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vlcomg_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

```   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.
```

```   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)

```   linear combination of two n-dimensional vectors
`Fri Dec 31 18:41:15 2021`