コード例 #1
0
ファイル: c2tcio.c プロジェクト: tohka/celes
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.
**
**--------------------------------------------------------------------*/
}
コード例 #2
0
ファイル: bp06.c プロジェクト: LouisStrous/LUX
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.
**
**  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
**
**  References:
**
**     Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
**     Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
**  This revision:  2009 December 17
**
**  SOFA release 2012-03-01
**
**  Copyright (C) 2012 IAU SOFA Board.  See notes at end.
*/
{
   double gamb, phib, psib, epsa, rbt[3][3];


/* B matrix. */
   iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &epsa);
   iauFw2m(gamb, phib, psib, epsa, rb);

/* PxB matrix. */
   iauPmat06(date1, date2, rbp);

/* P matrix. */
   iauTr(rb, rbt);
   iauRxr(rbp, rbt, rp);

   return;

/*----------------------------------------------------------------------
**
**  Copyright (C) 2012
**  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
**
**--------------------------------------------------------------------*/
}
コード例 #3
0
ファイル: pn00.c プロジェクト: DominicDirkx/sofa
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
**
**--------------------------------------------------------------------*/
}
コード例 #4
0
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    FK5 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 catalogue 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, iauFk5zhz.
**
**  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:  2013 June 18
**
**  SOFA release 2013-12-02
**
**  Copyright (C) 2013 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);

   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
**
**--------------------------------------------------------------------*/
}
コード例 #5
0
ファイル: bp06.c プロジェクト: tohka/celes
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.
**
**  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.
**
**  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
**
**  References:
**
**     Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
**
**     Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
**
**  This revision:  2009 December 17
**
**  Original version 2012-03-01
**
**  Copyright (C) 2013 Naoki Arita.  See notes at end.
*/
{
   double gamb, phib, psib, epsa, rbt[3][3];


/* B matrix. */
   iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &epsa);
   iauFw2m(gamb, phib, psib, epsa, rb);

/* PxB matrix. */
   iauPmat06(date1, date2, rbp);

/* P matrix. */
   iauTr(rb, rbt);
   iauRxr(rbp, rbt, rp);

   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.
**
**--------------------------------------------------------------------*/
}
コード例 #6
0
ファイル: bp00.c プロジェクト: tohka/celes
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.
**
**--------------------------------------------------------------------*/
}
コード例 #7
0
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
    size_t numRow,numVec;
    mxArray *retMat;
    double *xVec, *retData;
    double TT1, TT2, UT11, UT12;
    //The if-statements below should properly initialize all of the EOP.
    //The following initializations to zero are to suppress warnings when
    //compiling with -Wconditional-uninitialized.
    double xp=0;
    double yp=0;
    double deltaT=0;
    double LOD=0;
    double ITRS2TEME[3][3];
    double PEF2TEME[3][3];
    double WInv[3][3];//The inverse polar motion matrix to go from ITRS to PEF.
    double Omega[3];//The angular velocity vector for the Earth's rotation.
    
        
    if(nrhs<3||nrhs>6){
        mexErrMsgTxt("Wrong number of inputs");
    }
    
    if(nlhs>2) {
        mexErrMsgTxt("Wrong number of outputs.");
        return;
    }
 
    checkRealDoubleArray(prhs[0]);
    
    numRow = mxGetM(prhs[0]);
    numVec = mxGetN(prhs[0]);
    
    if(!(numRow==3||numRow==6)) {
        mexErrMsgTxt("The input vector has a bad dimensionality.");
    }
    
    xVec=(double*)mxGetData(prhs[0]);
    TT1=getDoubleFromMatlab(prhs[1]);
    TT2=getDoubleFromMatlab(prhs[2]);
    
    //If some values from the function getEOP will be needed
    if(nrhs<6||mxIsEmpty(prhs[3])||mxIsEmpty(prhs[4])||mxIsEmpty(prhs[5])) {
        mxArray *retVals[5];
        double *xpyp;
        mxArray *JulUTCMATLAB[2];
        double JulUTC[2];
        int retVal;
        
