strgn.f90 28.3 KB
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MODULE m_strgn
  USE m_juDFT
  !
  !     *********************************************************
  !     generate two- and three-dimensional stars
  !     for slab geometry
  !     e. wimmer   nov.1984    c.l.fu  1987
  !     implementation of new box-dimension: to treat nonorthogonal
  !     lattice systems
  !     S. Bl"ugel, IFF, 17.Nov.97
  !     *********************************************************
CONTAINS
  SUBROUTINE strgn1(&
       &                  stars,sym,atoms,&
       &                  vacuum,sphhar,input,cell,xcpot)
    !
    USE m_spgrot
    USE m_angle
    USE m_types
    USE m_boxdim
    USE m_sort
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    USE m_cdn_io
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    IMPLICIT NONE
    TYPE(t_stars),INTENT(INOUT)  :: stars
    TYPE(t_sym),INTENT(IN)       :: sym
    TYPE(t_atoms),INTENT(IN)     :: atoms
    TYPE(t_vacuum),INTENT(IN)    :: vacuum
    TYPE(t_sphhar),INTENT(IN)    :: sphhar
    TYPE(t_input),INTENT(IN)     :: input
    TYPE(t_cell),INTENT(IN)      :: cell
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    CLASS(t_xcpot),INTENT(IN)    :: xcpot
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    !     ..
    !     ..
    !     .. Local Scalars ..
    REAL arltv1,arltv2,arltv3,s
    REAL gmi,gla,eps 
    REAL gfx,gfy,pon,pon2
    INTEGER j,k,k1,k2,k3,m0,mxx1,mxx2,n
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    INTEGER ned1,nint,kdone,i,i_sym,n_sym
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    LOGICAL NEW,l_cdn1,l_xcExtended, l_error
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    INTEGER kfx,kfy,kfz,kidx,nfftx,nffty,nfftz,kfft
    INTEGER nfftxy,norm,n1,kidx2,k2i
    !     ..
    !     .. Local Arrays ..
    REAL,    ALLOCATABLE :: gsk3(:)
    INTEGER, ALLOCATABLE :: ig2p(:),INDEX(:),index3(:),kv3rev(:,:)
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    REAL g(3),phi3(stars%ng2),phi
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    COMPLEX phas(sym%nop)
    INTEGER kr(3,sym%nop),kv(3)
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    INTEGER index2(stars%ng2)
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    !     ..
    !     ..
    !
    !
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    nfftx = 3*stars%mx1
    nffty = 3*stars%mx2
    nfftz = 3*stars%mx3
    nfftxy= 9*stars%mx1*stars%mx2
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    ALLOCATE (gsk3(stars%ng3),INDEX(stars%ng3),index3(stars%ng3),kv3rev(stars%ng3,3))
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    !
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    !WRITE (*,*) ' stars are always ordered '
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    l_xcExtended = xcpot%needs_grad()
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    !--->    read in information if exists
    CALL readStars(stars,l_xcExtended,.TRUE.,l_error)
    IF(.NOT.l_error) THEN
       GOTO 270
    END IF
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    IF (input%film.AND.sym%invs.AND.(.not.sym%zrfs).AND.(.not.sym%symor)) THEN
      n_sym = 2 ! needs reordering of 2d-stars
    ELSE
      n_sym = 1 ! as before...
    ENDIF

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    mxx1 = 0
    mxx2 = 0
    stars%ng2 = 0
    kv(3) = 0

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    stars%kv2 = 0
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    DO  k1 = stars%mx1,-stars%mx1,-1
       kv(1) = k1
       k2_loop:DO  k2 = stars%mx2,-stars%mx2,-1
          kv(2) = k2
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          DO i_sym = 1, n_sym
            IF (i_sym == 2) THEN
               kv(1) = - kv(1) ; kv(2) = - kv(2)
            ENDIF

            DO j = 1,2
               g(j) = kv(1)*cell%bmat(1,j) + kv(2)*cell%bmat(2,j)
            ENDDO
            s = SQRT(g(1)**2+g(2)**2)
            !--->   determine the angle of the G_{||} needed in odim calculations
            !+odim YM cute little 'angle' is written by me to determine the phi2
            phi = angle(g(1),g(2))
            !-odim
            !
            !--->   check if generated vector belongs to a star already
            !--->   stars should be within the g_max-sphere !   (Oct.97) sbluegel
            !
            IF (s.LT.stars%gmax) THEN      
               CALL spgrot(&
                    &                     sym%nop,sym%symor,sym%mrot,sym%tau,sym%invtab,&
                    &                     kv,&
                    &                     kr)
               DO n = 1,sym%nop2
                  IF (mxx1.LT.kr(1,n)) mxx1 = kr(1,n)
                  IF (mxx2.LT.kr(2,n)) mxx2 = kr(2,n)
               ENDDO
               DO k = 1,stars%ng2 
                  DO n = 1,sym%nop2
                     IF (kr(1,n).EQ.stars%kv2(1,k) .AND.&
                          &                   kr(2,n).EQ.stars%kv2(2,k)) CYCLE k2_loop
                  ENDDO
               ENDDO
               !--->    new representative found
               stars%ng2 = stars%ng2 + 1
               IF (stars%ng2.GT.stars%ng2) THEN
                  WRITE (6,8070) stars%ng2,stars%ng2
                  CALL juDFT_error("nq2.GT.n2d",calledby="strgn")
               ENDIF
               DO j = 1,2
                  stars%kv2(j,stars%ng2) = kv(j)
               ENDDO
               stars%sk2(stars%ng2) = s
               stars%phi2(stars%ng2) = phi
            ENDIF
            ENDDO ! i_sym

