mirror of https://gitlab.com/QEF/q-e.git
67 lines
1.8 KiB
Fortran
67 lines
1.8 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 w_1gauss (x, n)
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!-----------------------------------------------------------------------
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!
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! the derivative of w0gauss:
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!
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! --> (n=-99): second derivative of Fermi-Dirac function
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!
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implicit none
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real (8) :: w_1gauss, x
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! output: the value of the function
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! input: the point where to compute the function
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integer :: n
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! input: the order of the smearing function
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!
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! here the local variables
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!
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real (8) :: a, arg, hp, hd, pi, aux1, aux2
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! the coefficients a_n
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! the argument of the exponential
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! the hermite function
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! the hermite function
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! pi
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! auxiliary variable
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! auxiliary variable
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integer :: i, ni
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! counter on n values
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! counter on 2n values
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! Fermi-Dirac smearing
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if (n.eq. - 99) then
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aux1 = exp (x)
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aux2 = exp ( - x)
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w_1gauss = (aux2 - aux1) / (2.d0 + aux1 + aux2) **2
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return
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endif
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!
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pi = 3.14159265358979d0
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arg = min (200.d0, x**2)
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w_1gauss = - 2.d0 * x * exp ( - arg) / sqrt (pi)
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if (n.eq.0) return
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hd = exp ( - arg)
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hp = 2.d0 * x * exp ( - arg)
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ni = 1
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a = 1.0 / sqrt (pi)
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do i = 1, n
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hd = 2.0d0 * x * hp - 2.0d0 * float (ni) * hd
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ni = ni + 1
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a = - a / (float (i) * 4.0d0)
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hp = 2.0d0 * x * hd-2.0d0 * float (ni) * hp
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ni = ni + 1
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w_1gauss = w_1gauss - a * hp
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enddo
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return
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end function w_1gauss
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