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Index Page vtmv_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

       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.

#### Required_Reading

       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)

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

       -CSPICE Version 1.0.0, 01-JUL-1999 (EDW) (WMO)

#### Index_Entries

       3-dimensional vector_transpose times matrix times vector

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

    Fri Dec 31 18:41:15 2021