M_orderpack__median Module

median(3f) - [M_orderpack:MEDIAN] Calculates median VALUE. If
             number of elements is even, returns average of the two
             "medians".

 Function Median (INVALS)

  ${TYPE} (Kind=${KIND}), Intent (In) :: INVALS(:)
  ${TYPE} (Kind=${KIND})              :: MEDIAN

Where ${TYPE}(kind=${KIND}) may be

   o Real(kind=real32)
   o Real(kind=real64)
   o Integer(kind=int32)

MEDIAN(3f) calculates the median value of the array INVALS(). It is
a modified version of MEDIANVAL(3f) that provides the average between
the two middle values in the case where size(INVALS) is even.

Internally, this routine uses a pivoting strategy similar to the
method of finding the median based on the Quick-sort algorithm, but
we skew the pivot choice to try to bring it to one-half the values 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 determine the median value of.

 MEDIAN     median value. If INVALS contains an even number
            of elements the value is the average of the
            two "medians".

program demo_median
! calculate median value
use M_orderpack, only : median
implicit none
character(len=*),parameter :: g='(*(g0,1x))'

   write(*,g) 'real   ',median(&
   [80.0,70.0,20.0,10.0,1000.0] )

   write(*,g) 'integer',median(&
   [11, 22, 33, 44, 55, 66, 77, 88] )

   write(*,g) 'double ',median(&
   [11.0d0,22.0d0,33.0d0,66.0d0,77.0d0,88.0d0])

end program demo_median

real    70.00000
integer 49
double  49.50000000000000

Michel Olagnon - Aug. 2000

John Urban, 2022.04.16

CC0-1.0