1 | !> @file random_generator_parallel_mod.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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6 | ! terms of the GNU General Public License as published by the Free Software |
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7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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8 | ! version. |
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9 | ! |
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10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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13 | ! |
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14 | ! You should have received a copy of the GNU General Public License along with |
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15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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16 | ! |
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17 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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18 | !------------------------------------------------------------------------------! |
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19 | ! |
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20 | ! Current revisions: |
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21 | ! ----------------- |
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22 | ! |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: random_generator_parallel_mod.f90 3241 2018-09-12 15:02:00Z suehring $ |
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27 | ! unused variable removed |
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28 | ! |
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29 | ! 2718 2018-01-02 08:49:38Z maronga |
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30 | ! Corrected "Former revisions" section |
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31 | ! |
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32 | ! 2696 2017-12-14 17:12:51Z kanani |
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33 | ! Change in file header (GPL part) |
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34 | ! Formatting (MS) |
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35 | ! |
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36 | ! 2255 2017-06-07 11:58:09Z knoop |
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37 | ! Implemented PALM specific error message handling |
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38 | ! |
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39 | ! 2173 2017-03-08 15:56:54Z knoop |
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40 | ! |
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41 | ! 2172 2017-03-08 15:55:25Z knoop |
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42 | ! Bugfix: added global initialization routine and removed global array |
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43 | ! |
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44 | ! 2144 2017-02-07 15:32:45Z knoop |
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45 | ! Bugfix: compile time parameter replacement prevented |
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46 | ! |
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47 | ! 2000 2016-08-20 18:09:15Z knoop |
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48 | ! Forced header and separation lines into 80 columns |
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49 | ! |
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50 | ! 1850 2016-04-08 13:29:27Z maronga |
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51 | ! Module renamed |
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52 | ! |
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53 | ! |
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54 | ! 1682 2015-10-07 23:56:08Z knoop |
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55 | ! Code annotations made doxygen readable |
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56 | ! |
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57 | ! 1400 2014-05-09 14:03:54Z knoop |
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58 | ! Initial revision |
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59 | ! |
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60 | ! |
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61 | ! Description: |
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62 | ! ------------ |
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63 | !> This module contains and supports the random number generating routine ran_parallel. |
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64 | !> ran_parallel returns a uniform random deviate between 0.0 and 1.0 |
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65 | !> (exclusive of the end point values). |
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66 | !> Additionally it provides the generator with five integer for use as initial state space. |
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67 | !> The first tree integers (iran, jran, kran) are maintained as non negative values, |
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68 | !> while the last two (mran, nran) have 32-bit nonzero values. |
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69 | !> Also provided by this module is support for initializing or reinitializing |
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70 | !> the state space to a desired standard sequence number, hashing the initial |
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71 | !> values to random values, and allocating and deallocating the internal workspace |
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72 | !> Random number generator, produces numbers equally distributed in interval |
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73 | !> |
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74 | !> This routine is taken from the "numerical recipies vol. 2" |
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75 | !------------------------------------------------------------------------------! |
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76 | MODULE random_generator_parallel |
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77 | |
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78 | |
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79 | USE kinds |
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80 | |
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81 | IMPLICIT NONE |
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82 | |
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83 | PRIVATE |
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84 | PUBLIC random_number_parallel, random_seed_parallel, random_dummy, & |
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85 | id_random_array, seq_random_array, init_parallel_random_generator |
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86 | |
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87 | INTEGER(isp), SAVE :: lenran=0 !< |
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88 | INTEGER(isp), SAVE :: seq=0 !< |
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89 | INTEGER(isp), SAVE :: iran0 !< |
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90 | INTEGER(isp), SAVE :: jran0 !< |
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91 | INTEGER(isp), SAVE :: kran0 !< |
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92 | INTEGER(isp), SAVE :: mran0 !< |
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93 | INTEGER(isp), SAVE :: nran0 !< |
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94 | INTEGER(isp), SAVE :: rans !< |
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95 | |
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96 | INTEGER(isp), DIMENSION(:, :), POINTER, SAVE :: ranseeds !< |
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97 | |
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98 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: iran !< |
