!BOP ! !MODULE: ice_spacecurve module ice_spacecurve 1,1 ! !DESCRIPTION: ! This module contains routines necessary to ! create space-filling curves. ! ! !REVISION HISTORY: ! SVN:$Id: $ ! ! author: John Dennis, NCAR ! !USES: use ice_kinds_mod implicit none ! !PUBLIC TYPES: type, public :: factor_t integer(int_kind) :: numfact ! The # of factors for a value integer(int_kind), dimension(:),pointer :: factors ! The factors integer(int_kind), dimension(:), pointer :: used end type ! !PUBLIC MEMBER FUNCTIONS: public :: GenSpaceCurve, & IsLoadBalanced public :: Factor, & IsFactorable, & PrintFactor, & ProdFactor, & MatchFactor ! !PRIVATE MEMBER FUNCTIONS: private :: map, & PeanoM, & Hilbert, & Cinco, & GenCurve private :: FirstFactor, & FindandMark integer(int_kind), dimension(:,:), allocatable :: & dir, &! direction to move along each level ordered ! the ordering integer(int_kind), dimension(:), allocatable :: & pos ! position along each of the axes integer(int_kind) :: & maxdim, &! dimensionality of entire space vcnt ! visitation count logical :: verbose=.FALSE. type (factor_t), public,save :: fact ! stores the factorization !EOP !EOC !*********************************************************************** contains !*********************************************************************** !BOP ! !IROUTINE: Cinco ! !INTERFACE: recursive function Cinco(l,type,ma,md,ja,jd) result(ierr) 2,150 ! !DESCRIPTION: ! This subroutine implements a Cinco space-filling curve. ! Cinco curves connect a Nb x Nb block of points where ! ! Nb = 5^p ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS integer(int_kind), intent(in) :: & l, & ! level of the space-filling curve type, & ! type of SFC curve ma, & ! Major axis [0,1] md, & ! direction of major axis [-1,1] ja, & ! joiner axis [0,1] jd ! direction of joiner axis [-1,1] ! !OUTPUT PARAMETERS integer(int_kind) :: ierr ! error return code !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & lma, &! local major axis (next level) lmd, &! local major direction (next level) lja, &! local joiner axis (next level) ljd, &! local joiner direction (next level) ltype, &! type of SFC on next level ll ! next level down logical :: debug = .FALSE. !----------------------------------------------------------------------- ll = l if(ll .gt. 1) ltype = fact%factors(ll-1) ! Set the next type of space curve !-------------------------------------------------------------- ! Position [0,0] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,21) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'Cinco: After Position [0,0] ',pos endif !-------------------------------------------------------------- ! Position [1,0] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,22) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [1,0] ',pos endif !-------------------------------------------------------------- ! Position [2,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,23) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [2,0] ',pos endif !-------------------------------------------------------------- ! Position [2,1] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,24) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [2,1] ',pos endif !-------------------------------------------------------------- ! Position [2,2] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = ma ljd = -md if(ll .gt. 1) then if(debug) write(*,25) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [2,2] ',pos endif !-------------------------------------------------------------- ! Position [1,2] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,26) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [1,2] ',pos endif !-------------------------------------------------------------- ! Position [1,1] !-------------------------------------------------------------- lma = ma lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,27) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [1,1] ',pos endif !-------------------------------------------------------------- ! Position [0,1] !-------------------------------------------------------------- lma = ma lmd = -md lja = MOD(ma+1,maxdim) ljd = md if(ll .gt. 1) then if(debug) write(*,28) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [0,1] ',pos endif !