code: import re
  import copy
  import warnings
  import operator
  
  import numpy as np
  
  from astropy import _erfa as erfa
  from astropy.utils.compat.misc import override__dir__
  from astropy import units as u
  from astropy.constants import c as speed_of_light
  from astropy.utils.data_info import MixinInfo
  from astropy.utils import ShapedLikeNDArray
  from astropy.time import Time
  from astropy.utils.exceptions import AstropyUserWarning
  
  from .distances import Distance
  from .angles import Angle
  from .baseframe import (BaseCoordinateFrame, frame_transform_graph,
                          GenericFrame)
  from .builtin_frames import ICRS, SkyOffsetFrame
  from .representation import (SphericalRepresentation,
                               UnitSphericalRepresentation, SphericalDifferential)
  from .sky_coordinate_parsers import (_get_frame_class, _get_frame_without_data,
                                       _parse_coordinate_data)
  
  __all__ = ['SkyCoord', 'SkyCoordInfo']
  
  
  class SkyCoordInfo(MixinInfo):
      """
      Container for meta information like name, description, format.  This is
      required when the object is used as a mixin column within a table, but can
      be used as a general way to store meta information.
      """
      attrs_from_parent = set(['unit'])  # Unit is read-only
      _supports_indexing = False
  
      @staticmethod
      def default_format(val):
          repr_data = val.info._repr_data
          formats = ['{0.' + compname + '.value:}' for compname
                     in repr_data.components]
          return ','.join(formats).format(repr_data)
  
      @property
      def unit(self):
          repr_data = self._repr_data
          unit = ','.join(str(getattr(repr_data, comp).unit) or 'None'
                          for comp in repr_data.components)
          return unit
  
      @property
      def _repr_data(self):
          if self._parent is None:
              return None
  
          sc = self._parent
          if (issubclass(sc.representation_type, SphericalRepresentation)
                  and isinstance(sc.data, UnitSphericalRepresentation)):
              repr_data = sc.represent_as(sc.data.__class__, in_frame_units=True)
          else:
              repr_data = sc.represent_as(sc.representation_type,
                                          in_frame_units=True)
          return repr_data
  
      def _represent_as_dict(self):
          obj = self._parent
          attrs = (list(obj.representation_component_names) +
                   list(frame_transform_graph.frame_attributes.keys()))
  
          # Don't output distance if it is all unitless 1.0
          if 'distance' in attrs and np.all(obj.distance == 1.0):
              attrs.remove('distance')
  
          out = super()._represent_as_dict(attrs)
  
          out['representation_type'] = obj.representation_type.get_name()
          out['frame'] = obj.frame.name
          # Note that obj.info.unit is a fake composite unit (e.g. 'deg,deg,None'
          # or None,None,m) and is not stored.  The individual attributes have
          # units.
  
          return out
  
      def new_like(self, skycoords, length, metadata_conflicts='warn', name=None):
          """
          Return a new SkyCoord instance which is consistent with the input
          SkyCoord objects ``skycoords`` and has ``length`` rows.  Being
          "consistent" is defined as being able to set an item from one to each of
          the rest without any exception being raised.
  
          This is intended for creating a new SkyCoord instance whose elements can
          be set in-place for table operations like join or vstack.  This is used
          when a SkyCoord object is used as a mixin column in an astropy Table.
  
          The data values are not predictable and it is expected that the consumer
          of the object will fill in all values.
  
          Parameters
          ----------
          skycoords : list
              List of input SkyCoord objects
          length : int
              Length of the output skycoord object
          metadata_conflicts : str ('warn'|'error'|'silent')
              How to handle metadata conflicts
          name : str
              Output name (sets output skycoord.info.name)
  
          Returns
          -------
          skycoord : SkyCoord (or subclass)
              Instance of this class consistent with ``skycoords``
  
          """
          # Get merged info attributes like shape, dtype, format, description, etc.
          attrs = self.merge_cols_attributes(skycoords, metadata_conflicts, name,
                                             ('meta', 'description'))
          skycoord0 = skycoords[0]
  
          # Make a new SkyCoord object with the desired length and attributes
          # by using the _apply / __getitem__ machinery to effectively return
          # skycoord0[[0, 0, ..., 0, 0]]. This will have the all the right frame
          # attributes with the right shape.
          indexes = np.zeros(length, dtype=np.int64)
          out = skycoord0[indexes]
  
          # Use __setitem__ machinery to check for consistency of all skycoords
          for skycoord in skycoords[1:]:
              try:
                  out[0] = skycoord[0]
              except Exception as err:
                  raise ValueError(f'input skycoords are inconsistent: {err}')
  
          # Set (merged) info attributes
          for attr in ('name', 'meta', 'description'):
              if attr in attrs:
                  setattr(out.info, attr, attrs[attr])
  
          return out
  
  
  class SkyCoord(ShapedLikeNDArray):
      """High-level object providing a flexible interface for celestial coordinate
      representation, manipulation, and transformation between systems.
  
      The `SkyCoord` class accepts a wide variety of inputs for initialization. At
      a minimum these must provide one or more celestial coordinate values with
      unambiguous units.  Inputs may be scalars or lists/tuples/arrays, yielding
      scalar or array coordinates (can be checked via ``SkyCoord.isscalar``).
      Typically one also specifies the coordinate frame, though this is not
      required. The general pattern for spherical representations is::
  
        SkyCoord(COORD, [FRAME], keyword_args ...)
        SkyCoord(LON, LAT, [FRAME], keyword_args ...)
        SkyCoord(LON, LAT, [DISTANCE], frame=FRAME, unit=UNIT, keyword_args ...)
        SkyCoord([FRAME], <lon_attr>=LON, <lat_attr>=LAT, keyword_args ...)
  
      It is also possible to input coordinate values in other representations
      such as cartesian or cylindrical.  In this case one includes the keyword
      argument ``representation_type='cartesian'`` (for example) along with data
      in ``x``, ``y``, and ``z``.
  
      See also: http://docs.astropy.org/en/stable/coordinates/
  
      Examples
      --------
      The examples below illustrate common ways of initializing a `SkyCoord`
      object.  For a complete description of the allowed syntax see the
      full coordinates documentation.  First some imports::
  
        >>> from astropy.coordinates import SkyCoord  # High-level coordinates
        >>> from astropy.coordinates import ICRS, Galactic, FK4, FK5  # Low-level frames
        >>> from astropy.coordinates import Angle, Latitude, Longitude  # Angles
        >>> import astropy.units as u
  
      The coordinate values and frame specification can now be provided using
      positional and keyword arguments::
  
        >>> c = SkyCoord(10, 20, unit="deg")  # defaults to ICRS frame
        >>> c = SkyCoord([1, 2, 3], [-30, 45, 8], frame="icrs", unit="deg")  # 3 coords
  
        >>> coords = ["1:12:43.2 +31:12:43", "1 12 43.2 +31 12 43"]
        >>> c = SkyCoord(coords, frame=FK4, unit=(u.hourangle, u.deg), obstime="J1992.21")
  
        >>> c = SkyCoord("1h12m43.2s +1d12m43s", frame=Galactic)  # Units from string
        >>> c = SkyCoord(frame="galactic", l="1h12m43.2s", b="+1d12m43s")
  
        >>> ra = Longitude([1, 2, 3], unit=u.deg)  # Could also use Angle
        >>> dec = np.array([4.5, 5.2, 6.3]) * u.deg  # Astropy Quantity
        >>> c = SkyCoord(ra, dec, frame='icrs')
        >>> c = SkyCoord(frame=ICRS, ra=ra, dec=dec, obstime='2001-01-02T12:34:56')
  
        >>> c = FK4(1 * u.deg, 2 * u.deg)  # Uses defaults for obstime, equinox
        >>> c = SkyCoord(c, obstime='J2010.11', equinox='B1965')  # Override defaults
  
        >>> c = SkyCoord(w=0, u=1, v=2, unit='kpc', frame='galactic',
        ...              representation_type='cartesian')
  
        >>> c = SkyCoord([ICRS(ra=1*u.deg, dec=2*u.deg), ICRS(ra=3*u.deg, dec=4*u.deg)])
  
      Velocity components (proper motions or radial velocities) can also be
      provided in a similar manner::
  
        >>> c = SkyCoord(ra=1*u.deg, dec=2*u.deg, radial_velocity=10*u.km/u.s)
  
        >>> c = SkyCoord(ra=1*u.deg, dec=2*u.deg, pm_ra_cosdec=2*u.mas/u.yr, pm_dec=1*u.mas/u.yr)
  
      As shown, the frame can be a `~astropy.coordinates.BaseCoordinateFrame`
      class or the corresponding string alias.  The frame classes that are built in
      to astropy are `ICRS`, `FK5`, `FK4`, `FK4NoETerms`, and `Galactic`.
      The string aliases are simply lower-case versions of the class name, and
      allow for creating a `SkyCoord` object and transforming frames without
      explicitly importing the frame classes.
  
