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vtmv_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

```   vtmv_c ( Vector transpose times matrix times vector, 3 dim )

SpiceDouble vtmv_c ( ConstSpiceDouble v1     [3],
ConstSpiceDouble matrix [3][3],
ConstSpiceDouble v2     [3] )

```

Abstract

```   Multiply the transpose of a 3-dimensional column vector,
a 3x3 matrix, and a 3-dimensional column vector.
```

```   None.
```

Keywords

```   MATRIX
VECTOR

```

Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
v1         I   3-dimensional double precision column vector.
matrix     I   3x3 double precision matrix.
v2         I   3-dimensional double precision column vector.

The function returns the result of multiplying the transpose of
`v1' by `matrix' by `v2'.
```

Detailed_Input

```   v1          is any double precision 3-dimensional column vector.

matrix      is any double precision 3x3 matrix.

v2          is any double precision 3-dimensional column vector.
```

Detailed_Output

```   The function returns the double precision value of the equation

T
v1  *  matrix * v2

Notice that vtmv_c is actually the dot product of the vector
resulting from multiplying the transpose of `v1' and `matrix' and the
vector `v2'.
```

Parameters

```   None.
```

Exceptions

```   Error free.
```

Files

```   None.
```

Particulars

```   This routine implements the following vector/matrix/vector
multiplication:

T
vtmv_c = v1  * matrix * v2;

`v1' is a column vector which becomes a row vector when transposed.
`v2' is a column vector.

No checking is performed to determine whether floating point
overflow has occurred.
```

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) Compute the multiplication of the transpose of a 3-dimensional
column vector, a 3x3 matrix, and a second 3-dimensional column
vector.

Example code begins here.

/.
Program vtmv_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceInt             i;

/.
Define `v1', `matrix' and `v2'.
./
SpiceDouble          v1     [3]    = {   2.0,  4.0, 6.0 };
SpiceDouble          matrix [3][3] = { { 0.0,  1.0, 0.0 },
{-1.0,  0.0, 0.0 },
{ 0.0,  0.0, 1.0 } };
SpiceDouble          v2     [3]    = {   1.0,  1.0, 1.0 };

printf( "V1:\n" );
for ( i = 0; i < 3; i++ )
{
printf( "%6.1f\n", v1[i] );
}

printf( "\n" );
printf( "MATRIX:\n" );
for ( i = 0; i < 3; i++ )
{
printf( "%6.1f %5.1f %5.1f\n",
matrix[i][0], matrix[i][1], matrix[i][2] );
}

printf( "\n" );
printf( "V2:\n" );
for ( i = 0; i < 3; i++ )
{
printf( "%6.1f\n", v2[i] );
}

/.
Compute the transpose of `v1' times `matrix' times `v2'.
./
printf( "\n" );
printf( "Transpose of V1 times MATRIX times V2: %5.1f\n",
vtmv_c ( v1, matrix, v2 ) );

return ( 0 );
}

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

V1:
2.0
4.0
6.0

MATRIX:
0.0   1.0   0.0
-1.0   0.0   0.0
0.0   0.0   1.0

V2:
1.0
1.0
1.0

Transpose of V1 times MATRIX times V2:   4.0
```

Restrictions

```   None.
```

Literature_References

```   None.
```

Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
W.M. Owen           (JPL)
E.D. Wright         (JPL)
```

Version

```   -CSPICE Version 1.0.1, 19-MAY-2020 (JDR)

```   3-dimensional vector_transpose times matrix times vector
`Fri Dec 31 18:41:15 2021`