-------------------------------------------------------------- ! Position [0,2] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,29) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [0,2] ',pos endif !-------------------------------------------------------------- ! Position [0,3] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,30) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [0,3] ',pos endif !-------------------------------------------------------------- ! Position [0,4] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,31) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [0,4] ',pos endif !-------------------------------------------------------------- ! Position [1,4] !-------------------------------------------------------------- lma = ma lmd = md lja = MOD(ma+1,maxdim) ljd = -md if(ll .gt. 1) then if(debug) write(*,32) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [1,4] ',pos endif !-------------------------------------------------------------- ! Position [1,3] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = ma ljd = md if(ll .gt. 1) then if(debug) write(*,33) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [1,3] ',pos endif !-------------------------------------------------------------- ! Position [2,3] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,34) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [2,3] ',pos endif !-------------------------------------------------------------- ! Position [2,4] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,35) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [2,4] ',pos endif !-------------------------------------------------------------- ! Position [3,4] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,36) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [3,4] ',pos endif !-------------------------------------------------------------- ! Position [4,4] !-------------------------------------------------------------- lma = ma lmd = md lja = MOD(ma+1,maxdim) ljd = -md if(ll .gt. 1) then if(debug) write(*,37) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [4,4] ',pos endif !-------------------------------------------------------------- ! Position [4,3] !-------------------------------------------------------------- lma = ma lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,38) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [4,3] ',pos endif !-------------------------------------------------------------- ! Position [3,3] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,39) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [3,3] ',pos endif !-------------------------------------------------------------- ! Position [3,2] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = ma ljd = md if(ll .gt. 1) then if(debug) write(*,40) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [3,2] ',pos endif !-------------------------------------------------------------- ! Position [4,2] !-------------------------------------------------------------- lma = ma lmd = md lja = MOD(ma+1,maxdim) ljd = -md if(ll .gt. 1) then if(debug) write(*,41) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [4,2] ',pos endif !-------------------------------------------------------------- ! Position [4,1] !-------------------------------------------------------------- lma = ma lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,42) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [4,1] ',pos endif !-------------------------------------------------------------- ! Position [3,1] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,43) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [3,1] ',pos endif !-------------------------------------------------------------- ! Position [3,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = ma ljd = md if(ll .gt. 1) then if(debug) write(*,44) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [3,0] ',pos endif !-------------------------------------------------------------- ! Position [4,0] !