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99 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: jran !< |
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100 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: kran !< |
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101 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: mran !< |
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102 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: nran !< |
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103 | INTEGER(isp), DIMENSION(:), POINTER, SAVE :: ranv !< |
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104 | |
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105 | |
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106 | |
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107 | INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: id_random_array !< |
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108 | INTEGER(isp), DIMENSION(:,:,:), ALLOCATABLE :: seq_random_array !< |
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109 | |
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110 | REAL(wp), SAVE :: amm !< |
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111 | |
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112 | REAL(wp) :: random_dummy=0.0 !< |
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113 | |
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114 | INTERFACE init_parallel_random_generator |
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115 | MODULE PROCEDURE init_parallel_random_generator |
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116 | END INTERFACE |
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117 | |
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118 | INTERFACE random_number_parallel |
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119 | MODULE PROCEDURE ran0_s |
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120 | END INTERFACE |
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121 | |
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122 | INTERFACE random_seed_parallel |
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123 | MODULE PROCEDURE random_seed_parallel |
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124 | END INTERFACE |
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125 | |
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126 | INTERFACE ran_hash |
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127 | MODULE PROCEDURE ran_hash_v |
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128 | END INTERFACE |
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129 | |
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130 | INTERFACE reallocate |
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131 | MODULE PROCEDURE reallocate_iv,reallocate_im |
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132 | END INTERFACE |
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133 | |
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134 | INTERFACE arth |
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135 | MODULE PROCEDURE arth_i |
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136 | END INTERFACE |
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137 | |
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138 | CONTAINS |
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139 | |
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140 | !------------------------------------------------------------------------------! |
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141 | ! Description: |
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142 | ! ------------ |
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143 | !> Initialize the parallel random number generator for a specific subdomain |
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144 | !------------------------------------------------------------------------------! |
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145 | SUBROUTINE init_parallel_random_generator( nx, nys, nyn, nxl, nxr ) |
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146 | |
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147 | USE kinds |
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148 | |
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149 | USE control_parameters, & |
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150 | ONLY: ensemble_member_nr |
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151 | |
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152 | IMPLICIT NONE |
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153 | |
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154 | INTEGER(isp), INTENT(IN) :: nx !< |
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155 | INTEGER(isp), INTENT(IN) :: nys !< |
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156 | INTEGER(isp), INTENT(IN) :: nyn !< |
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157 | INTEGER(isp), INTENT(IN) :: nxl !< |
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158 | INTEGER(isp), INTENT(IN) :: nxr !< |
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159 | |
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160 | INTEGER(iwp) :: i !< |
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161 | INTEGER(iwp) :: j !< |
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162 | |
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163 | !-- Allocate ID-array and state-space-array |
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164 | ALLOCATE ( seq_random_array(5,nys:nyn,nxl:nxr) ) |
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165 | ALLOCATE ( id_random_array(nys:nyn,nxl:nxr) ) |
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166 | seq_random_array = 0 |
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167 | id_random_array = 0 |
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168 | |
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169 | !-- Asigning an ID to every vertical gridpoint column |
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170 | !-- dependig on the ensemble run number. |
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171 | DO i=nxl, nxr |
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172 | DO j=nys, nyn |
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173 | id_random_array(j,i) = j*(nx+1.0_wp) + i + 1.0_wp + 1E6 * & |
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174 | ( ensemble_member_nr - 1000 ) |
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175 | ENDDO |
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176 | ENDDO |
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177 | !-- Initializing with random_seed_parallel for every vertical |
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178 | !-- gridpoint column. |
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179 | random_dummy=0 |
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180 | DO i = nxl, nxr |
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181 | DO j = nys, nyn |
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182 | CALL random_seed_parallel (random_sequence=id_random_array(j, i)) |
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183 | CALL random_number_parallel (random_dummy) |
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184 | CALL random_seed_parallel (get=seq_random_array(:, j, i)) |
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185 | ENDDO |
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186 | ENDDO |
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187 | |
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188 | END SUBROUTINE init_parallel_random_generator |
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189 | |
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190 | !------------------------------------------------------------------------------! |
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191 | ! Description: |
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192 | ! ------------ |
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193 | !> Lagged Fibonacci generator combined with a Marsaglia shiftsequence. |
