!-*- mode: F90 -*-!
!------------------------------------------------------------!
! Copyright (C) 2026 Wannier Developer Group !
! !
! This library is free software; you can redistribute it !
! and/or modify it under the terms of the GNU Lesser General !
! Public License as published by the Free Software !
! Foundation; either version 2.1 of the License, or (at your !
! option) any later version. !
! !
! This library is distributed in the hope that it will be !
! useful,but WITHOUT ANY WARRANTY; without even the implied !
! warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR !
! PURPOSE. See the GNU Lesser General Public License for !
! more details. !
! !
! You should have received a copy of the GNU Lesser General !
! Public License along with this library; if not, see !
! <https://www.gnu.org/licenses/>. !
! !
! The webpage of the Wannier90 code is !
! <https://www.wannier.org>. !
! !
! The Wannier90 code is hosted on GitHub !
! <https://github.com/wannier-developers/wannier90> !
!------------------------------------------------------------!
! !
! w90_kmesh: operations on BZ mesh !
! !
!------------------------------------------------------------!
module w90_kmesh
!! Routines to analyse the regular k-point mesh
!! and determine the overlaps neccessary for a finite
!! difference representation of the spread operator.
!! These overlaps are defined by a set of vectors (b-vectors) which
!! connect the Bloch states.
!! See Eq. B1 in Appendix B of Marzari and
!! Vanderbilt PRB 56 12847 (1997)
use w90_constants, only: dp
use w90_types, only: max_shells, num_nnmax ! used for dimensioning
use w90_error, only: w90_error_type, set_error_alloc, set_error_dealloc, set_error_fatal, &
set_error_input, set_error_file
use w90_comms, only: w90_comm_type
implicit none
private
! Definitions of system variables set in this module
! nnh ! the number of b-directions (bka)
! nntot ! total number of neighbours for each k-point
! nnlist ! list of neighbours for each k-point
! neigh
! nncell ! gives BZ of each neighbour of each k-point
! wbtot
! wb ! weights associated with neighbours of each k-point
! bk ! the b-vectors that go from each k-point to its neighbours
! bka ! the b-directions (not considering inversion) from
! 1st k-point to its neighbours
public :: kmesh_dealloc
public :: kmesh_get
public :: kmesh_write
integer, parameter :: nsupcell = 5
!! Size of supercell (of recip cell) in which to search for k-point shells
contains
!================================================
subroutine kmesh_get(kmesh_input, kmesh_info, print_output, kpt_latt, real_lattice, num_kpts, &
gamma_only, seedname, stdout, timer, error, comm)
!================================================
!
!! Main routine to calculate the b-vectors
!
!================================================
use w90_utility, only: utility_compar, utility_recip_lattice, utility_frac_to_cart, &
utility_cart_to_frac, utility_inverse_mat
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: kmesh_info_type, kmesh_input_type, print_output_type, timer_list_type
implicit none
! arguments
type(print_output_type), intent(in) :: print_output
type(kmesh_info_type), intent(inout) :: kmesh_info
type(kmesh_input_type), intent(inout) :: kmesh_input
type(timer_list_type), intent(inout) :: timer
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
character(len=*), intent(in) :: seedname
integer, intent(in) :: num_kpts
integer, intent(in) :: stdout
real(kind=dp), intent(in) :: real_lattice(3, 3)
real(kind=dp), intent(in) :: kpt_latt(:, :)
logical, intent(in) :: gamma_only
! local variables
real(kind=dp), allocatable :: bvec_tmp(:, :), bvec_inp(:, :, :) ! bvec_inp is allocated in kmesh_shell_from_file()
real(kind=dp), allocatable :: kpt_cart(:, :)
real(kind=dp), allocatable :: bk_local(:, :, :)
real(kind=dp), parameter :: eta = 99999999.0_dp ! eta = very large
real(kind=dp) :: dist, dnn0, dnn1, bb1, bbn, ddelta
real(kind=dp) :: dnn(max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n))
real(kind=dp) :: recip_lattice(3, 3), volume
real(kind=dp) :: vkpp(3), vkpp2(3), kpbvec(3)
integer :: bnum, nbvec ! context of kmesh_input%kmesh_shell_from_file
! higher-order finite-difference
integer, allocatable :: lmn(:, :) ! Order in which to search the cells (ordered in dist from origin)
integer, allocatable :: nnlist_tmp(:, :), nncell_tmp(:, :, :) ![ysl]
integer, allocatable :: nnshell(:, :)
integer :: ifound, counter, na, nap, loop_s, loop_b, shell !, nbvec, bnum
integer :: ifpos, ifneg, ierr, multi(max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n))
integer :: nlist, nkp, nkp2, l, m, n, ndnn, ndnnx, ndnntot
integer :: nnsh, nn, nnx, loop, i, j
integer :: num_first_shells, ndnn2, nnx2, multi_cumulative, lmn_temp(3)
integer :: num_x((1 + kmesh_input%higher_order_n)*(1 + 2*kmesh_input%higher_order_n))
integer :: num_y((1 + kmesh_input%higher_order_n)*(1 + 2*kmesh_input%higher_order_n))
integer :: num_z((1 + kmesh_input%higher_order_n)*(1 + 2*kmesh_input%higher_order_n))
real(kind=dp) :: bk_latt(3), inv_lattice(3, 3)
real(kind=dp) :: bweight(kmesh_input%max_shells_h)
real(kind=dp) :: wb_local(kmesh_input%num_nnmax_h)
if (print_output%timing_level > 0) call io_stopwatch_start('kmesh: get', timer)
allocate (bk_local(3, kmesh_input%num_nnmax_h, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating bk_local in kmesh_get', comm)
return
end if
allocate (lmn(3, (2*kmesh_input%search_supcell_size + 1)**3), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating lmn in kmesh_get', comm)
return
end if
allocate (nnshell(num_kpts, max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n)), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nnshell in kmesh_get', comm)
return
end if
call utility_recip_lattice(real_lattice, recip_lattice, volume, error, comm)
if (allocated(error)) return
call utility_inverse_mat(recip_lattice, inv_lattice)
if (print_output%iprint > 0) write (stdout, '(/1x,a)') &
'*---------------------------------- K-MESH ----------------------------------*'
! Sort the cell neighbours so we loop in order of distance from the home shell
call kmesh_supercell_sort(print_output, recip_lattice, lmn, timer)
allocate (kpt_cart(3, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating kpt_cart in kmesh_get', comm)
return
end if
do nkp = 1, num_kpts
call utility_frac_to_cart(kpt_latt(:, nkp), kpt_cart(:, nkp), recip_lattice)
end do
! find the distance between k-point 1 and its nearest-neighbour shells
! if we have only one k-point, the n-neighbours are its periodic images
dnn0 = 0.0_dp
dnn1 = eta
ndnntot = 0
do nlist = 1, kmesh_input%search_shells
do nkp = 1, num_kpts
do loop = 1, (2*kmesh_input%search_supcell_size + 1)**3
l = lmn(1, loop); m = lmn(2, loop); n = lmn(3, loop)
!
vkpp = kpt_cart(:, nkp) + matmul(lmn(:, loop), recip_lattice)
dist = sqrt((kpt_cart(1, 1) - vkpp(1))**2 &
+ (kpt_cart(2, 1) - vkpp(2))**2 + (kpt_cart(3, 1) - vkpp(3))**2)
if ((dist .gt. kmesh_input%tol) .and. (dist .gt. dnn0 + kmesh_input%tol)) then
if (dist .lt. dnn1 - kmesh_input%tol) then
dnn1 = dist ! found a closer shell
counter = 0
end if
if (dist .gt. (dnn1 - kmesh_input%tol) .and. dist .lt. (dnn1 + kmesh_input%tol)) then
counter = counter + 1 ! count the multiplicity of the shell
end if
end if
end do
end do
if (dnn1 .lt. eta - kmesh_input%tol) ndnntot = ndnntot + 1
dnn(nlist) = dnn1
multi(nlist) = counter
dnn0 = dnn1
dnn1 = eta
end do
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '+----------------------------------------------------------------------------+'
write (stdout, '(1x,a)') '| Distance to Nearest-Neighbour Shells |'
write (stdout, '(1x,a)') '| ------------------------------------ |'
if (trim(print_output%length_unit) == 'Ang') then
write (stdout, '(1x,a)') '| Shell Distance (Ang^-1) Multiplicity |'
write (stdout, '(1x,a)') '| ----- ----------------- ------------ |'
else
write (stdout, '(1x,a)') '| Shell Distance (Bohr^-1) Multiplicity |'
write (stdout, '(1x,a)') '| ----- ------------------ ------------ |'
end if
do ndnn = 1, ndnntot
write (stdout, '(1x,a,11x,i3,17x,f10.6,19x,i4,12x,a)') '|', ndnn, &
dnn(ndnn)/print_output%lenconfac, multi(ndnn), '|'
end do
write (stdout, '(1x,a)') '+----------------------------------------------------------------------------+'
end if
if (print_output%iprint >= 4) then
! Write out all the bvectors
if (print_output%iprint > 0) then
write (stdout, '(1x,"|",76(" "),"|")')
write (stdout, '(1x,a)') '| Complete list of b-vectors and their lengths |'
write (stdout, '(1x,"|",76(" "),"|")')
write (stdout, '(1x,"+",76("-"),"+")')
end if
allocate (bvec_tmp(3, maxval(multi)), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvec_tmp in kmesh_get', comm)
return
end if
bvec_tmp = 0.0_dp
counter = 0
do shell = 1, kmesh_input%search_shells
call kmesh_get_bvectors(kmesh_input, print_output, bvec_tmp(:, 1:multi(shell)), kpt_cart, &
recip_lattice, dnn(shell), lmn, 1, multi(shell), num_kpts, &
timer, error, comm)
if (allocated(error)) return
do loop = 1, multi(shell)
counter = counter + 1
if (print_output%iprint > 0) write (stdout, '(a,I4,1x,a,2x,3f12.6,2x,a,2x,f12.6,a)') ' | b-vector ', counter, ': (', &
bvec_tmp(:, loop)/print_output%lenconfac, ')', dnn(shell)/print_output%lenconfac, ' |'
end do
end do
deallocate (bvec_tmp, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating bvec_tmp in kmesh_get', comm)
return
end if
if (print_output%iprint > 0) write (stdout, '(1x,"|",76(" "),"|")')
if (print_output%iprint > 0) write (stdout, '(1x,"+",76("-"),"+")')
end if
! Get the shell weights to satisfy the B1 condition
if (kmesh_input%kmesh_shell_from_file) then
! note: B1 condition is not tested in kmesh_shell_from_file(); test occurs below
call kmesh_shell_from_file(kmesh_input, print_output, bvec_inp, bweight, dnn, kpt_cart, &
