma(2) = 0.24291996454816804366592249683314_dp |
---|
| 1866 | ros_gamma(3) = 0.21851380027664058511513169485832e+01_dp |
---|
| 1867 | |
---|
| 1868 | END SUBROUTINE ros3 |
---|
| 1869 | |
---|
| 1870 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1871 | |
---|
| 1872 | |
---|
| 1873 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1874 | SUBROUTINE ros4 |
---|
| 1875 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1876 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 4 STAGES |
---|
| 1877 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
---|
| 1878 | ! |
---|
| 1879 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
---|
| 1880 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
| 1881 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
| 1882 | ! SPRINGER-VERLAG (1990) |
---|
| 1883 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1884 | |
---|
| 1885 | |
---|
| 1886 | rosmethod = rs4 |
---|
| 1887 | !~~~> name of the method |
---|
| 1888 | ros_Name = 'ROS-4' |
---|
| 1889 | !~~~> number of stages |
---|
| 1890 | ros_s = 4 |
---|
| 1891 | |
---|
| 1892 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
| 1893 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 1894 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
| 1895 | ! The general mapping formula is: |
---|
| 1896 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
| 1897 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
| 1898 | |
---|
| 1899 | ros_a(1) = 0.2000000000000000e+01_dp |
---|
| 1900 | ros_a(2) = 0.1867943637803922e+01_dp |
---|
| 1901 | ros_a(3) = 0.2344449711399156_dp |
---|
| 1902 | ros_a(4) = ros_a(2) |
---|
| 1903 | ros_a(5) = ros_a(3) |
---|
| 1904 | ros_a(6) = 0.0_dp |
---|
| 1905 | |
---|
[3228] | 1906 | ros_c(1) = -0.7137615036412310e+01_dp |
---|
[2931] | 1907 | ros_c(2) = 0.2580708087951457e+01_dp |
---|
| 1908 | ros_c(3) = 0.6515950076447975_dp |
---|
[3228] | 1909 | ros_c(4) = -0.2137148994382534e+01_dp |
---|
| 1910 | ros_c(5) = -0.3214669691237626_dp |
---|
| 1911 | ros_c(6) = -0.6949742501781779_dp |
---|
[2931] | 1912 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 1913 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 1914 | ros_newf(1) = .TRUE. |
---|
| 1915 | ros_newf(2) = .TRUE. |
---|
| 1916 | ros_newf(3) = .TRUE. |
---|
| 1917 | ros_newf(4) = .FALSE. |
---|
[2931] | 1918 | !~~~> m_i = coefficients for new step solution |
---|
| 1919 | ros_m(1) = 0.2255570073418735e+01_dp |
---|
| 1920 | ros_m(2) = 0.2870493262186792_dp |
---|
| 1921 | ros_m(3) = 0.4353179431840180_dp |
---|
| 1922 | ros_m(4) = 0.1093502252409163e+01_dp |
---|
| 1923 | !~~~> e_i = coefficients for error estimator |
---|
[3228] | 1924 | ros_e(1) = -0.2815431932141155_dp |
---|
| 1925 | ros_e(2) = -0.7276199124938920e-01_dp |
---|
| 1926 | ros_e(3) = -0.1082196201495311_dp |
---|
| 1927 | ros_e(4) = -0.1093502252409163e+01_dp |
---|
| 1928 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 1929 | ! main and the embedded scheme orders plus 1 |
