#include "erfa.h"
void eraAticqn(double ri, double di, eraASTROM *astrom,
int n, eraLDBODY b[], double *rc, double *dc)
/*
** - - - - - - - - -
** e r a A t i c q n
** - - - - - - - - -
**
** Quick CIRS to ICRS astrometric place transformation, given the star-
** independent astrometry parameters plus a list of light-deflecting
** bodies.
**
** Use of this function is appropriate when efficiency is important and
** where many star positions are all to be transformed for one date.
** The star-independent astrometry parameters can be obtained by
** calling one of the functions eraApci[13], eraApcg[13], eraApco[13]
** or eraApcs[13].
*
* If the only light-deflecting body to be taken into account is the
* Sun, the eraAticq function can be used instead.
**
** Given:
** ri,di double CIRS RA,Dec (radians)
** astrom eraASTROM* star-independent astrometry parameters:
** pmt double PM time interval (SSB, Julian years)
** eb double[3] SSB to observer (vector, au)
** eh double[3] Sun to observer (unit vector)
** em double distance from Sun to observer (au)
** v double[3] barycentric observer velocity (vector, c)
** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
** bpn double[3][3] bias-precession-nutation matrix
** along double longitude + s' (radians)
** xpl double polar motion xp wrt local meridian (radians)
** ypl double polar motion yp wrt local meridian (radians)
** sphi double sine of geodetic latitude
** cphi double cosine of geodetic latitude
** diurab double magnitude of diurnal aberration vector
** eral double "local" Earth rotation angle (radians)
** refa double refraction constant A (radians)
** refb double refraction constant B (radians)
** n int number of bodies (Note 3)
** b eraLDBODY[n] data for each of the n bodies (Notes 3,4):
** bm double mass of the body (solar masses, Note 5)
** dl double deflection limiter (Note 6)
** pv [2][3] barycentric PV of the body (au, au/day)
**
** Returned:
** rc,dc double ICRS astrometric RA,Dec (radians)
**
** Notes:
**
** 1) Iterative techniques are used for the aberration and light
** deflection corrections so that the functions eraAticqn and
** eraAtciqn are accurate inverses; even at the edge of the Sun's
** disk the discrepancy is only about 1 nanoarcsecond.
**
** 2) If the only light-deflecting body to be taken into account is the
** Sun, the eraAticq function can be used instead.
**
** 3) The struct b contains n entries, one for each body to be
** considered. If n = 0, no gravitational light deflection will be
** applied, not even for the Sun.
**
** 4) The struct b should include an entry for the Sun as well as for
** any planet or other body to be taken into account. The entries
** should be in the order in which the light passes the body.
**
** 5) In the entry in the b struct for body i, the mass parameter
** b[i].bm can, as required, be adjusted in order to allow for such
** effects as quadrupole field.
**
** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is
** the angular separation (in radians) between star and body at
** which limiting is applied. As phi shrinks below the chosen
** threshold, the deflection is artificially reduced, reaching zero
** for phi = 0. Example values suitable for a terrestrial
** observer, together with masses, are as follows:
**
** body i b[i].bm b[i].dl
**
** Sun 1.0 6e-6
** Jupiter 0.00095435 3e-9
** Saturn 0.00028574 3e-10
**
** 7) For efficiency, validation of the contents of the b array is
** omitted. The supplied masses must be greater than zero, the
** position and velocity vectors must be right, and the deflection
** limiter greater than zero.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraTrxp product of transpose of r-matrix and p-vector
** eraZp zero p-vector
** eraAb stellar aberration
** eraLdn light deflection by n bodies
** eraC2s p-vector to spherical
** eraAnp normalize angle into range +/- pi
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j, i;
double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
after[3];
/* CIRS RA,Dec to Cartesian. */
eraS2c(ri, di, pi);
/* Bias-precession-nutation, giving GCRS proper direction. */
eraTrxp(astrom->bpn, pi, ppr);
/* Aberration, giving GCRS natural direction. */
eraZp(d);
for (j = 0; j < 2; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = ppr[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraAb(before, astrom->v, astrom->em, astrom->bm1, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = ppr[i] - d[i];
pnat[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pnat[i] /= r;
}
}
/* Light deflection, giving BCRS coordinate direction. */
eraZp(d);
for (j = 0; j < 5; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = pnat[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraLdn(n, b, astrom->eb, before, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = pnat[i] - d[i];
pco[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pco[i] /= r;
}
}
/* ICRS astrometric RA,Dec. */
eraC2s(pco, &w, dc);
*rc = eraAnp(w);
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
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** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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**
*/