mirror of https://gitlab.com/QEF/q-e.git
88 lines
2.3 KiB
Fortran
88 lines
2.3 KiB
Fortran
!
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! Copyright (C) 2001 PWSCF group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!
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!-----------------------------------------------------------------------
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function wgauss (x, n)
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!-----------------------------------------------------------------------
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!
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! this function computes the approximate theta function for the
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! given order n, at the point x.
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!
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! --> (n>=0) : Methfessel-Paxton case. See PRB 40, 3616 (1989).
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!
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! --> (n=-1 ): Cold smearing (Marzari-Vanderbilt-DeVita-Payne).
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! See PRL 82, 3296 (1999)
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! 1/2*erf(x-1/sqrt(2)) + 1/sqrt(2*pi)*exp(-(x-1/sqrt(2))**2) + 1/2
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!
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! --> (n=-99): Fermi-Dirac case: 1.0/(1.0+exp(-x)).
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!
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USE kinds, ONLY : DP
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USE constants, ONLY : pi
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implicit none
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real(DP) :: wgauss, x
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! output: the value of the function
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! input: the argument of the function
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integer :: n
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! input: the order of the function
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!
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! the local variables
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!
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real(DP) :: a, hp, arg, hd, xp
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! the coefficient a_n
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! the hermitean function
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! the argument of the exponential
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! the hermitean function
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! auxiliary variable (cold smearing)
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integer :: i, ni
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! counter on the n indices
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! counter on 2n
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real(DP), external :: gauss_freq, qe_erf
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real(DP), parameter :: maxarg = 200.d0
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! maximum value for the argument of the exponential
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! Fermi-Dirac smearing
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if (n.eq. - 99) then
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if (x.lt. - maxarg) then
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wgauss = 0.d0
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elseif (x.gt.maxarg) then
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wgauss = 1.d0
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else
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wgauss = 1.0d0 / (1.0d0 + exp ( - x) )
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endif
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return
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endif
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! Cold smearing
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if (n.eq. - 1) then
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xp = x - 1.0d0 / sqrt (2.0d0)
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arg = min (maxarg, xp**2)
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wgauss = 0.5d0 * qe_erf (xp) + 1.0d0 / sqrt (2.0d0 * pi) * exp ( - &
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arg) + 0.5d0
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return
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endif
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! Methfessel-Paxton
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wgauss = gauss_freq (x * sqrt (2.0d0) )
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if (n.eq.0) return
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hd = 0.d0
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arg = min (maxarg, x**2)
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hp = exp ( - arg)
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ni = 0
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a = 1.d0 / sqrt (pi)
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do i = 1, n
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hd = 2.0d0 * x * hp - 2.0d0 * DBLE (ni) * hd
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ni = ni + 1
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a = - a / (DBLE (i) * 4.0d0)
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wgauss = wgauss - a * hd
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hp = 2.0d0 * x * hd-2.0d0 * DBLE (ni) * hp
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ni = ni + 1
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enddo
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return
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end function wgauss
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