ordering function in Fortran - list

Question

Is there a Fortran library which has an implementation of an ordering function, i.e., a function ordering(list) (like Ordering[] in Mathematica) which gives the positions in list at which each successive element of the sorted list appears?
I can implement it but I don't want to reinvent the wheel (and my wheel could be far from perfect...). Since it is so basic I was searching for a lib containing such list operations but failed to find one.
Do you have any suggestions?

Answer 1

Since I had this already implemented a long time ago (which relies on and borrows heavily from the Numerical Recipes book of Bill Press et al), here is a self-contained implementation of it in Fortran:
module index_mod
use, intrinsic :: iso_fortran_env, only: IK=>int32, RK=>real64
implicit none
contains
subroutine indexArrayReal(n,Array,Index)
implicit none
integer(IK), intent(in) :: n
real(RK) , intent(in) :: Array(n)
integer(IK), intent(out) :: Index(n)
integer(IK), parameter :: nn=15, nstack=50
integer(IK) :: k,i,j,indext,jstack,l,r
integer(IK) :: istack(nstack)
real(RK) :: a
do j = 1,n
Index(j) = j
end do
jstack=0
l=1
r=n
do
if (r-l < nn) then
do j=l+1,r
indext=Index(j)
a=Array(indext)
do i=j-1,l,-1
if (Array(Index(i)) <= a) exit
Index(i+1)=Index(i)
end do
Index(i+1)=indext
end do
if (jstack == 0) return
r=istack(jstack)
l=istack(jstack-1)
jstack=jstack-2
else
k=(l+r)/2
call swap(Index(k),Index(l+1))
call exchangeIndex(Index(l),Index(r))
call exchangeIndex(Index(l+1),Index(r))
call exchangeIndex(Index(l),Index(l+1))
i=l+1
j=r
indext=Index(l+1)
a=Array(indext)
do
do
i=i+1
if (Array(Index(i)) >= a) exit
end do
do
j=j-1
if (Array(Index(j)) <= a) exit
end do
if (j < i) exit
call swap(Index(i),Index(j))
end do
Index(l+1)=Index(j)
Index(j)=indext
jstack=jstack+2
if (jstack > nstack) then
write(*,*) 'NSTACK too small in indexArrayReal()' ! xxx
error stop
end if
if (r-i+1 >= j-l) then
istack(jstack)=r
istack(jstack-1)=i
r=j-1
else
istack(jstack)=j-1
istack(jstack-1)=l
l=i
end if
end if
end do
contains
subroutine exchangeIndex(i,j)
integer(IK), intent(inout) :: i,j
integer(IK) :: swp
if (Array(j) < Array(i)) then
swp=i
i=j
j=swp
end if
end subroutine exchangeIndex
pure elemental subroutine swap(a,b)
implicit none
integer(IK), intent(inout) :: a,b
integer(IK) :: dum
dum=a
a=b
b=dum
end subroutine swap
end subroutine indexArrayReal
end module Index_mod
program Index_prog
use Index_mod, only: IK, RK, indexArrayReal
implicit none
integer(IK), parameter :: n = 5
integer(IK) :: Index(n)
real(RK) :: Array(n) = [ 1.,3.,4.,2.,-1. ]
call indexArrayReal(n,Array,Index)
write(*,*) "Index: ", Index
write(*,*) "Array(Index): ", Array(Index)
end program Index_prog
Compiled with GFortran 2008, here is the output:
$gfortran -std=f2008 *.f95 -o main
$main
Index: 5 1 4 2 3
Array(Index): -1.0000000000000000 1.0000000000000000 2.0000000000000000 3.0000000000000000 4.0000000000000000
The above routine was for sorting real-valued arrays. To sort integer arrays, simply change real(RK) :: Array(n) in the interface of subroutine indexArrayReal() to integer(IK) :: Array(n).