#include "sofa.h"

void iauAb(double pnat[3], double v[3], double s, double bm1,
           double ppr[3])
/*
**  - - - - - -
**   i a u A b
**  - - - - - -
**
**  Apply aberration to transform natural direction into proper
**  direction.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**    pnat    double[3]   natural direction to the source (unit vector)
**    v       double[3]   observer barycentric velocity in units of c
**    s       double      distance between the Sun and the observer (au)
**    bm1     double      sqrt(1-|v|^2): reciprocal of Lorenz factor
**
**  Returned:
**    ppr     double[3]   proper direction to source (unit vector)
**
**  Notes:
**
**  1) The algorithm is based on Expr. (7.40) in the Explanatory
**     Supplement (Urban & Seidelmann 2013), but with the following
**     changes:
**
**     o  Rigorous rather than approximate normalization is applied.
**
**     o  The gravitational potential term from Expr. (7) in
**        Klioner (2003) is added, taking into account only the Sun's
**        contribution.  This has a maximum effect of about
**        0.4 microarcsecond.
**
**  2) In almost all cases, the maximum accuracy will be limited by the
**     supplied velocity.  For example, if the SOFA iauEpv00 function is
**     used, errors of up to 5 microarcseconds could occur.
**
**  References:
**
**     Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
**     the Astronomical Almanac, 3rd ed., University Science Books
**     (2013).
**
**     Klioner, Sergei A., "A practical relativistic model for micro-
**     arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
**
**  Called:
**     iauPdp       scalar product of two p-vectors
**
**  This revision:   2013 October 9
**
**  SOFA release 2020-07-21
**
**  Copyright (C) 2020 IAU SOFA Board.  See notes at end.
*/
{
   int i;
   double pdv, w1, w2, r2, w, p[3], r;


   pdv = iauPdp(pnat, v);
   w1 = 1.0 + pdv/(1.0 + bm1);
   w2 = SRS/s;
   r2 = 0.0;
   for (i = 0; i < 3; i++) {
      w = pnat[i]*bm1 + w1*v[i] + w2*(v[i] - pdv*pnat[i]);
      p[i] = w;
      r2 = r2 + w*w;
   }
   r = sqrt(r2);
   for (i = 0; i < 3; i++) {
      ppr[i] = p[i]/r;
   }

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2020
**  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
**
**--------------------------------------------------------------------*/
}
