1 | !********************************************************************** |
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2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
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3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
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4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
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5 | ! * |
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6 | ! This file is part of FLEXPART. * |
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7 | ! * |
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8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
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9 | ! it under the terms of the GNU General Public License as published by* |
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10 | ! the Free Software Foundation, either version 3 of the License, or * |
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11 | ! (at your option) any later version. * |
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12 | ! * |
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13 | ! FLEXPART is distributed in the hope that it will be useful, * |
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14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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16 | ! GNU General Public License for more details. * |
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17 | ! * |
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18 | ! You should have received a copy of the GNU General Public License * |
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19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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20 | !********************************************************************** |
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21 | |
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22 | ! To be used, if the non-standard Fortran function erf does not exist on |
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23 | ! your machine |
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24 | ! |
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25 | !aus: Numerical Recipes (FORTRAN) / Chapter 6. |
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26 | ! |
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27 | !6.1 FUNCTION GAMMLN |
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28 | !6.2 FUNCTION GAMMP <6.2:GSER/6.2:GCF/6.1:GAMMLN> |
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29 | !6.2 FUNCTION GAMMQ <6.2:GSER/6.2:GCF/6.1:GAMMLN> |
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30 | !6.2 SUBROUTINE GSER <6.1:GAMMLN> |
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31 | !6.2 SUBROUTINE GCF <6.1:GAMMLN> |
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32 | !6.2 FUNCTION ERF <6.2:GAMMP/6.2:GSER/6.2:GCF/6.1:GAMMLN> |
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33 | !6.2 FUNCTION ERFC <6.2.:GAMMP/6.2:GAMMQ/6.2:GSER/ |
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34 | ! 6.2:GCF/6.1:GAMMLN> |
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35 | !6.2 FUNCTION ERFCC |
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36 | |
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37 | function gammln(xx) |
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38 | |
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39 | use par_mod, only: dp |
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40 | |
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41 | implicit none |
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42 | |
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43 | integer :: j |
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44 | real(kind=dp) :: x,tmp,ser,xx,gammln |
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45 | real(KIND=dp) :: cof(6) = (/ & |
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46 | 76.18009173_dp, -86.50532033_dp, 24.01409822_dp, & |
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47 | -1.231739516_dp, .120858003e-2_dp, -.536382e-5_dp /) |
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48 | real(KIND=dp) :: stp = 2.50662827465_dp |
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49 | real(KIND=dp) :: half = 0.5_dp, one = 1.0_dp, fpf = 5.5_dp |
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50 | |
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51 | x=xx-one |
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52 | tmp=x+fpf |
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53 | tmp=(x+half)*log(tmp)-tmp |
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54 | ser=one |
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55 | do j=1,6 |
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56 | x=x+one |
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57 | ser=ser+cof(j)/x |
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58 | end do |
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59 | gammln=tmp+log(stp*ser) |
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60 | end function gammln |
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61 | |
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62 | function gammp(a,x) |
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63 | |
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64 | use par_mod, only: dp |
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65 | |
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66 | implicit none |
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67 | |
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68 | real(KIND=dp) :: a, x, gln, gamser, gammp, gammcf |
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69 | |
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70 | if(x .lt. 0. .or. a .le. 0.) then |
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71 | print*, 'gammp' |
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72 | stop |
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73 | end if |
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74 | if(x.lt.a+1.)then |
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75 | call gser(gamser,a,x,gln) |
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76 | gammp=gamser |
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77 | else |
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78 | call gcf(gammcf,a,x,gln) |
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79 | gammp=1.-gammcf |
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80 | endif |
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81 | end function gammp |
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82 | |
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83 | function gammq(a,x) |
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84 | |
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85 | use par_mod, only: dp |
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86 | |
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87 | implicit none |
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88 | |
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89 | real(KIND=dp) :: a, x, gln, gamser, gammq, gammcf |
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90 | |
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91 | if(x.lt.0..or.a.le.0.) then |
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92 | print*, 'gammq' |
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93 | stop |
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94 | end if |
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95 | if(x.lt.a+1.)then |
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96 | call gser(gamser,a,x,gln) |
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97 | gammq=1.-gamser |
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98 | else |
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99 | call gcf(gammcf,a,x,gln) |
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100 | gammq=gammcf |
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101 | endif |
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102 | end function gammq |
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103 | |
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104 | subroutine gser(gamser,a,x,gln) |
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105 | |
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106 | use par_mod, only: dp |
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107 | |
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108 | implicit none |
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109 | |
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110 | integer :: n |