-------------------------------------------------------------- lma = ma lmd = md lja = ja ljd = jd if(ll .gt. 1) then if(debug) write(*,45) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'After Position [4,0] ',pos endif 21 format('Call Cinco Pos [0,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 22 format('Call Cinco Pos [1,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 23 format('Call Cinco Pos [2,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 24 format('Call Cinco Pos [2,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 25 format('Call Cinco Pos [2,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 26 format('Call Cinco Pos [1,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 27 format('Call Cinco Pos [1,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 28 format('Call Cinco Pos [0,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 29 format('Call Cinco Pos [0,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 30 format('Call Cinco Pos [0,3] Level ',i1,' at (',i2,',',i2,')',4(i3)) 31 format('Call Cinco Pos [0,4] Level ',i1,' at (',i2,',',i2,')',4(i3)) 32 format('Call Cinco Pos [1,4] Level ',i1,' at (',i2,',',i2,')',4(i3)) 33 format('Call Cinco Pos [1,3] Level ',i1,' at (',i2,',',i2,')',4(i3)) 34 format('Call Cinco Pos [2,3] Level ',i1,' at (',i2,',',i2,')',4(i3)) 35 format('Call Cinco Pos [2,4] Level ',i1,' at (',i2,',',i2,')',4(i3)) 36 format('Call Cinco Pos [3,4] Level ',i1,' at (',i2,',',i2,')',4(i3)) 37 format('Call Cinco Pos [4,4] Level ',i1,' at (',i2,',',i2,')',4(i3)) 38 format('Call Cinco Pos [4,3] Level ',i1,' at (',i2,',',i2,')',4(i3)) 39 format('Call Cinco Pos [3,3] Level ',i1,' at (',i2,',',i2,')',4(i3)) 40 format('Call Cinco Pos [3,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 41 format('Call Cinco Pos [4,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 42 format('Call Cinco Pos [4,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 43 format('Call Cinco Pos [3,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 44 format('Call Cinco Pos [3,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 45 format('Call Cinco Pos [4,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) !EOC !----------------------------------------------------------------------- end function Cinco !*********************************************************************** !BOP ! !IROUTINE: PeanoM ! !INTERFACE: recursive function PeanoM(l,type,ma,md,ja,jd) result(ierr) 2,54 ! !DESCRIPTION: ! This function implements a meandering Peano ! space-filling curve. A meandering Peano curve ! connects a Nb x Nb block of points where ! ! Nb = 3^p ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS integer(int_kind), intent(in) :: & l, & ! level of the space-filling curve type, & ! type of SFC curve ma, & ! Major axis [0,1] md, & ! direction of major axis [-1,1] ja, & ! joiner axis [0,1] jd ! direction of joiner axis [-1,1] ! !OUTPUT PARAMETERS integer(int_kind) :: ierr ! error return code !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & lma, &! local major axis (next level) lmd, &! local major direction (next level) lja, &! local joiner axis (next level) ljd, &! local joiner direction (next level) ltype, &! type of SFC on next level ll ! next level down logical :: debug = .FALSE. !----------------------------------------------------------------------- ll = l if(ll .gt. 1) ltype = fact%factors(ll-1) ! Set the next type of space curve !-------------------------------------------------------------- ! Position [0,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,21) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [0,0] ',pos endif !-------------------------------------------------------------- ! Position [0,1] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,22) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [0,1] ',pos endif !-------------------------------------------------------------- ! Position [0,2] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,23) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [0,2] ',pos endif !-------------------------------------------------------------- ! Position [1,2] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,24) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [1,2] ',pos endif !-------------------------------------------------------------- ! Position [2,2] !-------------------------------------------------------------- lma = ma lmd = md lja = MOD(lma+1,maxdim) ljd = -lmd if(ll .gt. 1) then if(debug) write(*,25) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [2,2] ',pos endif !