void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3],
double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t c i o
** - - - - - - - - - -
**
** Assemble the celestial to terrestrial matrix from CIO-based
** components (the celestial-to-intermediate matrix, the Earth Rotation
** Angle and the polar motion matrix).
**
** Status: support function.
**
** Given:
** rc2i double[3][3] celestial-to-intermediate matrix
** era double Earth rotation angle
** rpom double[3][3] polar-motion matrix
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix
**
** Notes:
**
** 1) This function constructs the rotation matrix that transforms
** vectors in the celestial system into vectors in the terrestrial
** system. It does so starting from precomputed components, namely
** the matrix which rotates from celestial coordinates to the
** intermediate frame, the Earth rotation angle and the polar motion
** matrix. One use of the present function is when generating a
** series of celestial-to-terrestrial matrices where only the Earth
** Rotation Angle changes, avoiding the considerable overhead of
** recomputing the precession-nutation more often than necessary to
** achieve given accuracy objectives.
**
** 2) The relationship between the arguments is as follows:
**
** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003).
**
** Called:
** iauCr copy r-matrix
** iauRz rotate around Z-axis
** iauRxr product of two r-matrices
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** This revision: 2008 May 11
**
** Original version 2012-03-01
**
** Copyright (C) 2013 Naoki Arita. See notes at end.
*/
{
double r[3][3];
/* Construct the matrix. */
iauCr(rc2i, r);
iauRz(era, r);
iauRxr(rpom, r, rc2t);
return;
/*----------------------------------------------------------------------
**
** Celes is a wrapper of the SOFA Library for Ruby.
**
** This file is redistributed and relicensed in accordance with
** the SOFA Software License (http://www.iausofa.org/tandc.html).
**
** The original library is available from IAU Standards of
** Fundamental Astronomy (http://www.iausofa.org/).
**
**
**
**
**
** Copyright (C) 2013, Naoki Arita
** All rights reserved.
**
** 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.
**
** 2 Redistributions in binary form must reproduce the above copyright
** 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
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
**--------------------------------------------------------------------*/
}
void iauPmat76(double date1, double date2, double rmatp[3][3])
/*
** - - - - - - - - - -
** i a u P m a t 7 6
** - - - - - - - - - -
**
** Precession matrix from J2000.0 to a specified date, IAU 1976 model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double ending date, TT (Note 1)
**
** Returned:
** rmatp double[3][3] precession matrix, J2000.0 -> date1+date2
**
** 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 matrix operates in the sense V(date) = RMATP * V(J2000),
** where the p-vector V(J2000) is with respect to the mean
** equatorial triad of epoch J2000.0 and the p-vector V(date)
** is with respect to the mean equatorial triad of the given
** date.
**
** 3) Though the matrix method itself is rigorous, the precession
** angles are expressed through canonical polynomials which are
** valid only for a limited time span. In addition, the IAU 1976
** precession rate is known to be imperfect. The absolute accuracy
** of the present formulation is better than 0.1 arcsec from
** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
** and remains below 3 arcsec for the whole of the period
** 500BC to 3000AD. The errors exceed 10 arcsec outside the
** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
**
** Called:
** iauPrec76 accumulated precession angles, IAU 1976
** iauIr initialize r-matrix to identity
** iauRz rotate around Z-axis
** iauRy rotate around Y-axis
** iauCr copy r-matrix
**
** References:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
** equations (6) & (7), p283.
**
** Kaplan,G.H., 1981. USNO circular no. 163, pA2.
**
** This revision: 2013 June 18
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double zeta, z, theta, wmat[3][3];
/* Precession Euler angles, J2000.0 to specified date. */
iauPrec76(DJ00, 0.0, date1, date2, &zeta, &z, &theta);
/* Form the rotation matrix. */
iauIr( wmat);
iauRz( -zeta, wmat);
iauRy( theta, wmat);
iauRz( -z, wmat);
iauCr( wmat, rmatp);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauPn00(double date1, double date2, double dpsi, double deps,
double *epsa,
double rb[3][3], double rp[3][3], double rbp[3][3],
double rn[3][3], double rbpn[3][3])
