Procedure

     XPOSE ( Transpose a matrix, 3x3 )

     SUBROUTINE XPOSE ( M1, MOUT )

Abstract

     Transpose a 3x3 matrix.

Required_Reading

     None.

Keywords

     MATRIX

Declarations

     IMPLICIT NONE

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

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   3x3 matrix to be transposed.
     MOUT       O   Transpose of M1.

Detailed_Input

     M1       is any double precision 3x3 matrix.

Detailed_Output

     MOUT     is a double precision, 3x3 matrix which contains the
              transpose of M1.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     XPOSE first copies the diagonal elements of M1 to MOUT. Then
     the off-diagonal elements are transposed using a temporary
     variable in the following order:

        (1,2) <---> (2,1)
        (1,3) <---> (3,1)
        (2,3) <---> (3,2)

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 double precision matrix, find its transpose.


        Example code begins here.


              PROGRAM XPOSE_EX1
              IMPLICIT NONE

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

              INTEGER               I
              INTEGER               J

        C
        C     Define the input matrix.
        C
              DATA                  M1     /  1.0D0,  0.0D0,  0.0D0,
             .                                2.0D0,  4.0D0,  6.0D0,
             .                                3.0D0,  5.0D0,  0.0D0 /

        C
        C     Compute the transpose of M1.
        C
              CALL XPOSE ( M1, MOUT )

        C
        C     Display the results.
        C
              WRITE(*,*) 'Input matrix (M1):'
              WRITE(*,*)
              DO I= 1, 3
                 WRITE(*,'(3F6.1)') ( M1(I,J), J= 1, 3 )
              END DO
              WRITE(*,*)
              WRITE(*,*) 'Transpose of M1:'
              WRITE(*,*)
              DO I= 1, 3
                 WRITE(*,'(3F6.1)') ( 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:


         Input matrix (M1):

           1.0   2.0   3.0
           0.0   4.0   5.0
           0.0   6.0   0.0

         Transpose of M1:

           1.0   0.0   0.0
           2.0   4.0   6.0
           3.0   5.0   0.0

Restrictions

     None.

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 example.

    SPICELIB Version 1.0.2, 23-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)