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194 | !> Returns as harvest a uniform random deviate between 0.0 and 1.0 (exclusive of the end point values). |
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195 | !> This generator has the same calling and initialization conventions as Fortran 90's random_number routine. |
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196 | !> Use random_seed_parallel to initialize or reinitialize to a particular sequence. |
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197 | !> The period of this generator is about 2.0 x 10^28, and it fully vectorizes. |
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198 | !> Validity of the integer model assumed by this generator is tested at initialization. |
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199 | !------------------------------------------------------------------------------! |
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200 | SUBROUTINE ran0_s(harvest) |
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201 | |
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202 | USE kinds |
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203 | |
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204 | IMPLICIT NONE |
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205 | |
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206 | REAL(wp), INTENT(OUT) :: harvest !< |
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207 | |
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208 | IF (lenran < 1) CALL ran_init(1) !- Initialization routine in ran_state. |
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209 | |
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210 | !- Update Fibonacci generator, which has period p^2 + p + 1, p = 2^31 - 69. |
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211 | rans = iran0 - kran0 |
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212 | |
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213 | IF (rans < 0) rans = rans + 2147483579_isp |
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214 | |
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215 | iran0 = jran0 |
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216 | jran0 = kran0 |
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217 | kran0 = rans |
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218 | |
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219 | nran0 = ieor( nran0, ishft (nran0, 13) ) !- Update Marsaglia shift sequence with period 2^32 - 1. |
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220 | nran0 = ieor( nran0, ishft (nran0, -17) ) |
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221 | nran0 = ieor( nran0, ishft (nran0, 5) ) |
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222 | |
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223 | rans = ieor( nran0, rans ) !- Combine the generators. |
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224 | |
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225 | harvest = amm * merge( rans, not(rans), rans < 0 ) !- Make the result positive definite (note that amm is negative). |
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226 | |
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227 | END SUBROUTINE ran0_s |
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228 | |
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229 | !------------------------------------------------------------------------------! |
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230 | ! Description: |
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231 | ! ------------ |
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232 | !> Initialize or reinitialize the random generator state space to vectors of size length. |
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233 | !> The saved variable seq is hashed (via calls to the module routine ran_hash) |
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234 | !> to create unique starting seeds, different for each vector component. |
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235 | !------------------------------------------------------------------------------! |
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236 | SUBROUTINE ran_init( length ) |
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237 | |
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238 | USE kinds |
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239 | |
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240 | IMPLICIT NONE |
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241 | |
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242 | INTEGER(isp), INTENT(IN) :: length !< |
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243 | |
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244 | INTEGER(isp) :: hg !< |
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245 | INTEGER(isp) :: hgm !< |
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246 | INTEGER(isp) :: hgng !< |
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247 | |
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248 | INTEGER(isp) :: new !< |
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249 | INTEGER(isp) :: j !< |
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250 | INTEGER(isp) :: hgt !< |
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251 | |
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252 | IF ( length < lenran ) RETURN !- Simply return if enough space is already allocated. |
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253 | |
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254 | hg=huge(1_isp) |
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255 | hgm=-hg |
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256 | hgng=hgm-1 |
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257 | hgt = hg |
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258 | |
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259 | !- The following lines check that kind value isp is in fact a 32-bit integer |
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260 | !- with the usual properties that we expect it to have (under negation and wrap-around addition). |
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261 | !- If all of these tests are satisfied, then the routines that use this module are portable, |
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262 | !- even though they go beyond Fortran 90's integer model. |
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263 | |
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264 | IF ( hg /= 2147483647 ) CALL ran_error('arithmetic assumption 1 failed') |
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265 | IF ( hgng >= 0 ) CALL ran_error('arithmetic assumption 2 failed') |
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266 | IF ( hgt+1 /= hgng ) CALL ran_error('arithmetic assumption 3 failed') |
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267 | IF ( not(hg) >= 0 ) CALL ran_error('arithmetic assumption 4 failed') |
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268 | IF ( not(hgng) < 0 ) CALL ran_error('arithmetic assumption 5 failed') |
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269 | IF ( hg+hgng >= 0 ) CALL ran_error('arithmetic assumption 6 failed') |
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270 | IF ( not(-1_isp) < 0 ) CALL ran_error('arithmetic assumption 7 failed') |
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271 | IF ( not(0_isp) >= 0 ) CALL ran_error('arithmetic assumption 8 failed') |
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272 | IF ( not(1_isp) >= 0 ) CALL ran_error('arithmetic assumption 9 failed') |
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273 | |
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274 | IF ( lenran > 0) THEN !- Reallocate space, or ... |
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275 | |
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276 | ranseeds => reallocate( ranseeds, length, 5) |
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277 | ranv => reallocate( ranv, length-1) |