      Parameters
      ----------
      frame : `~astropy.coordinates.BaseCoordinateFrame` class or string, optional
          Type of coordinate frame this `SkyCoord` should represent. Defaults to
          to ICRS if not given or given as None.
      unit : `~astropy.units.Unit`, string, or tuple of :class:`~astropy.units.Unit` or str, optional
          Units for supplied ``LON`` and ``LAT`` values, respectively.  If
          only one unit is supplied then it applies to both ``LON`` and
          ``LAT``.
      obstime : valid `~astropy.time.Time` initializer, optional
          Time(s) of observation.
      equinox : valid `~astropy.time.Time` initializer, optional
          Coordinate frame equinox.
      representation_type : str or Representation class
          Specifies the representation, e.g. 'spherical', 'cartesian', or
          'cylindrical'.  This affects the positional args and other keyword args
          which must correspond to the given representation.
      copy : bool, optional
          If `True` (default), a copy of any coordinate data is made.  This
          argument can only be passed in as a keyword argument.
      **keyword_args
          Other keyword arguments as applicable for user-defined coordinate frames.
          Common options include:
  
          ra, dec : valid `~astropy.coordinates.Angle` initializer, optional
              RA and Dec for frames where ``ra`` and ``dec`` are keys in the
              frame's ``representation_component_names``, including `ICRS`,
              `FK5`, `FK4`, and `FK4NoETerms`.
          pm_ra_cosdec, pm_dec  : `~astropy.units.Quantity`, optional
              Proper motion components, in angle per time units.
          l, b : valid `~astropy.coordinates.Angle` initializer, optional
              Galactic ``l`` and ``b`` for for frames where ``l`` and ``b`` are
              keys in the frame's ``representation_component_names``, including
              the `Galactic` frame.
          pm_l_cosb, pm_b : `~astropy.units.Quantity`, optional
              Proper motion components in the `Galactic` frame, in angle per time
              units.
          x, y, z : float or `~astropy.units.Quantity`, optional
              Cartesian coordinates values
          u, v, w : float or `~astropy.units.Quantity`, optional
              Cartesian coordinates values for the Galactic frame.
          radial_velocity : `~astropy.units.Quantity`, optional
              The component of the velocity along the line-of-sight (i.e., the
              radial direction), in velocity units.
      """
  
      # Declare that SkyCoord can be used as a Table column by defining the
      # info property.
      info = SkyCoordInfo()
  
      def __init__(self, *args, copy=True, **kwargs):
  
          # these are frame attributes set on this SkyCoord but *not* a part of
          # the frame object this SkyCoord contains
          self._extra_frameattr_names = set()
  
          # If all that is passed in is a frame instance that already has data,
          # we should bypass all of the parsing and logic below. This is here
          # to make this the fastest way to create a SkyCoord instance. Many of
          # the classmethods implemented for performance enhancements will use
          # this as the initialization path
          if (len(args) == 1 and len(kwargs) == 0
                  and isinstance(args[0], (BaseCoordinateFrame, SkyCoord))):
  
              coords = args[0]
              if isinstance(coords, SkyCoord):
                  self._extra_frameattr_names = coords._extra_frameattr_names
                  self.info = coords.info
  
                  # Copy over any extra frame attributes
                  for attr_name in self._extra_frameattr_names:
                      # Setting it will also validate it.
                      setattr(self, attr_name, getattr(coords, attr_name))
  
                  coords = coords.frame
  
              if not coords.has_data:
                  raise ValueError('Cannot initialize from a coordinate frame '
                                   'instance without coordinate data')
  
              if copy:
                  self._sky_coord_frame = coords.copy()
              else:
                  self._sky_coord_frame = coords
  
          else:
              # Get the frame instance without coordinate data but with all frame
              # attributes set - these could either have been passed in with the
              # frame as an instance, or passed in as kwargs here
              frame_cls, frame_kwargs = _get_frame_without_data(args, kwargs)
  
              # Parse the args and kwargs to assemble a sanitized and validated
              # kwargs dict for initializing attributes for this object and for
              # creating the internal self._sky_coord_frame object
              args = list(args)  # Make it mutable
              skycoord_kwargs, components, info = _parse_coordinate_data(
                  frame_cls(**frame_kwargs), args, kwargs)
  
              # In the above two parsing functions, these kwargs were identified
              # as valid frame attributes for *some* frame, but not the frame that
              # this SkyCoord will have. We keep these attributes as special
              # skycoord frame attributes:
              for attr in skycoord_kwargs:
                  # Setting it will also validate it.
                  setattr(self, attr, skycoord_kwargs[attr])
  
              if info is not None:
                  self.info = info
  
              # Finally make the internal coordinate object.
              frame_kwargs.update(components)
              self._sky_coord_frame = frame_cls(copy=copy, **frame_kwargs)
  
              if not self._sky_coord_frame.has_data:
                  raise ValueError('Cannot create a SkyCoord without data')
  
      @property
      def frame(self):
          return self._sky_coord_frame
  
      @property
      def representation_type(self):
          return self.frame.representation_type
  
      @representation_type.setter
      def representation_type(self, value):
          self.frame.representation_type = value
  
      # TODO: remove these in future
      @property
      def representation(self):
          return self.frame.representation
  
      @representation.setter
      def representation(self, value):
          self.frame.representation = value
  
      @property
      def shape(self):
          return self.frame.shape
  
      def __eq__(self, value):
          """Equality operator for SkyCoord
  
          This implements strict equality and requires that the frames are
          equivalent, extra frame attributes are equivalent, and that the
          representation data are exactly equal.
          """
          # Make sure that any extra frame attribute names are equivalent.
          for attr in self._extra_frameattr_names | value._extra_frameattr_names:
              if not self.frame._frameattr_equiv(getattr(self, attr),
                                                 getattr(value, attr)):
                  raise ValueError(f"cannot compare: extra frame attribute "
                                   f"'{attr}' is not equivalent "
                                   f"(perhaps compare the frames directly to avoid "
                                   f"this exception)")
  
          return self._sky_coord_frame == value._sky_coord_frame
  
      def __ne__(self, value):
          return np.logical_not(self == value)
  
      def _apply(self, method, *args, **kwargs):
          """Create a new instance, applying a method to the underlying data.
  
          In typical usage, the method is any of the shape-changing methods for
          `~numpy.ndarray` (``reshape``, ``swapaxes``, etc.), as well as those
          picking particular elements (``__getitem__``, ``take``, etc.), which
          are all defined in `~astropy.utils.shapes.ShapedLikeNDArray`. It will be
          applied to the underlying arrays in the representation (e.g., ``x``,
          ``y``, and ``z`` for `~astropy.coordinates.CartesianRepresentation`),
          as well as to any frame attributes that have a shape, with the results
          used to create a new instance.
  
          Internally, it is also used to apply functions to the above parts
          (in particular, `~numpy.broadcast_to`).
  
