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module selectionalgo
use, intrinsic :: iso_fortran_env
implicit none
real, parameter :: cost=1.4826, sqrt2=sqrt(2.)
integer, parameter :: sp = real32, dp=real64
interface qselect
procedure quickselectdp, quickselectscalardp
end interface qselect
interface iselect
procedure introselectdp, introselectscalardp
end interface iselect
contains
!!!!!!! DOUBLE PRECISION
recursive subroutine quickselectrecursivedp(invector,tovector,k,output)
real(kind=dp), dimension(:), allocatable, target, intent(inout) :: invector
real(kind=dp), intent(inout), pointer, contiguous :: tovector(:)
integer, intent(inout) :: k
real(kind=dp), intent(out) :: output
real(kind=dp) :: swapper, pvt
integer :: i, r, subst
real(kind=dp), pointer :: a,b,c
r=size(tovector)
select case(r)
case(1)
output=tovector(1)
return
case(2)
select case(k)
case(1)
output=minval(tovector)
case(2)
output=maxval(tovector)
end select
return
case(3)
select case(k)
case(1)
output=minval(tovector)
case(3)
output=maxval(tovector)
case(2)
i=r/2+1
output=sum(tovector)-minval(tovector)-maxval(tovector)
end select
return
case default
i=r/2+1
!pivoting section (pivot of 3)
a=>tovector(1)
b=>tovector(i)
c=>tovector(r)
pvt=a+b+c
swapper=max(a,b,c)
b=swapper
pvt=pvt-swapper
swapper=min(a,b,c)
a=swapper
pvt=pvt-swapper
c=pvt
!one pass section
subst=1
b=>tovector(subst)
do i=1,(r-1-3),3
a => tovector(i)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
a => tovector(i+1)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
a => tovector(i+2)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
end do
do i=i,(r-1)
a => tovector(i)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
end do
tovector(r)=tovector(subst)
tovector(subst)=pvt
!decide next step
select case(subst-k)
case(0)
output=tovector(k)
case(1:)
tovector => tovector(1:subst-1)
call quickselectrecursivedp(invector,tovector,k, output)
case(:-1)
k=k-subst
tovector => tovector(subst+1:)
call quickselectrecursivedp(invector,tovector,k, output)
end select
end select
end subroutine quickselectrecursivedp
recursive subroutine introselectrecursivedp(invector,tovector,k,output)
real(kind=dp), dimension(:), allocatable, target, intent(inout) :: invector
real(kind=dp), intent(inout), pointer, contiguous :: tovector(:)
integer, intent(inout) :: k
real(kind=dp), intent(out) :: output
real(kind=dp) :: swapper, pvt
integer, save :: switch
integer :: i, r, subst, r_min, switch_after
real(kind=dp), pointer :: a,b,c
r=ubound(tovector,1)
r_min = 3000 ! at least this bigger to switch to median of medians
switch_after = 5 ! at least fails this amount of time to reorder
! one third of the vector to consider med of med
select case(r)
case(1)
output=tovector(1)
switch=0
return
case(2)
select case(k)
case(1)
output=minval(tovector)
case(2)
output=maxval(tovector)
end select
switch=0
return
case(3)
select case(k)
case(1)
output=minval(tovector)
case(3)
output=maxval(tovector)
case(2)
i=r/2+1
output=sum(tovector)-minval(tovector)-maxval(tovector)
end select
switch=0
return
case default
i=r/2+1
!pivoting section (pivot of 3)
a=>tovector(1)
b=>tovector(i)
c=>tovector(r)
pvt=a+b+c
swapper=max(a,b,c)
b=swapper
pvt=pvt-swapper
swapper=min(a,b,c)
a=swapper
pvt=pvt-swapper
c=pvt
!one pass section
subst=1
b=>tovector(subst)
do i=1,(r-1-3),3
a => tovector(i)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
a => tovector(i+1)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
a => tovector(i+2)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
end do
do i=i,(r-1)
a => tovector(i)
if (a<pvt) then
swapper=b
b=a
a=swapper
subst=subst+1
b=>tovector(subst)
end if
end do
tovector(r)=tovector(subst)
tovector(subst)=pvt
!decide next step
select case(subst-k)
case(0)
output=tovector(k)
switch=0
case(1:)
tovector => tovector(1:subst-1)
if ((subst-1)>r*2/3) then
switch=switch+1
if (switch==switch_after .and. r>r_min) then
!reset switch and call medofmeddp
switch=0
call medofmeddp(invector,tovector,k, output)
else
call introselectrecursivedp(invector,tovector,k, output)
end if
else
switch=0
call introselectrecursivedp(invector,tovector,k, output)
end if
case(:-1)
k=k-subst
tovector => tovector(subst+1:)
if ((r-subst)>r*2/3) then
