strgn.f90 27.8 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
    TYPE(t_xcpot),INTENT(IN)     :: xcpot

    !     ..
    !     ..
    !     .. 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
    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%is_gga()
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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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    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
          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
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             IF (stars%ng2.GT.stars%ng2) THEN
                WRITE (6,8070) stars%ng2,stars%ng2
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                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 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%is_gga()) 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,&
522
         &  '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)),&
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            &                     stars%ig2(k),stars%nstr(k),stars%nstr2(stars%ig2(k))
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    ENDDO
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8050 FORMAT (1x,i5,3i4,2f12.6,i4,2i6)
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    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)),&
536
            &                     stars%ig2(k),stars%nstr(k),stars%nstr2(stars%ig2(k))
537 538 539 540
       kdone = k
    ENDDO

    IF (kdone.LT.stars%ng3) THEN
541 542 543
       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))
544 545 546 547 548 549 550 551 552 553 554 555 556 557
    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
558
    USE m_cdn_io
559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574
    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
    TYPE(t_xcpot),INTENT(IN)     :: xcpot
    !     ..
    !     .. 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
575
    LOGICAL NEW,l_cdn1,l_error,l_xcExtended
576
    INTEGER kfx,kfy,kfz,kidx,nfftx,nffty,nfftz,kfft
577
    INTEGER nfftxy,norm,n1,kidx2,k2i
578 579 580 581 582 583 584
    !     ..
    !     .. Local Arrays ..
    REAL, ALLOCATABLE :: gsk3(:)
    INTEGER, ALLOCATABLE :: INDEX(:),index3(:),kv3rev(:,:)
    REAL g(3)
    COMPLEX phas(sym%nop)
    INTEGER kr(3,sym%nop),kv(3)
585 586
    INTEGER index2(stars%ng2)

587 588
    !     ..
    !
589 590 591 592
    nfftx = 3*stars%mx1
    nffty = 3*stars%mx2
    nfftz = 3*stars%mx3
    nfftxy= 9*stars%mx1*stars%mx2
593

594
    ALLOCATE (gsk3(stars%ng3),INDEX(stars%ng3),index3(stars%ng3),kv3rev(stars%ng3,3))
595 596 597 598

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

599
    l_xcExtended = xcpot%is_gga()
600
    !--->    read in information if exists
601 602 603 604
    CALL readStars(stars,l_xcExtended,.FALSE.,l_error)
    IF(.NOT.l_error) THEN
       GOTO 270
    END IF
605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635

    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
636 637
                IF (stars%ng3.GT.stars%ng3) THEN
                   WRITE (6,'("nq3 = ",i5," > n3d =",i5)') stars%ng3,stars%ng3
638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654
                   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

655 656
    IF( mxx1.GT.stars%mx1) THEN
       WRITE (6,'(/'' mxx1.gt.k1d. mxx1,k1d='',2i4)')  mxx1,stars%mx1
657 658 659
       CALL juDFT_error("mxx1>k1d",calledby ="strgn")
    ENDIF

660 661
    IF (mxx2.GT.stars%mx2) THEN
       WRITE (6,'(/'' mxx2.gt.k2d. mxx2,k2d='',2i4)')  mxx2,stars%mx2
662 663 664
       CALL juDFT_error("mxx2>k2d",calledby ="strgn")
    ENDIF

665 666
    IF (mxx3.GT.stars%mx3) THEN
       WRITE (6,'(/'' mxx3.gt.k3d. mxx3,k3d='',2i4)')  mxx3,stars%mx3
667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722
       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')
723

724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739
    !--->    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
    !
740
    stars%rgphs(:,:,:) = cmplx(0.0,0.0)
741 742
    stars%igfft = 0
    stars%pgfft = cmplx(0.0,0.0)
743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
    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
817
       stars%rgphs(:,:,:) = cmplx(1.0,0.0)
818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840
    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
841
    if ( stars%mx1 < mxx1 .or. stars%mx2 < mxx2 .or. stars%mx3 < mxx3 ) call &
842
         judft_error("BUG 1 in strgen") 
843
    stars%ng2 = 2 ; stars%kv2 = 0 ; stars%ig2 = 0 ; stars%kimax2= 0 ; stars%igfft2 = 0
844
    stars%sk2 = 0.0 ; stars%pgfft2 = 0.0  ; stars%nstr2 = 0
845
    IF (xcpot%is_gga()) THEN
846 847
       stars%ft2_gfx = 0.0 ; stars%ft2_gfy = 0.0 
    ENDIF
848 849 850

    !--->    write /str0/ and /str1/ to file
    CALL writeStars(stars,l_xcExtended,.FALSE.)
851 852

270 CONTINUE
853

854 855
    !
    !-->  listing
856 857
    WRITE (16,FMT=8010) stars%gmax,stars%ng3
8010 FORMAT (' gmax=',f10.6,/,' nq3=  ',i7,/)
858 859 860 861 862 863
    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',/)


864
    WRITE (6,FMT=8010) stars%gmax,stars%ng3
865 866 867 868 869
    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)
870
8040 FORMAT(/6x,'no.',5x,'kv3',9x,'sk3',7x,'nstr'/)
871 872 873 874 875 876

    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
877
8050 FORMAT (1x,i7,3i4,f12.6,i6)
878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893

    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