#include "sofa.h"
#include "sofam.h"

void iauHfk5z(double rh, double dh, double date1, double date2,
              double *r5, double *d5, double *dr5, double *dd5)
/*
**  - - - - - - - - -
**   i a u H f k 5 z
**  - - - - - - - - -
**
**  Transform a Hipparcos star position into FK5 J2000.0, assuming
**  zero Hipparcos proper motion.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     rh            double    Hipparcos RA (radians)
**     dh            double    Hipparcos Dec (radians)
**     date1,date2   double    TDB date (Note 1)
**
**  Returned (all FK5, equinox J2000.0, date date1+date2):
**     r5            double    RA (radians)
**     d5            double    Dec (radians)
**     dr5           double    RA proper motion (rad/year, Note 4)
**     dd5           double    Dec proper motion (rad/year, Note 4)
**
**  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 proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
**  3) The FK5 to Hipparcos transformation is modeled as a pure rotation
**     and spin;  zonal errors in the FK5 catalog are not taken into
**     account.
**
**  4) It was the intention that Hipparcos should be a close
**     approximation to an inertial frame, so that distant objects have
**     zero proper motion;  such objects have (in general) non-zero
**     proper motion in FK5, and this function returns those fictitious
**     proper motions.
**
**  5) The position returned by this function is in the FK5 J2000.0
**     reference system but at date date1+date2.
**
**  6) See also iauFk52h, iauH2fk5, iauFk5hz.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauFk5hip    FK5 to Hipparcos rotation and spin
**     iauRxp       product of r-matrix and p-vector
**     iauSxp       multiply p-vector by scalar
**     iauRxr       product of two r-matrices
**     iauTrxp      product of transpose of r-matrix and p-vector
**     iauPxp       vector product of two p-vectors
**     iauPv2s      pv-vector to spherical
**     iauAnp       normalize angle into range 0 to 2pi
**
**  Reference:
**
**     F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
**  This revision:  2023 March 7
**
**  SOFA release 2023-10-11
**
**  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*/
{
   double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3],
   rst[3][3], r5ht[3][3], pv5e[2][3], vv[3],
   w, r, v;


/* Time interval from fundamental epoch J2000.0 to given date (JY). */
   t = ((date1 - DJ00) + date2) / DJY;

/* Hipparcos barycentric position vector (normalized). */
   iauS2c(rh, dh, ph);

/* FK5 to Hipparcos orientation matrix and spin vector. */
   iauFk5hip(r5h, s5h);

/* Rotate the spin into the Hipparcos system. */
   iauRxp(r5h, s5h, sh);

/* Accumulated Hipparcos wrt FK5 spin over that interval. */
   iauSxp(t, s5h, vst);

/* Express the accumulated spin as a rotation matrix. */
   iauRv2m(vst, rst);

/* Rotation matrix:  accumulated spin, then FK5 to Hipparcos. */
   iauRxr(r5h, rst, r5ht);

/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
   iauTrxp(r5ht, ph, pv5e[0]);

/* Apply spin to the position giving a space motion. */
   iauPxp(sh, ph, vv);

/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
   iauTrxp(r5ht, vv, pv5e[1]);

/* FK5 position/velocity pv-vector to spherical. */
   iauPv2s(pv5e, &w, d5, &r, dr5, dd5, &v);
   *r5 = iauAnp(w);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2023
**  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
**
**--------------------------------------------------------------------*/
}