---|
| 1930 | ros_elo = 4.0_dp |
---|
[3228] | 1931 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
[2931] | 1932 | ros_alpha(1) = 0.0_dp |
---|
| 1933 | ros_alpha(2) = 0.1145640000000000e+01_dp |
---|
| 1934 | ros_alpha(3) = 0.6552168638155900_dp |
---|
| 1935 | ros_alpha(4) = ros_alpha(3) |
---|
[3228] | 1936 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
[2931] | 1937 | ros_gamma(1) = 0.5728200000000000_dp |
---|
[3228] | 1938 | ros_gamma(2) = -0.1769193891319233e+01_dp |
---|
[2931] | 1939 | ros_gamma(3) = 0.7592633437920482_dp |
---|
[3228] | 1940 | ros_gamma(4) = -0.1049021087100450_dp |
---|
[2931] | 1941 | |
---|
| 1942 | END SUBROUTINE ros4 |
---|
| 1943 | |
---|
| 1944 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1945 | SUBROUTINE rodas3 |
---|
| 1946 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1947 | ! --- A STIFFLY-STABLE METHOD,4 stages,order 3 |
---|
| 1948 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1949 | |
---|
| 1950 | |
---|
| 1951 | rosmethod = rd3 |
---|
| 1952 | !~~~> name of the method |
---|
| 1953 | ros_Name = 'RODAS-3' |
---|
| 1954 | !~~~> number of stages |
---|
| 1955 | ros_s = 4 |
---|
| 1956 | |
---|
| 1957 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
| 1958 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 1959 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
| 1960 | ! The general mapping formula is: |
---|
| 1961 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
| 1962 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
| 1963 | |
---|
| 1964 | ros_a(1) = 0.0_dp |
---|
| 1965 | ros_a(2) = 2.0_dp |
---|
| 1966 | ros_a(3) = 0.0_dp |
---|
| 1967 | ros_a(4) = 2.0_dp |
---|
| 1968 | ros_a(5) = 0.0_dp |
---|
| 1969 | ros_a(6) = 1.0_dp |
---|
| 1970 | |
---|
| 1971 | ros_c(1) = 4.0_dp |
---|
| 1972 | ros_c(2) = 1.0_dp |
---|
[3228] | 1973 | ros_c(3) = -1.0_dp |
---|
[2931] | 1974 | ros_c(4) = 1.0_dp |
---|
[3228] | 1975 | ros_c(5) = -1.0_dp |
---|
| 1976 | ros_c(6) = -(8.0_dp/3.0_dp) |
---|
[2931] | 1977 | |
---|
| 1978 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 1979 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 1980 | ros_newf(1) = .TRUE. |
---|
| 1981 | ros_newf(2) = .FALSE. |
---|
| 1982 | ros_newf(3) = .TRUE. |
---|
| 1983 | ros_newf(4) = .TRUE. |
---|
[2931] | 1984 | !~~~> m_i = coefficients for new step solution |
---|
| 1985 | ros_m(1) = 2.0_dp |
---|
| 1986 | ros_m(2) = 0.0_dp |
---|
| 1987 | ros_m(3) = 1.0_dp |
---|
| 1988 | ros_m(4) = 1.0_dp |
---|
| 1989 | !~~~> e_i = coefficients for error estimator |
---|
| 1990 | ros_e(1) = 0.0_dp |
---|
| 1991 | ros_e(2) = 0.0_dp |
---|
| 1992 | ros_e(3) = 0.0_dp |
---|
| 1993 | ros_e(4) = 1.0_dp |
---|
[3228] | 1994 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 1995 | ! main and the embedded scheme orders plus 1 |
---|
| 1996 | ros_elo = 3.0_dp |
---|
[3228] | 1997 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
[2931] | 1998 | ros_alpha(1) = 0.0_dp |
---|
| 1999 | ros_alpha(2) = 0.0_dp |
