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quantum-espresso/flib/sort.f90

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!
! Copyright (C) 2002 FPMD group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
logical function cpgt(a,b)
USE kinds
USE constants, only: eps8
implicit none
REAL(dbl) :: a, b, r
r = abs(a-b)
if( r .lt. eps8 ) then
cpgt = .false.
else
cpgt = ( a .gt. b )
end if
end
logical function cplt(a,b)
USE kinds
USE constants, only: eps8
implicit none
REAL(dbl) :: a, b, r
r = abs(a-b)
if( r .lt. eps8 ) then
cplt = .false.
else
cplt = ( a .lt. b )
end if
end
!
! Copyright (C) 2001 PWSCF group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!---------------------------------------------------------------------
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".
! n is input, 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 (ra).
! in case of equal values in the data array (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
implicit none
!-input/output variables
integer, intent(in) :: n
integer, intent(inout) :: ind (n)
real(dbl), intent(inout) :: ra (n)
real(dbl), intent(in) :: eps
!-local variables
integer :: i, ir, j, l, iind
real(dbl) :: 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 ( hslt( ra (j), ra (j + 1) ) ) then
j = j + 1
endif
endif
! demote rra
if ( hslt( rra, 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
endif
enddo
ra (i) = rra
ind (i) = iind
end do sorting
contains
! internal function
! compare two real number and return the result
logical function hslt( a, b )
REAL(dbl) :: a, b
if( abs(a-b) < eps ) then
hslt = .false.
else
hslt = ( a < b )
end if
end function
!
end subroutine hpsort_eps
!
! Copyright (C) 2001 PWSCF group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!---------------------------------------------------------------------
subroutine hpsort (n, ra, ind)
!---------------------------------------------------------------------
! sort an array ra(1:n) into ascending order using heapsort algorithm.
! n is input, 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 (ra).
! in case of equal values in the data array (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
implicit none
!-input/output variables
integer :: n
integer :: ind (n)
real(dbl) :: ra (n)
!-local variables
integer :: i, ir, j, l, iind
real(dbl) :: 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
!
! Copyright (C) 2001 PWSCF group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!---------------------------------------------------------------------
subroutine ihpsort (n, ia, ind)
!---------------------------------------------------------------------
! sort an integer array ia(1:n) into ascending order using heapsort algorithm.
! n is input, ia 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 (ia).
! in case of equal values in the data array (ia) 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)
!
implicit none
!-input/output variables
integer :: n
integer :: ind (n)
integer :: ia (n)
!-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
! ==================================================================
SUBROUTINE gqsort(COUNT,N,INDEX)
! ==--------------------------------------------------------------==