recip_lattice, lmn, multi, num_kpts, seedname, stdout, timer, &
error, comm)
if (allocated(error)) return
elseif (kmesh_input%num_shells == 0) then
call kmesh_shell_automatic(kmesh_input, print_output, bweight, dnn, kpt_cart, recip_lattice, &
lmn, multi, num_kpts, stdout, timer, error, comm)
if (allocated(error)) return
elseif (kmesh_input%num_shells > 0) then
call kmesh_shell_fixed(kmesh_input, print_output, bweight, dnn, kpt_cart, recip_lattice, &
lmn, multi, num_kpts, stdout, timer, error, comm)
if (allocated(error)) return
end if
num_first_shells = kmesh_input%num_shells ! for convenience in printout error
if (print_output%iprint > 0) then
if (kmesh_input%higher_order_nearest_shells) then
write (stdout, '(1x,a)', advance='no') '| The following shells and their multiples are used: '
else
write (stdout, '(1x,a)', advance='no') '| The following shells are used: '
end if
do ndnn = 1, kmesh_input%num_shells
if (ndnn .eq. kmesh_input%num_shells) then
write (stdout, '(i3,1x)', advance='no') kmesh_input%shell_list(ndnn)
else
write (stdout, '(i3,",")', advance='no') kmesh_input%shell_list(ndnn)
end if
end do
do l = 1, 6 - kmesh_input%num_shells
write (stdout, '(4x)', advance='no')
end do
if (kmesh_input%higher_order_nearest_shells) then
write (stdout, '(20x)', advance='no')
end if
write (stdout, '("|")')
end if
kmesh_info%nntot = 0
do loop_s = 1, kmesh_input%num_shells
kmesh_info%nntot = kmesh_info%nntot + multi(kmesh_input%shell_list(loop_s))
end do
if (kmesh_info%nntot > kmesh_input%num_nnmax_h) then
if (print_output%iprint > 0) then
write (stdout, '(a,i2,a)') ' **WARNING: kmesh has found >', kmesh_input%num_nnmax_h, ' nearest neighbours**'
write (stdout, '(a)') ' '
write (stdout, '(a)') ' This is probably caused by an error in your unit cell specification'
write (stdout, '(a)') ' '
write (stdout, '(a)') ' If you think this is not the problem; please send your *.win file to the '
write (stdout, '(a)') ' wannier90 developers'
write (stdout, '(a)') ' '
write (stdout, '(a)') ' The problem may be caused by having accidentally degenerate shells of '
write (stdout, '(a)') ' kpoints. The solution is then to rerun wannier90 specifying the b-vectors '
write (stdout, '(a)') ' in each shell. Give kmesh_shell_from_file=T in the *.win file'
write (stdout, '(a)') ' and create a *.kshell file:'
write (stdout, '(a)') ' '
write (stdout, '(a)') ' $> cat hexagonal.kshell'
write (stdout, '(a)') ' $> 1 2'
write (stdout, '(a)') ' $> 5 6 7 8'
write (stdout, '(a)') ' '
write (stdout, '(a)') ' Where each line is a new shell (so num_shells in total)'
write (stdout, '(a)') ' The elements are the bvectors labelled according to the following '
write (stdout, '(a)') ' list (last column is distance)'
write (stdout, '(a)') ' '
end if
allocate (bvec_tmp(3, maxval(multi)), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvec_tmp in kmesh_get', comm)
return
end if
bvec_tmp = 0.0_dp
counter = 0
do shell = 1, kmesh_input%search_shells
call kmesh_get_bvectors(kmesh_input, print_output, bvec_tmp(:, 1:multi(shell)), kpt_cart, &
recip_lattice, dnn(shell), lmn, 1, multi(shell), num_kpts, timer, &
error, comm)
if (allocated(error)) return
do loop = 1, multi(shell)
counter = counter + 1
if (print_output%iprint > 0) write (stdout, '(a,I4,1x,a,2x,3f12.6,2x,a,2x,f12.6,a)') ' | b-vector ', counter, ': (', &
bvec_tmp(:, loop)/print_output%lenconfac, ')', dnn(shell)/print_output%lenconfac, ' |'
end do
end do
if (print_output%iprint > 0) write (stdout, '(a)') ' '
deallocate (bvec_tmp, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating bvec_tmp in kmesh_get', comm)
return
end if
call set_error_fatal(error, 'kmesh_get: something wrong, found too many nearest neighbours', comm)
return
end if
! higher-order algorithm: include 2b, 3b, ..., Nb shells, and modify bweights
if (kmesh_input%higher_order_nearest_shells) then
if (print_output%iprint > 0) write (stdout, '(a)') &
' | WARNING: higher_order_nearest_shells is an experimental feature, and has |', &
' | not been extensively tested. |'
else
kmesh_info%nntot = kmesh_info%nntot*kmesh_input%higher_order_n
end if
allocate (kmesh_info%nnlist(num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nnlist in kmesh_get', comm)
return
end if
allocate (kmesh_info%neigh(num_kpts, kmesh_info%nntot/2), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating neigh in kmesh_get', comm)
return
end if
allocate (kmesh_info%nncell(3, num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nncell in kmesh_get', comm)
return
end if
allocate (kmesh_info%wb(kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating wb in kmesh_get', comm)
return
end if
allocate (kmesh_info%bka(3, kmesh_info%nntot/2), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating bka in kmesh_get', comm)
return
end if
allocate (kmesh_info%bk(3, kmesh_info%nntot, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating bk in kmesh_get', comm)
return
end if
nnx = 0
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
nnx = nnx + 1
wb_local(nnx) = bweight(loop_s)
end do
end do
! Now build up the list of nearest-neighbour shells for each k-point.
! nnlist(nkp,1...nnx) points to the nnx neighbours (ordered along increa
! shells) of the k-point nkp. nncell(i,nkp,nnth) tells us in which BZ is
! nnth nearest-neighbour of the k-point nkp. Construct the nnx b-vectors
! go from k-point nkp to each neighbour bk(1:3,nkp,1...nnx).
! Comment: Now we have bk(3,nntot,num_kps) 09/04/2006
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '+----------------------------------------------------------------------------+'
write (stdout, '(1x,a)') '| Shell # Nearest-Neighbours |'
write (stdout, '(1x,a)') '| ----- -------------------- |'
end if
!if (index(print_output%devel_flag, 'kmesh_degen') == 0) then
!
! Standard routine
!
nnshell = 0
do nkp = 1, num_kpts
nnx = 0
ok: do ndnnx = 1, kmesh_input%num_shells
ndnn = kmesh_input%shell_list(ndnnx)
do loop = 1, (2*kmesh_input%search_supcell_size + 1)**3
l = lmn(1, loop); m = lmn(2, loop); n = lmn(3, loop)
vkpp2 = matmul(lmn(:, loop), recip_lattice)
do nkp2 = 1, num_kpts
vkpp = vkpp2 + kpt_cart(:, nkp2)
dist = sqrt((kpt_cart(1, nkp) - vkpp(1))**2 &
+ (kpt_cart(2, nkp) - vkpp(2))**2 + (kpt_cart(3, nkp) - vkpp(3))**2)
if ((dist .ge. dnn(ndnn) - kmesh_input%tol) .and. (dist .le. dnn(ndnn) + kmesh_input%tol)) then
nnx = nnx + 1
nnshell(nkp, ndnn) = nnshell(nkp, ndnn) + 1
kmesh_info%nnlist(nkp, nnx) = nkp2
kmesh_info%nncell(1, nkp, nnx) = l
kmesh_info%nncell(2, nkp, nnx) = m
kmesh_info%nncell(3, nkp, nnx) = n
bk_local(:, nnx, nkp) = vkpp(:) - kpt_cart(:, nkp)
end if
!if we have the right number of neighbours we can exit
if (nnshell(nkp, ndnn) == multi(ndnn)) cycle ok
end do
end do
! check to see if too few neighbours here
end do ok
end do
! higher-order algorithm: include 2b, 3b, ..., Nb shells, and modify bweights
if (.not. kmesh_input%higher_order_nearest_shells) then
! update num_shells, shell_list, dnn(distance to shells), multi, etc.
call kmesh_shell_reconstruct(kmesh_input, num_kpts, multi, dnn, nnshell, bweight)
! update bk_local
! update nnlist(neighboring kpts), and nncell(G_lmn vectors of neighbors)
do nkp = 1, num_kpts
do nn = 2, kmesh_input%higher_order_n
multi_cumulative = 0
do ndnn = 1, kmesh_input%num_shells/kmesh_input%higher_order_n !first-order shells
! ndnn: index of shells (first order)
! ndnn2: index of shells (nn-th-order)
ndnn2 = (nn - 1)*kmesh_input%num_shells/kmesh_input%higher_order_n + ndnn
do nnx = 1 + multi_cumulative, multi(ndnn) + multi_cumulative
counter = 0
! nnx: index of bvectors (first order)
! nnx2: index of bvectors (nn-th-order)
nnx2 = (nn - 1)*kmesh_info%nntot/kmesh_input%higher_order_n + nnx
bk_local(:, nnx2, nkp) = nn*bk_local(:, nnx, nkp)
! find nnlist and nncell
!do loop = 1, (2*kmesh_input%search_supcell_size + 1)**3
! l = lmn(1, loop); m = lmn(2, loop); n = lmn(3, loop)
! vkpp2 = matmul(lmn(:, loop), recip_lattice) !G_lmn vector
! do nkp2 = 1, num_kpts
! vkpp = vkpp2 + kpt_cart(:, nkp2) - kpt_cart(:, nkp)
! ! if kp2 - kp1 == bk_local(:, nnx2, :)
! call utility_compar(vkpp(1), bk_local(1, nnx2, nkp), ifpos, ifneg)
! if (ifpos .eq. 1) then
! counter = counter + 1
! kmesh_info%nnlist(nkp, nnx2) = nkp2
! kmesh_info%nncell(1, nkp, nnx2) = l
! kmesh_info%nncell(2, nkp, nnx2) = m
! kmesh_info%nncell(3, nkp, nnx2) = n
! endif
! enddo
!enddo
! do not search supcell
! find nnlist(nkp2) and nncell(lmn)
call utility_cart_to_frac(bk_local(:, nnx2, nkp), bk_latt, inv_lattice)
lmn_temp(1) = floor(kpt_latt(1, nkp) + bk_latt(1) + 1.e-6_dp) ! e.g. 3.999999999 is 4
lmn_temp(2) = floor(kpt_latt(2, nkp) + bk_latt(2) + 1.e-6_dp)
lmn_temp(3) = floor(kpt_latt(3, nkp) + bk_latt(3) + 1.e-6_dp)
vkpp2 = matmul(lmn_temp, recip_lattice) !G_lmn vector
vkpp = kpt_cart(:, nkp) + bk_local(:, nnx2, nkp) - vkpp2 ! k_2 = k_1 + Nb - G_lmn
do nkp2 = 1, num_kpts
call utility_compar(kpt_cart(:, nkp2), vkpp, ifpos, ifneg)
if (ifpos .eq. 1) then
counter = counter + 1
kmesh_info%nnlist(nkp, nnx2) = nkp2
kmesh_info%nncell(1, nkp, nnx2) = lmn_temp(1)
kmesh_info%nncell(2, nkp, nnx2) = lmn_temp(2)
kmesh_info%nncell(3, nkp, nnx2) = lmn_temp(3)
end if
end do
if (counter == 0) then
call set_error_fatal(error, 'Could not find Nb vectors in kmesh_get', comm)
end if
if (counter >= 2) then
call set_error_fatal(error, 'Error in kmesh_get, try to modify tolerance in utility_compar', comm)
end if
end do
multi_cumulative = multi_cumulative + multi(ndnn)
end do
end do
end do
end if
nnx = 0
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
nnx = nnx + 1
wb_local(nnx) = bweight(loop_s)
end do
end do
if (kmesh_input%kmesh_shell_from_file) then
! should this be moved to the kmesh_shell_from_file as a function to simplify?
