mirror of https://gitlab.com/QEF/q-e.git
163 lines
4.1 KiB
Fortran
163 lines
4.1 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 d_matrix (dy1, dy2, dy3)
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!---------------------------------------------------------------
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!
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#include "f_defs.h"
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USE kinds, only: DP
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USE cell_base, ONLY : at, bg
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USE symme, ONLY: nsym, s
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implicit none
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real(kind=DP) :: dy1 (3, 3, 48), dy2 (5, 5, 48), dy3 (7, 7, 48)
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!
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integer, parameter :: maxl = 3, maxm = 2*maxl+1, &
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maxlm = (maxl+1)*(maxl+1)
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! maxl = max value of l allowed
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! maxm = number of m components for l=maxl
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! maxlm= number of l,m spherical harmonics for l <= maxl
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integer :: m, n, ipol, isym
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real(kind=DP) :: ylm(maxm, maxlm), yl1 (3, 3), yl2(5, 5), yl3(7,7), &
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yl1_inv (3, 3), yl2_inv(5, 5), yl3_inv(7, 7), ylms(maxm, maxlm), &
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rl(3,maxm), rrl (maxm), srl(3,maxm), scart (3, 3), delta(7,7), capel
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real(kind=DP), parameter :: eps = 1.0d-9
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real(kind=DP), external :: rndm, DDOT
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!
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! randomly distributed points on a sphere
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!
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do m = 1, maxm
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rl (1, m) = rndm () - 0.5
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rl (2, m) = rndm () - 0.5
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rl (3, m) = rndm () - 0.5
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rrl (m) = rl (1,m)**2 + rl (2,m)**2 + rl (3,m)**2
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enddo
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call ylmr2 ( maxlm, 2*maxl+1, rl, rrl, ylm )
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!
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! invert Yl for each block of definite l (note the transpose operation)
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!
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! l = 1 block
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!
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do m = 1, 3
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do n = 1, 3
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yl1 (m, n) = ylm (n, 1+m)
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end do
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end do
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call invmat (3, yl1, yl1_inv, capel)
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!
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! l = 2 block
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!
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do m = 1, 5
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do n = 1, 5
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yl2 (m, n) = ylm (n, 4+m)
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end do
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end do
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call invmat (5, yl2, yl2_inv, capel)
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!
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! l = 3 block
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!
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do m = 1, 7
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do n = 1, 7
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yl3 (m, n) = ylm (n, 9+m)
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end do
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end do
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call invmat (7, yl3, yl3_inv, capel)
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!
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! now for each symmetry operation of the point-group ...
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!
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do isym = 1, nsym
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!
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! scart = symmetry operation in cartesian axis
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! srl(:,m) = rotated rl(:,m) vectors
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!
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call s_axis_to_cart (s (1, 1, isym), scart, at, bg)
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srl = matmul (scart, rl)
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!
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call ylmr2 ( maxlm, maxm, srl, rrl, ylms )
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!
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! find D_S = Yl_S * Yl_inv (again, beware the transpose)
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!
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! l = 1
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!
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do m = 1, 3
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do n = 1, 3
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yl1 (m, n) = ylms (n, 1+m)
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end do
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end do
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dy1 (:, :, isym) = matmul (yl1(:,:), yl1_inv(:,:))
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!
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! l = 2 block
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!
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do m = 1, 5
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do n = 1, 5
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yl2 (m, n) = ylms (n, 4+m)
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end do
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end do
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dy2 (:, :, isym) = matmul (yl2(:,:), yl2_inv(:,:))
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!
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! l = 3 block
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!
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do m = 1, 7
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do n = 1, 7
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yl3 (m, n) = ylms (n, 9+m)
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end do
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end do
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dy3 (:, :, isym) = matmul (yl3(:,:), yl3_inv(:,:))
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!
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enddo
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!
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! check that D_S matrices are orthogonal as they should if Ylm are
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! correctly defined.
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!
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delta(:,:) = 0.d0
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do m= 1, 7
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delta(m,m) = 1.d0
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end do
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do isym =1,nsym
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!
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! l = 1 block
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!
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capel = 0.d0
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do m = 1, 3
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do n = 1, 3
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capel = capel + &
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( DDOT(3,dy1(1,m,isym),1,dy1(1,n,isym),1) - delta(m,n) )**2
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end do
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end do
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if (capel.gt.eps) call errore ('d_matrix', &
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'D_S (l=1) for this symmetry operation is not orthogonal',isym)
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!
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! l = 2 block
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!
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capel = 0.d0
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do m = 1, 5
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do n = 1, 5
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capel = capel + &
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( DDOT(5,dy2(1,m,isym),1,dy2(1,n,isym),1) - delta(m,n) )**2
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end do
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end do
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if (capel.gt.eps) call errore ('d_matrix', &
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'D_S (l=2) for this symmetry operation is not orthogonal',isym)
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!
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! l = 3 block
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!
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capel = 0.d0
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do m = 1, 7
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do n = 1, 7
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capel = capel + &
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( DDOT(7,dy3(1,m,isym),1,dy3(1,n,isym),1) - delta(m,n) )**2
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end do
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end do
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if (capel.gt.eps) call errore ('d_matrix', &
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'D_S (l=3) for this symmetry operation is not orthogonal',isym)
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!
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end do
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return
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end subroutine d_matrix
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