Procedure

   vhatg_c ( "V-Hat", unit vector along V, general dimension ) 

   void vhatg_c ( ConstSpiceDouble   * v1,
                  SpiceInt             ndim,
                  SpiceDouble        * vout )

Abstract

   Find the unit vector along a double precision vector of
   arbitrary dimension.

Required_Reading

   None.

Keywords

   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   v1         I   Vector to be normalized.
   ndim       I   Dimension of `v1' (and also `vout').
   vout       O   Unit vector along `v1'.

Detailed_Input

   v1          is any double precision vector of arbitrary dimension.

   ndim        is the dimension of `v1' (and also `vout').

Detailed_Output

   vout        is the unit vector in the direction of `v1':

                            v1
                  vout = --------
                          ||v1||

               If `v1' represents the zero vector, then `vout' will also be
               the zero vector. `vout' may overwrite `v1'.

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   vhatg_c determines the magnitude of `v1' and then divides each
   component of `v1' by the magnitude. This process is highly stable
   over the whole range of multi-dimensional vectors.

   This routine will detect if `v1' the zero vector, and will not
   attempt to divide by zero.

Examples

   The numerical results shown for this example may differ across
   platforms. The results depend on the SPICE kernels used as
   input, the compiler and supporting libraries, and the machine
   specific arithmetic implementation.

   1) Define a set of n-dimensional vectors and find the unit vector
      along each of them.


      Example code begins here.


      /.
         Program vhatg_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local parameters.
         ./
         #define NDIM         4
         #define SETSIZ       2

         /.
         Local variables.
         ./
         SpiceDouble          vout   [NDIM];

         SpiceInt             i;

         /.
         Define the vector set.
         ./
         SpiceDouble          v1     [SETSIZ][NDIM] = {
                                   { 5.0,    12.0,  0.0,   0.0 },
                                   { 1.e-7,  2.e-7, 2.e-7, 0.0 } };

         /.
         Calculate the unit vectors.
         ./
         for ( i = 0; i < SETSIZ; i++ )
         {

            vhatg_c ( v1[i], NDIM, vout );

            printf( "Input vector:  %11.7f %11.7f %11.7f %11.7f\n",
                             v1[i][0], v1[i][1], v1[i][2], v1[i][3] );
            printf( "Unit vector :  %11.7f %11.7f %11.7f %11.7f\n",
                                 vout[0], vout[1], vout[2], vout[3] );
            printf( "\n" );

         }

         return ( 0 );
      }


      When this program was executed on a Mac/Intel/cc/64-bit
      platform, the output was:


      Input vector:    5.0000000  12.0000000   0.0000000   0.0000000
      Unit vector :    0.3846154   0.9230769   0.0000000   0.0000000

      Input vector:    0.0000001   0.0000002   0.0000002   0.0000000
      Unit vector :    0.3333333   0.6666667   0.6666667   0.0000000

Restrictions

   1)  The relative number of cases whereby floating point overflow
       may occur is negligible. Thus, no error recovery or reporting
       scheme is incorporated into this function.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)
   W.M. Owen           (JPL)

Version

   -CSPICE Version 1.0.1, 05-JUL-2021 (JDR)

       Edited the header to comply with NAIF standard. Added complete
       code example based on existing example.

   -CSPICE Version 1.0.0, 13-JUL-1999 (NJB) (WMO)

Index_Entries

   unitize a n-dimensional vector