1 | MODULE chem_gasphase_mod |
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2 | |
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3 | ! Mechanism: passive |
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4 | ! |
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5 | !------------------------------------------------------------------------------! |
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6 | ! |
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7 | ! ******Module chem_gasphase_mod is automatically generated by kpp4palm ****** |
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8 | ! |
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9 | ! *********Please do NOT change this Code,it will be ovewritten ********* |
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10 | ! |
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11 | !------------------------------------------------------------------------------! |
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12 | ! This file was created by KPP (http://people.cs.vt.edu/asandu/Software/Kpp/) |
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13 | ! and kpp4palm (created by Klaus Ketelsen). kpp4palm is an adapted version |
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14 | ! of KP4 (Jöckel,P.,Kerkweg,A.,Pozzer,A.,Sander,R.,Tost,H.,Riede, |
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15 | ! H.,Baumgaertner,A.,Gromov,S.,and Kern,B.,2010: Development cycle 2 of |
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16 | ! the Modular Earth Submodel System (MESSy2),Geosci. Model Dev.,3,717-752, |
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17 | ! https://doi.org/10.5194/gmd-3-717-2010). KP4 is part of the Modular Earth |
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18 | ! Submodel System (MESSy),which is is available under the GNU General Public |
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19 | ! License (GPL). |
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20 | ! |
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21 | ! KPP is free software; you can redistribute it and/or modify it under the terms |
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22 | ! of the General Public Licence as published by the Free Software Foundation; |
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23 | ! either version 2 of the License,or (at your option) any later version. |
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24 | ! KPP is distributed in the hope that it will be useful,but WITHOUT ANY WARRANTY; |
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25 | ! without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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26 | ! PURPOSE. See the GNU General Public Licence for more details. |
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27 | ! |
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28 | !------------------------------------------------------------------------------! |
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29 | ! This file is part of the PALM model system. |
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30 | ! |
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31 | ! PALM is free software: you can redistribute it and/or modify it under the |
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32 | ! terms of the GNU General Public License as published by the Free Software |
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33 | ! Foundation,either version 3 of the License,or (at your option) any later |
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34 | ! version. |
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35 | ! |
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36 | ! PALM is distributed in the hope that it will be useful,but WITHOUT ANY |
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37 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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38 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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39 | ! |
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40 | ! You should have received a copy of the GNU General Public License along with |
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41 | ! PALM. If not,see <http://www.gnu.org/licenses/>. |
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42 | ! |
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43 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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44 | !--------------------------------------------------------------------------------! |
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45 | ! |
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46 | ! Current revisions: |
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47 | ! ------------------ |
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48 | ! |
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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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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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58 | ! |
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59 | ! forkel Sept. 2017: Variables for photolyis added |
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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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72 | USE pegrid, ONLY: myid, threads_per_task |
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73 | |
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74 | IMPLICIT NONE |
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75 | PRIVATE |
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76 | !SAVE ! note: occurs again in automatically generated code ... |
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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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83 | PUBLIC :: eqn_names, phot_names, spc_names |
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84 | PUBLIC :: nmaxfixsteps |
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85 | PUBLIC :: atol, rtol |
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86 | PUBLIC :: nspec, nreact |
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87 | PUBLIC :: temp |
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88 | PUBLIC :: qvap |
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89 | PUBLIC :: fakt |
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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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94 | PUBLIC :: vl_dim ! PUBLIC to ebable other MODULEs to distiguish between scalar and vec |
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95 | |
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96 | PUBLIC :: initialize, integrate, update_rconst |
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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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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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107 | INTEGER :: vl |
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108 | |
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109 | INTEGER :: vl_glo |
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110 | INTEGER :: is, ie |
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111 | |
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112 | |
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113 | INTEGER, DIMENSION(vl_dim) :: kacc, krej |
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114 | INTEGER, DIMENSION(vl_dim) :: ierrv |
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115 | LOGICAL :: data_loaded = .FALSE. |
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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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131 | ! Time : Tue Sep 25 18:34:57 2018 |
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132 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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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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144 | INTEGER, PARAMETER :: nspec = 2 |
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145 | ! NVAR - Number of Variable species |
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146 | INTEGER, PARAMETER :: nvar = 2 |
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147 | ! NVARACT - Number of Active species |
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148 | INTEGER, PARAMETER :: nvaract = 2 |
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149 | ! NFIX - Number of Fixed species |
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150 | INTEGER, PARAMETER :: nfix = 1 |
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151 | ! NREACT - Number of reactions |
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152 | INTEGER, PARAMETER :: nreact = 2 |
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153 | ! NVARST - Starting of variables in conc. vect. |
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154 | INTEGER, PARAMETER :: nvarst = 1 |
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155 | ! NFIXST - Starting of fixed in conc. vect. |
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156 | INTEGER, PARAMETER :: nfixst = 3 |
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157 | ! NONZERO - Number of nonzero entries in Jacobian |
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158 | INTEGER, PARAMETER :: nonzero = 2 |
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159 | ! LU_NONZERO - Number of nonzero entries in LU factoriz. of Jacobian |
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160 | INTEGER, PARAMETER :: lu_nonzero = 2 |
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161 | ! CNVAR - (NVAR+1) Number of elements in compressed row format |
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162 | INTEGER, PARAMETER :: cnvar = 3 |
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163 | ! CNEQN - (NREACT+1) Number stoicm elements in compressed col format |
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164 | INTEGER, PARAMETER :: cneqn = 3 |
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165 | ! NHESS - Length of Sparse Hessian |
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166 | INTEGER, PARAMETER :: nhess = 1 |
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167 | ! NMASS - Number of atoms to check mass balance |
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168 | INTEGER, PARAMETER :: nmass = 1 |
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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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173 | INTEGER, PARAMETER, PUBLIC :: ind_pm10 = 1 |
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174 | INTEGER, PARAMETER, PUBLIC :: ind_pm25 = 2 |
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175 | |
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176 | ! Index declaration for fixed species in C |
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177 | ! C(ind_spc) |
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178 | |
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179 | |
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180 | ! Index declaration for fixed species in FIX |
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181 | ! FIX(indf_spc) = C(ind_spc) = C(NVAR+indf_spc) |
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182 | |
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183 | |
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184 | ! NJVRP - Length of sparse Jacobian JVRP |
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185 | INTEGER, PARAMETER :: njvrp = 2 |
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186 | |
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187 | ! NSTOICM - Length of Sparse Stoichiometric Matrix |
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188 | INTEGER, PARAMETER :: nstoicm = 1 |
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189 | |
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190 | |
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191 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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192 | ! |
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193 | ! Global Data Module File |
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194 | ! |
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195 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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196 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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197 | ! KPP is distributed under GPL,the general public licence |
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198 | ! (http://www.gnu.org/copyleft/gpl.html) |
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199 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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200 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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201 | ! With important contributions from: |
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202 | ! M. Damian,Villanova University,USA |
