#include "sofam.h"
 
void iauRm2v(double r[3][3], double w[3])
/*
**  - - - - - - - -
**   i a u R m 2 v
**  - - - - - - - -
**
**  Express an r-matrix as an r-vector.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards Of Fundamental Astronomy) software collection.
**
**  Status:  vector/matrix support function.
**
**  Given:
**     r        double[3][3]    rotation matrix
**
**  Returned:
**     w        double[3]       rotation vector (Note 1)
**
**  Notes:
**
**  1) A rotation matrix describes a rotation through some angle about
**     some arbitrary axis called the Euler axis.  The "rotation vector"
**     returned by this function has the same direction as the Euler axis,
**     and its magnitude is the angle in radians.  (The magnitude and
**     direction can be separated by means of the function iauPn.)
**
**  2) If r is null, so is the result.  If r is not a rotation matrix
**     the result is undefined;  r must be proper (i.e. have a positive
**     determinant) and real orthogonal (inverse = transpose).
**
**  3) The reference frame rotates clockwise as seen looking along
**     the rotation vector from the origin.
**
**  This revision:  2008 May 12
**
**  Copyright (C) 2008 IAU SOFA Review Board.  See notes at end.
*/
{
   double x, y, z, s2, c2, phi, f;


   x = r[1][2] - r[2][1];
   y = r[2][0] - r[0][2];
   z = r[0][1] - r[1][0];
   s2 = sqrt(x*x + y*y + z*z);
   if (s2 != 0) {
      c2 = r[0][0] + r[1][1] + r[2][2] - 1;
      phi = atan2(s2, c2);
      f =  phi / s2;
      w[0] = x * f;
      w[1] = y * f;
      w[2] = z * f;
   } else {
      w[0] = 0.0;
      w[1] = 0.0;
      w[2] = 0.0;
   }
 
   return;

/*-----------------------------------------------------------------------
**
**  Copyright (C) 2008
**  Standards Of Fundamental Astronomy Review Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
**  WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Review Board ("the Board").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and 
**     restrictions listed below.
**
**  3. You (the user) may copy and adapt the SOFA software and its 
**     algorithms for your own purposes and you may copy and distribute
**     a resulting "derived work" to others on a world-wide, royalty-free 
**     basis, provided that the derived work complies with the following
**     requirements: 
**
**     a) Your work shall be marked or carry a statement that it (i) uses
**        routines and computations derived by you from software provided 
**        by SOFA under license to you; and (ii) does not contain
**        software provided by SOFA or software that has been distributed
**        by or endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon and/or differs from the
**        original SOFA software.
**
**     c) The name(s) of all routine(s) that you distribute shall differ
**        from the SOFA names, even when the SOFA content has not been
**        otherwise changed.
**
**     d) The routine-naming prefix "iau" shall not be used.
**
**     e) The origin of the SOFA components of your derived work must not
**        be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     f) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have granted 
**        a further right to modify the source code of your derived work.
**
**  4. In any published work or commercial products which includes
**     results achieved by using the SOFA software, you shall acknowledge
**     that the SOFA software was used in obtaining those results.
**
**  5. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or by
**     inappropriate modification.
**
**  6. The SOFA software is provided "as is" and the Board makes no 
**     warranty as to its use or performance.   The Board does not and 
**     cannot warrant the performance or results which the user may obtain 
**     by using the SOFA software.  The Board makes no warranties, express 
**     or implied, as to non-infringement of third party rights,
**     merchantability, or fitness for any particular purpose.  In no
**     event will the Board be liable to the user for any consequential,
**     incidental, or special damages, including any lost profits or lost
**     savings, even if a Board representative has been advised of such
**     damages, or for any claim by any third party.
**
**  7. The provision of any version of the SOFA software under the terms 
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**     Internet email: sofa@rl.ac.uk
**     Postal address: IAU SOFA Center
**                     Rutherford Appleton Laboratory
**                     Chilton, Didcot, Oxon OX11 0QX
**                     United Kingdom
**
**---------------------------------------------------------------------*/
}