-------------------------------------------------------------- ! Position [2,1] !-------------------------------------------------------------- lma = ma lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,26) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [2,1] ',pos endif !-------------------------------------------------------------- ! Position [1,1] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,27) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [1,1] ',pos endif !-------------------------------------------------------------- ! Position [1,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = MOD(lma+1,maxdim) ljd = -lmd if(ll .gt. 1) then if(debug) write(*,28) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [1,0] ',pos endif !-------------------------------------------------------------- ! Position [2,0] !-------------------------------------------------------------- lma = ma lmd = md lja = ja ljd = jd if(ll .gt. 1) then if(debug) write(*,29) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'PeanoM: After Position [2,0] ',pos endif 21 format('Call PeanoM Pos [0,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 22 format('Call PeanoM Pos [0,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 23 format('Call PeanoM Pos [0,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 24 format('Call PeanoM Pos [1,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 25 format('Call PeanoM Pos [2,2] Level ',i1,' at (',i2,',',i2,')',4(i3)) 26 format('Call PeanoM Pos [2,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 27 format('Call PeanoM Pos [1,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 28 format('Call PeanoM Pos [1,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 29 format('Call PeanoM Pos [2,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) !EOC !----------------------------------------------------------------------- end function PeanoM !*********************************************************************** !BOP ! !IROUTINE: Hilbert ! !INTERFACE: recursive function Hilbert(l,type,ma,md,ja,jd) result(ierr) 2,24 ! !DESCRIPTION: ! This function implements a Hilbert space-filling curve. ! A Hilbert curve connect a Nb x Nb block of points where ! ! Nb = 2^p ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS integer(int_kind), intent(in) :: & l, & ! level of the space-filling curve type, & ! type of SFC curve ma, & ! Major axis [0,1] md, & ! direction of major axis [-1,1] ja, & ! joiner axis [0,1] jd ! direction of joiner axis [-1,1] ! !OUTPUT PARAMETERS integer(int_kind) :: ierr ! error return code !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & lma, &! local major axis (next level) lmd, &! local major direction (next level) lja, &! local joiner axis (next level) ljd, &! local joiner direction (next level) ltype, &! type of SFC on next level ll ! next level down logical :: debug = .FALSE. !----------------------------------------------------------------------- ll = l if(ll .gt. 1) ltype = fact%factors(ll-1) ! Set the next type of space curve !-------------------------------------------------------------- ! Position [0,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,21) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'Hilbert: After Position [0,0] ',pos endif !-------------------------------------------------------------- ! Position [0,1] !-------------------------------------------------------------- lma = ma lmd = md lja = lma ljd = lmd if(ll .gt. 1) then if(debug) write(*,22) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'Hilbert: After Position [0,1] ',pos endif !-------------------------------------------------------------- ! Position [1,1] !-------------------------------------------------------------- lma = ma lmd = md lja = MOD(ma+1,maxdim) ljd = -md if(ll .gt. 1) then if(debug) write(*,23) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'Hilbert: After Position [1,1] ',pos endif !-------------------------------------------------------------- ! Position [1,0] !