mirror of https://gitlab.com/QEF/q-e.git
210 lines
8.4 KiB
Fortran
210 lines
8.4 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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!-----------------------------------------------------------------------
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subroutine cubicsym (at, is, isname, nrot)
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!-----------------------------------------------------------------------
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!
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! Provides symmetry operations for all cubic and
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! lower-symmetry (excepted Hexagonal and Trigonal) bravais lattices
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!
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! Last revision 30 May 1995 by A. Di Pomponio
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!
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!
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use parameters
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implicit none
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!
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! first the input/output variables
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!
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real(kind=DP) :: at (3, 3)
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! input: the direct lattice vectors
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integer :: is (3, 3, 48), nrot
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! output: the symmetry matrices
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! output: the number of symmetry matrice
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character :: isname (48) * 45
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! output: full name of the rotational pa
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! ! each selected symmetry operati
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!
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! here the local parameters
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!
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real(kind=DP) :: sin3, cos3, msin3, mcos3
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! sin(pi/3)
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! cos(pi/3)
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! -sin(pi/3)
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! -sin(pi/3)
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parameter (sin3 = 0.866025403784438597d0, cos3 = 0.5d0, msin3 = &
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- 0.866025403784438597d0, mcos3 = - 0.5d0)
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!
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! and the local variables
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!
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real(kind=DP) :: s (3, 3, 24), overlap (3, 3), rat (3), rot (3, 3), &
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value
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! the s matrices in real variables
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! overlap matrix between direct lattice
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! the rotated of a direct vector ( carte
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! the rotated of a direct vector ( in ax
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! component of the s matrix in axis basi
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integer :: jpol, kpol, irot, mpol
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! counter over the polarizations
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! counter over the polarizations
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! counter over the rotations
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! counter over the polarizations
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character :: sname (48) * 45
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! full name of the rotational part of
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! ! each symmetry operation
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data s / 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, &
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- 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, - 1.d0, &
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0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 1.d0, 0.d0, &
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0.d0, 0.d0, - 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, 1.d0, 0.d0, &
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1.d0, 0.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, &
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0.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, 0.d0, 1.d0, 0.d0, &
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0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 1.d0, 0.d0, - 1.d0, 0.d0, 0.d0, &
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0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 1.d0, 0.d0, - 1.d0, 0.d0, 1.d0, &
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0.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, 0.d0, &
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0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, 1.d0, 0.d0, 1.d0, 0.d0, 0.d0, &
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0.d0, 0.d0, 1.d0, 0.d0, 1.d0, 0.d0, - 1.d0, 0.d0, 0.d0, - 1.d0, &
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0.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, 1.d0, 0.d0, - 1.d0, 0.d0, &
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0.d0, 0.d0, 0.d0, - 1.d0, 0.d0, - 1.d0, 0.d0, 1.d0, 0.d0, 0.d0, &
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0.d0, 0.d0, - 1.d0, 0.d0, 1.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, &
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0.d0, 1.d0, 0.d0, - 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 1.d0, 0.d0, &
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0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, - 1.d0, 0.d0, 0.d0, &
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0.d0, 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 1.d0, 0.d0, 0.d0, 0.d0, &
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- 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, - 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, &
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0.d0, 0.d0, 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 1.d0, 0.d0, 0.d0, 0.d0, &
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- 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, 1.d0, 0.d0, 0.d0, 0.d0, - 1.d0, &
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0.d0, 0.d0, 0.d0, 1.d0, - 1.d0, 0.d0, 0.d0, 0.d0, 1.d0, 0.d0, &
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0.d0, 0.d0, - 1.d0, - 1.d0, 0.d0, 0.d0 /
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data sname/&
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& 'identity ',&
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& '180 deg rotation - cart. axis [0,0,1] ',&
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& '180 deg rotation - cart. axis [0,1,0] ',&
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& '180 deg rotation - cart. axis [1,0,0] ',&
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& '180 deg rotation - cart. axis [1,1,0] ',&
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& '180 deg rotation - cart. axis [1,-1,0] ',&
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& ' 90 deg rotation - cart. axis [0,0,-1] ',&
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& ' 90 deg rotation - cart. axis [0,0,1] ',&
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& '180 deg rotation - cart. axis [1,0,1] ',&
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& '180 deg rotation - cart. axis [-1,0,1] ',&
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& ' 90 deg rotation - cart. axis [0,1,0] ',&
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& ' 90 deg rotation - cart. axis [0,-1,0] ',&
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& '180 deg rotation - cart. axis [0,1,1] ',&
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& '180 deg rotation - cart. axis [0,1,-1] ',&