        //Get the time in UTC to look up the parameters by going to TAI and
        //then UTC.
        retVal=iauTttai(TT1, TT2, &JulUTC[0], &JulUTC[1]);
        if(retVal!=0) {
            mexErrMsgTxt("An error occurred computing TAI.");
        }
        retVal=iauTaiutc(JulUTC[0], JulUTC[1], &JulUTC[0], &JulUTC[1]);
        switch(retVal){
            case 1:
                mexWarnMsgTxt("Dubious Date entered.");
                break;
            case -1:
                mexErrMsgTxt("Unacceptable date entered");
                break;
            default:
                break;
        }
        
        JulUTCMATLAB[0]=doubleMat2Matlab(&JulUTC[0],1,1);
        JulUTCMATLAB[1]=doubleMat2Matlab(&JulUTC[1],1,1);

        //Get the Earth orientation parameters for the given date.
        mexCallMATLAB(5,retVals,2,JulUTCMATLAB,"getEOP");
        mxDestroyArray(JulUTCMATLAB[0]);
        mxDestroyArray(JulUTCMATLAB[1]);
        
        checkRealDoubleArray(retVals[0]);
        checkRealDoubleArray(retVals[1]);
        if(mxGetM(retVals[0])!=2||mxGetN(retVals[0])!=1||mxGetM(retVals[1])!=2||mxGetN(retVals[1])!=1) {
            mxDestroyArray(retVals[0]);
            mxDestroyArray(retVals[1]);
            mxDestroyArray(retVals[2]);
            mxDestroyArray(retVals[3]);
            mxDestroyArray(retVals[4]);
            mexErrMsgTxt("Error using the getEOP function.");
            return;
        }
        
        xpyp=(double*)mxGetData(retVals[0]);
        xp=xpyp[0];
        yp=xpyp[1];
        //The celestial pole offsets are not used.
        
        //This is TT-UT1
        deltaT=getDoubleFromMatlab(retVals[3]);
        LOD=getDoubleFromMatlab(retVals[4]);
        //Free the returned arrays.
        mxDestroyArray(retVals[0]);
        mxDestroyArray(retVals[1]);
        mxDestroyArray(retVals[2]);
        mxDestroyArray(retVals[3]);
        mxDestroyArray(retVals[4]);
    }
    
    //If deltaT=TT-UT1 is given
    if(nrhs>3&&!mxIsEmpty(prhs[3])) {
        deltaT=getDoubleFromMatlab(prhs[3]);
    }
    
    //Obtain UT1 from terestrial time and deltaT.
    iauTtut1(TT1, TT2, deltaT, &UT11, &UT12);
    
    //Get polar motion values, if given.
    if(nrhs>4&&!mxIsEmpty(prhs[4])) {
        size_t dim1, dim2;
        
        checkRealDoubleArray(prhs[4]);
        dim1 = mxGetM(prhs[4]);
        dim2 = mxGetN(prhs[4]);
        
        if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) {
            double *xpyp=(double*)mxGetData(prhs[4]);
        
            xp=xpyp[0];
            yp=xpyp[1];
        } else {
            mexErrMsgTxt("The celestial pole offsets have the wrong dimensionality.");
            return;
        }
    }
    
    //If LOD is given
    if(nrhs>5&&!mxIsEmpty(prhs[5])) {
        LOD=getDoubleFromMatlab(prhs[5]);
    }

    {
     double GMST1982=iauGmst82(UT11, UT12);
     double TEME2PEF[3][3];
     double TEME2ITRS[3][3];
     double W[3][3];
     double omega;
    