nnshell = 0
do nkp = 1, num_kpts
nnx = 0
ok2: do loop = 1, (2*kmesh_input%search_supcell_size + 1)**3
l = lmn(1, loop); m = lmn(2, loop); n = lmn(3, loop)
vkpp2 = matmul(lmn(:, loop), recip_lattice)
do nkp2 = 1, num_kpts
vkpp = vkpp2 + kpt_cart(:, nkp2)
bnum = 0
do ndnnx = 1, kmesh_input%num_shells
do nbvec = 1, multi(ndnnx)
bnum = bnum + 1
kpbvec = kpt_cart(:, nkp) + bvec_inp(:, nbvec, ndnnx)
dist = sqrt((kpbvec(1) - vkpp(1))**2 &
+ (kpbvec(2) - vkpp(2))**2 + (kpbvec(3) - vkpp(3))**2)
if (abs(dist) < kmesh_input%tol) then
nnx = nnx + 1
nnshell(nkp, ndnnx) = nnshell(nkp, ndnnx) + 1
kmesh_info%nnlist(nkp, bnum) = nkp2
kmesh_info%nncell(1, nkp, bnum) = l
kmesh_info%nncell(2, nkp, bnum) = m
kmesh_info%nncell(3, nkp, bnum) = n
bk_local(:, bnum, nkp) = bvec_inp(:, nbvec, ndnnx)
end if
end do
end do
if (nnx == sum(multi)) exit ok2
end do
end do ok2
end do
end if ! kmesh_shell_from_file
if (kmesh_input%higher_order_n .eq. 1 .or. kmesh_input%higher_order_nearest_shells) then
do ndnnx = 1, kmesh_input%num_shells
ndnn = kmesh_input%shell_list(ndnnx)
if (print_output%iprint > 0) then
write (stdout, '(1x,a,24x,i3,13x,i3,33x,a)') '|', ndnn, nnshell(1, ndnn), '|'
end if
end do
else
do ndnnx = 1, num_first_shells
ndnn = kmesh_input%shell_list(ndnnx)
if (print_output%iprint > 0) then
write (stdout, '(1x,a,24x,i3,13x,i3,33x,a)') '|', ndnn, nnshell(1, ndnn), '|'
end if
end do
do i = 2, kmesh_input%higher_order_n
do ndnnx = 1, num_first_shells
ndnn = kmesh_input%shell_list(ndnnx)
if (print_output%iprint > 0) then
write (stdout, '(1x,a,20x,i3,a,i2,13x,i3,33x,a)') '|', i, ' x', ndnn, nnshell(1, ndnn), '|'
end if
end do
end do
end if
if (print_output%iprint > 0) write (stdout, '(1x,"+",76("-"),"+")')
do nkp = 1, num_kpts
nnx = 0
do ndnnx = 1, kmesh_input%num_shells
ndnn = kmesh_input%shell_list(ndnnx)
do nnsh = 1, nnshell(nkp, ndnn)
bb1 = 0.0_dp
bbn = 0.0_dp
nnx = nnx + 1
do i = 1, 3
bb1 = bb1 + bk_local(i, nnx, 1)*bk_local(i, nnx, 1)
bbn = bbn + bk_local(i, nnx, nkp)*bk_local(i, nnx, nkp)
end do
if (abs(sqrt(bb1) - sqrt(bbn)) .gt. kmesh_input%tol) then
if (print_output%iprint > 0) write (stdout, '(1x,2f10.6)') bb1, bbn
call set_error_fatal(error, 'Non-symmetric k-point neighbours in kmesh_get', comm)
return
end if
end do
end do
end do
! now check that the completeness relation is satisfied for every kpoint
! We know it is true for kpt=1; but we check the rest to be safe.
! Eq. B1 in Appendix B PRB 56 12847 (1997)
if ((.not. kmesh_input%skip_B1_tests) .and. kmesh_input%higher_order_nearest_shells) then
do nkp = 1, num_kpts
do i = 1, kmesh_input%higher_order_n
if ((.not. kmesh_input%higher_order_nearest_shells) .and. i > 1) exit
do j = 1, (1 + i)*(1 + 2*i) ! multiset coefficient ((3, 2i)) = (1 + i)*(1 + 2*i), 3: x,y,z, 2i: num. of b
! separate cartesian components
! e.g. for i=1
! j=1: num_x=2, num_y=0, num_z=0
! j=2: num_x=1, num_y=1, num_z=0
! j=3: num_x=0, num_y=2, num_z=0
! j=4: num_x=1, num_y=0, num_z=1
! j=5: num_x=0, num_y=1, num_z=1
! j=6: num_x=0, num_y=0, num_z=2
do l = 0, 2*i
if ((2*i + 1)*l - l*(l - 1)/2 <= j - 1 &
.and. (2*i + 1)*(l + 1) - (l + 1)*l/2 > j - 1) then
num_z(j) = l
exit
end if
end do
num_y(j) = j - 1 - ((2*i + 1)*num_z(j) - num_z(j)*(num_z(j) - 1)/2)
num_x(j) = 2*i - num_y(j) - num_z(j)
ddelta = 0.0_dp
nnx = 0
do ndnnx = 1, kmesh_input%num_shells
ndnn = kmesh_input%shell_list(ndnnx)
do nnsh = 1, nnshell(1, ndnn)
nnx = nnx + 1
ddelta = ddelta + wb_local(nnx)*(bk_local(1, nnx, nkp)**num_x(j)) &
*(bk_local(2, nnx, nkp)**num_y(j))*(bk_local(3, nnx, nkp)**num_z(j))
end do
end do
if (i .eq. 1 .and. (j .eq. 1 .or. j .eq. 3 .or. j .eq. 6)) then
if (abs(ddelta - 1.0_dp) .gt. kmesh_input%tol) then
if (print_output%iprint > 0) write (stdout, '(1x,3i3,f12.8)') num_x(j), num_y(j), num_z(j), ddelta
call set_error_fatal(error, 'Eq. (B1) not satisfied in kmesh_get (1)', comm)
end if
else
if (abs(ddelta) .gt. kmesh_input%tol) then
if (print_output%iprint > 0) write (stdout, '(1x,3i3,f12.8)') num_x(j), num_y(j), num_z(j), ddelta
call set_error_fatal(error, 'Eq. (B1) not satisfied in kmesh_get (2)', comm)
end if
end if
end do
end do
end do
end if
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '| Completeness relation is fully satisfied [Eq. (B1), PRB 56, 12847 (1997)] |'
if ((kmesh_input%higher_order_nearest_shells) .and. (kmesh_input%higher_order_n .gt. 1)) then
write (stdout, '(1x,a)') '| Completeness relations for higher-order are fully satisfied |'
end if
write (stdout, '(1x,"+",76("-"),"+")')
end if
kmesh_info%wbtot = 0.0_dp
nnx = 0
do ndnnx = 1, kmesh_input%num_shells
ndnn = kmesh_input%shell_list(ndnnx)
do nnsh = 1, nnshell(1, ndnn)
nnx = nnx + 1
kmesh_info%wbtot = kmesh_info%wbtot + wb_local(nnx)
end do
end do
kmesh_info%nnh = kmesh_info%nntot/2
! make list of bka vectors from neighbours of first k-point
! delete any inverse vectors as you collect them
na = 0
do nn = 1, kmesh_info%nntot
ifound = 0
if (na .ne. 0) then
do nap = 1, na
call utility_compar(kmesh_info%bka(1, nap), bk_local(1, nn, 1), ifpos, ifneg)
if (ifneg .eq. 1) ifound = 1
end do
end if
if (ifound .eq. 0) then
! found new vector to add to set
na = na + 1
kmesh_info%bka(1, na) = bk_local(1, nn, 1)
kmesh_info%bka(2, na) = bk_local(2, nn, 1)
kmesh_info%bka(3, na) = bk_local(3, nn, 1)
end if
end do
if (na .ne. kmesh_info%nnh) then
call set_error_fatal(error, 'Did not find right number of bk directions kmesh_get', comm)
return
end if
if (print_output%iprint > 0) then
if (trim(print_output%length_unit) == 'Ang') then
write (stdout, '(1x,a)') '| b_k Vectors (Ang^-1) and Weights (Ang^2) |'
write (stdout, '(1x,a)') '| ---------------------------------------- |'
else
write (stdout, '(1x,a)') '| b_k Vectors (Bohr^-1) and Weights (Bohr^2) |'
write (stdout, '(1x,a)') '| ------------------------------------------ |'
end if
write (stdout, '(1x,a)') '| No. b_k(x) b_k(y) b_k(z) w_b |'
write (stdout, '(1x,a)') '| --- -------------------------------- -------- |'
do i = 1, kmesh_info%nntot
write (stdout, '(1x,"|",11x,i3,5x,3f12.6,3x,f10.6,8x,"|")') &
i, (bk_local(j, i, 1)/print_output%lenconfac, j=1, 3), wb_local(i)*print_output%lenconfac**2
end do
write (stdout, '(1x,"+",76("-"),"+")')
if (trim(print_output%length_unit) == 'Ang') then
write (stdout, '(1x,a)') '| b_k Directions (Ang^-1) |'
write (stdout, '(1x,a)') '| ----------------------- |'
else
write (stdout, '(1x,a)') '| b_k Directions (Bohr^-1) |'
write (stdout, '(1x,a)') '| ------------------------ |'
end if
write (stdout, '(1x,a)') '| No. x y z |'
write (stdout, '(1x,a)') '| --- -------------------------------- |'
do i = 1, kmesh_info%nnh
write (stdout, '(1x,"|",11x,i3,5x,3f12.6,21x,"|")') i, (kmesh_info%bka(j, i)/print_output%lenconfac, j=1, 3)
end do
write (stdout, '(1x,"+",76("-"),"+")')
write (stdout, *) ' '
end if
! find index array
do nkp = 1, num_kpts
do na = 1, kmesh_info%nnh
! first, zero the index array so we can check it gets filled
kmesh_info%neigh(nkp, na) = 0
! now search through list of neighbours of this k-point
do nn = 1, kmesh_info%nntot
call utility_compar(kmesh_info%bka(1, na), bk_local(1, nn, nkp), ifpos, ifneg)
if (ifpos .eq. 1) kmesh_info%neigh(nkp, na) = nn
end do
! check found
if (kmesh_info%neigh(nkp, na) .eq. 0) then
if (print_output%iprint > 0) write (stdout, *) ' nkp,na=', nkp, na
call set_error_fatal(error, 'kmesh_get: failed to find neighbours for this kpoint', comm)
return
end if
end do
end do
!fill in the global arrays from the local ones
do loop = 1, kmesh_info%nntot
kmesh_info%wb(loop) = wb_local(loop)
end do
do loop_s = 1, num_kpts
do loop = 1, kmesh_info%nntot
kmesh_info%bk(:, loop, loop_s) = bk_local(:, loop, loop_s)
end do
end do
![ysl-b]
if (gamma_only) then
! use half of the b-vectors
if (num_kpts .ne. 1) then
call set_error_input(error, 'Error in kmesh_get: wrong choice of gamma_only option', comm)
return
end if
! reassign nnlist, nncell, wb, bk
allocate (nnlist_tmp(num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nnlist_tmp in kmesh_get', comm)
return
end if
allocate (nncell_tmp(3, num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nncell_tmp in kmesh_get', comm)
return
end if
nnlist_tmp(:, :) = kmesh_info%nnlist(:, :)
nncell_tmp(:, :, :) = kmesh_info%nncell(:, :, :)
deallocate (kmesh_info%nnlist, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nnlist in kmesh_get', comm)
return
end if
deallocate (kmesh_info%nncell, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nncell in kmesh_get', comm)
return
end if
deallocate (kmesh_info%wb, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating wb in kmesh_get', comm)
return
end if
deallocate (kmesh_info%bk, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating bk in kmesh_get', comm)
return
end if
kmesh_info%nntot = kmesh_info%nntot/2
allocate (kmesh_info%nnlist(num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nnlist in kmesh_get', comm)
return
end if
allocate (kmesh_info%nncell(3, num_kpts, kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating nncell in kmesh_get', comm)
return
end if
allocate (kmesh_info%wb(kmesh_info%nntot), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating wb in kmesh_get', comm)
return
end if
allocate (kmesh_info%bk(3, kmesh_info%nntot, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating bk in kmesh_get', comm)
return
end if
na = 0
do nn = 1, 2*kmesh_info%nntot
ifound = 0
if (na .ne. 0) then
do nap = 1, na
call utility_compar(kmesh_info%bk(1, nap, 1), bk_local(1, nn, 1), ifpos, ifneg)
if (ifneg .eq. 1) ifound = 1
end do
end if
if (ifound .eq. 0) then
! found new vector to add to set
na = na + 1
kmesh_info%bk(1, na, 1) = bk_local(1, nn, 1)
kmesh_info%bk(2, na, 1) = bk_local(2, nn, 1)
kmesh_info%bk(3, na, 1) = bk_local(3, nn, 1)
kmesh_info%wb(na) = 2.0_dp*wb_local(nn)
kmesh_info%nnlist(1, na) = nnlist_tmp(1, nn)
kmesh_info%nncell(1, 1, na) = nncell_tmp(1, 1, nn)
kmesh_info%nncell(2, 1, na) = nncell_tmp(2, 1, nn)
kmesh_info%nncell(3, 1, na) = nncell_tmp(3, 1, nn)
kmesh_info%neigh(1, na) = na
! check bk.eq.bka
call utility_compar(kmesh_info%bk(1, na, 1), kmesh_info%bka(1, na), ifpos, ifneg)
if (ifpos .ne. 1) then
call set_error_input(error, 'Error in kmesh_get: bk is not identical to bka in gamma_only option', comm)
return
end if
end if
end do
if (na .ne. kmesh_info%nnh) then
call set_error_fatal(error, 'kmesh_get: Did not find right number of b-vectors in gamma_only option', comm)
return
end if
if (print_output%iprint > 0) then
write (stdout, '(1x,"+",76("-"),"+")')
write (stdout, '(1x,a)') '| Gamma-point: number of the b-vectors is reduced by half |'
write (stdout, '(1x,"+",76("-"),"+")')
if (trim(print_output%length_unit) == 'Ang') then
write (stdout, '(1x,a)') '| b_k Vectors (Ang^-1) and Weights (Ang^2) |'
