SVRGP

Sorts a real array by algebraically increasing value and return the permutation that rearranges the array.

Required Arguments

RA — Vector of length N containing the array to be sorted.   (Input)

RB — Vector of length N containing the sorted array.   (Output)
If RA is not needed, RA and RB can share the same storage locations.

IPERM — Vector of length N.   (Input/Output)
On input, IPERM should be initialized to the values 1, 2, …, N. On output, IPERM contains a record of permutations made on the vector RA.

Optional Arguments

N — Number of elements in the array to be sorted.   (Input)
Default: N = size (IPERM,1).

FORTRAN 90 Interface

Generic:                              CALL SVRGP (RA, RB, IPERM [,…])

Specific:                             The specific interface names are S_SVRGP and D_SVRGP.

FORTRAN 77 Interface

Single:                                CALL SVRGP (N, RA, RB, IPERM)

Double:                              The double precision name is DSVRGP.

Description

Routine SVRGP sorts the elements of an array, A, into ascending order by algebraic value, keeping a record in P of the permutations to the array A. That is, the elements of P are moved in the same manner as are the elements in A as A is being sorted. The routine SVRGP uses the algorithm discussed in SVRGN. On completion, Aj Ai for j < i.

Comments

For wider applicability, integers (1, 2, …, N) that are to be associated with RA(I) for I = 1, 2, …, N may be entered into IPERM(I) in any order. Note that these integers must be unique.

Example

This example sorts the 10-element array RA algebraically.

 

      USE SVRGP_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    N, NOUT, J

      PARAMETER  (N=10)

      REAL       RA(N), RB(N)

      INTEGER    IPERM(N)

!                                 Set values for  RA and IPERM

!     RA    = ( 10.0  -9.0  8.0  -7.0  6.0  5.0  4.0  -3.0  -2.0  -1.0 )

!

!     IPERM = ( 1  2  3  4  5  6  7  8  9  10)

!

      DATA RA/10.0, -9.0, 8.0, -7.0, 6.0, 5.0, 4.0, -3.0, -2.0, -1.0/

      DATA IPERM/1, 2, 3, 4, 5, 6, 7, 8, 9, 10/

!                                 Sort RA by algebraic value into RB

      CALL SVRGP (RA, RB, IPERM)

!                                 Print results

      CALL UMACH (2,NOUT)

      WRITE (NOUT, 99998) (RB(J),J=1,N)

      WRITE (NOUT, 99999) (IPERM(J),J=1,N)

!

99998 FORMAT ('  The output vector is:', /, 10(1X,F5.1))

99999 FORMAT ('  The permutation vector is:', /, 10(1X,I5))

      END

Output

 

The output vector is:
-9.0  -7.0  -3.0  -2.0  -1.0   4.0   5.0   6.0   8.0  10.0

The permutation vector is:
2     4     8     9    10     7     6     5     3     1


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