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       ENDDO k2_loop
    ENDDO
8070 FORMAT ('nq2 = ',i5,' > n2d =',i5)

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    IF( mxx1.GT.stars%mx1) THEN
       WRITE (6,'(/'' mxx1.gt.k1d. mxx1,k1d='',2i4)')  mxx1,stars%mx1
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       CALL juDFT_error("mxx1.gt.k1d",calledby="strgn")
    ENDIF

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    IF (mxx2.GT.stars%mx2) THEN
       WRITE (6,'(/'' mxx2.gt.k2d. mxx2,k2d='',2i4)')  mxx2,stars%mx2
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       CALL juDFT_error("mxx2.gt.k2d",calledby="strgn")
    ENDIF

    !--->    sort for increasing length sk2

    CALL sort(stars%ng2,stars%sk2,index)
    DO k = 1,stars%ng2
       kv3rev(k,1) = stars%kv2(1,INDEX(k))
       kv3rev(k,2) = stars%kv2(2,INDEX(k))
       gsk3(k) = stars%sk2(INDEX(k))
       phi3(k) = stars%phi2(INDEX(k))
    ENDDO
    DO k = 1,stars%ng2
       stars%kv2(1,k) = kv3rev(k,1)
       stars%kv2(2,k) = kv3rev(k,2)
       stars%sk2(k) = gsk3(k)
       stars%phi2(k) = phi3(k)
    ENDDO

    !--roa   ....
    !......sort stars of equal length 2D .....
    i=1
    gla=0.
    gsk3(1)=0.0
    eps=1.e-10
    DO  k = 2,stars%ng2
       IF (stars%sk2(k)-gla.GE.eps) i=i+1
       gla=stars%sk2(k)
       gmi = (stars%mx1+stars%kv2(1,k)) + (stars%mx2+stars%kv2(2,k))*(2*stars%mx1+1)
       gsk3(k) = i * ((2*stars%mx1+1)*(2*stars%mx2+1)+9)+gmi
    ENDDO
    CALL sort(stars%ng2,gsk3,index2)
    DO  k = 1,stars%ng2
       kv3rev(k,1) = stars%kv2(1,index2(k))
       kv3rev(k,2) = stars%kv2(2,index2(k))
       gsk3(k) = stars%sk2(index2(k))
       phi3(k) = stars%phi2(index2(k))
    ENDDO
    DO  k = 1,stars%ng2
       stars%kv2(1,k) = kv3rev(k,1)
       stars%kv2(2,k) = kv3rev(k,2)
       stars%sk2(k) = gsk3(k)
       stars%phi2(k) = phi3(k)
       !         if (index2(k).ne.k) write(*,*) ' ic2: ',k,index2(k)
    ENDDO
    !--roa   ....

    WRITE (6,'(/'' nq2='',i4/'' k,kv2(1,2), sk2, phi2''&
         &     /(3i4,f10.5,f10.5))')&
         &  stars%ng2,(k,stars%kv2(1,k),stars%kv2(2,k),stars%sk2(k),stars%phi2(k),k=1,stars%ng2)
    !
    !     three dimensional stars
    !
    stars%ng3 = 0
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    stars%ig = 0
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    DO k3 = -stars%mx3,stars%mx3
       DO k2 = -stars%mx2,stars%mx2
          DO k1 = -stars%mx1,stars%mx1
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             stars%ig(k1,k2,k3) = 0
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             stars%rgphs(k1,k2,k3) = cmplx(0.0,0.0)
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          ENDDO
       ENDDO
    ENDDO
    !+gu
    stars%igfft2(:,:)=0
    stars%igfft(:,:)=0
    stars%pgfft=0.0
    stars%pgfft2=0.0
    !-gu
    WRITE (6,'(/'' bmat(3,3),mx3='',f10.5,i5)') cell%bmat(3,3),stars%mx3

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    IF (stars%mx3.GT.stars%mx3) THEN
       WRITE ( 6,FMT=8000) stars%mx3,stars%mx3
       WRITE (16,FMT=8000) stars%mx3,stars%mx3
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       CALL juDFT_error("mx3.gt.k3d",calledby="strgn")
    ENDIF
8000 FORMAT('   mx3.gt.k3d:',2i6)

    m0 = -stars%mx3
    !     zrfs,invs: z-reflection, inversion.
    IF (sym%zrfs .OR. sym%invs) m0 = 0