          Parameters
          ----------
          method : str or callable
              If str, it is the name of a method that is applied to the internal
              ``components``. If callable, the function is applied.
          args : tuple
              Any positional arguments for ``method``.
          kwargs : dict
              Any keyword arguments for ``method``.
          """
          def apply_method(value):
              if isinstance(value, ShapedLikeNDArray):
                  return value._apply(method, *args, **kwargs)
              else:
                  if callable(method):
                      return method(value, *args, **kwargs)
                  else:
                      return getattr(value, method)(*args, **kwargs)
  
          # create a new but empty instance, and copy over stuff
          new = super().__new__(self.__class__)
          new._sky_coord_frame = self._sky_coord_frame._apply(method,
                                                              *args, **kwargs)
          new._extra_frameattr_names = self._extra_frameattr_names.copy()
          for attr in self._extra_frameattr_names:
              value = getattr(self, attr)
              if getattr(value, 'shape', ()):
                  value = apply_method(value)
              elif method == 'copy' or method == 'flatten':
                  # flatten should copy also for a single element array, but
                  # we cannot use it directly for array scalars, since it
                  # always returns a one-dimensional array. So, just copy.
                  value = copy.copy(value)
              setattr(new, '_' + attr, value)
  
          # Copy other 'info' attr only if it has actually been defined.
          # See PR #3898 for further explanation and justification, along
          # with Quantity.__array_finalize__
          if 'info' in self.__dict__:
              new.info = self.info
  
          return new
  
      def __setitem__(self, item, value):
          """Implement self[item] = value for SkyCoord
  
          The right hand ``value`` must be strictly consistent with self:
          - Identical class
          - Equivalent frames
          - Identical representation_types
          - Identical representation differentials keys
          - Identical frame attributes
          - Identical "extra" frame attributes (e.g. obstime for an ICRS coord)
  
          With these caveats the setitem ends up as effectively a setitem on
          the representation data.
  
            self.frame.data[item] = value.frame.data
          """
          if self.__class__ is not value.__class__:
              raise TypeError(f'can only set from object of same class: '
                              f'{self.__class__.__name__} vs. '
                              f'{value.__class__.__name__}')
  
          # Make sure that any extra frame attribute names are equivalent.
          for attr in self._extra_frameattr_names | value._extra_frameattr_names:
              if not self.frame._frameattr_equiv(getattr(self, attr),
                                                 getattr(value, attr)):
                  raise ValueError(f'attribute {attr} is not equivalent')
  
          # Set the frame values.  This checks frame equivalence and also clears
          # the cache to ensure that the object is not in an inconsistent state.
          self._sky_coord_frame[item] = value._sky_coord_frame
  
      def insert(self, obj, values, axis=0):
          """
          Insert coordinate values before the given indices in the object and
          return a new Frame object.
  
          The values to be inserted must conform to the rules for in-place setting
          of ``SkyCoord`` objects.
  
          The API signature matches the ``np.insert`` API, but is more limited.
          The specification of insert index ``obj`` must be a single integer,
          and the ``axis`` must be ``0`` for simple insertion before the index.
  
          Parameters
          ----------
          obj : int
              Integer index before which ``values`` is inserted.
          values : array_like
              Value(s) to insert.  If the type of ``values`` is different
              from that of quantity, ``values`` is converted to the matching type.
          axis : int, optional
              Axis along which to insert ``values``.  Default is 0, which is the
              only allowed value and will insert a row.
  
          Returns
          -------
          out : `~astropy.coordinates.SkyCoord` instance
              New coordinate object with inserted value(s)
  
          """
          # Validate inputs: obj arg is integer, axis=0, self is not a scalar, and
          # input index is in bounds.
          try:
              idx0 = operator.index(obj)
          except TypeError:
              raise TypeError('obj arg must be an integer')
  
          if axis != 0:
              raise ValueError('axis must be 0')
  
          if not self.shape:
              raise TypeError('cannot insert into scalar {} object'
                              .format(self.__class__.__name__))
  
          if abs(idx0) > len(self):
              raise IndexError('index {} is out of bounds for axis 0 with size {}'
                               .format(idx0, len(self)))
  
          # Turn negative index into positive
          if idx0 < 0:
              idx0 = len(self) + idx0
  
          n_values = len(values) if values.shape else 1
  
          # Finally make the new object with the correct length and set values for the
          # three sections, before insert, the insert, and after the insert.
          out = self.__class__.info.new_like([self], len(self) + n_values, name=self.info.name)
  
          # Set the output values. This is where validation of `values` takes place to ensure
          # that it can indeed be inserted.
          out[:idx0] = self[:idx0]
          out[idx0:idx0 + n_values] = values
          out[idx0 + n_values:] = self[idx0:]
  
          return out
  
      def transform_to(self, frame, merge_attributes=True):
          """Transform this coordinate to a new frame.
  
          The precise frame transformed to depends on ``merge_attributes``.
          If `False`, the destination frame is used exactly as passed in.
          But this is often not quite what one wants.  E.g., suppose one wants to
          transform an ICRS coordinate that has an obstime attribute to FK4; in
          this case, one likely would want to use this information. Thus, the
          default for ``merge_attributes`` is `True`, in which the precedence is
          as follows: (1) explicitly set (i.e., non-default) values in the
          destination frame; (2) explicitly set values in the source; (3) default
          value in the destination frame.
  
          Note that in either case, any explicitly set attributes on the source
          `SkyCoord` that are not part of the destination frame's definition are
          kept (stored on the resulting `SkyCoord`), and thus one can round-trip
          (e.g., from FK4 to ICRS to FK4 without loosing obstime).
  
          Parameters
          ----------
          frame : str, `BaseCoordinateFrame` class or instance, or `SkyCoord` instance
              The frame to transform this coordinate into.  If a `SkyCoord`, the
              underlying frame is extracted, and all other information ignored.
          merge_attributes : bool, optional
              Whether the default attributes in the destination frame are allowed
              to be overridden by explicitly set attributes in the source
              (see note above; default: `True`).
  
          Returns
          -------
          coord : `SkyCoord`
              A new object with this coordinate represented in the `frame` frame.
  
          Raises
          ------
          ValueError
              If there is no possible transformation route.
  
          """
          from astropy.coordinates.errors import ConvertError
  
          frame_kwargs = {}
  
          # Frame name (string) or frame class?  Coerce into an instance.
          try:
              frame = _get_frame_class(frame)()
          except Exception:
              pass
  
          if isinstance(frame, SkyCoord):
              frame = frame.frame  # Change to underlying coord frame instance
  
          if isinstance(frame, BaseCoordinateFrame):
              new_frame_cls = frame.__class__
              # Get frame attributes, allowing defaults to be overridden by
              # explicitly set attributes of the source if ``merge_attributes``.
              for attr in frame_transform_graph.frame_attributes:
                  self_val = getattr(self, attr, None)
                  frame_val = getattr(frame, attr, None)
                  if (frame_val is not None
                      and not (merge_attributes
                               and frame.is_frame_attr_default(attr))):
                      frame_kwargs[attr] = frame_val
                  elif (self_val is not None
                        and not self.is_frame_attr_default(attr)):
                      frame_kwargs[attr] = self_val
                  elif frame_val is not None:
                      frame_kwargs[attr] = frame_val
          else:
              raise ValueError('Transform `frame` must be a frame name, class, or instance')
  
          # Get the composite transform to the new frame
          trans = frame_transform_graph.get_transform(self.frame.__class__, new_frame_cls)
          if trans is None:
              raise ConvertError('Cannot transform from {} to {}'
                                 .format(self.frame.__class__, new_frame_cls))
  
          # Make a generic frame which will accept all the frame kwargs that
          # are provided and allow for transforming through intermediate frames
          # which may require one or more of those kwargs.
          generic_frame = GenericFrame(frame_kwargs)
  
          # Do the transformation, returning a coordinate frame of the desired
          # final type (not generic).
          new_coord = trans(self.frame, generic_frame)
  
          # Finally make the new SkyCoord object from the `new_coord` and
          # remaining frame_kwargs that are not frame_attributes in `new_coord`.
          for attr in (set(new_coord.get_frame_attr_names()) &
                       set(frame_kwargs.keys())):
              frame_kwargs.pop(attr)
  
          return self.__class__(new_coord, **frame_kwargs)
  
      def apply_space_motion(self, new_obstime=None, dt=None):
          """
          Compute the position of the source represented by this coordinate object
          to a new time using the velocities stored in this object and assuming
          linear space motion (including relativistic corrections). This is
          sometimes referred to as an "epoch transformation."
  
          The initial time before the evolution is taken from the ``obstime``
          attribute of this coordinate.  Note that this method currently does not
          support evolving coordinates where the *frame* has an ``obstime`` frame
          attribute, so the ``obstime`` is only used for storing the before and
          after times, not actually as an attribute of the frame. Alternatively,
          if ``dt`` is given, an ``obstime`` need not be provided at all.
  
          Parameters
          ----------
          new_obstime : `~astropy.time.Time`, optional
              The time at which to evolve the position to. Requires that the
              ``obstime`` attribute be present on this frame.
          dt : `~astropy.units.Quantity`, `~astropy.time.TimeDelta`, optional
              An amount of time to evolve the position of the source. Cannot be
              given at the same time as ``new_obstime``.
  