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203 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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204 | ! |
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205 | ! File : chem_gasphase_mod_Global.f90 |
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206 | ! Time : Tue Sep 25 18:34:57 2018 |
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207 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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208 | ! Equation file : chem_gasphase_mod.kpp |
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209 | ! Output root filename : chem_gasphase_mod |
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210 | ! |
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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 | ! Declaration of global variables |
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219 | |
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220 | ! C - Concentration of all species |
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221 | REAL(kind=dp):: c(nspec) |
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222 | ! VAR - Concentrations of variable species (global) |
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223 | REAL(kind=dp):: var(nvar) |
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224 | ! FIX - Concentrations of fixed species (global) |
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225 | REAL(kind=dp):: fix(nfix) |
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226 | ! VAR,FIX are chunks of array C |
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227 | EQUIVALENCE( c(1), var(1)) |
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228 | ! RCONST - Rate constants (global) |
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229 | REAL(kind=dp):: rconst(nreact) |
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230 | ! TIME - Current integration time |
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231 | REAL(kind=dp):: time |
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232 | ! TEMP - Temperature |
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233 | REAL(kind=dp):: temp |
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234 | ! TSTART - Integration start time |
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235 | REAL(kind=dp):: tstart |
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236 | ! ATOL - Absolute tolerance |
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237 | REAL(kind=dp):: atol(nvar) |
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238 | ! RTOL - Relative tolerance |
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239 | REAL(kind=dp):: rtol(nvar) |
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240 | ! STEPMIN - Lower bound for integration step |
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241 | REAL(kind=dp):: stepmin |
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242 | ! CFACTOR - Conversion factor for concentration units |
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243 | REAL(kind=dp):: cfactor |
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244 | |
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245 | ! INLINED global variable declarations |
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246 | |
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247 | ! QVAP - Water vapor |
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248 | REAL(kind=dp):: qvap |
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249 | ! FAKT - Conversion factor |
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250 | REAL(kind=dp):: fakt |
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251 | |
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252 | |
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253 | ! INLINED global variable declarations |
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254 | |
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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 | ! Sparse Jacobian Data Structures File |
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260 | ! |
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261 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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262 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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263 | ! KPP is distributed under GPL,the general public licence |
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264 | ! (http://www.gnu.org/copyleft/gpl.html) |
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265 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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266 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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267 | ! With important contributions from: |
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268 | ! M. Damian,Villanova University,USA |
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269 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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270 | ! |
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271 | ! File : chem_gasphase_mod_JacobianSP.f90 |
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272 | ! Time : Tue Sep 25 18:34:57 2018 |
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273 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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274 | ! Equation file : chem_gasphase_mod.kpp |
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275 | ! Output root filename : chem_gasphase_mod |
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276 | ! |
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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 | ! Sparse Jacobian Data |
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285 | |
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286 | |
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287 | INTEGER, PARAMETER, DIMENSION(2):: lu_irow = (/ & |
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288 | 1, 2 /) |
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289 | |
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290 | INTEGER, PARAMETER, DIMENSION(2):: lu_icol = (/ & |
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291 | 1, 2 /) |
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292 | |
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293 | INTEGER, PARAMETER, DIMENSION(3):: lu_crow = (/ & |
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294 | 1, 2, 3 /) |
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295 | |
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296 | INTEGER, PARAMETER, DIMENSION(3):: lu_diag = (/ & |
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297 | 1, 2, 3 /) |
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298 | |
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299 | |
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300 | |
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301 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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302 | ! |
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303 | ! Utility Data Module File |
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304 | ! |
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305 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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306 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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307 | ! KPP is distributed under GPL,the general public licence |
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308 | ! (http://www.gnu.org/copyleft/gpl.html) |
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309 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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310 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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311 | ! With important contributions from: |
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312 | ! M. Damian,Villanova University,USA |
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313 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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314 | ! |
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315 | ! File : chem_gasphase_mod_Monitor.f90 |
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316 | ! Time : Tue Sep 25 18:34:57 2018 |
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317 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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318 | ! Equation file : chem_gasphase_mod.kpp |
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319 | ! Output root filename : chem_gasphase_mod |
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320 | ! |
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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 | CHARACTER(len=15), PARAMETER, DIMENSION(2):: spc_names = (/ & |
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328 | 'PM10 ','PM25 ' /) |
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329 | |
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330 | CHARACTER(len=100), PARAMETER, DIMENSION(2):: eqn_names = (/ & |
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331 | 'PM10 --> PM10 ',& |
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332 | 'PM25 --> PM25 ' /) |
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333 | |
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334 | ! INLINED global variables |
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335 | |
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336 | ! inline f90_data: declaration of global variables for photolysis |
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337 | ! REAL(kind=dp):: phot(nphot)must eventually be moved to global later for |
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338 | INTEGER, PARAMETER :: nphot = 1 |
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339 | ! phot photolysis frequencies |
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340 | REAL(kind=dp):: phot(nphot) |
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341 | |
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342 | INTEGER, PARAMETER, PUBLIC :: j_no2 = 1 |
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343 | |
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344 | CHARACTER(len=15), PARAMETER, DIMENSION(nphot):: phot_names = (/ & |
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345 | 'J_NO2 '/) |
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346 | |
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347 | ! End INLINED global variables |
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348 | |
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349 | |
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350 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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351 | |
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352 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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353 | |
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354 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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355 | |
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356 | ! Automatic generated PUBLIC Statements for ip_ and ihs_ variables |
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357 | |
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358 | |
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359 | ! variable definations from individual module headers |
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360 | |
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361 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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362 | ! |
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363 | ! Initialization File |
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364 | ! |
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365 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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366 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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367 | ! KPP is distributed under GPL,the general public licence |
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368 | ! (http://www.gnu.org/copyleft/gpl.html) |
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369 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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370 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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371 | ! With important contributions from: |
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372 | ! M. Damian,Villanova University,USA |
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373 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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374 | ! |
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375 | ! File : chem_gasphase_mod_Initialize.f90 |
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376 | ! Time : Tue Sep 25 18:34:57 2018 |
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377 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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378 | ! Equation file : chem_gasphase_mod.kpp |
