[Pw_forum] IFC's

Katalin Gaal-Nagy katalin.gaal-nagy at physik.uni-regensburg.de
Mon Sep 3 10:01:59 CEST 2007


Dear Ezad, dear Paolo,

well ... you can do it, with a trick.
If I understood correctly, you have the q points on a 3x3x3 grid and the q 
points on a 4x4x4 grid. A grid containing both sets of q points is the 
12x12x12 grid.
You can do the following: You calculate the force constants of the 4x4x4 
grid and do a back Fourier transform and calculate the dynamical matrices 
on a 12x12x12 grid. In this set of dynamical matrices, the ones 
corresponding to the 4x4x4 grid are identical (up to numerical noise, 
which is little). Then you take these  12x12x12 interpolated dynamical 
matrices, throw away the interpolated ones corresponding to the 3x3x3 mesh 
and put instead the 3x3x3 ones you have calculated with ph.x. You again 
have a full set of dynamical matrices and you can calculate from these the 
force constants, which correspond to a mixing of a 4x4x4 grid and a 3x3x3 
grid. Note, they DON'T correspond to a 12x12x12 grid, since there are 
still interpolated dynamical matrices left. With the resulting dynamical 
matrices also no physical meaning like range of corresponding forces can 
be connected any more.

The idea of this scheme can be found under condmat arXiv:0707.0384.

For the use of this scheme I modified the postprocessing routines 
matdyn.f90 of ESPRESSO (I am not sure about the version, if should have 
been espresso-3.1). I don't remember, if I was putting it in a nice, 
commented shape (for sure tha Makefile not ... ). The main modification 
was to tell the code to write out the dynamical matrices for all q in 
star(q) in a way, that q2r.x can read it again. The modified routines and 
a makefile are attached. I would apprechiate if you could test, if the 
compilation is working.

However, you have to use the routines q2r.x and matdyn.x ...
The matdyn.x has now an additional flag and the input reads as

  &input
     asr='simple',  amass(1)=28.086,
     flfrc='si.q888.force',
     flfrq='si.q16.16.16.freq.interpol',
     dynmatout=.true.
  /
349

.... list of k points created with kpoints.x ...

It creates (in this case) 349 files containing the interpolated dynamical 
matrices dynint.$number where $number is the number of the q point given 
in the list ...

Paolo, in case you want to include it to the ESPRESSO paackage and there 
are problems, please let me know.


Good luck,
Katalin






On Sun, 2 Sep 2007, Paolo Giannozzi wrote:

>
> On Sep 2, 2007, at 10:25 , Ezad Shojaee wrote:
>
>> i want to know that are we able to use the 'IFC's calculated with
>> two grids' together? for example we calculate them by a 3*3*3 grid,
>> and then 4*4*4 , then use all of them in calculating C(q) for an
>> arbitrary point in the Brillouin zone?
>
> no, it is not: you can use only one specific grid. In principle one
> could
> start with a coarser grid and then add the missing points needed to have
> a denser grid, I think, but it would be a mess
>
> Paolo
> ---
> Paolo Giannozzi, Democritos and University of Udine, Italy
>
>
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum
>
-------------- next part --------------
# Makefile for tools

include ../make.sys
PHOBJS = \
../PH/write_dyn_on_file.o \
../PH/star_q.o 
#../PH/dyndia.o \
#../PW/cdiagh.o \
#../Modules/clocks.o

#../PH/dynmatrix.o \
#../PH/symdyn_munu.o \
#../PH/stop_ph.o \
#../PH/q2qstar_ph.o \
#../PH/write_ramtns.o \
#../PH/trntnsc.o \
#../PH/symdynph_gq.o \
#../PH/print_clock_ph.o \
#../PH/rotate_and_add_dyn.o \
#../PH/write_epsilon_and_zeu.o \
#../PH/deallocate_part.o



PWOBJS = \
../PW/checksym.o \
../PW/coset.o \
../PW/cryst_to_car.o \
../PW/cubicsym.o \
../PW/eqvect.o \
../PW/error_handler.o \
../PW/hexsym.o \
../PW/irrek.o \
../PW/inverse_s.o \
../PW/kpoint_grid.o \
../PW/mode_group.o \
../PW/multable.o \
../PW/noncol.o \
../PW/pwcom.o \
../PW/sgam_at.o \
../PW/sgam_at_mag.o \
../PW/sgam_ph.o \
../PW/sgama.o \
../PW/smallg_q.o \
../PW/trnvecc.o \
../PW/w0gauss.o \
../PW/wsweight.o

MODULES = \
../Modules/basic_algebra_routines.o \
../Modules/cell_base.o \
../Modules/constants.o \
../Modules/control_flags.o \
../Modules/io_global.o \
../Modules/io_files.o \
../Modules/ions_base.o \
../Modules/fft_types.o \
../Modules/fft_scalar.o \
../Modules/kind.o \
../Modules/mp.o \
../Modules/mp_global.o \
../Modules/parallel_include.o \
../Modules/parameters.o \
../Modules/parser.o \
../Modules/path_formats.o \
../Modules/printout_base.o \
../Modules/random_numbers.o \
../Modules/recvec.o \
../Modules/splinelib.o \
../Modules/timestep.o \
../Modules/uspp.o


TLDEPS= bindir mods libs pw

all : tldeps dynmat.x kpoints.x matdyn.x \
      q2r.x q2r.old.x 
#      path_int.x pwi2xsf.x q2r.x q2r.old.x bands_FS.x kvecs_FS.x metadyn_pp.x

dynmat.x : dynmat.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS)
	$(MPIF90) $(LDFLAGS) -o $@ \
		dynmat.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS) $(LIBS)
	- ( cd ../bin ; ln -fs ../pwtools/$@ . )

kpoints.x : kpoints.o $(PWOBJS) $(MODULES) $(LIBOBJS)
	$(MPIF90) $(LDFLAGS) -o $@ \
		kpoints.o $(PWOBJS) $(MODULES) $(LIBOBJS) $(LIBS)
	- ( cd ../bin ; ln -fs ../pwtools/$@ . )

matdyn.x : matdyn.o rigid.o writemodes_dyn.o $(PWOBJS) $(PHOBJS)  $(MODULES) $(LIBOBJS)
	$(MPIF90) $(LDFLAGS) -o $@ \
		matdyn.o rigid.o writemodes_dyn.o $(PWOBJS) $(PHOBJS) $(MODULES) $(LIBOBJS) $(LIBS)
	- ( cd ../bin ; ln -fs ../pwtools/$@ . )

q2r.x : q2r.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS)
	$(MPIF90) $(LDFLAGS) -o $@ \
		q2r.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS) $(LIBS)
	- ( cd ../bin ; ln -fs ../pwtools/$@ . )
q2r.old.x : q2r.pw.2.0.2.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS)
	$(MPIF90) $(LDFLAGS) -o $@ \
		q2r.pw.2.0.2.o rigid.o $(PWOBJS) $(MODULES) $(LIBOBJS) $(LIBS)
	- ( cd ../bin ; ln -fs ../pwtools/$@ . )
tldeps:
	test -n "$(TLDEPS)" && ( cd .. ; $(MAKE) $(MFLAGS) $(TLDEPS) || exit 1) || :

clean :
	- /bin/rm -f pwi2xsf pwi2xsf_old *.x *.o *~ *.F90 *.mod *.d *.i work.pc

include make.depend
-------------- next part --------------
! Copyright (C) 2001-2004 PWSCF group
! 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 .
!
!
! Modifications Katalin Gaal-Nagy (search KG) November/December 2006
! Adding an input parameter dynmatout = .true./.false
! for writing out the dynamical matrix file for a given q_in for 
! all q in star(q_in). This file should be readable from dynmat.x
! The files with the dynamical matrices are called dynint.#q 
! where #q is the number of the q point in the input list.
! For having all informations (c/a, etc) which are necessary for dynmat.x, 
! also the readfc routine in this
! file has been modificated in order to return the corresponding information
! by adding celldm (it was already read, just not returned to the main).
!