          Returns
          -------
          new_coord : `SkyCoord`
              A new coordinate object with the evolved location of this coordinate
              at the new time.  ``obstime`` will be set on this object to the new
              time only if ``self`` also has ``obstime``.
          """
  
          if (new_obstime is None and dt is None or
                  new_obstime is not None and dt is not None):
              raise ValueError("You must specify one of `new_obstime` or `dt`, "
                               "but not both.")
  
          # Validate that we have velocity info
          if 's' not in self.frame.data.differentials:
              raise ValueError('SkyCoord requires velocity data to evolve the '
                               'position.')
  
          if 'obstime' in self.frame.frame_attributes:
              raise NotImplementedError("Updating the coordinates in a frame "
                                        "with explicit time dependence is "
                                        "currently not supported. If you would "
                                        "like this functionality, please open an "
                                        "issue on github:\n"
                                        "https://github.com/astropy/astropy")
  
          if new_obstime is not None and self.obstime is None:
              # If no obstime is already on this object, raise an error if a new
              # obstime is passed: we need to know the time / epoch at which the
              # the position / velocity were measured initially
              raise ValueError('This object has no associated `obstime`. '
                               'apply_space_motion() must receive a time '
                               'difference, `dt`, and not a new obstime.')
  
          # Compute t1 and t2, the times used in the starpm call, which *only*
          # uses them to compute a delta-time
          t1 = self.obstime
          if dt is None:
              # self.obstime is not None and new_obstime is not None b/c of above
              # checks
              t2 = new_obstime
          else:
              # new_obstime is definitely None b/c of the above checks
              if t1 is None:
                  # MAGIC NUMBER: if the current SkyCoord object has no obstime,
                  # assume J2000 to do the dt offset. This is not actually used
                  # for anything except a delta-t in starpm, so it's OK that it's
                  # not necessarily the "real" obstime
                  t1 = Time('J2000')
                  new_obstime = None  # we don't actually know the inital obstime
                  t2 = t1 + dt
              else:
                  t2 = t1 + dt
                  new_obstime = t2
          # starpm wants tdb time
          t1 = t1.tdb
          t2 = t2.tdb
  
          # proper motion in RA should not include the cos(dec) term, see the
          # erfa function eraStarpv, comment (4).  So we convert to the regular
          # spherical differentials.
          icrsrep = self.icrs.represent_as(SphericalRepresentation, SphericalDifferential)
          icrsvel = icrsrep.differentials['s']
  
          parallax_zero = False
          try:
              plx = icrsrep.distance.to_value(u.arcsecond, u.parallax())
          except u.UnitConversionError:  # No distance: set to 0 by convention
              plx = 0.
              parallax_zero = True
  
          try:
              rv = icrsvel.d_distance.to_value(u.km/u.s)
          except u.UnitConversionError:  # No RV
              rv = 0.
  
          starpm = erfa.pmsafe(icrsrep.lon.radian, icrsrep.lat.radian,
                               icrsvel.d_lon.to_value(u.radian/u.yr),
                               icrsvel.d_lat.to_value(u.radian/u.yr),
                               plx, rv, t1.jd1, t1.jd2, t2.jd1, t2.jd2)
  
          if parallax_zero:
              new_distance = None
          else:
              new_distance = Distance(parallax=starpm[4] << u.arcsec)
  
          icrs2 = ICRS(ra=u.Quantity(starpm[0], u.radian, copy=False),
                       dec=u.Quantity(starpm[1], u.radian, copy=False),
                       pm_ra=u.Quantity(starpm[2], u.radian/u.yr, copy=False),
                       pm_dec=u.Quantity(starpm[3], u.radian/u.yr, copy=False),
                       distance=new_distance,
                       radial_velocity=u.Quantity(starpm[5], u.km/u.s, copy=False),
                       differential_type=SphericalDifferential)
  
          # Update the obstime of the returned SkyCoord, and need to carry along
          # the frame attributes
          frattrs = {attrnm: getattr(self, attrnm)
                     for attrnm in self._extra_frameattr_names}
          frattrs['obstime'] = new_obstime
          return self.__class__(icrs2, **frattrs).transform_to(self.frame)
  
      def _is_name(self, string):
          """
          Returns whether a string is one of the aliases for the frame.
          """
          return (self.frame.name == string or
                  (isinstance(self.frame.name, list) and string in self.frame.name))
  
      def __getattr__(self, attr):
          """
          Overrides getattr to return coordinates that this can be transformed
          to, based on the alias attr in the master transform graph.
          """
          if '_sky_coord_frame' in self.__dict__:
              if self._is_name(attr):
                  return self  # Should this be a deepcopy of self?
  
              # Anything in the set of all possible frame_attr_names is handled
              # here. If the attr is relevant for the current frame then delegate
              # to self.frame otherwise get it from self._<attr>.
              if attr in frame_transform_graph.frame_attributes:
                  if attr in self.frame.get_frame_attr_names():
                      return getattr(self.frame, attr)
                  else:
                      return getattr(self, '_' + attr, None)
  
              # Some attributes might not fall in the above category but still
              # are available through self._sky_coord_frame.
              if not attr.startswith('_') and hasattr(self._sky_coord_frame, attr):
                  return getattr(self._sky_coord_frame, attr)
  
              # Try to interpret as a new frame for transforming.
              frame_cls = frame_transform_graph.lookup_name(attr)
              if frame_cls is not None and self.frame.is_transformable_to(frame_cls):
                  return self.transform_to(attr)
  
          # Fail
          raise AttributeError("'{}' object has no attribute '{}'"
                               .format(self.__class__.__name__, attr))
  
      def __setattr__(self, attr, val):
          # This is to make anything available through __getattr__ immutable
          if '_sky_coord_frame' in self.__dict__:
              if self._is_name(attr):
                  raise AttributeError(f"'{attr}' is immutable")
  
              if not attr.startswith('_') and hasattr(self._sky_coord_frame, attr):
                  setattr(self._sky_coord_frame, attr, val)
                  return
  
              frame_cls = frame_transform_graph.lookup_name(attr)
              if frame_cls is not None and self.frame.is_transformable_to(frame_cls):
                  raise AttributeError(f"'{attr}' is immutable")
  
          if attr in frame_transform_graph.frame_attributes:
              # All possible frame attributes can be set, but only via a private
              # variable.  See __getattr__ above.
              super().__setattr__('_' + attr, val)
              # Validate it
              frame_transform_graph.frame_attributes[attr].__get__(self)
              # And add to set of extra attributes
              self._extra_frameattr_names |= {attr}
  
          else:
              # Otherwise, do the standard Python attribute setting
              super().__setattr__(attr, val)
  
      def __delattr__(self, attr):
          # mirror __setattr__ above
          if '_sky_coord_frame' in self.__dict__:
              if self._is_name(attr):
                  raise AttributeError(f"'{attr}' is immutable")
  
              if not attr.startswith('_') and hasattr(self._sky_coord_frame,
                                                      attr):
                  delattr(self._sky_coord_frame, attr)
                  return
  
              frame_cls = frame_transform_graph.lookup_name(attr)
              if frame_cls is not None and self.frame.is_transformable_to(frame_cls):
                  raise AttributeError(f"'{attr}' is immutable")
  
          if attr in frame_transform_graph.frame_attributes:
              # All possible frame attributes can be deleted, but need to remove
              # the corresponding private variable.  See __getattr__ above.
              super().__delattr__('_' + attr)
              # Also remove it from the set of extra attributes
              self._extra_frameattr_names -= {attr}
  
          else:
              # Otherwise, do the standard Python attribute setting
              super().__delattr__(attr)
  
      @override__dir__
      def __dir__(self):
          """
          Override the builtin `dir` behavior to include:
          - Transforms available by aliases
          - Attribute / methods of the underlying self.frame object
          """
  
          # determine the aliases that this can be transformed to.
          dir_values = set()
          for name in frame_transform_graph.get_names():
              frame_cls = frame_transform_graph.lookup_name(name)
              if self.frame.is_transformable_to(frame_cls):
                  dir_values.add(name)
  
          # Add public attributes of self.frame
          dir_values.update(set(attr for attr in dir(self.frame) if not attr.startswith('_')))
  
          # Add all possible frame attributes
          dir_values.update(frame_transform_graph.frame_attributes.keys())
  
          return dir_values
  
      def __repr__(self):
          clsnm = self.__class__.__name__
          coonm = self.frame.__class__.__name__
          frameattrs = self.frame._frame_attrs_repr()
          if frameattrs:
              frameattrs = ': ' + frameattrs
  
          data = self.frame._data_repr()
          if data:
              data = ': ' + data
  
          return '<{clsnm} ({coonm}{frameattrs}){data}>'.format(**locals())
  
      def to_string(self, style='decimal', **kwargs):
          """
          A string representation of the coordinates.
  
