Procedure

   mtxm_c ( Matrix transpose times matrix, 3x3 ) 

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

Abstract

   Multiply the transpose of a 3x3 matrix and a 3x3 matrix.

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 produce m1 transpose times m2.

Detailed_Input

   m1          is any 3x3 double precision matrix. Typically,
               m1 will be a rotation matrix since then its
               transpose is its inverse (but this is not a
               requirement).

   m2          is any 3x3 double precision matrix.

Detailed_Output

   mout        is a 3x3 double precision matrix. mout is the
               product

                           t
                  mout = m1  m2

               mout may overwrite either m1 or 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[k][i] * m2[k][j]
                    k=0

   Note that the reversal of the `k' and `i' subscripts in the left-hand
   matrix `m1' is what makes `mout' the product of the TRANSPOSE of `m1'
   and not simply of `m1' itself. Also, the intermediate results of
   the operation above are buffered in a temporary matrix which is
   later moved to the output matrix. Thus `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 matrices, multiply the transpose of the first
      matrix by the second one.


      Example code begins here.


      /.
         Program mtxm_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,  2.0,  3.0},
                                                {4.0,  5.0,  6.0},
                                                {7.0,  8.0,  9.0} };

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

         /.
         Multiply the transpose of `m1' by `m2'.
         ./
         mtxm_c ( m1, m2, mout );

         printf( "Transpose of M1 times M2:\n" );
         for ( i = 0; i < 3; i++ )
         {

            printf( "%10.3f %9.3f %9.3f\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:


      Transpose of M1 times M2:
          -3.000     5.000     7.000
          -3.000     7.000     8.000
          -3.000     9.000     9.000

Restrictions

   1)  The user is responsible for checking the magnitudes of the
       elements of `m1' and `m2' so that a floating point overflow does
       not occur. (In the typical use where `m1' and `m2' are rotation
       matrices, this not a risk at all.)

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.0.1, 04-JUL-2021 (JDR)

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

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

Index_Entries

   matrix_transpose times matrix 3x3_case

Link to routine mtxm_c source file mtxm_c.c