Procedure

     VRELG ( Vector relative difference, general dimension )

     DOUBLE PRECISION FUNCTION VRELG ( V1, V2, NDIM )

Abstract

     Return the relative difference between two vectors of general
     dimension.

Required_Reading

     None.

Keywords

     MATH
     VECTOR

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      V1 ( * )
     DOUBLE PRECISION      V2 ( * )
     INTEGER               NDIM

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     V1,
     V2         I   Input vectors.
     NDIM       I   Dimension of V1 and V2.

     The function returns the relative difference between two vectors
     of general dimension.

Detailed_Input

     V1,
     V2       are two vectors for which the relative difference is to
              be computed.

     NDIM     is the dimension of V1 and V2.

Detailed_Output

     The function returns the relative difference between the two input
     n-dimensional vectors V1 and V2.

     It is defined as:

                          || V1 - V2 ||
        VRELG   =   ------------------------
                     MAX ( ||V1||, ||V2|| )

     where ||X|| indicates the Euclidean norm of the vector X.

     VRELG assumes values in the range [0,2]. If both V1 and V2 are
     zero vectors then VRELG is defined to be zero.

Parameters

     None.

Exceptions

     Error free.

     1)  If both V1 and V2 are zero vectors, then VRELG is defined to
         be zero.

Files

     None.

Particulars

     This function computes the relative difference between two vectors
     of general dimension as defined above.

     The function VREL may be used to find the relative difference
     for two 3-dimensional vectors.

Examples

     This example determines if the state of Jupiter, with respect
     to Voyager 2, for a set of times is the same for two different
     ephemeris files. Instead of insisting on absolute equality
     between the state vectors, the program will check if the relative
     difference between the vectors is greater than a fixed tolerance.

     C
     C     The NAIF code for Jupiter is 599 and for Voyager 2 is -32.
     C     Set the tolerance to be 0.0005.
     C
           INTEGER               JUP
           PARAMETER           ( JUP = 599 )

           INTEGER               VG2
           PARAMETER           ( VG2 = -32 )

           INTEGER               NUM
           PARAMETER           ( NUM = 500 )

           DOUBLE PRECISION      TOL
           PARAMETER           ( TOL = 5.D-04 )

     C
     C     SPICELIB function
     C
           DOUBLE PRECISION      VRELG
     C
     C     Local variables
     C
           DOUBLE PRECISION      STATE1 ( 6, NUM )
           DOUBLE PRECISION      STATE2 ( 6, NUM )
           DOUBLE PRECISION      ET     (    NUM )
           DOUBLE PRECISION      LT
           DOUBLE PRECISION      DIFF

           INTEGER               HANDLE
           INTEGER               I

           .
           .
           .

           C
           C     Load  the first SPK file.
           C
                 CALL SPKLEF ( 'VG2_SOURCE_1.BSP', HANDLE )
           C
           C     Find the states for each time in the array ET.
           C     This example assumes that the SPK file can
           C     provide states for all of the times in the array.
           C
                 DO I = 1, NUM

                    CALL SPKEZ ( JUP, ET(I),      'J2000', 'LT',
                .                VG2, STATE1(1,I), LT           )

                 END DO
           C
           C     Unload the first file and load the second one.
           C
                 CALL SPKUEF ( HANDLE )

                 CALL SPKLEF ( 'VG2_SOURCE_2.BSP', HANDLE )
           C
           C     Find the states from the new file.
           C
                 DO I = 1, NUM

                    CALL SPKEZ ( JUP, ET(I),      'J2000', 'LT',
                .                VG2, STATE2(1,I), LT           )

                 END DO
           C
           C     Now compare the two state vectors for each time.
           C
                 DO I = 1, NUM

                    DIFF = VRELG ( STATE1(1,I), STATE2(1,I), 6 )

                    IF ( DIFF .GT. TOL ) THEN

                       .
                       .
                       .

                    END IF

                 END DO

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     J.M. Lynch         (JPL)

Version

    SPICELIB Version 1.1.0, 12-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.0.0, 15-JUN-1992 (JML)