switch=switch+1
if (switch==switch_after .and. r>r_min) then
!reset switch and call medofmeddp
switch=0
call medofmeddp(invector,tovector,k, output)
else
call introselectrecursivedp(invector,tovector,k, output)
end if
else
switch=0
call introselectrecursivedp(invector,tovector,k, output)
end if
end select
end select
end subroutine introselectrecursivedp
recursive subroutine medofmeddp(invector,tovector,k,output)
real(kind=dp), dimension(:), allocatable, target, intent(inout) :: invector
real(kind=dp), intent(inout), pointer, contiguous :: tovector(:)
real(kind=dp), intent(out) :: output
integer, intent(inout) :: k
real(kind=dp), pointer, contiguous :: subsec(:)
real(kind=dp), dimension(:),allocatable :: meds
integer :: i,subst,r
real(kind=dp) :: pvt
!real(kind=dp) :: swapper
!real(kind=dp), pointer :: a,b
r=ubound(tovector,1)
select case(mod(r,5))
case(0)
allocate(meds(r/5))
do i=1,r-4,5
subsec=>tovector(i:i+4)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(int(i/5.0)+1)=pvt
end do
case(1)
allocate(meds(r/5+1))
do i=1,r-4,5
subsec=>tovector(i:i+4)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(int(i/5.0)+1)=pvt
end do
meds(r/5+1)=tovector(i)
case(2)
allocate(meds(r/5+1))
do i=1,r-4,5
subsec=>tovector(i:i+4)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(int(i/5.0)+1)=pvt
end do
subsec=>tovector(i:)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
meds(r/5+1)=subsec(2)
case(3)
allocate(meds(r/5+1))
do i=1,r-4,5
subsec=>tovector(i:i+4)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(int(i/5.0)+1)=pvt
end do
subsec=>tovector(i:)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
meds(r/5+1)=pvt
case(4)
allocate(meds(r/5+1))
do i=1,r-4,5
subsec=>tovector(i:i+4)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(int(i/5.0)+1)=pvt
end do
subsec=>tovector(i:)
subst=minloc(subsec,1)
pvt=subsec(subst)
subsec(subst)=subsec(1)
subsec(1)=pvt
subst=minloc(subsec(2:),1)+1
pvt=subsec(subst)
subsec(subst)=subsec(2)
subsec(2)=pvt
subst=minloc(subsec(3:),1)+2
pvt=subsec(subst)
subsec(subst)=subsec(3)
subsec(3)=pvt
meds(r/5+1)=pvt
end select
!set pivot
pvt=qselect(meds)
do i=1,r-3,3
if (tovector(i)==pvt) then
tovector(i)=tovector(r)
tovector(r)=pvt
exit
else if (tovector(i+1)==pvt) then
tovector(i+1)=tovector(r)
tovector(r)=pvt
exit
else if (tovector(i+2)==pvt) then
tovector(i+2)=tovector(r)
tovector(r)=pvt
exit
else
cycle
end if
end do
do i=i,r
if (tovector(i)==pvt) then
tovector(i)=tovector(r)
tovector(r)=pvt
exit
else
cycle
end if
end do
call introselectrecursivedp(invector,tovector,k, output)
end subroutine medofmeddp
function introselectdp(invector,ord,evencorrection)
real(kind=dp), intent(in), dimension(:) :: invector
logical, optional, intent(in) :: evencorrection
integer, intent(in), optional :: ord
real(kind=dp) :: introselectdp
real(kind=dp), dimension(:), allocatable, target :: vector
real(kind=dp), pointer, contiguous :: tovector(:) => null()
integer :: k1, k
k1=size(invector)
allocate(vector(k1))
vector=invector
tovector => vector
k1=ubound(invector,1)
if(present(ord)) then
k=ord
else
k=k1/2+1
end if
if(present(evencorrection)) then
if (k/=k1/2+1 .or. mod(k1,2)/=0) then
!write(*,'(a)') 'Warning: evencorrection argument ignored.'
k1=0
else
k1=0
if (evencorrection) k1=k-1
end if
else
k1=0
end if
call introselectrecursivedp(vector,tovector,k, introselectdp)
if (k1/=0) then
block
real(kind=dp) :: temp
temp=introselectdp
!tovector=>vector(1:k1+1)
tovector=>vector
call introselectrecursivedp(vector,tovector,k1, introselectdp)
introselectdp=(introselectdp+temp)/2.0
end block
end if
end function introselectdp
function quickselectdp(invector,ord,evencorrection)
real(kind=dp), intent(in), dimension(:) :: invector
logical, optional, intent(in) :: evencorrection
integer, intent(in), optional :: ord
real(kind=dp) :: quickselectdp
real(kind=dp), dimension(:), allocatable, target :: vector
real(kind=dp), pointer, contiguous :: tovector(:) => null()
integer :: k1, k
k1=size(invector)
allocate(vector(k1))
vector=invector
tovector => vector
k1=ubound(invector,1)
if(present(ord)) then
k=ord
else
k=k1/2+1
end if
if(present(evencorrection)) then
if (k/=k1/2+1 .or. mod(k1,2)/=0) then
!write(*,'(a)') 'Warning: evencorrection argument ignored.'
