mirror of https://gitlab.com/QEF/q-e.git
242 lines
7.0 KiB
Fortran
242 lines
7.0 KiB
Fortran
!
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! Copyright (C) 2001 PWSCF group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!---------------------------------------------------------------------
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subroutine set_sym_irr (nat, at, bg, xq, s, invs, nsym, rtau, irt, &
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irgq, nsymq, minus_q, irotmq, t, tmq, u, npert, nirr, gi, gimq, &
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iverbosity)
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!---------------------------------------------------------------------
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!
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! This subroutine computes a basis for all the irreducible
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! representations of the small group of q, which are contained
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! in the representation which has as basis the displacement vectors.
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! This is achieved by building a random hermitean matrix,
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! symmetrizing it and diagonalizing the result. The eigenvectors
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! give a basis for the irreducible representations of the
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! small group of q.
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!
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! Furthermore it computes:
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! 1) the small group of q
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! 2) the possible G vectors associated to every symmetry operation
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! 3) the matrices which represent the small group of q on the
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! pattern basis.
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!
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! Original routine was from C. Bungaro.
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! Revised Oct. 1995 by Andrea Dal Corso.
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! April 1997: parallel stuff added (SdG)
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!
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#include "machine.h"
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use parameters, only : DP
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#ifdef __PARA
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use para, only: me
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use mp, only: mp_bcast
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#endif
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implicit none
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!
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! first the dummy variables
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!
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integer :: nat, nsym, s (3, 3, 48), invs (48), irt (48, nat), &
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iverbosity, npert (3 * nat), irgq (48), nsymq, irotmq, nirr
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! input: the number of atoms
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! input: the number of symmetries
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! input: the symmetry matrices
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! input: the inverse of each matrix
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! input: the rotated of each atom
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! input: write control
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! output: the dimension of each represe
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! output: the small group of q
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! output: the order of the small group
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! output: the symmetry sending q -> -q+
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! output: the number of irr. representa
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real(kind=DP) :: xq (3), rtau (3, 48, nat), at (3, 3), bg (3, 3), &
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gi (3, 48), gimq (3)
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! input: the q point
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! input: the R associated to each tau
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! input: the direct lattice vectors
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! input: the reciprocal lattice vectors
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! output: [S(irotq)*q - q]
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! output: [S(irotmq)*q + q]
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complex(kind=DP) :: u (3 * nat, 3 * nat), t (3, 3, 48, 3 * nat), &
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tmq (3, 3, 3 * nat)
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! output: the pattern vectors
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! output: the symmetry matrices
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! output: the matrice sending q -> -q+G
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logical :: minus_q
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! output: if true one symmetry send q -
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!
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! here the local variables
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!
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real(kind=DP), parameter :: tpi = 2.0d0 * 3.14159265358979d0
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integer :: na, nb, imode, jmode, ipert, jpert, nsymtot, imode0, &
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irr, ipol, jpol, isymq, irot, sna
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! counter on atoms
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! counter on atoms
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! counter on modes
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! counter on modes
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! counter on perturbations
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! counter on perturbations
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! total number of symmetries
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! auxiliry variable for mode counting
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! counter on irreducible representation
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! counter on polarizations
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! counter on polarizations
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! counter on symmetries
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! counter on rotations
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! the rotated atom
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integer :: root = 0
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real(kind=DP) :: eigen (3 * nat), modul, arg
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! the eigenvalues of dynamical ma
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! the modulus of the mode
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! the argument of the phase
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complex(kind=DP) :: wdyn (3, 3, nat, nat), phi (3 * nat, 3 * nat), &
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wrk_u (3, nat), wrk_ru (3, nat), fase
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! the dynamical matrix
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! the bi-dimensional dynamical ma
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! one pattern
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! the rotated of one pattern
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! the phase factor
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logical :: lgamma
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! if true gamma point
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!
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! Allocate the necessary quantities
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!
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lgamma = (xq(1).eq.0.d0 .and. xq(2).eq.0.d0 .and. xq(3).eq.0.d0)
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!
