Procedure

   vlcomg_c ( Vector linear combination, general dimension ) 

   void vlcomg_c ( SpiceInt            n,
                   SpiceDouble         a,
                   ConstSpiceDouble *  v1,
                   SpiceDouble         b,
                   ConstSpiceDouble *  v2,
                   SpiceDouble      *  sum )

Abstract

   Compute a vector linear combination of two double precision
   vectors of arbitrary dimension.

Required_Reading

   None.

Keywords

   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   n          I   Dimension of vector space.
   a          I   Coefficient of `v1'.
   v1         I   Vector in n-space.
   b          I   Coefficient of `v2'.
   v2         I   Vector in n-space.
   sum        O   Linear vector combination a*v1 + b*v2.

Detailed_Input

   n           is the dimension of `v1', `v2' and `sum'.

   a           is the double precision scalar variable that multiplies
               `v1'.

   v1          is an arbitrary, double precision n-dimensional vector.

   b           is the double precision scalar variable that multiplies
               `v2'.

   v2          is an arbitrary, double precision n-dimensional vector.

Detailed_Output

   sum         is the double precision n-dimensional vector which
               contains the linear combination

                  a * v1 + b * v2

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

      For each value of the index `i', from 0 to n-1:

         sum[i] = a * v1[i] + b * v2[i]

   No error checking is performed to guard against numeric overflow.

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) Perform the projection of a 4-dimensional vector into a
      2-dimensional plane in 4-space.


      Example code begins here.


      /.
         Program vlcomg_ex1
      ./
      #include <math.h>
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local parameters.
         ./
         #define NDIM         4

         /.
         Local variables.
         ./
         SpiceDouble          puv    [NDIM];
         SpiceDouble          v      [NDIM];

         /.
         Let `x' be an arbitrary NDIM-vector
         ./
         SpiceDouble          x      [NDIM] = { 4.0, 35.0, -5.0, 7.0 };

         /.
         Let `u' and `v' be orthonormal NDIM-vectors spanning the
         plane of interest.
         ./
         SpiceDouble          u      [NDIM] = { 0.0,  0.0,  1.0, 0.0 };

         v[0] =  sqrt(3.0)/3.0;
         v[1] = -sqrt(3.0)/3.0;
         v[2] =  0.0;
         v[3] =  sqrt(3.0)/3.0;

         /.
         Compute the projection of `x' onto this 2-dimensional
         plane in NDIM-space.
         ./
         vlcomg_c ( NDIM, vdotg_c ( x, u, NDIM ), u,
                          vdotg_c ( x, v, NDIM ), v, puv );

         /.
         Display the results.
         ./
         printf( "Input vector             :  %5.1f %5.1f %5.1f %5.1f\n",
                                                   x[0], x[1], x[2], x[3] );
         printf( "Projection into 2-d plane:  %5.1f %5.1f %5.1f %5.1f\n",
                                           puv[0], puv[1], puv[2], puv[3] );

         return ( 0 );
      }


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


      Input vector             :    4.0  35.0  -5.0   7.0
      Projection into 2-d plane:   -8.0   8.0  -5.0  -8.0

Restrictions

   1)  No error checking is performed to guard against numeric
       overflow or underflow. The user is responsible for insuring
       that the input values are reasonable.

Literature_References

   None.

Author_and_Institution

   J. Diaz del Rio     (ODC Space)
   W.L. Taber          (JPL)

Version

   -CSPICE Version 1.0.1, 13-AUG-2021 (JDR)

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

   -CSPICE Version 1.0.0, 30-JUN-1999 (WLT)

Index_Entries

   linear combination of two n-dimensional vectors