/*
** - - - - - - - -
** i a u P n 0 0
** - - - - - - - -
**
** Precession-nutation, IAU 2000 model: a multi-purpose function,
** supporting classical (equinox-based) use directly and CIO-based
** use indirectly.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** dpsi,deps double nutation (Note 2)
**
** Returned:
** epsa double mean obliquity (Note 3)
** rb double[3][3] frame bias matrix (Note 4)
** rp double[3][3] precession matrix (Note 5)
** rbp double[3][3] bias-precession matrix (Note 6)
** rn double[3][3] nutation matrix (Note 7)
** rbpn double[3][3] GCRS-to-true matrix (Note 8)
**
** 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 caller is responsible for providing the nutation components;
** they are in longitude and obliquity, in radians and are with
** respect to the equinox and ecliptic of date. For high-accuracy
** applications, free core nutation should be included as well as
** any other relevant corrections to the position of the CIP.
**
** 3) The returned mean obliquity is consistent with the IAU 2000
** precession-nutation models.
**
** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean
** equator and equinox by applying frame bias.
**
** 5) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 6) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 7) The matrix rn transforms vectors from mean equator and equinox of
** date to true equator and equinox of date by applying the nutation
** (luni-solar + planetary).
**
** 8) The matrix rbpn transforms vectors from GCRS to true equator and
** equinox of date. It is the product rn x rbp, applying frame
** bias, precession and nutation in that order.
**
** 9) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauPr00 IAU 2000 precession adjustments
** iauObl80 mean obliquity, IAU 1980
** iauBp00 frame bias and precession matrices, IAU 2000
** iauCr copy r-matrix
** iauNumat form nutation matrix
** iauRxr product of two r-matrices
**
** Reference:
**
** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** This revision: 2013 June 18
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
double dpsipr, depspr, rbpw[3][3], rnw[3][3];
/* IAU 2000 precession-rate adjustments. */
iauPr00(date1, date2, &dpsipr, &depspr);
/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
*epsa = iauObl80(date1, date2) + depspr;
/* Frame bias and precession matrices and their product. */
iauBp00(date1, date2, rb, rp, rbpw);
iauCr(rbpw, rbp);
/* Nutation matrix. */
iauNumat(*epsa, dpsi, deps, rnw);
iauCr(rnw, rn);
/* Bias-precession-nutation matrix (classical). */
iauRxr(rnw, rbpw, rbpn);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauTr(double r[3][3], double rt[3][3])
/*
** - - - - - -
** i a u T r
** - - - - - -
**
** Transpose an r-matrix.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: vector/matrix support function.
**
** Given:
** r double[3][3] r-matrix
**
** Returned:
** rt double[3][3] transpose
**
** Note:
** It is permissible for r and rt to be the same array.
**
** Called:
** iauCr copy r-matrix
**
** This revision: 2013 June 18
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
double wm[3][3];
int i, j;
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
wm[i][j] = r[j][i];
}
}
iauCr(wm, rt);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauApco(double date1, double date2,
double ebpv[2][3], double ehp[3],
double x, double y, double s, double theta,
double elong, double phi, double hm,
double xp, double yp, double sp,
double refa, double refb,
iauASTROM *astrom)
/*
** - - - - - - - -
** i a u A p c o
** - - - - - - - -
**
** For a terrestrial observer, prepare star-independent astrometry
** parameters for transformations between ICRS and observed
** coordinates. The caller supplies the Earth ephemeris, the Earth
** rotation information and the refraction constants as well as the
** site coordinates.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1 double TDB as a 2-part...
** date2 double ...Julian Date (Note 1)
** ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2)
** ehp double[3] Earth heliocentric P (au, Note 2)
** x,y double CIP X,Y (components of unit vector)
** s double the CIO locator s (radians)
** theta double Earth rotation angle (radians)
** elong double longitude (radians, east +ve, Note 3)
** phi double latitude (geodetic, radians, Note 3)
** hm double height above ellipsoid (m, geodetic, Note 3)
** xp,yp double polar motion coordinates (radians, Note 4)
** sp double the TIO locator s' (radians, Note 4)
** refa double refraction constant A (radians, Note 5)
** refb double refraction constant B (radians, Note 5)
**
** Returned:
** astrom iauASTROM* 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)
**
** Notes:
**
** 1) The TDB date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TDB)=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. For most