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    stars%ig2 = 0
    stars%sk3 = 0.0
    stars%kv3 = 0
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    DO  k2 = 1,stars%ng2
       DO  k3 = m0,stars%mx3
          s = SQRT(stars%sk2(k2)**2+ (k3*cell%bmat(3,3))**2)
          !
          !--->   stars should be within the g_max-sphere !   (Oct.97) sbluegel
          IF (s.LT.stars%gmax) THEN      
             !
             stars%ng3 = stars%ng3 + 1
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             IF (stars%ng3.GT.stars%ng3) THEN
                WRITE (6,*) stars%ng3,stars%ng3
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                CALL juDFT_error("nq3.GT.n3d",calledby="strgn")
             ENDIF
             DO j = 1,2
                stars%kv3(j,stars%ng3) = stars%kv2(j,k2)
             ENDDO
             stars%kv3(3,stars%ng3) = k3
             stars%ig2(stars%ng3) = k2
             stars%sk3(stars%ng3) = s
          ENDIF
       ENDDO
    ENDDO

    !--->    sort for increasing length sk3

    CALL sort(stars%ng3,stars%sk3,index)

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    ALLOCATE (ig2p(stars%ng3))
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    DO k = 1,stars%ng3
       kv3rev(k,1) = stars%kv3(1,INDEX(k))
       kv3rev(k,2) = stars%kv3(2,INDEX(k))
       kv3rev(k,3) = stars%kv3(3,INDEX(k))
       gsk3(k) = stars%sk3(INDEX(k))
       ig2p(k) = stars%ig2(INDEX(k))
    ENDDO
    DO k = 1,stars%ng3
       stars%kv3(1,k) = kv3rev(k,1)
       stars%kv3(2,k) = kv3rev(k,2)
       stars%kv3(3,k) = kv3rev(k,3)
       stars%sk3(k) = gsk3(k)
       stars%ig2(k) = ig2p(k)
    ENDDO
    !
    !--roa   ....
    !......sort stars of equal length 3D .....
    i=1
    gla=0.
    gsk3(1)=0.
    eps=1.e-10
    DO  k = 2,stars%ng3
       IF (stars%sk3(k)-gla.GE.eps) i=i+1
       gla = stars%sk3(k)
       gmi = (stars%mx1+stars%kv3(1,k)) +&
            &           (stars%mx2+stars%kv3(2,k))*(2*stars%mx1+1) +&
            &           (stars%mx3+stars%kv3(3,k))*(2*stars%mx1+1)*(2*stars%mx2+1)
       gsk3(k) = i * (9.+(2*stars%mx1+1)*(2*stars%mx2+1)*(2*stars%mx3+1)) + gmi
    ENDDO
    CALL sort(stars%ng3,gsk3,index3)
    DO  k = 1,stars%ng3
       kv3rev(k,1) = stars%kv3(1,index3(k))
       kv3rev(k,2) = stars%kv3(2,index3(k))
       kv3rev(k,3) = stars%kv3(3,index3(k))
       gsk3(k) = stars%sk3(index3(k))
       ig2p(k) = stars%ig2(index3(k))
    ENDDO
    DO  k = 1,stars%ng3
       stars%kv3(1,k) = kv3rev(k,1)
       stars%kv3(2,k) = kv3rev(k,2)
       stars%kv3(3,k) = kv3rev(k,3)
       stars%sk3(k) = gsk3(k)
       stars%ig2(k) = ig2p(k)
       !           if (index3(k).ne.k) write(*,*) ' ic: ',k,index3(k)
    ENDDO

    DEALLOCATE (ig2p)

    !--roa   ....
    !
    !--->  determine true gmax and change old gmax to new gmax
    !
    WRITE (6,8060) stars%gmax, stars%sk3(stars%ng3)
    stars%gmax = stars%sk3(stars%ng3)
8060 FORMAT (/,1x,'old stars%gmax    =',f10.5, '(a.u.)**(-1) ==>  new stars%gmax  '&
         &       ,'  =',f10.5,'(a.u.)**(-1) ',/,t38,'==>  new E_cut   =',&
         &            f10.5,' Ry')

    !--->    generate all star members
    !+gu
    kidx=0
    kidx2=0
    !-gu
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    stars%rgphs(:,:,:) = cmplx(0.0,0.0)
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    stars%ft2_gfx = 0.0
    stars%ft2_gfy = 0.0
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    DO  k = 1,stars%ng3

       CALL spgrot(&
            &               sym%nop,sym%symor,sym%mrot,sym%tau,sym%invtab,&
            &               stars%kv3(:,k),&
            &               kr,phas)

       IF (stars%kv3(3,k).EQ.0) THEN

          DO  n = 1,sym%nop2
             !+gu
             ! -->       set up the igfft(*,3) array as (1d) fft-pointer:
             !
             !           star ------------> g-vector ------------> fft-grid & phase
             !                igfft(*,1)             igfft(*,2)           igfft(*,3)
             !
             !           size of fft-grid is chosen to be ( 3*k1d x 3*k2d x 3*k3d )
             !
             NEW=.TRUE.