! == Sorting routine for the reciprocal space vectors (g) ==
! == Warning, this is not an exact SORT!! This routine has been ==
! == designed to give always the same order for the G vectors of ==
! == a given shell, independently of the processor ==
! == THE WORK-SPACE 'MARK' OF LENGTH 50 PERMITS UP TO 2**(50/2) ==
! ==--------------------------------------------------------------==
USE kinds
INTEGER :: N, MARK, I, M, LA, IS, IF, MLOOP, IFKA, IS1, J, INT, &
IY, INTEST, K, IFK, K1, IP, LNGTH
logical :: cpgt,cplt
REAL(dbl) :: COUNT(N),AV,X
INTEGER :: INDEX(N)
DIMENSION :: MARK(50)
! ==--------------------------------------------------------------==
! == SET INDEX ARRAY TO ORIGINAL ORDER . ==
! ==--------------------------------------------------------------==
DO I=1,N
INDEX(I)=I
ENDDO
! ==--------------------------------------------------------------==
! == CHECK THAT A TRIVIAL CASE HAS NOT BEEN ENTERED. ==
! ==--------------------------------------------------------------==
IF(N.EQ.1)GOTO 200
IF(N.GE.1)GOTO 30
GOTO 200
! ==--------------------------------------------------------------==
! == 'M' IS THE LENGTH OF SEGMENT WHICH IS SHORT ENOUGH TO ENTER ==
! == THE FINAL SORTING ROUTINE. IT MAY BE EASILY CHANGED. ==
! ==--------------------------------------------------------------==
30 M=12
! ==--------------------------------------------------------------==
! == SET UP INITIAL VALUES. ==
! ==--------------------------------------------------------------==
LA=2
IS=1
IF=N
DO 190 MLOOP=1,N
! ==--------------------------------------------------------------==
! == IF SEGMENT IS SHORT ENOUGH SORT WITH FINAL SORTING ROUTINE. ==
! ==--------------------------------------------------------------==
IFKA=IF-IS
IF((IFKA+1).GT.M)GOTO 70
! ==--------------------------------------------------------------==
! == FINAL SORTING ( A SIMPLE BUBBLE SORT ) ==
! ==--------------------------------------------------------------==
IS1=IS+1
DO 60 J=IS1,IF
I=J
40 IF(cplt(COUNT(I-1),COUNT(I)) )GOTO 60
IF(cpgt(COUNT(I-1),COUNT(I)) )GOTO 50
IF(INDEX(I-1).LT.INDEX(I))GOTO 60
50 AV=COUNT(I-1)
COUNT(I-1)=COUNT(I)
COUNT(I)=AV
INT=INDEX(I-1)
INDEX(I-1)=INDEX(I)
INDEX(I)=INT
I=I-1
IF(I.GT.IS)GOTO 40
60 CONTINUE
LA=LA-2
GOTO 170
! ==--------------------------------------------------------------==
! == ******* QUICKSORT ******** ==
! == SELECT THE NUMBER IN THE CENTRAL POSITION IN THE SEGMENT AS ==
! == THE TEST NUMBER.REPLACE IT WITH THE NUMBER FROM THE SEGMENT'S==
! == HIGHEST ADDRESS. ==
! ==--------------------------------------------------------------==
70 IY=(IS+IF)/2
X=COUNT(IY)
INTEST=INDEX(IY)
COUNT(IY)=COUNT(IF)
INDEX(IY)=INDEX(IF)
! ==--------------------------------------------------------------==
! == THE MARKERS 'I' AND 'IFK' ARE USED FOR THE BEGINNING AND END ==
! == OF THE SECTION NOT SO FAR TESTED AGAINST THE PRESENT VALUE ==
! == OF X . ==
! ==--------------------------------------------------------------==
K=1
IFK=IF
! ==--------------------------------------------------------------==
! == WE ALTERNATE BETWEEN THE OUTER LOOP THAT INCREASES I AND THE ==
! == INNER LOOP THAT REDUCES IFK, MOVING NUMBERS AND INDICES AS ==
! == NECESSARY, UNTIL THEY MEET . ==