** applications of this function the choice will not be at all
** critical.
**
** TT can be used instead of TDB without any significant impact on
** accuracy.
**
** 2) The vectors eb, eh, and all the astrom vectors, are with respect
** to BCRS axes.
**
** 3) The geographical coordinates are with respect to the WGS84
** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN
** CONVENTION: the longitude required by the present function is
** right-handed, i.e. east-positive, in accordance with geographical
** convention.
**
** 4) xp and yp are the coordinates (in radians) of the Celestial
** Intermediate Pole with respect to the International Terrestrial
** Reference System (see IERS Conventions), measured along the
** meridians 0 and 90 deg west respectively. sp is the TIO locator
** s', in radians, which positions the Terrestrial Intermediate
** Origin on the equator. For many applications, xp, yp and
** (especially) sp can be set to zero.
**
** Internally, the polar motion is stored in a form rotated onto the
** local meridian.
**
** 5) The refraction constants refa and refb are for use in a
** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
** (i.e. refracted) zenith distance and dZ is the amount of
** refraction.
**
** 6) It is advisable to take great care with units, as even unlikely
** values of the input parameters are accepted and processed in
** accordance with the models used.
**
** 7) In cases where the caller does not wish to provide the Earth
** Ephemeris, the Earth rotation information and refraction
** constants, the function iauApco13 can be used instead of the
** present function. This starts from UTC and weather readings etc.
** and computes suitable values using other SOFA functions.
**
** 8) This is one of several functions that inserts into the astrom
** structure star-independent parameters needed for the chain of
** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.
**
** The various functions support different classes of observer and
** portions of the transformation chain:
**
** functions observer transformation
**
** iauApcg iauApcg13 geocentric ICRS <-> GCRS
** iauApci iauApci13 terrestrial ICRS <-> CIRS
** iauApco iauApco13 terrestrial ICRS <-> observed
** iauApcs iauApcs13 space ICRS <-> GCRS
** iauAper iauAper13 terrestrial update Earth rotation
** iauApio iauApio13 terrestrial CIRS <-> observed
**
** Those with names ending in "13" use contemporary SOFA models to
** compute the various ephemerides. The others accept ephemerides
** supplied by the caller.
**
** The transformation from ICRS to GCRS covers space motion,
** parallax, light deflection, and aberration. From GCRS to CIRS
** comprises frame bias and precession-nutation. From CIRS to
** observed takes account of Earth rotation, polar motion, diurnal
** aberration and parallax (unless subsumed into the ICRS <-> GCRS
** transformation), and atmospheric refraction.
**
** 9) The context structure astrom produced by this function is used by
** iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.
**
** Called:
** iauAper astrometry parameters: update ERA
** iauC2ixys celestial-to-intermediate matrix, given X,Y and s
** iauPvtob position/velocity of terrestrial station
** iauTrxpv product of transpose of r-matrix and pv-vector
** iauApcs astrometry parameters, ICRS-GCRS, space observer
** iauCr copy r-matrix
**
** This revision: 2013 October 9
**
** SOFA release 2013-12-02
**
** Copyright (C) 2013 IAU SOFA Board. See notes at end.
*/
{
double sl, cl, r[3][3], pvc[2][3], pv[2][3];
/* Longitude with adjustment for TIO locator s'. */
astrom->along = elong + sp;
/* Polar motion, rotated onto the local meridian. */
sl = sin(astrom->along);
cl = cos(astrom->along);
astrom->xpl = xp*cl - yp*sl;
astrom->ypl = xp*sl + yp*cl;
/* Functions of latitude. */
astrom->sphi = sin(phi);
astrom->cphi = cos(phi);
/* Refraction constants. */
astrom->refa = refa;
astrom->refb = refb;
/* Local Earth rotation angle. */
iauAper(theta, astrom);
/* Disable the (redundant) diurnal aberration step. */
astrom->diurab = 0.0;
/* CIO based BPN matrix. */
iauC2ixys(x, y, s, r);
/* Observer's geocentric position and velocity (m, m/s, CIRS). */
iauPvtob(elong, phi, hm, xp, yp, sp, theta, pvc);
/* Rotate into GCRS. */
iauTrxpv(r, pvc, pv);
/* ICRS <-> GCRS parameters. */
iauApcs(date1, date2, pv, ebpv, ehp, astrom);
/* Store the CIO based BPN matrix. */
iauCr(r, astrom->bpn );
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2013
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauBp06(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** i a u B p 0 6
** - - - - - - - -
**
** Frame bias and precession, IAU 2006.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (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 matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from mean J2000.0 to mean of
** date by applying precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean of date by
** applying frame bias then precession. It is the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauPfw06 bias-precession F-W angles, IAU 2006
