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Index Page vrelg_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       vrelg_c ( Vector relative difference, general dimension )

       SpiceDouble vrelg_c ( ConstSpiceDouble * v1,
                             ConstSpiceDouble * v2,
                             SpiceInt           ndim  )

#### Abstract

       Return the relative difference between two vectors of general
       dimension.

#### Required_Reading

       None.

#### Keywords

       MATH
       VECTOR

#### 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_c   =   -------------------------
                         maxd ( ||v1||, ||v2|| )

       where ||x|| indicates the Euclidean norm of the vector `x'.

       vrelg_c assumes values in the range [0,2]. If both `v1' and `v2' are
       zero vectors then vrelg_c is defined to be zero.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  If both `v1' and `v2' are zero vectors, then vrelg_c 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_c 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.

             #include "SpiceUsr.h"
                   .
                   .
                   .
             /.
             The NAIF code for Jupiter is 599 and for Voyager 2 is -32.
             Set the tolerance to be 0.0005.
             ./

             #define            NUM   500
             #define            JUP   599
             #define            VG2   -32
             #define            TOL   .0005

             /.
             Local variables
             ./
             SpiceDouble        state1 [6][NUM];
             SpiceDouble        state2 [6][NUM];
             SpiceDouble        et     [NUM];
             SpiceDouble        lt;
             SpiceDouble        diff;

             SpiceInt           i;

             .
             .
             .

             /.
             Load  the first SPK file.
             ./
             furnsh_c ( "VG2_SOURCE_1.BSP" );

             /.
             Find the states for each time in the array ET.
             This example assumes that the SPK file can
             provide states for all of the times in the array.
             ./
             for ( i = 0; i < NUM; i++ )
                {
                spkez_c ( JUP, et[i], "J2000", "lt", VG2,
                                       state1[1][i], &lt  );
                }

             /.
             Unload the first file and load the second one.
             ./
             unload_c ( "VG2_SOURCE_1.BSP" );

             furnsh_c ( "VG2_SOURCE_2.BSP" );

             /.
             Find the states from the new file.
             ./
             for ( i = 0; i < NUM; i++ )
                {
                spkez_c ( JUP, et[i], "J2000", "lt",
                          VG2, state2[1][i], &lt  );
                }

             /.
             Now compare the two state vectors for each time.
             ./
             for ( i = 0; i < NUM; i++ )
                {
                diff = vrelg_c ( state1[1][i], state2[1][i], 6 );

                if ( diff > TOL )
                   {
                     ...
                   }

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       J.M. Lynch          (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.0.1, 09-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

       -CSPICE Version 1.0.0, 28-AUG-2001 (NJB)

           Include interface macro definition file SpiceZim.h.
           Made some minor updates and corrections in the code example.

       -CSPICE Version 1.0.0, 06-JUL-1999 (EDW) (JML)

#### Index_Entries

       relative difference of n-dimensional vectors

#### Link to routine vrelg_c source file vrelg_c.c

    Fri Dec 31 18:41:15 2021