#include "f_defs.h"
!
Module ifconstants
  !
  ! All variables read from file that need dynamical allocation
  !
  USE kinds, ONLY: DP
  REAL(DP), ALLOCATABLE :: frc(:,:,:,:,:,:,:), tau_blk(:,:),  zeu(:,:,:)
  ! frc : interatomic force constants in real space
  ! tau_blk : atomic positions for the original cell
  ! zeu : effective charges for the original cell
  INTEGER, ALLOCATABLE  :: ityp_blk(:)
  ! ityp_blk : atomic types for each atom of the original cell
  !
end Module ifconstants
!
!---------------------------------------------------------------------
PROGRAM matdyn
  !-----------------------------------------------------------------------
  !  this program calculates the phonon frequencies for a list of generic 
  !  q vectors starting from the interatomic force constants generated 
  !  from the dynamical matrices as written by DFPT phonon code through 
  !  the companion program q2r
  !
  !  matdyn can generate a supercell of the original cell for mass
  !  approximation calculation. If supercell data are not specified
  !  in input, the unit cell, lattice vectors, atom types and positions
  !  are read from the force constant file
  !
  !  Input cards: namelist &input
  !     flfrc     file produced by q2r containing force constants (needed)
  !      asr      (character) indicates the type of Acoustic Sum Rule imposed
  !               - 'no': no Acoustic Sum Rules imposed (default)
  !               - 'simple':  previous implementation of the asr used 
  !                  (3 translational asr imposed by correction of 
  !                  the diagonal elements of the force constants matrix)
  !               - 'crystal': 3 translational asr imposed by optimized 
  !                  correction of the force constants (projection).
  !               - 'one-dim': 3 translational asr + 1 rotational asr
  !                  imposed by optimized correction of the force constants
  !                  (the rotation axis is the direction of periodicity; 
  !                   it will work only if this axis considered is one of
  !                   the cartesian axis).
  !               - 'zero-dim': 3 translational asr + 3 rotational asr
  !                  imposed by optimized correction of the force constants
  !               Note that in certain cases, not all the rotational asr
  !               can be applied (e.g. if there are only 2 atoms in a 
  !               molecule or if all the atoms are aligned, etc.). 
  !               In these cases the supplementary asr are cancelled
  !               during the orthonormalization procedure (see below).
  !     dos       if .true. calculate phonon Density of States (DOS)
  !               using tetrahedra and a uniform q-point grid (see below)
  !               NB: may not work properly in noncubic materials
  !               if .false. calculate phonon bands from the list of q-points
  !               supplied in input
  !     nk1,nk2,nk3  uniform q-point grid for DOS calculation (includes q=0)
  !     deltaE    energy step, in cm^(-1), for DOS calculation: from min
  !               to max phonon energy (default: 1 cm^(-1) if ndos is 
  !               not specified)
  !     ndos      number of energy steps for DOS calculations
  !               (no default: calculated from deltaE if not specified)
  !     fldos     output file for dos (default: 'matdyn.dos')
  !               the dos is in states/cm(-1) plotted vs omega in cm(-1)
  !               and is normalised to 3*nat, i.e. the number of phonons
  !     flfrq     output file for frequencies (default: 'matdyn.freq')
  !     flvec     output file for normal modes (default: 'matdyn.modes')
  !     at        supercell lattice vectors - must form a superlattice of the 
  !               original lattice
  !     l1,l2,l3  supercell lattice vectors are original cell vectors
  !               multiplied by l1, l2, l3 respectively
  !     ntyp      number of atom types in the supercell
  !     amass     masses of atoms in the supercell
  !     readtau   read  atomic positions of the supercell from input
  !               (used to specify different masses)
  !     fltau     write atomic positions of the supercell to file "fltau"
  !               (default: fltau=' ', do not write)
  !
  !  if (readtau) atom types and positions in the supercell follow:
  !     (tau(i,na),i=1,3), ityp(na)
  !  Then, if (.not.dos) :
  !     nq         number of q-points
  !     (q(i,n), i=1,3)    nq q-points in 2pi/a units
  !  If q = 0, the direction qhat (q=>0) for the non-analytic part
  !  is extracted from the sequence of q-points as follows:
  !     qhat = q(n) - q(n-1)  or   qhat = q(n) - q(n+1) 
  !  depending on which one is available and nonzero.
  !  For low-symmetry crystals, specify twice q = 0 in the list
  !  if you want to have q = 0 results for two different directions
  !
  USE kinds,      ONLY : DP
  USE mp,         ONLY : mp_start, mp_env, mp_end, mp_barrier
  USE mp_global,  ONLY : nproc, mpime, mp_global_start  
  USE ifconstants
  !
  IMPLICIT NONE
  !
  INTEGER :: gid
  !
  ! variables *_blk refer to the original cell, other variables
  ! to the (super)cell (which may coincide with the original cell)
  !
  INTEGER:: nax, nax_blk
  INTEGER, PARAMETER:: ntypx=10, nrwsx=200
  REAL(DP), PARAMETER :: eps=1.0e-6,  rydcm1 = 13.6058*8065.5, &
       amconv = 1.66042e-24/9.1095e-28*0.5
  INTEGER :: nr1, nr2, nr3, nsc, nk1, nk2, nk3, ntetra, ibrav
  CHARACTER(LEN=256) :: flfrc, flfrq, flvec, fltau, fldos
  CHARACTER(LEN=10)  :: asr
  CHARACTER(LEN=9)   :: symm_type
  LOGICAL :: dos, has_zstar
  COMPLEX(DP), ALLOCATABLE :: dyn(:,:,:,:), dyn_blk(:,:,:,:)
  COMPLEX(DP), ALLOCATABLE :: z(:,:)
  REAL(DP), ALLOCATABLE:: tau(:,:), q(:,:), w2(:,:), freq(:,:)
  INTEGER, ALLOCATABLE:: tetra(:,:), ityp(:), itau_blk(:)
  REAL(DP) :: at(3,3), bg(3,3), omega, alat, &! cell parameters and volume
                  at_blk(3,3), bg_blk(3,3),  &! original cell
                  omega_blk,                 &! original cell volume
                  epsil(3,3),                &! dielectric tensor
                  amass(ntypx),              &! atomic masses
                  amass_blk(ntypx),          &! original atomic masses
                  atws(3,3),      &! lattice vector for WS initialization
                  rws(0:3,nrwsx)   ! nearest neighbor list, rws(0,*) = norm^2
  !
  INTEGER :: nat, nat_blk, ntyp, ntyp_blk, &
             l1, l2, l3,                   &! supercell dimensions
             nrws                          ! number of nearest neighbor
  !
  LOGICAL :: readtau, la2F
  !
  REAL(DP) :: qhat(3), qh, DeltaE, Emin, Emax, E, DOSofE(1)
  INTEGER :: n, i, j, it, nq, nqx, na, nb, ndos, iout
  !
  ! KG: Additional parameters:
  !
  ! for star_q
  !
  CHARACTER(LEN=3)   :: atm(ntypx)
  ! list of vectors in the star of q
  logical :: noinv
  INTEGER, PARAMETER :: natmax=100
  integer :: nsym, s (3, 3, 48), invs (48), irt (48, natmax), isq (48), imq, modenum
  real(DP) :: rtau (3, 48, natmax), sxq (3, 48)
  !
  ! for doing the extra loop 
  !
  LOGICAL :: dynmatout
  INTEGER :: nn, nnn ! running index for the q in the star
  INTEGER :: nnq ! degeneracy of the star of q
  !
  ! for the dynmat_interpol file
  !
  INTEGER :: fildyn_lent
  CHARACTER(LEN=8) :: fildyn_int, fildyn_out
  CHARACTER :: fildyn_d(0:9)
  REAL(DP) :: celldm(6)
  data fildyn_d/'0','1','2','3','4','5','6','7','8','9'/
  INTEGER :: ios, iudyn
  CHARACTER(LEN=30) :: fildyn
  ! End KG

  ! KG: old namelist
  !  NAMELIST /input/ flfrc, amass, asr, flfrq, flvec, at, dos,  &
  !       &           fldos, nk1, nk2, nk3, l1, l2, l3, ntyp, readtau, fltau, & 
  !                  la2F, ndos
  ! KG: new namelist
  NAMELIST /input/ flfrc, amass, asr, flfrq, flvec, at, dos,  &
       &           fldos, nk1, nk2, nk3, l1, l2, l3, ntyp, readtau, fltau, & 
                   la2F, ndos, dynmatout
  !
  !
  CALL mp_start()
  !
  CALL mp_env( nproc, mpime, gid )
  !
  IF ( mpime == 0 ) THEN
     !
     ! ... all calculations are done by the first cpu
     !
     ! set namelist default
     !
     dos = .FALSE.
     deltaE = 1.0
     ndos = 1
     nk1 = 0 
     nk2 = 0 
     nk3 = 0 
     asr  ='no'
     readtau=.FALSE.
     flfrc=' '
     fldos='matdyn.dos'
     flfrq='matdyn.freq'
     flvec='matdyn.modes'
     fltau=' '
     amass(:) =0.d0
     amass_blk(:) =0.d0
     at(:,:) = 0.d0
     ntyp = 0
     l1=1
     l2=1
     l3=1
     la2F=.false.
     dos=.false.
     dynmatout=.false.
     !
     CALL input_from_file ( )
     !
     READ (5,input)
     !
     ! convert masses to atomic units
     !
     amass(:) = amass(:) * amconv
     !
     ! read force constants 
     !
     ntyp_blk = ntypx ! avoids fake out-of-bound error
     CALL readfc ( flfrc, nr1, nr2, nr3, epsil, nat_blk, &
          ibrav, symm_type, alat, celldm, at_blk, ntyp_blk, &
          amass_blk, omega_blk, has_zstar, atm)
     !
     CALL recips ( at_blk(1,1),at_blk(1,2),at_blk(1,3),  &
          bg_blk(1,1),bg_blk(1,2),bg_blk(1,3) )
     !
     ! set up (super)cell
     !
     if (ntyp < 0) then
        call errore ('matdyn','wrong ntyp ', abs(ntyp))
     else if (ntyp == 0) then
        ntyp=ntyp_blk
     end if
     !
     ! masses (for mass approximation)
     ! 
     DO it=1,ntyp
        IF (amass(it) < 0.d0) THEN
           CALL errore ('matdyn','wrong mass in the namelist',it)
        ELSE IF (amass(it) == 0.d0) THEN
           IF (it.LE.ntyp_blk) THEN
              WRITE (*,'(a,i3,a,a)') ' mass for atomic type ',it,      &
                   &                     ' not given; uses mass from file ',flfrc
              amass(it) = amass_blk(it)
           ELSE
              CALL errore ('matdyn','missing mass in the namelist',it)
           END IF
        END IF
     END DO
     !
     ! lattice vectors
     !
     IF (SUM(ABS(at(:,:))) == 0.d0) THEN
        IF (l1.LE.0 .OR. l2.LE.0 .OR. l3.LE.0) CALL                    &
             &             errore ('matdyn',' wrong l1,l2 or l3',1)
        at(:,1) = at_blk(:,1)*DBLE(l1)
        at(:,2) = at_blk(:,2)*DBLE(l2)
        at(:,3) = at_blk(:,3)*DBLE(l3)
     END IF
     !
     CALL check_at(at,bg_blk,alat,omega)
     !
     ! the supercell contains "nsc" times the original unit cell
     !
     nsc = NINT(omega/omega_blk)
     IF (ABS(omega/omega_blk-nsc) > eps) &
          CALL errore ('matdyn', 'volume ratio not integer', 1)
     !
     ! read/generate atomic positions of the (super)cell
     !
     nat = nat_blk * nsc
     nax = nat
     !!!
     nax_blk = nat_blk
     !!!
     ALLOCATE ( tau (3, nat), ityp(nat), itau_blk(nat_blk) )
     !
     IF (readtau) THEN
        CALL read_tau &
             (nat, nat_blk, ntyp, bg_blk, tau, tau_blk, ityp, itau_blk)
     ELSE
        CALL set_tau  &
             (nat, nat_blk, at, at_blk, tau, tau_blk, ityp, ityp_blk, itau_blk)
     ENDIF
     !
     IF (fltau.NE.' ') CALL write_tau (fltau, nat, tau, ityp)
     !
     ! reciprocal lattice vectors
     !
     CALL recips (at(1,1),at(1,2),at(1,3),bg(1,1),bg(1,2),bg(1,3))
     !
     ! build the WS cell corresponding to the force constant grid
     !
     atws(:,1) = at_blk(:,1)*DBLE(nr1)
     atws(:,2) = at_blk(:,2)*DBLE(nr2)
     atws(:,3) = at_blk(:,3)*DBLE(nr3)
     ! initialize WS r-vectors
     CALL wsinit(rws,nrwsx,nrws,atws)
     !
     ! end of (super)cell setup
     !
     IF (dos) THEN
        IF (nk1 < 1 .OR. nk2 < 1 .OR. nk3 < 1) &
             CALL errore  ('matdyn','specify correct q-point grid!',1)
        ntetra = 6 * nk1 * nk2 * nk3
        nqx = nk1*nk2*nk3
        ALLOCATE ( tetra(4,ntetra), q(3,nqx) )
        CALL gen_qpoints (ibrav, at, bg, nat, tau, ityp, nk1, nk2, nk3, &
             symm_type, ntetra, nqx, nq, q, tetra)
     ELSE
        !
        ! read q-point list
        !
        READ (5,*) nq
        ALLOCATE ( q(3,nq) )
        DO n = 1,nq
           READ (5,*) (q(i,n),i=1,3)
        END DO
     END IF
     !
     IF (asr /= 'no') THEN
        CALL set_asr (asr, nr1, nr2, nr3, frc, zeu, &
             nat_blk, ibrav, tau_blk)
     END IF
     !
     IF (flvec.EQ.' ') THEN
        iout=6
     ELSE
        iout=4
        OPEN (unit=iout,file=flvec,status='unknown',form='formatted')
     END IF

     ALLOCATE ( dyn(3,3,nat,nat), dyn_blk(3,3,nat_blk,nat_blk) )
     ALLOCATE ( z(3*nat,3*nat), w2(3*nat,nq) )

     if(la2F) open(300,file='dyna2F',status='unknown')
!
!    KG: Modifications here: In the case of dynmatout=.true there is an additional
!    loop over the q in star(q_in)
!
     DO n=1, nq
        dyn(:,:,:,:) = (0.d0, 0.d0)
        CALL setupmat (q(1,n), dyn, nat, at, bg, tau, itau_blk, nsc, alat, &
             dyn_blk, nat_blk, at_blk, bg_blk, tau_blk, omega_blk,  &
             epsil, zeu, frc, nr1,nr2,nr3, has_zstar, rws, nrws)
        IF (q(1,n)==0.d0 .AND. q(2,n)==0.d0 .AND. q(3,n)==0.d0) THEN
           !
           ! q = 0 : we need the direction q => 0 for the non-analytic part
           !
           IF ( n == 1 ) THEN
              ! if q is the first point in the list
              IF ( nq > 1 ) THEN
                 ! one more point
                 qhat(:) = q(:,n) - q(:,n+1)
              ELSE
                 ! no more points
                 qhat(:) = 0.d0
              END IF
           ELSE IF ( n > 1 ) THEN
              ! if q is not the first point in the list
              IF ( q(1,n-1)==0.d0 .AND. &
                   q(2,n-1)==0.d0 .AND. &
                   q(3,n-1)==0.d0 .AND. n < nq ) THEN
                 ! if the preceding q is also 0 :
                 qhat(:) = q(:,n) - q(:,n+1)
              ELSE
                 ! if the preceding q is npt 0 :
                 qhat(:) = q(:,n) - q(:,n-1)
              END IF
           END IF
           qh = SQRT(qhat(1)**2+qhat(2)**2+qhat(3)**2)
           ! write(*,*) ' qh,  has_zstar ',qh,  has_zstar
           IF (qh /= 0.d0) qhat(:) = qhat(:) / qh
           IF (qh /= 0.d0 .AND. .NOT. has_zstar) CALL infomsg  &
                ('matdyn','Z* not found in file '//TRIM(flfrc)// &
                ', TO-LO splitting at q=0 will be absent!', -1)
           !
           CALL nonanal (nat, nat_blk, itau_blk, epsil, qhat, zeu, omega, dyn)
           !
        END IF
        !
        CALL dyndiag(nat,ntyp,amass,ityp,dyn,w2(1,n),z)
        !
        if(la2F) then
           write(300,*) n
           do na=1,3*nat
              write(300,*) (z(na,nb),nb=1,3*nat)
           end do ! na
        endif
        !
        CALL writemodes(nax,nat,q(1,n),w2(1,n),z,iout)        
!
!    KG: here the additional loop, creating an output-file for each q_in, etc
!
!    KG: Here starts the calculation of the dynamical matrices for all q in the star(q)
!    and its writeout to a file
!
        IF (dynmatout) THEN

