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find_water_triplets_noncommercial.f95
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find_water_triplets_noncommercial.f95
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! HND XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
! HND X
! HND X GAP (Gaussian Approximation Potental)
! HND X
! HND X
! HND X Portions of GAP were written by Albert Bartok-Partay, Gabor Csanyi,
! HND X Copyright 2006-2021.
! HND X
! HND X Portions of GAP were written by Noam Bernstein as part of
! HND X his employment for the U.S. Government, and are not subject
! HND X to copyright in the USA.
! HND X
! HND X GAP is published and distributed under the
! HND X Academic Software License v1.0 (ASL)
! HND X
! HND X GAP is distributed in the hope that it will be useful for non-commercial
! HND X academic research, but WITHOUT ANY WARRANTY; without even the implied
! HND X warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! HND X ASL for more details.
! HND X
! HND X You should have received a copy of the ASL along with this program
! HND X (e.g. in a LICENSE.md file); if not, you can write to the original licensors,
! HND X Gabor Csanyi or Albert Bartok-Partay. The ASL is also published at
! HND X http://github.com/gabor1/ASL
! HND X
! HND X When using this software, please cite the following reference:
! HND X
! HND X A. P. Bartok et al Physical Review Letters vol 104 p136403 (2010)
! HND X
! HND X When using the SOAP kernel or its variants, please additionally cite:
! HND X
! HND X A. P. Bartok et al Physical Review B vol 87 p184115 (2013)
! HND X
! HND XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
!!!!!!!!
!!! This file was written by Jonatan Öström (@sujona, [email protected]) and Lars G.M. Pettersson, Stockholm University
!!! Here are implementations of water-trimer search routines, that work only for orthogonal unit cells with the shortest dimension longer than 2 x (3-body cutoff)
!!!!!!!!
module find_water_triplets
! use backend
implicit none
integer, parameter :: dp = kind(0d0)
interface insert
module procedure insert_i2, insert_r2, insert_i1
end interface
contains
! ////////////////////////////////////////////////
! Dynamic insert in allocatable array
! insert(a,i,x) does a(i) = x but reallocates a to length 2*i if len(a) < i
subroutine insert_i1(array,ii,val)
integer, intent(inout), allocatable :: array(:)
integer, intent(in) :: ii, val
integer, allocatable :: tmp(:)
if (ii>size(array))then
tmp = array
deallocate(array)
allocate(array(2*ii))
array(:size(tmp)) = tmp
endif
array(ii) = val
end
subroutine insert_i2(array,ii,val)
integer, intent(inout), allocatable :: array(:,:)
integer, intent(in) :: ii, val(:)
integer, allocatable :: tmp(:,:)
if (ii>size(array,2))then
tmp = array
deallocate(array)
allocate(array(size(tmp,1),2*ii))
array(:,:size(tmp,2)) = tmp
endif
array(:,ii) = val
end
subroutine insert_r2(array,ii,val)
real(dp), intent(inout), allocatable :: array(:,:)
real(dp), intent(in) :: val(:)
integer, intent(in) :: ii
real(dp), allocatable :: tmp(:,:)
if (ii>size(array,2))then
tmp = array
deallocate(array)
allocate(array(size(tmp,1),2*ii))
array(:,:size(tmp,2)) = tmp
endif
array(:,ii) = val
end
! ////////////////////////////////////////////////
! Utilitity routines