-------------------------------------------------------------- lma = MOD(ma+1,maxdim) lmd = -md lja = ja ljd = jd if(ll .gt. 1) then if(debug) write(*,24) ll-1,pos(0),pos(1),lma,lmd,lja,ljd ierr = GenCurve(ll-1,ltype,lma,lmd,lja,ljd) if(debug) call PrintCurve(ordered) else ierr = IncrementCurve(lja,ljd) if(debug) print *,'Hilbert: After Position [1,0] ',pos endif 21 format('Call Hilbert Pos [0,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) 22 format('Call Hilbert Pos [0,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 23 format('Call Hilbert Pos [1,1] Level ',i1,' at (',i2,',',i2,')',4(i3)) 24 format('Call Hilbert Pos [1,0] Level ',i1,' at (',i2,',',i2,')',4(i3)) !EOC !----------------------------------------------------------------------- end function hilbert !*********************************************************************** !BOP ! !IROUTINE: IncrementCurve ! !INTERFACE: function IncrementCurve(ja,jd) result(ierr) 76 ! !DESCRIPTION: ! This function creates the curve which is stored in the ! the ordered array. The curve is implemented by ! incrementing the curve in the direction [jd] of axis [ja]. ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS: integer(int_kind) :: & ja, &! axis to increment jd ! direction along axis ! !OUTPUT PARAMETERS: integer(int_kind) :: ierr ! error return code !----------------------------- ! mark the newly visited point !----------------------------- ordered(pos(0)+1,pos(1)+1) = vcnt !------------------------------------ ! increment curve and update position !------------------------------------ vcnt = vcnt + 1 pos(ja) = pos(ja) + jd ierr = 0 !EOC !----------------------------------------------------------------------- end function IncrementCurve !*********************************************************************** !BOP ! !IROUTINE: log2 ! !INTERFACE: function log2( n) 2,2 ! !DESCRIPTION: ! This function calculates the log2 of its integer ! input. ! ! !REVISION HISTORY: ! same as module ! !INPUT PARAMETERS: integer(int_kind), intent(in) :: n ! integer value to find the log2 ! !OUTPUT PARAMETERS: integer(int_kind) :: log2 !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: tmp !------------------------------- ! Find the log2 of input value !------------------------------- log2 = 1 tmp =n do while (tmp/2 .ne. 1) tmp=tmp/2 log2=log2+1 enddo !EOP !----------------------------------------------------------------------- end function log2 !*********************************************************************** !BOP ! !IROUTINE: IsLoadBalanced ! !INTERFACE: function IsLoadBalanced(nelem,npart) ! !DESCRIPTION: ! This function determines if we can create ! a perfectly load-balanced partitioning. ! ! !REVISION HISTORY: ! same as module ! !INTPUT PARAMETERS: integer(int_kind), intent(in) :: & nelem, & ! number of blocks/elements to partition npart ! size of partition ! !OUTPUT PARAMETERS: logical :: IsLoadBalanced ! .TRUE. if a perfectly load balanced ! partition is possible !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: tmp1 ! temporary int !----------------------------------------------------------------------- tmp1 = nelem/npart if(npart*tmp1 == nelem ) then IsLoadBalanced=.TRUE. else IsLoadBalanced=.FALSE. endif !EOP !----------------------------------------------------------------------- end function IsLoadBalanced !*********************************************************************** !BOP ! !IROUTINE: GenCurve ! !INTERFACE: function GenCurve(l,type,ma,md,ja,jd) result(ierr) 78,6 ! !DESCRIPTION: ! This subroutine generates the next level down ! space-filling curve ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS integer(int_kind), intent(in) :: & l, & ! level of the space-filling curve type, & ! type of SFC curve ma, & ! Major axis [0,1] md, & ! direction of major axis [-1,1] ja, & ! joiner axis [0,1] jd ! direction of joiner axis [-1,1] ! !OUTPUT PARAMETERS integer(int_kind) :: ierr ! error return code !EOP !BOC !----------------------------------------------------------------------- !------------------------------------------------- ! create the space-filling curve on the next level !------------------------------------------------- if(type == 2) then ierr = Hilbert(l,type,ma,md,ja,jd) elseif ( type == 3) then ierr = PeanoM(l,type,ma,md,ja,jd) elseif ( type == 5) then ierr = Cinco(l,type,ma,md,ja,jd) endif !EOP !