quantum-espresso/Modules/sort.f90

325 lines
9.0 KiB
Fortran

!
! Copyright (C) 2001-2022 Quantum ESPRESSO Foundation
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!---------------------------------------------------------------------
subroutine hpsort_eps (n, ra, ind, eps)
!---------------------------------------------------------------------
!! Sort an array ra(1:n) into ascending order using heapsort algorithm,
!! and considering two elements being equal if their values differ
!! for less than "eps". IMPORTANT NOTICE (PG February 2022):
!! Assume you have in input a,b,c with c < b < a and a-b < eps, b-c < eps,
!! but a-c > eps. The resulting output order should be c,a,b, but may turn
!! out to be a,b,c instead. I think this is a bug. I don't know how to fix
!! it, I am not sure it does any harm, but re-ordering k+G with this same
!! routine may yield a different ordering for k+G and G vectors even if k=0.
!! This is a bug that has been around for years. The current work-around
!! (in routine gk_sort) is to avoid recomputing indices for k+G if k=0.
!!
!! \(\text{n}\) is input, \(\text{ra}\) is replaced on output by its
!! sorted rearrangement.
!! Create an index table (ind) by making an exchange in the index array
!! whenever an exchange is made on the sorted data array (\(\text{ra}\)).
!! In case of equal values in the data array (\(\text{ra}\)) the values
!! in the index array (ind) are used to order the entries.
!! If on input ind(1) = 0 then indices are initialized in the routine,
!! if on input ind(1) != 0 then indices are assumed to have been
!! initialized before entering the routine and these indices are carried
!! around during the sorting process.
!
! no work space needed !
! free us from machine-dependent sorting-routines !
!
! adapted from Numerical Recipes pg. 329 (new edition)
!
use kinds, only : DP
implicit none
!-input/output variables
integer, intent(in) :: n
integer, intent(inout) :: ind (*)
real(DP), intent(inout) :: ra (*)
real(DP), intent(in) :: eps
!-local variables
integer :: i, ir, j, l, iind
real(DP) :: rra
! initialize index array
if (ind (1) .eq.0) then
do i = 1, n
ind (i) = i
enddo
endif
! nothing to order
if (n.lt.2) return
! initialize indices for hiring and retirement-promotion phase
l = n / 2 + 1
ir = n
sorting: do
! still in hiring phase
if ( l .gt. 1 ) then
l = l - 1
rra = ra (l)
iind = ind (l)
! in retirement-promotion phase.
else
! clear a space at the end of the array
rra = ra (ir)
!
iind = ind (ir)
! retire the top of the heap into it
ra (ir) = ra (1)
!
ind (ir) = ind (1)
! decrease the size of the corporation
ir = ir - 1
! done with the last promotion
if ( ir .eq. 1 ) then
! the least competent worker at all !
ra (1) = rra
!
ind (1) = iind
exit sorting
endif
endif
! wheter in hiring or promotion phase, we
i = l
! set up to place rra in its proper level
j = l + l
!
do while ( j .le. ir )
if ( j .lt. ir ) then
! compare to better underling
if ( abs(ra(j)-ra(j+1)).ge.eps ) then
if (ra(j).lt.ra(j+1)) j = j + 1
else
! this means ra(j) == ra(j+1) within tolerance
if (ind (j) .lt.ind (j + 1) ) j = j + 1
endif
endif
! demote rra
if ( abs(rra - ra(j)).ge.eps ) then
if (rra.lt.ra(j)) then
ra (i) = ra (j)
ind (i) = ind (j)
i = j
j = j + j
else
! set j to terminate do-while loop
j = ir + 1
end if
else
!this means rra == ra(j) within tolerance
! demote rra
if (iind.lt.ind (j) ) then
ra (i) = ra (j)
ind (i) = ind (j)
i = j
j = j + j
else
! set j to terminate do-while loop
j = ir + 1
endif
end if
enddo
ra (i) = rra
ind (i) = iind
end do sorting
!
end subroutine hpsort_eps
!
!---------------------------------------------------------------------
subroutine hpsort (n, ra, ind)
!---------------------------------------------------------------------
!! Sort an array ra(1:n) into ascending order using heapsort algorithm.
