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quantum-espresso/PHonon/PH/set_irr.f90

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!
! Copyright (C) 2001-2003 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 .
!
!---------------------------------------------------------------------
subroutine set_irr_new (xq, u, npert, nirr, eigen)
!---------------------------------------------------------------------
!
! This subroutine computes a basis for all the irreducible
! representations of the small group of q, which are contained
! in the representation which has as basis the displacement vectors.
! This is achieved by building a random hermitean matrix,
! symmetrizing it and diagonalizing the result. The eigenvectors
! give a basis for the irreducible representations of the
! small group of q.
!
! Original routine was from C. Bungaro.
! Revised Oct. 1995 by Andrea Dal Corso.
! April 1997: parallel stuff added (SdG)
!
USE io_global, ONLY : stdout
USE kinds, only : DP
USE ions_base, ONLY : nat, tau, ntyp => nsp, ityp, amass
USE cell_base, ONLY : at, bg
USE symm_base, ONLY : s, sr, invs, nsym, irt, t_rev
USE modes, ONLY : num_rap_mode, name_rap_mode
USE noncollin_module, ONLY : noncolin, nspin_mag
USE spin_orb, ONLY : domag
USE constants, ONLY: tpi
USE control_ph, ONLY : search_sym
USE control_flags, ONLY : iverbosity
USE random_numbers, ONLY : randy
USE rap_point_group, ONLY : name_rap
use mp, only: mp_bcast
use io_global, only : ionode_id
use mp_images, only : intra_image_comm
USE lr_symm_base, ONLY : nsymq, minus_q, irotmq, gi, gimq, rtau
USE control_lr, ONLY : lgamma
implicit none
!
! first the dummy variables
!
real(DP), INTENT(IN) :: xq (3)
! input: the q point
complex(DP), INTENT(OUT) :: u(3*nat, 3*nat)
INTEGER, INTENT(OUT) :: npert(3*nat), nirr
REAL(DP), INTENT(OUT) :: eigen(3*nat)
!
! here the local variables
!
integer :: na, nb, imode, jmode, ipert, jpert, nsymtot, imode0, &
irr, ipol, jpol, isymq, irot, sna, isym
! counters and auxiliary variables
integer :: info, mode_per_rap(0:12), count_rap(0:12), rap, init, pos, irap, &
num_rap_aux( 3 * nat ), ierr
real(DP) :: modul, arg, eig(3*nat)
! the eigenvalues of dynamical matrix
! the modulus of the mode
! the argument of the phase
complex(DP) :: wdyn (3, 3, nat, nat), phi (3 * nat, 3 * nat), &
wrk_u (3, nat), wrk_ru (3, nat), fase
! the dynamical matrix
! the dynamical matrix with two indices
! pattern
! rotated pattern
! the phase factor
logical :: magnetic_sym
magnetic_sym=noncolin.AND.domag
!
! then we generate a random hermitean matrix
!
arg = randy(0)
call random_matrix_new (irt,nsymq,minus_q,irotmq,nat,wdyn,lgamma)
!call write_matrix('random matrix',wdyn,nat)
!
! symmetrize the random matrix with the little group of q
!
call symdynph_gq_new (xq,wdyn,s,invs,rtau,irt,nsymq,nat,irotmq,minus_q)
!call write_matrix('symmetrized matrix',wdyn,nat)
!
! Diagonalize the symmetrized random matrix.
! Transform the symmetrized matrix, currently in crystal coordinates,
! in cartesian coordinates.
!
do na = 1, nat
do nb = 1, nat
call trntnsc( wdyn(1,1,na,nb), at, bg, 1 )
enddo
enddo
!
! We copy the dynamical matrix in a bidimensional array
!
CALL compact_dyn(nat, phi, wdyn)
!
! Diagonalize
!
call cdiagh (3 * nat, phi, 3 * nat, eigen, u)
!
! We adjust the phase of each mode in such a way that the first
! non zero element is real
!
do imode = 1, 3 * nat
do na = 1, 3 * nat
modul = abs (u(na, imode) )
if (modul.gt.1d-9) then
fase = u (na, imode) / modul
goto 110
endif
enddo
call errore ('set_irr', 'one mode is zero', imode)
110 do na = 1, 3 * nat
u (na, imode) = - u (na, imode) * CONJG(fase)
enddo
enddo
!
! We have here a test which writes eigenvectors and eigenvalues
!
if (iverbosity.eq.1) then
npert=1
do imode=1,3*nat
WRITE( stdout, '(2x,"autoval = ", e10.4)') eigen(imode)
CALL write_modes_out(imode,imode-1)
end do
end if
IF (search_sym.AND.nspin_mag/=4) THEN
CALL find_mode_sym_new (u, eigen, tau, nat, nsymq, s, sr, irt, xq, &
rtau, amass, ntyp, ityp, 0, .FALSE., .TRUE., num_rap_mode, ierr)
!
