quantum-espresso/upflib/dqvan2.f90

172 lines
5.1 KiB
Fortran

!
! Copyright (C) 2001-2018 Quantum ESPRESSO Foundation
! 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 .
!
!-----------------------------------------------------------------------
SUBROUTINE dqvan2( ih, jh, np, ipol, ngy, g, tpiba, qmod, ylmk0, dylmk0, dqg )
!-----------------------------------------------------------------------
!! This routine computes the derivatives of the Fourier transform of
!! the Q function needed in stress assuming that the radial Fourier
!! transform is already computed and stored in table \(\text{tab_qrad}\).
!! The implemented formula:
!
!! \[ \text{dq}(g,i,j) = \sum_lm (-i)^l \text{ap}(lm,i,j) *
!! ( \text{yr}_{lm}(g^) \text{dqrad}(g,l,i,j) +
!! \text{dyr}_{lm}(g') \text{qrad}(g,l,i,j)) \]
!
USE upf_kinds, ONLY: DP
USE qrad_mod, ONLY: dq, tab_qrad
USE uspp_param, ONLY: lmaxq, nbetam
USE uspp, ONLY: nlx, lpl, lpx, ap, indv, nhtol, nhtolm
!
IMPLICIT NONE
!
INTEGER, INTENT(IN) :: ngy
!! the number of G vectors to compute
INTEGER, INTENT(IN) :: ih
!! first index of Q(ih,jh)
INTEGER, INTENT(IN) :: jh
!! second index of Q(ih,jh)
INTEGER, INTENT(IN) :: np
!! pseudopotential index
INTEGER, INTENT(IN) :: ipol
!! the polarization of the derivative
REAL(DP), INTENT(IN) :: g(3,ngy)
!! G vectors
REAL(DP), INTENT(IN) :: tpiba
!! 2pi/a factor, multiplies G vectors
REAL(DP), INTENT(IN) :: qmod(ngy)
!! moduli of q+G vectors
REAL(DP), INTENT(IN) :: ylmk0(ngy,lmaxq*lmaxq)
!! spherical harmonics
REAL(DP), INTENT(IN) :: dylmk0(ngy,lmaxq*lmaxq)
!! derivetives of spherical harmonics
COMPLEX(DP), INTENT(OUT) :: dqg(ngy)
!! the fourier transform of interest
!
! ... local variables
!
COMPLEX(DP) :: sig, dqg_bgr
! (-i)^L
INTEGER :: nb, mb, ijv, ivl, jvl, ig, lp, l, lm, i0, i1, i2, i3
! the atomic index corresponding to ih
! the atomic index corresponding to jh
! combined index (nb,mb)
! the lm corresponding to ih
! the lm corresponding to jh
! counter on g vectors
! the actual LM
! the angular momentum L
! the possible LM's compatible with ih,j
! counters for interpolation table
!
REAL(DP) :: sixth, dqi, qm, px, ux, vx, wx, uvx, pwx, work, work1
! 1 divided by six
! 1 divided dq
! qmod/dq
! measures for interpolation table
! auxiliary variables for intepolation
! auxiliary variable
! auxiliary variable
!
! ... compute the indices which correspond to ih,jh
!
!$acc data present_or_copyin(g,qmod,ylmk0,dylmk0) present_or_copyout(dqg) present(tab_qrad)
!
sixth = 1.d0 / 6.d0
nb = indv(ih, np)
mb = indv(jh, np)
IF (nb >= mb) THEN
ijv = nb * (nb - 1) / 2 + mb
ELSE
ijv = mb * (mb - 1) / 2 + nb
ENDIF
!
ivl = nhtolm(ih, np)
jvl = nhtolm(jh, np)
!
IF (nb > nbetam .OR. mb > nbetam) &
CALL upf_error (' dqvan2 ', ' wrong dimensions (1)', MAX(nb,mb))
IF (ivl > nlx .OR. jvl > nlx) &
CALL upf_error (' dqvan2 ', ' wrong dimensions (2)', MAX(ivl,jvl))
!
!$acc kernels
dqg(:) = (0.d0,0.d0)
!$acc end kernels
!
! ... and make the sum over the non zero LM
!
dqi = 1 / dq
DO lm = 1, lpx(ivl,jvl)
lp = lpl(ivl,jvl,lm)
!
! ... extraction of angular momentum l from lp:
!
IF (lp==1) THEN
l = 1
ELSEIF ( (lp>=2) .AND. (lp<=4) ) THEN
l = 2
ELSEIF ( (lp>=5) .AND. (lp<=9) ) THEN
l = 3
ELSEIF ( (lp>=10) .AND. (lp<=16) ) THEN
l = 4
ELSEIF ( (lp>=17) .AND. (lp<=25) ) THEN
l = 5
ELSEIF ( (lp>=26) .AND. (lp<=36) ) THEN
l = 6
ELSEIF ( (lp>=37) .AND. (lp<=49) ) THEN
l = 7
ELSE
CALL upf_error (' dqvan2 ', ' lp.gt.49 ', lp)
ENDIF
!
sig = (0.d0, -1.d0)**(l - 1)
sig = sig * ap(lp,ivl,jvl)
!
!$acc parallel loop
DO ig = 1, ngy
!
qm = qmod (ig) * dqi
px = qm - INT(qm)
ux = 1.d0 - px
vx = 2.d0 - px
wx = 3.d0 - px
i0 = qm + 1
i1 = qm + 2
i2 = qm + 3
i3 = qm + 4
uvx = ux * vx * sixth
!
pwx = px * wx * 0.5d0
!
work = tab_qrad(i0, ijv, l, np) * uvx * wx + &
tab_qrad(i1, ijv, l, np) * pwx * vx - &
tab_qrad(i2, ijv, l, np) * pwx * ux + &
tab_qrad(i3, ijv, l, np) * px * uvx
work1 = (- tab_qrad(i0, ijv, l, np) * (ux*vx + vx*wx + ux*wx) * sixth &
+ tab_qrad(i1, ijv, l, np) * (wx*vx - px*wx - px*vx) * 0.5d0 &
- tab_qrad(i2, ijv, l, np) * (wx*ux - px*wx - px*ux) * 0.5d0 &
+ tab_qrad(i3, ijv, l, np) * (ux*vx - px*ux - px*vx) * sixth) * dqi
!
IF (qmod(ig) > 1.d-9) THEN
dqg_bgr = sig * ylmk0(ig,lp) * work1 * tpiba * g(ipol,ig) / qmod(ig)
ELSE
dqg_bgr = (0.d0,0.d0)
ENDIF
!
dqg(ig) = dqg(ig) + sig * dylmk0(ig,lp) * work / tpiba + dqg_bgr
!
ENDDO
!
ENDDO
!
!$acc end data
!
RETURN
!
END SUBROUTINE dqvan2