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C Library Functions  - orderval (3)

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NAME

orderval(3f) - [M_orderpack:FRACTILE] Return VALUE of Nth ordered element of array (Quick-Sort-like)

CONTENTS

Synopsis
Description
Options
Returns
Examples
Author
Maintainer
License

SYNOPSIS

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)

DESCRIPTION

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.

OPTIONS

INVALS	array to search
NORD	Nth lowest value to find

RETURNS

orderval
	Nth lowest value

EXAMPLES

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

AUTHOR

Michel Olagnon - Aug. 2000

MAINTAINER

John Urban, 2022.04.16

LICENSE

CC0-1.0

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Nemo Release 3.1

orderval (3)

July 22, 2023

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