          The default styles definitions are::
  
            'decimal': 'lat': {'decimal': True, 'unit': "deg"}
                       'lon': {'decimal': True, 'unit': "deg"}
            'dms': 'lat': {'unit': "deg"}
                   'lon': {'unit': "deg"}
            'hmsdms': 'lat': {'alwayssign': True, 'pad': True, 'unit': "deg"}
                      'lon': {'pad': True, 'unit': "hour"}
  
          See :meth:`~astropy.coordinates.Angle.to_string` for details and
          keyword arguments (the two angles forming the coordinates are are
          both :class:`~astropy.coordinates.Angle` instances). Keyword
          arguments have precedence over the style defaults and are passed
          to :meth:`~astropy.coordinates.Angle.to_string`.
  
          Parameters
          ----------
          style : {'hmsdms', 'dms', 'decimal'}
              The formatting specification to use. These encode the three most
              common ways to represent coordinates. The default is `decimal`.
          kwargs
              Keyword args passed to :meth:`~astropy.coordinates.Angle.to_string`.
          """
  
          sph_coord = self.frame.represent_as(SphericalRepresentation)
  
          styles = {'hmsdms': {'lonargs': {'unit': u.hour, 'pad': True},
                               'latargs': {'unit': u.degree, 'pad': True, 'alwayssign': True}},
                    'dms': {'lonargs': {'unit': u.degree},
                            'latargs': {'unit': u.degree}},
                    'decimal': {'lonargs': {'unit': u.degree, 'decimal': True},
                                'latargs': {'unit': u.degree, 'decimal': True}}
                    }
  
          lonargs = {}
          latargs = {}
  
          if style in styles:
              lonargs.update(styles[style]['lonargs'])
              latargs.update(styles[style]['latargs'])
          else:
              raise ValueError('Invalid style.  Valid options are: {}'.format(",".join(styles)))
  
          lonargs.update(kwargs)
          latargs.update(kwargs)
  
          if np.isscalar(sph_coord.lon.value):
              coord_string = (sph_coord.lon.to_string(**lonargs) +
                              " " + sph_coord.lat.to_string(**latargs))
          else:
              coord_string = []
              for lonangle, latangle in zip(sph_coord.lon.ravel(), sph_coord.lat.ravel()):
                  coord_string += [(lonangle.to_string(**lonargs) +
                                   " " + latangle.to_string(**latargs))]
              if len(sph_coord.shape) > 1:
                  coord_string = np.array(coord_string).reshape(sph_coord.shape)
  
          return coord_string
  
      def is_equivalent_frame(self, other):
          """
          Checks if this object's frame as the same as that of the ``other``
          object.
  
          To be the same frame, two objects must be the same frame class and have
          the same frame attributes. For two `SkyCoord` objects, *all* of the
          frame attributes have to match, not just those relevant for the object's
          frame.
  
          Parameters
          ----------
          other : SkyCoord or BaseCoordinateFrame
              The other object to check.
  
          Returns
          -------
          isequiv : bool
              True if the frames are the same, False if not.
  
          Raises
          ------
          TypeError
              If ``other`` isn't a `SkyCoord` or a `BaseCoordinateFrame` or subclass.
          """
          if isinstance(other, BaseCoordinateFrame):
              return self.frame.is_equivalent_frame(other)
          elif isinstance(other, SkyCoord):
              if other.frame.name != self.frame.name:
                  return False
  
              for fattrnm in frame_transform_graph.frame_attributes:
                  if not BaseCoordinateFrame._frameattr_equiv(getattr(self, fattrnm),
                                                              getattr(other, fattrnm)):
                      return False
              return True
          else:
              # not a BaseCoordinateFrame nor a SkyCoord object
              raise TypeError("Tried to do is_equivalent_frame on something that "
                              "isn't frame-like")
  
      # High-level convenience methods
      def separation(self, other):
          """
          Computes on-sky separation between this coordinate and another.
  
          .. note::
  
              If the ``other`` coordinate object is in a different frame, it is
              first transformed to the frame of this object. This can lead to
              unintuitive behavior if not accounted for. Particularly of note is
              that ``self.separation(other)`` and ``other.separation(self)`` may
              not give the same answer in this case.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          other : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The coordinate to get the separation to.
  
          Returns
          -------
          sep : `~astropy.coordinates.Angle`
              The on-sky separation between this and the ``other`` coordinate.
  
          Notes
          -----
          The separation is calculated using the Vincenty formula, which
          is stable at all locations, including poles and antipodes [1]_.
  
          .. [1] https://en.wikipedia.org/wiki/Great-circle_distance
  
          """
          from . import Angle
          from .angle_utilities import angular_separation
  
          if not self.is_equivalent_frame(other):
              try:
                  kwargs = {'merge_attributes': False} if isinstance(other, SkyCoord) else {}
                  other = other.transform_to(self, **kwargs)
              except TypeError:
                  raise TypeError('Can only get separation to another SkyCoord '
                                  'or a coordinate frame with data')
  
          lon1 = self.spherical.lon
          lat1 = self.spherical.lat
          lon2 = other.spherical.lon
          lat2 = other.spherical.lat
  
          # Get the separation as a Quantity, convert to Angle in degrees
          sep = angular_separation(lon1, lat1, lon2, lat2)
          return Angle(sep, unit=u.degree)
  
      def separation_3d(self, other):
          """
          Computes three dimensional separation between this coordinate
          and another.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          other : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The coordinate to get the separation to.
  
          Returns
          -------
          sep : `~astropy.coordinates.Distance`
              The real-space distance between these two coordinates.
  
          Raises
          ------
          ValueError
              If this or the other coordinate do not have distances.
          """
          if not self.is_equivalent_frame(other):
              try:
                  kwargs = {'merge_attributes': False} if isinstance(other, SkyCoord) else {}
                  other = other.transform_to(self, **kwargs)
              except TypeError:
                  raise TypeError('Can only get separation to another SkyCoord '
                                  'or a coordinate frame with data')
  
          if issubclass(self.data.__class__, UnitSphericalRepresentation):
              raise ValueError('This object does not have a distance; cannot '
                               'compute 3d separation.')
          if issubclass(other.data.__class__, UnitSphericalRepresentation):
              raise ValueError('The other object does not have a distance; '
                               'cannot compute 3d separation.')
  
          c1 = self.cartesian.without_differentials()
          c2 = other.cartesian.without_differentials()
          return Distance((c1 - c2).norm())
  
      def spherical_offsets_to(self, tocoord):
          r"""
          Computes angular offsets to go *from* this coordinate *to* another.
  
          Parameters
          ----------
          tocoord : `~astropy.coordinates.BaseCoordinateFrame`
              The coordinate to find the offset to.
  
          Returns
          -------
          lon_offset : `~astropy.coordinates.Angle`
              The angular offset in the longitude direction (i.e., RA for
              equatorial coordinates).
          lat_offset : `~astropy.coordinates.Angle`
              The angular offset in the latitude direction (i.e., Dec for
              equatorial coordinates).
  
          Raises
          ------
          ValueError
              If the ``tocoord`` is not in the same frame as this one. This is
              different from the behavior of the `separation`/`separation_3d`
              methods because the offset components depend critically on the
              specific choice of frame.
  
          Notes
          -----
          This uses the sky offset frame machinery, and hence will produce a new
          sky offset frame if one does not already exist for this object's frame
          class.
  
          See Also
          --------
          separation : for the *total* angular offset (not broken out into components).
          position_angle : for the direction of the offset.
  
          """
          if not self.is_equivalent_frame(tocoord):
              raise ValueError('Tried to use spherical_offsets_to with two non-matching frames!')
  
          aframe = self.skyoffset_frame()
          acoord = tocoord.transform_to(aframe)
  
          dlon = acoord.spherical.lon.view(Angle)
          dlat = acoord.spherical.lat.view(Angle)
          return dlon, dlat
  
      def directional_offset_by(self, position_angle, separation):
          """
          Computes coordinates at the given offset from this coordinate.
  
