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Index Page det_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       det_c ( Determinant of a double precision 3x3 matrix )

       SpiceDouble det_c ( ConstSpiceDouble m1[3][3] )

#### Abstract

       Compute the determinant of a double precision 3x3 matrix.

#### Required_Reading

       None.

#### Keywords

       MATH
       MATRIX

#### 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_c 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
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Set `m1' and `m2'.
             ./
             SpiceDouble          m1     [3][3] = { {1.0,  2.0,  3.0},
                                                    {4.0,  5.0,  6.0},
                                                    {7.0,  8.0,  9.0} };

             SpiceDouble          m2     [3][3] = { {1.0,  2.0,  3.0},
                                                    {0.0,  5.0,  6.0},
                                                    {0.0,  0.0,  9.0} };

             /.
             Display the determinant of `m1' and `m2'.
             ./
             printf( "Determinant of M1: %5.2f\n", det_c ( m1 ) );
             printf( "Determinant of M2: %5.2f\n", det_c ( m2 ) );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/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_c to operate on.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       W.M. Owen           (JPL)

#### Version

       -CSPICE Version 1.0.1, 02-JUL-2021 (JDR)

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

       -CSPICE Version 1.0.0, 21-OCT-1998 (NJB) (WMO)

#### Index_Entries

       determinant of a d.p. 3x3_matrix

#### Link to routine det_c source file det_c.c

    Fri Dec 31 18:41:04 2021