!    Open file and write the header
!
           iudyn = 26
!
!    Creating filename with extention of the number of the point
!
           fildyn_lent = int(alog10(real(n)))+1
           write(fildyn_int,'(i'//fildyn_d(fildyn_lent)//')') n
           read(fildyn_int,'(a'//fildyn_d(fildyn_lent)//')') fildyn_out
           fildyn = 'dynint.'//fildyn_out
!
           OPEN (unit=iudyn, file=fildyn, status='unknown', err=100, iostat=ios)
           write (iudyn, '("Dynamical matrix file")')
           write (iudyn, '(a)') ' '
           write (iudyn, '(i3,i5,i3,6f11.7)') ntyp, nat, ibrav, celldm
           write(*,*) alat
           if (ibrav==0) then
              write (iudyn,'(a)') symm_type
              write (iudyn,'(2x,3f15.9)') ((at(i,j),i=1,3),j=1,3)
           end if
           do it = 1, ntyp
              write (iudyn, * ) it, ' ''', atm (it) , ' '' ', amass (it)
           enddo
           do na = 1, nat
              write (iudyn, '(2i5,3f15.7)') na, ityp (na) , (tau (j, na) , j = 1, 3)
           enddo
!
!     Calculate the star of the q given by q(1,n)
!
! KG: email Paolo Giannozzi, pw_forum, Thu, 23 Nov 2006 10:22:23 +0100
! all modes are calculated:
!
        modenum=0
        noinv=.false.
!       
        sxq=0.0
        call star_q (q(1,n),at, bg, ibrav, symm_type, nat, tau, ityp, nr1, &
             nr2, nr3, &
             nsym, s, invs, irt, &
             rtau, nnq, sxq, isq, imq,&
             noinv, modenum)
        write(*,*) nnq
!
!       Loop over q in star(q_in)
!
        Do nn=1,nnq 

           dyn(:,:,:,:) = (0.d0, 0.d0)

           CALL setupmat (sxq(1,nn), dyn, nat, at, bg, tau, itau_blk, nsc, alat, &
                dyn_blk, nat_blk, at_blk, bg_blk, tau_blk, omega_blk,  &
                epsil, zeu, frc, nr1,nr2,nr3, has_zstar, rws, nrws)
           