!! As hpsort_eps, without the "eps" trick (or equivalently, eps=0)
!
use kinds, only : DP
implicit none
!-input/output variables
integer :: n
integer :: ind (*)
real(DP) :: ra (*)
!-local variables
integer :: i, ir, j, l, iind
real(DP) :: rra
! initialize index array
if (ind (1) .eq.0) then
do i = 1, n
ind (i) = i
enddo
endif
! nothing to order
if (n.lt.2) return
! initialize indices for hiring and retirement-promotion phase
l = n / 2 + 1
ir = n
10 continue
! still in hiring phase
if (l.gt.1) then
l = l - 1
rra = ra (l)
iind = ind (l)
! in retirement-promotion phase.
else
! clear a space at the end of the array
rra = ra (ir)
!
iind = ind (ir)
! retire the top of the heap into it
ra (ir) = ra (1)
!
ind (ir) = ind (1)
! decrease the size of the corporation
ir = ir - 1
! done with the last promotion
if (ir.eq.1) then
! the least competent worker at all !
ra (1) = rra
!
ind (1) = iind
return
endif
endif
! wheter in hiring or promotion phase, we
i = l
! set up to place rra in its proper level
j = l + l
!
do while (j.le.ir)
if (j.lt.ir) then
! compare to better underling
if (ra (j) .lt.ra (j + 1) ) then
j = j + 1
elseif (ra (j) .eq.ra (j + 1) ) then
if (ind (j) .lt.ind (j + 1) ) j = j + 1
endif
endif
! demote rra
if (rra.lt.ra (j) ) then
ra (i) = ra (j)
ind (i) = ind (j)
i = j
j = j + j
elseif (rra.eq.ra (j) ) then
! demote rra
if (iind.lt.ind (j) ) then
ra (i) = ra (j)
ind (i) = ind (j)
i = j
j = j + j
else
! set j to terminate do-while loop
j = ir + 1
endif
! this is the right place for rra
else
! set j to terminate do-while loop
j = ir + 1
endif
enddo
ra (i) = rra
ind (i) = iind
goto 10
!
end subroutine hpsort
!
!---------------------------------------------------------------------
subroutine ihpsort (n, ia, ind)
!---------------------------------------------------------------------
!! As "hpsort", for integer array ia(1:n)
!
implicit none
!-input/output variables
integer :: n
integer :: ind (*)
integer :: ia (*)
!-local variables
integer :: i, ir, j, l, iind
integer :: iia
! initialize index array
if (ind (1) .eq.0) then
do i = 1, n
ind (i) = i
enddo
endif
! nothing to order
if (n.lt.2) return
! initialize indices for hiring and retirement-promotion phase
l = n / 2 + 1
ir = n
10 continue
! still in hiring phase
if (l.gt.1) then
l = l - 1
iia = ia (l)
iind = ind (l)
! in retirement-promotion phase.
else
! clear a space at the end of the array
iia = ia (ir)
!
iind = ind (ir)
! retire the top of the heap into it
ia (ir) = ia (1)
!
ind (ir) = ind (1)
! decrease the size of the corporation
ir = ir - 1
! done with the last promotion
if (ir.eq.1) then
! the least competent worker at all !
ia (1) = iia
!
ind (1) = iind
return
endif
endif
! wheter in hiring or promotion phase, we
i = l
! set up to place iia in its proper level
j = l + l
!
do while (j.le.ir)
if (j.lt.ir) then
! compare to better underling
if (ia (j) .lt.ia (j + 1) ) then
j = j + 1
elseif (ia (j) .eq.ia (j + 1) ) then
if (ind (j) .lt.ind (j + 1) ) j = j + 1
endif
endif
! demote iia
if (iia.lt.ia (j) ) then
ia (i) = ia (j)
ind (i) = ind (j)
i = j
j = j + j
elseif (iia.eq.ia (j) ) then
! demote iia
if (iind.lt.ind (j) ) then
ia (i) = ia (j)
ind (i) = ind (j)
i = j
j = j + j
else
! set j to terminate do-while loop
j = ir + 1
endif
! this is the right place for iia
else
! set j to terminate do-while loop
j = ir + 1
endif
enddo
ia (i) = iia
ind (i) = iind
goto 10
!
end subroutine ihpsort