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379 | ! Output root filename : chem_gasphase_mod |
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380 | ! |
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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 | ! Numerical Integrator (Time-Stepping) File |
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390 | ! |
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391 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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392 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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393 | ! KPP is distributed under GPL,the general public licence |
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394 | ! (http://www.gnu.org/copyleft/gpl.html) |
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395 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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396 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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397 | ! With important contributions from: |
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398 | ! M. Damian,Villanova University,USA |
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399 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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400 | ! |
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401 | ! File : chem_gasphase_mod_Integrator.f90 |
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402 | ! Time : Tue Sep 25 18:34:57 2018 |
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403 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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404 | ! Equation file : chem_gasphase_mod.kpp |
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405 | ! Output root filename : chem_gasphase_mod |
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406 | ! |
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407 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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408 | |
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409 | |
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410 | |
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411 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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412 | ! |
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413 | ! INTEGRATE - Integrator routine |
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414 | ! Arguments : |
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415 | ! TIN - Start Time for Integration |
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416 | ! TOUT - End Time for Integration |
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417 | ! |
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418 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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419 | |
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420 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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421 | ! Rosenbrock - Implementation of several Rosenbrock methods: ! |
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422 | ! *Ros2 ! |
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423 | ! *Ros3 ! |
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424 | ! *Ros4 ! |
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425 | ! *Rodas3 ! |
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426 | ! *Rodas4 ! |
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427 | ! By default the code employs the KPP sparse linear algebra routines ! |
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428 | ! Compile with -DFULL_ALGEBRA to use full linear algebra (LAPACK) ! |
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429 | ! ! |
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430 | ! (C) Adrian Sandu,August 2004 ! |
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431 | ! Virginia Polytechnic Institute and State University ! |
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432 | ! Contact: sandu@cs.vt.edu ! |
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433 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 ! ! |
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434 | ! This implementation is part of KPP - the Kinetic PreProcessor ! |
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435 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~! |
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436 | |
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437 | |
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438 | SAVE |
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439 | |
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440 | !~~~> statistics on the work performed by the rosenbrock method |
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441 | INTEGER, PARAMETER :: nfun=1, njac=2, nstp=3, nacc=4, & |
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442 | nrej=5, ndec=6, nsol=7, nsng=8, & |
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443 | ntexit=1, nhexit=2, nhnew = 3 |
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444 | |
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445 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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446 | ! |
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447 | ! Linear Algebra Data and Routines File |
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448 | ! |
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449 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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450 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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451 | ! KPP is distributed under GPL,the general public licence |
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452 | ! (http://www.gnu.org/copyleft/gpl.html) |
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453 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
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454 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
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455 | ! With important contributions from: |
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456 | ! M. Damian,Villanova University,USA |
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457 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
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458 | ! |
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459 | ! File : chem_gasphase_mod_LinearAlgebra.f90 |
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460 | ! Time : Tue Sep 25 18:34:57 2018 |
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461 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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462 | ! Equation file : chem_gasphase_mod.kpp |
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463 | ! Output root filename : chem_gasphase_mod |
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464 | ! |
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465 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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466 | |
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467 | |
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468 | |
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469 | |
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470 | |
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471 | |
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472 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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473 | ! |
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474 | ! The ODE Jacobian of Chemical Model File |
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475 | ! |
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476 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
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477 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
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478 | ! KPP is distributed under GPL,the general public licence |
---|
479 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
480 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
481 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
482 | ! With important contributions from: |
---|
483 | ! M. Damian,Villanova University,USA |
---|
484 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
485 | ! |
---|
486 | ! File : chem_gasphase_mod_Jacobian.f90 |
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487 | ! Time : Tue Sep 25 18:34:57 2018 |
---|
488 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
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489 | ! Equation file : chem_gasphase_mod.kpp |
---|
490 | ! Output root filename : chem_gasphase_mod |
---|
491 | ! |
---|
492 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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493 | |
---|
494 | |
---|
495 | |
---|
496 | |
---|
497 | |
---|
498 | |
---|
499 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
500 | ! |
---|
501 | ! The ODE Function of Chemical Model File |
---|
502 | ! |
---|
503 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
504 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
505 | ! KPP is distributed under GPL,the general public licence |
---|
506 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
507 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
508 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
509 | ! With important contributions from: |
---|
510 | ! M. Damian,Villanova University,USA |
---|
511 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
512 | ! |
---|
513 | ! File : chem_gasphase_mod_Function.f90 |
---|
514 | ! Time : Tue Sep 25 18:34:57 2018 |
---|
515 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
516 | ! Equation file : chem_gasphase_mod.kpp |
---|
517 | ! Output root filename : chem_gasphase_mod |
---|
518 | ! |
---|
519 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
520 | |
---|
521 | |
---|
522 | |
---|
523 | |
---|
524 | |
---|
525 | ! A - Rate for each equation |
---|
526 | REAL(kind=dp):: a(nreact) |
---|
527 | |
---|
528 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
529 | ! |
---|
530 | ! The Reaction Rates File |
---|
531 | ! |
---|
532 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
533 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
534 | ! KPP is distributed under GPL,the general public licence |
---|
535 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
536 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
537 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
538 | ! With important contributions from: |
---|
539 | ! M. Damian,Villanova University,USA |
---|
540 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
541 | ! |
---|
542 | ! File : chem_gasphase_mod_Rates.f90 |
---|
543 | ! Time : Tue Sep 25 18:34:57 2018 |
---|
544 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
545 | ! Equation file : chem_gasphase_mod.kpp |
---|
546 | ! Output root filename : chem_gasphase_mod |
---|
547 | ! |
---|
548 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
549 | |
---|
550 | |
---|
551 | |
---|
552 | |
---|
553 | |
---|
554 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
555 | ! |
---|
556 | ! Auxiliary Routines File |
---|
557 | ! |
---|
558 | ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor |
---|
559 | ! (http://www.cs.vt.edu/~asandu/Software/KPP) |
---|
560 | ! KPP is distributed under GPL,the general public licence |
---|
561 | ! (http://www.gnu.org/copyleft/gpl.html) |
---|
562 | ! (C) 1995-1997,V. Damian & A. Sandu,CGRER,Univ. Iowa |
---|
563 | ! (C) 1997-2005,A. Sandu,Michigan Tech,Virginia Tech |
---|
564 | ! With important contributions from: |
---|
565 | ! M. Damian,Villanova University,USA |
---|
566 | ! R. Sander,Max-Planck Institute for Chemistry,Mainz,Germany |
---|
567 | ! |
---|
568 | ! File : chem_gasphase_mod_Util.f90 |
---|
569 | ! Time : Tue Sep 25 18:34:57 2018 |
---|
570 | ! Working directory : /home/forkel-r/palmstuff/work/chemistry20180925/UTIL/chemistry/gasphase_preproc/tmp_kpp4palm |
---|
571 | ! Equation file : chem_gasphase_mod.kpp |
---|
572 | ! Output root filename : chem_gasphase_mod |
---|
573 | ! |
---|
574 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
575 | |
---|
576 | |
---|
577 | |
---|
578 | |
---|
579 | |
---|
580 | |
---|
581 | ! header MODULE initialize_kpp_ctrl_template |
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582 | |
---|
583 | ! notes: |
---|
584 | ! - l_vector is automatically defined by kp4 |
---|
585 | ! - vl_dim is automatically defined by kp4 |
---|
586 | ! - i_lu_di is automatically defined by kp4 |
---|
587 | ! - wanted is automatically defined by xmecca |
---|
588 | ! - icntrl rcntrl are automatically defined by kpp |
---|
589 | ! - "USE messy_main_tools" is in MODULE_header of messy_mecca_kpp.f90 |
---|
590 | ! - SAVE will be automatically added by kp4 |
---|
591 | |
---|
592 | !SAVE |
---|
593 | |
---|
594 | ! for fixed time step control |
---|
595 | ! ... max. number of fixed time steps (sum must be 1) |
---|
596 | INTEGER, PARAMETER :: nmaxfixsteps = 50 |
---|
597 | ! ... switch for fixed time stepping |