---|
| 2000 | ros_alpha(3) = 1.0_dp |
---|
| 2001 | ros_alpha(4) = 1.0_dp |
---|
[3228] | 2002 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
[2931] | 2003 | ros_gamma(1) = 0.5_dp |
---|
| 2004 | ros_gamma(2) = 1.5_dp |
---|
| 2005 | ros_gamma(3) = 0.0_dp |
---|
| 2006 | ros_gamma(4) = 0.0_dp |
---|
| 2007 | |
---|
| 2008 | END SUBROUTINE rodas3 |
---|
| 2009 | |
---|
| 2010 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2011 | SUBROUTINE rodas4 |
---|
| 2012 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2013 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 6 STAGES |
---|
| 2014 | ! |
---|
| 2015 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
---|
| 2016 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
| 2017 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
| 2018 | ! SPRINGER-VERLAG (1996) |
---|
| 2019 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2020 | |
---|
| 2021 | |
---|
| 2022 | rosmethod = rd4 |
---|
| 2023 | !~~~> name of the method |
---|
| 2024 | ros_Name = 'RODAS-4' |
---|
| 2025 | !~~~> number of stages |
---|
| 2026 | ros_s = 6 |
---|
| 2027 | |
---|
[3228] | 2028 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
[2931] | 2029 | ros_alpha(1) = 0.000_dp |
---|
| 2030 | ros_alpha(2) = 0.386_dp |
---|
| 2031 | ros_alpha(3) = 0.210_dp |
---|
| 2032 | ros_alpha(4) = 0.630_dp |
---|
| 2033 | ros_alpha(5) = 1.000_dp |
---|
| 2034 | ros_alpha(6) = 1.000_dp |
---|
| 2035 | |
---|
[3228] | 2036 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
[2931] | 2037 | ros_gamma(1) = 0.2500000000000000_dp |
---|
[3228] | 2038 | ros_gamma(2) = -0.1043000000000000_dp |
---|
[2931] | 2039 | ros_gamma(3) = 0.1035000000000000_dp |
---|
[3228] | 2040 | ros_gamma(4) = -0.3620000000000023e-01_dp |
---|
[2931] | 2041 | ros_gamma(5) = 0.0_dp |
---|
| 2042 | ros_gamma(6) = 0.0_dp |
---|
| 2043 | |
---|
| 2044 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
| 2045 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
| 2046 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
| 2047 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
| 2048 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
| 2049 | |
---|
| 2050 | ros_a(1) = 0.1544000000000000e+01_dp |
---|
| 2051 | ros_a(2) = 0.9466785280815826_dp |
---|
| 2052 | ros_a(3) = 0.2557011698983284_dp |
---|
| 2053 | ros_a(4) = 0.3314825187068521e+01_dp |
---|
| 2054 | ros_a(5) = 0.2896124015972201e+01_dp |
---|
| 2055 | ros_a(6) = 0.9986419139977817_dp |
---|
| 2056 | ros_a(7) = 0.1221224509226641e+01_dp |
---|
| 2057 | ros_a(8) = 0.6019134481288629e+01_dp |
---|
| 2058 | ros_a(9) = 0.1253708332932087e+02_dp |
---|
[3228] | 2059 | ros_a(10) = -0.6878860361058950_dp |
---|
[2931] | 2060 | ros_a(11) = ros_a(7) |
---|
| 2061 | ros_a(12) = ros_a(8) |
---|
| 2062 | ros_a(13) = ros_a(9) |
---|
| 2063 | ros_a(14) = ros_a(10) |
---|
| 2064 | ros_a(15) = 1.0_dp |
---|
| 2065 | |
---|
[3228] | 2066 | ros_c(1) = -0.5668800000000000e+01_dp |
---|
| 2067 | ros_c(2) = -0.2430093356833875e+01_dp |
