C Library Functions  - medianloc (3)

NAME
medianloc(3f) - [M_orderpack:MEDIAN] Returns median value’s INDEX.

CONTENTS

Synopsis
Description
Options
Examples
Author
Maintainer
License

SYNOPSIS
Subroutine MedianLoc (INVALS, OUTORD) 

      ${TYPE} (kind=${KIND}), Intent (In) :: INVALS(:)
      Integer, Intent (Out)               :: OUTORD
Where ${TYPE}(kind=${KIND}) may be
o Real(kind=real32)
o Real(kind=real64)
o Integer(kind=int32)
o Character(kind=selected_char_kind("DEFAULT"),len=*)

DESCRIPTION
MEDIANLOC(3f) Returns the index of the median (((Size(INVALS)+1))/2^th value).

Internally, MEDIANLOC(3f) Finds the index of the median of the array INVALS() using the recursive procedure described in Knuth, The Art of Computer Programming, vol. 3, 5.3.3.

This procedure is linear in time, and does not require to be able to interpolate in the set as the one used in ORDERLOC(3f), which can also be used to calculate a median. It also has better worst-case behavior than ORDERLOC(3f), but is about 10% slower on average for random uniformly distributed values.

OPTIONS
INVALS array to find the median value of.
OUTORD index of the median value.

EXAMPLES
Sample program: 

   program demo_medianloc
   ! return index of median value
   use M_orderpack, only : medianloc
   implicit none
   real,allocatable :: INVALS(:)
   character(len=:),allocatable :: cdont(:)
   character(len=*),parameter :: fmt=’(i5,t11,g0)’
   integer :: ii
      write(*,*) ’location  median’


      INVALS=[80.0,70.0,20.0,10.0,1000.0]
      call medianloc(INVALS,ii)
      write(*,fmt) ii,INVALS(ii)
      !
      INVALS=[11, 22, 33, 44, 55, 66, 77, 88]
      call medianloc(INVALS,ii)
      write(*,fmt) ii,INVALS(ii)
      !
      INVALS=[11.0d0,77.0d0,22.0d0,66.0d0,33.0d0,88.0d0]
      call medianloc(INVALS,ii)
      write(*,fmt) ii,INVALS(ii)
      !
      cdont=[character(len=20) :: ’apple’,’bee’,’cherry’,’duck’,&
              ’elephant’,’finger’,’goose’,’h’,’insect’,’j’]
      call medianloc(cdont,ii)
      write(*,fmt) ii,cdont(ii)
      !
   end program demo_medianloc
Results: 

    location  median
       2     70.00000
       4     44.00000
       5     33.00000
       5     elephant

AUTHOR
Michel Olagnon, 2000-2012

MAINTAINER
John Urban, 2022.04.16

LICENSE
CC0-1.0

Nemo Release 3.1 medianloc (3) July 22, 2023
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