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 mtxv_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

       mtxv_c ( Matrix transpose times vector, 3x3 )

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

#### Abstract

       Multiply the transpose of a 3x3 matrix on the left with a vector
       on the right.

#### 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**t * vin.

#### Detailed_Input

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

       vin         is an arbitrary 3-dimensional double precision
                   vector.

#### Detailed_Output

       vout        is a 3-dimensional double precision vector. `vout' is
                   the product vout = (m**t)  x (vin). `vout' can
                   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[k][i] * vin[k]
                        /
                       '-----
                         k=0

       Note that the reversal of the `k' and `i' subscripts in the left-hand
       matrix `m' is what makes `vout' the product of the TRANSPOSE of
       and not simply of `m' itself.

#### 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 transpose of
          the matrix by the vector.

          Example code begins here.

          /.
             Program mtxv_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

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

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

             SpiceDouble          vin    [3] = { 5.0,  10.0,  15.0 };

             /.
             Multiply the transpose of `m' by `vin'.
             ./
             mtxv_c ( m, vin, vout );

             printf( "Transpose of 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:

          Transpose of M times VIN:
              -5.000    15.000    15.000

          Note that typically the matrix `m' will be a rotation matrix.
          Because the transpose of an orthogonal matrix is equivalent to
          its inverse, applying the rotation to the vector is
          accomplished by multiplying the vector by the transpose of the
          matrix.

          Let

                 -1
                m   * vin = vout

          If `m' is an orthogonal matrix, then (m**T) * vin = vout.

#### 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)
       W.M. Owen           (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.1.0, 25-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.

       -CSPICE Version 1.0.1, 10-NOV-2006 (EDW)

           Added -Parameters section header.

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

#### Index_Entries

       matrix_transpose times 3-dimensional vector

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

    Fri Dec 31 18:41:09 2021