---|
| 2068 | ros_c(3) = -0.2063599157091915_dp |
---|
| 2069 | ros_c(4) = -0.1073529058151375_dp |
---|
| 2070 | ros_c(5) = -0.9594562251023355e+01_dp |
---|
| 2071 | ros_c(6) = -0.2047028614809616e+02_dp |
---|
[2931] | 2072 | ros_c(7) = 0.7496443313967647e+01_dp |
---|
[3228] | 2073 | ros_c(8) = -0.1024680431464352e+02_dp |
---|
| 2074 | ros_c(9) = -0.3399990352819905e+02_dp |
---|
[2931] | 2075 | ros_c(10) = 0.1170890893206160e+02_dp |
---|
| 2076 | ros_c(11) = 0.8083246795921522e+01_dp |
---|
[3228] | 2077 | ros_c(12) = -0.7981132988064893e+01_dp |
---|
| 2078 | ros_c(13) = -0.3152159432874371e+02_dp |
---|
[2931] | 2079 | ros_c(14) = 0.1631930543123136e+02_dp |
---|
[3228] | 2080 | ros_c(15) = -0.6058818238834054e+01_dp |
---|
[2931] | 2081 | |
---|
| 2082 | !~~~> m_i = coefficients for new step solution |
---|
| 2083 | ros_m(1) = ros_a(7) |
---|
| 2084 | ros_m(2) = ros_a(8) |
---|
| 2085 | ros_m(3) = ros_a(9) |
---|
| 2086 | ros_m(4) = ros_a(10) |
---|
| 2087 | ros_m(5) = 1.0_dp |
---|
| 2088 | ros_m(6) = 1.0_dp |
---|
| 2089 | |
---|
| 2090 | !~~~> e_i = coefficients for error estimator |
---|
| 2091 | ros_e(1) = 0.0_dp |
---|
| 2092 | ros_e(2) = 0.0_dp |
---|
| 2093 | ros_e(3) = 0.0_dp |
---|
| 2094 | ros_e(4) = 0.0_dp |
---|
| 2095 | ros_e(5) = 0.0_dp |
---|
| 2096 | ros_e(6) = 1.0_dp |
---|
| 2097 | |
---|
| 2098 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 2099 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 2100 | ros_newf(1) = .TRUE. |
---|
| 2101 | ros_newf(2) = .TRUE. |
---|
| 2102 | ros_newf(3) = .TRUE. |
---|
| 2103 | ros_newf(4) = .TRUE. |
---|
| 2104 | ros_newf(5) = .TRUE. |
---|
| 2105 | ros_newf(6) = .TRUE. |
---|
[2931] | 2106 | |
---|
[3228] | 2107 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 2108 | ! main and the embedded scheme orders plus 1 |
---|
| 2109 | ros_elo = 4.0_dp |
---|
| 2110 | |
---|
| 2111 | END SUBROUTINE rodas4 |
---|
| 2112 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2113 | SUBROUTINE rang3 |
---|
| 2114 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2115 | ! STIFFLY-STABLE W METHOD OF ORDER 3,WITH 4 STAGES |
---|
| 2116 | ! |
---|
| 2117 | ! J. RANG and L. ANGERMANN |
---|
| 2118 | ! NEW ROSENBROCK W-METHODS OF ORDER 3 |
---|
| 2119 | ! FOR PARTIAL DIFFERENTIAL ALGEBRAIC |
---|
| 2120 | ! EQUATIONS OF INDEX 1 |
---|
| 2121 | ! BIT Numerical Mathematics (2005) 45: 761-787 |
---|
| 2122 | ! DOI: 10.1007/s10543-005-0035-y |
---|
| 2123 | ! Table 4.1-4.2 |
---|
| 2124 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2125 | |
---|
| 2126 | |
---|
| 2127 | rosmethod = rg3 |
---|
| 2128 | !~~~> name of the method |
---|
| 2129 | ros_Name = 'RANG-3' |
---|
| 2130 | !~~~> number of stages |
---|
| 2131 | ros_s = 4 |
---|
| 2132 | |
---|
| 2133 | ros_a(1) = 5.09052051067020d+00; |
---|
| 2134 | ros_a(2) = 5.09052051067020d+00; |
---|
| 2135 | ros_a(3) = 0.0d0; |
---|
| 2136 | ros_a(4) = 4.97628111010787d+00; |
---|
| 2137 | ros_a(5) = 2.77268164715849d-02; |
---|
