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# pn06a

erfa.pn06a(date1, date2)

  Precession-nutation, IAU 2006/2000A models: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

  Parameters
    date1 double array
    date2 double array
  Returns
    dpsi double array
    deps double array
    epsa double array
    rb double array
    rp double array
    rbp double array
    rn double array
    rbpn double array

  Notes

  Wraps ERFA function `eraPn06a`. The ERFA documentation is:

      - - - - - - - - -
       e r a P n 0 6 a
      - - - - - - - - -

      Precession-nutation, IAU 2006/2000A models:  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)

      Returned:
         dpsi,deps    double          nutation (Note 2)
         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 (Notes 8,9)

      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 nutation components (luni-solar + planetary, IAU 2000A) in
          longitude and obliquity are in radians and with respect to the
          equinox and ecliptic of date.  Free core nutation is omitted;
          for the utmost accuracy, use the eraPn06 function, where the
          nutation components are caller-specified.

      3)  The mean obliquity is consistent with the IAU 2006 precession.

      4)  The matrix rb transforms vectors from GCRS to mean J2000.0 by
          applying frame bias.

      5)  The matrix rp transforms vectors from mean J2000.0 to mean of
          date by applying precession.

      6)  The matrix rbp transforms vectors from GCRS to mean of date by
          applying frame bias then precession.  It is the product rp x rb.

      7)  The matrix rn transforms vectors from mean of date to true of
          date by applying the nutation (luni-solar + planetary).

      8)  The matrix rbpn transforms vectors from GCRS to true of date
          (CIP/equinox).  It is the product rn x rbp, applying frame bias,
          precession and nutation in that order.

      9)  The X,Y,Z coordinates of the IAU 2006/2000A 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:
         eraNut06a    nutation, IAU 2006/2000A
         eraPn06      bias/precession/nutation results, IAU 2006

      Reference:

         Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

      This revision:  2021 May 11

      Copyright (C) 2013-2021, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.