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278 | new = lenran+1 |
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279 | |
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280 | ELSE !- allocate space. |
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281 | |
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282 | ALLOCATE(ranseeds(length,5)) |
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283 | ALLOCATE(ranv(length-1)) |
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284 | new = 1 !- Index of first location not yet initialized. |
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285 | amm = nearest(1.0_wp,-1.0_wp)/hgng |
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286 | !- Use of nearest is to ensure that returned random deviates are strictly lessthan 1.0. |
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287 | IF (amm*hgng >= 1.0 .or. amm*hgng <= 0.0) & |
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288 | CALL ran_error('arithmetic assumption 10 failed') |
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289 | |
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290 | END IF |
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291 | |
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292 | !- Set starting values, unique by seq and vector component. |
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293 | ranseeds(new:,1) = seq |
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294 | ranseeds(new:,2:5)=spread(arth(new,1,size(ranseeds(new:,1))),2,4) |
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295 | |
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296 | DO j=1,4 !- Hash them. |
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297 | CALL ran_hash(ranseeds(new:,j), ranseeds(new:,j+1)) |
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298 | END DO |
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299 | |
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300 | WHERE (ranseeds (new: ,1:3) < 0) & |
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301 | ranseeds(new: ,1:3)=not(ranseeds(new: ,1:3)) !- Enforce nonnegativity. |
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302 | |
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303 | WHERE (ranseeds(new: ,4:5) == 0) ranseeds(new: ,4:5)=1 !- Enforce nonzero. |
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304 | |
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305 | IF (new == 1) THEN !- Set scalar seeds. |
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306 | |
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307 | iran0 = ranseeds(1,1) |
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308 | jran0 = ranseeds(1,2) |
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309 | kran0 = ranseeds(1,3) |
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310 | mran0 = ranseeds(1,4) |
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311 | nran0 = ranseeds(1,5) |
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312 | rans = nran0 |
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313 | |
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314 | END IF |
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315 | |
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316 | IF (length > 1) THEN !- Point to vector seeds. |
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317 | |
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318 | iran => ranseeds(2:,1) |
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319 | jran => ranseeds(2:,2) |
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320 | kran => ranseeds(2:,3) |
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321 | mran => ranseeds(2:,4) |
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322 | nran => ranseeds(2:,5) |
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323 | ranv = nran |
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324 | |
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325 | END IF |
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326 | |
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327 | lenran = length |
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328 | |
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329 | END SUBROUTINE ran_init |
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330 | |
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331 | !------------------------------------------------------------------------------! |
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332 | ! Description: |
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333 | ! ------------ |
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334 | !> User interface to release the workspace used by the random number routines. |
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335 | !------------------------------------------------------------------------------! |
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336 | SUBROUTINE ran_deallocate |
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337 | |
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338 | IF ( lenran > 0 ) THEN |
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339 | |
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340 | DEALLOCATE(ranseeds, ranv) |
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341 | NULLIFY(ranseeds, ranv, iran, jran, kran, mran, nran) |
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342 | lenran = 0 |
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343 | |
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344 | END IF |
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345 | |
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346 | END SUBROUTINE ran_deallocate |
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347 | |
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348 | !------------------------------------------------------------------------------! |
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349 | ! Description: |
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350 | ! ------------ |
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351 | !> User interface for seeding the random number routines. |
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352 | !> Syntax is exactly like Fortran 90's random_seed routine, |
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353 | !> with one additional argument keyword: random_sequence, set to any integer |
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354 | !> value, causes an immediate new initialization, seeded by that integer. |
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355 | !------------------------------------------------------------------------------! |
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356 | SUBROUTINE random_seed_parallel( random_sequence, state_size, put, get ) |
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357 | |
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358 | IMPLICIT NONE |
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359 | |
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360 | INTEGER(isp), OPTIONAL, INTENT(IN) :: random_sequence !< |
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361 | INTEGER(isp), OPTIONAL, INTENT(OUT) :: state_size !< |
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362 | |
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363 | INTEGER(isp), DIMENSION(:), OPTIONAL, INTENT(IN) :: put !< |
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364 | INTEGER(isp), DIMENSION(:), OPTIONAL, INTENT(OUT) :: get !< |
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365 | |
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366 | IF ( present(state_size) ) THEN |
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367 | |
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368 | state_size = 5 * lenran |
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369 | |
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370 | ELSE IF ( present(put) ) THEN |
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371 | |
