quantum-espresso/Modules/ws_base.f90

275 lines
8.6 KiB
Fortran

!
! Copyright (C) 2009 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 .
!
MODULE ws_base
!============================================================================
!! Module containing type definitions and auxiliary routines to deal with
!! basic operations on the Wigner-Seitz cell associated to a given set
!! of Bravais fundamental lattice vectors.
!
! It should contain low level routines and no reference to other modules
! (with the possible exception of kinds and parameters) so as to be
! call-able from any other module.
!
! content:
!
! - ws_type : derived type definition used to encoded the auxiliary
! quantities needed by the other WS functions or routines
!
! - ws_init(a,ws)
! : a routine that initializes a ws_type variable
!
! - ws_clear(ws)
! : a routine that un-sets a ws_type variable
!
! - ws_test(ws)
! : a routine that tests whether a ws_type variable has been
! initialized
!
! - ws_vect(r,ws,r_ws)
! : a routine that given a vector returns an equivalent
! vector inside the WS cell
!
! - ws_dist(r,ws)
! : a routine that, given a vector, returns the shortest
! distance from any point in the Bravais lattice
!
! - ws_weight(r,ws)
! : a routine that given a vector
! returns 1.0 if the vector is inside the WS cell
! returns 0.0 if the vector is outside the WS cell
! returns 1/(1+NR) if the vector is on the frontier of the
! WS cell and NR is the number of Bravais
! lattice points whose distance is the same
! as the one from the origin
!
!============================================================================
!
USE kinds, ONLY: DP
!
IMPLICIT NONE
!
TYPE ws_type
!! derived type definition used to encode the auxiliary
!! quantities needed by the other WS functions or routines.
PRIVATE ! this means (I hope) that internal variables can only
! be accessed through calls of routines inside the module.
REAL(DP) :: a(3,3)
!! the fundamental Bravais lattice vectors
REAL(DP) :: aa(3,3)
!! a^T*a
REAL(DP) :: b(3,3)
!! the inverse of a, i.e. the transponse of the fundamental
!! reciprocal lattice vectors
REAL(DP) :: norm_b(3)
!! the norm of the fundamental reciprocal lattice vectors
LOGICAL :: initialized = .FALSE.
!! .TRUE. when initialized
END TYPE ws_type
!
PRIVATE
PUBLIC :: ws_type, ws_init, ws_clean, ws_test, ws_vect, ws_dist, ws_weight, ws_dist_stupid
!
!============================================================================
!
CONTAINS
!---------------------------------------------------------------
SUBROUTINE ws_init(a,ws)
!---------------------------------------------------------------
!! Initializes a \(\texttt{ws_type}\) variable.
!
USE matrix_inversion
REAL(DP), INTENT(IN) :: a(3,3)
TYPE(ws_type), INTENT(OUT) :: ws
INTEGER :: i
!
ws%a = a
CALL invmat( 3, ws%a, ws%b )
ws%aa = MATMUL(TRANSPOSE(a),a)
do i=1,3
ws%norm_b(i) = DSQRT(SUM(ws%b(i,:)*ws%b(i,:)))
end do
ws%initialized = .TRUE.
RETURN
END SUBROUTINE ws_init
!
!---------------------------------------------------------------
SUBROUTINE ws_clean(ws)
!---------------------------------------------------------------
!! Un-sets a \(\texttt{ws_type}\) variable.
!
TYPE(ws_type), INTENT(OUT) :: ws
!
ws%initialized = .FALSE.
!
RETURN
END SUBROUTINE ws_clean
!
!---------------------------------------------------------------
SUBROUTINE ws_test(ws)
!---------------------------------------------------------------
!! Tests whether a ws_type variable has been initialized.
!
TYPE(ws_type), INTENT(IN) :: ws
!
IF (.NOT.ws%initialized) CALL errore &
('ws_test','trying to use an uninitialized ws_type variable',1)
!
RETURN
END SUBROUTINE ws_test
!
!---------------------------------------------------------------
SUBROUTINE ws_vect(r,ws,r_ws)
!---------------------------------------------------------------
!! Given a vector returns an equivalent vector inside the WS cell.
!
