Procedure

   mxv_c ( Matrix times vector, 3x3 ) 

   void mxv_c ( ConstSpiceDouble    m   [3][3],
                ConstSpiceDouble    vin [3],
                SpiceDouble         vout[3]    )

Abstract

   Multiply a 3x3 double precision matrix with a 3-dimensional
   double precision vector.

Required_Reading

   None.

Keywords

   MATRIX
   VECTOR

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   m          I   3x3 double precision matrix.
   vin        I   3-dimensional double precision vector.
   vout       O   3-dimensional double precision vector. `vout' is
                  the product m*vin.

Detailed_Input

   m           is an arbitrary 3x3 double precision matrix.

   vin         is an arbitrary 3-dimensional double precision vector.

Detailed_Output

   vout        is a 3-dimensional double precision vector. `vout' is
               the product m * v. `vout' may overwrite `vin'.

Parameters

   None.

Exceptions

   Error free.

Files

   None.

Particulars

   The code reflects precisely the following mathematical expression

      For each value of the subscript `i' from 0 to 2:

                      2
                   .-----
                    \
         vout[i] =   )  m[i][k] * vin[k]
                    /
                   '-----
                     k=0

   The intermediate results of the operation performed by this routine
   are buffered in a temporary vector which is later moved to the output
   vector.  Thus `vout' can be actually be `vin' if desired without
   interfering with the computation.

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 a 3x3 matrix and a 3-vector, multiply the matrix by
      the vector.


      Example code begins here.


      /.
         Program mxv_ex1
      ./
      #include <stdio.h>
      #include "SpiceUsr.h"

      int main( )
      {

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

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

         SpiceDouble          vin    [3] = { 1.0,  2.0,  3.0 };

         /.
         Multiply `m' by `vin'.
         ./
         mxv_c ( m, vin, vout );

         printf( "M times VIN:\n" );
         printf( "%10.3f %9.3f %9.3f\n", vout[0], vout[1], vout[2] );

         return ( 0 );
      }


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


      M times VIN:
           2.000    -1.000     3.000

Restrictions

   1)  The user is responsible for checking the magnitudes of the
       elements of `m' and `vin' so that a floating point overflow does
       not occur.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.1.0, 13-AUG-2021 (JDR)

       Changed input argument name "m1" to "m" for consistency with
       other routines.

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

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

Index_Entries

   matrix times 3-dimensional vector