| 2138 | ros_a(6) = 2.29428036027904d-01; |
---|
| 2139 | |
---|
| 2140 | ros_c(1) = - 1.16790812312283d+01; |
---|
| 2141 | ros_c(2) = - 1.64057326467367d+01; |
---|
| 2142 | ros_c(3) = - 2.77268164715850d-01; |
---|
| 2143 | ros_c(4) = - 8.38103960500476d+00; |
---|
| 2144 | ros_c(5) = - 8.48328409199343d-01; |
---|
| 2145 | ros_c(6) = 2.87009860433106d-01; |
---|
| 2146 | |
---|
| 2147 | ros_m(1) = 5.22582761233094d+00; |
---|
| 2148 | ros_m(2) = - 5.56971148154165d-01; |
---|
| 2149 | ros_m(3) = 3.57979469353645d-01; |
---|
| 2150 | ros_m(4) = 1.72337398521064d+00; |
---|
| 2151 | |
---|
| 2152 | ros_e(1) = - 5.16845212784040d+00; |
---|
| 2153 | ros_e(2) = - 1.26351942603842d+00; |
---|
| 2154 | ros_e(3) = - 1.11022302462516d-16; |
---|
| 2155 | ros_e(4) = 2.22044604925031d-16; |
---|
| 2156 | |
---|
| 2157 | ros_alpha(1) = 0.0d00; |
---|
| 2158 | ros_alpha(2) = 2.21878746765329d+00; |
---|
| 2159 | ros_alpha(3) = 2.21878746765329d+00; |
---|
| 2160 | ros_alpha(4) = 1.55392337535788d+00; |
---|
| 2161 | |
---|
| 2162 | ros_gamma(1) = 4.35866521508459d-01; |
---|
| 2163 | ros_gamma(2) = - 1.78292094614483d+00; |
---|
| 2164 | ros_gamma(3) = - 2.46541900496934d+00; |
---|
| 2165 | ros_gamma(4) = - 8.05529997906370d-01; |
---|
| 2166 | |
---|
| 2167 | |
---|
| 2168 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
| 2169 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
[3228] | 2170 | ros_newf(1) = .TRUE. |
---|
| 2171 | ros_newf(2) = .TRUE. |
---|
| 2172 | ros_newf(3) = .TRUE. |
---|
| 2173 | ros_newf(4) = .TRUE. |
---|
[2931] | 2174 | |
---|
[3228] | 2175 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
[2931] | 2176 | ! main and the embedded scheme orders plus 1 |
---|
| 2177 | ros_elo = 3.0_dp |
---|
| 2178 | |
---|
| 2179 | END SUBROUTINE rang3 |
---|
| 2180 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2181 | |
---|
| 2182 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2183 | ! End of the set of internal Rosenbrock subroutines |
---|
| 2184 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2185 | END SUBROUTINE rosenbrock |
---|
| 2186 | |
---|
[3228] | 2187 | SUBROUTINE funtemplate( t, y, ydot) |
---|
[2931] | 2188 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2189 | ! Template for the ODE function call. |
---|
| 2190 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
| 2191 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2192 | !~~~> input variables |
---|
[3228] | 2193 | REAL(kind=dp):: t, y(nvar) |
---|
[2931] | 2194 | !~~~> output variables |
---|
| 2195 | REAL(kind=dp):: ydot(nvar) |
---|
| 2196 | !~~~> local variables |
---|
| 2197 | REAL(kind=dp):: told |
---|
| 2198 | |
---|
| 2199 | told = time |
---|
| 2200 | time = t |
---|
[3228] | 2201 | CALL fun( y, fix, rconst, ydot) |
---|
[2931] | 2202 | time = told |
---|
| 2203 | |
---|
| 2204 | END SUBROUTINE funtemplate |
---|
| 2205 | |
---|
[3228] | 2206 | SUBROUTINE jactemplate( t, y, jcb) |
---|