---|
598 | LOGICAL, PUBLIC :: l_fixed_step = .FALSE. |
---|
599 | INTEGER, PUBLIC :: nfsteps = 1 |
---|
600 | ! ... number of kpp control PARAMETERs |
---|
601 | INTEGER, PARAMETER, PUBLIC :: nkppctrl = 20 |
---|
602 | ! |
---|
603 | INTEGER, DIMENSION(nkppctrl), PUBLIC :: icntrl = 0 |
---|
604 | REAL(dp), DIMENSION(nkppctrl), PUBLIC :: rcntrl = 0.0_dp |
---|
605 | REAL(dp), DIMENSION(nmaxfixsteps), PUBLIC :: t_steps = 0.0_dp |
---|
606 | |
---|
607 | ! END header MODULE initialize_kpp_ctrl_template |
---|
608 | |
---|
609 | |
---|
610 | ! Interface Block |
---|
611 | |
---|
612 | INTERFACE initialize |
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613 | MODULE PROCEDURE initialize |
---|
614 | END INTERFACE initialize |
---|
615 | |
---|
616 | INTERFACE integrate |
---|
617 | MODULE PROCEDURE integrate |
---|
618 | END INTERFACE integrate |
---|
619 | |
---|
620 | INTERFACE fun |
---|
621 | MODULE PROCEDURE fun |
---|
622 | END INTERFACE fun |
---|
623 | |
---|
624 | INTERFACE kppsolve |
---|
625 | MODULE PROCEDURE kppsolve |
---|
626 | END INTERFACE kppsolve |
---|
627 | |
---|
628 | INTERFACE jac_sp |
---|
629 | MODULE PROCEDURE jac_sp |
---|
630 | END INTERFACE jac_sp |
---|
631 | |
---|
632 | INTERFACE k_arr |
---|
633 | MODULE PROCEDURE k_arr |
---|
634 | END INTERFACE k_arr |
---|
635 | |
---|
636 | INTERFACE update_rconst |
---|
637 | MODULE PROCEDURE update_rconst |
---|
638 | END INTERFACE update_rconst |
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639 | |
---|
640 | INTERFACE arr2 |
---|
641 | MODULE PROCEDURE arr2 |
---|
642 | END INTERFACE arr2 |
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643 | |
---|
644 | INTERFACE initialize_kpp_ctrl |
---|
645 | MODULE PROCEDURE initialize_kpp_ctrl |
---|
646 | END INTERFACE initialize_kpp_ctrl |
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647 | |
---|
648 | INTERFACE error_output |
---|
649 | MODULE PROCEDURE error_output |
---|
650 | END INTERFACE error_output |
---|
651 | |
---|
652 | INTERFACE wscal |
---|
653 | MODULE PROCEDURE wscal |
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654 | END INTERFACE wscal |
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655 | |
---|
656 | !INTERFACE not working INTERFACE waxpy |
---|
657 | !INTERFACE not working MODULE PROCEDURE waxpy |
---|
658 | !INTERFACE not working END INTERFACE waxpy |
---|
659 | |
---|
660 | INTERFACE rosenbrock |
---|
661 | MODULE PROCEDURE rosenbrock |
---|
662 | END INTERFACE rosenbrock |
---|
663 | |
---|
664 | INTERFACE funtemplate |
---|
665 | MODULE PROCEDURE funtemplate |
---|
666 | END INTERFACE funtemplate |
---|
667 | |
---|
668 | INTERFACE jactemplate |
---|
669 | MODULE PROCEDURE jactemplate |
---|
670 | END INTERFACE jactemplate |
---|
671 | |
---|
672 | INTERFACE kppdecomp |
---|
673 | MODULE PROCEDURE kppdecomp |
---|
674 | END INTERFACE kppdecomp |
---|
675 | |
---|
676 | INTERFACE chem_gasphase_integrate |
---|
677 | MODULE PROCEDURE chem_gasphase_integrate |
---|
678 | END INTERFACE chem_gasphase_integrate |
---|
679 | |
---|
680 | |
---|
681 | CONTAINS |
---|
682 | |
---|
683 | SUBROUTINE initialize() |
---|
684 | |
---|
685 | |
---|
686 | INTEGER :: j, k |
---|
687 | |
---|
688 | INTEGER :: i |
---|
689 | REAL(kind=dp):: x |
---|
690 | k = is |
---|
691 | cfactor = 1.000000e+00_dp |
---|
692 | |
---|
693 | x = (0.) * cfactor |
---|
694 | DO i = 1 , nvar |
---|
695 | ENDDO |
---|
696 | |
---|
697 | x = (0.) * cfactor |
---|
698 | DO i = 1 , nfix |
---|
699 | fix(i) = x |
---|
700 | ENDDO |
---|
701 | |
---|
702 | ! constant rate coefficients |
---|
703 | ! END constant rate coefficients |
---|
704 | |
---|
705 | ! INLINED initializations |
---|
706 | |
---|
707 | ! End INLINED initializations |
---|
708 | |
---|
709 | |
---|
710 | END SUBROUTINE initialize |
---|
711 | |
---|
712 | SUBROUTINE integrate( tin, tout, & |
---|
713 | icntrl_u, rcntrl_u, istatus_u, rstatus_u, ierr_u) |
---|
714 | |
---|
715 | |
---|
716 | REAL(kind=dp), INTENT(IN):: tin ! start time |
---|
717 | REAL(kind=dp), INTENT(IN):: tout ! END time |
---|
718 | ! OPTIONAL input PARAMETERs and statistics |
---|
719 | INTEGER, INTENT(IN), OPTIONAL :: icntrl_u(20) |
---|
720 | REAL(kind=dp), INTENT(IN), OPTIONAL :: rcntrl_u(20) |
---|
721 | INTEGER, INTENT(OUT), OPTIONAL :: istatus_u(20) |
---|
722 | REAL(kind=dp), INTENT(OUT), OPTIONAL :: rstatus_u(20) |
---|
723 | INTEGER, INTENT(OUT), OPTIONAL :: ierr_u |
---|
724 | |
---|
725 | REAL(kind=dp):: rcntrl(20), rstatus(20) |
---|
726 | INTEGER :: icntrl(20), istatus(20), ierr |
---|
727 | |
---|
728 | INTEGER, SAVE :: ntotal = 0 |
---|
729 | |
---|
730 | icntrl(:) = 0 |
---|
731 | rcntrl(:) = 0.0_dp |
---|
732 | istatus(:) = 0 |
---|
733 | rstatus(:) = 0.0_dp |
---|
734 | |
---|
735 | !~~~> fine-tune the integrator: |
---|
736 | icntrl(1) = 0 ! 0 - non- autonomous, 1 - autonomous |
---|
737 | icntrl(2) = 0 ! 0 - vector tolerances, 1 - scalars |
---|
738 | |
---|
739 | ! IF OPTIONAL PARAMETERs are given, and IF they are >0, |
---|
740 | ! THEN they overwrite default settings. |
---|
741 | IF (PRESENT(icntrl_u))THEN |
---|
742 | WHERE(icntrl_u(:)> 0)icntrl(:) = icntrl_u(:) |
---|
743 | ENDIF |
---|
744 | IF (PRESENT(rcntrl_u))THEN |
---|
745 | WHERE(rcntrl_u(:)> 0)rcntrl(:) = rcntrl_u(:) |
---|
746 | ENDIF |
---|
747 | |
---|
748 | |
---|
749 | CALL rosenbrock(nvar, var, tin, tout, & |
---|
750 | atol, rtol, & |
---|
751 | rcntrl, icntrl, rstatus, istatus, ierr) |
---|
752 | |
---|
753 | !~~~> debug option: show no of steps |
---|
754 | ! ntotal = ntotal + istatus(nstp) |
---|
755 | ! PRINT*,'NSTEPS=',ISTATUS(Nstp),' (',Ntotal,')',' O3=',VAR(ind_O3) |
---|
756 | |
---|
757 | stepmin = rstatus(nhexit) |
---|
758 | ! IF OPTIONAL PARAMETERs are given for output they |
---|
759 | ! are updated with the RETURN information |
---|
760 | IF (PRESENT(istatus_u))istatus_u(:) = istatus(:) |
---|
761 | IF (PRESENT(rstatus_u))rstatus_u(:) = rstatus(:) |
---|
762 | IF (PRESENT(ierr_u)) ierr_u = ierr |
---|
763 | |
---|
764 | END SUBROUTINE integrate |
---|
765 | |
---|
766 | SUBROUTINE fun(v, f, rct, vdot) |
---|
767 | |
---|
768 | ! V - Concentrations of variable species (local) |
---|
769 | REAL(kind=dp):: v(nvar) |
---|
770 | ! F - Concentrations of fixed species (local) |
---|
771 | REAL(kind=dp):: f(nfix) |
---|
772 | ! RCT - Rate constants (local) |
---|
773 | REAL(kind=dp):: rct(nreact) |
---|
774 | ! Vdot - Time derivative of variable species concentrations |
---|
775 | REAL(kind=dp):: vdot(nvar) |
---|
776 | |
---|
777 | |
---|
778 | ! Computation of equation rates |
---|
779 | |
---|
780 | ! Aggregate function |
---|
781 | vdot(1) = 0 |
---|
782 | vdot(2) = 0 |
---|
783 | |
---|
784 | END SUBROUTINE fun |
---|
785 | |
---|
786 | SUBROUTINE kppsolve(jvs, x) |
---|
787 | |
---|
788 | ! JVS - sparse Jacobian of variables |
---|
789 | REAL(kind=dp):: jvs(lu_nonzero) |
---|
790 | ! X - Vector for variables |
---|
791 | REAL(kind=dp):: x(nvar) |
---|
792 | |
---|
793 | x(2) = x(2) / jvs(2) |
---|
794 | x(1) = x(1) / jvs(1) |
---|
795 | |
---|
796 | END SUBROUTINE kppsolve |
---|
797 | |
---|
798 | SUBROUTINE jac_sp(v, f, rct, jvs) |
---|
799 | |
---|
800 | ! V - Concentrations of variable species (local) |
---|
801 | REAL(kind=dp):: v(nvar) |
---|
802 | ! F - Concentrations of fixed species (local) |
---|
803 | REAL(kind=dp):: f(nfix) |
---|
804 | ! RCT - Rate constants (local) |
---|
805 | REAL(kind=dp):: rct(nreact) |
---|
806 | ! JVS - sparse Jacobian of variables |
---|
807 | REAL(kind=dp):: jvs(lu_nonzero) |
---|
808 | |
---|
809 | |
---|
810 | ! Local variables |
---|
811 | ! B - Temporary array |
---|
812 | REAL(kind=dp):: b(2) |
---|
813 | |
---|
814 | ! B(1) = dA(1)/dV(1) |
---|
815 | b(1) = rct(1) |
---|
816 | ! B(2) = dA(2)/dV(2) |
---|
817 | b(2) = rct(2) |
---|
818 | |
---|
819 | ! Construct the Jacobian terms from B's |
---|
820 | ! JVS(1) = Jac_FULL(1,1) |
---|
821 | jvs(1) = 0 |
---|
822 | ! JVS(2) = Jac_FULL(2,2) |
---|
823 | jvs(2) = 0 |
---|
824 | |
---|
825 | END SUBROUTINE jac_sp |
---|
826 | |
---|
827 | elemental REAL(kind=dp)FUNCTION k_arr (k_298, tdep, temp) |
---|
828 | ! arrhenius FUNCTION |
---|
829 | |
---|
830 | REAL, INTENT(IN):: k_298 ! k at t = 298.15k |
---|
831 | REAL, INTENT(IN):: tdep ! temperature dependence |
---|
832 | REAL(kind=dp), INTENT(IN):: temp ! temperature |
---|
833 | |
---|
834 | intrinsic exp |
---|
835 | |
---|
836 | k_arr = k_298 * exp(tdep* (1._dp/temp- 3.3540e-3_dp))! 1/298.15=3.3540e-3 |
---|
837 | |
---|
838 | END FUNCTION k_arr |
---|
839 | |
---|
840 | SUBROUTINE update_rconst() |
---|
841 | INTEGER :: k |
---|
842 | |
---|
843 | k = is |
---|
844 | |
---|
845 | ! Begin INLINED RCONST |
---|
846 | |
---|
847 | |
---|
848 | ! End INLINED RCONST |
---|
849 | |
---|
850 | rconst(1) = (1.0_dp) |
---|
851 | rconst(2) = (1.0_dp) |
---|
852 | |
---|
853 | END SUBROUTINE update_rconst |
---|
854 | |
---|
855 | ! END FUNCTION ARR2 |
---|
856 | REAL(kind=dp)FUNCTION arr2( a0, b0, temp) |
---|
857 | REAL(kind=dp):: temp |
---|
858 | REAL(kind=dp):: a0, b0 |
---|
859 | arr2 = a0 * exp( - b0 / temp) |
---|
860 | END FUNCTION arr2 |
---|
861 | |
---|
862 | SUBROUTINE initialize_kpp_ctrl(status) |
---|
863 | |
---|
864 | |
---|
865 | ! i/o |
---|
866 | INTEGER, INTENT(OUT):: status |
---|
867 | |
---|
868 | ! local |
---|
869 | REAL(dp):: tsum |
---|
870 | INTEGER :: i |
---|
871 | |
---|
872 | ! check fixed time steps |
---|
873 | tsum = 0.0_dp |
---|
874 | DO i=1, nmaxfixsteps |
---|
875 | IF (t_steps(i)< tiny(0.0_dp))exit |
---|
876 | tsum = tsum + t_steps(i) |
---|
877 | ENDDO |
---|
878 | |
---|
879 | nfsteps = i- 1 |
---|
880 | |
---|
881 | l_fixed_step = (nfsteps > 0).and.((tsum - 1.0)< tiny(0.0_dp)) |
---|
882 | |
---|
883 | IF (l_vector)THEN |
---|
884 | WRITE(*,*) ' MODE : VECTOR (LENGTH=',VL_DIM,')' |
---|
885 | ELSE |
---|
886 | WRITE(*,*) ' MODE : SCALAR' |
---|
887 | ENDIF |
---|
888 | ! |
---|
889 | WRITE(*,*) ' DE-INDEXING MODE :',I_LU_DI |
---|
890 | ! |
---|
891 | WRITE(*,*) ' ICNTRL : ',icntrl |
---|
892 | WRITE(*,*) ' RCNTRL : ',rcntrl |
---|
893 | ! |
---|
894 | ! note: this is ONLY meaningful for vectorized (kp4)rosenbrock- methods |
---|
895 | IF (l_vector)THEN |
---|
896 | IF (l_fixed_step)THEN |
---|
897 | WRITE(*,*) ' TIME STEPS : FIXED (',t_steps(1:nfsteps),')' |
---|
898 | ELSE |
---|
899 | WRITE(*,*) ' TIME STEPS : AUTOMATIC' |
---|
900 | ENDIF |
---|
901 | ELSE |
---|
902 | WRITE(*,*) ' TIME STEPS : AUTOMATIC '//& |
---|
903 | &'(t_steps (CTRL_KPP) ignored in SCALAR MODE)' |
---|
904 | ENDIF |
---|
905 | ! mz_pj_20070531- |
---|
906 | |
---|
907 | status = 0 |
---|
908 | |
---|
909 | |
---|
910 | END SUBROUTINE initialize_kpp_ctrl |
---|
911 | |
---|
912 | SUBROUTINE error_output(c, ierr, pe) |
---|
913 | |
---|
914 | |
---|
915 | INTEGER, INTENT(IN):: ierr |
---|
916 | INTEGER, INTENT(IN):: pe |
---|
917 | REAL(dp), DIMENSION(:), INTENT(IN):: c |
---|
918 | |
---|
919 | write(6,*) 'ERROR in chem_gasphase_mod ',ierr,C(1) |
---|
920 | |
---|
921 | |
---|
922 | END SUBROUTINE error_output |
---|
923 | |
---|
924 | SUBROUTINE wscal(n, alpha, x, incx) |
---|
925 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
926 | ! constant times a vector: x(1:N) <- Alpha*x(1:N) |
---|
927 | ! only for incX=incY=1 |
---|
928 | ! after BLAS |
---|
929 | ! replace this by the function from the optimized BLAS implementation: |
---|
930 | ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) |
---|
931 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
932 | |
---|
933 | INTEGER :: i, incx, m, mp1, n |
---|
934 | REAL(kind=dp) :: x(n), alpha |
---|
935 | REAL(kind=dp), PARAMETER :: zero=0.0_dp, one=1.0_dp |
---|
936 | |
---|
937 | IF (alpha .eq. one)RETURN |
---|
938 | IF (n .le. 0)RETURN |
---|
939 | |
---|
940 | m = mod(n, 5) |
---|
941 | IF ( m .ne. 0)THEN |
---|
942 | IF (alpha .eq. (- one))THEN |
---|
943 | DO i = 1, m |
---|
944 | x(i) = - x(i) |
---|
945 | ENDDO |
---|
946 | ELSEIF (alpha .eq. zero)THEN |
---|
947 | DO i = 1, m |
---|
948 | x(i) = zero |
---|
949 | ENDDO |
---|
950 | ELSE |
---|
951 | DO i = 1, m |
---|
952 | x(i) = alpha* x(i) |
---|
953 | ENDDO |
---|
954 | ENDIF |
---|
955 | IF ( n .lt. 5)RETURN |
---|
956 | ENDIF |
---|
957 | mp1 = m + 1 |
---|
958 | IF (alpha .eq. (- one))THEN |
---|
959 | DO i = mp1, n, 5 |
---|
960 | x(i) = - x(i) |
---|
961 | x(i + 1) = - x(i + 1) |
---|
962 | x(i + 2) = - x(i + 2) |
---|
963 | x(i + 3) = - x(i + 3) |
---|
964 | x(i + 4) = - x(i + 4) |
---|
965 | ENDDO |
---|
966 | ELSEIF (alpha .eq. zero)THEN |
---|
967 | DO i = mp1, n, 5 |
---|
968 | x(i) = zero |
---|
969 | x(i + 1) = zero |
---|
970 | x(i + 2) = zero |
---|
971 | x(i + 3) = zero |
---|
972 | x(i + 4) = zero |
---|
973 | ENDDO |
---|
974 | ELSE |
---|
975 | DO i = mp1, n, 5 |
---|
976 | x(i) = alpha* x(i) |
---|
977 | x(i + 1) = alpha* x(i + 1) |
---|
978 | x(i + 2) = alpha* x(i + 2) |
---|
979 | x(i + 3) = alpha* x(i + 3) |
---|
980 | x(i + 4) = alpha* x(i + 4) |
---|
981 | ENDDO |
---|
982 | ENDIF |
---|
983 | |
---|
984 | END SUBROUTINE wscal |
---|
985 | |
---|
986 | SUBROUTINE waxpy(n, alpha, x, incx, y, incy) |
---|
987 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
988 | ! constant times a vector plus a vector: y <- y + Alpha*x |
---|
989 | ! only for incX=incY=1 |
---|
990 | ! after BLAS |
---|
991 | ! replace this by the function from the optimized BLAS implementation: |
---|
992 | ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) |
---|
993 | !- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
---|
994 | |
---|
995 | INTEGER :: i, incx, incy, m, mp1, n |
---|
996 | REAL(kind=dp):: x(n), y(n), alpha |
---|
997 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
