Procedure

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

Abstract

 
    Compute the determinant of a double precision 3x3 matrix. 
 

Required_Reading

 
   None. 
 

Keywords

 
    MATRIX,  MATH 
 

Brief_I/O

 
   VARIABLE  I/O  DESCRIPTION 
   --------  ---  -------------------------------------------------- 
   m1         I     Matrix whose determinant is to be found. 
 

Detailed_Input

 
   m1      This variable may be any double precision, 3x3 matrix. 
 

Detailed_Output

 
   det_c   This is 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

 
          | 1  2  3 | 
     M1 = | 4  5  6 |   ---->   det_c(m1) = 0 
          | 7  8  9 | 
  
          | 1  2  3 | 
     M1 = | 0  5  6 |   ---->   det_c(m1) = 45 
          | 0  0  9 | 
 

Restrictions

 
   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)
   W.M. Owen       (JPL) 
 

Version

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

Index_Entries

 
   determinant of a d.p. 3x3_matrix 
 

Link to routine det_c source file det_c.c