Procedure

     DET  ( Determinant of a double precision 3x3 matrix )

     DOUBLE PRECISION FUNCTION  DET ( M1 )

Abstract

     Compute the determinant of a double precision 3x3 matrix.

Required_Reading

     None.

Keywords

     MATH
     MATRIX

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION    M1 ( 3,3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     M1         I   Matrix whose determinant is to be found.

     The function returns the value of the determinant found by direct
     application of the definition of the determinant.

Detailed_Input

     M1       is any double precision, 3x3 matrix.

Detailed_Output

     The function returns the value of the determinant found by direct
     application of the definition of the determinant.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     DET calculates the determinant of M1 in a single arithmetic
     expression which is, effectively, the expansion of M1 about its
     first row. Since the calculation of the determinant involves
     the multiplication of numbers whose magnitudes are unrestricted,
     there is the possibility of floating point overflow or underflow.
     NO error checking or recovery is implemented in this routine.

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 determinant.

        Example code begins here.


              PROGRAM DET_EX1
              IMPLICIT NONE

        C
        C     SPICELIB functions.
        C
              DOUBLE PRECISION      DET

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

        C
        C     Set M1 and M2.
        C
              DATA                  M1 /  1.D0,  2.D0,  3.D0,
             .                            4.D0,  5.D0,  6.D0,
             .                            7.D0,  8.D0,  9.D0  /

              DATA                  M2 /  1.D0,  2.D0,  3.D0,
             .                            0.D0,  5.D0,  6.D0,
             .                            0.D0,  0.D0,  9.D0  /

        C
        C     Display the determinant of M1 and M2.
        C
              WRITE(*,'(A,F6.2)') 'Determinant of M1:', DET(M1)
              WRITE(*,'(A,F6.2)') 'Determinant of M2:', DET(M2)


              END


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


        Determinant of M1:  0.00
        Determinant of M2: 45.00

Restrictions

     1)  No checking is implemented to determine whether M1 will cause
         overflow or underflow in the process of calculating the
         determinant. In most cases, this will not pose a problem.
         The user is required to determine if M1 is suitable matrix
         for DET to operate on.

Literature_References

     None.

Author_and_Institution

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

Version

    SPICELIB Version 1.0.2, 02-JUL-2021 (JDR)

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

        Added missing 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 (WMO)