Procedure

   mxm_c ( Matrix times matrix, 3x3 ) 

   void mxm_c ( ConstSpiceDouble   m1  [3][3],
                ConstSpiceDouble   m2  [3][3],
                SpiceDouble        mout[3][3] )

Abstract

   Multiply two 3x3 matrices.

Required_Reading

   None.

Keywords

   MATRIX

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   m1         I   3x3 double precision matrix.
   m2         I   3x3 double precision matrix.
   mout       O   The 3x3 double precision matrix product m1*m2.

Detailed_Input

   m1          is an arbitrary 3x3 double precision matrix.

   m2          is an arbitrary 3x3 double precision matrix.

Detailed_Output

   mout        is a 3x3 double precision matrix. `mout' is the product
               m1*m2.

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

      For each value of the subscripts `i' and `j' from 0 to 2:

                         2
                      .-----
                       \
         mout[i][j] =   )  m1[i][k] * m2[k][j]
                       /
                      '-----
                        k=0

   The intermediate results of the operation above are buffered in a
   temporary matrix which is later moved to the output matrix.
   Thus, to save space in the calling program, `mout' can be actually
   be `m1' or `m2' if desired without interfering with the computations.

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 two 3x3 double precision matrices, compute their
      product.


      Example code begins here.


      /.
         Program mxm_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

         /.
         Local variables.
         ./
         SpiceDouble          mout   [3][3];

         SpiceInt             i;

         /.
         Define `m1' and `m2'.
         ./
         SpiceDouble          m1     [3][3] = { { 1.0,  1.0,  0.0},
                                                {-1.0,  1.0,  0.0},
                                                { 0.0,  0.0,  1.0} };

         SpiceDouble          m2     [3][3] = { { 1.0,  0.0,  0.0},
                                                { 0.0,  1.0,  1.0},
                                                { 0.0, -1.0,  1.0} };

         /.
         Compute `m1' times `m2'.
         ./
         mxm_c ( m1, m2, mout );

         printf( "M1:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%16.7f %15.7f %15.7f\n", m1[i][0], m1[i][1], m1[i][2] );
         }

         printf( "\n" );
         printf( "M2:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%16.7f %15.7f %15.7f\n", m2[i][0], m2[i][1], m2[i][2] );
         }

         printf( "\n" );
         printf( "M1 times M2:\n" );
         for ( i = 0; i < 3; i++ )
         {
            printf( "%16.7f %15.7f %15.7f\n",
                    mout[i][0], mout[i][1], mout[i][2] );
         }

         return ( 0 );
      }


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


      M1:
             1.0000000       1.0000000       0.0000000
            -1.0000000       1.0000000       0.0000000
             0.0000000       0.0000000       1.0000000

      M2:
             1.0000000       0.0000000       0.0000000
             0.0000000       1.0000000       1.0000000
             0.0000000      -1.0000000       1.0000000

      M1 times M2:
             1.0000000       1.0000000       1.0000000
            -1.0000000       1.0000000       1.0000000
             0.0000000      -1.0000000       1.0000000

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.0.1, 05-JUN-2020 (JDR)

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

   -CSPICE Version 1.0.0, 16-APR-1999 (EDW)

Index_Entries

   matrix times matrix 3x3_case