---|
998 | |
---|
999 | IF (alpha .eq. zero)RETURN |
---|
1000 | IF (n .le. 0)RETURN |
---|
1001 | |
---|
1002 | m = mod(n, 4) |
---|
1003 | IF ( m .ne. 0)THEN |
---|
1004 | DO i = 1, m |
---|
1005 | y(i) = y(i) + alpha* x(i) |
---|
1006 | ENDDO |
---|
1007 | IF ( n .lt. 4)RETURN |
---|
1008 | ENDIF |
---|
1009 | mp1 = m + 1 |
---|
1010 | DO i = mp1, n, 4 |
---|
1011 | y(i) = y(i) + alpha* x(i) |
---|
1012 | y(i + 1) = y(i + 1) + alpha* x(i + 1) |
---|
1013 | y(i + 2) = y(i + 2) + alpha* x(i + 2) |
---|
1014 | y(i + 3) = y(i + 3) + alpha* x(i + 3) |
---|
1015 | ENDDO |
---|
1016 | |
---|
1017 | END SUBROUTINE waxpy |
---|
1018 | |
---|
1019 | SUBROUTINE rosenbrock(n, y, tstart, tend, & |
---|
1020 | abstol, reltol, & |
---|
1021 | rcntrl, icntrl, rstatus, istatus, ierr) |
---|
1022 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1023 | ! |
---|
1024 | ! Solves the system y'=F(t,y) using a Rosenbrock method defined by: |
---|
1025 | ! |
---|
1026 | ! G = 1/(H*gamma(1)) - Jac(t0,Y0) |
---|
1027 | ! T_i = t0 + Alpha(i)*H |
---|
1028 | ! Y_i = Y0 + \sum_{j=1}^{i-1} A(i,j)*K_j |
---|
1029 | ! G *K_i = Fun( T_i,Y_i)+ \sum_{j=1}^S C(i,j)/H *K_j + |
---|
1030 | ! gamma(i)*dF/dT(t0,Y0) |
---|
1031 | ! Y1 = Y0 + \sum_{j=1}^S M(j)*K_j |
---|
1032 | ! |
---|
1033 | ! For details on Rosenbrock methods and their implementation consult: |
---|
1034 | ! E. Hairer and G. Wanner |
---|
1035 | ! "Solving ODEs II. Stiff and differential-algebraic problems". |
---|
1036 | ! Springer series in computational mathematics,Springer-Verlag,1996. |
---|
1037 | ! The codes contained in the book inspired this implementation. |
---|
1038 | ! |
---|
1039 | ! (C) Adrian Sandu,August 2004 |
---|
1040 | ! Virginia Polytechnic Institute and State University |
---|
1041 | ! Contact: sandu@cs.vt.edu |
---|
1042 | ! Revised by Philipp Miehe and Adrian Sandu,May 2006 |
---|
1043 | ! This implementation is part of KPP - the Kinetic PreProcessor |
---|
1044 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1045 | ! |
---|
1046 | !~~~> input arguments: |
---|
1047 | ! |
---|
1048 | !- y(n) = vector of initial conditions (at t=tstart) |
---|
1049 | !- [tstart, tend] = time range of integration |
---|
1050 | ! (if Tstart>Tend the integration is performed backwards in time) |
---|
1051 | !- reltol, abstol = user precribed accuracy |
---|
1052 | !- SUBROUTINE fun( t, y, ydot) = ode FUNCTION, |
---|
1053 | ! returns Ydot = Y' = F(T,Y) |
---|
1054 | !- SUBROUTINE jac( t, y, jcb) = jacobian of the ode FUNCTION, |
---|
1055 | ! returns Jcb = dFun/dY |
---|
1056 | !- icntrl(1:20) = INTEGER inputs PARAMETERs |
---|
1057 | !- rcntrl(1:20) = REAL inputs PARAMETERs |
---|
1058 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1059 | ! |
---|
1060 | !~~~> output arguments: |
---|
1061 | ! |
---|
1062 | !- y(n) - > vector of final states (at t- >tend) |
---|
1063 | !- istatus(1:20) - > INTEGER output PARAMETERs |
---|
1064 | !- rstatus(1:20) - > REAL output PARAMETERs |
---|
1065 | !- ierr - > job status upon RETURN |
---|
1066 | ! success (positive value) or |
---|
1067 | ! failure (negative value) |
---|
1068 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1069 | ! |
---|
1070 | !~~~> input PARAMETERs: |
---|
1071 | ! |
---|
1072 | ! Note: For input parameters equal to zero the default values of the |
---|
1073 | ! corresponding variables are used. |
---|
1074 | ! |
---|
1075 | ! ICNTRL(1) = 1: F = F(y) Independent of T (AUTONOMOUS) |
---|
1076 | ! = 0: F = F(t,y) Depends on T (NON-AUTONOMOUS) |
---|
1077 | ! |
---|
1078 | ! ICNTRL(2) = 0: AbsTol,RelTol are N-dimensional vectors |
---|
1079 | ! = 1: AbsTol,RelTol are scalars |
---|
1080 | ! |
---|
1081 | ! ICNTRL(3) -> selection of a particular Rosenbrock method |
---|
1082 | ! = 0 : Rodas3 (default) |
---|
1083 | ! = 1 : Ros2 |
---|
1084 | ! = 2 : Ros3 |
---|
1085 | ! = 3 : Ros4 |
---|
1086 | ! = 4 : Rodas3 |
---|
1087 | ! = 5 : Rodas4 |
---|
1088 | ! |
---|
1089 | ! ICNTRL(4) -> maximum number of integration steps |
---|
1090 | ! For ICNTRL(4) =0) the default value of 100000 is used |
---|
1091 | ! |
---|
1092 | ! RCNTRL(1) -> Hmin,lower bound for the integration step size |
---|
1093 | ! It is strongly recommended to keep Hmin = ZERO |
---|
1094 | ! RCNTRL(2) -> Hmax,upper bound for the integration step size |
---|
1095 | ! RCNTRL(3) -> Hstart,starting value for the integration step size |
---|
1096 | ! |
---|
1097 | ! RCNTRL(4) -> FacMin,lower bound on step decrease factor (default=0.2) |
---|
1098 | ! RCNTRL(5) -> FacMax,upper bound on step increase factor (default=6) |
---|
1099 | ! RCNTRL(6) -> FacRej,step decrease factor after multiple rejections |
---|
1100 | ! (default=0.1) |
---|
1101 | ! RCNTRL(7) -> FacSafe,by which the new step is slightly smaller |
---|
1102 | ! than the predicted value (default=0.9) |
---|
1103 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1104 | ! |
---|
1105 | ! |
---|
1106 | ! OUTPUT ARGUMENTS: |
---|
1107 | ! ----------------- |
---|
1108 | ! |
---|
1109 | ! T -> T value for which the solution has been computed |
---|
1110 | ! (after successful return T=Tend). |
---|
1111 | ! |
---|
1112 | ! Y(N) -> Numerical solution at T |
---|
1113 | ! |
---|
1114 | ! IDID -> Reports on successfulness upon return: |
---|
1115 | ! = 1 for success |
---|
1116 | ! < 0 for error (value equals error code) |
---|
1117 | ! |
---|
1118 | ! ISTATUS(1) -> No. of function calls |
---|
1119 | ! ISTATUS(2) -> No. of jacobian calls |
---|
1120 | ! ISTATUS(3) -> No. of steps |
---|
1121 | ! ISTATUS(4) -> No. of accepted steps |
---|
1122 | ! ISTATUS(5) -> No. of rejected steps (except at very beginning) |
---|
1123 | ! ISTATUS(6) -> No. of LU decompositions |
---|
1124 | ! ISTATUS(7) -> No. of forward/backward substitutions |
---|
1125 | ! ISTATUS(8) -> No. of singular matrix decompositions |
---|
1126 | ! |
---|
1127 | ! RSTATUS(1) -> Texit,the time corresponding to the |
---|
1128 | ! computed Y upon return |
---|
1129 | ! RSTATUS(2) -> Hexit,last accepted step before exit |
---|
1130 | ! RSTATUS(3) -> Hnew,last predicted step (not yet taken) |
---|
1131 | ! For multiple restarts,use Hnew as Hstart |
---|
1132 | ! in the subsequent run |
---|
1133 | ! |
---|
1134 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1135 | |
---|
1136 | |
---|
1137 | !~~~> arguments |
---|
1138 | INTEGER, INTENT(IN) :: n |
---|
1139 | REAL(kind=dp), INTENT(INOUT):: y(n) |
---|
1140 | REAL(kind=dp), INTENT(IN) :: tstart, tend |
---|
1141 | REAL(kind=dp), INTENT(IN) :: abstol(n), reltol(n) |
---|
1142 | INTEGER, INTENT(IN) :: icntrl(20) |
---|
1143 | REAL(kind=dp), INTENT(IN) :: rcntrl(20) |
---|
1144 | INTEGER, INTENT(INOUT):: istatus(20) |
---|
1145 | REAL(kind=dp), INTENT(INOUT):: rstatus(20) |
---|
1146 | INTEGER, INTENT(OUT) :: ierr |
---|
1147 | !~~~> PARAMETERs of the rosenbrock method, up to 6 stages |
---|
1148 | INTEGER :: ros_s, rosmethod |
---|
1149 | INTEGER, PARAMETER :: rs2=1, rs3=2, rs4=3, rd3=4, rd4=5, rg3=6 |
---|
1150 | REAL(kind=dp):: ros_a(15), ros_c(15), ros_m(6), ros_e(6), & |
---|
1151 | ros_alpha(6), ros_gamma(6), ros_elo |
---|
1152 | LOGICAL :: ros_newf(6) |
---|
1153 | CHARACTER(len=12):: ros_name |
---|
1154 | !~~~> local variables |
---|
1155 | REAL(kind=dp):: roundoff, facmin, facmax, facrej, facsafe |
---|
1156 | REAL(kind=dp):: hmin, hmax, hstart |
---|
1157 | REAL(kind=dp):: texit |
---|
1158 | INTEGER :: i, uplimtol, max_no_steps |
---|
1159 | LOGICAL :: autonomous, vectortol |
---|
1160 | !~~~> PARAMETERs |
---|
1161 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
---|
1162 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
---|
1163 | |
---|
1164 | !~~~> initialize statistics |
---|
1165 | istatus(1:8) = 0 |
---|
1166 | rstatus(1:3) = zero |
---|
1167 | |
---|
1168 | !~~~> autonomous or time dependent ode. default is time dependent. |
---|
1169 | autonomous = .not.(icntrl(1) == 0) |
---|
1170 | |
---|
1171 | !~~~> for scalar tolerances (icntrl(2).ne.0) the code uses abstol(1)and reltol(1) |
---|
1172 | ! For Vector tolerances (ICNTRL(2) == 0) the code uses AbsTol(1:N) and RelTol(1:N) |
---|
1173 | IF (icntrl(2) == 0)THEN |
---|
1174 | vectortol = .TRUE. |
---|
1175 | uplimtol = n |
---|
1176 | ELSE |
---|
1177 | vectortol = .FALSE. |
---|
1178 | uplimtol = 1 |
---|
1179 | ENDIF |
---|
1180 | |
---|
1181 | !~~~> initialize the particular rosenbrock method selected |
---|
1182 | select CASE (icntrl(3)) |
---|
1183 | CASE (1) |
---|
1184 | CALL ros2 |
---|
1185 | CASE (2) |
---|
1186 | CALL ros3 |
---|
1187 | CASE (3) |
---|
1188 | CALL ros4 |
---|
1189 | CASE (0, 4) |
---|
1190 | CALL rodas3 |
---|
1191 | CASE (5) |
---|
1192 | CALL rodas4 |
---|
1193 | CASE (6) |
---|
1194 | CALL rang3 |
---|
1195 | CASE default |
---|
1196 | PRINT *,'Unknown Rosenbrock method: ICNTRL(3) =',ICNTRL(3) |
---|
1197 | CALL ros_errormsg(- 2, tstart, zero, ierr) |
---|
1198 | RETURN |
---|
1199 | END select |
---|
1200 | |
---|
1201 | !~~~> the maximum number of steps admitted |
---|
1202 | IF (icntrl(4) == 0)THEN |
---|
1203 | max_no_steps = 200000 |
---|
1204 | ELSEIF (icntrl(4)> 0)THEN |
---|
1205 | max_no_steps=icntrl(4) |
---|
1206 | ELSE |
---|
1207 | PRINT *,'User-selected max no. of steps: ICNTRL(4) =',ICNTRL(4) |
---|
1208 | CALL ros_errormsg(- 1, tstart, zero, ierr) |
---|
1209 | RETURN |
---|
1210 | ENDIF |
---|
1211 | |
---|
1212 | !~~~> unit roundoff (1+ roundoff>1) |
---|
1213 | roundoff = epsilon(one) |
---|
1214 | |
---|
1215 | !~~~> lower bound on the step size: (positive value) |
---|
1216 | IF (rcntrl(1) == zero)THEN |
---|
1217 | hmin = zero |
---|
1218 | ELSEIF (rcntrl(1)> zero)THEN |
---|
1219 | hmin = rcntrl(1) |
---|
1220 | ELSE |
---|
1221 | PRINT *,'User-selected Hmin: RCNTRL(1) =',RCNTRL(1) |
---|
1222 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
1223 | RETURN |
---|
1224 | ENDIF |
---|
1225 | !~~~> upper bound on the step size: (positive value) |
---|
1226 | IF (rcntrl(2) == zero)THEN |
---|
1227 | hmax = abs(tend-tstart) |
---|
1228 | ELSEIF (rcntrl(2)> zero)THEN |
---|
1229 | hmax = min(abs(rcntrl(2)), abs(tend-tstart)) |
---|
1230 | ELSE |
---|
1231 | PRINT *,'User-selected Hmax: RCNTRL(2) =',RCNTRL(2) |
---|
1232 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
1233 | RETURN |
---|
1234 | ENDIF |
---|
1235 | !~~~> starting step size: (positive value) |
---|
1236 | IF (rcntrl(3) == zero)THEN |
---|
1237 | hstart = max(hmin, deltamin) |
---|
1238 | ELSEIF (rcntrl(3)> zero)THEN |
---|
1239 | hstart = min(abs(rcntrl(3)), abs(tend-tstart)) |
---|
1240 | ELSE |
---|
1241 | PRINT *,'User-selected Hstart: RCNTRL(3) =',RCNTRL(3) |
---|
1242 | CALL ros_errormsg(- 3, tstart, zero, ierr) |
---|
1243 | RETURN |
---|
1244 | ENDIF |
---|
1245 | !~~~> step size can be changed s.t. facmin < hnew/hold < facmax |
---|
1246 | IF (rcntrl(4) == zero)THEN |
---|
1247 | facmin = 0.2_dp |
---|
1248 | ELSEIF (rcntrl(4)> zero)THEN |
---|
1249 | facmin = rcntrl(4) |
---|
1250 | ELSE |
---|
1251 | PRINT *,'User-selected FacMin: RCNTRL(4) =',RCNTRL(4) |
---|
1252 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
1253 | RETURN |
---|
1254 | ENDIF |
---|
1255 | IF (rcntrl(5) == zero)THEN |
---|
1256 | facmax = 6.0_dp |
---|
1257 | ELSEIF (rcntrl(5)> zero)THEN |
---|
1258 | facmax = rcntrl(5) |
---|
1259 | ELSE |
---|
1260 | PRINT *,'User-selected FacMax: RCNTRL(5) =',RCNTRL(5) |
---|
1261 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
1262 | RETURN |
---|
1263 | ENDIF |
---|
1264 | !~~~> facrej: factor to decrease step after 2 succesive rejections |
---|
1265 | IF (rcntrl(6) == zero)THEN |
---|
1266 | facrej = 0.1_dp |
---|
1267 | ELSEIF (rcntrl(6)> zero)THEN |
---|
1268 | facrej = rcntrl(6) |
---|
1269 | ELSE |
---|
1270 | PRINT *,'User-selected FacRej: RCNTRL(6) =',RCNTRL(6) |
---|
1271 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
1272 | RETURN |
---|
1273 | ENDIF |
---|
1274 | !~~~> facsafe: safety factor in the computation of new step size |
---|
1275 | IF (rcntrl(7) == zero)THEN |
---|
1276 | facsafe = 0.9_dp |
---|
1277 | ELSEIF (rcntrl(7)> zero)THEN |
---|
1278 | facsafe = rcntrl(7) |
---|
1279 | ELSE |
---|
1280 | PRINT *,'User-selected FacSafe: RCNTRL(7) =',RCNTRL(7) |
---|
1281 | CALL ros_errormsg(- 4, tstart, zero, ierr) |
---|
1282 | RETURN |
---|
1283 | ENDIF |
---|
1284 | !~~~> check IF tolerances are reasonable |
---|
1285 | DO i=1, uplimtol |
---|
1286 | IF ((abstol(i)<= zero).or. (reltol(i)<= 10.0_dp* roundoff)& |
---|
1287 | .or. (reltol(i)>= 1.0_dp))THEN |
---|
1288 | PRINT *,' AbsTol(',i,') = ',AbsTol(i) |
---|
1289 | PRINT *,' RelTol(',i,') = ',RelTol(i) |
---|
1290 | CALL ros_errormsg(- 5, tstart, zero, ierr) |
---|
1291 | RETURN |
---|
1292 | ENDIF |
---|
1293 | ENDDO |
---|
1294 | |
---|
1295 | |
---|
1296 | !~~~> CALL rosenbrock method |
---|
1297 | CALL ros_integrator(y, tstart, tend, texit, & |
---|
1298 | abstol, reltol, & |
---|
1299 | ! Integration parameters |
---|
1300 | autonomous, vectortol, max_no_steps, & |
---|
1301 | roundoff, hmin, hmax, hstart, & |
---|
1302 | facmin, facmax, facrej, facsafe, & |
---|
1303 | ! Error indicator |
---|
1304 | ierr) |
---|
1305 | |
---|
1306 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1307 | CONTAINS ! SUBROUTINEs internal to rosenbrock |
---|
1308 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1309 | |
---|
1310 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1311 | SUBROUTINE ros_errormsg(code, t, h, ierr) |
---|
1312 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1313 | ! Handles all error messages |
---|
1314 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1315 | |
---|
1316 | REAL(kind=dp), INTENT(IN):: t, h |
---|
1317 | INTEGER, INTENT(IN) :: code |
---|
