SVIGP

Sorts an integer array by algebraically increasing value and return the permutation that rearranges the array.

Required Arguments

IA — Integer vector of length N containing the array to be sorted. (Input)

IB — Integer vector of length N containing the sorted array. (Output)
If IA is not needed, IA and IB 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 IA.

Optional Arguments

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

FORTRAN 90 Interface

Generic: CALL SVIGP (IA, IB, IPERM [, …])

Specific: The specific interface name is S_SVIGP.

FORTRAN 77 Interface

Single: CALL SVIGP (N, IA, IB, IPERM)

Description

Routine SVIGP sorts the elements of an integer 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 SVIGP 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 IA(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 IA algebraically.

 

USE SVIGP_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER N, J, NOUT

PARAMETER (N=10)

INTEGER IA(N), IB(N), IPERM(N)

! Set values for IA and IPERM

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

!

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

!

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

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

! Sort IA by algebraic value into IB

CALL SVIGP (IA, IB, IPERM)

! Print results

CALL UMACH (2,NOUT)

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

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

!

99998 FORMAT (' The output vector is:', /, 10(1X,I5))

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

END

Output

 

The Output vector is:

-9 -7 -3 -2 -1 4 5 6 8 10

 

The permutation vector is:

2 4 8 9 10 7 6 5 3 1