          Parameters
          ----------
          position_angle : `~astropy.coordinates.Angle`
              position_angle of offset
          separation : `~astropy.coordinates.Angle`
              offset angular separation
  
          Returns
          -------
          newpoints : `~astropy.coordinates.SkyCoord`
              The coordinates for the location that corresponds to offsetting by
              the given `position_angle` and `separation`.
  
          Notes
          -----
          Returned SkyCoord frame retains only the frame attributes that are for
          the resulting frame type.  (e.g. if the input frame is
          `~astropy.coordinates.ICRS`, an ``equinox`` value will be retained, but
          an ``obstime`` will not.)
  
          For a more complete set of transform offsets, use `~astropy.wcs.WCS`.
          `~astropy.coordinates.SkyCoord.skyoffset_frame()` can also be used to
          create a spherical frame with (lat=0, lon=0) at a reference point,
          approximating an xy cartesian system for small offsets. This method
          is distinct in that it is accurate on the sphere.
  
          See Also
          --------
          position_angle : inverse operation for the ``position_angle`` component
          separation : inverse operation for the ``separation`` component
  
          """
          from . import angle_utilities
  
          slat = self.represent_as(UnitSphericalRepresentation).lat
          slon = self.represent_as(UnitSphericalRepresentation).lon
  
          newlon, newlat = angle_utilities.offset_by(
              lon=slon, lat=slat,
              posang=position_angle, distance=separation)
  
          return SkyCoord(newlon, newlat, frame=self.frame)
  
      def match_to_catalog_sky(self, catalogcoord, nthneighbor=1):
          """
          Finds the nearest on-sky matches of this coordinate in a set of
          catalog coordinates.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          catalogcoord : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The base catalog in which to search for matches. Typically this
              will be a coordinate object that is an array (i.e.,
              ``catalogcoord.isscalar == False``)
          nthneighbor : int, optional
              Which closest neighbor to search for.  Typically ``1`` is
              desired here, as that is correct for matching one set of
              coordinates to another. The next likely use case is ``2``,
              for matching a coordinate catalog against *itself* (``1``
              is inappropriate because each point will find itself as the
              closest match).
  
          Returns
          -------
          idx : integer array
              Indices into ``catalogcoord`` to get the matched points for
              each of this object's coordinates. Shape matches this
              object.
          sep2d : `~astropy.coordinates.Angle`
              The on-sky separation between the closest match for each
              element in this object in ``catalogcoord``. Shape matches
              this object.
          dist3d : `~astropy.units.Quantity`
              The 3D distance between the closest match for each element
              in this object in ``catalogcoord``. Shape matches this
              object. Unless both this and ``catalogcoord`` have associated
              distances, this quantity assumes that all sources are at a
              distance of 1 (dimensionless).
  
          Notes
          -----
          This method requires `SciPy <https://www.scipy.org/>`_ to be
          installed or it will fail.
  
          See Also
          --------
          astropy.coordinates.match_coordinates_sky
          SkyCoord.match_to_catalog_3d
          """
          from .matching import match_coordinates_sky
  
          if (isinstance(catalogcoord, (SkyCoord, BaseCoordinateFrame))
                  and catalogcoord.has_data):
              self_in_catalog_frame = self.transform_to(catalogcoord)
          else:
              raise TypeError('Can only get separation to another SkyCoord or a '
                              'coordinate frame with data')
  
          res = match_coordinates_sky(self_in_catalog_frame, catalogcoord,
                                      nthneighbor=nthneighbor,
                                      storekdtree='_kdtree_sky')
          return res
  
      def match_to_catalog_3d(self, catalogcoord, nthneighbor=1):
          """
          Finds the nearest 3-dimensional matches of this coordinate to a set
          of catalog coordinates.
  
          This finds the 3-dimensional closest neighbor, which is only different
          from the on-sky distance if ``distance`` is set in this object or the
          ``catalogcoord`` object.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          catalogcoord : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The base catalog in which to search for matches. Typically this
              will be a coordinate object that is an array (i.e.,
              ``catalogcoord.isscalar == False``)
          nthneighbor : int, optional
              Which closest neighbor to search for.  Typically ``1`` is
              desired here, as that is correct for matching one set of
              coordinates to another.  The next likely use case is
              ``2``, for matching a coordinate catalog against *itself*
              (``1`` is inappropriate because each point will find
              itself as the closest match).
  
          Returns
          -------
          idx : integer array
              Indices into ``catalogcoord`` to get the matched points for
              each of this object's coordinates. Shape matches this
              object.
          sep2d : `~astropy.coordinates.Angle`
              The on-sky separation between the closest match for each
              element in this object in ``catalogcoord``. Shape matches
              this object.
          dist3d : `~astropy.units.Quantity`
              The 3D distance between the closest match for each element
              in this object in ``catalogcoord``. Shape matches this
              object.
  
          Notes
          -----
          This method requires `SciPy <https://www.scipy.org/>`_ to be
          installed or it will fail.
  
          See Also
          --------
          astropy.coordinates.match_coordinates_3d
          SkyCoord.match_to_catalog_sky
          """
          from .matching import match_coordinates_3d
  
          if (isinstance(catalogcoord, (SkyCoord, BaseCoordinateFrame))
                  and catalogcoord.has_data):
              self_in_catalog_frame = self.transform_to(catalogcoord)
          else:
              raise TypeError('Can only get separation to another SkyCoord or a '
                              'coordinate frame with data')
  
          res = match_coordinates_3d(self_in_catalog_frame, catalogcoord,
                                     nthneighbor=nthneighbor,
                                     storekdtree='_kdtree_3d')
  
          return res
  
      def search_around_sky(self, searcharoundcoords, seplimit):
          """
          Searches for all coordinates in this object around a supplied set of
          points within a given on-sky separation.
  
          This is intended for use on `~astropy.coordinates.SkyCoord` objects
          with coordinate arrays, rather than a scalar coordinate.  For a scalar
          coordinate, it is better to use
          `~astropy.coordinates.SkyCoord.separation`.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          searcharoundcoords : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The coordinates to search around to try to find matching points in
              this `SkyCoord`. This should be an object with array coordinates,
              not a scalar coordinate object.
          seplimit : `~astropy.units.Quantity` with angle units
              The on-sky separation to search within.
  
          Returns
          -------
          idxsearcharound : integer array
              Indices into ``searcharoundcoords`` that match the
              corresponding elements of ``idxself``. Shape matches
              ``idxself``.
          idxself : integer array
              Indices into ``self`` that match the
              corresponding elements of ``idxsearcharound``. Shape matches
              ``idxsearcharound``.
          sep2d : `~astropy.coordinates.Angle`
              The on-sky separation between the coordinates. Shape matches
              ``idxsearcharound`` and ``idxself``.
          dist3d : `~astropy.units.Quantity`
              The 3D distance between the coordinates. Shape matches
              ``idxsearcharound`` and ``idxself``.
  
          Notes
          -----
          This method requires `SciPy <https://www.scipy.org/>`_ (>=0.12.0) to be
          installed or it will fail.
  
          In the current implementation, the return values are always sorted in
          the same order as the ``searcharoundcoords`` (so ``idxsearcharound`` is
          in ascending order).  This is considered an implementation detail,
          though, so it could change in a future release.
  
          See Also
          --------
          astropy.coordinates.search_around_sky
          SkyCoord.search_around_3d
          """
          from .matching import search_around_sky
  
          return search_around_sky(searcharoundcoords, self, seplimit,
                                   storekdtree='_kdtree_sky')
  
      def search_around_3d(self, searcharoundcoords, distlimit):
          """
          Searches for all coordinates in this object around a supplied set of
          points within a given 3D radius.
  
          This is intended for use on `~astropy.coordinates.SkyCoord` objects
          with coordinate arrays, rather than a scalar coordinate.  For a scalar
          coordinate, it is better to use
          `~astropy.coordinates.SkyCoord.separation_3d`.
  
          For more on how to use this (and related) functionality, see the
          examples in :doc:`/coordinates/matchsep`.
  
