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Index Page vzerog_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

       vzerog_c ( Is a vector the zero vector? -- general dim. )

       SpiceBoolean vzerog_c ( ConstSpiceDouble * v, SpiceInt ndim )

#### Abstract

       Indicate whether an n-dimensional vector is the zero vector.

#### Required_Reading

       None.

#### Keywords

       MATH
       VECTOR

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       v          I   Vector to be tested.
       ndim       I   Dimension of `v'.

       The function returns the value SPICETRUE if and only if `v' is the
       zero vector.

#### Detailed_Input

       v,
       ndim        are, respectively, an n-dimensional vector and its
                   dimension.

#### Detailed_Output

       The function returns the value SPICETRUE if and only if `v' is the
       zero vector.

#### Parameters

       None.

#### Exceptions

       Error free.

       1)  When `ndim' is non-positive, this function returns the value
           SPICEFALSE (A vector of non-positive dimension cannot be the
           zero vector.)

#### Files

       None.

#### Particulars

       This function has the same truth value as the logical expression

          ( vnormg_c ( v, ndim )  ==  0. )

       Replacing the above expression by

          vzerog_c ( v, ndim );

       has several advantages: the latter expresses the test more
       clearly, looks better, and doesn't go through the work of scaling,
       squaring, taking a square root, and re-scaling (all of which
       vnormg_c must do) just to find out that a vector is non-zero.

       A related function is vzero_c, which accepts three-dimensional
       vectors.

#### Examples

       The numerical results shown for these examples 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) Given a set of n-dimensional vectors, check which ones are
          the zero vector.

          Example code begins here.

          /.
             Program vzerog_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

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

             /.
             Local variables.
             ./
             SpiceInt             i;

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

             /.
             Check each n-dimensional vector within the set.
             ./
             for ( i = 0; i < SETSIZ; i++ )
             {

                /.
                Check if the i'th vector is the zero vector.
                ./
                printf( "\n" );
                printf( "Input vector:  %10.7f %10.7f %10.7f %10.7f\n",
                                     v[i][0], v[i][1], v[i][2], v[i][3] );

                if ( vzerog_c ( v[i], NDIM ) )
                {
                   printf( "   The zero vector.\n" );
                }
                else
                {
                   printf( "   Not all elements of the vector are zero.\n" );
                }

             }

             return ( 0 );
          }

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

          Input vector:   0.0000000  0.0000000  0.0000000  0.0000002
             Not all elements of the vector are zero.

          Input vector:   0.0000000  0.0000000  0.0000000  0.0000000
             The zero vector.

       2) Define a unit quaternion and confirm that it is non-zero
          before converting it to a rotation matrix.

          Example code begins here.

          /.
             Program vzerog_ex2
          ./
          #include <math.h>
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables.
             ./
             SpiceDouble          q      [4];
             SpiceDouble          m      [3][3];
             SpiceDouble          s;

             SpiceInt             i;

             /.
             Define a unit quaternion.
             ./
             s = sqrt( 2.0 ) / 2.0;

             q[0] = s;
             q[1] = 0.0;
             q[2] = 0.0;
             q[3] = -s;

             printf( "Quaternion : %11.7f %11.7f %11.7f %11.7f\n",
                                            q[0], q[1], q[2], q[3] );

             /.
             Confirm that it is non-zero and
             ./
             if ( vzerog_c ( q, 4 ) )
             {
                printf( "   Quaternion is the zero vector.\n" );
             }
             else
             {

                /.
                Confirm q satisfies ||q|| = 1.
                ./
                printf( "Norm       : %11.7f\n", vnormg_c ( q, 4 ) );

                /.
                Convert the quaternion to a matrix form.
                ./
                q2m_c ( q, m );

                printf( "Matrix form:\n" );
                for ( i = 0; i < 3; i++ )
                {
                   printf( "%12.7f %11.7f %11.7f\n", m[i][0], m[i][1], m[i][2] );
                }
             }

             return ( 0 );
          }

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

          Quaternion :   0.7071068   0.0000000   0.0000000  -0.7071068
          Norm       :   1.0000000
          Matrix form:
             0.0000000   1.0000000   0.0000000
            -1.0000000   0.0000000  -0.0000000
            -0.0000000   0.0000000   1.0000000

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

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

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

       -CSPICE Version 1.0.0, 29-JUN-1999 (EDW) (NJB) (IMU)

#### Index_Entries

       test whether an n-dimensional vector is the zero vector

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

    Fri Dec 31 18:41:15 2021