Procedure

     TRACE ( Trace of a 3x3 matrix )

     DOUBLE PRECISION FUNCTION  TRACE ( MATRIX )

Abstract

     Return the trace of a 3x3 matrix.

Required_Reading

     None.

Keywords

     MATRIX

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   MATRIX ( 3, 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     MATRIX     I   3x3 matrix of double precision numbers.

     The function returns the trace of MATRIX.

Detailed_Input

     MATRIX   is a double precision 3x3 matrix.

Detailed_Output

     The function returns the trace of MATRIX, i.e. it is the sum of
     the diagonal elements of MATRIX.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     The code reflects precisely the following mathematical
     expression:

                  3
                .----
                 \
        TRACE =   )  MATRIX(I,I)
                 /
                '----
                 I=1

     No error detection or correction is implemented within this
     function.

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, compute its trace.


        Example code begins here.


              PROGRAM TRACE_EX1
              IMPLICIT NONE

        C
        C     SPICELIB functions.
        C
              DOUBLE PRECISION      TRACE

        C
        C     Local variables.
        C
              DOUBLE PRECISION      MATRIX ( 3, 3 )

              INTEGER               I
              INTEGER               J

        C
        C     Define MATRIX.
        C
              DATA                  MATRIX  /  3.D0,  0.D0,  4.D0,
             .                                 5.D0, -2.D0,  0.D0,
             .                                 7.D0,  8.D0, -1.D0  /


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

                 WRITE(*,'(3F6.1)') ( MATRIX(I,J), J=1,3 )

              END DO

        C
        C     Compute the trace of MATRIX and display the result.
        C
              WRITE(*,*)
              WRITE(*,'(A,F4.1)') 'Trace: ', TRACE ( MATRIX )

              END


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


        MATRIX:
           3.0   5.0   7.0
           0.0  -2.0   8.0
           4.0   0.0  -1.0

        Trace:  0.0

Restrictions

     1)  No checking is performed to guard against floating point
         overflow or underflow. This routine should probably not be
         used if the input matrix is expected to have large double
         precision numbers along the diagonal.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.0.2, 03-JUL-2020 (JDR)

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

        Added IMPLICIT NONE statement.

    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 (WLT)