#include "sofa.h"

void iauPb06(double date1, double date2,
             double *bzeta, double *bz, double *btheta)
/*
**  - - - - - - - -
**   i a u P b 0 6
**  - - - - - - - -
**
**  This function forms three Euler angles which implement general
**  precession from epoch J2000.0, using the IAU 2006 model.  Frame
**  bias (the offset between ICRS and mean J2000.0) is included.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards Of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     date1,date2  double   TT as a 2-part Julian Date (Note 1)
**
**  Returned:
**     bzeta        double   1st rotation: radians cw around z
**     bz           double   3rd rotation: radians cw around z
**     btheta       double   2nd rotation: radians ccw around y
**
**  Notes:
**
**  1) The TT date date1+date2 is a Julian Date, apportioned in any
**     convenient way between the two arguments.  For example,
**     JD(TT)=2450123.7 could be expressed in any of these ways,
**     among others:
**
**            date1          date2
**
**         2450123.7           0.0       (JD method)
**         2451545.0       -1421.3       (J2000 method)
**         2400000.5       50123.2       (MJD method)
**         2450123.5           0.2       (date & time method)
**
**     The JD method is the most natural and convenient to use in
**     cases where the loss of several decimal digits of resolution
**     is acceptable.  The J2000 method is best matched to the way
**     the argument is handled internally and will deliver the
**     optimum resolution.  The MJD method and the date & time methods
**     are both good compromises between resolution and convenience.
**
**  2) The traditional accumulated precession angles zeta_A, z_A,
**     theta_A cannot be obtained in the usual way, namely through
**     polynomial expressions, because of the frame bias.  The latter
**     means that two of the angles undergo rapid changes near this
**     date.  They are instead the results of decomposing the
**     precession-bias matrix obtained by using the Fukushima-Williams
**     method, which does not suffer from the problem.  The
**     decomposition returns values which can be used in the
**     conventional formulation and which include frame bias.
**
**  3) The three angles are returned in the conventional order, which
**     is not the same as the order of the corresponding Euler
**     rotations.  The precession-bias matrix is
**     R_3(-z) x R_2(+theta) x R_3(-zeta).
**
**  4) Should zeta_A, z_A, theta_A angles be required that do not
**     contain frame bias, they are available by calling the SOFA
**     function iauP06e.
**
**  Called:
**     iauPmat06    PB matrix, IAU 2006
**     iauRz        rotate around Z-axis
**
**  This revision:  2013 June 18
**
**  SOFA release 2016-05-03
**
**  Copyright (C) 2016 IAU SOFA Board.  See notes at end.
*/
{
   double r[3][3], r31, r32;


/* Precession matrix via Fukushima-Williams angles. */
   iauPmat06(date1, date2, r);

/* Solve for z. */
   *bz = atan2(r[1][2], r[0][2]);

/* Remove it from the matrix. */
   iauRz(*bz, r);

/* Solve for the remaining two angles. */
   *bzeta = atan2 (r[1][0], r[1][1]);
   r31 = r[2][0];
   r32 = r[2][1];
   *btheta = atan2(-dsign(sqrt(r31 * r31 + r32 * r32), r[0][2]),
                   r[2][2]);

   return;

/*----------------------------------------------------------------------
**
**  Copyright (C) 2016
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA 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 names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     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. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. 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.
**
**  6. 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.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  sofa@ukho.gov.uk
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}