write (stdout, '(1x,a)') '| ---------------------------------------- |'
else
write (stdout, '(1x,a)') '| b_k Vectors (Bohr^-1) and Weights (Bohr^2) |'
write (stdout, '(1x,a)') '| ------------------------------------------ |'
end if
write (stdout, '(1x,a)') '| No. b_k(x) b_k(y) b_k(z) w_b |'
write (stdout, '(1x,a)') '| --- -------------------------------- -------- |'
do i = 1, kmesh_info%nntot
write (stdout, '(1x,"|",11x,i3,5x,3f12.6,3x,f10.6,8x,"|")') &
i, (kmesh_info%bk(j, i, 1)/print_output%lenconfac, j=1, 3), kmesh_info%wb(i)*print_output%lenconfac**2
end do
write (stdout, '(1x,"+",76("-"),"+")')
write (stdout, *) ' '
end if
deallocate (nnlist_tmp, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nnlist_tmp in kmesh_get', comm)
return
end if
deallocate (nncell_tmp, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nncell_tmp in kmesh_get', comm)
return
end if
end if
![ysl-e]
! JJ, is use_ss_functional necessarily defined here, or must it be moved to "special"
!if (wann_control%use_ss_functional) then
if (.not. gamma_only) then
allocate (kmesh_info%nnord(kmesh_info%nntot, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating kmesh_info%nnord in kmesh_get', comm)
return
end if
allocate (kmesh_info%nninv(kmesh_info%nntot, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating kmesh_info%nninv in kmesh_get', comm)
return
end if
allocate (kmesh_info%nnrev(kmesh_info%nntot, num_kpts), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error in allocating kmesh_info%nnrev in kmesh_get', comm)
return
end if
call kmesh_bvectors_perm(kmesh_info%bk(:, :, :), kmesh_info%bk(:, :, 1), num_kpts, &
kmesh_info%nntot, kmesh_info%nnord, kmesh_info%nninv, &
kmesh_info%nnrev, error, comm)
if (allocated(error)) return
end if
deallocate (kpt_cart, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating kpt_cart in kmesh_get', comm)
return
end if
deallocate (bk_local, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating bk_local in kmesh_get', comm)
return
end if
deallocate (lmn, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating lmn in kmesh_get', comm)
return
end if
deallocate (nnshell, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nnshell in kmesh_get', comm)
return
end if
if (print_output%timing_level > 0) call io_stopwatch_stop('kmesh: get', timer)
return
end subroutine kmesh_get
!================================================!
subroutine kmesh_write(exclude_bands, kmesh_info, lauto_proj, proj, print_output, kpt_latt, &
real_lattice, num_kpts, num_proj, calc_only_A, spinors, seedname, timer)
!==================================================================!
! !
!! Writes nnkp file (list of overlaps needed)
! !
! Note that the format is different to (and more compact than) !
! that used by the old f77 code. !
! !
! The file consists of num_kpts blocks of data, one block for each !
! k-point of the mesh. Each block consists of nntot+1 lines, !
! where nntot is the (integer) number of nearest neighbours !
! belonging to k-point nkp. !
! !
! The first line in each block is just nntot. !
! !
! The second line consists of 5 integers. The first is the k-point !
! nkp. The second to the fifth specify it's nearest neighbours !
! k+b: the second integer points to the k-point that is the !
! periodic image of k+b that we want; the last three integers give !
! the G-vector, in reciprocal lattice units, that brings the !
! k-point specified by the second integer (which is in the first !
! BZ) to the actual k+b that we need. !
! !
! So wannier.nnkp specifies the nearest neighbours of each !
! k-point, and therefore provides the information required to !
! calculate the M_mn(k,b) matrix elements -- Marzari & Vanderbilt !
! PRB 56, 12847 (1997) Eq. (25) -- for each pair of band indices !
! m and n. !
!==================================================================!
use w90_io, only: io_date, io_stopwatch_start, io_stopwatch_stop
use w90_utility, only: utility_recip_lattice_base
use w90_types, only: kmesh_info_type, kmesh_input_type, &
proj_type, print_output_type, timer_list_type
implicit none
character(len=*), intent(in) :: seedname
integer, allocatable, intent(in) :: exclude_bands(:)
integer, intent(in) :: num_kpts
integer, intent(inout) :: num_proj
logical, intent(in) :: calc_only_A
logical, intent(in) :: spinors
logical, intent(in) :: lauto_proj
real(kind=dp), intent(in) :: kpt_latt(:, :)
real(kind=dp), intent(in) :: real_lattice(3, 3)
type(kmesh_info_type), intent(in) :: kmesh_info
type(print_output_type), intent(in) :: print_output
type(proj_type), allocatable, intent(in) :: proj(:) ! alloc only because allocation status is tested
type(timer_list_type), intent(inout) :: timer
real(kind=dp) :: recip_lattice(3, 3), volume
integer :: i, nkp, nn, nnkpout, num_exclude_bands
character(len=9) :: cdate, ctime
if (print_output%timing_level > 0) call io_stopwatch_start('kmesh: write', timer)
open (newunit=nnkpout, file=trim(seedname)//'.nnkp', form='formatted')
! Date and time
call io_date(cdate, ctime)
write (nnkpout, '(4(a),/)') '# File written on ', cdate, ' at ', ctime
! Calc_only_A
write (nnkpout, '(a,l2,/)') 'calc_only_A : ', calc_only_A
! Real lattice
write (nnkpout, '(a)') 'begin real_lattice'
write (nnkpout, '(3(f12.7))') (real_lattice(1, i), i=1, 3)
write (nnkpout, '(3(f12.7))') (real_lattice(2, i), i=1, 3)
write (nnkpout, '(3(f12.7))') (real_lattice(3, i), i=1, 3)
write (nnkpout, '(a/)') 'end real_lattice'
! Reciprocal lattice
call utility_recip_lattice_base(real_lattice, recip_lattice, volume)
write (nnkpout, '(a)') 'begin recip_lattice'
write (nnkpout, '(3f12.7)') (recip_lattice(1, i), i=1, 3)
write (nnkpout, '(3f12.7)') (recip_lattice(2, i), i=1, 3)
write (nnkpout, '(3f12.7)') (recip_lattice(3, i), i=1, 3)
write (nnkpout, '(a/)') 'end recip_lattice'
! K-points
write (nnkpout, '(a)') 'begin kpoints'
write (nnkpout, '(i6)') num_kpts
do nkp = 1, num_kpts
write (nnkpout, '(3f14.8)') (kpt_latt(i, nkp), i=1, 3)
end do
write (nnkpout, '(a/)') 'end kpoints'
if (spinors) then
! Projections
write (nnkpout, '(a)') 'begin spinor_projections'
if (allocated(proj)) then
write (nnkpout, '(i6)') num_proj
do i = 1, num_proj
write (nnkpout, '(3(f10.5,1x),2x,3i3)') &
proj(i)%site(1), proj(i)%site(2), proj(i)%site(3), &
proj(i)%l, proj(i)%m, proj(i)%radial
write (nnkpout, '(2x,3f11.7,1x,3f11.7,1x,f7.2)') &
proj(i)%z(1), proj(i)%z(2), proj(i)%z(3), &
proj(i)%x(1), proj(i)%x(2), proj(i)%x(3), &
proj(i)%zona
write (nnkpout, '(2x,1i3,1x,3f11.7)') &
proj(i)%s, &
proj(i)%s_qaxis(1), proj(i)%s_qaxis(2), proj(i)%s_qaxis(3)
end do
else
! No projections
write (nnkpout, '(i6)') 0
end if
write (nnkpout, '(a/)') 'end spinor_projections'
else
! Projections
write (nnkpout, '(a)') 'begin projections'
if (allocated(proj)) then
write (nnkpout, '(i6)') num_proj
do i = 1, num_proj
write (nnkpout, '(3(f10.5,1x),2x,3i3)') &
proj(i)%site(1), proj(i)%site(2), proj(i)%site(3), &
proj(i)%l, proj(i)%m, proj(i)%radial
write (nnkpout, '(2x,3f11.7,1x,3f11.7,1x,f7.2)') &
proj(i)%z(1), proj(i)%z(2), proj(i)%z(3), &
proj(i)%x(1), proj(i)%x(2), proj(i)%x(3), &
proj(i)%zona
end do
else
! No projections
write (nnkpout, '(i6)') 0
end if
write (nnkpout, '(a/)') 'end projections'
end if
! Info for automatic generation of projections
if (lauto_proj) then
write (nnkpout, '(a)') 'begin auto_projections'
write (nnkpout, '(i6)') num_proj
write (nnkpout, '(i6)') 0
write (nnkpout, '(a/)') 'end auto_projections'
end if
! Nearest neighbour k-points
write (nnkpout, '(a)') 'begin nnkpts'
write (nnkpout, '(i4)') kmesh_info%nntot
do nkp = 1, num_kpts
do nn = 1, kmesh_info%nntot
write (nnkpout, '(2i8,3x,3i4)') &
nkp, kmesh_info%nnlist(nkp, nn), (kmesh_info%nncell(i, nkp, nn), i=1, 3)
end do
end do
write (nnkpout, '(a/)') 'end nnkpts'
!states to exclude
num_exclude_bands = 0
if (allocated(exclude_bands)) num_exclude_bands = size(exclude_bands)
write (nnkpout, '(a)') 'begin exclude_bands'
write (nnkpout, '(i4)') num_exclude_bands
if (num_exclude_bands > 0) then
do i = 1, num_exclude_bands
write (nnkpout, '(i4)') exclude_bands(i)
end do
end if
write (nnkpout, '(a)') 'end exclude_bands'
close (nnkpout)
if (print_output%timing_level > 0) call io_stopwatch_stop('kmesh: write', timer)
return
end subroutine kmesh_write
!================================================
subroutine kmesh_dealloc(kmesh_info, error, comm)
!================================================
!! Release memory from the kmesh module
! This routine now check to see if arrays
! are allocated, as there are some code
! paths that will not allocate on all nodes
!================================================
use w90_types, only: kmesh_info_type
implicit none
type(kmesh_info_type), intent(inout) :: kmesh_info
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
integer :: ierr
! Deallocate real arrays
if (allocated(kmesh_info%bk)) then
deallocate (kmesh_info%bk, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating bk in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%bka)) then
deallocate (kmesh_info%bka, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating bka in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%wb)) then
deallocate (kmesh_info%wb, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating wb in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%nnord)) then
deallocate (kmesh_info%wb, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating wb in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%nninv)) then
deallocate (kmesh_info%wb, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating wb in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%nnrev)) then
deallocate (kmesh_info%wb, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating wb in kmesh_dealloc', comm)
return
end if
end if
! Deallocate integer arrays
if (allocated(kmesh_info%neigh)) then
deallocate (kmesh_info%neigh, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating neigh in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%nncell)) then
deallocate (kmesh_info%nncell, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nncell in kmesh_dealloc', comm)
return
end if
end if
if (allocated(kmesh_info%nnlist)) then
deallocate (kmesh_info%nnlist, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error in deallocating nnlist in kmesh_dealloc', comm)
return
end if
end if
return
end subroutine kmesh_dealloc
!================================================
subroutine kmesh_supercell_sort(print_output, recip_lattice, lmn, timer)
!================================================
!! We look for kpoint neighbours in a large supercell of reciprocal
!! unit cells. Done sequentially this is very slow.
