Procedure

     MTXVG ( Matrix transpose times vector, general dimension )

     SUBROUTINE MTXVG ( M1, V2, NC1, NR1R2, VOUT )

Abstract

     Multiply the transpose of a matrix and a vector of
     arbitrary size.

Required_Reading

     None.

Keywords

     MATRIX
     VECTOR

Declarations

     IMPLICIT NONE

     INTEGER            NC1
     INTEGER            NR1R2
     DOUBLE PRECISION   M1   ( NR1R2,NC1 )
     DOUBLE PRECISION   V2   ( NR1R2     )
     DOUBLE PRECISION   VOUT (       NC1 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   Left-hand matrix whose transpose is to be
                    multiplied.
     V2         I   Right-hand vector to be multiplied.
     NC1        I   Column dimension of M1 and length of VOUT.
     NR1R2      I   Row dimension of M1 and length of V2.
     VOUT       O   Product vector M1**T * V2.

Detailed_Input

     M1       is a double precision matrix of arbitrary size whose
              transpose forms the left-hand matrix of the
              multiplication.

     V2       is a double precision vector on the right of the
              multiplication.

     NC1      is the column dimension of M1 and length of VOUT.

     NR1R2    is the row dimension of M1 and length of V2.

Detailed_Output

     VOUT     is the double precision vector which results from
              the expression

                            T
                 VOUT = (M1)  x V2

              where the T denotes the transpose of M1.

              VOUT must NOT overwrite either M1 or V2.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     The code reflects precisely the following mathematical expression

     For each value of the subscript I from 1 to NC1,

     VOUT(I) = Summation from K=1 to NR1R2 of  ( M1(K,I) * V2(K) )

     Note that the reversal of the K and I subscripts in the left-hand
     matrix M1 is what makes VOUT the product of the TRANSPOSE of M1
     and not simply of M1 itself.

     Since this subroutine operates on matrices of arbitrary size, it
     is not feasible to buffer intermediate results. Thus, VOUT
     should NOT overwrite either M1 or V2.

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) Given a 3x2 matrix and a 3-vector, multiply the transpose of
        the matrix by the vector.


        Example code begins here.


              PROGRAM MTXVG_EX1
              IMPLICIT NONE

        C
        C     Local variables.
        C
              DOUBLE PRECISION      M    ( 3, 2 )
              DOUBLE PRECISION      VIN  ( 3    )
              DOUBLE PRECISION      VOUT ( 2    )

              INTEGER               I
              INTEGER               J

        C
        C     Define M and VIN.
        C
              DATA                  M    /  1.0D0,  1.0D0,  1.0D0,
             .                              2.0D0,  3.0D0,  4.0D0  /

              DATA                  VIN  /  1.0D0,  2.0D0,  3.0D0  /

        C
        C     Multiply the transpose of M by VIN.
        C
              CALL MTXVG ( M, VIN, 2, 3, VOUT )

              WRITE(*,'(A)') 'Transpose of M times VIN:'
              WRITE(*,'(2F10.3)') VOUT

              END


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


        Transpose of M times VIN:
             6.000    20.000

Restrictions

     1)  The user is responsible for checking the magnitudes of the
         elements of M1 and V2 so that a floating point overflow does
         not occur.

     2)  VOUT not overwrite M1 or V2 or else the intermediate
         will affect the final result.

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, 04-JUL-2021 (JDR)

        Added IMPLICIT NONE statement.

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

    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)