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# ae2hd

erfa.ae2hd(az, el, phi)

  Horizon to equatorial coordinates: transform azimuth and altitude to hour angle and declination.

  Parameters:
    az double array
    el double array
    phi double array
  Returns:
    ha double array
    dec double array

  Notes

  Wraps ERFA function `eraAe2hd`. The ERFA documentation is:

      - - - - - - - - -
       e r a A e 2 h d
      - - - - - - - - -

      Horizon to equatorial coordinates:  transform azimuth and altitude
      to hour angle and declination.

      Given:
         az       double       azimuth
         el       double       altitude (informally, elevation)
         phi      double       site latitude

      Returned:
         ha       double       hour angle (local)
         dec      double       declination

      Notes:

      1)  All the arguments are angles in radians.

      2)  The sign convention for azimuth is north zero, east +pi/2.

      3)  HA is returned in the range +/-pi.  Declination is returned in
          the range +/-pi/2.

      4)  The latitude phi is pi/2 minus the angle between the Earth's
          rotation axis and the adopted zenith.  In many applications it
          will be sufficient to use the published geodetic latitude of the
          site.  In very precise (sub-arcsecond) applications, phi can be
          corrected for polar motion.

      5)  The azimuth az must be with respect to the rotational north pole,
          as opposed to the ITRS pole, and an azimuth with respect to north
          on a map of the Earth's surface will need to be adjusted for
          polar motion if sub-arcsecond accuracy is required.

      6)  Should the user wish to work with respect to the astronomical
          zenith rather than the geodetic zenith, phi will need to be
          adjusted for deflection of the vertical (often tens of
          arcseconds), and the zero point of ha will also be affected.

      7)  The transformation is the same as Ve = Ry(phi-pi/2)*Rz(pi)*Vh,
          where Ve and Vh are lefthanded unit vectors in the (ha,dec) and
          (az,el) systems respectively and Rz and Ry are rotations about
          first the z-axis and then the y-axis.  (n.b. Rz(pi) simply
          reverses the signs of the x and y components.)  For efficiency,
          the algorithm is written out rather than calling other utility
          functions.  For applications that require even greater
          efficiency, additional savings are possible if constant terms
          such as functions of latitude are computed once and for all.

      8)  Again for efficiency, no range checking of arguments is carried
          out.

      Last revision:   2017 September 12

      ERFA release 2023-10-11

      Copyright (C) 2023 IAU ERFA Board.  See notes at end.