!! Here we order the cells by the distance from the origin.
!! Doing the search in this order gives a dramatic speed up
!================================================
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: print_output_type, timer_list_type
implicit none
type(print_output_type), intent(in) :: print_output
integer, intent(inout) :: lmn(:, :)
real(kind=dp), intent(in) :: recip_lattice(3, 3)
type(timer_list_type), intent(inout) :: timer
integer :: counter, l, m, n, loop
!! Order in which to search the cells (ordered in dist from origin)
integer :: lmn_cp(3, (2*nsupcell + 1)**3), indx(1)
real(kind=dp) :: pos(3)
real(kind=dp) :: dist((2*nsupcell + 1)**3)
real(kind=dp) :: dist_cp((2*nsupcell + 1)**3)
if (print_output%timing_level > 1) call io_stopwatch_start('kmesh: supercell_sort', timer)
counter = 1
lmn(:, counter) = 0
dist(counter) = 0.0_dp
do l = -nsupcell, nsupcell
do m = -nsupcell, nsupcell
do n = -nsupcell, nsupcell
if (l == 0 .and. m == 0 .and. n == 0) cycle
counter = counter + 1
lmn(1, counter) = l; lmn(2, counter) = m; lmn(3, counter) = n
pos = matmul(lmn(:, counter), recip_lattice)
dist(counter) = sqrt(dot_product(pos, pos))
end do
end do
end do
do loop = (2*nsupcell + 1)**3, 1, -1
indx = internal_maxloc(dist, nsupcell)
dist_cp(loop) = dist(indx(1))
lmn_cp(:, loop) = lmn(:, indx(1))
dist(indx(1)) = -1.0_dp
end do
lmn = lmn_cp
dist = dist_cp
if (print_output%timing_level > 1) call io_stopwatch_stop('kmesh: supercell_sort', timer)
end subroutine kmesh_supercell_sort
!================================================
subroutine kmesh_get_bvectors(kmesh_input, print_output, bvector, kpt_cart, recip_lattice, &
shell_dist, lmn, kpt, multi, num_kpts, timer, error, comm)
!================================================
!
!! Returns the b-vectors for a given shell and kpoint.
!
!================================================
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: kmesh_input_type, print_output_type, timer_list_type
implicit none
! arguments
type(print_output_type), intent(in) :: print_output
type(kmesh_input_type), intent(in) :: kmesh_input
type(timer_list_type), intent(inout) :: timer
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
integer, intent(in) :: num_kpts
integer, intent(in) :: lmn(:, :)
integer, intent(in) :: multi ! the number of kpoints in the shell
integer, intent(in) :: kpt ! which kpt is our 'origin'
real(kind=dp), intent(in) :: recip_lattice(3, 3)
real(kind=dp), intent(in) ::kpt_cart(:, :)
real(kind=dp), intent(in) :: shell_dist ! the bvectors
real(kind=dp), intent(out) :: bvector(3, multi) ! the bvectors
! local variables
integer :: loop, nkp2, num_bvec
real(kind=dp) :: dist, vkpp2(3), vkpp(3)
if (print_output%timing_level > 1) call io_stopwatch_start('kmesh: get_bvectors', timer)
bvector = 0.0_dp
num_bvec = 0
ok: do loop = 1, (2*kmesh_input%search_supcell_size + 1)**3
vkpp2 = matmul(lmn(:, loop), recip_lattice)
do nkp2 = 1, num_kpts
vkpp = vkpp2 + kpt_cart(:, nkp2)
dist = sqrt((kpt_cart(1, kpt) - vkpp(1))**2 &
+ (kpt_cart(2, kpt) - vkpp(2))**2 + (kpt_cart(3, kpt) - vkpp(3))**2)
if ((dist .ge. shell_dist - kmesh_input%tol) .and. (dist .le. shell_dist + kmesh_input%tol)) then
num_bvec = num_bvec + 1
bvector(:, num_bvec) = vkpp(:) - kpt_cart(:, kpt)
end if
!if we have the right number of neighbours we can exit
if (num_bvec == multi) cycle ok
end do
end do ok
if (num_bvec < multi) then
call set_error_fatal(error, 'kmesh_get_bvector: Not enough bvectors found', comm)
return
end if
if (print_output%timing_level > 1) call io_stopwatch_stop('kmesh: get_bvectors', timer)
return
end subroutine kmesh_get_bvectors
!================================================
subroutine kmesh_shell_automatic(kmesh_input, print_output, bweight, dnn, kpt_cart, &
recip_lattice, lmn, multi, num_kpts, stdout, timer, error, &
comm)
!================================================
!! Find the correct set of shells to satisfy B1
!! The stratagy is:
!! 1) Take the bvectors from the next shell
!! 2) Reject them if they are parallel to exisiting b vectors
!! 3) Test to see if we satisfy B1, if not add another shell and repeat
!
!================================================
use w90_constants, only: eps5, eps6
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: kmesh_input_type, print_output_type, timer_list_type
implicit none
! arguments
type(print_output_type), intent(in) :: print_output
type(kmesh_input_type), intent(inout) :: kmesh_input
type(timer_list_type), intent(inout) :: timer
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
integer, intent(in) :: num_kpts
integer, intent(in) :: stdout
integer, intent(in) :: lmn(:, :)
integer, intent(in) :: multi(kmesh_input%search_shells) ! the number of kpoints in the shell
real(kind=dp), intent(in) :: recip_lattice(3, 3)
real(kind=dp), intent(in) :: kpt_cart(:, :)
real(kind=dp), intent(in) :: dnn(kmesh_input%search_shells) ! the bvectors
real(kind=dp), intent(out) :: bweight(kmesh_input%max_shells_h)
! local variables
integer :: loop_bn, loop_b, loop_s, info, cur_shell, ierr, loop, shell
logical :: lpar
real(kind=dp), allocatable :: amat(:, :), umat(:, :), vmat(:, :), smat(:, :), tmp0(:, :)
real(kind=dp), allocatable :: bvector(:, :, :) ! the bvectors
real(kind=dp), allocatable :: singv(:), tmp1(:), tmp2(:), tmp3(:)
real(kind=dp) :: delta
real(kind=dp) :: target(kmesh_input%max_shells_aux)
real(kind=dp) :: work((kmesh_input%max_shells_aux)*10)
! variables for higher-order finite-difference
integer, dimension(:, :), allocatable :: num_x, num_y, num_z
logical :: bsat
integer :: loop_order, num_of_eqs, higher_order_n_local
if (kmesh_input%higher_order_nearest_shells) then
higher_order_n_local = kmesh_input%higher_order_n
else
higher_order_n_local = 1 !find 1st-order b and weights first in this subroutine
end if
target = 0.0_dp; target(1) = 1.0_dp; target(3) = 1.0_dp; target(6) = 1.0_dp
if (print_output%timing_level > 1) call io_stopwatch_start('kmesh: shell_automatic', timer)
allocate (bvector(3, maxval(multi), kmesh_input%max_shells_h), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvector in kmesh_shell_automatic', comm)
return
end if
bvector = 0.0_dp; bweight = 0.0_dp
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '| The b-vectors are chosen automatically |'
end if
! note allocation of kmesh_input%shell list in subroutine w90_readwrite_read_kmesh_data()
! kmesh_input%num_shells = 0 in same place
bsat = .false.
do shell = 1, kmesh_input%search_shells
cur_shell = kmesh_input%num_shells + 1
! get the b vectors for the new shell
call kmesh_get_bvectors(kmesh_input, print_output, bvector(:, 1:multi(shell), cur_shell), &
kpt_cart, recip_lattice, dnn(shell), lmn, 1, multi(shell), num_kpts, &
timer, error, comm)
if (allocated(error)) return
if (print_output%iprint >= 3) then
write (stdout, '(1x,a8,1x,I2,a14,1x,I2,49x,a)') '| Shell:', shell, ' Multiplicity:', multi(shell), '|'
do loop = 1, multi(shell)
write (stdout, '(1x,a10,I2,1x,a1,4x,3f12.6,5x,a9,9x,a)') '| b-vector ', loop, ':', &
bvector(:, loop, cur_shell)/print_output%lenconfac, '('//trim(print_output%length_unit)//'^-1)', '|'
end do
end if
! We check that the new shell is not parrallel to an existing shell (cosine=1)
if (higher_order_n_local == 1) then
lpar = .false.
if (kmesh_input%num_shells > 0) then
do loop_bn = 1, multi(shell)
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
delta = dot_product(bvector(:, loop_bn, cur_shell), bvector(:, loop_b, loop_s))/ &
sqrt(dot_product(bvector(:, loop_bn, cur_shell), bvector(:, loop_bn, cur_shell))* &
dot_product(bvector(:, loop_b, loop_s), bvector(:, loop_b, loop_s)))
if (abs(abs(delta) - 1.0_dp) < eps6) lpar = .true.