     //Get Greenwhich mean sidereal time under the IAU's 1982 model. This
     //is given in radians and will be used to build a rotation matrix to
     //rotate into the PEF system.
     GMST1982=iauGmst82(UT11, UT12);
     {
         double cosGMST,sinGMST;
         cosGMST=cos(GMST1982);
         sinGMST=sin(GMST1982);
         //Build the rotation matrix to rotate by GMST about the z-axis. This
         //will put the position vector in the PEF system.
         TEME2PEF[0][0]=cosGMST;
         TEME2PEF[0][1]=sinGMST;
         TEME2PEF[0][2]=0;
         TEME2PEF[1][0]=-sinGMST;
         TEME2PEF[1][1]=cosGMST;
         TEME2PEF[1][2]=0;
         TEME2PEF[2][0]=0;
         TEME2PEF[2][1]=0;
         TEME2PEF[2][2]=1.0;
     }
     //The inverse rotation is just the transpose
     iauTr(TEME2PEF, PEF2TEME);
     //To go from PEF to ITRS, we need to build the polar motion matrix
     //using the IAU's 1980 conventions.
     {
         double cosXp,sinXp,cosYp,sinYp;
         cosXp=cos(xp);
         sinXp=sin(xp);
         cosYp=cos(yp);
         sinYp=sin(yp);
         W[0][0]=cosXp;
         W[0][1]=sinXp*sinYp;
         W[0][2]=sinXp*cosYp;
         W[1][0]=0;
         W[1][1]=cosYp;
         W[1][2]=-sinYp;
         W[2][0]=-sinXp;
         W[2][1]=cosXp*sinXp;
         W[2][2]=cosXp*cosYp;
     }
     //The inverse rotation is just the transpose
     iauTr(W, WInv);
     
     //The total rotation matrix is thus the product of the two rotations.
     //TEME2ITRS=W*TEME2PEF;
     iauRxr(W, TEME2PEF, TEME2ITRS);
     //We want the inverse rotation
     iauTr(TEME2ITRS, ITRS2TEME);
     //The angular velocity vector of the Earth in the TIRS in radians.
     omega=getScalarMatlabClassConst("Constants","IERSMeanEarthRotationRate");
     //Adjust for LOD
     omega=omega*(1-LOD/86400.0);//86400.0 is the number of seconds in a TT day.
     Omega[0]=0;
     Omega[1]=0;
     Omega[2]=omega;     
    }
    
    //Allocate space for the return vectors.
    retMat=mxCreateDoubleMatrix(numRow,numVec,mxREAL);
    retData=(double*)mxGetData(retMat);
    
    {
        size_t curVec;
        
        for(curVec=0;curVec<numVec;curVec++) {
            //Multiply the position vector with the rotation matrix.
            iauRxp(ITRS2TEME, xVec+numRow*curVec, retData+numRow*curVec);
            //If a velocity vector was given.
            if(numRow>3) {
                double *posITRS=xVec+numRow*curVec;
                double *velITRS=xVec+numRow*curVec+3;//Velocity in TEME
                double posPEF[3];
                double velPEF[3];
                double *retDataVel=retData+numRow*curVec+3;
                double rotVel[3];
                //If a velocity was provided with the position, first
                //convert to PEF coordinates, then account for the rotation
                //of the Earth, then rotate into TEME coordinates.
                
                //Convert velocity from ITRS to PEF.
                iauRxp(WInv, velITRS, velPEF);
                //Convert position from ITRS to PEF
                iauRxp(WInv, posITRS, posPEF);

                //Evaluate the cross product for the angular velocity due
                //to the Earth's rotation.
                iauPxp(Omega, posPEF, rotVel);

                //Add the instantaneous velocity due to rotation.
                iauPpp(velPEF, rotVel, retDataVel);

                //Rotate from the PEF into the TEME
                iauRxp(PEF2TEME, retDataVel, retDataVel);
            }
        }
    }
    
    plhs[0]=retMat;
    
    if(nlhs>1) {
        double *elPtr;
        size_t i,j;
        
        plhs[1]=mxCreateDoubleMatrix(3,3,mxREAL);
        elPtr=(double*)mxGetData(plhs[1]);
        
        for (i=0;i<3;i++) {
            for(j=0;j<3;j++) {
                elPtr[i+3*j]=ITRS2TEME[i][j];
            }
        }
    }
}
コード例 #8
0
ファイル: bp00.c プロジェクト: ddj116/gmat
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
**  =====================
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**  WHICH APPLY TO ITS USE.
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**
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**--------------------------------------------------------------------*/
}