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! find the small group of q
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!
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call smallgq (xq,at,bg,s,nsym,irgq,nsymq,irotmq,minus_q,gi,gimq)
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!
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! And we compute the matrices which represent the symmetry transformat
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! in the basis of the displacements
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!
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t(:,:,:,:) = (0.d0, 0.d0)
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tmq(:,:,:) = (0.d0, 0.d0)
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if (minus_q) then
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nsymtot = nsymq + 1
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else
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nsymtot = nsymq
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endif
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do isymq = 1, nsymtot
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if (isymq.le.nsymq) then
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irot = irgq (isymq)
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else
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irot = irotmq
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endif
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imode0 = 0
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do irr = 1, nirr
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do ipert = 1, npert (irr)
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imode = imode0 + ipert
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do na = 1, nat
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do ipol = 1, 3
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jmode = 3 * (na - 1) + ipol
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wrk_u (ipol, na) = u (jmode, imode)
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enddo
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enddo
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!
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! transform this pattern to crystal basis
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!
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do na = 1, nat
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call trnvecc (wrk_u (1, na), at, bg, - 1)
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enddo
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!
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! the patterns are rotated with this symmetry
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!
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wrk_ru(:,:) = (0.d0, 0.d0)
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do na = 1, nat
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sna = irt (irot, na)
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arg = 0.d0
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do ipol = 1, 3
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arg = arg + xq (ipol) * rtau (ipol, irot, na)
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enddo
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arg = arg * tpi
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if (isymq.eq.nsymtot.and.minus_q) then
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fase = DCMPLX (cos (arg), sin (arg) )
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else
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fase = DCMPLX (cos (arg), - sin (arg) )
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endif
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do ipol = 1, 3
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do jpol = 1, 3
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wrk_ru (ipol, sna) = wrk_ru (ipol, sna) + s (jpol, ipol, irot) &
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* wrk_u (jpol, na) * fase
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enddo
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enddo
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enddo
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!
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! Transform back the rotated pattern
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!
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do na = 1, nat
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call trnvecc (wrk_ru (1, na), at, bg, 1)
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enddo
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!
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! Computes the symmetry matrices on the basis of the pattern
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!
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do jpert = 1, npert (irr)
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imode = imode0 + jpert
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do na = 1, nat
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do ipol = 1, 3
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jmode = ipol + (na - 1) * 3
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if (isymq.eq.nsymtot.and.minus_q) then
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tmq (jpert, ipert, irr) = tmq (jpert, ipert, irr) + conjg (u ( &
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jmode, imode) * wrk_ru (ipol, na) )
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else
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t (jpert, ipert, irot, irr) = t (jpert, ipert, irot, irr) &
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+ conjg (u (jmode, imode) ) * wrk_ru (ipol, na)
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endif
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enddo
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enddo
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enddo
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enddo
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imode0 = imode0 + npert (irr)
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enddo
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enddo
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!
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! Note: the following lines are for testing purposes
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!
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! nirr = 1
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! npert(1)=1
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! do na=1,3*nat/2
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! u(na,1)=(0.d0,0.d0)
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! u(na+3*nat/2,1)=(0.d0,0.d0)
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! enddo
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! u(1,1)=(-1.d0,0.d0)
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! write(6,'(" Setting mode for testing ")')
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! do na=1,3*nat
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! write(6,*) u(na,1)
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! enddo
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! nsymq=1
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! minus_q=.false.
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#ifdef __PARA
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!
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! parallel stuff: first node broadcasts everything to all nodes
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!
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400 continue
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call mp_bcast (gi, root)
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call mp_bcast (gimq, root)
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call mp_bcast (t, root)
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call mp_bcast (tmq, root)
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call mp_bcast (u, root)
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call mp_bcast (nsymq, root)
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call mp_bcast (npert, root)
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call mp_bcast (nirr, root)
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call mp_bcast (irotmq, root)
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call mp_bcast (irgq, root)
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call mp_bcast (minus_q, root)
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#endif
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return
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end subroutine set_sym_irr
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