             DO n1=1,n-1
                norm=(kr(1,n)-kr(1,n1))**2 +&
                     &                (kr(2,n)-kr(2,n1))**2 +&
                     &                (kr(3,n)-kr(3,n1))**2
                IF (norm.EQ.0) NEW=.FALSE.
             ENDDO

             IF (NEW) THEN

                kfx = kr(1,n)
                kfy = kr(2,n)
                kfz = kr(3,n)
                !+guta
                gfx = cell%bmat(1,1)*kfx+cell%bmat(2,1)*kfy+cell%bmat(3,1)*kfz 
                gfy = cell%bmat(1,2)*kfx+cell%bmat(2,2)*kfy+cell%bmat(3,2)*kfz
                !-guta
                IF (kfx.LT.0) kfx = kfx+nfftx
                IF (kfy.LT.0) kfy = kfy+nffty
                IF (kfz.LT.0) kfz = kfz+nfftz
                kfft = kfx + kfy*nfftx + kfz*nfftxy
                !
                ! -->            store the number of the star, its position 
                !c                 on fft-grid and phase
                !
                stars%igfft(kidx,1) = k
                stars%igfft(kidx,2) = kfft
                stars%pgfft(kidx)   = phas(n)
                kidx          = kidx+1
                !
                ! -->            now for 2d - stars
                !
                kfft=kfx + kfy*nfftx
                DO k2 = 1,stars%ng2
                   IF ((stars%kv3(1,k).EQ.stars%kv2(1,k2)).AND.&
                        &                 (stars%kv3(2,k).EQ.stars%kv2(2,k2))) k2i = k2
                ENDDO
                stars%igfft2(kidx2,1) = k2i
                stars%igfft2(kidx2,2) = kfft
                stars%pgfft2(kidx2)   = phas(n)
                !+guta
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                IF (xcpot%needs_grad()) THEN
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                   !!                   pgft2x: exp(i*(gfx,gfy,gfz)*tau)*gfx.
                   !!                        y                             y.
                   !!                   pgft2xx: exp(i*(gfx,gfy,gfz)*tau)*gfx*gfx.
                   !!                        yy                             y   y
                   !!                        xy                             x   y

                   stars%ft2_gfx(kidx2)  = gfx
                   stars%ft2_gfy(kidx2)  = gfy
                   !                    stars%pgft2xx(kidx2) = phas(n)*gfx*gfx
                   !                    stars%pgft2yy(kidx2) = phas(n)*gfy*gfy
                   !                    stars%pgft2xy(kidx2) = phas(n)*gfx*gfy
                ENDIF
                !-guta
                kidx2=kidx2+1

             ENDIF
             !-gu
             stars%ig(kr(1,n),kr(2,n),kr(3,n)) = k
             stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) = &
                  &         stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) + phas(n)

          ENDDO

       ELSE
          !        here: kv3(3,k) =/= 0 

          DO  n = 1,sym%nop
             !+gu
             NEW=.TRUE.
             DO n1 = 1,n-1
                norm=(kr(1,n)-kr(1,n1))**2 +&
                     &                (kr(2,n)-kr(2,n1))**2 +&
                     &                (kr(3,n)-kr(3,n1))**2
                IF (norm.EQ.0) NEW = .FALSE.
             ENDDO

             IF (NEW) THEN

                kfx = kr(1,n)
                kfy = kr(2,n)
                kfz = kr(3,n)
                IF (kfx.LT.0) kfx = kfx+nfftx
                IF (kfy.LT.0) kfy = kfy+nffty
                IF (kfz.LT.0) kfz = kfz+nfftz

                kfft=kfx + kfy*nfftx + kfz*nfftxy
                stars%igfft(kidx,1)=k
                stars%igfft(kidx,2)=kfft
                stars%pgfft(kidx)=phas(n)
                kidx=kidx+1

             ENDIF
             !-gu
             stars%ig(kr(1,n),kr(2,n),kr(3,n)) = k
             stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) = &
                  &         stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) + phas(n)

          ENDDO

       ENDIF

    ENDDO
    !    
    stars%kimax=kidx-1
    stars%kimax2=kidx2-1
    !
    !     count number of members for each star
    !     nstr2 ... members of 2-dim stars
    !
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    stars%nstr2(:) = 0
    stars%nstr(:) = 0
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    DO k3 = -stars%mx3,stars%mx3
       DO k2 = -mxx2,mxx2
          DO k1 = -mxx1,mxx1
             k = stars%ig(k1,k2,k3)
             IF ( k .NE. 0 ) THEN
                stars%nstr(k) = stars%nstr(k) + 1
                stars%nstr2(stars%ig2(k)) = stars%nstr2(stars%ig2(k)) +(1-min0(iabs(k3),1))
             ENDIF
          ENDDO
       ENDDO
    ENDDO
    !
    ! normalize phases:
    !
    IF (sym%symor) THEN
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       stars%rgphs(:,:,:) = cmplx(1.0,0.0)
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    ELSE
       pon = 1.0 / sym%nop
       pon2 = 1.0 / sym%nop2
       DO k3 = -stars%mx3,stars%mx3
          DO k2 = -mxx2,mxx2
             DO k1 = -mxx1,mxx1

                kfx = k1 ; kfy = k2; kfz = k3
                k = stars%ig(k1,k2,k3)