! ==--------------------------------------------------------------==
DO 110 I=IS,IF
IF(cpgt(X,COUNT(I)))GOTO 110
IF(cplt(X,COUNT(I)))GOTO 80
IF(INTEST.GT.INDEX(I))GOTO 110
80 IF(I.GE.IFK)GOTO 120
COUNT(IFK)=COUNT(I)
INDEX(IFK)=INDEX(I)
K1=K
DO 100 K=K1,IFKA
IFK=IF-K
IF(cpgt(COUNT(IFK),X))GOTO 100
IF(cplt(COUNT(IFK),X))GOTO 90
IF(INTEST.LE.INDEX(IFK))GOTO 100
90 IF(I.GE.IFK)GOTO 130
COUNT(I)=COUNT(IFK)
INDEX(I)=INDEX(IFK)
GO TO 110
100 CONTINUE
GOTO 120
110 CONTINUE
! ==--------------------------------------------------------------==
! == RETURN THE TEST NUMBER TO THE POSITION MARKED BY THE MARKER ==
! == WHICH DID NOT MOVE LAST. IT DIVIDES THE INITIAL SEGMENT INTO ==
! == 2 PARTS. ANY ELEMENT IN THE FIRST PART IS LESS THAN OR EQUAL ==
! == TO ANY ELEMENT IN THE SECOND PART, AND THEY MAY NOW BE SORTED==
! == INDEPENDENTLY . ==
! ==--------------------------------------------------------------==
120 COUNT(IFK)=X
INDEX(IFK)=INTEST
IP=IFK
GOTO 140
130 COUNT(I)=X
INDEX(I)=INTEST
IP=I
! ==--------------------------------------------------------------==
! == STORE THE LONGER SUBDIVISION IN WORKSPACE. ==
! ==--------------------------------------------------------------==
140 IF((IP-IS).GT.(IF-IP))GOTO 150
MARK(LA)=IF
MARK(LA-1)=IP+1
IF=IP-1
GOTO 160
150 MARK(LA)=IP-1
MARK(LA-1)=IS
IS=IP+1
! ==--------------------------------------------------------------==
! == FIND THE LENGTH OF THE SHORTER SUBDIVISION. ==
! ==--------------------------------------------------------------==
160 LNGTH=IF-IS
IF(LNGTH.LE.0)GOTO 180
! ==--------------------------------------------------------------==
! == IF IT CONTAINS MORE THAN ONE ELEMENT SUPPLY IT WITH WORKSPACE==
! ==--------------------------------------------------------------==
LA=LA+2
GOTO 190
170 IF(LA.LE.0)GOTO 200
! ==--------------------------------------------------------------==
! == OBTAIN THE ADDRESS OF THE SHORTEST SEGMENT AWAITING QUICKSORT==
! ==--------------------------------------------------------------==
180 IF=MARK(LA)
IS=MARK(LA-1)
190 CONTINUE
! ==--------------------------------------------------------------==
200 RETURN
END
! ==================================================================
! ==================================================================
SUBROUTINE iqsort(COUNT,N,INDEX)
! ==--------------------------------------------------------------==
! == same as rqsort but for array of integers ==
! ==--------------------------------------------------------------==
USE kinds
INTEGER :: N, I, M, LA, IS, IF, MLOOP, IFKA, IS1, J, INT, &
IY, INTEST, K, IFK, K1, IP, LNGTH
INTEGER :: COUNT(N),AV,X
INTEGER INDEX(N)
INTEGER MARK(50)
! ==--------------------------------------------------------------==
! == SET INDEX ARRAY TO ORIGINAL ORDER . ==
! ==--------------------------------------------------------------==
DO I=1,N
INDEX(I)=I
ENDDO
! ==--------------------------------------------------------------==
! == CHECK THAT A TRIVIAL CASE HAS NOT BEEN ENTERED. ==
! ==--------------------------------------------------------------==
IF(N.EQ.1)GOTO 200
IF(N.GE.1)GOTO 30
GOTO 200
! ==--------------------------------------------------------------==
! == 'M' IS THE LENGTH OF SEGMENT WHICH IS SHORT ENOUGH TO ENTER ==
! == THE FINAL SORTING ROUTINE. IT MAY BE EASILY CHANGED. ==