** iauFw2m F-W angles to r-matrix
** iauPmat06 PB matrix, IAU 2006
** iauTr transpose r-matrix
** iauRxr product of two r-matrices
** iauCr copy r-matrix
**
** References:
**
** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
** This revision: 2013 August 21
**
** SOFA release 2013-12-02
**
** Copyright (C) 2013 IAU SOFA Board. See notes at end.
*/
{
double gamb, phib, psib, epsa, rbpw[3][3], rbt[3][3];
/* B matrix. */
iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &epsa);
iauFw2m(gamb, phib, psib, epsa, rb);
/* PxB matrix (temporary). */
iauPmat06(date1, date2, rbpw);
/* P matrix. */
iauTr(rb, rbt);
iauRxr(rbpw, rbt, rp);
/* PxB matrix. */
iauCr(rbpw, rbp);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2013
** 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: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** i a u B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (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 matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauBi00 frame bias components, IAU 2000
** iauPr00 IAU 2000 precession adjustments
** iauIr initialize r-matrix to identity
** iauRx rotate around X-axis
** iauRy rotate around Y-axis
** iauRz rotate around Z-axis
** iauCr copy r-matrix
** iauRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** This revision: 2010 January 18
**
** Original version 2012-03-01
**
** Copyright (C) 2013 Naoki Arita. See notes at end.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
const double EPS0 = 84381.448 * DAS2R;
double t, dpsibi, depsbi;
double dra0, psia77, oma77, chia, dpsipr, depspr, psia, oma,
rbw[3][3];
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* Frame bias. */
iauBi00(&dpsibi, &depsbi, &dra0);
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * DAS2R;
oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * DAS2R;
chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * DAS2R;
/* Apply IAU 2000 precession corrections. */
iauPr00(date1, date2, &dpsipr, &depspr);
psia = psia77 + dpsipr;
oma = oma77 + depspr;
/* Frame bias matrix: GCRS to J2000.0. */
iauIr(rbw);
iauRz(dra0, rbw);
iauRy(dpsibi * sin(EPS0), rbw);
iauRx(-depsbi, rbw);
iauCr(rbw, rb);
/* Precession matrix: J2000.0 to mean of date. */
iauIr(rp);
iauRx(EPS0, rp);
iauRz(-psia, rp);
iauRx(-oma, rp);
iauRz(chia, rp);
/* Bias-precession matrix: GCRS to mean of date. */
iauRxr(rp, rbw, rbp);
return;
/*----------------------------------------------------------------------
**
** Celes is a wrapper of the SOFA Library for Ruby.
**
** This file is redistributed and relicensed in accordance with
** the SOFA Software License (http://www.iausofa.org/tandc.html).
**
** The original library is available from IAU Standards of
** Fundamental Astronomy (http://www.iausofa.org/).
**
**
**
**
**
** Copyright (C) 2013, Naoki Arita
** All rights reserved.
**
** 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.
**
** 2 Redistributions in binary form must reproduce the above copyright
** 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
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
**--------------------------------------------------------------------*/
}
void iauBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** i a u B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: canonical model.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (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 matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** iauBi00 frame bias components, IAU 2000
** iauPr00 IAU 2000 precession adjustments
** iauIr initialize r-matrix to identity
** iauRx rotate around X-axis
** iauRy rotate around Y-axis
** iauRz rotate around Z-axis
** iauCr copy r-matrix
** iauRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** This revision: 2010 January 18
**
** SOFA release 2010-12-01
**
** Copyright (C) 2010 IAU SOFA Board. See notes at end.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
const double EPS0 = 84381.448 * DAS2R;
double t, dpsibi, depsbi;
double dra0, psia77, oma77, chia, dpsipr, depspr, psia, oma,
rbw[3][3];
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - DJ00) + date2) / DJC;
/* Frame bias. */
iauBi00(&dpsibi, &depsbi, &dra0);
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * DAS2R;
oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * DAS2R;
chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * DAS2R;
/* Apply IAU 2000 precession corrections. */
iauPr00(date1, date2, &dpsipr, &depspr);
psia = psia77 + dpsipr;
oma = oma77 + depspr;
/* Frame bias matrix: GCRS to J2000.0. */
iauIr(rbw);
iauRz(dra0, rbw);
iauRy(dpsibi * sin(EPS0), rbw);
iauRx(-depsbi, rbw);
iauCr(rbw, rb);
/* Precession matrix: J2000.0 to mean of date. */
iauIr(rp);
iauRx(EPS0, rp);
iauRz(-psia, rp);
iauRx(-oma, rp);
iauRz(chia, rp);
/* Bias-precession matrix: GCRS to mean of date. */
iauRxr(rp, rbw, rbp);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2010
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING 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 name(s) of all routine(s) in your derived work shall not
** include the prefix "iau".
**
** 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. In any published work or commercial products which includes
** results achieved by using the SOFA software, you shall
** acknowledge that the SOFA software was used in obtaining those
** results.
**
** 5. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 6. 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.
**
** 7. 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.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
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}