end do
end do
end do
end if
if (lpar) then
if (print_output%iprint >= 3) then
write (stdout, '(1x,a)') '| This shell is linearly dependent on existing shells: Trying next shell |'
end if
cycle
end if
end if
kmesh_input%num_shells = kmesh_input%num_shells + 1
kmesh_input%shell_list(kmesh_input%num_shells) = shell
allocate (tmp0(kmesh_input%max_shells_aux, kmesh_input%max_shells_aux), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating tmp0 in kmesh_shell_automatic', comm)
return
end if
allocate (tmp1(kmesh_input%max_shells_aux), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating tmp1 in kmesh_shell_automatic', comm)
return
end if
allocate (tmp2(kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating tmp2 in kmesh_shell_automatic', comm)
return
end if
allocate (tmp3(kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating tmp3 in kmesh_shell_automatic', comm)
return
end if
allocate (amat(kmesh_input%max_shells_aux, kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating amat in kmesh_shell_automatic', comm)
return
end if
allocate (umat(kmesh_input%max_shells_aux, kmesh_input%max_shells_aux), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating umat in kmesh_shell_automatic', comm)
return
end if
allocate (vmat(kmesh_input%num_shells, kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating vmat in kmesh_shell_automatic', comm)
return
end if
allocate (smat(kmesh_input%num_shells, kmesh_input%max_shells_aux), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating smat in kmesh_shell_automatic', comm)
return
end if
allocate (singv(kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating singv in kmesh_shell_automatic', comm)
return
end if
amat(:, :) = 0.0_dp; umat(:, :) = 0.0_dp; vmat(:, :) = 0.0_dp; smat(:, :) = 0.0_dp; singv(:) = 0.0_dp
num_of_eqs = (1 + higher_order_n_local)*(1 + 2*higher_order_n_local)
allocate (num_x(higher_order_n_local, num_of_eqs), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating num_x in kmesh_shell_automatic', comm)
return
end if
allocate (num_y(higher_order_n_local, num_of_eqs), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating num_y in kmesh_shell_automatic', comm)
return
end if
allocate (num_z(higher_order_n_local, num_of_eqs), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating num_z in kmesh_shell_automatic', comm)
return
end if
!find higher finite-diff weights
! make test suite(compare nnkp files)
do loop_order = 1, higher_order_n_local
call kmesh_get_amat(kmesh_input, amat, bvector, multi, loop_order, &
num_x(loop_order, :), num_y(loop_order, :), num_z(loop_order, :))
end do
info = 0
call dgesvd('A', 'A', kmesh_input%max_shells_aux, kmesh_input%num_shells, amat, &
kmesh_input%max_shells_aux, singv, umat, &
kmesh_input%max_shells_aux, vmat, kmesh_input%num_shells, work, kmesh_input%max_shells_aux*10, info)
if (info < 0) then
if (print_output%iprint > 0) then
write (stdout, '(1x,a,1x,I1,1x,a)') 'kmesh_shell_automatic: Argument', abs(info), &
'of dgesvd is incorrect'
end if
call set_error_fatal(error, 'kmesh_shell_automatic: Problem with Singular Value Decomposition', comm)
return
else if (info > 0) then
call set_error_fatal(error, 'kmesh_shell_automatic: Singular Value Decomposition did not converge', comm)
return
end if
if (any(abs(singv) < eps5)) then
if (kmesh_input%num_shells == 1) then
call set_error_fatal(error, &
'kmesh_shell_automatic: Singular Value Decomposition has found a very small singular value', comm)
return
else
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '| SVD found small singular value, Rejecting this shell and trying the next |'
end if
bsat = .false.
kmesh_input%num_shells = kmesh_input%num_shells - 1
goto 200
end if
end if
smat = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
smat(loop_s, loop_s) = 1.0_dp/singv(loop_s)
end do
! S. Ponce: The following below is correct but had to be unpacked because of PGI-15
! bweight(1:num_shells)=matmul(transpose(vmat),matmul(smat,matmul(transpose(umat),target)))
tmp0 = transpose(umat)
tmp1 = matmul(tmp0, target)
tmp2 = matmul(smat, tmp1)
tmp3 = matmul(transpose(vmat), tmp2)
bweight(1:kmesh_input%num_shells) = tmp3
if (print_output%iprint >= 2) then
do loop_s = 1, kmesh_input%num_shells
write (stdout, '(1x,a,I2,a,f12.7,5x,a8,36x,a)') '| Shell: ', loop_s, &
' w_b ', bweight(loop_s)*print_output%lenconfac**2, '('//trim(print_output%length_unit)//'^2)', '|'
end do
end if
!check if the conditions including (B1) for finite-difference are satisfied
bsat = .true.
do loop_order = 1, higher_order_n_local
call kmesh_check_condition(kmesh_input, bsat, bvector, bweight, multi, loop_order, &
num_x(loop_order, :), num_y(loop_order, :), num_z(loop_order, :))
end do
if (.not. bsat) then
if (shell < kmesh_input%search_shells .and. print_output%iprint >= 3) then
if (print_output%iprint > 0) write (stdout, '(1x,a,24x,a1)') '| B1 condition is not satisfied: Adding another shell', '|'
elseif (shell == kmesh_input%search_shells) then
if (print_output%iprint > 0) then
write (stdout, *) ' '
write (stdout, '(1x,a,i3,a)') 'Unable to satisfy the higher-order version of B1 with any of the first ' &
, kmesh_input%search_shells, ' shells'
write (stdout, '(1x,a)') 'Check that you have specified your unit cell to a high precision'
write (stdout, '(1x,a)') 'Low precision might cause a loss of symmetry.'
write (stdout, '(1x,a)') ' '
write (stdout, '(1x,a)') 'If your cell is very long, or you have an irregular MP grid'
write (stdout, '(1x,a)') 'Try increasing the parameter search_shells in the win file (default=30)'
write (stdout, *) ' '
call set_error_fatal(error, 'kmesh_shell_automatic: unable to satisfy the higher-order version of B1', comm)
return
end if
end if
end if
200 continue
deallocate (tmp0, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating tmp0 in kmesh_shell_automatic', comm)
return
end if
deallocate (tmp1, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating tmp1 in kmesh_shell_automatic', comm)
return
end if
deallocate (tmp2, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating tmp2 in kmesh_shell_automatic', comm)
return
end if
deallocate (tmp3, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating tmp3 in kmesh_shell_automatic', comm)
return
end if
deallocate (amat, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating amat in kmesh_shell_automatic', comm)
return
end if
deallocate (umat, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating umat in kmesh_shell_automatic', comm)
return
end if
deallocate (vmat, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating vmat in kmesh_shell_automatic', comm)
return
end if
deallocate (smat, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating smat in kmesh_shell_automatic', comm)
return
end if
deallocate (singv, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating singv in kmesh_shell_automatic', comm)
return
end if
deallocate (num_x, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating num_x in kmesh_shell_automatic', comm)
return
end if
deallocate (num_y, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating num_y in kmesh_shell_automatic', comm)
return
end if
deallocate (num_z, stat=ierr)
if (ierr /= 0) then
call set_error_dealloc(error, 'Error deallocating num_z in kmesh_shell_automatic', comm)
return
end if
if (bsat) exit
end do
if (.not. bsat) then
if (print_output%iprint > 0) then
write (stdout, *) ' '
write (stdout, '(1x,a,i3,a)') 'Unable to satisfy B1 with any of the first ', &
kmesh_input%search_shells, ' shells'
write (stdout, '(1x,a)') 'Your cell might be very long, or you may have an irregular MP grid'
write (stdout, '(1x,a)') 'Try increasing the parameter search_shells in the win file (default=36)'
write (stdout, *) ' '
end if
call set_error_fatal(error, 'kmesh_shell_automatic: Unable to satisfy B1 condition', comm)
return
end if
if (print_output%timing_level > 1) call io_stopwatch_stop('kmesh: shell_automatic', timer)
return
end subroutine kmesh_shell_automatic
subroutine kmesh_shell_reconstruct(kmesh_input, num_kpts, multi, dnn, nnshell, bweight)
!================================================
!
!! Include more shells to calculate higher-order finite difference: 2b, 3b, ... Nb shells
!! Note: some shells are overwritten
!================================================
use w90_types, only: kmesh_input_type, print_output_type
implicit none
! arguments
type(kmesh_input_type), intent(inout) :: kmesh_input
integer, intent(in) :: num_kpts
integer, intent(inout) :: multi(max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n)) ! the number of bvectors in the shell
real(kind=dp), intent(inout) :: dnn(max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n))
integer, intent(inout) :: nnshell(num_kpts, max(kmesh_input%search_shells, 6*kmesh_input%higher_order_n))
real(kind=dp), intent(inout) :: bweight(kmesh_input%max_shells_h)
! local variables
real(kind=dp) :: bweight_temp, fact
integer :: shell, order, loop_j, temp_multi(kmesh_input%num_shells), temp_nnshell(num_kpts, kmesh_input%num_shells)
real(kind=dp) :: temp_dnn(kmesh_input%num_shells)
! update new shells (after simplify the first-order shell list, e.g. 1,4,6, ... -> 1,2,3,...)
do shell = 1, kmesh_input%num_shells
temp_multi(shell) = multi(kmesh_input%shell_list(shell))
temp_nnshell(:, shell) = nnshell(:, kmesh_input%shell_list(shell))
temp_dnn(shell) = dnn(kmesh_input%shell_list(shell))
end do
do shell = 1, kmesh_input%num_shells
kmesh_input%shell_list(shell) = shell
multi(shell) = temp_multi(shell)
nnshell(:, shell) = temp_nnshell(:, shell)
dnn(shell) = temp_dnn(shell)
end do
do order = 2, kmesh_input%higher_order_n
do shell = 1, kmesh_input%num_shells
kmesh_input%shell_list((order - 1)*kmesh_input%num_shells + shell) = &
(order - 1)*kmesh_input%num_shells + shell
multi((order - 1)*kmesh_input%num_shells + shell) = multi(shell)
nnshell(:, (order - 1)*kmesh_input%num_shells + shell) = nnshell(:, shell)
dnn((order - 1)*kmesh_input%num_shells + shell) = dnn(shell)*order
end do
end do
! calculate new bweights w_b, w_2b, ..., w_Nb
do shell = 1, kmesh_input%num_shells
bweight_temp = bweight(shell)
do order = 1, kmesh_input%higher_order_n
fact = 1.0_dp/REAL(order**2, DP)
do loop_j = 1, kmesh_input%higher_order_n
if (loop_j == order) cycle
fact = (fact*REAL(loop_j**2, DP))/REAL(loop_j**2 - order**2, DP)
end do
bweight(kmesh_input%num_shells*(order - 1) + shell) = bweight_temp*fact
end do
end do
kmesh_input%num_shells = kmesh_input%num_shells*kmesh_input%higher_order_n
return
end subroutine kmesh_shell_reconstruct
!================================================
subroutine kmesh_get_amat(kmesh_input, amat, bvector, multi, loop_order, num_x, num_y, num_z)
!================================================
!
!! Find amat(coefficients to find bweight) and the numbers of x, y, z components for a given order
!
