Procedure

     MXMT ( Matrix times matrix transpose, 3x3 )

     SUBROUTINE MXMT ( M1, M2, MOUT )

Abstract

     Multiply a 3x3 matrix and the transpose of another 3x3 matrix.

Required_Reading

     None.

Keywords

     MATRIX

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   M1   ( 3,3 )
     DOUBLE PRECISION   M2   ( 3,3 )
     DOUBLE PRECISION   MOUT ( 3,3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   3x3 double precision matrix.
     M2         I   3x3 double precision matrix.
     MOUT       O   The product M1 times transpose of M2.

Detailed_Input

     M1       is an arbitrary 3x3 double precision matrix.

     M2       is an arbitrary 3x3 double precision matrix.
              Typically, M2 will be a rotation matrix since
              then its transpose is its inverse (but this is
              NOT a requirement).

Detailed_Output

     MOUT     is a 3x3 double precision matrix. MOUT is the product

                               T
                 MOUT = M1 x M2

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     The code reflects precisely the following mathematical expression

        For each value of the subscripts I and J from 1 to 3:

                          3
                       .-----
                        \
           MOUT(I,J) =   )  M1(I,K) * M2(J,K)
                        /
                       '-----
                         K=1

     Note that the reversal of the K and J subscripts in the right-
     hand matrix M2 is what makes MOUT the product of the TRANSPOSE of
     M2 and not simply of M2 itself.

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 two 3x3 double precision matrices, multiply the first
        matrix by the transpose of the second one.


        Example code begins here.


              PROGRAM MXMT_EX1
              IMPLICIT NONE

        C
        C     Local variables.
        C
              DOUBLE PRECISION      M1   ( 3, 3 )
              DOUBLE PRECISION      M2   ( 3, 3 )
              DOUBLE PRECISION      MOUT ( 3, 3 )

              INTEGER               I
              INTEGER               J

        C
        C     Define M1.
        C
              DATA                  M1   /  0.0D0, -1.0D0,  0.0D0,
             .                              1.0D0,  0.0D0,  0.0D0,
             .                              0.0D0,  0.0D0,  1.0D0  /

        C
        C     Make M2 equal to M1.
        C
              CALL MEQU ( M1, M2 )

        C
        C     Multiply M1 by the transpose of M2.
        C
              CALL MXMT ( M1, M2, MOUT )

              WRITE(*,'(A)') 'M1:'
              DO I=1, 3

                 WRITE(*,'(3F16.7)') ( M1(I,J), J=1,3 )

              END DO

              WRITE(*,*)
              WRITE(*,'(A)') 'M2:'
              DO I=1, 3

                 WRITE(*,'(3F16.7)') ( M2(I,J), J=1,3 )

              END DO

              WRITE(*,*)
              WRITE(*,'(A)') 'M1 times transpose of M2:'
              DO I=1, 3

                 WRITE(*,'(3F16.7)') ( MOUT(I,J), J=1,3 )

              END DO

              END


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


        M1:
               0.0000000       1.0000000       0.0000000
              -1.0000000       0.0000000       0.0000000
               0.0000000       0.0000000       1.0000000

        M2:
               0.0000000       1.0000000       0.0000000
              -1.0000000       0.0000000       0.0000000
               0.0000000       0.0000000       1.0000000

        M1 times transpose of M2:
               1.0000000       0.0000000       0.0000000
               0.0000000       1.0000000       0.0000000
               0.0000000       0.0000000       1.0000000

Restrictions

     1)  The user is responsible for checking the magnitudes of the
         elements of M1 and M2 so that a floating point overflow does
         not occur. (In the typical use where M1 and M2 are rotation
         matrices, this not a risk at all.)

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, 06-JUL-2021 (JDR)

        Added IMPLICIT NONE statement.

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

    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)