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372 | IF ( lenran == 0 ) RETURN |
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373 | |
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374 | ranseeds = reshape( put,shape(ranseeds) ) |
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375 | |
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376 | WHERE (ranseeds(:,1:3) < 0) ranseeds(: ,1:3) = not(ranseeds(: ,1:3)) |
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377 | !- Enforce nonnegativity and nonzero conditions on any user-supplied seeds. |
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378 | |
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379 | WHERE (ranseeds(:,4:5) == 0) ranseeds(:,4:5) = 1 |
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380 | |
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381 | iran0 = ranseeds(1,1) |
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382 | jran0 = ranseeds(1,2) |
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383 | kran0 = ranseeds(1,3) |
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384 | mran0 = ranseeds(1,4) |
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385 | nran0 = ranseeds(1,5) |
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386 | |
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387 | ELSE IF ( present(get) ) THEN |
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388 | |
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389 | IF (lenran == 0) RETURN |
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390 | |
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391 | ranseeds(1,1:5) = (/ iran0,jran0,kran0,mran0,nran0 /) |
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392 | get = reshape( ranseeds, shape(get) ) |
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393 | |
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394 | ELSE IF ( present(random_sequence) ) THEN |
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395 | |
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396 | CALL ran_deallocate |
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397 | seq = random_sequence |
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398 | |
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399 | END IF |
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400 | |
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401 | END SUBROUTINE random_seed_parallel |
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402 | |
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403 | !------------------------------------------------------------------------------! |
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404 | ! Description: |
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405 | ! ------------ |
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406 | !> DES-like hashing of two 32-bit integers, using shifts, |
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407 | !> xor's, and adds to make the internal nonlinear function. |
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408 | !------------------------------------------------------------------------------! |
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409 | SUBROUTINE ran_hash_v( il, ir ) |
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410 | |
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411 | IMPLICIT NONE |
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412 | |
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413 | INTEGER(isp), DIMENSION(:), INTENT(INOUT) :: il !< |
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414 | INTEGER(isp), DIMENSION(:), INTENT(INOUT) :: ir !< |
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415 | |
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416 | INTEGER(isp), DIMENSION(size(il)) :: is !< |
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417 | |
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418 | INTEGER(isp) :: j !< |
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419 | |
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420 | DO j=1,4 |
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421 | |
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422 | is = ir |
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423 | ir = ieor( ir, ishft(ir,5) ) + 1422217823 |
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424 | ir = ieor( ir, ishft(ir,-16) ) + 1842055030 |
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425 | ir = ieor( ir, ishft(ir,9) ) + 80567781 |
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426 | ir = ieor( il, ir ) |
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427 | il = is |
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428 | END DO |
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429 | |
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430 | END SUBROUTINE ran_hash_v |
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431 | |
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432 | !------------------------------------------------------------------------------! |
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433 | ! Description: |
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434 | ! ------------ |
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435 | !> User interface to process error-messages |
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436 | !> produced by the random_number_parallel module |
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437 | !------------------------------------------------------------------------------! |
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438 | SUBROUTINE ran_error(string) |
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439 | |
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440 | USE control_parameters, & |
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441 | ONLY: message_string |
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442 | |
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443 | CHARACTER(LEN=*), INTENT(IN) :: string !< Error message string |
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444 | |
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445 | message_string = 'incompatible integer arithmetic: ' // TRIM( string ) |
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446 | CALL message( 'ran_init', 'PA0453', 1, 2, 0, 6, 0 ) |
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447 | |
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448 | END SUBROUTINE ran_error |
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449 | |
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450 | !------------------------------------------------------------------------------! |
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451 | ! Description: |
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452 | ! ------------ |
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453 | !> Reallocates the generators state space "ranseeds" to vectors of size length. |
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454 | !------------------------------------------------------------------------------! |
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455 | FUNCTION reallocate_iv( p, n ) |
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456 | |
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457 | USE control_parameters, & |
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458 | ONLY: message_string |
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459 | |
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460 | INTEGER(isp), DIMENSION(:), POINTER :: p !< |
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461 | INTEGER(isp), DIMENSION(:), POINTER :: reallocate_iv !< |
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462 | |
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463 | INTEGER(isp), INTENT(IN) :: n !< |
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464 | |
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465 | INTEGER(isp) :: nold !< |
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466 | INTEGER(isp) :: ierr !< |