           IF (q(1,nn)==0.d0 .AND. q(2,nn)==0.d0 .AND. q(3,nn)==0.d0) THEN
              !
              ! q = 0 : we need the direction q => 0 for the non-analytic part
              !
              IF ( nn == 1 ) THEN
                 ! if q is the first point in the list
                 IF ( nnq > 1 ) THEN
                    ! one more point
                    qhat(:) = q(:,nn) - q(:,nn+1)
                 ELSE
                    ! no more points
                    qhat(:) = 0.d0
                 END IF
              ELSE IF ( nn > 1 ) THEN
                 ! if q is not the first point in the list
                 IF ( q(1,nn-1)==0.d0 .AND. &
                      q(2,nn-1)==0.d0 .AND. &
                      q(3,nn-1)==0.d0 .AND. nn < nnq ) THEN
                    ! if the preceding q is also 0 :
                    qhat(:) = q(:,nn) - q(:,nn+1)
                 ELSE
                    ! if the preceding q is npt 0 :
                    qhat(:) = q(:,nn) - q(:,nn-1)
                 END IF
              END IF
              qh = SQRT(qhat(1)**2+qhat(2)**2+qhat(3)**2)
              ! write(*,*) ' qh,  has_zstar ',qh,  has_zstar
              IF (qh /= 0.d0) qhat(:) = qhat(:) / qh
              IF (qh /= 0.d0 .AND. .NOT. has_zstar) CALL infomsg  &
                   ('matdyn','Z* not found in file '//TRIM(flfrc)// &
                   ', TO-LO splitting at q=0 will be absent!', -1)
              !
              CALL nonanal (nat, nat_blk, itau_blk, epsil, qhat, zeu, omega, dyn)
              !
           END IF
!
           call write_dyn_on_file (sxq(1, nn), dyn, nat, iudyn)
!
        END DO ! nnq
        write(iudyn,*) ' '
        CALL writemodes(nax,nat,q(1,n),w2(1,n),z,iudyn)
!
!       close the file with the interpolated dynamical matrices
!
        close (iudyn)
!
     ENDIF
!
     END DO  !nq
!
!    KG: End of modifications
!
!
     if(la2F) close(300)
     !
     IF(iout .NE. 6) CLOSE(unit=iout)
     !
     ALLOCATE (freq(3*nat, nq))
     DO n=1,nq
        ! freq(i,n) = frequencies in cm^(-1), with negative sign if omega^2 is negative
        DO i=1,3*nat
           freq(i,n)= SQRT(ABS(w2(i,n))) * rydcm1
           IF (w2(i,n) < 0.0) freq(i,n) = -freq(i,n)
        END DO
     END DO
     !
     IF(flfrq.NE.' ') THEN
        OPEN (unit=2,file=flfrq ,status='unknown',form='formatted')
        WRITE(2, '(" &plot nbnd=",i4,", nks=",i4," /")') 3*nat, nq
        DO n=1, nq
           WRITE(2, '(10x,3f10.6)')  q(1,n), q(2,n), q(3,n)
           WRITE(2,'(6f10.4)') (freq(i,n), i=1,3*nat)
        END DO
        CLOSE(unit=2)
     END IF
     !
     !
     IF (dos) THEN
        Emin = 0.0 
        Emax = 0.0
        DO n=1,nq
           DO i=1, 3*nat
              Emin = MIN (Emin, freq(i,n))
              Emax = MAX (Emax, freq(i,n))
           END DO
        END DO
        !
        if (ndos > 1) then
           DeltaE = (Emax - Emin)/(ndos-1)
        else
           ndos = NINT ( (Emax - Emin) / DeltaE + 1.51 )  
        end if
        OPEN (unit=2,file=fldos,status='unknown',form='formatted')
        DO n= 1, ndos  
           E = Emin + (n - 1) * DeltaE  
           CALL dos_t(freq, 1, 3*nat, nq, ntetra, tetra, E, DOSofE)
           !
           ! The factor 0.5 corrects for the factor 2 in dos_t,
           ! that accounts for the spin in the electron DOS.
           !
           !WRITE (2, '(F15.10,F15.2,F15.6,F20.5)') &
           !     E, E*rydcm1, E*rydTHz, 0.5d0*DOSofE(1)
           WRITE (2, '(E12.4,E12.4)') E, 0.5d0*DOSofE(1)
        END DO
        CLOSE(unit=2)
     END IF  !dos
     DEALLOCATE (z, w2, dyn, dyn_blk)
     !
     !    for a2F
     !
     IF(la2F) THEN
         !
         ! convert frequencies to Ry
         !
         freq(:,:)= freq(:,:) / rydcm1
         Emin  = Emin / rydcm1
         DeltaE=DeltaE/ rydcm1
         !
         call a2Fdos (nat, nq, nr1, nr2, nr3, ibrav, at, bg, tau, alat, &
                           nsc, nat_blk, at_blk, bg_blk, itau_blk, omega_blk, &
                           rws, nrws, dos, Emin, DeltaE, ndos, &
                           ntetra, tetra, asr, q, freq)
     END IF
     DEALLOCATE ( freq)
     !
  END IF
  ! 
  CALL mp_barrier()
  !
  CALL mp_end()
  !
100 CALL errore ('openfilq', 'opening file'//fildyn, ABS (ios) )
  REWIND (iudyn)
  STOP
  !
END PROGRAM matdyn
!
!-----------------------------------------------------------------------
SUBROUTINE readfc ( flfrc, nr1, nr2, nr3, epsil, nat,    &
                    ibrav, symm_type, alat, celldm, at, ntyp, amass, omega, has_zstar, atm )
  !-----------------------------------------------------------------------
  !
  ! Modification K.GN:
  ! return also celldm, since it is required for the dynmat files
  ! 
  USE kinds,      ONLY : DP
  USE ifconstants,ONLY : tau => tau_blk, ityp => ityp_blk, frc, zeu
  !
  IMPLICIT NONE
  ! I/O variable
  CHARACTER(LEN=256) flfrc
  INTEGER ibrav, nr1,nr2,nr3,nat, ntyp
  REAL(DP) alat, at(3,3), epsil(3,3)
  LOGICAL has_zstar
  ! local variables
  INTEGER i, j, na, nb, m1,m2,m3
  INTEGER ibid, jbid, nabid, nbbid, m1bid,m2bid,m3bid
  REAL(DP) amass(ntyp), amass_from_file, celldm(6), omega
  INTEGER nt
  CHARACTER(LEN=3) atm(ntyp)
  CHARACTER(LEN=9) symm_type
  !
  !
  OPEN (unit=1,file=flfrc,status='old',form='formatted')
  !
  !  read cell data
  !
  READ(1,*) ntyp,nat,ibrav,(celldm(i),i=1,6)
  if (ibrav==0) then
     read(1,'(a)') symm_type
     read(1,*) ((at(i,j),i=1,3),j=1,3)
  end if
  !
  CALL latgen(ibrav,celldm,at(1,1),at(1,2),at(1,3),omega)
  alat = celldm(1)
  at = at / alat !  bring at in units of alat
  CALL volume(alat,at(1,1),at(1,2),at(1,3),omega)
  !
  !  read atomic types, positions and masses
  !
  DO nt = 1,ntyp
     READ(1,*) i,atm(nt),amass_from_file
     IF (i.NE.nt) CALL errore ('readfc','wrong data read',nt)
     IF (amass(nt).EQ.0.d0) THEN
        amass(nt) = amass_from_file
     ELSE
        WRITE(*,*) 'for atomic type',nt,' mass from file not used'
     END IF
  END DO
  !
  ALLOCATE (tau(3,nat), ityp(nat), zeu(3,3,nat))
  !
  DO na=1,nat
     READ(1,*) i,ityp(na),(tau(j,na),j=1,3)
     IF (i.NE.na) CALL errore ('readfc','wrong data read',na)
  END DO
  !
  !  read macroscopic variable
  !
  READ (1,*) has_zstar
  IF (has_zstar) THEN
     READ(1,*) ((epsil(i,j),j=1,3),i=1,3)
     DO na=1,nat
        READ(1,*) 
        READ(1,*) ((zeu(i,j,na),j=1,3),i=1,3)
     END DO
  ELSE
     zeu  (:,:,:) = 0.d0
     epsil(:,:) = 0.d0
  END IF
  !
  READ (1,*) nr1,nr2,nr3
  !
  !  read real-space interatomic force constants
  !
  ALLOCATE ( frc(nr1,nr2,nr3,3,3,nat,nat) )
  frc(:,:,:,:,:,:,:) = 0.d0
  DO i=1,3
     DO j=1,3
        DO na=1,nat
           DO nb=1,nat
              READ (1,*) ibid, jbid, nabid, nbbid
              IF(i .NE.ibid  .OR. j .NE.jbid .OR.                   &
                 na.NE.nabid .OR. nb.NE.nbbid)                      &
                 CALL errore  ('readfc','error in reading',1)
              READ (1,*) (((m1bid, m2bid, m3bid,                    &
                          frc(m1,m2,m3,i,j,na,nb),                  &
                           m1=1,nr1),m2=1,nr2),m3=1,nr3)
           END DO
        END DO
     END DO
  END DO
  !
  CLOSE(unit=1)
  !
  RETURN
END SUBROUTINE readfc
!
!-----------------------------------------------------------------------
SUBROUTINE frc_blk(dyn,q,tau,nat,nr1,nr2,nr3,frc,at,bg,rws,nrws)
  !-----------------------------------------------------------------------
  ! calculates the dynamical matrix at q from the (short-range part of the)
  ! force constants 
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  INTEGER nr1, nr2, nr3, nat, n1, n2, n3, &
          ipol, jpol, na, nb, m1, m2, m3, nint, i,j, nrws
  COMPLEX(DP) dyn(3,3,nat,nat)
  REAL(DP) frc(nr1,nr2,nr3,3,3,nat,nat), tau(3,nat), q(3), arg, &
               at(3,3), bg(3,3), r(3), weight, r_ws(3),  &
               total_weight, rws(0:3,nrws)
  REAL(DP), PARAMETER:: tpi = 2.0*3.14159265358979d0
  REAL(DP), EXTERNAL :: wsweight
  !
  DO na=1, nat
     DO nb=1, nat
        total_weight=0.0d0
        DO n1=-2*nr1,2*nr1
           DO n2=-2*nr2,2*nr2
              DO n3=-2*nr3,2*nr3
                 !
                 ! SUM OVER R VECTORS IN THE SUPERCELL - VERY VERY SAFE RANGE!
                 !
                 DO i=1, 3
                    r(i) = n1*at(i,1)+n2*at(i,2)+n3*at(i,3)
                    r_ws(i) = r(i) + tau(i,na)-tau(i,nb)
                 END DO
                 weight = wsweight(r_ws,rws,nrws)
                 IF (weight .GT. 0.0) THEN
                    !
                    ! FIND THE VECTOR CORRESPONDING TO R IN THE ORIGINAL CELL
                    !
                    m1 = MOD(n1+1,nr1)
                    IF(m1.LE.0) m1=m1+nr1
                    m2 = MOD(n2+1,nr2)
                    IF(m2.LE.0) m2=m2+nr2
                    m3 = MOD(n3+1,nr3)
                    IF(m3.LE.0) m3=m3+nr3
                    !
                    ! FOURIER TRANSFORM
                    !
                    arg = tpi*(q(1)*r(1) + q(2)*r(2) + q(3)*r(3))
                    DO ipol=1, 3
                       DO jpol=1, 3
                          dyn(ipol,jpol,na,nb) =                 &
                               dyn(ipol,jpol,na,nb) +            &
                               frc(m1,m2,m3,ipol,jpol,na,nb)     &
                               *CMPLX(COS(arg),-SIN(arg))*weight
                       END DO
                    END DO
                 END IF
                 total_weight=total_weight + weight
              END DO
           END DO
        END DO
        IF (ABS(total_weight-nr1*nr2*nr3).GT.1.0d-8) THEN
           WRITE(*,*) total_weight
           CALL errore ('frc_blk','wrong total_weight',1)
        END IF
     END DO
  END DO
  !
  RETURN
END SUBROUTINE frc_blk
!
!-----------------------------------------------------------------------
SUBROUTINE setupmat (q,dyn,nat,at,bg,tau,itau_blk,nsc,alat, &
     &         dyn_blk,nat_blk,at_blk,bg_blk,tau_blk,omega_blk, &
     &                 epsil,zeu,frc,nr1,nr2,nr3,has_zstar,rws,nrws)
  !-----------------------------------------------------------------------
  ! compute the dynamical matrix (the analytic part only)
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  REAL(DP), PARAMETER :: tpi=2.d0*3.14159265358979d0
  !
  ! I/O variables
  !
  INTEGER:: nr1, nr2, nr3, nat, nat_blk, nsc, nrws, itau_blk(nat)
  REAL(DP) :: q(3), tau(3,nat), at(3,3), bg(3,3), alat,      &
                  epsil(3,3), zeu(3,3,nat_blk), rws(0:3,nrws),   &
                  frc(nr1,nr2,nr3,3,3,nat_blk,nat_blk)
  REAL(DP) :: tau_blk(3,nat_blk), at_blk(3,3), bg_blk(3,3), omega_blk
  COMPLEX(DP) dyn_blk(3,3,nat_blk,nat_blk)
  COMPLEX(DP) ::  dyn(3,3,nat,nat)
  LOGICAL has_zstar
  !
  ! local variables
  !
  REAL(DP) :: arg
  COMPLEX(DP) :: cfac(nat)
  INTEGER :: i,j,k, na,nb, na_blk, nb_blk, iq
  REAL(DP) qp(3), qbid(3,nsc) ! automatic array
  !
  !
  CALL q_gen(nsc,qbid,at_blk,bg_blk,at,bg)
  !
  DO iq=1,nsc
     !
     DO k=1,3
        qp(k)= q(k) + qbid(k,iq)
     END DO
     !
     dyn_blk(:,:,:,:) = (0.d0,0.d0)
     CALL frc_blk (dyn_blk,qp,tau_blk,nat_blk,              &
          &              nr1,nr2,nr3,frc,at_blk,bg_blk,rws,nrws)
     IF (has_zstar) &
          CALL rgd_blk(nr1,nr2,nr3,nat_blk,dyn_blk,qp,tau_blk,   &
                       epsil,zeu,bg_blk,omega_blk,+1.d0)
     !
     DO na=1,nat
        na_blk = itau_blk(na)
        DO nb=1,nat
           nb_blk = itau_blk(nb)
           !
           arg=tpi* ( qp(1) * ( (tau(1,na)-tau_blk(1,na_blk)) -   &
                                (tau(1,nb)-tau_blk(1,nb_blk)) ) + &
                      qp(2) * ( (tau(2,na)-tau_blk(2,na_blk)) -   &
                                (tau(2,nb)-tau_blk(2,nb_blk)) ) + &
                      qp(3) * ( (tau(3,na)-tau_blk(3,na_blk)) -   &
                                (tau(3,nb)-tau_blk(3,nb_blk)) ) )
           !
           cfac(nb) = CMPLX(COS(arg),SIN(arg))/nsc
           !
        END DO ! nb
        !
        DO i=1,3
           DO j=1,3
              !
              DO nb=1,nat
                 nb_blk = itau_blk(nb)
                 dyn(i,j,na,nb) = dyn(i,j,na,nb) + cfac(nb) * &
                      dyn_blk(i,j,na_blk,nb_blk)
              END DO ! nb
              !
           END DO ! j
        END DO ! i
     END DO ! na
     !
  END DO ! iq
  !
  RETURN
END SUBROUTINE setupmat
!
!
!----------------------------------------------------------------------
SUBROUTINE set_asr (asr, nr1, nr2, nr3, frc, zeu, nat, ibrav, tau)
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  CHARACTER (LEN=10) :: asr
  INTEGER :: nr1, nr2, nr3, nat, ibrav
  REAL(DP) :: frc(nr1,nr2,nr3,3,3,nat,nat), zeu(3,3,nat),tau(3,nat)
  !
  INTEGER :: axis, n, i, j, na, nb, n1,n2,n3, m,p,k,l,q,r, i1,j1,na1
  REAL(DP) :: frc_new(nr1,nr2,nr3,3,3,nat,nat), zeu_new(3,3,nat)
  type vector
     real(DP),pointer :: vec(:,:,:,:,:,:,:)
  end type vector
  ! 
  type (vector) u(6*3*nat)
  ! These are the "vectors" associated with the sum rules on force-constants
  !
  integer u_less(6*3*nat),n_less,i_less
  ! indices of the vectors u that are not independent to the preceding ones,
  ! n_less = number of such vectors, i_less = temporary parameter
  !
  integer ind_v(9*nat*nat*nr1*nr2*nr3,2,7)
  real(DP) v(9*nat*nat*nr1*nr2*nr3,2)
  ! These are the "vectors" associated with symmetry conditions, coded by 
  ! indicating the positions (i.e. the seven indices) of the non-zero elements (there
  ! should be only 2 of them) and the value of that element. We do so in order
  ! to limit the amount of memory used. 
  !
  real(DP) w(nr1,nr2,nr3,3,3,nat,nat), x(nr1,nr2,nr3,3,3,nat,nat)
  ! temporary vectors and parameters  
  real(DP) :: scal,norm2, sum
  !
  real(DP) zeu_u(6*3,3,3,nat)
  ! These are the "vectors" associated with the sum rules on effective charges
  !
  integer zeu_less(6*3),nzeu_less,izeu_less
  ! indices of the vectors zeu_u that are not independent to the preceding ones,
  ! nzeu_less = number of such vectors, izeu_less = temporary parameter
  !
  real(DP) zeu_w(3,3,nat), zeu_x(3,3,nat)
  ! temporary vectors



  ! Initialization. n is the number of sum rules to be considered (if asr.ne.'simple')
  ! and 'axis' is the rotation axis in the case of a 1D system
  ! (i.e. the rotation axis is (Ox) if axis='1', (Oy) if axis='2' and (Oz) if axis='3') 
  !
  if((asr.ne.'simple').and.(asr.ne.'crystal').and.(asr.ne.'one-dim') &
                      .and.(asr.ne.'zero-dim')) then
     call errore('matdyn','invalid Acoustic Sum Rule:' // asr, 1)
  endif
  if(asr.eq.'crystal') n=3
  if(asr.eq.'one-dim') then
     ! the direction of periodicity is the rotation axis
     ! It will work only if the crystal axis considered is one of
     ! the cartesian axis (typically, ibrav=1, 6 or 8, or 4 along the
     ! z-direction)
     if (nr1*nr2*nr3.eq.1) axis=3
     if ((nr1.ne.1).and.(nr2*nr3.eq.1)) axis=1
     if ((nr2.ne.1).and.(nr1*nr3.eq.1)) axis=2
     if ((nr3.ne.1).and.(nr1*nr2.eq.1)) axis=3
     if (((nr1.ne.1).and.(nr2.ne.1)).or.((nr2.ne.1).and. &
          (nr3.ne.1)).or.((nr1.ne.1).and.(nr3.ne.1))) then
        call errore('matdyn','too many directions of &
             & periodicity in 1D system',axis)
     endif
     if ((ibrav.ne.1).and.(ibrav.ne.6).and.(ibrav.ne.8).and. &
          ((ibrav.ne.4).or.(axis.ne.3)) ) then
        write(6,*) 'asr: rotational axis may be wrong'
     endif
     write(6,'("asr rotation axis in 1D system= ",I4)') axis
     n=4
  endif
  if(asr.eq.'zero-dim') n=6
  
