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Index Page mxmt_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

       mxmt_c ( Matrix times matrix transpose, 3x3 )

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

#### Abstract

       Multiply a 3x3 matrix and the transpose of another 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 product `m1' times transpose of `m2'.

#### Detailed_Input

       m1          is an arbitrary 3x3 double precision matrix.

       m2          is an arbitrary 3x3 double precision matrix.
                   Typically, `m2' will be a rotation matrix since
                   then its transpose is its inverse (but this is
                   NOT a requirement).

#### Detailed_Output

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

                                    T
                      mout = m1 x 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[i][k] * m2[j][k]
                           /
                          '-----
                            k=0

       Note that the reversal of the `k' and `j' subscripts in the right-
       hand matrix `m2' is what makes `mout' the product of the TRANSPOSE of
       `m2' and not simply of `m2' 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 double precision matrices, multiply the first
          matrix by the transpose of the second one.

          Example code begins here.

          /.
             Program mxmt_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables.
             ./
             SpiceDouble          m2     [3][3];
             SpiceDouble          mout   [3][3];

             SpiceInt             i;

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

             /.
             Make `m2' equal to `m1'.
             ./
             mequ_c ( m1, m2 );

             /.
             Multiply `m1' by the transpose of `m2'.
             ./
             mxmt_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 transpose of 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:
                 0.0000000       1.0000000       0.0000000
                -1.0000000       0.0000000       0.0000000
                 0.0000000       0.0000000       1.0000000

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

          M1 times transpose of M2:
                 1.0000000       0.0000000       0.0000000
                 0.0000000       1.0000000       0.0000000
                 0.0000000       0.0000000       1.0000000

#### 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 examples based on existing code fragments.

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

#### Index_Entries

       matrix times matrix_transpose 3x3_case

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

    Fri Dec 31 18:41:09 2021