! ==--------------------------------------------------------------==
30 M=12
! ==--------------------------------------------------------------==
! == SET UP INITIAL VALUES. ==
! ==--------------------------------------------------------------==
LA=2
IS=1
IF=N
DO 190 MLOOP=1,N
! ==--------------------------------------------------------------==
! == IF SEGMENT IS SHORT ENOUGH SORT WITH FINAL SORTING ROUTINE. ==
! ==--------------------------------------------------------------==
IFKA=IF-IS
IF((IFKA+1).GT.M)GOTO 70
! ==--------------------------------------------------------------==
! == FINAL SORTING ( A SIMPLE BUBBLE SORT ) ==
! ==--------------------------------------------------------------==
IS1=IS+1
DO 60 J=IS1,IF
I=J
40 IF((COUNT(I-1).LT.COUNT(I)) )GOTO 60
IF((COUNT(I-1).GT.COUNT(I)) )GOTO 50
IF(INDEX(I-1).LT.INDEX(I))GOTO 60
50 AV=COUNT(I-1)
COUNT(I-1)=COUNT(I)
COUNT(I)=AV
INT=INDEX(I-1)
INDEX(I-1)=INDEX(I)
INDEX(I)=INT
I=I-1
IF(I.GT.IS)GOTO 40
60 CONTINUE
LA=LA-2
GOTO 170
! ==--------------------------------------------------------------==
! == ******* QUICKSORT ******** ==
! == SELECT THE NUMBER IN THE CENTRAL POSITION IN THE SEGMENT AS ==
! == THE TEST NUMBER.REPLACE IT WITH THE NUMBER FROM THE SEGMENT'S==
! == HIGHEST ADDRESS. ==
! ==--------------------------------------------------------------==
70 IY=(IS+IF)/2
X=COUNT(IY)
INTEST=INDEX(IY)
COUNT(IY)=COUNT(IF)
INDEX(IY)=INDEX(IF)
! ==--------------------------------------------------------------==
! == THE MARKERS 'I' AND 'IFK' ARE USED FOR THE BEGINNING AND END ==
! == OF THE SECTION NOT SO FAR TESTED AGAINST THE PRESENT VALUE ==
! == OF X . ==
! ==--------------------------------------------------------------==
K=1
IFK=IF
! ==--------------------------------------------------------------==
! == WE ALTERNATE BETWEEN THE OUTER LOOP THAT INCREASES I AND THE ==
! == INNER LOOP THAT REDUCES IFK, MOVING NUMBERS AND INDICES AS ==
! == NECESSARY, UNTIL THEY MEET . ==
! ==--------------------------------------------------------------==
DO 110 I=IS,IF
IF((X.GT.COUNT(I)))GOTO 110
IF((X.LT.COUNT(I)))GOTO 80
IF(INTEST.GT.INDEX(I))GOTO 110
80 IF(I.GE.IFK)GOTO 120
COUNT(IFK)=COUNT(I)
INDEX(IFK)=INDEX(I)
K1=K
DO 100 K=K1,IFKA
IFK=IF-K
IF((COUNT(IFK).GT.X))GOTO 100
IF((COUNT(IFK).LT.X))GOTO 90
IF(INTEST.LE.INDEX(IFK))GOTO 100
90 IF(I.GE.IFK)GOTO 130
COUNT(I)=COUNT(IFK)
INDEX(I)=INDEX(IFK)
GO TO 110
100 CONTINUE
GOTO 120
110 CONTINUE
! ==--------------------------------------------------------------==
! == RETURN THE TEST NUMBER TO THE POSITION MARKED BY THE MARKER ==
! == WHICH DID NOT MOVE LAST. IT DIVIDES THE INITIAL SEGMENT INTO ==
! == 2 PARTS. ANY ELEMENT IN THE FIRST PART IS LESS THAN OR EQUAL ==
! == TO ANY ELEMENT IN THE SECOND PART, AND THEY MAY NOW BE SORTED==
! == INDEPENDENTLY . ==
! ==--------------------------------------------------------------==
120 COUNT(IFK)=X
INDEX(IFK)=INTEST
IP=IFK
GOTO 140
130 COUNT(I)=X
INDEX(I)=INTEST
IP=I
! ==--------------------------------------------------------------==
! == STORE THE LONGER SUBDIVISION IN WORKSPACE. ==
! ==--------------------------------------------------------------==
140 IF((IP-IS).GT.(IF-IP))GOTO 150
MARK(LA)=IF
MARK(LA-1)=IP+1