  ! Acoustic Sum Rule on effective charges
  !
  if(asr.eq.'simple') then
      do i=1,3
         do j=1,3
            sum=0.0
            do na=1,nat
               sum = sum + zeu(i,j,na)
            end do
            do na=1,nat
               zeu(i,j,na) = zeu(i,j,na) - sum/nat
            end do
         end do
      end do
    else
      ! generating the vectors of the orthogonal of the subspace to project 
      ! the effective charges matrix on
      !
      zeu_u(:,:,:,:)=0.0d0
      do i=1,3
        do j=1,3
          do na=1,nat
            zeu_new(i,j,na)=zeu(i,j,na)
          enddo
        enddo
      enddo
      !
      p=0
      do i=1,3
        do j=1,3
          ! These are the 3*3 vectors associated with the 
          ! translational acoustic sum rules
          p=p+1
          zeu_u(p,i,j,:)=1.0d0
          !
        enddo
      enddo
      !
      if (n.eq.4) then
         do i=1,3
           ! These are the 3 vectors associated with the 
           ! single rotational sum rule (1D system)
           p=p+1
           do na=1,nat
             zeu_u(p,i,MOD(axis,3)+1,na)=-tau(MOD(axis+1,3)+1,na)
             zeu_u(p,i,MOD(axis+1,3)+1,na)=tau(MOD(axis,3)+1,na)
           enddo
           !
         enddo
      endif
      !
      if (n.eq.6) then
         do i=1,3
           do j=1,3
             ! These are the 3*3 vectors associated with the 
             ! three rotational sum rules (0D system - typ. molecule)
             p=p+1
             do na=1,nat
               zeu_u(p,i,MOD(j,3)+1,na)=-tau(MOD(j+1,3)+1,na)
               zeu_u(p,i,MOD(j+1,3)+1,na)=tau(MOD(j,3)+1,na)
             enddo
             !
           enddo
         enddo
      endif
      !
      ! Gram-Schmidt orthonormalization of the set of vectors created.
      !
      nzeu_less=0
      do k=1,p
        zeu_w(:,:,:)=zeu_u(k,:,:,:)
        zeu_x(:,:,:)=zeu_u(k,:,:,:)
        do q=1,k-1
          r=1
          do izeu_less=1,nzeu_less
            if (zeu_less(izeu_less).eq.q) r=0
          enddo
          if (r.ne.0) then
              call sp_zeu(zeu_x,zeu_u(q,:,:,:),nat,scal)
              zeu_w(:,:,:) = zeu_w(:,:,:) - scal* zeu_u(q,:,:,:)
          endif
        enddo
        call sp_zeu(zeu_w,zeu_w,nat,norm2)
        if (norm2.gt.1.0d-16) then
           zeu_u(k,:,:,:) = zeu_w(:,:,:) / DSQRT(norm2)
          else
           nzeu_less=nzeu_less+1
           zeu_less(nzeu_less)=k
        endif
      enddo
      !
      !
      ! Projection of the effective charge "vector" on the orthogonal of the 
      ! subspace of the vectors verifying the sum rules
      !
      zeu_w(:,:,:)=0.0d0
      do k=1,p
        r=1
        do izeu_less=1,nzeu_less
          if (zeu_less(izeu_less).eq.k) r=0
        enddo
        if (r.ne.0) then
            zeu_x(:,:,:)=zeu_u(k,:,:,:)
            call sp_zeu(zeu_x,zeu_new,nat,scal)
            zeu_w(:,:,:) = zeu_w(:,:,:) + scal*zeu_u(k,:,:,:)
        endif
      enddo
      !
      ! Final substraction of the former projection to the initial zeu, to get
      ! the new "projected" zeu
      !
      zeu_new(:,:,:)=zeu_new(:,:,:) - zeu_w(:,:,:)
      call sp_zeu(zeu_w,zeu_w,nat,norm2)
      write(6,'("Norm of the difference between old and new effective ", &
           & "charges: ",F25.20)') SQRT(norm2)
      !
      ! Check projection
      !
      !write(6,'("Check projection of zeu")')
      !do k=1,p
      !  zeu_x(:,:,:)=zeu_u(k,:,:,:)
      !  call sp_zeu(zeu_x,zeu_new,nat,scal)
      !  if (DABS(scal).gt.1d-10) write(6,'("k= ",I8," zeu_new|zeu_u(k)= ",F15.10)') k,scal
      !enddo
      !
      do i=1,3
        do j=1,3
          do na=1,nat
            zeu(i,j,na)=zeu_new(i,j,na)
          enddo
        enddo
      enddo
  endif
  !
  !
  !
  !
  !         
  !
  ! Acoustic Sum Rule on force constants in real space
  !
  if(asr.eq.'simple') then
      do i=1,3
         do j=1,3
            do na=1,nat
               sum=0.0
               do nb=1,nat
                  do n1=1,nr1
                     do n2=1,nr2
                        do n3=1,nr3
                           sum=sum+frc(n1,n2,n3,i,j,na,nb)
                        end do
                     end do
                  end do
               end do
               frc(1,1,1,i,j,na,na) = frc(1,1,1,i,j,na,na) - sum
               !               write(6,*) ' na, i, j, sum = ',na,i,j,sum
            end do
         end do
      end do
      