1318 | INTEGER, INTENT(OUT):: ierr |
---|
1319 | |
---|
1320 | ierr = code |
---|
1321 | print * , & |
---|
1322 | 'Forced exit from Rosenbrock due to the following error:' |
---|
1323 | |
---|
1324 | select CASE (code) |
---|
1325 | CASE (- 1) |
---|
1326 | PRINT *,'--> Improper value for maximal no of steps' |
---|
1327 | CASE (- 2) |
---|
1328 | PRINT *,'--> Selected Rosenbrock method not implemented' |
---|
1329 | CASE (- 3) |
---|
1330 | PRINT *,'--> Hmin/Hmax/Hstart must be positive' |
---|
1331 | CASE (- 4) |
---|
1332 | PRINT *,'--> FacMin/FacMax/FacRej must be positive' |
---|
1333 | CASE (- 5) |
---|
1334 | PRINT *,'--> Improper tolerance values' |
---|
1335 | CASE (- 6) |
---|
1336 | PRINT *,'--> No of steps exceeds maximum bound' |
---|
1337 | CASE (- 7) |
---|
1338 | PRINT *,'--> Step size too small: T + 10*H = T',& |
---|
1339 | ' or H < Roundoff' |
---|
1340 | CASE (- 8) |
---|
1341 | PRINT *,'--> Matrix is repeatedly singular' |
---|
1342 | CASE default |
---|
1343 | PRINT *,'Unknown Error code: ',Code |
---|
1344 | END select |
---|
1345 | |
---|
1346 | print * , "t=", t, "and h=", h |
---|
1347 | |
---|
1348 | END SUBROUTINE ros_errormsg |
---|
1349 | |
---|
1350 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1351 | SUBROUTINE ros_integrator (y, tstart, tend, t, & |
---|
1352 | abstol, reltol, & |
---|
1353 | !~~~> integration PARAMETERs |
---|
1354 | autonomous, vectortol, max_no_steps, & |
---|
1355 | roundoff, hmin, hmax, hstart, & |
---|
1356 | facmin, facmax, facrej, facsafe, & |
---|
1357 | !~~~> error indicator |
---|
1358 | ierr) |
---|
1359 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1360 | ! Template for the implementation of a generic Rosenbrock method |
---|
1361 | ! defined by ros_S (no of stages) |
---|
1362 | ! and its coefficients ros_{A,C,M,E,Alpha,Gamma} |
---|
1363 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1364 | |
---|
1365 | |
---|
1366 | !~~~> input: the initial condition at tstart; output: the solution at t |
---|
1367 | REAL(kind=dp), INTENT(INOUT):: y(n) |
---|
1368 | !~~~> input: integration interval |
---|
1369 | REAL(kind=dp), INTENT(IN):: tstart, tend |
---|
1370 | !~~~> output: time at which the solution is RETURNed (t=tendIF success) |
---|
1371 | REAL(kind=dp), INTENT(OUT):: t |
---|
1372 | !~~~> input: tolerances |
---|
1373 | REAL(kind=dp), INTENT(IN):: abstol(n), reltol(n) |
---|
1374 | !~~~> input: integration PARAMETERs |
---|
1375 | LOGICAL, INTENT(IN):: autonomous, vectortol |
---|
1376 | REAL(kind=dp), INTENT(IN):: hstart, hmin, hmax |
---|
1377 | INTEGER, INTENT(IN):: max_no_steps |
---|
1378 | REAL(kind=dp), INTENT(IN):: roundoff, facmin, facmax, facrej, facsafe |
---|
1379 | !~~~> output: error indicator |
---|
1380 | INTEGER, INTENT(OUT):: ierr |
---|
1381 | ! ~~~~ Local variables |
---|
1382 | REAL(kind=dp):: ynew(n), fcn0(n), fcn(n) |
---|
1383 | REAL(kind=dp):: k(n* ros_s), dfdt(n) |
---|
1384 | #ifdef full_algebra |
---|
1385 | REAL(kind=dp):: jac0(n, n), ghimj(n, n) |
---|
1386 | #else |
---|
1387 | REAL(kind=dp):: jac0(lu_nonzero), ghimj(lu_nonzero) |
---|
1388 | #endif |
---|
1389 | REAL(kind=dp):: h, hnew, hc, hg, fac, tau |
---|
1390 | REAL(kind=dp):: err, yerr(n) |
---|
1391 | INTEGER :: pivot(n), direction, ioffset, j, istage |
---|
1392 | LOGICAL :: rejectlasth, rejectmoreh, singular |
---|
1393 | !~~~> local PARAMETERs |
---|
1394 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp, one = 1.0_dp |
---|
1395 | REAL(kind=dp), PARAMETER :: deltamin = 1.0e-5_dp |
---|
1396 | !~~~> locally called FUNCTIONs |
---|
1397 | ! REAL(kind=dp) WLAMCH |
---|
1398 | ! EXTERNAL WLAMCH |
---|
1399 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1400 | |
---|
1401 | |
---|
1402 | !~~~> initial preparations |
---|
1403 | t = tstart |
---|
1404 | rstatus(nhexit) = zero |
---|
1405 | h = min( max(abs(hmin), abs(hstart)), abs(hmax)) |
---|
1406 | IF (abs(h)<= 10.0_dp* roundoff)h = deltamin |
---|
1407 | |
---|
1408 | IF (tend >= tstart)THEN |
---|
1409 | direction = + 1 |
---|
1410 | ELSE |
---|
1411 | direction = - 1 |
---|
1412 | ENDIF |
---|
1413 | h = direction* h |
---|
1414 | |
---|
1415 | rejectlasth=.FALSE. |
---|
1416 | rejectmoreh=.FALSE. |
---|
1417 | |
---|
1418 | !~~~> time loop begins below |
---|
1419 | |
---|
1420 | timeloop: DO WHILE((direction > 0).and.((t- tend) + roundoff <= zero)& |
---|
1421 | .or. (direction < 0).and.((tend-t) + roundoff <= zero)) |
---|
1422 | |
---|
1423 | IF (istatus(nstp)> max_no_steps)THEN ! too many steps |
---|
1424 | CALL ros_errormsg(- 6, t, h, ierr) |
---|
1425 | RETURN |
---|
1426 | ENDIF |
---|
1427 | IF (((t+ 0.1_dp* h) == t).or.(h <= roundoff))THEN ! step size too small |
---|
1428 | CALL ros_errormsg(- 7, t, h, ierr) |
---|
1429 | RETURN |
---|
1430 | ENDIF |
---|
1431 | |
---|
1432 | !~~~> limit h IF necessary to avoid going beyond tend |
---|
1433 | h = min(h, abs(tend-t)) |
---|
1434 | |
---|
1435 | !~~~> compute the FUNCTION at current time |
---|
1436 | CALL funtemplate(t, y, fcn0) |
---|
1437 | istatus(nfun) = istatus(nfun) + 1 |
---|
1438 | |
---|
1439 | !~~~> compute the FUNCTION derivative with respect to t |
---|
1440 | IF (.not.autonomous)THEN |
---|
1441 | CALL ros_funtimederivative(t, roundoff, y, & |
---|
1442 | fcn0, dfdt) |
---|
1443 | ENDIF |
---|
1444 | |
---|
1445 | !~~~> compute the jacobian at current time |
---|
1446 | CALL jactemplate(t, y, jac0) |
---|
1447 | istatus(njac) = istatus(njac) + 1 |
---|
1448 | |
---|
1449 | !~~~> repeat step calculation until current step accepted |
---|
1450 | untilaccepted: do |
---|
1451 | |
---|
1452 | CALL ros_preparematrix(h, direction, ros_gamma(1), & |
---|
1453 | jac0, ghimj, pivot, singular) |
---|
1454 | IF (singular)THEN ! more than 5 consecutive failed decompositions |
---|
1455 | CALL ros_errormsg(- 8, t, h, ierr) |
---|
1456 | RETURN |
---|
1457 | ENDIF |
---|
1458 | |
---|
1459 | !~~~> compute the stages |
---|
1460 | stage: DO istage = 1, ros_s |
---|
1461 | |
---|
1462 | ! current istage offset. current istage vector is k(ioffset+ 1:ioffset+ n) |
---|
1463 | ioffset = n* (istage-1) |
---|
1464 | |
---|
1465 | ! for the 1st istage the FUNCTION has been computed previously |
---|
1466 | IF (istage == 1)THEN |
---|
1467 | !slim: CALL wcopy(n, fcn0, 1, fcn, 1) |
---|
1468 | fcn(1:n) = fcn0(1:n) |
---|
1469 | ! istage>1 and a new FUNCTION evaluation is needed at the current istage |
---|
1470 | ELSEIF(ros_newf(istage))THEN |
---|
1471 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
---|
1472 | ynew(1:n) = y(1:n) |
---|
1473 | DO j = 1, istage-1 |
---|
1474 | CALL waxpy(n, ros_a((istage-1) * (istage-2) /2+ j), & |
---|
1475 | k(n* (j- 1) + 1), 1, ynew, 1) |
---|
1476 | ENDDO |
---|
1477 | tau = t + ros_alpha(istage) * direction* h |
---|
1478 | CALL funtemplate(tau, ynew, fcn) |
---|
1479 | istatus(nfun) = istatus(nfun) + 1 |
---|
1480 | ENDIF ! IF istage == 1 ELSEIF ros_newf(istage) |
---|
1481 | !slim: CALL wcopy(n, fcn, 1, k(ioffset+ 1), 1) |
---|
1482 | k(ioffset+ 1:ioffset+ n) = fcn(1:n) |
---|
1483 | DO j = 1, istage-1 |
---|
1484 | hc = ros_c((istage-1) * (istage-2) /2+ j) /(direction* h) |
---|
1485 | CALL waxpy(n, hc, k(n* (j- 1) + 1), 1, k(ioffset+ 1), 1) |
---|
1486 | ENDDO |
---|
1487 | IF ((.not. autonomous).and.(ros_gamma(istage).ne.zero))THEN |
---|
1488 | hg = direction* h* ros_gamma(istage) |
---|
1489 | CALL waxpy(n, hg, dfdt, 1, k(ioffset+ 1), 1) |
---|
1490 | ENDIF |
---|
1491 | CALL ros_solve(ghimj, pivot, k(ioffset+ 1)) |
---|
1492 | |
---|
1493 | END DO stage |
---|
1494 | |
---|
1495 | |
---|
1496 | !~~~> compute the new solution |
---|
1497 | !slim: CALL wcopy(n, y, 1, ynew, 1) |
---|
1498 | ynew(1:n) = y(1:n) |
---|
1499 | DO j=1, ros_s |
---|
1500 | CALL waxpy(n, ros_m(j), k(n* (j- 1) + 1), 1, ynew, 1) |
---|
1501 | ENDDO |
---|
1502 | |
---|
1503 | !~~~> compute the error estimation |
---|
1504 | !slim: CALL wscal(n, zero, yerr, 1) |
---|
1505 | yerr(1:n) = zero |
---|
1506 | DO j=1, ros_s |
---|
1507 | CALL waxpy(n, ros_e(j), k(n* (j- 1) + 1), 1, yerr, 1) |
---|
1508 | ENDDO |
---|
1509 | err = ros_errornorm(y, ynew, yerr, abstol, reltol, vectortol) |
---|
1510 | |
---|
1511 | !~~~> new step size is bounded by facmin <= hnew/h <= facmax |
---|
1512 | fac = min(facmax, max(facmin, facsafe/err** (one/ros_elo))) |
---|
1513 | hnew = h* fac |
---|
1514 | |
---|
1515 | !~~~> check the error magnitude and adjust step size |
---|
1516 | istatus(nstp) = istatus(nstp) + 1 |
---|
1517 | IF ((err <= one).or.(h <= hmin))THEN !~~~> accept step |
---|
1518 | istatus(nacc) = istatus(nacc) + 1 |
---|
1519 | !slim: CALL wcopy(n, ynew, 1, y, 1) |
---|
1520 | y(1:n) = ynew(1:n) |
---|
1521 | t = t + direction* h |
---|
1522 | hnew = max(hmin, min(hnew, hmax)) |
---|
1523 | IF (rejectlasth)THEN ! no step size increase after a rejected step |
---|
1524 | hnew = min(hnew, h) |
---|
1525 | ENDIF |
---|
1526 | rstatus(nhexit) = h |
---|
1527 | rstatus(nhnew) = hnew |
---|
1528 | rstatus(ntexit) = t |
---|
1529 | rejectlasth = .FALSE. |
---|
1530 | rejectmoreh = .FALSE. |
---|
1531 | h = hnew |
---|
1532 | exit untilaccepted ! exit the loop: WHILE step not accepted |
---|
1533 | ELSE !~~~> reject step |
---|
1534 | IF (rejectmoreh)THEN |
---|
1535 | hnew = h* facrej |
---|
1536 | ENDIF |
---|
1537 | rejectmoreh = rejectlasth |
---|
1538 | rejectlasth = .TRUE. |
---|
1539 | h = hnew |
---|
1540 | IF (istatus(nacc)>= 1) istatus(nrej) = istatus(nrej) + 1 |
---|
1541 | ENDIF ! err <= 1 |
---|
1542 | |
---|
1543 | END DO untilaccepted |
---|
1544 | |
---|
1545 | END DO timeloop |
---|
1546 | |
---|
1547 | !~~~> succesful exit |
---|
1548 | ierr = 1 !~~~> the integration was successful |
---|
1549 | |
---|
1550 | END SUBROUTINE ros_integrator |
---|
1551 | |
---|
1552 | |
---|
1553 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1554 | REAL(kind=dp)FUNCTION ros_errornorm(y, ynew, yerr, & |
---|
1555 | abstol, reltol, vectortol) |
---|
1556 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1557 | !~~~> computes the "scaled norm" of the error vector yerr |
---|
1558 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1559 | |
---|
1560 | ! Input arguments |
---|
1561 | REAL(kind=dp), INTENT(IN):: y(n), ynew(n), & |
---|
1562 | yerr(n), abstol(n), reltol(n) |
---|
1563 | LOGICAL, INTENT(IN):: vectortol |
---|
1564 | ! Local variables |
---|
1565 | REAL(kind=dp):: err, scale, ymax |
---|
1566 | INTEGER :: i |
---|
1567 | REAL(kind=dp), PARAMETER :: zero = 0.0_dp |
---|
1568 | |
---|
1569 | err = zero |
---|
1570 | DO i=1, n |
---|
1571 | ymax = max(abs(y(i)), abs(ynew(i))) |
---|
1572 | IF (vectortol)THEN |
---|
1573 | scale = abstol(i) + reltol(i) * ymax |
---|
1574 | ELSE |
---|
1575 | scale = abstol(1) + reltol(1) * ymax |
---|
1576 | ENDIF |
---|
1577 | err = err+ (yerr(i) /scale) ** 2 |
---|
1578 | ENDDO |
---|
1579 | err = sqrt(err/n) |
---|
1580 | |
---|
1581 | ros_errornorm = max(err, 1.0d-10) |
---|
1582 | |
---|
1583 | END FUNCTION ros_errornorm |
---|
1584 | |
---|
1585 | |
---|
1586 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1587 | SUBROUTINE ros_funtimederivative(t, roundoff, y, & |
---|
1588 | fcn0, dfdt) |
---|
1589 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1590 | !~~~> the time partial derivative of the FUNCTION by finite differences |
---|
1591 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1592 | |
---|
1593 | !~~~> input arguments |
---|
1594 | REAL(kind=dp), INTENT(IN):: t, roundoff, y(n), fcn0(n) |
---|
1595 | !~~~> output arguments |
---|
1596 | REAL(kind=dp), INTENT(OUT):: dfdt(n) |
---|
1597 | !~~~> local variables |
---|
1598 | REAL(kind=dp):: delta |
---|
1599 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, deltamin = 1.0e-6_dp |
---|
1600 | |
---|
1601 | delta = sqrt(roundoff) * max(deltamin, abs(t)) |
---|
1602 | CALL funtemplate(t+ delta, y, dfdt) |
---|
1603 | istatus(nfun) = istatus(nfun) + 1 |
---|
1604 | CALL waxpy(n, (- one), fcn0, 1, dfdt, 1) |
---|
1605 | CALL wscal(n, (one/delta), dfdt, 1) |
---|
1606 | |
---|
1607 | END SUBROUTINE ros_funtimederivative |
---|
1608 | |
---|
1609 | |
---|
1610 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1611 | SUBROUTINE ros_preparematrix(h, direction, gam, & |
---|
1612 | jac0, ghimj, pivot, singular) |
---|
1613 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
1614 | ! Prepares the LHS matrix for stage calculations |
---|
1615 | ! 1. Construct Ghimj = 1/(H*ham) - Jac0 |
---|
1616 | ! "(Gamma H) Inverse Minus Jacobian" |
---|
1617 | ! 2. Repeat LU decomposition of Ghimj until successful. |
---|
1618 | ! -half the step size if LU decomposition fails and retry |
---|
1619 | ! -exit after 5 consecutive fails |
---|
1620 | ! --- --- --- --- --- --- --- --- --- --- --- --- --- |
---|
1621 | |
---|
1622 | !~~~> input arguments |
---|
1623 | #ifdef full_algebra |
---|
1624 | REAL(kind=dp), INTENT(IN):: jac0(n, n) |
---|
1625 | #else |
---|
1626 | REAL(kind=dp), INTENT(IN):: jac0(lu_nonzero) |
---|
1627 | #endif |
---|
1628 | REAL(kind=dp), INTENT(IN):: gam |
---|
1629 | INTEGER, INTENT(IN):: direction |
---|
1630 | !~~~> output arguments |
---|
1631 | #ifdef full_algebra |
---|
1632 | REAL(kind=dp), INTENT(OUT):: ghimj(n, n) |
---|
1633 | #else |
---|
1634 | REAL(kind=dp), INTENT(OUT):: ghimj(lu_nonzero) |
---|
1635 | #endif |
---|
1636 | LOGICAL, INTENT(OUT):: singular |
---|
1637 | INTEGER, INTENT(OUT):: pivot(n) |
---|
1638 | !~~~> inout arguments |
---|
1639 | REAL(kind=dp), INTENT(INOUT):: h ! step size is decreased when lu fails |
---|
1640 | !~~~> local variables |
---|
1641 | INTEGER :: i, ising, nconsecutive |
---|
1642 | REAL(kind=dp):: ghinv |
---|
1643 | REAL(kind=dp), PARAMETER :: one = 1.0_dp, half = 0.5_dp |
---|
1644 | |
---|
