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!**********************************************************************
! 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 <http://www.gnu.org/licenses/>. *
!**********************************************************************
! 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(kind=dp) :: x,tmp,ser,xx,gammln
real(KIND=dp) :: cof(6) = (/ &
76.18009173_dp, -86.50532033_dp, 24.01409822_dp, &
-1.231739516_dp, .120858003e-2_dp, -.536382e-5_dp /)
real(KIND=dp) :: stp = 2.50662827465_dp
real(KIND=dp) :: 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
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