    else
      ! generating the vectors of the orthogonal of the subspace to project 
      ! the force-constants matrix on
      !
      do k=1,18*nat
        allocate(u(k) % vec(nr1,nr2,nr3,3,3,nat,nat))
        u(k) % vec (:,:,:,:,:,:,:)=0.0d0
      enddo
      do i=1,3
        do j=1,3
          do na=1,nat
            do nb=1,nat
              do n1=1,nr1
                do n2=1,nr2
                  do n3=1,nr3
                    frc_new(n1,n2,n3,i,j,na,nb)=frc(n1,n2,n3,i,j,na,nb)
                  enddo
                enddo
              enddo
            enddo
          enddo
        enddo
      enddo
      !
      p=0
      do i=1,3
        do j=1,3
          do na=1,nat
            ! These are the 3*3*nat vectors associated with the 
            ! translational acoustic sum rules
            p=p+1
            u(p) % vec (:,:,:,i,j,na,:)=1.0d0
            !
          enddo
        enddo
      enddo
      !
      if (n.eq.4) then
         do i=1,3
           do na=1,nat
             ! These are the 3*nat vectors associated with the 
             ! single rotational sum rule (1D system)
             p=p+1
             do nb=1,nat
               u(p) % vec (:,:,:,i,MOD(axis,3)+1,na,nb)=-tau(MOD(axis+1,3)+1,nb)
               u(p) % vec (:,:,:,i,MOD(axis+1,3)+1,na,nb)=tau(MOD(axis,3)+1,nb)
             enddo
             !
           enddo
         enddo
      endif
      !
      if (n.eq.6) then
         do i=1,3
           do j=1,3
             do na=1,nat
               ! These are the 3*3*nat vectors associated with the 
               ! three rotational sum rules (0D system - typ. molecule)
               p=p+1
               do nb=1,nat
                 u(p) % vec (:,:,:,i,MOD(j,3)+1,na,nb)=-tau(MOD(j+1,3)+1,nb)
                 u(p) % vec (:,:,:,i,MOD(j+1,3)+1,na,nb)=tau(MOD(j,3)+1,nb)
               enddo
               !
             enddo
           enddo
         enddo
      endif
      !
      m=0
      do i=1,3
        do j=1,3
          do na=1,nat
            do nb=1,nat
              do n1=1,nr1
                do n2=1,nr2
                  do n3=1,nr3
                    ! These are the vectors associated with the symmetry constraints
                    q=1
                    l=1
                    do while((l.le.m).and.(q.ne.0))
                      if ((ind_v(l,1,1).eq.n1).and.(ind_v(l,1,2).eq.n2).and. &
                           (ind_v(l,1,3).eq.n3).and.(ind_v(l,1,4).eq.i).and. &
                           (ind_v(l,1,5).eq.j).and.(ind_v(l,1,6).eq.na).and. &
                           (ind_v(l,1,7).eq.nb)) q=0
                      if ((ind_v(l,2,1).eq.n1).and.(ind_v(l,2,2).eq.n2).and. &
                           (ind_v(l,2,3).eq.n3).and.(ind_v(l,2,4).eq.i).and. &
                           (ind_v(l,2,5).eq.j).and.(ind_v(l,2,6).eq.na).and. &
                           (ind_v(l,2,7).eq.nb)) q=0
                      l=l+1
                    enddo
                    if ((n1.eq.MOD(nr1+1-n1,nr1)+1).and.(n2.eq.MOD(nr2+1-n2,nr2)+1) &
                        .and.(n3.eq.MOD(nr3+1-n3,nr3)+1).and.(i.eq.j).and.(na.eq.nb)) q=0
                    if (q.ne.0) then
                       m=m+1
                       ind_v(m,1,1)=n1
                       ind_v(m,1,2)=n2
                       ind_v(m,1,3)=n3
                       ind_v(m,1,4)=i
                       ind_v(m,1,5)=j
                       ind_v(m,1,6)=na
                       ind_v(m,1,7)=nb
                       v(m,1)=1.0d0/DSQRT(2.0d0)
                       ind_v(m,2,1)=MOD(nr1+1-n1,nr1)+1
                       ind_v(m,2,2)=MOD(nr2+1-n2,nr2)+1
                       ind_v(m,2,3)=MOD(nr3+1-n3,nr3)+1
                       ind_v(m,2,4)=j
                       ind_v(m,2,5)=i
                       ind_v(m,2,6)=nb
                       ind_v(m,2,7)=na
                       v(m,2)=-1.0d0/DSQRT(2.0d0)
                    endif
                  enddo
                enddo
              enddo
            enddo
          enddo
        enddo
      enddo
      !
      ! Gram-Schmidt orthonormalization of the set of vectors created.
      ! Note that the vectors corresponding to symmetry constraints are already
      ! orthonormalized by construction.
      !
      n_less=0
      do k=1,p
        w(:,:,:,:,:,:,:)=u(k) % vec (:,:,:,:,:,:,:)
        x(:,:,:,:,:,:,:)=u(k) % vec (:,:,:,:,:,:,:)
        do l=1,m
          !
          call sp2(x,v(l,:),ind_v(l,:,:),nr1,nr2,nr3,nat,scal)
          do r=1,2
            n1=ind_v(l,r,1)
            n2=ind_v(l,r,2)
            n3=ind_v(l,r,3)
            i=ind_v(l,r,4)
            j=ind_v(l,r,5)
            na=ind_v(l,r,6)
            nb=ind_v(l,r,7)
            w(n1,n2,n3,i,j,na,nb)=w(n1,n2,n3,i,j,na,nb)-scal*v(l,r)
          enddo
        enddo
        if (k.le.(9*nat)) then
            na1=MOD(k,nat)
            if (na1.eq.0) na1=nat
            j1=MOD((k-na1)/nat,3)+1
            i1=MOD((((k-na1)/nat)-j1+1)/3,3)+1
          else
            q=k-9*nat
            if (n.eq.4) then
                na1=MOD(q,nat)
                if (na1.eq.0) na1=nat
                i1=MOD((q-na1)/nat,3)+1
              else
                na1=MOD(q,nat)
                if (na1.eq.0) na1=nat
                j1=MOD((q-na1)/nat,3)+1
                i1=MOD((((q-na1)/nat)-j1+1)/3,3)+1
            endif
        endif
        do q=1,k-1
          r=1
          do i_less=1,n_less
            if (u_less(i_less).eq.q) r=0
          enddo
          if (r.ne.0) then
              call sp3(x,u(q) % vec (:,:,:,:,:,:,:), i1,na1,nr1,nr2,nr3,nat,scal)
              w(:,:,:,:,:,:,:) = w(:,:,:,:,:,:,:) - scal* u(q) % vec (:,:,:,:,:,:,:)
          endif
        enddo
        call sp1(w,w,nr1,nr2,nr3,nat,norm2)
        if (norm2.gt.1.0d-16) then
           u(k) % vec (:,:,:,:,:,:,:) = w(:,:,:,:,:,:,:) / DSQRT(norm2)
          else
           n_less=n_less+1
           u_less(n_less)=k
        endif
      enddo
      !
      ! Projection of the force-constants "vector" on the orthogonal of the 
      ! subspace of the vectors verifying the sum rules and symmetry contraints
      !
      w(:,:,:,:,:,:,:)=0.0d0
      do l=1,m
        call sp2(frc_new,v(l,:),ind_v(l,:,:),nr1,nr2,nr3,nat,scal)
        do r=1,2
          n1=ind_v(l,r,1)
          n2=ind_v(l,r,2)
          n3=ind_v(l,r,3)
          i=ind_v(l,r,4)
          j=ind_v(l,r,5)
          na=ind_v(l,r,6)
          nb=ind_v(l,r,7)
          w(n1,n2,n3,i,j,na,nb)=w(n1,n2,n3,i,j,na,nb)+scal*v(l,r)
        enddo
      enddo
      do k=1,p
        r=1
        do i_less=1,n_less
          if (u_less(i_less).eq.k) r=0
        enddo
        if (r.ne.0) then
            x(:,:,:,:,:,:,:)=u(k) % vec (:,:,:,:,:,:,:)
            call sp1(x,frc_new,nr1,nr2,nr3,nat,scal)
            w(:,:,:,:,:,:,:) = w(:,:,:,:,:,:,:) + scal*u(k)%vec(:,:,:,:,:,:,:)
        endif
        deallocate(u(k) % vec)
      enddo
      !
      ! Final substraction of the former projection to the initial frc, to get
      ! the new "projected" frc
      !
      frc_new(:,:,:,:,:,:,:)=frc_new(:,:,:,:,:,:,:) - w(:,:,:,:,:,:,:)
      call sp1(w,w,nr1,nr2,nr3,nat,norm2)
      write(6,'("Norm of the difference between old and new force-constants:",&
           &     F25.20)') SQRT(norm2)
      !
      ! Check projection
      !
      !write(6,'("Check projection IFC")')
      !do l=1,m
      !  call sp2(frc_new,v(l,:),ind_v(l,:,:),nr1,nr2,nr3,nat,scal)
      !  if (DABS(scal).gt.1d-10) write(6,'("l= ",I8," frc_new|v(l)= ",F15.10)') l,scal
      !enddo
      !do k=1,p
      !  x(:,:,:,:,:,:,:)=u(k) % vec (:,:,:,:,:,:,:)
      !  call sp1(x,frc_new,nr1,nr2,nr3,nat,scal)
      !  if (DABS(scal).gt.1d-10) write(6,'("k= ",I8," frc_new|u(k)= ",F15.10)') k,scal
      !  deallocate(u(k) % vec)
      !enddo
      !
      do i=1,3
        do j=1,3
          do na=1,nat
            do nb=1,nat
              do n1=1,nr1
                do n2=1,nr2
                  do n3=1,nr3
                    frc(n1,n2,n3,i,j,na,nb)=frc_new(n1,n2,n3,i,j,na,nb)
                  enddo
                enddo
              enddo
            enddo
          enddo
        enddo
      enddo
  endif
  !
  !
  return
end subroutine set_asr
!
!----------------------------------------------------------------------
subroutine sp_zeu(zeu_u,zeu_v,nat,scal)
  !-----------------------------------------------------------------------
  !
  ! does the scalar product of two effective charges matrices zeu_u and zeu_v 
  ! (considered as vectors in the R^(3*3*nat) space, and coded in the usual way)
  !
  USE kinds, ONLY: DP
  implicit none
  integer i,j,na,nat
  real(DP) zeu_u(3,3,nat)
  real(DP) zeu_v(3,3,nat)
  real(DP) scal  
  !
  !
  scal=0.0d0
  do i=1,3
    do j=1,3
      do na=1,nat
        scal=scal+zeu_u(i,j,na)*zeu_v(i,j,na)
      enddo
    enddo
  enddo
  !
  return
  !
end subroutine sp_zeu
!
!
!----------------------------------------------------------------------
subroutine sp1(u,v,nr1,nr2,nr3,nat,scal)
  !-----------------------------------------------------------------------
  !
  ! does the scalar product of two force-constants matrices u and v (considered as
  ! vectors in the R^(3*3*nat*nat*nr1*nr2*nr3) space, and coded in the usual way)
  !
  USE kinds, ONLY: DP
  implicit none
  integer nr1,nr2,nr3,i,j,na,nb,n1,n2,n3,nat
  real(DP) u(nr1,nr2,nr3,3,3,nat,nat)
  real(DP) v(nr1,nr2,nr3,3,3,nat,nat)
  real(DP) scal  
  !
  !
  scal=0.0d0
  do i=1,3
    do j=1,3
      do na=1,nat
        do nb=1,nat
          do n1=1,nr1
            do n2=1,nr2
              do n3=1,nr3
                scal=scal+u(n1,n2,n3,i,j,na,nb)*v(n1,n2,n3,i,j,na,nb)
              enddo
            enddo
          enddo
        enddo
      enddo
    enddo
  enddo
  !
  return
  !
end subroutine sp1
!
!----------------------------------------------------------------------
subroutine sp2(u,v,ind_v,nr1,nr2,nr3,nat,scal)
  !-----------------------------------------------------------------------
  !
  ! does the scalar product of two force-constants matrices u and v (considered as
  ! vectors in the R^(3*3*nat*nat*nr1*nr2*nr3) space). u is coded in the usual way
  ! but v is coded as explained when defining the vectors corresponding to the 
  ! symmetry constraints
  !
  USE kinds, ONLY: DP
  implicit none
  integer nr1,nr2,nr3,i,nat
  real(DP) u(nr1,nr2,nr3,3,3,nat,nat)
  integer ind_v(2,7)
  real(DP) v(2)
  real(DP) scal  
  !
  !
  scal=0.0d0
  do i=1,2
    scal=scal+u(ind_v(i,1),ind_v(i,2),ind_v(i,3),ind_v(i,4),ind_v(i,5),ind_v(i,6), &
         ind_v(i,7))*v(i)
  enddo
  !
  return
  !
end subroutine sp2
!
!----------------------------------------------------------------------
subroutine sp3(u,v,i,na,nr1,nr2,nr3,nat,scal)
  !-----------------------------------------------------------------------
  !
  ! like sp1, but in the particular case when u is one of the u(k)%vec
  ! defined in set_asr (before orthonormalization). In this case most of the
  ! terms are zero (the ones that are not are characterized by i and na), so 
  ! that a lot of computer time can be saved (during Gram-Schmidt). 
  !
  USE kinds, ONLY: DP
  implicit none
  integer nr1,nr2,nr3,i,j,na,nb,n1,n2,n3,nat
  real(DP) u(nr1,nr2,nr3,3,3,nat,nat)
  real(DP) v(nr1,nr2,nr3,3,3,nat,nat)
  real(DP) scal  
  !
  !
  scal=0.0d0
  do j=1,3
    do nb=1,nat
      do n1=1,nr1
        do n2=1,nr2
          do n3=1,nr3
            scal=scal+u(n1,n2,n3,i,j,na,nb)*v(n1,n2,n3,i,j,na,nb)
          enddo
        enddo
      enddo
    enddo
  enddo
  !
  return
  !
end subroutine sp3
!
!-----------------------------------------------------------------------
SUBROUTINE q_gen(nsc,qbid,at_blk,bg_blk,at,bg)
  !-----------------------------------------------------------------------
  ! generate list of q (qbid) that are G-vectors of the supercell
  ! but not of the bulk
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  INTEGER :: nsc
  REAL(DP) qbid(3,nsc), at_blk(3,3), bg_blk(3,3), at(3,3), bg(3,3)
  !
  INTEGER, PARAMETER:: nr1=4, nr2=4, nr3=4, &
                       nrm=(2*nr1+1)*(2*nr2+1)*(2*nr3+1)
  REAL(DP), PARAMETER:: eps=1.0e-7
  INTEGER :: i, j, k,i1, i2, i3, idum(nrm), iq
  REAL(DP) :: qnorm(nrm), qbd(3,nrm) ,qwork(3), delta
  LOGICAL lbho
  !
  i = 0
  DO i1=-nr1,nr1
     DO i2=-nr2,nr2
        DO i3=-nr3,nr3
           i = i + 1
           DO j=1,3
              qwork(j) = i1*bg(j,1) + i2*bg(j,2) + i3*bg(j,3)
           END DO ! j
           !
           qnorm(i)  = qwork(1)**2 + qwork(2)**2 + qwork(3)**2
           !
           DO j=1,3
              !
              qbd(j,i) = at_blk(1,j)*qwork(1) + &
                         at_blk(2,j)*qwork(2) + &
                         at_blk(3,j)*qwork(3)
           END DO ! j
           !
           idum(i) = 1
           !
        END DO ! i3
     END DO ! i2
  END DO ! i1
  !
  DO i=1,nrm-1
     IF (idum(i).EQ.1) THEN
        DO j=i+1,nrm
           IF (idum(j).EQ.1) THEN
              lbho=.TRUE.
              DO k=1,3
                 delta = qbd(k,i)-qbd(k,j)
                 lbho = lbho.AND. (ABS(NINT(delta)-delta).LT.eps)
              END DO ! k
              IF (lbho) THEN
                 IF(qnorm(i).GT.qnorm(j)) THEN
                    qbd(1,i) = qbd(1,j)
                    qbd(2,i) = qbd(2,j)
                    qbd(3,i) = qbd(3,j)
                    qnorm(i) = qnorm(j)
                 END IF
                 idum(j) = 0
              END IF
           END IF
        END DO ! j
     END IF
  END DO ! i
  !
  iq = 0
  DO i=1,nrm
     IF (idum(i).EQ.1) THEN
        iq=iq+1
        qbid(1,iq)= bg_blk(1,1)*qbd(1,i) +  &
                    bg_blk(1,2)*qbd(2,i) +  &
                    bg_blk(1,3)*qbd(3,i)
        qbid(2,iq)= bg_blk(2,1)*qbd(1,i) +  &
                    bg_blk(2,2)*qbd(2,i) +  &
                    bg_blk(2,3)*qbd(3,i)
        qbid(3,iq)= bg_blk(3,1)*qbd(1,i) +  &
                    bg_blk(3,2)*qbd(2,i) +  &
                    bg_blk(3,3)*qbd(3,i)
     END IF
  END DO ! i
  !
  IF (iq.NE.nsc) CALL errore('q_gen',' probably nr1,nr2,nr3 too small ', iq)
  RETURN
END SUBROUTINE q_gen
!
!-----------------------------------------------------------------------
SUBROUTINE check_at(at,bg_blk,alat,omega)
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  !
  REAL(DP) :: at(3,3), bg_blk(3,3), alat, omega
  REAL(DP) :: work(3,3)
  INTEGER :: i,j
  REAL(DP), PARAMETER :: small=1.d-6
  !
  work(:,:) = at(:,:)
  CALL cryst_to_cart(3,work,bg_blk,-1)
  !
  DO j=1,3
     DO i =1,3
        IF ( ABS(work(i,j)-NINT(work(i,j))) > small) THEN
           WRITE (*,'(3f9.4)') work(:,:)
           CALL errore ('check_at','at not multiple of at_blk',1)
        END IF
     END DO
  END DO
  !
  omega =alat**3 * ABS(at(1,1)*(at(2,2)*at(3,3)-at(3,2)*at(2,3))- &
                       at(1,2)*(at(2,1)*at(3,3)-at(2,3)*at(3,1))+ &
                       at(1,3)*(at(2,1)*at(3,2)-at(2,2)*at(3,1)))
  !
  RETURN
END SUBROUTINE check_at
!
!-----------------------------------------------------------------------
SUBROUTINE set_tau (nat, nat_blk, at, at_blk, tau, tau_blk, &
     ityp, ityp_blk, itau_blk)
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  INTEGER nat, nat_blk,ityp(nat),ityp_blk(nat_blk), itau_blk(nat)
  REAL(DP) at(3,3),at_blk(3,3),tau(3,nat),tau_blk(3,nat_blk)
  !
  REAL(DP) bg(3,3), r(3) ! work vectors
  INTEGER i,i1,i2,i3,na,na_blk
  REAL(DP) small
  INTEGER NN1,NN2,NN3
  PARAMETER (NN1=8, NN2=8, NN3=8, small=1.d-8)
  !
  CALL recips (at(1,1),at(1,2),at(1,3),bg(1,1),bg(1,2),bg(1,3))
  !
  na = 0
  !
  DO i1 = -NN1,NN1
     DO i2 = -NN2,NN2
        DO i3 = -NN3,NN3
           r(1) = i1*at_blk(1,1) + i2*at_blk(1,2) + i3*at_blk(1,3)
           r(2) = i1*at_blk(2,1) + i2*at_blk(2,2) + i3*at_blk(2,3)
           r(3) = i1*at_blk(3,1) + i2*at_blk(3,2) + i3*at_blk(3,3)
           CALL cryst_to_cart(1,r,bg,-1)
           !
           IF ( r(1).GT.-small .AND. r(1).LT.1.d0-small .AND.          &
                r(2).GT.-small .AND. r(2).LT.1.d0-small .AND.          &
                r(3).GT.-small .AND. r(3).LT.1.d0-small ) THEN
              CALL cryst_to_cart(1,r,at,+1)
              !
              DO na_blk=1, nat_blk
                 na = na + 1
                 IF (na.GT.nat) CALL errore('set_tau','too many atoms',na)
                 tau(1,na)    = tau_blk(1,na_blk) + r(1)
                 tau(2,na)    = tau_blk(2,na_blk) + r(2)
                 tau(3,na)    = tau_blk(3,na_blk) + r(3)
                 ityp(na)     = ityp_blk(na_blk)
                 itau_blk(na) = na_blk
              END DO
              !
           END IF
           !
        END DO
     END DO
  END DO
  !
  IF (na.NE.nat) CALL errore('set_tau','too few atoms: increase NNs',na)
  !
  RETURN
END SUBROUTINE set_tau
!
!-----------------------------------------------------------------------
SUBROUTINE read_tau &
     (nat, nat_blk, ntyp, bg_blk, tau, tau_blk, ityp, itau_blk)
  !---------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  !
  INTEGER nat, nat_blk, ntyp, ityp(nat),itau_blk(nat)
  REAL(DP) bg_blk(3,3),tau(3,nat),tau_blk(3,nat_blk)
  !
  REAL(DP) r(3) ! work vectors
  INTEGER i,na,na_blk
  !
  REAL(DP) small
  PARAMETER ( small = 1.d-6 )
  !
  DO na=1,nat
     READ(*,*) (tau(i,na),i=1,3), ityp(na)
     IF (ityp(na).LE.0 .OR. ityp(na) .GT. ntyp) &
          CALL errore('read_tau',' wrong atomic type', na)
     DO na_blk=1,nat_blk
        r(1) = tau(1,na) - tau_blk(1,na_blk)
        r(2) = tau(2,na) - tau_blk(2,na_blk)
        r(3) = tau(3,na) - tau_blk(3,na_blk)
        CALL cryst_to_cart(1,r,bg_blk,-1)
        IF (ABS( r(1)-NINT(r(1)) ) .LT. small .AND.                 &
            ABS( r(2)-NINT(r(2)) ) .LT. small .AND.                 &
            ABS( r(3)-NINT(r(3)) ) .LT. small ) THEN
           itau_blk(na) = na_blk
           go to 999
        END IF
     END DO
     CALL errore ('read_tau',' wrong atomic position ', na)
999  CONTINUE
  END DO
  !
  RETURN
END SUBROUTINE read_tau
!
!-----------------------------------------------------------------------
SUBROUTINE write_tau(fltau,nat,tau,ityp)
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  !
  INTEGER nat, ityp(nat)
  REAL(DP) tau(3,nat)
  CHARACTER(LEN=*) fltau
  !
  INTEGER i,na
  !
  OPEN (unit=4,file=fltau, status='new')
  DO na=1,nat
     WRITE(4,'(3(f12.6),i3)') (tau(i,na),i=1,3), ityp(na)
  END DO
  CLOSE (4)
  !
  RETURN 
END SUBROUTINE write_tau
!
!-----------------------------------------------------------------------
SUBROUTINE gen_qpoints (ibrav, at, bg, nat, tau, ityp, nk1, nk2, nk3, &
     symm_type, ntetra, nqx, nq, q, tetra)
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  !
  IMPLICIT NONE
  ! input 
  INTEGER :: ibrav, nat, nk1, nk2, nk3, ntetra, ityp(*)
  REAL(DP) :: at(3,3), bg(3,3), tau(3,nat)
  character(LEN=9)    :: symm_type
  ! output 
  INTEGER :: nqx, nq, tetra(4,ntetra)
  REAL(DP) :: q(3,nqx)
  ! local
  INTEGER :: nrot, nsym, s(3,3,48), ftau(3,48), irt(48,nat)
  INTEGER :: t_rev = 0
  LOGICAL :: minus_q, invsym
  REAL(DP) :: xqq(3), wk(nqx), mdum(3,nat)
  CHARACTER(LEN=45)   ::  sname(48)
  !
  xqq (:) =0.d0
  IF (ibrav == 4 .OR. ibrav == 5) THEN  
     !
     !  hexagonal or trigonal bravais lattice
     !
     CALL hexsym (at, s, sname, nrot)  
  ELSEIF (ibrav >= 1 .AND. ibrav <= 14) THEN  
     !
     !  cubic bravais lattice
     !
     CALL cubicsym (at, s, sname, nrot)  
  ELSEIF (ibrav == 0) THEN  