! Order the modes so that we first make all those that belong to the first
! representation, then the second ect.
!
!
! First count, for each irreducible representation, how many modes
! belong to that representation. Modes that could not be classified
! have num_rap_mode 0.
!
mode_per_rap=0
DO imode=1,3*nat
mode_per_rap(num_rap_mode(imode))= &
mode_per_rap(num_rap_mode(imode))+1
ENDDO
!
! The position of each mode on the list is the following:
! The positions from 1 to mode_per_rap(0) contain the modes that transform
! according to the first representation. From mode_per_rap(1)+1 to
! mode_per_rap(1) + mode_per_rap(2) the mode that transform according
! to the second ecc.
!
count_rap=1
DO imode=1,3*nat
rap=num_rap_mode(imode)
IF (rap>12) call errore('set_irr',&
'problem with the representation',1)
!
! Determine the first position for the representation rap
!
init=0
DO irap=0,rap-1
init=init+mode_per_rap(irap)
ENDDO
!
! Determine in which position to put this mode. count_rap keep into
! account how many modes of that representation we have already
! assigned
!
pos=init+count_rap(rap)
!
! the eigenvalue, the mode and the number of its representation are
! copied in the auxiliary list
!
!
eig(pos)=eigen(imode)
phi(:,pos)=u(:,imode)
num_rap_aux(pos)=num_rap_mode(imode)
!
! Update the number of modes already found for a representation
!
count_rap(rap)=count_rap(rap)+1
ENDDO
!
! Copy the new exchanged array in the old ones
!
eigen=eig
u=phi
num_rap_mode=num_rap_aux
!
! If two almost degenerate modes have been assigned to different
! representations, we force them to be close in the list independently
! from their representation in order not to change previous behaviour
! of the code. These instructions should not be needed.
!
DO imode=1,3*nat-1
DO jmode = imode+1, 3*nat
IF ((num_rap_mode(imode) /= num_rap_mode(jmode)).AND. &
(ABS(eigen(imode) - eigen(jmode))/ &
(ABS(eigen(imode)) + ABS (eigen (jmode) )) < 1.d-4) ) THEN
WRITE(stdout,'("Eigenvectors exchange needed",2i5)') imode, &
jmode
eig(1)=eigen(jmode)
phi(:,1)=u(:,jmode)
num_rap_aux(1)=num_rap_mode(jmode)
eigen(jmode)=eigen(imode+1)
u(:,jmode)=u(:,imode+1)
num_rap_mode(jmode)=num_rap_mode(imode+1)
eigen(imode+1)=eig(1)
u(:,imode+1)=phi(:,1)
num_rap_mode(imode+1)=num_rap_aux(1)
ENDIF
ENDDO
ENDDO
ENDIF
!
! Here we count the irreducible representations and their dimensions
do imode = 1, 3 * nat
! initialization
npert (imode) = 0
enddo
nirr = 1
npert (1) = 1
do imode = 2, 3 * nat
if (abs (eigen (imode) - eigen (imode-1) ) / (abs (eigen (imode) ) &
+ abs (eigen (imode-1) ) ) .lt.1.d-4) then
npert (nirr) = npert (nirr) + 1
else
nirr = nirr + 1
npert (nirr) = 1
endif
enddo
IF (search_sym.AND.nspin_mag/=4) THEN
!
! Here we set the name of the representation for each mode
!
name_rap_mode=' '
DO imode = 1, 3*nat
IF (num_rap_mode(imode) > 0 ) &
name_rap_mode(imode)=name_rap(num_rap_mode(imode))
ENDDO
ENDIF
! Note: the following lines are for testing purposes
!
! nirr = 1
! npert(1)=1
! do na=1,3*nat/2
! u(na,1)=(0.d0,0.d0)
! u(na+3*nat/2,1)=(0.d0,0.d0)
! enddo
! u(1,1)=(-1.d0,0.d0)
! WRITE( stdout,'(" Setting mode for testing ")')
! do na=1,3*nat
! WRITE( stdout,*) u(na,1)
! enddo
! nsymq=1
! minus_q=.false.
!
! parallel stuff: first node broadcasts everything to all nodes
!
400 continue
call mp_bcast (gi, ionode_id, intra_image_comm)
call mp_bcast (gimq, ionode_id, intra_image_comm)
call mp_bcast (u, ionode_id, intra_image_comm)
call mp_bcast (nsymq, ionode_id, intra_image_comm)
call mp_bcast (npert, ionode_id, intra_image_comm)
call mp_bcast (nirr, ionode_id, intra_image_comm)
call mp_bcast (irotmq, ionode_id, intra_image_comm)
call mp_bcast (minus_q, ionode_id, intra_image_comm)
call mp_bcast (num_rap_mode, ionode_id, intra_image_comm)
call mp_bcast (name_rap_mode, ionode_id, intra_image_comm)
return
end subroutine set_irr_new
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