Procedure

     VTMVG  ( Vector transpose times matrix times vector )

     DOUBLE PRECISION FUNCTION VTMVG ( V1, MATRIX, V2, NROW, 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

Declarations

     IMPLICIT NONE

     INTEGER               NROW
     INTEGER               NCOL
     DOUBLE PRECISION      V1      ( NROW       )
     DOUBLE PRECISION      MATRIX  ( NROW, NCOL )
     DOUBLE PRECISION      V2      (       NCOL )

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 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 = [   V1   ] |  MATRIX  |  |V2|
                           |          |  |  |

     by calculating over all values of the indices K and L from 1 to
     NROW and 1 to NCOL, respectively, the expression

        VTMVG = 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 checking is performed to determine whether floating point
     overflow has occurred.

Examples

     If  V1 = | 1.0D0 |  MATRIX = | 2.0D0  0.0D0 |  V2 = | 1.0D0 |
              |       |           |              |       |       |
              | 2.0D0 |           | 1.0D0  2.0D0 |       | 2.0D0 |
              |       |           |              |
              | 3.0D0 |           | 1.0D0  1.0D0 |

     NROW = 3
     NCOL = 2

     then the value of the function is  21.0D0.

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)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 13-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Added comments
        to the code and moved the declaration of each local variable to
        a separate line.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WMO)