[2931] | 2207 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2208 | ! Template for the ODE Jacobian call. |
---|
| 2209 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
| 2210 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2211 | !~~~> input variables |
---|
[3228] | 2212 | REAL(kind=dp):: t, y(nvar) |
---|
[2931] | 2213 | !~~~> output variables |
---|
| 2214 | #ifdef full_algebra |
---|
[3228] | 2215 | REAL(kind=dp):: jv(lu_nonzero), jcb(nvar, nvar) |
---|
[2931] | 2216 | #else |
---|
| 2217 | REAL(kind=dp):: jcb(lu_nonzero) |
---|
| 2218 | #endif |
---|
| 2219 | !~~~> local variables |
---|
| 2220 | REAL(kind=dp):: told |
---|
| 2221 | #ifdef full_algebra |
---|
[3228] | 2222 | INTEGER :: i, j |
---|
[2931] | 2223 | #endif |
---|
| 2224 | |
---|
| 2225 | told = time |
---|
| 2226 | time = t |
---|
| 2227 | #ifdef full_algebra |
---|
[3228] | 2228 | CALL jac_sp(y, fix, rconst, jv) |
---|
| 2229 | DO j=1, nvar |
---|
| 2230 | DO i=1, nvar |
---|
| 2231 | jcb(i, j) = 0.0_dp |
---|
[2931] | 2232 | ENDDO |
---|
| 2233 | ENDDO |
---|
[3228] | 2234 | DO i=1, lu_nonzero |
---|
| 2235 | jcb(lu_irow(i), lu_icol(i)) = jv(i) |
---|
[2931] | 2236 | ENDDO |
---|
| 2237 | #else |
---|
[3228] | 2238 | CALL jac_sp( y, fix, rconst, jcb) |
---|
[2931] | 2239 | #endif |
---|
| 2240 | time = told |
---|
| 2241 | |
---|
| 2242 | END SUBROUTINE jactemplate |
---|
| 2243 | |
---|
[3228] | 2244 | SUBROUTINE kppdecomp( jvs, ier) |
---|
| 2245 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2246 | ! sparse lu factorization |
---|
| 2247 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 2248 | ! loop expansion generated by kp4 |
---|
| 2249 | |
---|
| 2250 | INTEGER :: ier |
---|
| 2251 | REAL(kind=dp):: jvs(lu_nonzero), w(nvar), a |
---|
| 2252 | INTEGER :: k, kk, j, jj |
---|
| 2253 | |
---|
| 2254 | a = 0. |
---|
| 2255 | ier = 0 |
---|
| 2256 | |
---|
| 2257 | ! i = 1 |
---|
| 2258 | ! i = 2 |
---|
| 2259 | jvs(4) = (jvs(4)) / jvs(1) |
---|
| 2260 | jvs(5) = jvs(5) - jvs(2) * jvs(4) |
---|
| 2261 | jvs(6) = jvs(6) - jvs(3) * jvs(4) |
---|
| 2262 | ! i = 3 |
---|
| 2263 | jvs(7) = (jvs(7)) / jvs(1) |
---|
| 2264 | a = 0.0; a = a - jvs(2) * jvs(7) |
---|
| 2265 | jvs(8) = (jvs(8) + a) / jvs(5) |
---|
| 2266 | jvs(9) = jvs(9) - jvs(3) * jvs(7) - jvs(6) * jvs(8) |
---|
| 2267 | RETURN |
---|
| 2268 | |
---|
| 2269 | END SUBROUTINE kppdecomp |
---|
| 2270 | |
---|
| 2271 | SUBROUTINE chem_gasphase_integrate (time_step_len, conc, tempi, qvapi, fakti, photo, ierrf, xnacc, xnrej, istatus, l_debug, pe, & |
---|
| 2272 | icntrl_i, rcntrl_i) |
---|
[2931] | 2273 | |
---|
| 2274 | IMPLICIT NONE |
---|
| 2275 | |
---|
[3228] | 2276 | REAL(dp), INTENT(IN) :: time_step_len |
---|
| 2277 | REAL(dp), DIMENSION(:, :), INTENT(INOUT) :: conc |
---|
| 2278 | REAL(dp), DIMENSION(:, :), INTENT(IN) :: photo |
---|
| 2279 | REAL(dp), DIMENSION(:), INTENT(IN) :: tempi |
---|
| 2280 | REAL(dp), DIMENSION(:), INTENT(IN) :: qvapi |
---|
| 2281 | REAL(dp), DIMENSION(:), INTENT(IN) :: fakti |
---|
| 2282 | INTEGER, INTENT(OUT), OPTIONAL :: ierrf(:) |