subroutine min_img(XO,NO,i1,i2,box,lsq,x12,s12)
real(dp), intent(in) :: XO(3,NO), box(3)
integer, intent(in) :: NO, i1, i2
real(dp), intent(out) :: lsq
real(dp), intent(out) :: x12(3)
integer, intent(out) :: s12(3)
x12 = XO(:,i1)-XO(:,i2)
s12 = nint(x12/box)
x12 = x12 - s12*box
lsq = sum(x12**2)
end
subroutine min_img_c(XO,XC,NO,i1,i2,box,lsq,x12,c12,s12)
real(dp), intent(in) :: XO(3,NO), XC(3,NO), box(3)
integer, intent(in) :: NO, i1, i2
real(dp), intent(out) :: lsq
real(dp), intent(out) :: x12(3), c12(3)
integer, intent(out) :: s12(3)
c12 = XC(:,i2)-XC(:,i1)
s12 = -nint(c12/box)
x12 = XO(:,i2)-XO(:,i1)
x12 = x12 + s12*box
c12 = c12 + s12*box
lsq = sum(x12**2)
end
subroutine average_position(NW,XW,XC,XO)
integer, intent(in) :: NW
real(dp), intent(in) :: XW(3,NW*3)
real(dp), intent(out) :: XC(3,NW),XO(3,NW)
integer ii,jj,kk
do ii = 1,NW
jj = 3*(ii-1) !+1,2,3 for O,H,H
XO(:,ii) = XW(:,jj+1)
XC(:,ii) = 0
do kk = 1,3
XC(:,ii) = XC(:,ii) + XW(:,jj+kk)/3
enddo
enddo
end
function wall_time() result(tt)
integer count,count_rate
real(dp) tt
call system_clock(count,count_rate)
tt = dble(count)/count_rate
end
subroutine take(tt,text)
real(dp), intent(inout) :: tt
real(dp) :: old
character(*), intent(in) :: text
old = tt
tt = wall_time()
print'(f6.3,a)',tt-old,"s "//text
end
! ////////////////////////////////////////////////
! Finding triplets
subroutine find_triplets_brute_force(XW,NW,box,rcut,n_trip)
! find water triplets with brute force
integer, intent(in) :: NW
real(dp), intent(in) :: XW(3,NW*3), box(3), rcut
integer, intent(out) :: n_trip
real(dp) :: rcut2, d2ij, d2ik,d2jk, XC(3,NW),XO(3,NW)
integer ii,jj,kk, n_short !n_2, n_3,
real(dp),dimension(3) :: xij,xik,xjk ! Oxygen diff
real(dp),dimension(3) :: cij,cik,cjk ! Center diff
integer, dimension(3) :: sij,sik,sjk ! Shifts
rcut2 = rcut**2
call average_position(NW,XW,XC,XO)
!!! $omp parallel do private(d2ij, d2ik,d2jk,n_short) reduction(+:n_2,n_3)
write(13,'(a)') ' '
write(13,'(a)') ' TRIPLETS'
write(13,'(a)') ' '
do ii = 1,NW
do jj = ii+1,NW
call min_img_c(XO,XC,NW,ii,jj,box,d2ij,xij,cij,sij)
do kk = jj+1,NW
call min_img_c(XO,XC,NW,ii,kk,box,d2ik,xik,cik,sik)
call min_img_c(XO,XC,NW,jj,kk,box,d2jk,xjk,cjk,sjk)
n_short = count([d2ij,d2ik,d2jk]<rcut2)
! Counting "linear" and "triangular" separately
if (n_short>1)then
n_trip = n_trip+1
write(13,'(3i5,2(3i3,2x),2(3f10.5,2x))') ii,jj,kk, sij, sik, cij,cik
endif
enddo
enddo
enddo
end
subroutine find_pairs_jona(XW,NO,box,rcut,n_pair,id2, sh2, dx2)
integer, intent(in) :: NO
real(dp), intent(in) :: XW(3,NO*3), box(3), rcut
integer, intent(out) :: n_pair
real(dp) :: rcut2, d2ij, xij(3), cij(3), XO(3,NO*3), XC(3,NO*3)
integer ii,jj, sij(3)
integer, allocatable, dimension(:,:), intent(out) :: id2, sh2
real(dp), allocatable, dimension(:,:), intent(out) :: dx2
allocate(id2(2,0), sh2(3,0), dx2(3,0))
call average_position(NO,XW,XC,XO)
rcut2 = rcut**2
n_pair = 0
do ii = 1,NO
do jj = ii+1,NO
call min_img_c(XO,XC,NO,ii,jj,box,d2ij,xij,cij,sij)
if (d2ij<rcut2) then
n_pair = n_pair + 1
call insert(id2, n_pair, [ii,jj])
call insert(sh2, n_pair, sij)
call insert(dx2, n_pair, xij)
endif
enddo
enddo
! Automatic reallocation to the correct size upon assignment
id2 = id2(:,:n_pair)
sh2 = sh2(:,:n_pair)
dx2 = dx2(:,:n_pair)
end
