SUBROUTINE fft6_g2r_green_ex (f_g, f_r)
! 6-D fourier transform used for G(G,G'). 
! which agrees with convention in FG's paper.

  USE io_files,         ONLY : prefix, iunigk
  USE kinds,            ONLY : DP 
  USE cell_base,        ONLY : omega, alat
  USE control_gw,       ONLY : lgamma
  USE wvfct,            ONLY : npw, npwx, igk
  USE qpoint,           ONLY : xq, npwq, igkq, nksq, ikks, ikqs
  USE gwsigma,          ONLY : ngmsex, nrsex, nr1sex, nr2sex, nr3sex, nlsex

  IMPLICIT NONE

  INTEGER                          :: ios
  INTEGER                          :: ig, igp, ir, irp
  INTEGER                          :: ngmtmp
  COMPLEX(DP)                      :: czero
  INTEGER                          :: nr1tmp, nr2tmp, nr3tmp, nrtmp
  COMPLEX(DP), INTENT(INOUT)       :: f_g(ngmsex,ngmsex)
  COMPLEX(DP), INTENT(INOUT)       :: f_r (nrsex,nrsex)
  COMPLEX(DP)                      :: aux(nrsex)

  czero = (0.0d0, 0.0d0)
  f_r(:,:) = czero

  ngmtmp = ngmsex
  if (ngmsex.gt.npwq) ngmtmp = npwq

  do ig = 1, ngmtmp
      aux(:) = czero

      do igp = 1, ngmtmp
        aux(nlsex(igkq(igp))) = f_g(ig,igp)
      enddo

      call cft3s (aux, nr1sex, nr2sex, nr3sex, nr1sex, nr2sex, nr3sex, +2)
      f_r(ig, 1:nrsex) = aux / omega
  enddo

! the conjg/conjg is to calculate sum_G f(G) exp(-iGr)
! following the convention set in the paper
! because the standard transform is sum_G f(G) exp(iGr).

  do irp = 1, nrsex
     aux = czero

     do ig = 1, ngmtmp
            aux(nlsex(igkq(ig))) = conjg( f_r(ig,irp) )
     enddo

     call cft3s (aux, nr1sex, nr2sex, nr3sex, nr1sex, nr2sex, nr3sex, +2)
     f_r(1:nrsex,irp) = conjg ( aux )
  enddo
END SUBROUTINE fft6_g2r_green_ex