!================================================
use w90_types, only: kmesh_input_type
implicit none
! arguments
type(kmesh_input_type), intent(inout) :: kmesh_input
real(kind=dp), intent(inout) :: amat(:, :)
integer, intent(inout) :: num_x(:)
integer, intent(inout) :: num_y(:)
integer, intent(inout) :: num_z(:)
integer, intent(in) :: multi(kmesh_input%search_shells) ! the number of kpoints in the shell
integer, intent(in) :: loop_order
real(kind=dp), intent(in) :: bvector(3, maxval(multi), kmesh_input%max_shells_h)
! local variables
integer :: num_of_eqs, num_of_eqs_prev
integer :: loop_i, loop_j, loop_s, loop_b
num_of_eqs = (1 + loop_order)*(1 + 2*loop_order) !((3, 2n)) (combi. with repetition)
num_of_eqs_prev = loop_order*(2*loop_order - 1)
if (loop_order .eq. 1) num_of_eqs_prev = 0
do loop_s = 1, kmesh_input%num_shells
do loop_i = 1, num_of_eqs
! equation index, e.g. If loop_order == 3, (1,2,...,15) -> (xxx, xxy, xyy, yyy, xxz, xyz, ..., zzz)
! find the number of z components corresponding to the current loop_i
do loop_j = 0, 2*loop_order
if ((2*loop_order + 1)*loop_j - loop_j*(loop_j - 1)/2 <= loop_i - 1 &
.and. (2*loop_order + 1)*(loop_j + 1) - (loop_j + 1)*loop_j/2 > loop_i - 1) then
num_z(loop_i) = loop_j
exit
end if
end do
! find the number of x and y components
num_y(loop_i) = loop_i - 1 - ((2*loop_order + 1)*num_z(loop_i) - num_z(loop_i) &
*(num_z(loop_i) - 1)/2)
num_x(loop_i) = 2*loop_order - num_y(loop_i) - num_z(loop_i)
! calculate sum_b bb...bbbb
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
amat(num_of_eqs_prev + loop_i, loop_s) = amat(num_of_eqs_prev + loop_i, loop_s) &
+ (bvector(1, loop_b, loop_s)**num_x(loop_i)) &
*(bvector(2, loop_b, loop_s)**num_y(loop_i)) &
*(bvector(3, loop_b, loop_s)**num_z(loop_i))
end do
end do
end do
end subroutine kmesh_get_amat
!================================================
subroutine kmesh_check_condition(kmesh_input, bsat, bvector, bweight, multi, loop_order, num_x, num_y, num_z)
!================================================
!
!! Check if the obtained bweight satisfy the conditions for finite-difference, including (B1).
!
!================================================
use w90_types, only: kmesh_input_type
implicit none
! arguments
type(kmesh_input_type), intent(inout) :: kmesh_input
logical, intent(inout) :: bsat
integer, intent(inout) :: num_x(:)
integer, intent(inout) :: num_y(:)
integer, intent(inout) :: num_z(:)
integer, intent(in) :: multi(kmesh_input%search_shells) ! the number of kpoints in the shell
integer, intent(in) :: loop_order
real(kind=dp), intent(in) :: bvector(3, maxval(multi), kmesh_input%max_shells_h)
real(kind=dp), intent(in) :: bweight(kmesh_input%max_shells_h)
! local variables
integer :: num_of_eqs
integer :: loop_i, loop_s, loop_b
real(kind=dp) :: delta
num_of_eqs = (1 + loop_order)*(1 + 2*loop_order)
do loop_i = 1, num_of_eqs
delta = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
delta = delta + bweight(loop_s)*(bvector(1, loop_b, loop_s)**num_x(loop_i)) &
*(bvector(2, loop_b, loop_s)**num_y(loop_i)) &
*(bvector(3, loop_b, loop_s)**num_z(loop_i))
end do
end do
if (loop_order .eq. 1 .and. (loop_i .eq. 1 .or. loop_i .eq. 3 .or. loop_i .eq. 6)) then
if (abs(delta - 1.0_dp) > kmesh_input%tol) bsat = .false.
else
if (abs(delta) > kmesh_input%tol) bsat = .false.
end if
end do
end subroutine kmesh_check_condition
!================================================
subroutine kmesh_shell_fixed(kmesh_input, print_output, bweight, dnn, kpt_cart, recip_lattice, &
lmn, multi, num_kpts, stdout, timer, error, comm)
!================================================
!
!! Find the B1 weights for a set of shells specified by the user
!
!================================================
use w90_constants, only: eps7
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: kmesh_input_type, print_output_type, timer_list_type
implicit none
! arguments
type(print_output_type), intent(in) :: print_output
type(kmesh_input_type), intent(in) :: kmesh_input
type(timer_list_type), intent(inout) :: timer
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
integer, intent(in) :: num_kpts
integer, intent(in) :: stdout
integer, intent(in) :: lmn(:, :)
integer, intent(in) :: multi(kmesh_input%search_shells) ! the number of kpoints in the shell
real(kind=dp), intent(in) :: recip_lattice(3, 3)
real(kind=dp), intent(in) ::kpt_cart(:, :)
real(kind=dp), intent(in) :: dnn(kmesh_input%search_shells) ! the bvectors
real(kind=dp), intent(out) :: bweight(max_shells)
! local variables
real(kind=dp), allocatable :: bvector(:, :, :)
real(kind=dp) :: singv(kmesh_input%num_shells)
real(kind=dp) :: amat(max_shells, kmesh_input%num_shells)
real(kind=dp) :: umat(max_shells, max_shells)
real(kind=dp) :: vmat(kmesh_input%num_shells, kmesh_input%num_shells)
real(kind=dp) :: smat(kmesh_input%num_shells, max_shells)
integer, parameter :: lwork = max_shells*10
real(kind=dp) :: work(lwork)
real(kind=dp), parameter :: target(6) = (/1.0_dp, 1.0_dp, 1.0_dp, 0.0_dp, 0.0_dp, 0.0_dp/)
logical :: b1sat
integer :: ierr, loop_i, loop_j, loop_b, loop_s, info
real(kind=dp) :: delta
integer :: loop, shell
if (print_output%timing_level > 1) call io_stopwatch_start('kmesh: shell_fixed', timer)
allocate (bvector(3, maxval(multi), kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvector in kmesh_shell_fixed', comm)
return
end if
bvector = 0.0_dp; bweight = 0.0_dp
amat = 0.0_dp; umat = 0.0_dp; vmat = 0.0_dp; smat = 0.0_dp; singv = 0.0_dp
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '| The b-vectors are set in the win file |'
end if
do shell = 1, kmesh_input%num_shells
! get the b vectors for this shell
call kmesh_get_bvectors(kmesh_input, print_output, &
bvector(:, 1:multi(kmesh_input%shell_list(shell)), shell), kpt_cart, &
recip_lattice, dnn(kmesh_input%shell_list(shell)), lmn, 1, &
multi(kmesh_input%shell_list(shell)), num_kpts, timer, error, comm)
if (allocated(error)) return
end do
if (print_output%iprint >= 3) then
do shell = 1, kmesh_input%num_shells
write (stdout, '(1x,a8,1x,I2,a14,1x,I2,49x,a)') '| Shell:', shell, ' Multiplicity:', &
multi(kmesh_input%shell_list(shell)), '|'
do loop = 1, multi(kmesh_input%shell_list(shell))
write (stdout, '(1x,a10,I2,1x,a1,4x,3f12.6,5x,a9,9x,a)') '| b-vector ', loop, ':', &
bvector(:, loop, shell)/print_output%lenconfac, '('//trim(print_output%length_unit)//'^-1)', '|'
end do
end do
end if
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
amat(1, loop_s) = amat(1, loop_s) + bvector(1, loop_b, loop_s)*bvector(1, loop_b, loop_s)
amat(2, loop_s) = amat(2, loop_s) + bvector(2, loop_b, loop_s)*bvector(2, loop_b, loop_s)
amat(3, loop_s) = amat(3, loop_s) + bvector(3, loop_b, loop_s)*bvector(3, loop_b, loop_s)
amat(4, loop_s) = amat(4, loop_s) + bvector(1, loop_b, loop_s)*bvector(2, loop_b, loop_s)
amat(5, loop_s) = amat(5, loop_s) + bvector(2, loop_b, loop_s)*bvector(3, loop_b, loop_s)
amat(6, loop_s) = amat(6, loop_s) + bvector(3, loop_b, loop_s)*bvector(1, loop_b, loop_s)
end do
end do
info = 0
call dgesvd('A', 'A', max_shells, kmesh_input%num_shells, amat, max_shells, singv, umat, &
max_shells, vmat, kmesh_input%num_shells, work, lwork, info)
if (info < 0) then
if (print_output%iprint > 0) then
write (stdout, '(1x,a,1x,I1,1x,a)') 'kmesh_shell_fixed: Argument', abs(info), &
'of dgesvd is incorrect'
end if
call set_error_fatal(error, 'kmesh_shell_fixed: Problem with Singular Value Decomposition', comm)
return
else if (info > 0) then
call set_error_fatal(error, 'kmesh_shell_fixed: Singular Value Decomposition did not converge', comm)
return
end if
if (any(abs(singv) < eps7)) then
call set_error_fatal(error, 'kmesh_shell_fixed: Singular Value Decomposition has found a very small singular value', comm)
return
end if
smat = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
smat(loop_s, loop_s) = 1/singv(loop_s)
end do
bweight(1:kmesh_input%num_shells) = matmul(transpose(vmat), matmul(smat, matmul(transpose(umat), target)))
if (print_output%iprint >= 2) then
do loop_s = 1, kmesh_input%num_shells
write (stdout, '(1x,a,I2,a,f12.7,5x,a8,36x,a)') '| Shell: ', loop_s, &
' w_b ', bweight(loop_s)*print_output%lenconfac**2, '('//trim(print_output%length_unit)//'^2)', '|'
end do
end if
!check b1
b1sat = .true.
if (.not. kmesh_input%skip_B1_tests) then
do loop_i = 1, 3
do loop_j = loop_i, 3
delta = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(kmesh_input%shell_list(loop_s))
delta = delta + bweight(loop_s)*bvector(loop_i, loop_b, loop_s)*bvector(loop_j, loop_b, loop_s)
end do
end do
if (loop_i == loop_j) then
if (abs(delta - 1.0_dp) > kmesh_input%tol) b1sat = .false.
end if
if (loop_i /= loop_j) then
if (abs(delta) > kmesh_input%tol) b1sat = .false.
end if
end do
end do
end if
if (.not. b1sat) then
call set_error_fatal(error, 'kmesh_shell_fixed: B1 condition not satisfied', comm)
return
end if
if (print_output%timing_level > 1) call io_stopwatch_stop('kmesh: shell_fixed', timer)
return
end subroutine kmesh_shell_fixed
!================================================
subroutine kmesh_shell_from_file(kmesh_input, print_output, bvec_inp, bweight, dnn, kpt_cart, &
recip_lattice, lmn, multi, num_kpts, seedname, stdout, timer, &
error, comm)
!================================================
!! Find the B1 weights for a set of b-vectors given in a file.
!! This routine is activated via kmesh_shell_from_file = T
!! It is not intended for regular use.
!