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& ' 90 deg rotation - cart. axis [-1,0,0] ',&
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& ' 90 deg rotation - cart. axis [1,0,0] ',&
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& '120 deg rotation - cart. axis [-1,-1,1] ',&
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& '120 deg rotation - cart. axis [-1,1,1] ',&
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& '120 deg rotation - cart. axis [-1,-1,1] ',&
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& '120 deg rotation - cart. axis [-1,1,-1] ',&
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& '120 deg rotation - cart. axis [1,1,1] ',&
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& '120 deg rotation - cart. axis [1,-1,1] ',&
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& '120 deg rotation - cart. axis [1,-1,-1] ',&
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& '120 deg rotation - cart. axis [1,1,-1] ',&
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& 'inversion ',&
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& 'inv. 180 deg rotation - cart. axis [0,0,1] ',&
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& 'inv. 180 deg rotation - cart. axis [0,1,0] ',&
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& 'inv. 180 deg rotation - cart. axis [1,0,0] ',&
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& 'inv. 180 deg rotation - cart. axis [1,1,0] ',&
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& 'inv. 180 deg rotation - cart. axis [1,-1,0] ',&
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& 'inv. 90 deg rotation - cart. axis [0,0,-1] ',&
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& 'inv. 90 deg rotation - cart. axis [0,0,1] ',&
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& 'inv. 180 deg rotation - cart. axis [1,0,1] ',&
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& 'inv. 180 deg rotation - cart. axis [-1,0,1] ',&
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& 'inv. 90 deg rotation - cart. axis [0,1,0] ',&
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& 'inv. 90 deg rotation - cart. axis [0,-1,0] ',&
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& 'inv. 180 deg rotation - cart. axis [0,1,1] ',&
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& 'inv. 180 deg rotation - cart. axis [0,1,-1] ',&
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& 'inv. 90 deg rotation - cart. axis [-1,0,0] ',&
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& 'inv. 90 deg rotation - cart. axis [1,0,0] ',&
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& 'inv. 120 deg rotation - cart. axis [-1,-1,1]',&
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& 'inv. 120 deg rotation - cart. axis [-1,1,1] ',&
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& 'inv. 120 deg rotation - cart. axis [-1,-1,1]',&
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& 'inv. 120 deg rotation - cart. axis [-1,1,-1]',&
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& 'inv. 120 deg rotation - cart. axis [1,1,1] ',&
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& 'inv. 120 deg rotation - cart. axis [1,-1,1] ',&
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& 'inv. 120 deg rotation - cart. axis [1,-1,-1]',&
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& 'inv. 120 deg rotation - cart. axis [1,1,-1] ' /
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do jpol = 1,3
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do kpol = 1,3
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overlap(kpol,jpol) = at(1,kpol)*at(1,jpol) +&
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& at(2,kpol)*at(2,jpol) +&
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& at(3,kpol)*at(3,jpol)
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enddo
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enddo
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!
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! then its inverse
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!
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call invmat(overlap,overlap,3)
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nrot = 1
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do irot = 1,24
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!
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! for each possible symmetry
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!
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do jpol = 1,3
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do mpol = 1,3
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!
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! compute, in cartesian coordinates the rotated vector
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!
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rat(mpol) = s(mpol,1,irot)*at(1,jpol) +&
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& s(mpol,2,irot)*at(2,jpol) +&
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& s(mpol,3,irot)*at(3,jpol)
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enddo
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do kpol = 1,3
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!
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! the rotated vector is projected on the direct lattice
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!
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rot(kpol,jpol) = at(1,kpol)*rat(1) +&
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& at(2,kpol)*rat(2) +&
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& at(3,kpol)*rat(3)
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enddo
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enddo
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!
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! and the inverse of the overlap matrix is applied
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!
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do jpol = 1,3
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do kpol = 1,3
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value = overlap(jpol,1)*rot(1,kpol) +&
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& overlap(jpol,2)*rot(2,kpol) +&
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& overlap(jpol,3)*rot(3,kpol)
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if ( abs(float(nint(value))-value).gt.1.0d-8) then
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!
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! if a noninteger is obtained, this implies that this operation
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! is not a symmetry operation for the given lattice
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!
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go to 10
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end if
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is(kpol,jpol,nrot) = nint(value)
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isname(nrot)=sname(irot)
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enddo
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enddo
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nrot = nrot+1
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10 continue
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enddo
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nrot = nrot-1
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!
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! set the inversion symmetry ( Bravais lattices have always inversio
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!
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do irot = 1, nrot
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do kpol = 1,3
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do jpol = 1,3
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is(kpol,jpol,irot+nrot) = -is(kpol,jpol,irot)
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isname(irot+nrot) = sname(irot+24)
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end do
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end do
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end do
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nrot = 2*nrot
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return
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end subroutine cubicsym
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