                IF (kfx.LT.0) kfx = kfx+nfftx
                IF (kfy.LT.0) kfy = kfy+nffty
                IF (kfz.LT.0) kfz = kfz+nfftz
                kfft=kfx + kfy*nfftx + kfz*nfftxy
                IF (k.GT.0) THEN
                   IF (stars%kv3(3,k).EQ.0) THEN
                      stars%rgphs(k1,k2,k3) = stars%rgphs(k1,k2,k3) * stars%nstr(k)*pon2
                   ELSE
                      stars%rgphs(k1,k2,k3) = stars%rgphs(k1,k2,k3) * stars%nstr(k)*pon
                   ENDIF
                   kidx = -90
                   DO i = 1, stars%kimax
                      IF ( stars%igfft(i,2) == kfft ) kidx = i
                   ENDDO
                   IF ( kidx > 0 ) stars%pgfft(kidx)=stars%rgphs(k1,k2,k3)
                ENDIF
             ENDDO
          ENDDO
       ENDDO
    ENDIF

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    IF (stars%mx1< mxx1 .or.  stars%mx2< mxx2) then
          print *,stars%mx1, mxx1, stars%mx2, mxx2       
          CALL judft_error("BUG in strgn")
    endif
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    !stars%mx1=mxx1
    !stars%mx2=mxx2
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    !--->    write /str0/ and /str1/ to file
    CALL writeStars(stars,l_xcExtended,.TRUE.)
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270 CONTINUE
    !
    !-->  listing
    !
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    WRITE (16,FMT=8010) stars%gmax,stars%ng3,stars%ng2
8010 FORMAT (' gmax=',f10.6,/,' nq3=  ',i5,/,' nq2=  ',i5,/)
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    WRITE (16,FMT=8020) stars%mx1,stars%mx2
8020 FORMAT (' mx1= ',i5,/,' mx2= ',i5,/)
    WRITE (6,FMT=8030)
8030 FORMAT (/,/,/,'   s t a r   l i s t',/)

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    WRITE (6,FMT=8010) stars%gmax,stars%ng3,stars%ng2
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    WRITE (6,'('' mx1,mx2,mx3='',3i3)') stars%mx1,stars%mx2,stars%mx3
    WRITE (6,'('' kimax2,kimax='',2i7,'', (start from 0)'')') stars%kimax2,&
         &  stars%kimax

    WRITE (6,FMT=8040)
8040 FORMAT(/4x,'no.',5x,'kv3',9x,'sk3',9x,'sk2',5x,&
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         &  'ig2',1x,'nstr',2x,'nstr2'/)
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    ned1=9
    nint=30
    DO k = 1,ned1
       WRITE (6,FMT=8050) k,(stars%kv3(j,k),j=1,3),stars%sk3(k),&
            &                     stars%sk2(stars%ig2(k)),&
543
            &                     stars%ig2(k),stars%nstr(k),stars%nstr2(stars%ig2(k))
544
    ENDDO
545
8050 FORMAT (1x,i5,3i4,2f12.6,i4,2i6)
546 547 548 549

    DO k = ned1+1,stars%ng3,nint
       WRITE (6,FMT=8050) k,(stars%kv3(j,k),j=1,3),stars%sk3(k),&
            &                     stars%sk2(stars%ig2(k)),&
550
            &                     stars%ig2(k),stars%nstr(k),stars%nstr2(stars%ig2(k))
551 552 553 554
       kdone = k
    ENDDO

    IF (kdone.LT.stars%ng3) THEN
555 556 557
       WRITE (6,FMT=8050) stars%ng3,(stars%kv3(j,stars%ng3),j=1,3),stars%sk3(stars%ng3),&
            &                     stars%sk2(stars%ig2(stars%ng3)),&
            &                     stars%ig2(stars%ng3),stars%nstr(stars%ng3),stars%nstr2(stars%ig2(stars%ng3))
558 559 560 561 562 563 564 565 566 567 568 569 570 571
    ENDIF

    DEALLOCATE (gsk3,index,index3,kv3rev)

