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#include "sofa.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: 2015 December 6
**
** SOFA release 2020-07-21
**
** Copyright (C) 2020 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];
/*----------------------------------------------------------------------
**
** 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
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** United Kingdom
**
**--------------------------------------------------------------------*/
}