Procedure

     MXV ( Matrix times vector, 3x3 )

     SUBROUTINE MXV ( M, VIN, VOUT )

Abstract

     Multiply a 3x3 double precision matrix with a 3-dimensional
     double precision vector.

Required_Reading

     None.

Keywords

     MATRIX
     VECTOR

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   M      ( 3, 3 )
     DOUBLE PRECISION   VIN    (    3 )
     DOUBLE PRECISION   VOUT   (    3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M          I   3x3 double precision matrix.
     VIN        I   3-dimensional double precision vector.
     VOUT       O   3-dimensional double precision vector. VOUT is
                    the product M*VIN.

Detailed_Input

     M        is an arbitrary 3x3 double precision matrix.

     VIN      is an arbitrary 3-dimensional double precision vector.

Detailed_Output

     VOUT     is a 3-dimensional double precision vector. VOUT is
              the product M * V.

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 3:

                        3
                     .-----
                      \
           VOUT(I) =   )  M(I,K) * VIN(K)
                      /
                     '-----
                       K=1

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


        Example code begins here.


              PROGRAM MXV_EX1
              IMPLICIT NONE

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

        C
        C     Define M and VIN.
        C
              DATA                  M    /  0.0D0, -1.0D0,  0.0D0,
             .                              1.0D0,  0.0D0,  0.0D0,
             .                              0.0D0,  0.0D0,  1.0D0  /

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

        C
        C     Multiply M by VIN.
        C
              CALL MXV ( M, VIN, VOUT )

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

              END


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


        M times VIN:
             2.000    -1.000     3.000

Restrictions

     1)  The user is responsible for checking the magnitudes of the
         elements of M and VIN 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, 13-AUG-2021 (JDR)

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

        Changed input argument name MATRIX to M for consistency with
        other routines.

        Added IMPLICIT NONE statement.

    SPICELIB Version 1.0.2, 22-APR-2010 (NJB)

        Header correction: assertions that the output
        can overwrite the input have been removed.

    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)