  END SUBROUTINE strgn1
  !----------------------------------------------------------------
  SUBROUTINE strgn2(&
       &                  stars,sym,atoms,&
       &                  vacuum,sphhar,input,cell,xcpot)
    USE m_boxdim
    USE m_sort
    USE m_spgrot
    USE m_constants
    USE m_types
572
    USE m_cdn_io
573 574 575 576 577 578 579 580
    IMPLICIT NONE
    TYPE(t_stars),INTENT(INOUT)  :: stars
    TYPE(t_sym),INTENT(IN)       :: sym
    TYPE(t_atoms),INTENT(IN)     :: atoms
    TYPE(t_vacuum),INTENT(IN)    :: vacuum
    TYPE(t_sphhar),INTENT(IN)    :: sphhar
    TYPE(t_input),INTENT(IN)     :: input
    TYPE(t_cell),INTENT(IN)      :: cell
581
    CLASS(t_xcpot),INTENT(IN)    :: xcpot
582 583 584 585 586 587 588
    !     ..
    !     .. Local Scalars ..
    REAL arltv1,arltv2,arltv3,s
    REAL gmi,gla,eps,gmax2,pon
    REAL gfx,gfy
    INTEGER j,k,k1,k2,k3,m0,mxx1,mxx2,mxx3,n
    INTEGER ned1,nint,kdone,i
589
    LOGICAL NEW,l_cdn1,l_error,l_xcExtended
590
    INTEGER kfx,kfy,kfz,kidx,nfftx,nffty,nfftz,kfft
591
    INTEGER nfftxy,norm,n1,kidx2,k2i
592 593 594 595 596 597 598
    !     ..
    !     .. Local Arrays ..
    REAL, ALLOCATABLE :: gsk3(:)
    INTEGER, ALLOCATABLE :: INDEX(:),index3(:),kv3rev(:,:)
    REAL g(3)
    COMPLEX phas(sym%nop)
    INTEGER kr(3,sym%nop),kv(3)
599 600
    INTEGER index2(stars%ng2)

601 602
    !     ..
    !
603 604 605 606
    nfftx = 3*stars%mx1
    nffty = 3*stars%mx2
    nfftz = 3*stars%mx3
    nfftxy= 9*stars%mx1*stars%mx2
607

608
    ALLOCATE (gsk3(stars%ng3),INDEX(stars%ng3),index3(stars%ng3),kv3rev(stars%ng3,3))
609 610 611 612

    !
    WRITE (*,*) ' stars are always ordered '

613
    l_xcExtended = xcpot%needs_grad()
614
    !--->    read in information if exists
615 616 617 618
    CALL readStars(stars,l_xcExtended,.FALSE.,l_error)
    IF(.NOT.l_error) THEN
       GOTO 270
    END IF
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    mxx1 = 0
    mxx2 = 0
    mxx3 = 0
    stars%ng3 = 0
    stars%ig = 0
    gmax2 = stars%gmax * stars%gmax

    x_dim: DO k1 = stars%mx1,-stars%mx1,-1
       kv(1) = k1
       y_dim: DO k2 = stars%mx2,-stars%mx2,-1
          kv(2) = k2
          z_dim: DO k3 = stars%mx3,-stars%mx3,-1
             IF ( stars%ig(k1,k2,k3) .NE. 0 ) CYCLE z_dim
             kv(3) = k3

             DO j = 1,3
                g(j) = kv(1)*cell%bmat(1,j) + kv(2)*cell%bmat(2,j) +&
                     &                kv(3)*cell%bmat(3,j)
             ENDDO
             s = g(1)**2 + g(2)**2 + g(3)**2
             !
             !--->   check if generated vector belongs to a star already
             IF (s.LT.gmax2) THEN      
                !
                !--->    new representative found
                CALL spgrot(&
                     &                     sym%nop,sym%symor,sym%mrot,sym%tau,sym%invtab,&
                     &                     kv,&
                     &                     kr)
                stars%ng3 = stars%ng3 + 1
650 651
                IF (stars%ng3.GT.stars%ng3) THEN
                   WRITE (6,'("nq3 = ",i5," > n3d =",i5)') stars%ng3,stars%ng3
652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668
                   CALL juDFT_error("nq3>n3d",calledby ="strgn")
                ENDIF
                DO j = 1,3
                   stars%kv3(j,stars%ng3) = kv(j)
                ENDDO
                stars%sk3(stars%ng3) = SQRT(s)
                DO n = 1,sym%nop
                   IF (mxx1.LT.kr(1,n)) mxx1 = kr(1,n)
                   IF (mxx2.LT.kr(2,n)) mxx2 = kr(2,n)
                   IF (mxx3.LT.kr(3,n)) mxx3 = kr(3,n)
                   stars%ig(kr(1,n),kr(2,n),kr(3,n)) = stars%ng3
                ENDDO
             ENDIF
          ENDDO z_dim
       ENDDO y_dim
    ENDDO x_dim

669 670
    IF( mxx1.GT.stars%mx1) THEN
       WRITE (6,'(/'' mxx1.gt.k1d. mxx1,k1d='',2i4)')  mxx1,stars%mx1
671 672 673
       CALL juDFT_error("mxx1>k1d",calledby ="strgn")
    ENDIF

674 675
    IF (mxx2.GT.stars%mx2) THEN
       WRITE (6,'(/'' mxx2.gt.k2d. mxx2,k2d='',2i4)')  mxx2,stars%mx2
676 677 678
       CALL juDFT_error("mxx2>k2d",calledby ="strgn")
    ENDIF

679 680
    IF (mxx3.GT.stars%mx3) THEN
       WRITE (6,'(/'' mxx3.gt.k3d. mxx3,k3d='',2i4)')  mxx3,stars%mx3
681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736
       CALL juDFT_error("mxx3>k3d",calledby ="strgn")
    ENDIF