subroutine find_triplets_jona(XW,NO,box,rcut,n_trip,id3,sh3,dx3)
! Finds water triplets using a full pair list
integer , intent(in) :: NO
real(dp), intent(in) :: XW(3,NO*3), box(3), rcut
integer , intent(out) :: n_trip
! Allocatable pair-lists for use in trimers (with trimer cutoff)
integer , allocatable :: nindex(:), sh2(:,:)
real(dp), allocatable :: dx2(:,:)
real(dp), dimension(3,NO) :: XC,XO
real(dp), dimension(3) :: xij , cij, cik
integer , dimension(3) :: sij, sik
integer :: ii, jj, kk, jl, kl
integer :: i0, j0, i1, n_pair
real(dp) :: rcut2, d2ij
integer :: ncount(NO), offset(NO+1)
! Allocatable output arrays (id=atom index, sh=shift, dx=diff)
integer, allocatable, dimension(:,:), intent(out) :: id3, sh3
real(dp), allocatable, dimension(:,:), intent(out) :: dx3
allocate(id3(3,0), sh3(6,0), dx3(6,0))
allocate(nindex(0),sh2(3,0),dx2(3,0))
! Get molecular center (XC) and oxygen positions (XO) from water coordinates (XW)
call average_position(NO,XW,XC,XO)
! Square cutoffs for speed
rcut2 = rcut**2
n_pair = 0
n_trip = 0
ncount = 0
offset = 0
! PAIRS (with triplet cutoff)
do ii = 1,NO
do jj = 1,NO ! Double counting for full neighbor-lists
if (ii==jj) cycle
call min_img_c(XO,XC,NO,ii,jj,box,d2ij,xij,cij,sij)
if (d2ij<rcut2) then
n_pair = n_pair + 1
ncount(ii) = ncount(ii) + 1
call insert(nindex, n_pair, jj)
call insert(sh2, n_pair, sij)
call insert(dx2, n_pair, cij)
endif
enddo
offset(ii+1) = n_pair
enddo
! TRIPLETS
! a, b, c represent actual atomic indices
! All unique triplets with a<b<c are:
! 1. c-a-b(-c)
! 2. a-b-c
! 3. a-c-b
! where "-" is a distance shorter than cutoff.
! Loop indices ii, jj, kk run over molecules.
! G(ii) is the set of nighbors of ii, etc.
do ii = 1,NO
i0 = offset(ii)
i1 = offset(ii+1)
! Take jj>ii in G(ii)
do jl = 1,ncount(ii)
jj = nindex(i0+jl)
j0 = offset(jj)
sij = sh2(:,i0+jl)
cij = dx2(:,i0+jl)
if (ii<jj)then
! 1. c-a-b(-c): take kk>jj in G(ii) to get ii=a, jj=b, kk=c
do kl = jl+1,ncount(ii)
kk = nindex(i0+kl)
n_trip = n_trip + 1
sik = sh2(:,i0+kl)
cik = dx2(:,i0+kl)
call insert(id3, n_trip, [ii,jj,kk])
call insert(sh3, n_trip, [sij,sik])
call insert(dx3, n_trip, [cij,cik])
enddo
! 2. a-b-c & 3. a-c-b: take kk>ii in G(jj)\G(ii) so that ii=a, jj=b/c, kk=c/b
do kl = 1,ncount(jj)
kk = nindex(j0+kl)
if (ii<kk.and..not.any(nindex(i0+1:i1)==kk)) then
n_trip = n_trip + 1
sik = sh2(:,i0+jl) + sh2(:,j0+kl)
cik = dx2(:,i0+jl) + dx2(:,j0+kl)
call insert(id3, n_trip, [ii,jj,kk])
call insert(sh3, n_trip, [sij,sik])
call insert(dx3, n_trip, [cij,cik])
endif
enddo
endif
enddo
enddo
! Automatic reallocation to the correct size upon assignment
id3 = id3(:,:n_trip)
sh3 = sh3(:,:n_trip)
dx3 = dx3(:,:n_trip)
end
subroutine find_triplets_lars(XW,NO,box,rcut,id3,dx3,n_trip)!sh3,
! Finds water triplets using a pair list of only unique pairs
integer, intent(in) :: NO
real(dp), intent(in) :: rcut, box(3), XW(3,3*NO)
real(dp), intent(out), allocatable :: dx3(:,:)
integer, intent(out), allocatable :: id3(:,:)!, ma p3(:)!sh3(:,:)
integer, intent(out) :: n_trip
! internal
integer i0, i1, ii, jj, jl, kk, kl, jn, j0, k0
integer n_pair, num(NO), ioff(NO)
integer, allocatable :: neighbor(:) !sh2(:,:),
real(dp) , allocatable :: dx2(:,:)
real(dp) rcut2, dd, oij(3)
real(dp) XC(3,NO), XO(3,NO)
real(dp), dimension(3) :: cij,cik
integer, dimension(3) :: sij!,sik