     if (symm_type=='cubic') then
        CALL cubicsym (at, s, sname, nrot)  
     elseif (symm_type=='hexagonal') then
        CALL hexsym (at, s, sname, nrot)  
     else
        CALL infomsg ('gen_qpoints', 'symm_type missing: assuming cubic symmetry', -1)  
        CALL cubicsym (at, s, sname, nrot)  
     end if

  ELSE  
     CALL errore ('gen_qpoints', 'wrong ibrav', 1)  
  ENDIF
  !
  CALL kpoint_grid ( nrot, s, bg, nqx, 0,0,0, nk1,nk2,nk3, nq, q, wk)
  !
  CALL sgama (nrot, nat, s, sname, t_rev, at, bg, tau, ityp, nsym, 6, &
       6, 6, irt, ftau, nqx, nq, q, wk, invsym, minus_q, xqq, &
       0, 0, .FALSE., mdum)
  
  IF (ntetra /= 6 * nk1 * nk2 * nk3) &
       CALL errore ('gen_qpoints','inconsistent ntetra',1)

  CALL tetrahedra (nsym, s, minus_q, at, bg, nqx, 0, 0, 0, &
       nk1, nk2, nk3, nq, q, wk, ntetra, tetra)
  !
  RETURN
END SUBROUTINE gen_qpoints
!
!---------------------------------------------------------------------
SUBROUTINE a2Fdos &
     (nat, nq, nr1, nr2, nr3, ibrav, at, bg, tau, alat, &
     nsc, nat_blk, at_blk, bg_blk, itau_blk, omega_blk, rws, nrws, &
     dos, Emin, DeltaE, ndos, ntetra, tetra, asr, q, freq )
  !-----------------------------------------------------------------------
  !
  USE kinds,      ONLY : DP
  USE ifconstants
  !
  IMPLICIT NONE
  !
  INTEGER, INTENT(in) :: nat, nq, nr1, nr2, nr3, ibrav, ndos, ntetra, &
       tetra(4, ntetra)
  LOGICAL, INTENT(in) :: dos
  CHARACTER(LEN=*), INTENT(IN) :: asr
  REAL(DP), INTENT(in) :: freq(3*nat,nq), q(3,nq), at(3,3), bg(3,3), &
       tau(3,nat), alat, Emin, DeltaE
  !
  INTEGER, INTENT(in) :: nsc, nat_blk, itau_blk, nrws
  REAL(DP), INTENT(in) :: rws(0:3,nrws), at_blk(3,3), bg_blk(3,3), omega_blk
  !
  REAL(DP), ALLOCATABLE    :: gamma(:,:), frcg(:,:,:,:,:,:,:)
  COMPLEX(DP), ALLOCATABLE :: gam(:,:,:,:), gam_blk(:,:,:,:), z(:,:)

