#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
**
**  SOFA release 2009-12-31
**
**  Copyright (C) 2009 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) 2009
**  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 ("SOFA").
**
**  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 distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     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 itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The name(s) of all routine(s) in your derived work shall not
**        include the prefix "iau_".
**
**     d) 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.
**
**     e) 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.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  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 SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA 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 SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA 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:
**
**      By email:  sofa@rl.ac.uk
**      By post:   IAU SOFA Center
**                 STFC Rutherford Appleton Laboratory
**                 Harwell Science and Innovation Campus
**                 Didcot, Oxfordshire, OX11 0QX
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}