Procedure

   vtmvg_c ( Vector transpose times matrix times vector ) 

   SpiceDouble vtmvg_c ( const void          * v1,
                         const void          * matrix,
                         const void          * v2,
                         SpiceInt              nrow,
                         SpiceInt              ncol    )

Abstract

   Multiply the transpose of a n-dimensional column vector,
   a nxm matrix, and a m-dimensional column vector.

Required_Reading

   None.

Keywords

   MATRIX
   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   v1         I   n-dimensional double precision column vector.
   matrix     I   nxm double precision matrix.
   v2         I   m-dimensional double precision column vector.
   nrow       I   Number of rows in matrix (number of rows in `v1'.)
   ncol       I   Number of columns in matrix (number of rows in `v2'.)

   The function returns the result of (v1**t * matrix * v2 ).

Detailed_Input

   v1          is an n-dimensional double precision vector.

   matrix      is an n x m double precision matrix.

   v2          is an m-dimensional double precision vector.

   nrow        is the number of rows in matrix. this is also
               equivalent to the number of rows in the vector `v1'.

   ncol        is the number of columns in matrix. this is also
               equivalent to the number of rows in the vector `v2'.

Detailed_Output

   The function returns the double precision value of the equation
   (v1**t * matrix * v2 ).

   Notice that vtmvg_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 |          |  |  |
      vtmvg_c = [   v1   ]  |  matrix  |  |v2|
                            |          |  |  |

   by calculating over all values of the indices `k' and `l' from 0 to
   nrow-1 and 0 to ncol-1, respectively, the expression

      vtmvg_c = Summation of ( v1(k)*matrix(k,l)*v2(l) ) .

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

   No check performed to determine whether floating point
   overflow has occurred.

Examples

   If  v1 = | 1.0 |  matrix = | 2.0  0.0 |  v2 = | 1.0 |
            |     |           |          |       |     |
            | 2.0 |           | 1.0  2.0 |       | 2.0 |
            |     |           |          |
            | 3.0 |           | 1.0  1.0 |

   nrow = 3
   ncol = 2

   Then the value of the function is  21.0.

Restrictions

   1)  Since no error detection or recovery is implemented, the
       programmer is required to insure that the inputs to this routine
       are both valid and within the proper range.

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, 13-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

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

Index_Entries

   n-dimensional vector_transpose times matrix times vector