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# pn06

erfa.pn06(date1, date2, dpsi, deps)

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

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

  Notes

  Wraps ERFA function `eraPn06`. The ERFA documentation is:

      - - - - - - - -
       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 (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 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

      This revision:  2021 May 11

      Copyright (C) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.