# ipsort.f

          SUBROUTINE IPSORT (IX, N, IPERM, KFLAG, IER)
    C***BEGIN PROLOGUE  IPSORT
    C***PURPOSE  Return the permutation vector generated by sorting a given
    C            array and, optionally, rearrange the elements of the array.
    C            The array may be sorted in increasing or decreasing order.
    C            A slightly modified quicksort algorithm is used.
    C***LIBRARY   SLATEC
    C***CATEGORY  N6A1A, N6A2A
    C***TYPE      INTEGER (SPSORT-S, DPSORT-D, IPSORT-I, HPSORT-H)
    C***KEYWORDS  NUMBER SORTING, PASSIVE SORTING, SINGLETON QUICKSORT, SORT
    C***AUTHOR  Jones, R. E., (SNLA)
    C           Kahaner, D. K., (NBS)
    C           Rhoads, G. S., (NBS)
    C           Wisniewski, J. A., (SNLA)
    C***DESCRIPTION
    C
    C   IPSORT returns the permutation vector IPERM generated by sorting
    C   the array IX and, optionally, rearranges the values in IX.  IX may
    C   be sorted in increasing or decreasing order.  A slightly modified
    C   quicksort algorithm is used.
    C
    C   IPERM is such that IX(IPERM(I)) is the Ith value in the
    C   rearrangement of IX.  IPERM may be applied to another array by
    C   calling IPPERM, SPPERM, DPPERM or HPPERM.
    C
    C   The main difference between IPSORT and its active sorting equivalent
    C   ISORT is that the data are referenced indirectly rather than
    C   directly.  Therefore, IPSORT should require approximately twice as
    C   long to execute as ISORT.  However, IPSORT is more general.
    C
    C   Description of Parameters
    C      IX - input/output -- integer array of values to be sorted.
    C           If ABS(KFLAG) = 2, then the values in IX will be
    C           rearranged on output; otherwise, they are unchanged.
    C      N  - input -- number of values in array IX to be sorted.
    C      IPERM - output -- permutation array such that IPERM(I) is the
    C              index of the value in the original order of the
    C              IX array that is in the Ith location in the sorted
    C              order.
    C      KFLAG - input -- control parameter:
    C            =  2  means return the permutation vector resulting from
    C                  sorting IX in increasing order and sort IX also.
    C            =  1  means return the permutation vector resulting from
    C                  sorting IX in increasing order and do not sort IX.
    C            = -1  means return the permutation vector resulting from
    C                  sorting IX in decreasing order and do not sort IX.
    C            = -2  means return the permutation vector resulting from
    C                  sorting IX in decreasing order and sort IX also.
    C      IER - output -- error indicator:
    C          =  0  if no error,
    C          =  1  if N is zero or negative,
    C          =  2  if KFLAG is not 2, 1, -1, or -2.
    C***REFERENCES  R. C. Singleton, Algorithm 347, An efficient algorithm
    C                 for sorting with minimal storage, Communications of
    C                 the ACM, 12, 3 (1969), pp. 185-187.
    C***ROUTINES CALLED  XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   761101  DATE WRITTEN
    C   761118  Modified by John A. Wisniewski to use the Singleton
    C           quicksort algorithm.
    C   810801  Further modified by David K. Kahaner.
    C   870423  Modified by Gregory S. Rhoads for passive sorting with the
    C           option for the rearrangement of the original data.
    C   890620  Algorithm for rearranging the data vector corrected by R.
    C           Boisvert.
    C   890622  Prologue upgraded to Version 4.0 style by D. Lozier.
    C   891128  Error when KFLAG.LT.0 and N=1 corrected by R. Boisvert.
    C   920507  Modified by M. McClain to revise prologue text.
    C   920818  Declarations section rebuilt and code restructured to use
    C           IF-THEN-ELSE-ENDIF.  (SMR, WRB)
    C***END PROLOGUE  IPSORT