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vrelg_c

 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.
```

```   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;

.
.
.

/.
./
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  );
}

/.
./

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.
```   relative difference of n-dimensional vectors
`Fri Dec 31 18:41:15 2021`