          Parameters
          ----------
          searcharoundcoords : `~astropy.coordinates.SkyCoord` or `~astropy.coordinates.BaseCoordinateFrame`
              The coordinates to search around to try to find matching points in
              this `SkyCoord`. This should be an object with array coordinates,
              not a scalar coordinate object.
          distlimit : `~astropy.units.Quantity` with distance units
              The physical radius to search within.
  
          Returns
          -------
          idxsearcharound : integer array
              Indices into ``searcharoundcoords`` that match the
              corresponding elements of ``idxself``. Shape matches
              ``idxself``.
          idxself : integer array
              Indices into ``self`` that match the
              corresponding elements of ``idxsearcharound``. Shape matches
              ``idxsearcharound``.
          sep2d : `~astropy.coordinates.Angle`
              The on-sky separation between the coordinates. Shape matches
              ``idxsearcharound`` and ``idxself``.
          dist3d : `~astropy.units.Quantity`
              The 3D distance between the coordinates. Shape matches
              ``idxsearcharound`` and ``idxself``.
  
          Notes
          -----
          This method requires `SciPy <https://www.scipy.org/>`_ (>=0.12.0) to be
          installed or it will fail.
  
          In the current implementation, the return values are always sorted in
          the same order as the ``searcharoundcoords`` (so ``idxsearcharound`` is
          in ascending order).  This is considered an implementation detail,
          though, so it could change in a future release.
  
          See Also
          --------
          astropy.coordinates.search_around_3d
          SkyCoord.search_around_sky
          """
          from .matching import search_around_3d
  
          return search_around_3d(searcharoundcoords, self, distlimit,
                                  storekdtree='_kdtree_3d')
  
      def position_angle(self, other):
          """
          Computes the on-sky position angle (East of North) between this
          `SkyCoord` and another.
  
          Parameters
          ----------
          other : `SkyCoord`
              The other coordinate to compute the position angle to.  It is
              treated as the "head" of the vector of the position angle.
  
          Returns
          -------
          pa : `~astropy.coordinates.Angle`
              The (positive) position angle of the vector pointing from ``self``
              to ``other``.  If either ``self`` or ``other`` contain arrays, this
              will be an array following the appropriate `numpy` broadcasting
              rules.
  
          Examples
          --------
  
          >>> c1 = SkyCoord(0*u.deg, 0*u.deg)
          >>> c2 = SkyCoord(1*u.deg, 0*u.deg)
          >>> c1.position_angle(c2).degree
          90.0
          >>> c3 = SkyCoord(1*u.deg, 1*u.deg)
          >>> c1.position_angle(c3).degree  # doctest: +FLOAT_CMP
          44.995636455344844
          """
          from . import angle_utilities
  
          if not self.is_equivalent_frame(other):
              try:
                  other = other.transform_to(self, merge_attributes=False)
              except TypeError:
                  raise TypeError('Can only get position_angle to another '
                                  'SkyCoord or a coordinate frame with data')
  
          slat = self.represent_as(UnitSphericalRepresentation).lat
          slon = self.represent_as(UnitSphericalRepresentation).lon
          olat = other.represent_as(UnitSphericalRepresentation).lat
          olon = other.represent_as(UnitSphericalRepresentation).lon
  
          return angle_utilities.position_angle(slon, slat, olon, olat)
  
      def skyoffset_frame(self, rotation=None):
          """
          Returns the sky offset frame with this `SkyCoord` at the origin.
  
          Returns
          -------
          astrframe : `~astropy.coordinates.SkyOffsetFrame`
              A sky offset frame of the same type as this `SkyCoord` (e.g., if
              this object has an ICRS coordinate, the resulting frame is
              SkyOffsetICRS, with the origin set to this object)
          rotation : `~astropy.coordinates.Angle` or `~astropy.units.Quantity` with angle units
              The final rotation of the frame about the ``origin``. The sign of
              the rotation is the left-hand rule. That is, an object at a
              particular position angle in the un-rotated system will be sent to
              the positive latitude (z) direction in the final frame.
          """
          return SkyOffsetFrame(origin=self, rotation=rotation)
  
      def get_constellation(self, short_name=False, constellation_list='iau'):
          """
          Determines the constellation(s) of the coordinates this `SkyCoord`
          contains.
  
          Parameters
          ----------
          short_name : bool
              If True, the returned names are the IAU-sanctioned abbreviated
              names.  Otherwise, full names for the constellations are used.
          constellation_list : str
              The set of constellations to use.  Currently only ``'iau'`` is
              supported, meaning the 88 "modern" constellations endorsed by the IAU.
  
          Returns
          -------
          constellation : str or string array
              If this is a scalar coordinate, returns the name of the
              constellation.  If it is an array `SkyCoord`, it returns an array of
              names.
  
          Notes
          -----
          To determine which constellation a point on the sky is in, this first
          precesses to B1875, and then uses the Delporte boundaries of the 88
          modern constellations, as tabulated by
          `Roman 1987 <http://cdsarc.u-strasbg.fr/viz-bin/Cat?VI/42>`_.
  
          See Also
          --------
          astropy.coordinates.get_constellation
          """
          from .funcs import get_constellation
  
          # because of issue #7028, the conversion to a PrecessedGeocentric
          # system fails in some cases.  Work around is to  drop the velocities.
          # they are not needed here since only position infromation is used
          extra_frameattrs = {nm: getattr(self, nm)
                              for nm in self._extra_frameattr_names}
          novel = SkyCoord(self.realize_frame(self.data.without_differentials()),
                           **extra_frameattrs)
          return get_constellation(novel, short_name, constellation_list)
  
          # the simpler version below can be used when gh-issue #7028 is resolved
          # return get_constellation(self, short_name, constellation_list)
  
      # WCS pixel to/from sky conversions
      def to_pixel(self, wcs, origin=0, mode='all'):
          """
          Convert this coordinate to pixel coordinates using a `~astropy.wcs.WCS`
          object.
  
          Parameters
          ----------
          wcs : `~astropy.wcs.WCS`
              The WCS to use for convert
          origin : int
              Whether to return 0 or 1-based pixel coordinates.
          mode : 'all' or 'wcs'
              Whether to do the transformation including distortions (``'all'``) or
              only including only the core WCS transformation (``'wcs'``).
  
          Returns
          -------
          xp, yp : `numpy.ndarray`
              The pixel coordinates
  
          See Also
          --------
          astropy.wcs.utils.skycoord_to_pixel : the implementation of this method
          """
          from astropy.wcs.utils import skycoord_to_pixel
          return skycoord_to_pixel(self, wcs=wcs, origin=origin, mode=mode)
  
      @classmethod
      def from_pixel(cls, xp, yp, wcs, origin=0, mode='all'):
          """
          Create a new `SkyCoord` from pixel coordinates using an
          `~astropy.wcs.WCS` object.
  
          Parameters
          ----------
          xp, yp : float or `numpy.ndarray`
              The coordinates to convert.
          wcs : `~astropy.wcs.WCS`
              The WCS to use for convert
          origin : int
              Whether to return 0 or 1-based pixel coordinates.
          mode : 'all' or 'wcs'
              Whether to do the transformation including distortions (``'all'``) or
              only including only the core WCS transformation (``'wcs'``).
  
          Returns
          -------
          coord : an instance of this class
              A new object with sky coordinates corresponding to the input ``xp``
              and ``yp``.
  
          See Also
          --------
          to_pixel : to do the inverse operation
          astropy.wcs.utils.pixel_to_skycoord : the implementation of this method
          """
          from astropy.wcs.utils import pixel_to_skycoord
          return pixel_to_skycoord(xp, yp, wcs=wcs, origin=origin, mode=mode, cls=cls)
  
      def contained_by(self, wcs, image=None, **kwargs):
          """
          Determines if the SkyCoord is contained in the given wcs footprint.
  
          Parameters
          ----------
          wcs : `~astropy.wcs.WCS`
              The coordinate to check if it is within the wcs coordinate.
          image : array
              Optional.  The image associated with the wcs object that the cooordinate
              is being checked against. If not given the naxis keywords will be used
              to determine if the coordinate falls within the wcs footprint.
          **kwargs :
             Additional arguments to pass to `~astropy.coordinates.SkyCoord.to_pixel`
  
          Returns
          -------
          response : bool
             True means the WCS footprint contains the coordinate, False means it does not.
          """
  
          if image is not None:
              ymax, xmax = image.shape
          else:
              xmax, ymax = wcs._naxis
  
          import warnings
          with warnings.catch_warnings():
              #  Suppress warnings since they just mean we didn't find the coordinate
              warnings.simplefilter("ignore")
              try:
                  x, y = self.to_pixel(wcs, **kwargs)
              except Exception:
                  return False
  
          return (x < xmax) & (x > 0) & (y < ymax) & (y > 0)
  
      def radial_velocity_correction(self, kind='barycentric', obstime=None,
                                     location=None):
          """
          Compute the correction required to convert a radial velocity at a given
          time and place on the Earth's Surface to a barycentric or heliocentric
          velocity.
  