----------------------------------------------------------------------- end function GenCurve function FirstFactor(fac) result(res) 2 type (factor_t) :: fac integer :: res logical :: found integer (int_kind) :: i found = .false. i=1 do while (i<=fac%numfact .and. (.not. found)) if(fac%used(i) == 0) then res = fac%factors(i) found = .true. endif i=i+1 enddo end function FirstFactor function FindandMark(fac,val,f2) result(found) 4 type (factor_t) :: fac integer :: val logical :: found logical :: f2 integer (int_kind) :: i found = .false. i=1 do while (i<=fac%numfact .and. (.not. found)) if(fac%used(i) == 0) then if(fac%factors(i) .eq. val) then if(f2) then fac%used(i) = 1 found = .true. else if( .not. f2) then fac%used(i) = -1 found = .false. endif endif endif i=i+1 enddo end function FindandMark subroutine MatchFactor(fac1,fac2,val,found) 3,6 type (factor_t) :: fac1 type (factor_t) :: fac2 integer :: val integer :: val1 logical :: found logical :: tmp found = .false. val1 = FirstFactor(fac1) !JMD print *,'Matchfactor: found value: ',val1 found = FindandMark(fac2,val1,.true.) tmp = FindandMark(fac1,val1,found) if (found) then val = val1 else val = 1 endif end subroutine MatchFactor function ProdFactor(fac) result(res) 6 type (factor_t) :: fac integer :: res integer (int_kind) :: i res = 1 do i=1,fac%numfact if(fac%used(i) <= 0) then res = res * fac%factors(i) endif enddo end function ProdFactor subroutine PrintFactor(msg,fac) character(len=*) :: msg type (factor_t) :: fac integer (int_kind) :: i write(*,*) ' ' write(*,*) 'PrintFactor: ',msg write(*,*) (fac%factors(i),i=1,fac%numfact) write(*,*) (fac%used(i),i=1,fac%numfact) end subroutine PrintFactor !*********************************************************************** !BOP ! !IROUTINE: Factor ! !INTERFACE: function Factor(num) result(res) 10,2 ! !DESCRIPTION: ! This function factors the input value num into a ! product of 2,3, and 5. ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS: integer(int_kind), intent(in) :: num ! number to factor ! !OUTPUT PARAMETERS: type (factor_t) :: res !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & tmp,tmp2,tmp3,tmp5 ! tempories for the factorization algorithm integer(int_kind) :: i,n ! loop tempories logical :: found ! logical temporary ! -------------------------------------- ! Allocate allocate for max # of factors ! -------------------------------------- tmp = num tmp2 = log2(num) allocate(res%factors(tmp2)) allocate(res%used(tmp2)) res%used = 0 n=0 !----------------------- ! Look for factors of 2 !----------------------- found=.TRUE. do while (found) found = .FALSE. tmp2 = tmp/2 if( tmp2*2 == tmp ) then n = n + 1 res%factors(n) = 2 found = .TRUE. tmp = tmp2 endif enddo !----------------------- ! Look for factors of 3 !----------------------- found=.TRUE. do while (found) found = .FALSE. tmp3 = tmp/3 if( tmp3*3 == tmp ) then n = n + 1 res%factors(n) = 3 found = .TRUE. tmp = tmp3 endif enddo !----------------------- ! Look for factors of 5 !----------------------- found=.TRUE. do while (found) found = .FALSE. tmp5 = tmp/5 if( tmp5*5 == tmp ) then n = n + 1 res%factors(n) = 5 found = .TRUE. tmp = tmp5 endif enddo !------------------------------------ ! make sure that the input value ! only contains factors of 2,3,and 5 !------------------------------------ tmp=1 do i=1,n tmp = tmp * res%factors(i) enddo if(tmp == num) then res%numfact = n else res%numfact = -1 endif !EOP !--------------------------------------------------------- end function Factor !*********************************************************************** !BOP ! !IROUTINE: IsFactorable ! !INTERFACE: function IsFactorable(n) 6,2 ! !DESCRIPTION: ! This function determines if we can factor ! n into 2,3,and 5. ! ! !REVISION HISTORY: ! same as module ! !INTPUT PARAMETERS: integer(int_kind), intent(in) :: n ! number to factor ! !OUTPUT PARAMETERS: logical :: IsFactorable ! .TRUE. if it is factorable !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- type (factor_t) :: fact ! data structure to store factor information fact = Factor(n) if(fact%numfact .ne. -1) then IsFactorable = .TRUE. else IsFactorable = .FALSE. endif !EOP !----------------------------------------------------------------------- end function IsFactorable !*********************************************************************** !BOP ! !IROUTINE: map ! !INTERFACE: subroutine map(l) 2,2 ! !DESCRIPTION: ! Interface routine between internal subroutines and public ! subroutines. ! ! !REVISION HISTORY: ! same as module ! !INPUT PARAMETERS: integer(int_kind) :: l ! level of space-filling curve !