Index of Functions: A B C D E F G H I J K L M N O P Q R S T U V W X
Index Page mtxm_c

Table of contents

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

       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

    Fri Dec 31 18:41:09 2021