Abstract

   CSPICE_DET computes the determinant of a double precision 3x3 matrix.

I/O

   Given:

      m1       an arbitrary 3x3 double precision matrix.

               help, m1
                  DOUBLE = Array[3,3]

   the call:

      det = cspice_det( m1 )

   returns:

      det      the value of the determinant found by direct application of the
               definition of the determinant.

               help, det
                  DOUBLE = Scalar

Parameters

   None.

Examples

   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   1) Given a 3x3 double precision matrix, compute its determinant.

      Example code begins here.


      PRO det_ex1

         ;;
         ;; Set `m1' and `m2'.
         ;;
         m1 = [[1.D0,  2.D0,  3.D0],                                         $
               [4.D0,  5.D0,  6.D0],                                         $
               [7.D0,  8.D0,  9.D0]]

         m2 = [[1.D0,  2.D0,  3.D0],                                         $
               [0.D0,  5.D0,  6.D0],                                         $
               [0.D0,  0.D0,  9.D0]]

         ;;
         ;; Display the determinant of `m1' and `m2'.
         ;;
         print, format='(A,F6.2)', 'Determinant of M1:', cspice_det( m1 )
         print, format='(A,F6.2)', 'Determinant of M2:', cspice_det( m2 )

      END


      When this program was executed on a Mac/Intel/IDL8.x/64-bit
      platform, the output was:


      Determinant of M1:  0.00
      Determinant of M2: 45.00

Particulars

   cspice_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.

   The native IDL code to calculate the same scalar result is:

      det = determ( m1 )

         or

      det = la_determ( m1 )

   The IDL functions accepts an arbitrary size NxN matrix.

Exceptions

   1)  If the input argument `m1' is undefined, an error is signaled
       by the IDL error handling system.

   2)  If the input argument `m1' is not of the expected type, or it
       does not have the expected dimensions and size, an error is
       signaled by the Icy interface.

Files

   None.

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 cspice_det to operate on.

Required_Reading

   ICY.REQ

Literature_References

   None.

Author_and_Institution

   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version

   -Icy Version 1.0.3, 10-AUG-2021 (JDR)

       Changed input argument name "mat" to "m1" for consistency with other
       routines.

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

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections, and
       completed -Particulars section.

       Removed reference to the routine's corresponding CSPICE header from
       -Abstract section.

       Added arguments' type and size information in the -I/O section.

   -Icy Version 1.0.2, 13-JUN-2011 (EDW)

       Edits to comply with NAIF standard for Icy headers.

   -Icy Version 1.0.1, 09-DEC-2005 (EDW)

       Added -Examples section.

   -Icy Version 1.0.0, 16-JUN-2003 (EDW)

Index_Entries

   determinant of a d.p. 3x3_matrix