---|
| 2283 | INTEGER, INTENT(OUT), OPTIONAL :: xnacc(:) |
---|
| 2284 | INTEGER, INTENT(OUT), OPTIONAL :: xnrej(:) |
---|
| 2285 | INTEGER, INTENT(INOUT), OPTIONAL :: istatus(:) |
---|
| 2286 | INTEGER, INTENT(IN), OPTIONAL :: pe |
---|
| 2287 | LOGICAL, INTENT(IN), OPTIONAL :: l_debug |
---|
| 2288 | INTEGER, DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: icntrl_i |
---|
| 2289 | REAL(dp), DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: rcntrl_i |
---|
[2931] | 2290 | |
---|
| 2291 | INTEGER :: k ! loop variable |
---|
[3228] | 2292 | REAL(dp) :: dt |
---|
| 2293 | INTEGER, DIMENSION(20) :: istatus_u |
---|
| 2294 | INTEGER :: ierr_u |
---|
[3249] | 2295 | INTEGER :: istatf |
---|
[3228] | 2296 | INTEGER :: vl_dim_lo |
---|
[2931] | 2297 | |
---|
| 2298 | |
---|
[3228] | 2299 | IF (PRESENT (istatus)) istatus = 0 |
---|
| 2300 | IF (PRESENT (icntrl_i)) icntrl = icntrl_i |
---|
| 2301 | IF (PRESENT (rcntrl_i)) rcntrl = rcntrl_i |
---|
[2931] | 2302 | |
---|
[3263] | 2303 | vl_glo = size(tempi, 1) |
---|
[3249] | 2304 | |
---|
[3228] | 2305 | vl_dim_lo = vl_dim |
---|
| 2306 | DO k=1, vl_glo, vl_dim_lo |
---|
[2931] | 2307 | is = k |
---|
[3228] | 2308 | ie = min(k+ vl_dim_lo-1, vl_glo) |
---|
| 2309 | vl = ie-is+ 1 |
---|
[2931] | 2310 | |
---|
[3228] | 2311 | c(:) = conc(is, :) |
---|
[2931] | 2312 | |
---|
[3228] | 2313 | temp = tempi(is) |
---|
[2931] | 2314 | |
---|
[3228] | 2315 | qvap = qvapi(is) |
---|
[2931] | 2316 | |
---|
[3228] | 2317 | fakt = fakti(is) |
---|
| 2318 | |
---|
| 2319 | CALL initialize |
---|
| 2320 | |
---|
| 2321 | phot(:) = photo(is, :) |
---|
| 2322 | |
---|
[2931] | 2323 | CALL update_rconst |
---|
| 2324 | |
---|
| 2325 | dt = time_step_len |
---|
| 2326 | |
---|
| 2327 | ! integrate from t=0 to t=dt |
---|
[3228] | 2328 | CALL integrate(0._dp, dt, icntrl, rcntrl, istatus_u = istatus_u, ierr_u=ierr_u) |
---|
[2931] | 2329 | |
---|
| 2330 | |
---|
[3228] | 2331 | IF (PRESENT(l_debug) .AND. PRESENT(pe)) THEN |
---|
| 2332 | IF (l_debug) CALL error_output(conc(is, :), ierr_u, pe) |
---|
| 2333 | ENDIF |
---|
| 2334 | |
---|
| 2335 | conc(is, :) = c(:) |
---|
[2931] | 2336 | |
---|
[3228] | 2337 | ! RETURN diagnostic information |
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[2931] | 2338 | |
---|
[3228] | 2339 | IF (PRESENT(ierrf)) ierrf(is) = ierr_u |
---|
| 2340 | IF (PRESENT(xnacc)) xnacc(is) = istatus_u(4) |
---|
| 2341 | IF (PRESENT(xnrej)) xnrej(is) = istatus_u(5) |
---|
[2931] | 2342 | |
---|
[3228] | 2343 | IF (PRESENT (istatus)) THEN |
---|
| 2344 | istatus(1:8) = istatus(1:8) + istatus_u(1:8) |
---|
[2931] | 2345 | ENDIF |
---|
| 2346 | |
---|
| 2347 | END DO |
---|
| 2348 | |
---|
| 2349 | |
---|
| 2350 | ! Deallocate input arrays |
---|
| 2351 | |
---|
| 2352 | |
---|
[3228] | 2353 | data_loaded = .FALSE. |
---|
[2931] | 2354 | |
---|
| 2355 | RETURN |
---|
| 2356 | END SUBROUTINE chem_gasphase_integrate |
---|
| 2357 | |
---|
| 2358 | END MODULE chem_gasphase_mod |
---|
| 2359 | |
---|