orderval(3f) - [M_orderpack:FRACTILE] Return VALUE of Nth ordered
element of array (Quick-Sort-like)
Function OrderVal (INVALS, NORD)
${TYPE} (Kind=${KIND}), Intent (In) :: INVALS(:)
${TYPE} (Kind=${KIND}) :: orderval
Integer, Intent (In) :: NORD
Where ${TYPE}(kind=${KIND}) may be
o Real(kind=real32)
o Real(kind=real64)
o Integer(kind=int32)
ORDERVAL(3f) returns the NORDth (ascending order) value of INVALS, i.e. the fractile of order NORD/SIZE(INVALS).
Internally, this subroutine simply calls ORDERLOC(3f).
This routine uses a pivoting strategy such as the one of finding the median based on the Quick-Sort algorithm, but we skew the pivot choice to try to bring it to NORD as fast as possible. It uses two temporary arrays, where it stores the indices of the values smaller than the pivot (ILOWT), and the indices of values larger than the pivot that we might still need later on (IHIGT). It iterates until it can bring the number of values in ILOWT to exactly NORD, and then finds the maximum of this set.
INVALS array to search
NORD Nth lowest value to find
orderval Nth lowest value
Sample program:
program demo_orderval
! Return value of Nth lowest value of array
use M_orderpack, only : orderval
implicit none
character(len=*),parameter :: list= '(*(g0:,", "))'
character(len=*),parameter :: sp='(*(g0,1x))'
real,parameter :: INVALS(*)=[1.1,20.20,3.3,10.10,5.5,4.4,2.2]
integer :: i
integer :: imiddle
write(*,list) 'ORIGINAL:',INVALS
! can return the same values as intrinsics minval(3f) and maxval(3f)
print sp, 'minval',orderval(INVALS,1), minval(INVALS)
print sp, 'maxval',orderval(INVALS,size(INVALS)), maxval(INVALS)
! but more generally it can return the Nth lowest value.
print sp,'nord=',4, ' fractile=',orderval(INVALS,4)
! so a value at the middle would be
imiddle=(size(INVALS)+1)/2
print sp,'median',orderval(INVALS,imiddle)
! sorting the hard way
do i=1,size(INVALS)
write(*,list)i,orderval(INVALS,i)
enddo
end program demo_orderval
Results:
ORIGINAL:, 1.1000, 20.200, 3.300, 10.100, 5.500, 4.400, 2.200
minval 1.100 1.100
maxval 20.200 20.200
nord= 4 fractile= 4.400
median 4.400
1, 1.100
2, 2.200
3, 3.300
4, 4.400
5, 5.500
6, 10.100
7, 20.200
Michel Olagnon - Aug. 2000
John Urban, 2022.04.16
CC0-1.0
!!! CASE DEFAULT !!! write (unit=,fmt=) “Assertion failed” !!! STOP
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in), | Dimension (:) | :: | INVALS | ||
| integer, | intent(in) | :: | NORD |
!!! CASE DEFAULT !!! write (unit=,fmt=) “Assertion failed” !!! STOP
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real32), | intent(in), | Dimension (:) | :: | INVALS | ||
| integer, | intent(in) | :: | NORD |
!!! CASE DEFAULT !!! write (unit=,fmt=) “Assertion failed” !!! STOP
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer(kind=int32), | intent(in), | Dimension (:) | :: | INVALS | ||
| integer, | intent(in) | :: | NORD |