IF=IP-1
GOTO 160
150 MARK(LA)=IP-1
MARK(LA-1)=IS
IS=IP+1
! ==--------------------------------------------------------------==
! == FIND THE LENGTH OF THE SHORTER SUBDIVISION. ==
! ==--------------------------------------------------------------==
160 LNGTH=IF-IS
IF(LNGTH.LE.0)GOTO 180
! ==--------------------------------------------------------------==
! == IF IT CONTAINS MORE THAN ONE ELEMENT SUPPLY IT WITH WORKSPACE==
! ==--------------------------------------------------------------==
LA=LA+2
GOTO 190
170 IF(LA.LE.0)GOTO 200
! ==--------------------------------------------------------------==
! == OBTAIN THE ADDRESS OF THE SHORTEST SEGMENT AWAITING QUICKSORT==
! ==--------------------------------------------------------------==
180 IF=MARK(LA)
IS=MARK(LA-1)
190 CONTINUE
! ==--------------------------------------------------------------==
200 RETURN
END
! ==================================================================
! ==================================================================
SUBROUTINE rqsort(COUNT,N,INDEX)
! ==--------------------------------------------------------------==
! == Sorting routine for the double precison arrayis ==
! == THE WORK-SPACE 'MARK' OF LENGTH 50 PERMITS UP TO 2**(50/2) ==
! ==--------------------------------------------------------------==
USE kinds
INTEGER :: N, MARK, I, M, LA, IS, IF, MLOOP, IFKA, IS1, J, INT, &
IY, INTEST, K, IFK, K1, IP, LNGTH
REAL(dbl) COUNT(N),AV,X
INTEGER INDEX(N)
DIMENSION MARK(50)
! ==--------------------------------------------------------------==
! == SET INDEX ARRAY TO ORIGINAL ORDER . ==
! ==--------------------------------------------------------------==
DO I=1,N
INDEX(I)=I
ENDDO
! ==--------------------------------------------------------------==
! == CHECK THAT A TRIVIAL CASE HAS NOT BEEN ENTERED. ==
! ==--------------------------------------------------------------==
IF(N.EQ.1)GOTO 200
IF(N.GE.1)GOTO 30
GOTO 200
! ==--------------------------------------------------------------==
! == 'M' IS THE LENGTH OF SEGMENT WHICH IS SHORT ENOUGH TO ENTER ==
! == THE FINAL SORTING ROUTINE. IT MAY BE EASILY CHANGED. ==
! ==--------------------------------------------------------------==
30 M=12
! ==--------------------------------------------------------------==
! == SET UP INITIAL VALUES. ==
! ==--------------------------------------------------------------==
LA=2
IS=1
IF=N
DO 190 MLOOP=1,N
! ==--------------------------------------------------------------==
! == IF SEGMENT IS SHORT ENOUGH SORT WITH FINAL SORTING ROUTINE. ==
! ==--------------------------------------------------------------==
IFKA=IF-IS
IF((IFKA+1).GT.M)GOTO 70
! ==--------------------------------------------------------------==
! == FINAL SORTING ( A SIMPLE BUBBLE SORT ) ==
! ==--------------------------------------------------------------==
IS1=IS+1
DO 60 J=IS1,IF
I=J
40 IF( (COUNT(I-1) .LT. COUNT(I)) )GOTO 60
IF( (COUNT(I-1) .GT. COUNT(I)) )GOTO 50
IF(INDEX(I-1).LT.INDEX(I))GOTO 60
50 AV=COUNT(I-1)
COUNT(I-1)=COUNT(I)
COUNT(I)=AV
INT=INDEX(I-1)
INDEX(I-1)=INDEX(I)
INDEX(I)=INT
I=I-1
IF(I.GT.IS)GOTO 40
60 CONTINUE
LA=LA-2
GOTO 170
! ==--------------------------------------------------------------==
! == ******* QUICKSORT ******** ==