    !--->    sort for increasing length sk3
    !
    CALL sort(stars%ng3,stars%sk3,index)
    DO k = 1,stars%ng3
       kv3rev(k,1) = stars%kv3(1,INDEX(k))
       kv3rev(k,2) = stars%kv3(2,INDEX(k))
       kv3rev(k,3) = stars%kv3(3,INDEX(k))
       gsk3(k) = stars%sk3(INDEX(k))
    ENDDO
    DO k = 1,stars%ng3
       stars%kv3(1,k) = kv3rev(k,1)
       stars%kv3(2,k) = kv3rev(k,2)
       stars%kv3(3,k) = kv3rev(k,3)
       stars%sk3(k) = gsk3(k)
    ENDDO
    !
    !--roa   ....
    !......sort stars of equal length 3D .....
    i=1
    gla=0.
    gsk3(1)=0.
    eps=1.e-10
    DO  k = 2,stars%ng3
       IF (stars%sk3(k)-gla.GE.eps) i=i+1
       gla = stars%sk3(k)
       gmi = (stars%mx1+stars%kv3(1,k)) +&
            &           (stars%mx2+stars%kv3(2,k))*(2*stars%mx1+1) +&
            &           (stars%mx3+stars%kv3(3,k))*(2*stars%mx1+1)*(2*stars%mx2+1)
       gsk3(k) = i * (9.+(2*stars%mx1+1)*(2*stars%mx2+1)*(2*stars%mx3+1)) + gmi
    ENDDO
    CALL sort(stars%ng3,gsk3,index3)
    DO  k = 1,stars%ng3
       kv3rev(k,1) = stars%kv3(1,index3(k))
       kv3rev(k,2) = stars%kv3(2,index3(k))
       kv3rev(k,3) = stars%kv3(3,index3(k))
       gsk3(k) = stars%sk3(index3(k))
    ENDDO
    DO  k = 1,stars%ng3
       stars%kv3(1,k) = kv3rev(k,1)
       stars%kv3(2,k) = kv3rev(k,2)
       stars%kv3(3,k) = kv3rev(k,3)
       stars%sk3(k) = gsk3(k)
       !           if (index3(k).ne.k) write(*,*) ' ic: ',k,index3(k)
    ENDDO
    !--roa   ....
    !
    !--->  determine true gmax and change old gmax to new gmax
    !
    WRITE (6,8060) stars%gmax, stars%sk3(stars%ng3)
    stars%gmax = stars%sk3(stars%ng3)
8060 FORMAT (/,1x,'gmax    =',f10.5, '(a.u.)**(-1) ==>  new gmax  '&
         &       ,'  =',f10.5,'(a.u.)**(-1) ',/,t38,'==>  new E_cut   =',&
         &            f10.5,' Ry')
737

738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753
    !--->    generate all star members
    !+gu
    kidx=0
    kidx2=0
    DO k3 = -mxx3,mxx3
       DO k2 = -mxx2,mxx2
          DO k1 = -mxx1,mxx1
             stars%ig(k1,k2,k3) = 0
          ENDDO
       ENDDO
    ENDDO

    !-gu
    !
    ! sum over phases
    !
754
    stars%rgphs(:,:,:) = cmplx(0.0,0.0)
755 756
    stars%igfft = 0
    stars%pgfft = cmplx(0.0,0.0)
757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830
    starloop: DO k = 1,stars%ng3

       CALL spgrot(&
            &               sym%nop,sym%symor,sym%mrot,sym%tau,sym%invtab,&
            &               stars%kv3(:,k),&
            &               kr,phas)
       !
       ! -->    set up the igfft(*,3) array as (1d) fft-pointer:
       !
       !        star ------------> g-vector ------------> fft-grid & phase
       !             igfft(*,1)             igfft(*,2)           igfft(*,3)
       !
       !        size of fft-grid is chosen to be ( 3*k1d x 3*k2d x 3*k3d )
       !
       ops: DO n = 1,sym%nop

          NEW=.TRUE.
          DO n1 = 1,n-1
             norm=(kr(1,n)-kr(1,n1))**2 +&
                  &             (kr(2,n)-kr(2,n1))**2 +&
                  &             (kr(3,n)-kr(3,n1))**2
             IF (norm.EQ.0) NEW = .FALSE.
          ENDDO

          IF (NEW) THEN

             kfx = kr(1,n)
             kfy = kr(2,n)
             kfz = kr(3,n)
             IF (kfx.LT.0) kfx = kfx+nfftx
             IF (kfy.LT.0) kfy = kfy+nffty
             IF (kfz.LT.0) kfz = kfz+nfftz

             kfft=kfx + kfy*nfftx + kfz*nfftxy
             stars%igfft(kidx,1)=k
             stars%igfft(kidx,2)=kfft
             stars%pgfft(kidx)=phas(n)
             kidx=kidx+1

