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# hd2ae

erfa.hd2ae(ha, dec, phi)

  Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude.

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

  Notes

  Wraps ERFA function `eraHd2ae`. The ERFA documentation is:

      - - - - - - - - -
       e r a H d 2 a e
      - - - - - - - - -

      Equatorial to horizon coordinates:  transform hour angle and
      declination to azimuth and altitude.

      Given:
         ha       double       hour angle (local)
         dec      double       declination
         phi      double       site latitude

      Returned:
         *az      double       azimuth
         *el      double       altitude (informally, elevation)

      Notes:

      1)  All the arguments are angles in radians.

      2)  Azimuth is returned in the range 0-2pi;  north is zero, and east
          is +pi/2.  Altitude is returned in the range +/- pi/2.

      3)  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.

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

      5)  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 the hour angle ha will also
          be affected.

      6)  The transformation is the same as Vh = Rz(pi)*Ry(pi/2-phi)*Ve,
          where Vh and Ve are lefthanded unit vectors in the (az,el) and
          (ha,dec) systems respectively and Ry and Rz are rotations about
          first the y-axis and then the z-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.

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

      Last revision:   2021 February 24

      ERFA release 2023-10-11

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