Procedure

     MXVG ( Matrix time vector, general dimension )

     SUBROUTINE MXVG ( M1, V2, NR1, NC1R2, VOUT )

Abstract

     Multiply a matrix and a vector of arbitrary size.

Required_Reading

     None.

Keywords

     MATRIX
     VECTOR

Declarations

     IMPLICIT NONE

     INTEGER            NR1
     INTEGER            NC1R2
     DOUBLE PRECISION   M1   ( NR1,NC1R2 )
     DOUBLE PRECISION   V2   (     NC1R2 )
     DOUBLE PRECISION   VOUT ( NR1       )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   Left-hand matrix to be multiplied.
     V2         I   Right-hand vector to be multiplied.
     NR1        I   Row dimension of M1 and length of VOUT.
     NC1R2      I   Column dimension of M1 and length of V2.
     VOUT       O   Product vector M1*V2.

Detailed_Input

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

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

     NR1      is the row dimension of M1 and length of VOUT.

     NC1R2    is the column dimension of M1 and length of V2.

Detailed_Output

     VOUT     is the double precision vector which results from
              the expression VOUT = (M1) x 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 NR1,

        VOUT(I) = Summation from K=1 to NC1R2 of  ( M1(I,K) * V2(K) )

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 2x3 matrix and a 3-vector, multiply the matrix by
        the vector.


        Example code begins here.


              PROGRAM MXVG_EX1
              IMPLICIT NONE

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

              INTEGER               I
              INTEGER               J

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

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

        C
        C     Multiply M by VIN.
        C
              CALL MXVG ( M, VIN, 2, 3, VOUT )

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

              END


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


        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.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     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 1.0.2, 23-APR-2010 (NJB)

        Re-ordered header sections and made minor formatting
        changes.

    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)