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467 | |
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468 | ALLOCATE(reallocate_iv(n),stat=ierr) |
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469 | |
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470 | IF (ierr /= 0) THEN |
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471 | message_string = 'problem in attempt to allocate memory' |
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472 | CALL message( 'reallocate_iv', 'PA0454', 1, 2, 0, 6, 0 ) |
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473 | END IF |
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474 | |
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475 | IF (.not. associated(p)) RETURN |
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476 | |
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477 | nold = size(p) |
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478 | |
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479 | reallocate_iv(1:min(nold,n)) = p(1:min(nold,n)) |
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480 | |
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481 | DEALLOCATE(p) |
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482 | |
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483 | END FUNCTION reallocate_iv |
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484 | |
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485 | FUNCTION reallocate_im( p, n, m ) |
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486 | |
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487 | USE control_parameters, & |
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488 | ONLY: message_string |
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489 | |
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490 | INTEGER(isp), DIMENSION(:,:), POINTER :: p !< |
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491 | INTEGER(isp), DIMENSION(:,:), POINTER :: reallocate_im !< |
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492 | |
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493 | INTEGER(isp), INTENT(IN) :: m !< |
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494 | INTEGER(isp), INTENT(IN) :: n !< |
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495 | |
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496 | INTEGER(isp) :: mold !< |
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497 | INTEGER(isp) :: nold !< |
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498 | INTEGER(isp) :: ierr !< |
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499 | |
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500 | ALLOCATE(reallocate_im(n,m),stat=ierr) |
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501 | |
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502 | IF (ierr /= 0) THEN |
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503 | message_string = 'problem in attempt to allocate memory' |
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504 | CALL message( 'reallocate_im', 'PA0454', 1, 2, 0, 6, 0 ) |
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505 | END IF |
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506 | |
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507 | IF (.not. associated(p)) RETURN |
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508 | |
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509 | nold = size(p,1) |
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510 | mold = size(p,2) |
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511 | |
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512 | reallocate_im(1:min(nold,n),1:min(mold,m)) = & |
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513 | p(1:min(nold,n),1:min(mold,m)) |
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514 | |
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515 | DEALLOCATE(p) |
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516 | |
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517 | END FUNCTION reallocate_im |
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518 | |
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519 | !------------------------------------------------------------------------------! |
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520 | ! Description: |
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521 | ! ------------ |
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522 | !> Reallocates the generators state space "ranseeds" to vectors of size length. |
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523 | !------------------------------------------------------------------------------! |
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524 | FUNCTION arth_i(first,increment,n) |
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525 | |
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526 | INTEGER(isp), INTENT(IN) :: first !< |
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527 | INTEGER(isp), INTENT(IN) :: increment !< |
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528 | INTEGER(isp), INTENT(IN) :: n !< |
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529 | |
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530 | INTEGER(isp), DIMENSION(n) :: arth_i !< |
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531 | |
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532 | INTEGER(isp) :: k !< |
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533 | INTEGER(isp) :: k2 !< |
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534 | INTEGER(isp) :: temp !< |
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535 | |
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536 | INTEGER(isp), PARAMETER :: npar_arth=16 !< |
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537 | INTEGER(isp), PARAMETER :: npar2_arth=8 !< |
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538 | |
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539 | IF (n > 0) arth_i(1) = first |
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540 | |
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541 | IF (n <= npar_arth) THEN |
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542 | |
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543 | DO k=2,n |
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544 | arth_i(k) = arth_i(k-1)+increment |
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545 | END DO |
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546 | |
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547 | ELSE |
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548 | |
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549 | DO k=2,npar2_arth |
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550 | arth_i(k) = arth_i(k-1) + increment |
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551 | END DO |
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552 | |
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553 | temp = increment * npar2_arth |
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554 | k = npar2_arth |
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555 | |
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556 | DO |
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557 | IF (k >= n) EXIT |
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558 | k2 = k + k |
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559 | arth_i(k+1:min(k2,n)) = temp + arth_i(1:min(k,n-k)) |
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560 | temp = temp + temp |
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561 | k = k2 |
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562 | END DO |
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563 | |
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564 | END IF |
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565 | |
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566 | END FUNCTION arth_i |
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567 | |
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568 | END MODULE random_generator_parallel |
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