allocate(id3(3,0),dx3(6,0))!,sh3(6,0)
allocate(neighbor(0),dx2(3,0)) !sh2(3,0),
call average_position(NO,XW,XC,XO)
! PAIRS
rcut2 = rcut**2
n_pair = 0
ioff(1) = 0
do ii = 1, NO - 1
num(ii) = 0
do jj = ii + 1, NO
oij = XO(:,jj) - XO(:,ii)
cij = XC(:,jj) - XC(:,ii)
sij = -nint(oij/box)
oij = oij + sij*box
cij = cij + sij*box
dd = sum(oij**2)
if (dd .gt. rcut2) cycle
num(ii) = num(ii) + 1
n_pair = n_pair + 1
call insert(neighbor, n_pair, jj)
! call insert(sh2, n_pair, sij)
call insert(dx2, n_pair, cij)
enddo
ioff(ii+1) = n_pair
enddo
! ioff(NO) = npairs ! important
num(NO) = 0 ! important
! TRIPLETS
! With a < b < c being actual atomic indices of unique oxygen/molecule triplets
! all forms we have are three cases
! 1. c-a-b-(c-)
! 2. a-b-c
! 3. a-c-b
! j -> N(i) means j runs over the (N)eighbors of i
! case 1. c-a-b-(c-) : let i<j<k and j -> N(i) and k -> N(i)
n_trip = 0
do ii = 1, NO - 1
i0 = ioff(ii)
i1 = ioff(ii+1)
do jl = 1, num(ii) - 1
jj = neighbor(i0 + jl)
! sij = sh2(:,i0 + jl)
cij = dx2(:,i0 + jl)
do kl = jl + 1, num(ii)
kk = neighbor(i0 + kl)
n_trip = n_trip + 1
! sik = sh2(:,i0 + kl)
cik = dx2(:,i0 + kl)
call insert(id3, n_trip, [ii,jj,kk])
! call insert(sh3, n_trip, [sij,sik])
call insert(dx3, n_trip, [cij,cik])
enddo
enddo
! case 2. a-b-c : let i<j<k and find j->N(i) and k -> N(j)\N(i)
do jl = 1, num(ii)
jj = neighbor(i0 + jl)
j0 = ioff(jj)
! sij = sh2(:,i0 + jl)
cij = dx2(:,i0 + jl)
do kl = 1, num(jj) !(1)
kk = neighbor(j0 + kl) !(2)
if (any(neighbor(i0+1:i1)==kk)) cycle
n_trip = n_trip + 1
! sik = sh2(:,i0 + jl) + sh2(:,j0 + kl)
cik = dx2(:,i0 + jl) + dx2(:,j0 + kl)
call insert(id3, n_trip, [ii,jj,kk])
! call insert(sh3, n_trip, [sij,sik])
call insert(dx3, n_trip, [cij,cik])
enddo
! case 3. a-c-b : let i=a < k=b < j=c, so for j->N(i) find k->N(j)\N(i)
! since k<j is not listed in N(j) we take k->[i+1,j-1], exclude k->N(i) and include k when j->N(k)
do kk = ii + 1, jj - 1
k0 = ioff(kk)
do jn = 1, num(kk)
if (jj /= neighbor(k0+jn)) cycle ! include j->N(k)
if (any(kk==neighbor(i0+1:i1))) cycle ! exclude k->N(i)
n_trip = n_trip + 1
! sik = sh2(:,i0 + jl) - sh2(:,k0 + jn)
cik = dx2(:,i0 + jl) - dx2(:,k0 + jn)
! insert in i<k<j order
call insert(id3, n_trip, [ii,kk,jj])
! call insert(sh3, n_trip, [sik,sij])
call insert(dx3, n_trip, [cik,cij])
enddo
enddo
enddo
enddo
! Automatic reallocation to the correct size upon assignment
id3 = id3(:,:n_trip)
! sh3 = sh3(:,:n_trip)
dx3 = dx3(:,:n_trip)
! allocate(map3(n_trip))
! do ii = 1,n_trip
! map3(ii) = ii
! enddo
end
! ////////////////////////////////////////////////
! Printing
subroutine print_pairs_or_triplets(idx,shift,diff,NO)
real(dp), allocatable,dimension(:,:), intent(inout) :: diff
integer, allocatable,dimension(:,:), intent(inout) :: idx,shift
integer, intent(in) :: NO
integer ii, nn
character(:), allocatable :: form, phrase, name
character(100) ctemp
nn = size(idx,2)
if (size(idx,1)==2)then
form = '(2i5,3i3,3f10.5)'
phrase = ' PAIRS Fast #'
write(ctemp,'(a,i0,a)') "water",NO,"-2.dat"
else
form = '(3i5,2(3i3,2x),2(3f10.5,2x))'
phrase = "Triplets Fast #"
write(ctemp,'(a,i0,a)') "water",NO,"-3.dat"
endif
name = trim(ctemp)
open(44,file=name,action="write")
write(44,'(a,i0)') phrase,nn
do ii = 1,nn
write(44,form) idx(:,ii),shift(:,ii),diff(:,ii)
enddo
close(44)
end
end module