!********************************************************************** ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * ! * ! This file is part of FLEXPART. * ! * ! FLEXPART is free software: you can redistribute it and/or modify * ! it under the terms of the GNU General Public License as published by* ! the Free Software Foundation, either version 3 of the License, or * ! (at your option) any later version. * ! * ! FLEXPART is distributed in the hope that it will be useful, * ! but WITHOUT ANY WARRANTY; without even the implied warranty of * ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * ! GNU General Public License for more details. * ! * ! You should have received a copy of the GNU General Public License * ! along with FLEXPART. If not, see . * !********************************************************************** ! To be used, if the non-standard Fortran function erf does not exist on ! your machine ! !aus: Numerical Recipes (FORTRAN) / Chapter 6. ! !6.1 FUNCTION GAMMLN !6.2 FUNCTION GAMMP <6.2:GSER/6.2:GCF/6.1:GAMMLN> !6.2 FUNCTION GAMMQ <6.2:GSER/6.2:GCF/6.1:GAMMLN> !6.2 SUBROUTINE GSER <6.1:GAMMLN> !6.2 SUBROUTINE GCF <6.1:GAMMLN> !6.2 FUNCTION ERF <6.2:GAMMP/6.2:GSER/6.2:GCF/6.1:GAMMLN> !6.2 FUNCTION ERFC <6.2.:GAMMP/6.2:GAMMQ/6.2:GSER/ ! 6.2:GCF/6.1:GAMMLN> !6.2 FUNCTION ERFCC function gammln(xx) use par_mod, only: dp implicit none integer :: j real :: x,tmp,ser,xx,gammln real :: cof(6) = (/ & 76.18009173_dp, -86.50532033_dp, 24.01409822_dp, & -1.231739516_dp, .120858003e-2_dp, -.536382e-5_dp /) real :: stp = 2.50662827465_dp real :: half = 0.5_dp, one = 1.0_dp, fpf = 5.5_dp x=xx-one tmp=x+fpf tmp=(x+half)*log(tmp)-tmp ser=one do j=1,6 x=x+one ser=ser+cof(j)/x end do gammln=tmp+log(stp*ser) end function gammln function gammp(a,x) implicit none real :: a, x, gln, gamser, gammp, gammcf if(x .lt. 0. .or. a .le. 0.) then print*, 'gammp' stop end if if(x.lt.a+1.)then call gser(gamser,a,x,gln) gammp=gamser else call gcf(gammcf,a,x,gln) gammp=1.-gammcf endif end function gammp function gammq(a,x) implicit none real :: a, x, gln, gamser, gammq, gammcf if(x.lt.0..or.a.le.0.) then print*, 'gammq' stop end if if(x.lt.a+1.)then call gser(gamser,a,x,gln) gammq=1.-gamser else call gcf(gammcf,a,x,gln) gammq=gammcf endif end function gammq subroutine gser(gamser,a,x,gln) implicit none integer :: n real :: gamser, a, x, gln, ap, summ, del real, external :: gammln integer,parameter :: itmax=100 real,parameter :: eps=3.e-7 gln=gammln(a) if(x.le.0.)then if(x.lt.0.) then print*, 'gser' stop end if gamser=0. return endif ap=a summ=1./a del=summ do n=1,itmax ap=ap+1. del=del*x/ap summ=summ+del if(abs(del).lt.abs(summ)*eps)go to 1 end do print*, 'gser: a too large, itmax too small' stop 1 gamser=summ*exp(-x+a*log(x)-gln) end subroutine gser subroutine gcf(gammcf,a,x,gln) implicit none integer :: n real :: gammcf, a, x, gln, gold, a0, a1, b0, b1, fac, an, anf, ana, g real, external :: gammln integer,parameter :: itmax=100 real,parameter :: eps=3.e-7 gln=gammln(a) gold=0. a0=1. a1=x b0=0. b1=1. fac=1. do n=1,itmax an=real(n) ana=an-a a0=(a1+a0*ana)*fac b0=(b1+b0*ana)*fac anf=an*fac a1=x*a0+anf*a1 b1=x*b0+anf*b1 if(a1.ne.0.)then fac=1./a1 g=b1*fac if(abs((g-gold)/g).lt.eps)go to 1 gold=g endif end do print*, 'gcf: a too large, itmax too small' stop 1 gammcf=exp(-x+a*alog(x)-gln)*g end subroutine gcf function erf(x) implicit none real :: x, erf real, external :: gammp if(x.lt.0.)then erf=-gammp(.5,x**2) else erf=gammp(.5,x**2) endif end function erf function erfc(x) implicit none real :: x, erfc real, external :: gammp, gammq if(x.lt.0.)then erfc=1.+gammp(.5,x**2) else erfc=gammq(.5,x**2) endif end function erfc function erfcc(x) implicit none real :: x, z, t, erfcc z=abs(x) t=1./(1.+0.5*z) erfcc=t*exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+ & t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+ & t*(1.48851587+t*(-.82215223+t*.17087277))))))))) if (x.lt.0.) erfcc=2.-erfcc end function erfcc