! == SELECT THE NUMBER IN THE CENTRAL POSITION IN THE SEGMENT AS ==
! == THE TEST NUMBER.REPLACE IT WITH THE NUMBER FROM THE SEGMENT'S==
! == HIGHEST ADDRESS. ==
! ==--------------------------------------------------------------==
70 IY=(IS+IF)/2
X=COUNT(IY)
INTEST=INDEX(IY)
COUNT(IY)=COUNT(IF)
INDEX(IY)=INDEX(IF)
! ==--------------------------------------------------------------==
! == THE MARKERS 'I' AND 'IFK' ARE USED FOR THE BEGINNING AND END ==
! == OF THE SECTION NOT SO FAR TESTED AGAINST THE PRESENT VALUE ==
! == OF X . ==
! ==--------------------------------------------------------------==
K=1
IFK=IF
! ==--------------------------------------------------------------==
! == WE ALTERNATE BETWEEN THE OUTER LOOP THAT INCREASES I AND THE ==
! == INNER LOOP THAT REDUCES IFK, MOVING NUMBERS AND INDICES AS ==
! == NECESSARY, UNTIL THEY MEET . ==
! ==--------------------------------------------------------------==
DO 110 I=IS,IF
IF((X .GT. COUNT(I)))GOTO 110
IF((X .LT. COUNT(I)))GOTO 80
IF(INTEST.GT.INDEX(I))GOTO 110
80 IF(I.GE.IFK)GOTO 120
COUNT(IFK)=COUNT(I)
INDEX(IFK)=INDEX(I)
K1=K
DO 100 K=K1,IFKA
IFK=IF-K
IF((COUNT(IFK) .GT. X))GOTO 100
IF((COUNT(IFK) .LT. X))GOTO 90
IF(INTEST.LE.INDEX(IFK))GOTO 100
90 IF(I.GE.IFK)GOTO 130
COUNT(I)=COUNT(IFK)
INDEX(I)=INDEX(IFK)
GO TO 110
100 CONTINUE
GOTO 120
110 CONTINUE
! ==--------------------------------------------------------------==
! == RETURN THE TEST NUMBER TO THE POSITION MARKED BY THE MARKER ==
! == WHICH DID NOT MOVE LAST. IT DIVIDES THE INITIAL SEGMENT INTO ==
! == 2 PARTS. ANY ELEMENT IN THE FIRST PART IS LESS THAN OR EQUAL ==
! == TO ANY ELEMENT IN THE SECOND PART, AND THEY MAY NOW BE SORTED==
! == INDEPENDENTLY . ==
! ==--------------------------------------------------------------==
120 COUNT(IFK)=X
INDEX(IFK)=INTEST
IP=IFK
GOTO 140
130 COUNT(I)=X
INDEX(I)=INTEST
IP=I
! ==--------------------------------------------------------------==
! == STORE THE LONGER SUBDIVISION IN WORKSPACE. ==
! ==--------------------------------------------------------------==
140 IF((IP-IS).GT.(IF-IP))GOTO 150
MARK(LA)=IF
MARK(LA-1)=IP+1
IF=IP-1
GOTO 160
150 MARK(LA)=IP-1
MARK(LA-1)=IS
IS=IP+1
! ==--------------------------------------------------------------==
! == FIND THE LENGTH OF THE SHORTER SUBDIVISION. ==
! ==--------------------------------------------------------------==
160 LNGTH=IF-IS
IF(LNGTH.LE.0)GOTO 180
! ==--------------------------------------------------------------==
! == IF IT CONTAINS MORE THAN ONE ELEMENT SUPPLY IT WITH WORKSPACE==
! ==--------------------------------------------------------------==
LA=LA+2
GOTO 190
170 IF(LA.LE.0)GOTO 200
! ==--------------------------------------------------------------==
! == OBTAIN THE ADDRESS OF THE SHORTEST SEGMENT AWAITING QUICKSORT==
! ==--------------------------------------------------------------==
180 IF=MARK(LA)
IS=MARK(LA-1)
190 CONTINUE
! ==--------------------------------------------------------------==
200 RETURN
END
! ==================================================================
!-------------------------------------------------------------------------
subroutine kb07ad_cp90(count,n,index)
!-------------------------------------------------------------------------
!