!================================================
use w90_constants, only: eps7, maxlen
use w90_io, only: io_stopwatch_start, io_stopwatch_stop
use w90_types, only: kmesh_input_type, print_output_type, timer_list_type
implicit none
! arguments
type(print_output_type), intent(in) :: print_output
type(kmesh_input_type), intent(inout) :: kmesh_input
type(timer_list_type), intent(inout) :: timer
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
integer, intent(in) :: num_kpts, stdout
integer, intent(in) :: lmn(:, :)
integer, intent(inout) :: multi(kmesh_input%search_shells) ! the number of kpoints in the shell
real(kind=dp), intent(in) :: recip_lattice(3, 3)
real(kind=dp), intent(in) ::kpt_cart(:, :)
real(kind=dp), allocatable, intent(inout) :: bvec_inp(:, :, :)
real(kind=dp), intent(in) :: dnn(kmesh_input%search_shells) ! the bvectors
real(kind=dp), intent(out) :: bweight(max_shells)
character(len=50), intent(in) :: seedname
! local variables
real(kind=dp), allocatable :: bvector(:, :)
real(kind=dp), dimension(:), allocatable :: singv
real(kind=dp), dimension(:, :), allocatable :: amat, umat, vmat, smat
integer, parameter :: lwork = max_shells*10
real(kind=dp) :: work(lwork)
integer :: bvec_list(num_nnmax, max_shells)
real(kind=dp), parameter :: target(6) = (/1.0_dp, 1.0_dp, 1.0_dp, 0.0_dp, 0.0_dp, 0.0_dp/)
integer :: ierr, loop_b, loop_s, info
integer :: loop, shell, pos, kshell_in, counter, length, i, loop2, num_lines, tot_num_lines
character(len=maxlen) :: dummy, dummy2
if (print_output%timing_level > 1) call io_stopwatch_start('kmesh: shell_from_file', timer)
allocate (bvector(3, sum(multi)), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvector in kmesh_shell_from_file', comm)
return
end if
bvector = 0.0_dp; bweight = 0.0_dp
if (print_output%iprint > 0) then
write (stdout, '(1x,a)') '| The b-vectors are defined in the kshell file |'
end if
counter = 1
do shell = 1, kmesh_input%search_shells
! get the b vectors
call kmesh_get_bvectors(kmesh_input, print_output, bvector(:, counter:counter + multi(shell) - 1), &
kpt_cart, recip_lattice, dnn(shell), lmn, 1, multi(shell), num_kpts, &
timer, error, comm)
if (allocated(error)) return
counter = counter + multi(shell)
end do
open (newunit=kshell_in, file=trim(seedname)//'.kshell', form='formatted', status='old', &
action='read', iostat=ierr)
if (ierr /= 0) then
call set_error_file(error, 'Error: Problem (1) opening input file '//trim(seedname)//'.kshell', comm)
return
end if
num_lines = 0; tot_num_lines = 0
do
read (kshell_in, '(a)', iostat=ierr) dummy
if (ierr == 0) then !read ok, proceed
dummy = adjustl(dummy)
tot_num_lines = tot_num_lines + 1
if (.not. dummy(1:1) == '!' .and. .not. dummy(1:1) == '#') then
if (len(trim(dummy)) > 0) num_lines = num_lines + 1
end if
else if (ierr > 0) then !error case
call set_error_input(error, 'Error: Problem (2) reading input file '//trim(seedname)//'.kshell', comm)
return
else if (ierr < 0) then !end of record or end of file
exit
end if
end do
rewind (kshell_in)
kmesh_input%num_shells = num_lines
multi(:) = 0
bvec_list = 1
counter = 0
do loop = 1, tot_num_lines
read (kshell_in, '(a)', err=103, end=103) dummy2
dummy2 = adjustl(dummy2)
if (dummy2(1:1) == '!' .or. dummy2(1:1) == '#' .or. (len(trim(dummy2)) == 0)) cycle
counter = counter + 1
kmesh_input%shell_list(counter) = counter
dummy = dummy2
length = 1
dummy = adjustl(dummy)
do
pos = index(dummy, ' ')
dummy = dummy(pos + 1:)
dummy = adjustl(dummy)
if (len_trim(dummy) > 0) then
length = length + 1
else
exit
end if
end do
multi(counter) = length
read (dummy2, *, err=230, end=230) (bvec_list(i, loop), i=1, length)
end do
allocate (bvec_inp(3, maxval(multi), kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating bvec_inp in kmesh_shell_from_file', comm)
return
end if
bvec_inp = 0.0_dp
do loop = 1, kmesh_input%num_shells
do loop2 = 1, multi(loop)
bvec_inp(:, loop2, loop) = bvector(:, bvec_list(loop2, loop))
end do
end do
if (print_output%iprint >= 3) then
do shell = 1, kmesh_input%num_shells
write (stdout, '(1x,a8,1x,I2,a14,1x,I2,49x,a)') '| Shell:', shell, ' Multiplicity:', multi(shell), '|'
do loop = 1, multi(shell)
write (stdout, '(1x,a10,I2,1x,a1,4x,3f12.6,5x,a9,9x,a)') '| b-vector ', loop, ':', &
bvec_inp(:, loop, shell)/print_output%lenconfac, '('//trim(print_output%length_unit)//'^-1)', '|'
end do
end do
end if
allocate (amat(max_shells, kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating amat in kmesh_shell_from_file', comm)
return
end if
allocate (umat(max_shells, max_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating umat in kmesh_shell_from_file', comm)
return
end if
allocate (vmat(kmesh_input%num_shells, kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating vmat in kmesh_shell_from_file', comm)
return
end if
allocate (smat(kmesh_input%num_shells, max_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating smat in kmesh_shell_from_file', comm)
return
end if
allocate (singv(kmesh_input%num_shells), stat=ierr)
if (ierr /= 0) then
call set_error_alloc(error, 'Error allocating singv in kmesh_shell_from_file', comm)
return
end if
amat = 0.0_dp; umat = 0.0_dp; vmat = 0.0_dp; smat = 0.0_dp; singv = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
do loop_b = 1, multi(loop_s)
amat(1, loop_s) = amat(1, loop_s) + bvec_inp(1, loop_b, loop_s)*bvec_inp(1, loop_b, loop_s)
amat(2, loop_s) = amat(2, loop_s) + bvec_inp(2, loop_b, loop_s)*bvec_inp(2, loop_b, loop_s)
amat(3, loop_s) = amat(3, loop_s) + bvec_inp(3, loop_b, loop_s)*bvec_inp(3, loop_b, loop_s)
amat(4, loop_s) = amat(4, loop_s) + bvec_inp(1, loop_b, loop_s)*bvec_inp(2, loop_b, loop_s)
amat(5, loop_s) = amat(5, loop_s) + bvec_inp(2, loop_b, loop_s)*bvec_inp(3, loop_b, loop_s)
amat(6, loop_s) = amat(6, loop_s) + bvec_inp(3, loop_b, loop_s)*bvec_inp(1, loop_b, loop_s)
end do
end do
info = 0
call dgesvd('A', 'A', max_shells, kmesh_input%num_shells, amat, max_shells, singv, umat, &
max_shells, vmat, kmesh_input%num_shells, work, lwork, info)
if (info < 0) then
if (print_output%iprint > 0) then
write (stdout, '(1x,a,1x,I1,1x,a)') 'kmesh_shell_fixed: Argument', abs(info), &
'of dgesvd is incorrect'
end if
call set_error_fatal(error, 'kmesh_shell_from_file: Problem with Singular Value Decomposition', comm)
return
else if (info > 0) then
call set_error_fatal(error, 'kmesh_shell_from_file: Singular Value Decomposition did not converge', comm)
return
end if
if (any(abs(singv) < eps7)) then
call set_error_fatal(error, 'kmesh_shell_from_file: Singular Value Decomposition has found a very small singular value', comm)
return
end if
smat = 0.0_dp
do loop_s = 1, kmesh_input%num_shells
smat(loop_s, loop_s) = 1/singv(loop_s)
end do
bweight(1:kmesh_input%num_shells) = matmul(transpose(vmat), matmul(smat, matmul(transpose(umat), target)))
if (print_output%iprint >= 2) then
do loop_s = 1, kmesh_input%num_shells
write (stdout, '(1x,a,I2,a,f12.7,5x,a8,36x,a)') '| Shell: ', loop_s, &
' w_b ', bweight(loop_s)*print_output%lenconfac**2, '('//trim(print_output%length_unit)//'^2)', '|'
end do
end if
! note: B1 condition is not tested here; test follows this function call
if (print_output%timing_level > 1) call io_stopwatch_stop('kmesh: shell_from_file', timer)
return
103 call set_error_input(error, 'Error: Problem (3) reading input file '//trim(seedname)//'.kshell', comm)
return
230 call set_error_input(error, 'Error: Problem reading in kmesh_shell_from_file', comm)
return
end subroutine kmesh_shell_from_file
!================================================
function internal_maxloc(dist, nsupcell)
!================================================
!! A reproducible maxloc function
!! so b-vectors come in the same
!! order each time
!================================================
use w90_constants, only: eps8
implicit none
integer, intent(in) :: nsupcell
real(kind=dp), intent(in) :: dist((2*nsupcell + 1)**3)
!! Distances from the origin of the unit cells in the supercell.
integer :: internal_maxloc
integer :: guess(1), loop, counter
integer :: list((2*nsupcell + 1)**3)
list = 0
counter = 1
guess = maxloc(dist)
list(1) = guess(1)
! look for any degenerate values
do loop = 1, (2*nsupcell + 1)**3
if (loop == guess(1)) cycle
if (abs(dist(loop) - dist(guess(1))) < eps8) then
counter = counter + 1
list(counter) = loop
end if
end do
! and always return the lowest index
internal_maxloc = minval(list(1:counter))
end function internal_maxloc
!================================================
subroutine kmesh_bvectors_perm(bvec, bref, num_kpt, num_bvec, perm, invperm, revind, error, comm)
!================================================
!
!! Obtain possible permutation in ordering of b-vectors at different kpoints
!
!================================================
implicit none
! arguments
real(kind=dp), intent(in) :: bvec(:, :, :) ! set of bvecs for each k, possibly permuted, size (3,num_bvec,num_kpt)
real(kind=dp), intent(in) :: bref(:, :) ! reference vector ordering, size (3,num_bvec)
integer, intent(in) :: num_kpt, num_bvec
integer, intent(inout) :: perm(:, :) ! assumed allocated
integer, intent(inout) :: invperm(:, :) ! assumed allocated
integer, intent(inout) :: revind(:, :)
type(w90_error_type), allocatable, intent(out) :: error
type(w90_comm_type), intent(in) :: comm
! local variables
real(kind=dp), parameter :: tol = 1d-7 ! this should not be smaller than the k-point precision in the .win file
integer :: ik, n, m
logical :: found, found2
do ik = 1, num_kpt
do n = 1, num_bvec
found = .false.
found2 = .false.
do m = 1, num_bvec
if (all(abs(bvec(:, m, ik) - bref(:, n)) < tol)) then
found = .true.
perm(n, ik) = m
invperm(m, ik) = n ! inverse mapping, used in postw90
cycle
end if
if (all(abs(bvec(:, m, ik) + bref(:, n)) < tol)) then
found2 = .true.
revind(n, ik) = m
cycle
end if
end do
if (.not. found .or. .not. found2) then
call set_error_fatal(error, &
'Unable to identify bk-vector permutation (kmesh_bvectors_perm); consider k-point precision', &
comm)
return
end if
end do
end do
end subroutine kmesh_bvectors_perm
end module w90_kmesh