  real(DP)                 :: lambda, dos_a2F(50), temp, dos_ee(10), dos_tot, &
                              deg(10), fermi(10), E
  real(DP), parameter      :: rydTHz = 3289.828d0, eps_w2 = 0.0000001d0 
  integer                  :: isig, ifn, n, m, na, nb, nc, nu, nmodes, &
                              i,j,k, ngauss, jsig, p1, p2, p3, filea2F
  character(len=14)        :: name
  !
  !
  nmodes = 3*nat
  do isig=1,10
     filea2F = 60 + isig
     write(name,"(A10,I2)") 'a2Fmatdyn.',filea2F
     open(filea2F, file=name, STATUS = 'unknown')
     READ(filea2F,*) deg(isig), fermi(isig), dos_ee(isig)
  enddo
  !
  IF(dos) then
     open(400,file='lambda',status='unknown')
     write(400,*)
     write(400,*) ' Electron-phonon coupling constant, lambda '
     write(400,*)
  ELSE
     open (20,file='gam.lines' ,status='unknown')
     write(20,*) 
     write(20,*) ' Gamma lines for all modes [THz] '
     write(20,*)
     write(6,*)
     write(6,*) ' Gamma lines for all modes [Rydberg] '
     write(6,*)
  ENDIF
  !
  ALLOCATE ( frcg(nr1,nr2,nr3,3,3,nat,nat) )
  ALLOCATE ( gamma(3*nat,nq), gam(3,3,nat,nat), gam_blk(3,3,nat_blk,nat_blk) )
  ALLOCATE ( z(3*nat,3*nat) )
  !
  frcg(:,:,:,:,:,:,:) = 0.d0
  DO isig = 1, 10
     filea2F = 60 + isig 
     CALL readfg ( filea2F, nr1, nr2, nr3, nat, frcg )
     !
     if ( asr /= 'no') then
        CALL set_asr (asr, nr1, nr2, nr3, frcg, zeu, nat_blk, ibrav, tau_blk)
     endif
     !
     open(300,file='dyna2F',status='old')
     !
     do n = 1 ,nq
        gam(:,:,:,:) = (0.d0, 0.d0)
        read(300,*)
        do na=1,nmodes
           read(300,*) (z(na,m),m=1,nmodes)
        end do ! na
        !
        CALL setgam (q(1,n), gam, nat, at, bg, tau, itau_blk, nsc, alat, &
             gam_blk, nat_blk, at_blk,bg_blk,tau_blk, omega_blk, &
             frcg, nr1,nr2,nr3, rws, nrws)
        !
        ! here multiply dyn*gam*dyn for gamma and divide by w2 for lambda at given q
        !
        do nc = 1, nat
           do k =1, 3
              p1 = (nc-1)*3+k
              nu = p1
              gamma(nu,n) = 0.0d0
              do i=1,3
                 do na=1,nat
                    p2 = (na-1)*3+i
                    do j=1,3
                       do nb=1,nat
                          p3 = (nb-1)*3+j
                          gamma(nu,n) = gamma(nu,n) + DBLE(conjg(z(p2,p1)) * &
                               gam(i,j,na,nb) * z(p3,p1))
                       enddo  ! nb
                    enddo  ! j
                 enddo  ! na
              enddo  !i
              gamma(nu,n) = gamma(nu,n) * 3.1415926d0 / 2.0d0
           enddo  ! k
        enddo  !nc
        !
        !
     EndDo !nq    all points in BZ
     close(300)   ! file with dyn vectors
     !
     ! after we know gamma(q) and lambda(q) calculate  DOS(omega) for spectrum a2F
     !
     if(dos) then
        ! 
        if(isig.le.9) then
           write(name,'(A8,I1.1)') 'a2F.dos.',isig
        else
           write(name,'(A8,I2.2)') 'a2F.dos.',isig
        endif
        ifn = 200 + isig
        open (ifn,file=name,status='unknown',form='formatted')
        write(ifn,*)
        write(ifn,*) ' Eliashberg function a2F (per both spin)'
        write(ifn,*) '  frequencies in Rydberg  '
        write(ifn,*) ' DOS normalized to E in Rydberg: a2F_total, a2F(mode) '
        write(ifn,*)
        !
        !      correction for small frequencies
        !
        do n = 1, nq
           do i = 1, nmodes 
              if (freq(i,n).LE.eps_w2) then
                 gamma(i,n) = 0.0d0                 
              endif
           enddo
        enddo
        !
        lambda = 0.0d0
        do n= 1, ndos
           !
           E = Emin + (n-1)*DeltaE + 0.5d0*DeltaE
           dos_tot = 0.0d0 
           do j=1,nmodes
              !
              dos_a2F(j) = 0.0d0
              CALL dos_gam(nmodes, nq, j, ntetra, tetra, &
                   gamma, freq, E, dos_a2F(j))
              dos_a2F(j) = dos_a2F(j) / dos_ee(isig)
              dos_tot = dos_tot + dos_a2F(j)
              !
           enddo
           lambda = lambda + dos_tot/E * DeltaE / 3.1415926d0
           write (ifn, 1050) E, dos_tot, (dos_a2F(j),j=1,nmodes)
        enddo  !ndos
        write(ifn,*) " lambda =",lambda,'   Delta = ',DeltaE
        close (ifn)
        write(400,'(" Broadening ",F8.4," lambda ",F12.4," dos_el ",F8.4)') &
             deg(isig),lambda, dos_ee(isig)
        !
     endif !dos
     !
     !  OUTPUT
     !
     if(.not.dos) then
        write(20,'(" Broadening ",F8.4)')  deg(isig)
        write(6,'(" Broadening ",F8.4)')  deg(isig)
        do n=1, nq
           write(20,1030) n,(gamma(i,n)*rydTHz,i=1,3*nat)
           write(6,1040) n, (gamma(i,n),i=1,3*nat)
        end do
     endif
     !
  ENDDO !isig
  !
  DEALLOCATE (z, frcg, gamma, gam, gam_blk )
  !
  close(400)   !lambda
  close(20)
  !
1030 FORMAT( 3x,I5,'  ',9F8.4 )
1040 FORMAT( 3x,I5,'  ',6F12.9 )
1050 FORMAT( 3x,F12.6,6F16.8 )
  !
  RETURN
END SUBROUTINE a2Fdos
!
!-----------------------------------------------------------------------
subroutine setgam (q, gam, nat, at,bg,tau,itau_blk,nsc,alat, &
     &             gam_blk, nat_blk,    at_blk,bg_blk,tau_blk,omega_blk, &
     &             frcg, nr1,nr2,nr3, rws,nrws)
  !-----------------------------------------------------------------------
  ! compute the dynamical matrix (the analytic part only)
  !
  USE kinds,       ONLY : DP
  implicit none
  real(DP), parameter :: tpi=2.d0*3.14159265358979d0
  !
  ! I/O variables
  !
  integer        :: nr1, nr2, nr3, nat, nat_blk,  &
                    nsc, nrws, itau_blk(nat)
  real(DP)       :: q(3), tau(3,nat), at(3,3), bg(3,3), alat, rws(0:3,nrws)
  real(DP)       :: tau_blk(3,nat_blk), at_blk(3,3), bg_blk(3,3), omega_blk, &
                    frcg(nr1,nr2,nr3,3,3,nat_blk,nat_blk)
  COMPLEX(DP)  :: gam_blk(3,3,nat_blk,nat_blk)
  COMPLEX(DP) ::  gam(3,3,nat,nat)
  !
  ! local variables
  !
  real(DP)        :: arg
  complex(DP)     :: cfac(nat)
  integer         :: i,j,k, na,nb, na_blk, nb_blk, iq
  real(DP)        :: qp(3), qbid(3,nsc) ! automatic array
  !
  !
  call q_gen(nsc,qbid,at_blk,bg_blk,at,bg)
  !
  do iq=1,nsc
     !
     do k=1,3
        qp(k)= q(k) + qbid(k,iq)
     end do
     !
     gam_blk(:,:,:,:) = (0.d0,0.d0)
     CALL frc_blk (gam_blk,qp,tau_blk,nat_blk,              &
                   nr1,nr2,nr3,frcg,at_blk,bg_blk,rws,nrws)
     !
     do na=1,nat
        na_blk = itau_blk(na)
        do nb=1,nat
           nb_blk = itau_blk(nb)
           !
           arg = tpi * ( qp(1) * ( (tau(1,na)-tau_blk(1,na_blk)) -   &
                                (tau(1,nb)-tau_blk(1,nb_blk)) ) + &
                      qp(2) * ( (tau(2,na)-tau_blk(2,na_blk)) -   &
                                (tau(2,nb)-tau_blk(2,nb_blk)) ) + &
                      qp(3) * ( (tau(3,na)-tau_blk(3,na_blk)) -   &
                                (tau(3,nb)-tau_blk(3,nb_blk)) ) )
           !
           cfac(nb) = cmplx(cos(arg),sin(arg))/nsc
           !
        end do ! nb
        do nb=1,nat
           do i=1,3
              do j=1,3
                 nb_blk = itau_blk(nb)
                 gam(i,j,na,nb) = gam(i,j,na,nb) + cfac(nb) * &
                     gam_blk(i,j,na_blk,nb_blk)
              end do ! j
              end do ! i 
        end do ! nb
     end do ! na
     !
  end do ! iq
  !
  return
end subroutine setgam
!
!--------------------------------------------------------------------
subroutine dos_gam (nbndx, nq, jbnd, ntetra, &
                    tetra, gamma, et, ef, dos_a2F)
  !--------------------------------------------------------------------
  ! calculates weights with the tetrahedron method (Bloechl version)
  ! this subroutine is based on tweights.f90 belonging to PW 
  ! it calculates a2F on the surface of given frequency <=> histogram
  ! Band index means the frequency mode here 
  ! and "et" means the frequency(mode,q-point)
  !
  USE kinds,       ONLY: DP
  use parameters
!  USE ifconstants, ONLY : gamma
  implicit none
  !
  integer :: nq, nbndx, ntetra, tetra(4,ntetra), jbnd
  real(DP) :: et(nbndx,nq), gamma(nbndx,nq), func
  
  real(DP) :: ef, dos_a2F
  real(DP) :: e1, e2, e3, e4, c1, c2, c3, c4, etetra(4)
  integer      :: ik, ibnd, nt, nk, ns, i, ik1, ik2, ik3, ik4, itetra(4)

  real(DP) ::   f12,f13,f14,f23,f24,f34, f21,f31,f41,f42,f32,f43
  real(DP) ::   P1,P2,P3,P4, G, Z, o13, Y1,Y2,Y3,Y4, WW, eps,vol, Tint


      Tint = 0.0d0
      eps  = 1.0d-14
      vol  = 1.0d0/ntetra

     do nt = 1, ntetra
         ibnd = jbnd
           !
           ! etetra are the energies at the vertexes of the nt-th tetrahedron
           !
           do i = 1, 4
              etetra(i) = et(ibnd, tetra(i,nt))
           enddo
           itetra(1) = 0
           call hpsort (4,etetra,itetra)
           !
           ! ...sort in ascending order: e1 < e2 < e3 < e4
           !
           e1 = etetra (1)
           e2 = etetra (2)
           e3 = etetra (3)
           e4 = etetra (4)
           !
           ! kp1-kp4 are the irreducible k-points corresponding to e1-e4
           !
           ik1 = tetra(itetra(1),nt)
           ik2 = tetra(itetra(2),nt)
           ik3 = tetra(itetra(3),nt)
           ik4 = tetra(itetra(4),nt)
           Y1  = gamma(ibnd,ik1)/et(ibnd,ik1)
           Y2  = gamma(ibnd,ik2)/et(ibnd,ik2)
           Y3  = gamma(ibnd,ik3)/et(ibnd,ik3)
           Y4  = gamma(ibnd,ik4)/et(ibnd,ik4)


           f12 = (ef-e2)/(e1-e2)
           f13 = (ef-e3)/(e1-e3)
           f14 = (ef-e4)/(e1-e4)
           f23 = (ef-e3)/(e2-e3)
           f24 = (ef-e4)/(e2-e4)
           f34 = (ef-e4)/(e3-e4)

           f21 = 1.0d0 - f12
           f31 = 1.0d0 - f13
           f41 = 1.0d0 - f14
           f32 = 1.0d0 - f23
           f42 = 1.0d0 - f24
           f43 = 1.0d0 - f34

           o13 = 1.0d0/3.0d0
           G   = 0.0d0
           P1  = 0.0d0
           P2  = 0.0d0
           P3  = 0.0d0
           P4  = 0.0d0

           IF(e1.gt.ef.or.e4.lt.ef) then
                 goto 500
           ENDIF

       IF(e3.lt.ef.and.ef.lt.e4) THEN

         Z  =  (1.0d0 - f14 * f24 * f34)
         G  =  3.0d0 * (1.0d0 - Z) / (e4-ef)
         P1 =  f14 * o13
         P2 =  f24 * o13
         P3 =  f34 * o13
         P4 =  (f41 + f42 + f43) * o13
         goto 200

       ENDIF


       IF(e2.lt.ef.and.ef.lt.e3) THEN

         G   =  3.0d0 * (f23*f31 + f32*f24)
         P1  =  f14 * o13 + f13*f31*f23 / G
         P2  =  f23 * o13 + f24*f24*f32 / G
         P3  =  f32 * o13 + f31*f31*f23 / G
         P4  =  f41 * o13 + f42*f24*f32 / G
         G   =  G / (e4-e1)
         goto 200

       ENDIF


       IF(e1.lt.ef.and.ef.lt.e2) THEN

         Z  =  f21 * f31 * f41
         G  =  3.0d0 * Z / (ef-e1)
         P1 =  o13 * (f12 + f12 + f14)
         P2 =  o13 * f21
         P3 =  o13 * f31
         P4 =  o13 * f41
         goto 200

       ENDIF

200      WW = G * (Y1*P1 + Y2*P2 + Y3*P3 + Y4*P4)

         Tint = Tint + WW * vol

500     continue
     enddo   ! ntetra


  dos_a2F = Tint  !2 because DOS_ee is per 1 spin

  return
end subroutine dos_gam
!
!
!-----------------------------------------------------------------------
subroutine readfg ( ifn, nr1, nr2, nr3, nat, frcg )
  !-----------------------------------------------------------------------
  !
  USE kinds,       ONLY : DP
  implicit none
  ! I/O variable
  integer, intent(in) ::  nr1,nr2,nr3, nat
  real(DP), intent(out) :: frcg(nr1,nr2,nr3,3,3,nat,nat)
  ! local variables
  integer i, j, na, nb, m1,m2,m3, ifn
  integer ibid, jbid, nabid, nbbid, m1bid,m2bid,m3bid
  !
  !
  READ (ifn,*) m1, m2, m3
  if ( m1 /= nr1 .or. m2 /= nr2 .or. m3 /= nr3) &
       call errore('readfG','inconsistent nr1, nr2, nr3 read',1)
  do i=1,3
     do j=1,3
        do na=1,nat
           do nb=1,nat
              read (ifn,*) ibid, jbid, nabid, nbbid
              if(i.ne.ibid.or.j.ne.jbid.or.na.ne.nabid.or.nb.ne.nbbid)  then
                  write(*,*) i,j,na,nb,'  <>  ', ibid, jbid, nabid, nbbid 
                  call errore  ('readfG','error in reading',1)
              else
                  read (ifn,*) (((m1bid, m2bid, m3bid,     &
                                 frcg(m1,m2,m3,i,j,na,nb), &
                                 m1=1,nr1),m2=1,nr2),m3=1,nr3)
              endif
           end do
        end do
     end do
  end do
  !
  close(ifn)
  !
  return
end subroutine readfg


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