mirror of https://gitlab.com/QEF/q-e.git
68 lines
1.8 KiB
Fortran
68 lines
1.8 KiB
Fortran
!
|
|
! Copyright (C) 2001 PWSCF group
|
|
! This file is distributed under the terms of the
|
|
! GNU General Public License. See the file `License'
|
|
! in the root directory of the present distribution,
|
|
! or http://www.gnu.org/copyleft/gpl.txt .
|
|
!
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
function w_1gauss (x, n)
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
! the derivative of w0gauss:
|
|
!
|
|
! --> (n=-99): second derivative of Fermi-Dirac function
|
|
!
|
|
USE kinds, ONLY : DP
|
|
USE constants, ONLY : sqrtpm1
|
|
!
|
|
implicit none
|
|
real (DP) :: w_1gauss, x
|
|
! output: the value of the function
|
|
! input: the point where to compute the function
|
|
|
|
integer :: n
|
|
! input: the order of the smearing function
|
|
!
|
|
! here the local variables
|
|
!
|
|
real (DP) :: a, arg, hp, hd, aux1, aux2
|
|
! the coefficients a_n
|
|
! the argument of the exponential
|
|
! the hermite function
|
|
! the hermite function
|
|
! auxiliary variable
|
|
! auxiliary variable
|
|
integer :: i, ni
|
|
! counter on n values
|
|
! counter on 2n values
|
|
! Fermi-Dirac smearing
|
|
if (n.eq. - 99) then
|
|
aux1 = exp (x)
|
|
aux2 = exp ( - x)
|
|
w_1gauss = (aux2 - aux1) / (2.d0 + aux1 + aux2) **2
|
|
return
|
|
endif
|
|
!
|
|
arg = min (200.d0, x**2)
|
|
w_1gauss = - 2.d0 * x * exp ( - arg) * sqrtpm1
|
|
if (n.eq.0) return
|
|
hd = exp ( - arg)
|
|
hp = 2.d0 * x * exp ( - arg)
|
|
ni = 1
|
|
a = sqrtpm1
|
|
do i = 1, n
|
|
hd = 2.0d0 * x * hp - 2.0d0 * DBLE (ni) * hd
|
|
ni = ni + 1
|
|
a = - a / (DBLE (i) * 4.0d0)
|
|
hp = 2.0d0 * x * hd-2.0d0 * DBLE (ni) * hp
|
|
ni = ni + 1
|
|
w_1gauss = w_1gauss - a * hp
|
|
enddo
|
|
return
|
|
|
|
|
|
|
|
end function w_1gauss
|