1645 | nconsecutive = 0 |
---|
1646 | singular = .TRUE. |
---|
1647 | |
---|
1648 | DO WHILE (singular) |
---|
1649 | |
---|
1650 | !~~~> construct ghimj = 1/(h* gam) - jac0 |
---|
1651 | #ifdef full_algebra |
---|
1652 | !slim: CALL wcopy(n* n, jac0, 1, ghimj, 1) |
---|
1653 | !slim: CALL wscal(n* n, (- one), ghimj, 1) |
---|
1654 | ghimj = - jac0 |
---|
1655 | ghinv = one/(direction* h* gam) |
---|
1656 | DO i=1, n |
---|
1657 | ghimj(i, i) = ghimj(i, i) + ghinv |
---|
1658 | ENDDO |
---|
1659 | #else |
---|
1660 | !slim: CALL wcopy(lu_nonzero, jac0, 1, ghimj, 1) |
---|
1661 | !slim: CALL wscal(lu_nonzero, (- one), ghimj, 1) |
---|
1662 | ghimj(1:lu_nonzero) = - jac0(1:lu_nonzero) |
---|
1663 | ghinv = one/(direction* h* gam) |
---|
1664 | DO i=1, n |
---|
1665 | ghimj(lu_diag(i)) = ghimj(lu_diag(i)) + ghinv |
---|
1666 | ENDDO |
---|
1667 | #endif |
---|
1668 | !~~~> compute lu decomposition |
---|
1669 | CALL ros_decomp( ghimj, pivot, ising) |
---|
1670 | IF (ising == 0)THEN |
---|
1671 | !~~~> IF successful done |
---|
1672 | singular = .FALSE. |
---|
1673 | ELSE ! ising .ne. 0 |
---|
1674 | !~~~> IF unsuccessful half the step size; IF 5 consecutive fails THEN RETURN |
---|
1675 | istatus(nsng) = istatus(nsng) + 1 |
---|
1676 | nconsecutive = nconsecutive+1 |
---|
1677 | singular = .TRUE. |
---|
1678 | PRINT*,'Warning: LU Decomposition returned ISING = ',ISING |
---|
1679 | IF (nconsecutive <= 5)THEN ! less than 5 consecutive failed decompositions |
---|
1680 | h = h* half |
---|
1681 | ELSE ! more than 5 consecutive failed decompositions |
---|
1682 | RETURN |
---|
1683 | ENDIF ! nconsecutive |
---|
1684 | ENDIF ! ising |
---|
1685 | |
---|
1686 | END DO ! WHILE singular |
---|
1687 | |
---|
1688 | END SUBROUTINE ros_preparematrix |
---|
1689 | |
---|
1690 | |
---|
1691 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1692 | SUBROUTINE ros_decomp( a, pivot, ising) |
---|
1693 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1694 | ! Template for the LU decomposition |
---|
1695 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1696 | !~~~> inout variables |
---|
1697 | #ifdef full_algebra |
---|
1698 | REAL(kind=dp), INTENT(INOUT):: a(n, n) |
---|
1699 | #else |
---|
1700 | REAL(kind=dp), INTENT(INOUT):: a(lu_nonzero) |
---|
1701 | #endif |
---|
1702 | !~~~> output variables |
---|
1703 | INTEGER, INTENT(OUT):: pivot(n), ising |
---|
1704 | |
---|
1705 | #ifdef full_algebra |
---|
1706 | CALL dgetrf( n, n, a, n, pivot, ising) |
---|
1707 | #else |
---|
1708 | CALL kppdecomp(a, ising) |
---|
1709 | pivot(1) = 1 |
---|
1710 | #endif |
---|
1711 | istatus(ndec) = istatus(ndec) + 1 |
---|
1712 | |
---|
1713 | END SUBROUTINE ros_decomp |
---|
1714 | |
---|
1715 | |
---|
1716 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1717 | SUBROUTINE ros_solve( a, pivot, b) |
---|
1718 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1719 | ! Template for the forward/backward substitution (using pre-computed LU decomposition) |
---|
1720 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1721 | !~~~> input variables |
---|
1722 | #ifdef full_algebra |
---|
1723 | REAL(kind=dp), INTENT(IN):: a(n, n) |
---|
1724 | INTEGER :: ising |
---|
1725 | #else |
---|
1726 | REAL(kind=dp), INTENT(IN):: a(lu_nonzero) |
---|
1727 | #endif |
---|
1728 | INTEGER, INTENT(IN):: pivot(n) |
---|
1729 | !~~~> inout variables |
---|
1730 | REAL(kind=dp), INTENT(INOUT):: b(n) |
---|
1731 | |
---|
1732 | #ifdef full_algebra |
---|
1733 | CALL DGETRS( 'N',N ,1,A,N,Pivot,b,N,ISING) |
---|
1734 | IF (info < 0)THEN |
---|
1735 | print* , "error in dgetrs. ising=", ising |
---|
1736 | ENDIF |
---|
1737 | #else |
---|
1738 | CALL kppsolve( a, b) |
---|
1739 | #endif |
---|
1740 | |
---|
1741 | istatus(nsol) = istatus(nsol) + 1 |
---|
1742 | |
---|
1743 | END SUBROUTINE ros_solve |
---|
1744 | |
---|
1745 | |
---|
1746 | |
---|
1747 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1748 | SUBROUTINE ros2 |
---|
1749 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1750 | ! --- AN L-STABLE METHOD,2 stages,order 2 |
---|
1751 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1752 | |
---|
1753 | double precision g |
---|
1754 | |
---|
1755 | g = 1.0_dp + 1.0_dp/sqrt(2.0_dp) |
---|
1756 | rosmethod = rs2 |
---|
1757 | !~~~> name of the method |
---|
1758 | ros_Name = 'ROS-2' |
---|
1759 | !~~~> number of stages |
---|
1760 | ros_s = 2 |
---|
1761 | |
---|
1762 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
1763 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1764 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
1765 | ! The general mapping formula is: |
---|
1766 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
1767 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
1768 | |
---|
1769 | ros_a(1) = (1.0_dp) /g |
---|
1770 | ros_c(1) = (- 2.0_dp) /g |
---|
1771 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
1772 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
1773 | ros_newf(1) = .TRUE. |
---|
1774 | ros_newf(2) = .TRUE. |
---|
1775 | !~~~> m_i = coefficients for new step solution |
---|
1776 | ros_m(1) = (3.0_dp) /(2.0_dp* g) |
---|
1777 | ros_m(2) = (1.0_dp) /(2.0_dp* g) |
---|
1778 | ! E_i = Coefficients for error estimator |
---|
1779 | ros_e(1) = 1.0_dp/(2.0_dp* g) |
---|
1780 | ros_e(2) = 1.0_dp/(2.0_dp* g) |
---|
1781 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
1782 | ! main and the embedded scheme orders plus one |
---|
1783 | ros_elo = 2.0_dp |
---|
1784 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
1785 | ros_alpha(1) = 0.0_dp |
---|
1786 | ros_alpha(2) = 1.0_dp |
---|
1787 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
1788 | ros_gamma(1) = g |
---|
1789 | ros_gamma(2) = -g |
---|
1790 | |
---|
1791 | END SUBROUTINE ros2 |
---|
1792 | |
---|
1793 | |
---|
1794 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1795 | SUBROUTINE ros3 |
---|
1796 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1797 | ! --- AN L-STABLE METHOD,3 stages,order 3,2 function evaluations |
---|
1798 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1799 | |
---|
1800 | rosmethod = rs3 |
---|
1801 | !~~~> name of the method |
---|
1802 | ros_Name = 'ROS-3' |
---|
1803 | !~~~> number of stages |
---|
1804 | ros_s = 3 |
---|
1805 | |
---|
1806 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
1807 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1808 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
1809 | ! The general mapping formula is: |
---|
1810 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
1811 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
1812 | |
---|
1813 | ros_a(1) = 1.0_dp |
---|
1814 | ros_a(2) = 1.0_dp |
---|
1815 | ros_a(3) = 0.0_dp |
---|
1816 | |
---|
1817 | ros_c(1) = - 0.10156171083877702091975600115545e+01_dp |
---|
1818 | ros_c(2) = 0.40759956452537699824805835358067e+01_dp |
---|
1819 | ros_c(3) = 0.92076794298330791242156818474003e+01_dp |
---|
1820 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
1821 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
1822 | ros_newf(1) = .TRUE. |
---|
1823 | ros_newf(2) = .TRUE. |
---|
1824 | ros_newf(3) = .FALSE. |
---|
1825 | !~~~> m_i = coefficients for new step solution |
---|
1826 | ros_m(1) = 0.1e+01_dp |
---|
1827 | ros_m(2) = 0.61697947043828245592553615689730e+01_dp |
---|
1828 | ros_m(3) = - 0.42772256543218573326238373806514_dp |
---|
1829 | ! E_i = Coefficients for error estimator |
---|
1830 | ros_e(1) = 0.5_dp |
---|
1831 | ros_e(2) = - 0.29079558716805469821718236208017e+01_dp |
---|
1832 | ros_e(3) = 0.22354069897811569627360909276199_dp |
---|
1833 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
1834 | ! main and the embedded scheme orders plus 1 |
---|
1835 | ros_elo = 3.0_dp |
---|
1836 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
1837 | ros_alpha(1) = 0.0_dp |
---|
1838 | ros_alpha(2) = 0.43586652150845899941601945119356_dp |
---|
1839 | ros_alpha(3) = 0.43586652150845899941601945119356_dp |
---|
1840 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
1841 | ros_gamma(1) = 0.43586652150845899941601945119356_dp |
---|
1842 | ros_gamma(2) = 0.24291996454816804366592249683314_dp |
---|
1843 | ros_gamma(3) = 0.21851380027664058511513169485832e+01_dp |
---|
1844 | |
---|
1845 | END SUBROUTINE ros3 |
---|
1846 | |
---|
1847 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1848 | |
---|
1849 | |
---|
1850 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1851 | SUBROUTINE ros4 |
---|
1852 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1853 | ! L-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 4 STAGES |
---|
1854 | ! L-STABLE EMBEDDED ROSENBROCK METHOD OF ORDER 3 |
---|
1855 | ! |
---|
1856 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
---|
1857 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
1858 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
1859 | ! SPRINGER-VERLAG (1990) |
---|
1860 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1861 | |
---|
1862 | |
---|
1863 | rosmethod = rs4 |
---|
1864 | !~~~> name of the method |
---|
1865 | ros_Name = 'ROS-4' |
---|
1866 | !~~~> number of stages |
---|
1867 | ros_s = 4 |
---|
1868 | |
---|
1869 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
1870 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1871 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
1872 | ! The general mapping formula is: |
---|
1873 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
1874 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
1875 | |
---|
1876 | ros_a(1) = 0.2000000000000000e+01_dp |
---|
1877 | ros_a(2) = 0.1867943637803922e+01_dp |
---|
1878 | ros_a(3) = 0.2344449711399156_dp |
---|
1879 | ros_a(4) = ros_a(2) |
---|
1880 | ros_a(5) = ros_a(3) |
---|
1881 | ros_a(6) = 0.0_dp |
---|
1882 | |
---|
1883 | ros_c(1) = -0.7137615036412310e+01_dp |
---|
1884 | ros_c(2) = 0.2580708087951457e+01_dp |
---|
1885 | ros_c(3) = 0.6515950076447975_dp |
---|
1886 | ros_c(4) = -0.2137148994382534e+01_dp |
---|
1887 | ros_c(5) = -0.3214669691237626_dp |
---|
1888 | ros_c(6) = -0.6949742501781779_dp |
---|
1889 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
1890 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
1891 | ros_newf(1) = .TRUE. |
---|
1892 | ros_newf(2) = .TRUE. |
---|
1893 | ros_newf(3) = .TRUE. |
---|
1894 | ros_newf(4) = .FALSE. |
---|
1895 | !~~~> m_i = coefficients for new step solution |
---|
1896 | ros_m(1) = 0.2255570073418735e+01_dp |
---|
1897 | ros_m(2) = 0.2870493262186792_dp |
---|
1898 | ros_m(3) = 0.4353179431840180_dp |
---|
1899 | ros_m(4) = 0.1093502252409163e+01_dp |
---|
1900 | !~~~> e_i = coefficients for error estimator |
---|
1901 | ros_e(1) = -0.2815431932141155_dp |
---|
1902 | ros_e(2) = -0.7276199124938920e-01_dp |
---|
1903 | ros_e(3) = -0.1082196201495311_dp |
---|
1904 | ros_e(4) = -0.1093502252409163e+01_dp |
---|
1905 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
1906 | ! main and the embedded scheme orders plus 1 |
---|
1907 | ros_elo = 4.0_dp |
---|
1908 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
1909 | ros_alpha(1) = 0.0_dp |
---|
1910 | ros_alpha(2) = 0.1145640000000000e+01_dp |
---|
1911 | ros_alpha(3) = 0.6552168638155900_dp |
---|
1912 | ros_alpha(4) = ros_alpha(3) |
---|
1913 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
1914 | ros_gamma(1) = 0.5728200000000000_dp |
---|
1915 | ros_gamma(2) = -0.1769193891319233e+01_dp |
---|
1916 | ros_gamma(3) = 0.7592633437920482_dp |
---|
1917 | ros_gamma(4) = -0.1049021087100450_dp |
---|
1918 | |
---|
1919 | END SUBROUTINE ros4 |
---|
1920 | |
---|
1921 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1922 | SUBROUTINE rodas3 |
---|
1923 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1924 | ! --- A STIFFLY-STABLE METHOD,4 stages,order 3 |
---|
1925 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1926 | |
---|
1927 | |
---|
1928 | rosmethod = rd3 |
---|
1929 | !~~~> name of the method |
---|
1930 | ros_Name = 'RODAS-3' |
---|
1931 | !~~~> number of stages |
---|
1932 | ros_s = 4 |
---|
1933 | |
---|
1934 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
1935 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
1936 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
1937 | ! The general mapping formula is: |
---|
1938 | ! A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
1939 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
1940 | |
---|
1941 | ros_a(1) = 0.0_dp |
---|
1942 | ros_a(2) = 2.0_dp |
---|
1943 | ros_a(3) = 0.0_dp |
---|
1944 | ros_a(4) = 2.0_dp |
---|
1945 | ros_a(5) = 0.0_dp |
---|
1946 | ros_a(6) = 1.0_dp |
---|
1947 | |
---|
1948 | ros_c(1) = 4.0_dp |
---|
1949 | ros_c(2) = 1.0_dp |
---|
1950 | ros_c(3) = -1.0_dp |
---|
1951 | ros_c(4) = 1.0_dp |
---|
1952 | ros_c(5) = -1.0_dp |
---|
1953 | ros_c(6) = -(8.0_dp/3.0_dp) |
---|
1954 | |
---|
1955 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
1956 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
1957 | ros_newf(1) = .TRUE. |
---|
1958 | ros_newf(2) = .FALSE. |
---|
1959 | ros_newf(3) = .TRUE. |
---|
1960 | ros_newf(4) = .TRUE. |
---|
1961 | !~~~> m_i = coefficients for new step solution |
---|
1962 | ros_m(1) = 2.0_dp |
---|
1963 | ros_m(2) = 0.0_dp |
---|
1964 | ros_m(3) = 1.0_dp |
---|
1965 | ros_m(4) = 1.0_dp |
---|
1966 | !~~~> e_i = coefficients for error estimator |
---|
1967 | ros_e(1) = 0.0_dp |
---|
1968 | ros_e(2) = 0.0_dp |
---|
1969 | ros_e(3) = 0.0_dp |
---|
1970 | ros_e(4) = 1.0_dp |
---|
1971 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
1972 | ! main and the embedded scheme orders plus 1 |
---|
1973 | ros_elo = 3.0_dp |
---|
1974 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
