#include "erfa.h"

void eraRm2v(double r[3][3], double w[3])
/*
**  - - - - - - - -
**   e r a R m 2 v
**  - - - - - - - -
**
**  Express an r-matrix as an r-vector.
**
**  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 eraPn.)
**
**  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.
**
**  Copyright (C) 2013-2020, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   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] - 1.0;
      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) 2013-2020, NumFOCUS Foundation.
**  All rights reserved.
**  
**  This library is derived, with permission, from the International
**  Astronomical Union's "Standards of Fundamental Astronomy" library,
**  available from http://www.iausofa.org.
**  
**  The ERFA version is intended to retain identical functionality to
**  the SOFA library, but made distinct through different function and
**  file names, as set out in the SOFA license conditions.  The SOFA
**  original has a role as a reference standard for the IAU and IERS,
**  and consequently redistribution is permitted only in its unaltered
**  state.  The ERFA version is not subject to this restriction and
**  therefore can be included in distributions which do not support the
**  concept of "read only" software.
**  
**  Although the intent is to replicate the SOFA API (other than
**  replacement of prefix names) and results (with the exception of
**  bugs;  any that are discovered will be fixed), SOFA is not
**  responsible for any errors found in this version of the library.
**  
**  If you wish to acknowledge the SOFA heritage, please acknowledge
**  that you are using a library derived from SOFA, rather than SOFA
**  itself.
**  
**  
**  TERMS AND CONDITIONS
**  
**  Redistribution and use in source and binary forms, with or without
**  modification, are permitted provided that the following conditions
**  are met:
**  
**  1 Redistributions of source code must retain the above copyright
**    notice, this list of conditions and the following disclaimer.
**  
**  2 Redistributions in binary form must reproduce the above copyright
**    notice, this list of conditions and the following disclaimer in
**    the documentation and/or other materials provided with the
**    distribution.
**  
**  3 Neither the name of the Standards Of Fundamental Astronomy Board,
**    the International Astronomical Union nor the names of its
**    contributors may be used to endorse or promote products derived
**    from this software without specific prior written permission.
**  
**  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
**  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
**  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
**  FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
**  COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
**  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
**  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
**  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
**  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
**  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
**  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
**  POSSIBILITY OF SUCH DAMAGE.
**  
*/
