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Index Page vlcomg_c

Table of contents

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

       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

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

    Fri Dec 31 18:41:15 2021