1975 | ros_alpha(1) = 0.0_dp |
---|
1976 | ros_alpha(2) = 0.0_dp |
---|
1977 | ros_alpha(3) = 1.0_dp |
---|
1978 | ros_alpha(4) = 1.0_dp |
---|
1979 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
1980 | ros_gamma(1) = 0.5_dp |
---|
1981 | ros_gamma(2) = 1.5_dp |
---|
1982 | ros_gamma(3) = 0.0_dp |
---|
1983 | ros_gamma(4) = 0.0_dp |
---|
1984 | |
---|
1985 | END SUBROUTINE rodas3 |
---|
1986 | |
---|
1987 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1988 | SUBROUTINE rodas4 |
---|
1989 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1990 | ! STIFFLY-STABLE ROSENBROCK METHOD OF ORDER 4,WITH 6 STAGES |
---|
1991 | ! |
---|
1992 | ! E. HAIRER AND G. WANNER,SOLVING ORDINARY DIFFERENTIAL |
---|
1993 | ! EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS. |
---|
1994 | ! SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS, |
---|
1995 | ! SPRINGER-VERLAG (1996) |
---|
1996 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
1997 | |
---|
1998 | |
---|
1999 | rosmethod = rd4 |
---|
2000 | !~~~> name of the method |
---|
2001 | ros_Name = 'RODAS-4' |
---|
2002 | !~~~> number of stages |
---|
2003 | ros_s = 6 |
---|
2004 | |
---|
2005 | !~~~> y_stage_i ~ y( t + h* alpha_i) |
---|
2006 | ros_alpha(1) = 0.000_dp |
---|
2007 | ros_alpha(2) = 0.386_dp |
---|
2008 | ros_alpha(3) = 0.210_dp |
---|
2009 | ros_alpha(4) = 0.630_dp |
---|
2010 | ros_alpha(5) = 1.000_dp |
---|
2011 | ros_alpha(6) = 1.000_dp |
---|
2012 | |
---|
2013 | !~~~> gamma_i = \sum_j gamma_{i, j} |
---|
2014 | ros_gamma(1) = 0.2500000000000000_dp |
---|
2015 | ros_gamma(2) = -0.1043000000000000_dp |
---|
2016 | ros_gamma(3) = 0.1035000000000000_dp |
---|
2017 | ros_gamma(4) = -0.3620000000000023e-01_dp |
---|
2018 | ros_gamma(5) = 0.0_dp |
---|
2019 | ros_gamma(6) = 0.0_dp |
---|
2020 | |
---|
2021 | !~~~> the coefficient matrices a and c are strictly lower triangular. |
---|
2022 | ! The lower triangular (subdiagonal) elements are stored in row-wise order: |
---|
2023 | ! A(2,1) = ros_A(1),A(3,1) =ros_A(2),A(3,2) =ros_A(3),etc. |
---|
2024 | ! The general mapping formula is: A(i,j) = ros_A( (i-1)*(i-2)/2 + j) |
---|
2025 | ! C(i,j) = ros_C( (i-1)*(i-2)/2 + j) |
---|
2026 | |
---|
2027 | ros_a(1) = 0.1544000000000000e+01_dp |
---|
2028 | ros_a(2) = 0.9466785280815826_dp |
---|
2029 | ros_a(3) = 0.2557011698983284_dp |
---|
2030 | ros_a(4) = 0.3314825187068521e+01_dp |
---|
2031 | ros_a(5) = 0.2896124015972201e+01_dp |
---|
2032 | ros_a(6) = 0.9986419139977817_dp |
---|
2033 | ros_a(7) = 0.1221224509226641e+01_dp |
---|
2034 | ros_a(8) = 0.6019134481288629e+01_dp |
---|
2035 | ros_a(9) = 0.1253708332932087e+02_dp |
---|
2036 | ros_a(10) = -0.6878860361058950_dp |
---|
2037 | ros_a(11) = ros_a(7) |
---|
2038 | ros_a(12) = ros_a(8) |
---|
2039 | ros_a(13) = ros_a(9) |
---|
2040 | ros_a(14) = ros_a(10) |
---|
2041 | ros_a(15) = 1.0_dp |
---|
2042 | |
---|
2043 | ros_c(1) = -0.5668800000000000e+01_dp |
---|
2044 | ros_c(2) = -0.2430093356833875e+01_dp |
---|
2045 | ros_c(3) = -0.2063599157091915_dp |
---|
2046 | ros_c(4) = -0.1073529058151375_dp |
---|
2047 | ros_c(5) = -0.9594562251023355e+01_dp |
---|
2048 | ros_c(6) = -0.2047028614809616e+02_dp |
---|
2049 | ros_c(7) = 0.7496443313967647e+01_dp |
---|
2050 | ros_c(8) = -0.1024680431464352e+02_dp |
---|
2051 | ros_c(9) = -0.3399990352819905e+02_dp |
---|
2052 | ros_c(10) = 0.1170890893206160e+02_dp |
---|
2053 | ros_c(11) = 0.8083246795921522e+01_dp |
---|
2054 | ros_c(12) = -0.7981132988064893e+01_dp |
---|
2055 | ros_c(13) = -0.3152159432874371e+02_dp |
---|
2056 | ros_c(14) = 0.1631930543123136e+02_dp |
---|
2057 | ros_c(15) = -0.6058818238834054e+01_dp |
---|
2058 | |
---|
2059 | !~~~> m_i = coefficients for new step solution |
---|
2060 | ros_m(1) = ros_a(7) |
---|
2061 | ros_m(2) = ros_a(8) |
---|
2062 | ros_m(3) = ros_a(9) |
---|
2063 | ros_m(4) = ros_a(10) |
---|
2064 | ros_m(5) = 1.0_dp |
---|
2065 | ros_m(6) = 1.0_dp |
---|
2066 | |
---|
2067 | !~~~> e_i = coefficients for error estimator |
---|
2068 | ros_e(1) = 0.0_dp |
---|
2069 | ros_e(2) = 0.0_dp |
---|
2070 | ros_e(3) = 0.0_dp |
---|
2071 | ros_e(4) = 0.0_dp |
---|
2072 | ros_e(5) = 0.0_dp |
---|
2073 | ros_e(6) = 1.0_dp |
---|
2074 | |
---|
2075 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
2076 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
2077 | ros_newf(1) = .TRUE. |
---|
2078 | ros_newf(2) = .TRUE. |
---|
2079 | ros_newf(3) = .TRUE. |
---|
2080 | ros_newf(4) = .TRUE. |
---|
2081 | ros_newf(5) = .TRUE. |
---|
2082 | ros_newf(6) = .TRUE. |
---|
2083 | |
---|
2084 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
2085 | ! main and the embedded scheme orders plus 1 |
---|
2086 | ros_elo = 4.0_dp |
---|
2087 | |
---|
2088 | END SUBROUTINE rodas4 |
---|
2089 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2090 | SUBROUTINE rang3 |
---|
2091 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2092 | ! STIFFLY-STABLE W METHOD OF ORDER 3,WITH 4 STAGES |
---|
2093 | ! |
---|
2094 | ! J. RANG and L. ANGERMANN |
---|
2095 | ! NEW ROSENBROCK W-METHODS OF ORDER 3 |
---|
2096 | ! FOR PARTIAL DIFFERENTIAL ALGEBRAIC |
---|
2097 | ! EQUATIONS OF INDEX 1 |
---|
2098 | ! BIT Numerical Mathematics (2005) 45: 761-787 |
---|
2099 | ! DOI: 10.1007/s10543-005-0035-y |
---|
2100 | ! Table 4.1-4.2 |
---|
2101 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2102 | |
---|
2103 | |
---|
2104 | rosmethod = rg3 |
---|
2105 | !~~~> name of the method |
---|
2106 | ros_Name = 'RANG-3' |
---|
2107 | !~~~> number of stages |
---|
2108 | ros_s = 4 |
---|
2109 | |
---|
2110 | ros_a(1) = 5.09052051067020d+00; |
---|
2111 | ros_a(2) = 5.09052051067020d+00; |
---|
2112 | ros_a(3) = 0.0d0; |
---|
2113 | ros_a(4) = 4.97628111010787d+00; |
---|
2114 | ros_a(5) = 2.77268164715849d-02; |
---|
2115 | ros_a(6) = 2.29428036027904d-01; |
---|
2116 | |
---|
2117 | ros_c(1) = - 1.16790812312283d+01; |
---|
2118 | ros_c(2) = - 1.64057326467367d+01; |
---|
2119 | ros_c(3) = - 2.77268164715850d-01; |
---|
2120 | ros_c(4) = - 8.38103960500476d+00; |
---|
2121 | ros_c(5) = - 8.48328409199343d-01; |
---|
2122 | ros_c(6) = 2.87009860433106d-01; |
---|
2123 | |
---|
2124 | ros_m(1) = 5.22582761233094d+00; |
---|
2125 | ros_m(2) = - 5.56971148154165d-01; |
---|
2126 | ros_m(3) = 3.57979469353645d-01; |
---|
2127 | ros_m(4) = 1.72337398521064d+00; |
---|
2128 | |
---|
2129 | ros_e(1) = - 5.16845212784040d+00; |
---|
2130 | ros_e(2) = - 1.26351942603842d+00; |
---|
2131 | ros_e(3) = - 1.11022302462516d-16; |
---|
2132 | ros_e(4) = 2.22044604925031d-16; |
---|
2133 | |
---|
2134 | ros_alpha(1) = 0.0d00; |
---|
2135 | ros_alpha(2) = 2.21878746765329d+00; |
---|
2136 | ros_alpha(3) = 2.21878746765329d+00; |
---|
2137 | ros_alpha(4) = 1.55392337535788d+00; |
---|
2138 | |
---|
2139 | ros_gamma(1) = 4.35866521508459d-01; |
---|
2140 | ros_gamma(2) = - 1.78292094614483d+00; |
---|
2141 | ros_gamma(3) = - 2.46541900496934d+00; |
---|
2142 | ros_gamma(4) = - 8.05529997906370d-01; |
---|
2143 | |
---|
2144 | |
---|
2145 | !~~~> does the stage i require a new FUNCTION evaluation (ros_newf(i) =true) |
---|
2146 | ! or does it re-use the function evaluation from stage i-1 (ros_NewF(i) =FALSE) |
---|
2147 | ros_newf(1) = .TRUE. |
---|
2148 | ros_newf(2) = .TRUE. |
---|
2149 | ros_newf(3) = .TRUE. |
---|
2150 | ros_newf(4) = .TRUE. |
---|
2151 | |
---|
2152 | !~~~> ros_elo = estimator of local order - the minimum between the |
---|
2153 | ! main and the embedded scheme orders plus 1 |
---|
2154 | ros_elo = 3.0_dp |
---|
2155 | |
---|
2156 | END SUBROUTINE rang3 |
---|
2157 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2158 | |
---|
2159 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2160 | ! End of the set of internal Rosenbrock subroutines |
---|
2161 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2162 | END SUBROUTINE rosenbrock |
---|
2163 | |
---|
2164 | SUBROUTINE funtemplate( t, y, ydot) |
---|
2165 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2166 | ! Template for the ODE function call. |
---|
2167 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
2168 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2169 | !~~~> input variables |
---|
2170 | REAL(kind=dp):: t, y(nvar) |
---|
2171 | !~~~> output variables |
---|
2172 | REAL(kind=dp):: ydot(nvar) |
---|
2173 | !~~~> local variables |
---|
2174 | REAL(kind=dp):: told |
---|
2175 | |
---|
2176 | told = time |
---|
2177 | time = t |
---|
2178 | CALL fun( y, fix, rconst, ydot) |
---|
2179 | time = told |
---|
2180 | |
---|
2181 | END SUBROUTINE funtemplate |
---|
2182 | |
---|
2183 | SUBROUTINE jactemplate( t, y, jcb) |
---|
2184 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2185 | ! Template for the ODE Jacobian call. |
---|
2186 | ! Updates the rate coefficients (and possibly the fixed species) at each call |
---|
2187 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2188 | !~~~> input variables |
---|
2189 | REAL(kind=dp):: t, y(nvar) |
---|
2190 | !~~~> output variables |
---|
2191 | #ifdef full_algebra |
---|
2192 | REAL(kind=dp):: jv(lu_nonzero), jcb(nvar, nvar) |
---|
2193 | #else |
---|
2194 | REAL(kind=dp):: jcb(lu_nonzero) |
---|
2195 | #endif |
---|
2196 | !~~~> local variables |
---|
2197 | REAL(kind=dp):: told |
---|
2198 | #ifdef full_algebra |
---|
2199 | INTEGER :: i, j |
---|
2200 | #endif |
---|
2201 | |
---|
2202 | told = time |
---|
2203 | time = t |
---|
2204 | #ifdef full_algebra |
---|
2205 | CALL jac_sp(y, fix, rconst, jv) |
---|
2206 | DO j=1, nvar |
---|
2207 | DO i=1, nvar |
---|
2208 | jcb(i, j) = 0.0_dp |
---|
2209 | ENDDO |
---|
2210 | ENDDO |
---|
2211 | DO i=1, lu_nonzero |
---|
2212 | jcb(lu_irow(i), lu_icol(i)) = jv(i) |
---|
2213 | ENDDO |
---|
2214 | #else |
---|
2215 | CALL jac_sp( y, fix, rconst, jcb) |
---|
2216 | #endif |
---|
2217 | time = told |
---|
2218 | |
---|
2219 | END SUBROUTINE jactemplate |
---|
2220 | |
---|
2221 | SUBROUTINE kppdecomp( jvs, ier) |
---|
2222 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2223 | ! sparse lu factorization |
---|
2224 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
2225 | ! loop expansion generated by kp4 |
---|
2226 | |
---|
2227 | INTEGER :: ier |
---|
2228 | REAL(kind=dp):: jvs(lu_nonzero), w(nvar), a |
---|
2229 | INTEGER :: k, kk, j, jj |
---|
2230 | |
---|
2231 | a = 0. |
---|
2232 | ier = 0 |
---|
2233 | |
---|
2234 | ! i = 1 |
---|
2235 | ! i = 2 |
---|
2236 | RETURN |
---|
2237 | |
---|
2238 | END SUBROUTINE kppdecomp |
---|
2239 | |
---|
2240 | SUBROUTINE chem_gasphase_integrate (time_step_len, conc, tempi, qvapi, fakti, photo, ierrf, xnacc, xnrej, istatus, l_debug, pe, & |
---|
2241 | icntrl_i, rcntrl_i) |
---|
2242 | |
---|
2243 | IMPLICIT NONE |
---|
2244 | |
---|
2245 | REAL(dp), INTENT(IN) :: time_step_len |
---|
2246 | REAL(dp), DIMENSION(:, :), INTENT(INOUT) :: conc |
---|
2247 | REAL(dp), DIMENSION(:, :), INTENT(IN) :: photo |
---|
2248 | REAL(dp), DIMENSION(:), INTENT(IN) :: tempi |
---|
2249 | REAL(dp), DIMENSION(:), INTENT(IN) :: qvapi |
---|
2250 | REAL(dp), DIMENSION(:), INTENT(IN) :: fakti |
---|
2251 | INTEGER, INTENT(OUT), OPTIONAL :: ierrf(:) |
---|
2252 | INTEGER, INTENT(OUT), OPTIONAL :: xnacc(:) |
---|
2253 | INTEGER, INTENT(OUT), OPTIONAL :: xnrej(:) |
---|
2254 | INTEGER, INTENT(INOUT), OPTIONAL :: istatus(:) |
---|
2255 | INTEGER, INTENT(IN), OPTIONAL :: pe |
---|
2256 | LOGICAL, INTENT(IN), OPTIONAL :: l_debug |
---|
2257 | INTEGER, DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: icntrl_i |
---|
2258 | REAL(dp), DIMENSION(nkppctrl), INTENT(IN), OPTIONAL :: rcntrl_i |
---|
2259 | |
---|
2260 | INTEGER :: k ! loop variable |
---|
2261 | REAL(dp) :: dt |
---|
2262 | INTEGER, DIMENSION(20) :: istatus_u |
---|
2263 | INTEGER :: ierr_u |
---|
2264 | INTEGER :: istatf |
---|
2265 | INTEGER :: vl_dim_lo |
---|
2266 | |
---|
2267 | |
---|
2268 | IF (PRESENT (istatus)) istatus = 0 |
---|
2269 | IF (PRESENT (icntrl_i)) icntrl = icntrl_i |
---|
2270 | IF (PRESENT (rcntrl_i)) rcntrl = rcntrl_i |
---|
2271 | |
---|
2272 | vl_glo = size(tempi, 1) |
---|
2273 | |
---|
2274 | vl_dim_lo = vl_dim |
---|
2275 | DO k=1, vl_glo, vl_dim_lo |
---|
2276 | is = k |
---|
2277 | ie = min(k+ vl_dim_lo-1, vl_glo) |
---|
2278 | vl = ie-is+ 1 |
---|
2279 | |
---|
2280 | c(:) = conc(is, :) |
---|
2281 | |
---|
2282 | temp = tempi(is) |
---|
2283 | |
---|
2284 | qvap = qvapi(is) |
---|
2285 | |
---|
2286 | fakt = fakti(is) |
---|
2287 | |
---|
2288 | CALL initialize |
---|
2289 | |
---|
2290 | phot(:) = photo(is, :) |
---|
2291 | |
---|
2292 | CALL update_rconst |
---|
2293 | |
---|
2294 | dt = time_step_len |
---|
2295 | |
---|
2296 | ! integrate from t=0 to t=dt |
---|
2297 | CALL integrate(0._dp, dt, icntrl, rcntrl, istatus_u = istatus_u, ierr_u=ierr_u) |
---|
2298 | |
---|
2299 | |
---|
2300 | IF (PRESENT(l_debug) .AND. PRESENT(pe)) THEN |
---|
2301 | IF (l_debug) CALL error_output(conc(is, :), ierr_u, pe) |
---|
2302 | ENDIF |
---|
2303 | |
---|
2304 | conc(is, :) = c(:) |
---|
2305 | |
---|
2306 | ! RETURN diagnostic information |
---|
2307 | |
---|
2308 | IF (PRESENT(ierrf)) ierrf(is) = ierr_u |
---|
2309 | IF (PRESENT(xnacc)) xnacc(is) = istatus_u(4) |
---|
2310 | IF (PRESENT(xnrej)) xnrej(is) = istatus_u(5) |
---|
2311 | |
---|
2312 | IF (PRESENT (istatus)) THEN |
---|
2313 | istatus(1:8) = istatus(1:8) + istatus_u(1:8) |
---|
2314 | ENDIF |
---|
2315 | |
---|
2316 | END DO |
---|
2317 | |
---|
2318 | |
---|
2319 | ! Deallocate input arrays |
---|
2320 | |
---|
2321 | |
---|
2322 | data_loaded = .FALSE. |
---|
2323 | |
---|
2324 | RETURN |
---|
2325 | END SUBROUTINE chem_gasphase_integrate |
---|
2326 | |
---|
2327 | END MODULE chem_gasphase_mod |
---|
2328 | |
---|