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & d, & ! dimension of curve only 2D is supported type, & ! type of space-filling curve to start off ierr ! error return code d = SIZE(pos) pos=0 maxdim=d vcnt=0 type = fact%factors(l) ierr = GenCurve(l,type,0,1,0,1) !EOP !----------------------------------------------------------------------- end subroutine map !*********************************************************************** !BOP ! !IROUTINE: PrintCurve ! !INTERFACE: subroutine PrintCurve(Mesh) 81,4 ! !DESCRIPTION: ! This subroutine prints the several low order ! space-filling curves in an easy to read format ! ! !REVISION HISTORY: ! same as module ! ! !INPUT PARAMETERS: integer(int_kind), intent(in), target :: Mesh(:,:) ! SFC to be printed !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & gridsize, &! order of space-filling curve i ! loop temporary !----------------------------------------------------------------------- gridsize = SIZE(Mesh,dim=1) if(gridsize == 2) then write (*,*) "A Level 1 Hilbert Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,2) Mesh(1,i),Mesh(2,i) enddo else if(gridsize == 3) then write (*,*) "A Level 1 Peano Meandering Curve:" write (*,*) "---------------------------------" do i=1,gridsize write(*,3) Mesh(1,i),Mesh(2,i),Mesh(3,i) enddo else if(gridsize == 4) then write (*,*) "A Level 2 Hilbert Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,4) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i) enddo else if(gridsize == 5) then write (*,*) "A Level 1 Cinco Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,5) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i),Mesh(5,i) enddo else if(gridsize == 6) then write (*,*) "A Level 1 Hilbert and Level 1 Peano Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,6) Mesh(1,i),Mesh(2,i),Mesh(3,i), & Mesh(4,i),Mesh(5,i),Mesh(6,i) enddo else if(gridsize == 8) then write (*,*) "A Level 3 Hilbert Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,8) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i), & Mesh(5,i),Mesh(6,i),Mesh(7,i),Mesh(8,i) enddo else if(gridsize == 9) then write (*,*) "A Level 2 Peano Meandering Curve:" write (*,*) "---------------------------------" do i=1,gridsize write(*,9) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i), & Mesh(5,i),Mesh(6,i),Mesh(7,i),Mesh(8,i), & Mesh(9,i) enddo else if(gridsize == 10) then write (*,*) "A Level 1 Hilbert and Level 1 Cinco Curve:" write (*,*) "---------------------------------" do i=1,gridsize write(*,10) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i), & Mesh(5,i),Mesh(6,i),Mesh(7,i),Mesh(8,i), & Mesh(9,i),Mesh(10,i) enddo else if(gridsize == 12) then write (*,*) "A Level 2 Hilbert and Level 1 Peano Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,12) Mesh(1,i),Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i),Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i),Mesh(10,i),Mesh(11,i),Mesh(12,i) enddo else if(gridsize == 15) then write (*,*) "A Level 1 Peano and Level 1 Cinco Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,15) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i), & Mesh(5,i),Mesh(6,i),Mesh(7,i),Mesh(8,i), & Mesh(9,i),Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i) enddo else if(gridsize == 16) then write (*,*) "A Level 4 Hilbert Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,16) Mesh(1,i),Mesh(2,i),Mesh(3,i),Mesh(4,i), & Mesh(5,i),Mesh(6,i),Mesh(7,i),Mesh(8,i), & Mesh(9,i),Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i) enddo else if(gridsize == 18) then write (*,*) "A Level 1 Hilbert and Level 2 Peano Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,18) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i) enddo else if(gridsize == 20) then write (*,*) "A Level 2 Hilbert and Level 1 Cinco Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,20) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i),Mesh(19,i),Mesh(20,i) enddo else if(gridsize == 24) then write (*,*) "A Level 3 Hilbert and Level 1 Peano Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,24) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i),Mesh(19,i),Mesh(20,i), & Mesh(21,i),Mesh(22,i),Mesh(23,i),Mesh(24,i) enddo