pn06.c

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#include "erfa.h"

void eraPn06(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])
/*
**  - - - - - - - -
**   e r a P n 0 6
**  - - - - - - - -
**
**  Precession-nutation, IAU 2006 model:  a multi-purpose function,
**  supporting classical (equinox-based) use directly and CIO-based use
**  indirectly.
**
**  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 2006
**      precession.
**
**  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)  The X,Y,Z coordinates of the Celestial Intermediate Pole are
**      elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].
**
**  10) It is permissible to re-use the same array in the returned
**      arguments.  The arrays are filled in the stated order.
**
**  Called:
**     eraPfw06     bias-precession F-W angles, IAU 2006
**     eraFw2m      F-W angles to r-matrix
**     eraCr        copy r-matrix
**     eraTr        transpose r-matrix
**     eraRxr       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
**
**  Copyright (C) 2013-2015, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3];

/* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
   eraPfw06(ERFA_DJM0, ERFA_DJM00, &gamb, &phib, &psib, &eps);

/* B matrix. */
   eraFw2m(gamb, phib, psib, eps, r1);
   eraCr(r1, rb);

/* Bias-precession Fukushima-Williams angles of date. */
   eraPfw06(date1, date2, &gamb, &phib, &psib, &eps);

/* Bias-precession matrix. */
   eraFw2m(gamb, phib, psib, eps, r2);
   eraCr(r2, rbp);

/* Solve for precession matrix. */
   eraTr(r1, rt);
   eraRxr(r2, rt, rp);

/* Equinox-based bias-precession-nutation matrix. */
   eraFw2m(gamb, phib, psib + dpsi, eps + deps, r1);
   eraCr(r1, rbpn);

/* Solve for nutation matrix. */
   eraTr(r2, rt);
   eraRxr(r1, rt, rn);

/* Obliquity, mean of date. */
   *epsa = eps;

   return;

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2015, NumFOCUS Foundation.
**  All rights reserved.
**  
**  This library is derived, with permission, from the International
**  Astronomical Union's "Standards of Fundamental Astronomy" library,
**  available from http://www.iausofa.org.
**  
**  The ERFA version is intended to retain identical functionality to
**  the SOFA library, but made distinct through different function and
**  file names, as set out in the SOFA license conditions.  The SOFA
**  original has a role as a reference standard for the IAU and IERS,
**  and consequently redistribution is permitted only in its unaltered
**  state.  The ERFA version is not subject to this restriction and
**  therefore can be included in distributions which do not support the
**  concept of "read only" software.
**  
**  Although the intent is to replicate the SOFA API (other than
**  replacement of prefix names) and results (with the exception of
**  bugs;  any that are discovered will be fixed), SOFA is not
**  responsible for any errors found in this version of the library.
**  
**  If you wish to acknowledge the SOFA heritage, please acknowledge
**  that you are using a library derived from SOFA, rather than SOFA
**  itself.
**  
**  
**  TERMS AND CONDITIONS
**  
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**  modification, are permitted provided that the following conditions
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**  
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**    notice, this list of conditions and the following disclaimer.
**  
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