Procedure

   ident_c ( Return the 3x3 identity matrix ) 

   void ident_c ( SpiceDouble    matrix[3][3] )

Abstract

   Return the 3x3 identity matrix.

Required_Reading

   None.

Keywords

   MATRIX

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   matrix     O   The 3x3 identity matrix.

Detailed_Input

   None.

Detailed_Output

   matrix      is the 3x3 Identity matrix. That `matrix' is
               the following

                  .-                 -.
                  |  1.0   0.0   0.0  |
                  |  0.0   1.0   0.0  |
                  |  0.0   0.0   1.0  |
                  `-                 -'

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   This is a utility routine for obtaining the 3x3 identity matrix
   so that you may avoid having to write the loop or assignments
   needed to get the matrix.

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) Define a 3x3 matrix and compute its inverse using the CSPICE
      routine invert_c. Verify the accuracy of the computed inverse
      using the mathematical identity

              -1
         m x m   - i = 0

      where `i' is the 3x3 identity matrix.


      Example code begins here.


      /.
         Program ident_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          idmat  [3][3];
         SpiceDouble          imat   [3][3];
         SpiceDouble          mout   [3][3];
         SpiceDouble          mzero  [3][3];

         SpiceInt             i;

         /.
         Define a matrix to invert.
         ./
         SpiceDouble          m      [3][3] = { {0.0,  -1.0, 0.0},
                                                {0.5,   0.0, 0.0},
                                                {0.0,   0.0, 1.0} };

         printf( "Original Matrix:\n" );
         for ( i = 0; i < 3; i++ )
         {

            printf( "%16.7f %15.7f %15.7f\n", m[i][0], m[i][1], m[i][2] );

         }

         /.
         Invert the matrix, then output.
         ./
         invert_c ( m, mout );

         printf( "\n" );
         printf( "Inverse Matrix:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%16.7f %15.7f %15.7f\n",
                    mout[i][0], mout[i][1], mout[i][2] );
         }

         /.
         Check the `m' times `mout' produces the identity matrix.
         ./
         ident_c ( idmat );
         mxm_c   ( m, mout, imat );

         vsubg_c ( (SpiceDouble *)imat, (SpiceDouble *)idmat,
                    9,                  (SpiceDouble *)mzero );

         printf( "\n" );
         printf( "Original times inverse minus identity:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%16.7f %15.7f %15.7f\n",
                    mzero[i][0], mzero[i][1], mzero[i][2] );
         }

         return ( 0 );
      }


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


      Original Matrix:
             0.0000000      -1.0000000       0.0000000
             0.5000000       0.0000000       0.0000000
             0.0000000       0.0000000       1.0000000

      Inverse Matrix:
             0.0000000       2.0000000      -0.0000000
            -1.0000000       0.0000000      -0.0000000
             0.0000000      -0.0000000       1.0000000

      Original times inverse minus identity:
             0.0000000       0.0000000       0.0000000
             0.0000000       0.0000000       0.0000000
             0.0000000       0.0000000       0.0000000

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

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

Version

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

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

   -CSPICE Version 1.0.0, 01-JUN-1999 (NJB) (WLT)

Index_Entries

   Get the 3x3 identity matrix