else if(gridsize == 25) then write (*,*) "A Level 2 Cinco Curve:" write (*,*) "------------------------------------------" do i=1,gridsize write(*,25) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i),Mesh(19,i),Mesh(20,i), & Mesh(21,i),Mesh(22,i),Mesh(23,i),Mesh(24,i), & Mesh(25,i) enddo else if(gridsize == 27) then write (*,*) "A Level 3 Peano Meandering Curve:" write (*,*) "---------------------------------" do i=1,gridsize write(*,27) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i),Mesh(19,i),Mesh(20,i), & Mesh(21,i),Mesh(22,i),Mesh(23,i),Mesh(24,i), & Mesh(25,i),Mesh(26,i),Mesh(27,i) enddo else if(gridsize == 32) then write (*,*) "A Level 5 Hilbert Curve:" write (*,*) "------------------------" do i=1,gridsize write(*,32) Mesh(1,i), Mesh(2,i), Mesh(3,i), Mesh(4,i), & Mesh(5,i), Mesh(6,i), Mesh(7,i), Mesh(8,i), & Mesh(9,i), Mesh(10,i),Mesh(11,i),Mesh(12,i), & Mesh(13,i),Mesh(14,i),Mesh(15,i),Mesh(16,i), & Mesh(17,i),Mesh(18,i),Mesh(19,i),Mesh(20,i), & Mesh(21,i),Mesh(22,i),Mesh(23,i),Mesh(24,i), & Mesh(25,i),Mesh(26,i),Mesh(27,i),Mesh(28,i), & Mesh(29,i),Mesh(30,i),Mesh(31,i),Mesh(32,i) enddo endif 2 format('|',2(i2,'|')) 3 format('|',3(i2,'|')) 4 format('|',4(i2,'|')) 5 format('|',5(i2,'|')) 6 format('|',6(i2,'|')) 8 format('|',8(i2,'|')) 9 format('|',9(i2,'|')) 10 format('|',10(i2,'|')) 12 format('|',12(i3,'|')) 15 format('|',15(i3,'|')) 16 format('|',16(i3,'|')) 18 format('|',18(i3,'|')) 20 format('|',20(i3,'|')) 24 format('|',24(i3,'|')) 25 format('|',25(i3,'|')) 27 format('|',27(i3,'|')) 32 format('|',32(i4,'|')) !EOC !----------------------------------------------------------------------- end subroutine PrintCurve !*********************************************************************** !BOP ! !IROUTINE: GenSpaceCurve ! !INTERFACE: subroutine GenSpaceCurve(Mesh) 3 ! !DESCRIPTION: ! This subroutine is the public interface into the ! space-filling curve functionality ! ! !REVISION HISTORY: ! same as module ! ! !INPUT/OUTPUT PARAMETERS: integer(int_kind), target,intent(inout) :: & Mesh(:,:) ! The SFC ordering in 2D array !EOP !BOC !----------------------------------------------------------------------- ! ! local variables ! !----------------------------------------------------------------------- integer(int_kind) :: & level, &! Level of space-filling curve dim ! dimension of SFC... currently limited to 2D integer(int_kind) :: gridsize ! number of points on a side !----------------------------------------------------------------------- !----------------------------------------- ! Setup the size of the grid to traverse !----------------------------------------- dim = 2 gridsize = SIZE(Mesh,dim=1) fact = factor(gridsize) level = fact%numfact if(verbose) print *,'GenSpacecurve: level is ',level allocate(ordered(gridsize,gridsize)) !-------------------------------------------- ! Setup the working arrays for the traversal !-------------------------------------------- allocate(pos(0:dim-1)) !----------------------------------------------------- ! The array ordered will contain the visitation order !----------------------------------------------------- ordered(:,:) = 0 call map(level) Mesh(:,:) = ordered(:,:) deallocate(pos,ordered) !EOP !----------------------------------------------------------------------- end subroutine GenSpaceCurve recursive subroutine qsort(a) 2,3 integer, intent(inout) :: a(:) integer :: split if(SIZE(a) > 1) then call partition(a,split) call qsort(a(:split-1)) call qsort(a(split:)) endif end subroutine qsort subroutine partition(a,marker) 1 INTEGER, INTENT(IN OUT) :: a(:) INTEGER, INTENT(OUT) :: marker INTEGER :: left, right, pivot, temp pivot = (a(1) + a(size(a))) / 2 ! Average of first and last elements to prevent quadratic left = 0 ! behavior with sorted or reverse sorted data right = size(a) + 1 DO WHILE (left < right) right = right - 1 DO WHILE (a(right) > pivot) right = right-1 END DO left = left + 1 DO WHILE (a(left) < pivot) left = left + 1 END DO IF (left < right) THEN temp = a(left) a(left) = a(right) a(right) = temp END IF END DO IF (left == right) THEN marker = left + 1 ELSE marker = left END IF end subroutine partition end module ice_spacecurve !|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||