k1=0
else
k1=0
if (evencorrection) k1=k-1
end if
else
k1=0
end if
call quickselectrecursivedp(vector,tovector,k, quickselectdp)
if (k1/=0) then
block
real(kind=dp) :: temp
temp=quickselectdp
tovector=>vector(1:k1+1)
call quickselectrecursivedp(vector,tovector,k1, quickselectdp)
quickselectdp=(quickselectdp+temp)/2.0
end block
end if
end function quickselectdp
!deal with scalar input
function introselectscalardp(invector,ord, evencorrection)
real(kind=dp), intent(in) :: invector
integer, intent(in), optional :: ord
logical, optional, intent(in) :: evencorrection
real(kind=dp) :: introselectscalardp
if (present(evencorrection) .or. present(ord)) then
continue
end if
introselectscalardp=invector
end function introselectscalardp
function quickselectscalardp(invector,ord, evencorrection)
real(kind=dp), intent(in) :: invector
integer, intent(in), optional :: ord
logical, optional, intent(in) :: evencorrection
real(kind=dp) :: quickselectscalardp
if (present(evencorrection) .or. present(ord)) then
continue
end if
quickselectscalardp=invector
end function quickselectscalardp
end module selectionalgo
subroutine cormadvecdp(matrix,nrow,ncol,res,ressize,correcteven)
use selectionalgo
implicit none
!note kind dp is defined in selectionalgo
integer, intent(in) :: nrow, ncol,ressize, correcteven !.Fortran R function will not deal with deferred size arrays
real(kind=dp), dimension(nrow,ncol), intent(inout) :: matrix
real(kind=dp), dimension(ressize), intent(out) :: res
integer :: i, j, n, p
real(kind=dp) :: med,mad
!real(kind=dp) :: fresh
real(kind=dp), dimension(:), allocatable :: U, V
!real(kind=dp), dimension(:), allocatable :: A, B
p=ubound(matrix,2)
n=ubound(matrix,1)
allocate(U(n),V(n))
if (correcteven==1) then
do i=1,p-3,3
U=matrix(:,i)
med=iselect(U,evencorrection=.true.)
matrix(:,i)=(U-med)/(sqrt2*cost*iselect(abs(U-med),evencorrection=.true.))
U=matrix(:,i+1)
med=iselect(U,evencorrection=.true.)
matrix(:,i+1)=(U-med)/(sqrt2*cost*iselect(abs(U-med),evencorrection=.true.))
U=matrix(:,i+2)
med=iselect(U,evencorrection=.true.)
matrix(:,i+2)=(U-med)/(sqrt2*cost*iselect(abs(U-med),evencorrection=.true.))
end do
do i=i,p
U=matrix(:,i)
med=iselect(U,evencorrection=.true.)
matrix(:,i)=(U-med)/(sqrt2*cost*iselect(abs(U-med),evencorrection=.true.))
end do
!unrolled loops
n=1
do i=1,p-1
do j=i+1,p
U=matrix(:,i)+matrix(:,j)
V=-matrix(:,i)+matrix(:,j)
mad=(cost*iselect(abs(U-iselect(U,evencorrection=.true.)),evencorrection=.true.))**2
med=(cost*iselect(abs(V-iselect(V,evencorrection=.true.)),evencorrection=.true.))**2
res(n)=(mad-med)/(mad+med)
n=n+1
end do
end do
else
do i=1,p-3,3
U=matrix(:,i)
med=iselect(U)
matrix(:,i)=(U-med)/(sqrt2*cost*iselect(abs(U-med)))
U=matrix(:,i+1)
med=iselect(U)
matrix(:,i+1)=(U-med)/(sqrt2*cost*iselect(abs(U-med)))
U=matrix(:,i+2)
med=iselect(U)
matrix(:,i+2)=(U-med)/(sqrt2*cost*iselect(abs(U-med)))
end do
do i=i,p
U=matrix(:,i)
med=iselect(U)
matrix(:,i)=(U-med)/(sqrt2*cost*iselect(abs(U-med)))
end do
!unrolled loops
n=1
do i=1,p-1
do j=i+1,p
U=matrix(:,i)+matrix(:,j)
V=-matrix(:,i)+matrix(:,j)
mad=(cost*iselect(abs(U-iselect(U))))**2
med=(cost*iselect(abs(V-iselect(V))))**2
res(n)=(mad-med)/(mad+med)
n=n+1
end do
end do
end if
end subroutine cormadvecdp
|
