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

void iauLtecm(double epj, double rm[3][3])
/*
**  - - - - - - - - -
**   i a u L t e c m
**  - - - - - - - - -
**
**  ICRS equatorial to ecliptic rotation matrix, long-term.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     epj     double         Julian epoch (TT)
**
**  Returned:
**     rm      double[3][3]   ICRS to ecliptic rotation matrix
**
**  Notes:
**
**  1) The matrix is in the sense
**
**        E_ep = rm x P_ICRS,
**
**     where P_ICRS is a vector with respect to ICRS right ascension
**     and declination axes and E_ep is the same vector with respect to
**     the (inertial) ecliptic and equinox of epoch epj.
**
**  2) P_ICRS is a free vector, merely a direction, typically of unit
**     magnitude, and not bound to any particular spatial origin, such
**     as the Earth, Sun or SSB.  No assumptions are made about whether
**     it represents starlight and embodies astrometric effects such as
**     parallax or aberration.  The transformation is approximately that
**     between mean J2000.0 right ascension and declination and ecliptic
**     longitude and latitude, with only frame bias (always less than
**     25 mas) to disturb this classical picture.
**
**  3) The Vondrak et al. (2011, 2012) 400 millennia precession model
**     agrees with the IAU 2006 precession at J2000.0 and stays within
**     100 microarcseconds during the 20th and 21st centuries.  It is
**     accurate to a few arcseconds throughout the historical period,
**     worsening to a few tenths of a degree at the end of the
**     +/- 200,000 year time span.
**
**  Called:
**     iauLtpequ    equator pole, long term
**     iauLtpecl    ecliptic pole, long term
**     iauPxp       vector product
**     iauPn        normalize vector
**
**  References:
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
**    expressions, valid for long time intervals, Astron.Astrophys. 534,
**    A22
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
**    expressions, valid for long time intervals (Corrigendum),
**    Astron.Astrophys. 541, C1
**
**  This revision:  2021 May 11
**
**  SOFA release 2023-10-11
**
**  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*/
{
/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
   const double dx = -0.016617 * DAS2R,
                de = -0.0068192 * DAS2R,
                dr = -0.0146 * DAS2R;

   double p[3], z[3], w[3], s, x[3], y[3];


/* Equator pole. */
   iauLtpequ(epj, p);

/* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */
   iauLtpecl(epj, z);

/* Equinox (top row of matrix). */
   iauPxp(p, z, w);
   iauPn(w, &s, x);

/* Middle row of matrix. */
   iauPxp(z, x, y);

/* Combine with frame bias. */
   rm[0][0] =   x[0]    - x[1]*dr + x[2]*dx;
   rm[0][1] =   x[0]*dr + x[1]    + x[2]*de;
   rm[0][2] = - x[0]*dx - x[1]*de + x[2];
   rm[1][0] =   y[0]    - y[1]*dr + y[2]*dx;
   rm[1][1] =   y[0]*dr + y[1]    + y[2]*de;
   rm[1][2] = - y[0]*dx - y[1]*de + y[2];
   rm[2][0] =   z[0]    - z[1]*dr + z[2]*dx;
   rm[2][1] =   z[0]*dr + z[1]    + z[2]*de;
   rm[2][2] = - z[0]*dx - z[1]*de + z[2];

/* 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.
**
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**
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**
**     Note that, as originally distributed, the SOFA software is
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**
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**
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*
**  In any published work or commercial product which uses the SOFA
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**
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**
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**                 HM Nautical Almanac Office
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**
**--------------------------------------------------------------------*/
}