! kb07ad handles double precision variables
! standard fortran 66 (a verified pfort subroutine)
! the work-space 'mark' of length 50 permits up to 2**(50/2) numbers
! to be sorted.
implicit none
integer n, index(n)
real(kind=8) count(n)
real(kind=8) av, x
integer k1, ifk, lngth, ip, k, int, ifka, intest, iy
integer i, m, la, is, if, mloop, ifca, is1, j, mark(50)
! set index array to original order .
do i=1,n
index(i)=i
end do
! check that a trivial case has not been entered .
if(n.eq.1) go to 10
if(n.gt.1) go to 30
write(6,20)
20 format(///20x,'***kb07ad***no numbers to be sorted ** return to', &
& ' calling program' )
goto 10
! 'm' is the length of segment which is short enough to enter
! the final sorting routine. it may be easily changed.
30 m=12
! set up initial values.
la=2
is=1
if=n
do 190 mloop=1,n
! if segment is short enough sort with final sorting routine .
ifka=if-is
if((ifka+1).gt.m)goto 70
!********* final sorting ***
! ( a simple bubble sort )
is1=is+1
do 60 j=is1,if
i=j
40 if(count(i-1).lt.count(i))goto 60
if(count(i-1).gt.count(i))goto 50
if(index(i-1).lt.index(i))goto 60
50 av=count(i-1)
count(i-1)=count(i)
count(i)=av
int=index(i-1)
index(i-1)=index(i)
index(i)=int
i=i-1
if(i.gt.is)goto 40
60 continue
la=la-2
goto 170
! ******* quicksort ********
! select the number in the central position in the segment as
! the test number.replace it with the number from the segment's
! highest address.
70 iy=(is+if)/2
x=count(iy)
intest=index(iy)
count(iy)=count(if)
index(iy)=index(if)
! the markers 'i' and 'ifk' are used for the beginning and end
! of the section not so far tested against the present value
! of x .
k=1
ifk=if
! we alternate between the outer loop that increases i and the
! inner loop that reduces ifk, moving numbers and indices as
! necessary, until they meet .
do 110 i=is,if
if(x.gt.count(i))goto 110
if(x.lt.count(i))goto 80
if(intest.gt.index(i))goto 110
80 if(i.ge.ifk)goto 120
count(ifk)=count(i)
index(ifk)=index(i)
k1=k
do 100 k=k1,ifka
ifk=if-k
if(count(ifk).gt.x)goto 100
if(count(ifk).lt.x)goto 90
if(intest.le.index(ifk))goto 100
90 if(i.ge.ifk)goto 130
count(i)=count(ifk)
index(i)=index(ifk)
go to 110
100 continue
goto 120
110 continue
! return the test number to the position marked by the marker
! which did not move last. it divides the initial segment into
! 2 parts. any element in the first part is less than or equal
! to any element in the second part, and they may now be sorted
! independently .
120 count(ifk)=x
index(ifk)=intest
ip=ifk
goto 140
130 count(i)=x
index(i)=intest
ip=i
! store the longer subdivision in workspace.
140 if((ip-is).gt.(if-ip))goto 150
mark(la)=if
mark(la-1)=ip+1
if=ip-1
goto 160
150 mark(la)=ip-1
mark(la-1)=is
is=ip+1
! find the length of the shorter subdivision.
160 lngth=if-is
if(lngth.le.0)goto 180
! if it contains more than one element supply it with workspace .
la=la+2
goto 190
170 if(la.le.0)goto 10
! obtain the address of the shortest segment awaiting quicksort
180 if=mark(la)
is=mark(la-1)
190 continue
10 return
end
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