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111 | real(KIND=dp) :: gamser, a, x, gln, ap, summ, del |
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112 | real(KIND=dp), external :: gammln |
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113 | |
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114 | integer,parameter :: itmax=100 |
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115 | real,parameter :: eps=3.e-7 |
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116 | |
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117 | gln=gammln(a) |
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118 | if(x.le.0.)then |
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119 | if(x.lt.0.) then |
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120 | print*, 'gser' |
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121 | stop |
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122 | end if |
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123 | gamser=0. |
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124 | return |
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125 | endif |
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126 | ap=a |
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127 | summ=1./a |
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128 | del=summ |
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129 | do n=1,itmax |
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130 | ap=ap+1. |
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131 | del=del*x/ap |
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132 | summ=summ+del |
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133 | if(abs(del).lt.abs(summ)*eps)go to 1 |
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134 | end do |
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135 | print*, 'gser: a too large, itmax too small' |
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136 | stop |
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137 | 1 gamser=summ*exp(-x+a*log(x)-gln) |
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138 | end subroutine gser |
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139 | |
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140 | subroutine gcf(gammcf,a,x,gln) |
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141 | |
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142 | use par_mod, only: dp |
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143 | |
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144 | implicit none |
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145 | |
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146 | integer :: n |
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147 | real(KIND=4) :: gammcf, x, a, gln, gold, a0, a1, b0, b1, fac, an, anf, ana, g |
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148 | real(KIND=dp), external :: gammln |
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149 | |
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150 | integer,parameter :: itmax=100 |
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151 | real,parameter :: eps=3.e-7 |
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152 | |
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153 | gln=gammln(a) |
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154 | gold=0. |
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155 | a0=1. |
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156 | a1=x |
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157 | b0=0. |
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158 | b1=1. |
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159 | fac=1. |
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160 | do n=1,itmax |
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161 | an=real(n) |
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162 | ana=an-a |
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163 | a0=(a1+a0*ana)*fac |
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164 | b0=(b1+b0*ana)*fac |
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165 | anf=an*fac |
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166 | a1=x*a0+anf*a1 |
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167 | b1=x*b0+anf*b1 |
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168 | if(a1.ne.0.)then |
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169 | fac=1./a1 |
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170 | g=b1*fac |
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171 | if(abs((g-gold)/g).lt.eps)go to 1 |
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172 | gold=g |
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173 | endif |
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174 | end do |
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175 | print*, 'gcf: a too large, itmax too small' |
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176 | stop |
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177 | 1 gammcf=exp(-x+a*alog(x)-gln)*g |
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178 | end subroutine gcf |
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179 | |
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180 | function erf(x) |
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181 | |
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182 | use par_mod, only: dp |
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183 | |
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184 | implicit none |
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185 | |
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186 | real(KIND=dp) :: x, erf |
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187 | real(KIND=dp), external :: gammp |
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188 | |
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189 | if(x.lt.0.)then |
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190 | erf=-gammp(.5,x**2) |
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191 | else |
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192 | erf=gammp(.5,x**2) |
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193 | endif |
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194 | end function erf |
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195 | |
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196 | function erfc(x) |
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197 | |
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198 | use par_mod, only: dp |
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199 | |
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200 | implicit none |
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201 | |
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202 | real(KIND=dp) :: x, erfc |
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203 | real(KIND=dp), external :: gammp, gammq |
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204 | |
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205 | if(x.lt.0.)then |
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206 | erfc=1.+gammp(.5,x**2) |
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207 | else |
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208 | erfc=gammq(.5,x**2) |
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209 | endif |
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210 | end function erfc |
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211 | |
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212 | function erfcc(x) |
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213 | |
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214 | use par_mod, only: dp |
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215 | |
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216 | implicit none |
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217 | |
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218 | real(KIND=dp) :: x, z, t, erfcc |
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219 | |
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220 | z=abs(x) |
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221 | t=1./(1.+0.5*z) |
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222 | erfcc=t*exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+ & |
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223 | t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+ & |
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224 | t*(1.48851587+t*(-.82215223+t*.17087277))))))))) |
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225 | if (x.lt.0.) erfcc=2.-erfcc |
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226 | end function erfcc |
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