          ENDIF
          stars%ig(kr(1,n),kr(2,n),kr(3,n)) = k
          stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) = &
               &      stars%rgphs(kr(1,n),kr(2,n),kr(3,n)) + phas(n)

       ENDDO ops
    ENDDO starloop
    !    
    stars%kimax=kidx-1
    !
    !     count number of members for each star
    !
    DO k = 1,stars%ng3
       stars%nstr(k) = 0
    ENDDO

    DO k3 = -mxx3,mxx3
       DO k2 = -mxx2,mxx2
          DO k1 = -mxx1,mxx1
             k = stars%ig(k1,k2,k3)
             IF ( k .NE. 0 ) THEN
                stars%nstr(k) = stars%nstr(k) + 1
             ENDIF
             !               DO k = 1,nq3
             !                  IF (ig(k1,k2,k3).eq.k) THEN
             !                     nstr(k) = nstr(k) + 1
             !                  ENDIF
             !               ENDDO
          ENDDO
       ENDDO
    ENDDO
    !
    ! normalize phases:
    !
    IF (sym%symor) THEN
831
       stars%rgphs(:,:,:) = cmplx(1.0,0.0)
832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854
    ELSE
       pon = 1.0 / sym%nop
       DO k3 = -mxx3,mxx3
          DO k2 = -mxx2,mxx2
             DO k1 = -mxx1,mxx1
                k = stars%ig(k1,k2,k3)
                IF (k.GT.0) THEN
                   stars%rgphs(k1,k2,k3) = stars%rgphs(k1,k2,k3) * stars%nstr(k)*pon
                   kfx = k1 ; kfy = k2; kfz = k3
                   IF (kfx.LT.0) kfx = kfx+nfftx
                   IF (kfy.LT.0) kfy = kfy+nffty
                   IF (kfz.LT.0) kfz = kfz+nfftz
                   kfft=kfx + kfy*nfftx + kfz*nfftxy
                   kidx = -90
                   DO i = 1, stars%kimax
                      IF ( stars%igfft(i,2) == kfft ) kidx = i
                   ENDDO
                   IF (kidx > 0 ) stars%pgfft(kidx)=stars%rgphs(k1,k2,k3)
                ENDIF
             ENDDO
          ENDDO
       ENDDO
    ENDIF
855
    if ( stars%mx1 < mxx1 .or. stars%mx2 < mxx2 .or. stars%mx3 < mxx3 ) call &
856
         judft_error("BUG 1 in strgen") 
857
    stars%ng2 = 2 ; stars%kv2 = 0 ; stars%ig2 = 0 ; stars%kimax2= 0 ; stars%igfft2 = 0
858
    stars%sk2 = 0.0 ; stars%pgfft2 = 0.0  ; stars%nstr2 = 0
859
    IF (xcpot%needs_grad()) THEN
860 861
       stars%ft2_gfx = 0.0 ; stars%ft2_gfy = 0.0 
    ENDIF
862 863 864

    !--->    write /str0/ and /str1/ to file
    CALL writeStars(stars,l_xcExtended,.FALSE.)
865 866

270 CONTINUE
867

868 869
    !
    !-->  listing
870 871
    WRITE (16,FMT=8010) stars%gmax,stars%ng3
8010 FORMAT (' gmax=',f10.6,/,' nq3=  ',i7,/)
872 873 874 875 876 877
    WRITE (16,FMT=8020) stars%mx1,stars%mx2,stars%mx3
8020 FORMAT (' mx1= ',i5,/,' mx2= ',i5,' mx3= ',i5,/)
    WRITE (6,FMT=8030)
8030 FORMAT (/,/,/,'   s t a r   l i s t',/)


878
    WRITE (6,FMT=8010) stars%gmax,stars%ng3
879 880 881 882 883
    WRITE (6,'('' mx1,mx2,mx3='',3i3)') stars%mx1,stars%mx2,stars%mx3
    WRITE (6,'('' kimax2,kimax='',2i7,'', (start from 0)'')') stars%kimax2,&
         &  stars%kimax

    WRITE (6,FMT=8040)
884
8040 FORMAT(/6x,'no.',5x,'kv3',9x,'sk3',7x,'nstr'/)
885 886 887 888 889 890

    ned1=9
    nint=30
    DO k = 1,ned1
       WRITE (6,FMT=8050) k,(stars%kv3(j,k),j=1,3),stars%sk3(k),stars%nstr(k)
    ENDDO
891
8050 FORMAT (1x,i7,3i4,f12.6,i6)
892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907

    DO k = ned1+1,stars%ng3,nint
       WRITE (6,FMT=8050) k,(stars%kv3(j,k),j=1,3),stars%sk3(k),stars%nstr(k)
       kdone = k
    ENDDO

    IF (kdone.LT.stars%ng3) THEN
       WRITE (6,FMT=8050) stars%ng3,(stars%kv3(j,stars%ng3),j=1,3),&
            &                     stars%sk3(stars%ng3),stars%nstr(stars%ng3)
    ENDIF


    DEALLOCATE (gsk3,index,index3,kv3rev)

  END SUBROUTINE strgn2
END MODULE m_strgn