REAL(DP), INTENT(IN) :: r(3)
TYPE(ws_type), INTENT(IN) :: ws
REAL(DP), INTENT(OUT) :: r_ws(3)
REAL(DP) :: x(3), y(3), c, ctest
INTEGER :: lb(3), ub(3), i1, i2, i3, m(3)
CALL ws_test(ws)
x = MATMUL(ws%b,r)
x(:) = x(:) - NINT(x(:))
c = SUM(x*MATMUL(ws%aa,x))
m = 0
lb(:) = NINT ( x(:) - DSQRT (c) * ws%norm_b(:) )
! CEILING should be enough for lb but NINT might be safer
ub(:) = NINT ( x(:) + DSQRT (c) * ws%norm_b(:) )
! FLOOR should be enough for ub but NINT might be safer
DO i1 = lb(1), ub(1)
DO i2 = lb(2), ub(2)
DO i3 = lb(3), ub(3)
y = x - (/i1,i2,i3/)
ctest = SUM(y*MATMUL(ws%aa,y))
IF (ctest < c) THEN
c = ctest
m = (/i1,i2,i3/)
END IF
END DO
END DO
END DO
y = x-m
r_ws = MATMUL(ws%a,y)
RETURN
END SUBROUTINE ws_vect
!
!---------------------------------------------------------------
FUNCTION ws_dist_stupid(r,ws)
!---------------------------------------------------------------
!
REAL(DP), INTENT(IN) :: r(3)
TYPE(ws_type), INTENT(IN) :: ws
REAL(DP) :: ws_dist_stupid
REAL(DP) :: r_ws(3)
integer :: i1,i2,i3
real(DP) :: rr, rmin, rtest(3)
CALL ws_test(ws)
rmin = 1.d+9
do i1=-3,3
do i2=-3,3
do i3=-3,3
rtest(:) = r(:) + ws%a(:,1)*i1 + ws%a(:,2)*i2 + ws%a(:,3)*i3
rr = sum(rtest(:)**2)
if (rr < rmin) rmin = rr
end do
end do
end do
ws_dist_stupid = DSQRT(rmin)
RETURN
END FUNCTION ws_dist_stupid
!
!---------------------------------------------------------------
FUNCTION ws_dist(r,ws)
!---------------------------------------------------------------
!! Given a vector, returns the shortest distance from any point
!! in the Bravais lattice.
!
REAL(DP), INTENT(IN) :: r(3)
TYPE(ws_type), INTENT(IN) :: ws
REAL(DP) :: ws_dist
REAL(DP) :: r_ws(3)
CALL ws_test(ws)
CALL ws_vect(r,ws,r_ws)
ws_dist = DSQRT(SUM(r_ws**2))
RETURN
END FUNCTION ws_dist
!
!---------------------------------------------------------------
FUNCTION ws_weight(r,ws)
!---------------------------------------------------------------
!! Given a vector, it returns:
!
!! * 1.0 if the vector is inside the WS cell;
!! * 0.0 if the vector is outside the WS cell;
!! * 1/(1+NR) if the vector is on the frontier of the WS cell
!! and NR is the number of Bravais lattice points whose
!! distance is the same as the one from the origin.
!
REAL(DP), INTENT(IN) :: r(3)
TYPE(ws_type), INTENT(IN) :: ws
REAL(DP) :: ws_weight
REAL(DP) :: x(3), y(3), c, ctest
INTEGER :: lb(3), ub(3), i1, i2, i3, m(3)
REAL(DP), PARAMETER :: eps6 = 1.0E-6_DP
ws_weight = 0.0_DP
CALL ws_test(ws)
x = MATMUL(ws%b,r)
c = SUM(x*MATMUL(ws%aa,x))
lb(:) = NINT ( x(:) - DSQRT (c) * ws%norm_b(:) )
! CEILING should be enough for lb but NINT might be safer
ub(:) = NINT ( x(:) + DSQRT (c) * ws%norm_b(:) )
! FLOOR should be enough for ub but NINT might be safer
DO i1 = lb(1), ub(1)
DO i2 = lb(2), ub(2)
DO i3 = lb(3), ub(3)
y = x - (/i1,i2,i3/)
ctest = SUM(y*MATMUL(ws%aa,y))
IF (ctest < c - eps6 ) THEN
ws_weight = 0.0_DP
RETURN
END IF
IF (ctest < c + eps6 ) THEN
ws_weight = ws_weight + 1.0_DP
END IF
END DO
END DO
END DO
IF (ws_weight == 0.0_DP) CALL errore ('ws_weight','unexpected error',1)
ws_weight = 1.0_dp / ws_weight
RETURN
END FUNCTION ws_weight
!
END MODULE ws_base