          Parameters
          ----------
          kind : str
              The kind of velocity correction.  Must be 'barycentric' or
              'heliocentric'.
          obstime : `~astropy.time.Time` or None, optional
              The time at which to compute the correction.  If `None`, the
              ``obstime`` frame attribute on the `SkyCoord` will be used.
          location : `~astropy.coordinates.EarthLocation` or None, optional
              The observer location at which to compute the correction.  If
              `None`, the  ``location`` frame attribute on the passed-in
              ``obstime`` will be used, and if that is None, the ``location``
              frame attribute on the `SkyCoord` will be used.
  
          Raises
          ------
          ValueError
              If either ``obstime`` or ``location`` are passed in (not ``None``)
              when the frame attribute is already set on this `SkyCoord`.
          TypeError
              If ``obstime`` or ``location`` aren't provided, either as arguments
              or as frame attributes.
  
          Returns
          -------
          vcorr : `~astropy.units.Quantity` with velocity units
              The  correction with a positive sign.  I.e., *add* this
              to an observed radial velocity to get the barycentric (or
              heliocentric) velocity. If m/s precision or better is needed,
              see the notes below.
  
          Notes
          -----
          The barycentric correction is calculated to higher precision than the
          heliocentric correction and includes additional physics (e.g time dilation).
          Use barycentric corrections if m/s precision is required.
  
          The algorithm here is sufficient to perform corrections at the mm/s level, but
          care is needed in application. The barycentric correction returned uses the optical
          approximation v = z * c. Strictly speaking, the barycentric correction is
          multiplicative and should be applied as::
  
            >>> from astropy.time import Time
            >>> from astropy.coordinates import SkyCoord, EarthLocation
            >>> from astropy.constants import c
            >>> t = Time(56370.5, format='mjd', scale='utc')
            >>> loc = EarthLocation('149d33m00.5s','-30d18m46.385s',236.87*u.m)
            >>> sc = SkyCoord(1*u.deg, 2*u.deg)
            >>> vcorr = sc.radial_velocity_correction(kind='barycentric', obstime=t, location=loc)  # doctest: +REMOTE_DATA
            >>> rv = rv + vcorr + rv * vcorr / c  # doctest: +SKIP
  
          Also note that this method returns the correction velocity in the so-called
          *optical convention*::
  
            >>> vcorr = zb * c  # doctest: +SKIP
  
          where ``zb`` is the barycentric correction redshift as defined in section 3
          of Wright & Eastman (2014). The application formula given above follows from their
          equation (11) under assumption that the radial velocity ``rv`` has also been defined
          using the same optical convention. Note, this can be regarded as a matter of
          velocity definition and does not by itself imply any loss of accuracy, provided
          sufficient care has been taken during interpretation of the results. If you need
          the barycentric correction expressed as the full relativistic velocity (e.g., to provide
          it as the input to another software which performs the application), the
          following recipe can be used::
  
            >>> zb = vcorr / c  # doctest: +REMOTE_DATA
            >>> zb_plus_one_squared = (zb + 1) ** 2  # doctest: +REMOTE_DATA
            >>> vcorr_rel = c * (zb_plus_one_squared - 1) / (zb_plus_one_squared + 1)  # doctest: +REMOTE_DATA
  
          or alternatively using just equivalencies::
  
            >>> vcorr_rel = vcorr.to(u.Hz, u.doppler_optical(1*u.Hz)).to(vcorr.unit, u.doppler_relativistic(1*u.Hz))  # doctest: +REMOTE_DATA
  
          See also `~astropy.units.equivalencies.doppler_optical`,
          `~astropy.units.equivalencies.doppler_radio`, and
          `~astropy.units.equivalencies.doppler_relativistic` for more information on
          the velocity conventions.
  
          The default is for this method to use the builtin ephemeris for
          computing the sun and earth location.  Other ephemerides can be chosen
          by setting the `~astropy.coordinates.solar_system_ephemeris` variable,
          either directly or via ``with`` statement.  For example, to use the JPL
          ephemeris, do::
  
            >>> from astropy.coordinates import solar_system_ephemeris
            >>> sc = SkyCoord(1*u.deg, 2*u.deg)
            >>> with solar_system_ephemeris.set('jpl'):  # doctest: +REMOTE_DATA
            ...     rv += sc.radial_velocity_correction(obstime=t, location=loc)  # doctest: +SKIP
  
          """
          # has to be here to prevent circular imports
          from .solar_system import get_body_barycentric_posvel
  
          # location validation
          timeloc = getattr(obstime, 'location', None)
          if location is None:
              if self.location is not None:
                  location = self.location
                  if timeloc is not None:
                      raise ValueError('`location` cannot be in both the '
                                       'passed-in `obstime` and this `SkyCoord` '
                                       'because it is ambiguous which is meant '
                                       'for the radial_velocity_correction.')
              elif timeloc is not None:
                  location = timeloc
              else:
                  raise TypeError('Must provide a `location` to '
                                  'radial_velocity_correction, either as a '
                                  'SkyCoord frame attribute, as an attribute on '
                                  'the passed in `obstime`, or in the method '
                                  'call.')
  
          elif self.location is not None or timeloc is not None:
              raise ValueError('Cannot compute radial velocity correction if '
                               '`location` argument is passed in and there is '
                               'also a  `location` attribute on this SkyCoord or '
                               'the passed-in `obstime`.')
  
          # obstime validation
          coo_at_rv_obstime = self  # assume we need no space motion for now
          if obstime is None:
              obstime = self.obstime
              if obstime is None:
                  raise TypeError('Must provide an `obstime` to '
                                  'radial_velocity_correction, either as a '
                                  'SkyCoord frame attribute or in the method '
                                  'call.')
          elif self.obstime is not None and self.frame.data.differentials:
              # we do need space motion after all
              coo_at_rv_obstime = self.apply_space_motion(obstime)
          elif self.obstime is None:
              # warn the user if the object has differentials set
              if 's' in self.data.differentials:
                  warnings.warn(
                      "SkyCoord has space motion, and therefore the specified "
                      "position of the SkyCoord may not be the same as "
                      "the `obstime` for the radial velocity measurement. "
                      "This may affect the rv correction at the order of km/s"
                      "for very high proper motions sources. If you wish to "
                      "apply space motion of the SkyCoord to correct for this"
                      "the `obstime` attribute of the SkyCoord must be set",
                      AstropyUserWarning
                  )
  
          pos_earth, v_earth = get_body_barycentric_posvel('earth', obstime)
          if kind == 'barycentric':
              v_origin_to_earth = v_earth
          elif kind == 'heliocentric':
              v_sun = get_body_barycentric_posvel('sun', obstime)[1]
              v_origin_to_earth = v_earth - v_sun
          else:
              raise ValueError("`kind` argument to radial_velocity_correction must "
                               "be 'barycentric' or 'heliocentric', but got "
                               "'{}'".format(kind))
  
          gcrs_p, gcrs_v = location.get_gcrs_posvel(obstime)
          # transforming to GCRS is not the correct thing to do here, since we don't want to
          # include aberration (or light deflection)? Instead, only apply parallax if necessary
          icrs_cart = coo_at_rv_obstime.icrs.cartesian
          icrs_cart_novel = icrs_cart.without_differentials()
          if self.data.__class__ is UnitSphericalRepresentation:
              targcart = icrs_cart_novel
          else:
              # skycoord has distances so apply parallax
              obs_icrs_cart = pos_earth + gcrs_p
              targcart = icrs_cart_novel - obs_icrs_cart
              targcart /= targcart.norm()
  
          if kind == 'barycentric':
              beta_obs = (v_origin_to_earth + gcrs_v) / speed_of_light
              gamma_obs = 1 / np.sqrt(1 - beta_obs.norm()**2)
              gr = location.gravitational_redshift(obstime)
              # barycentric redshift according to eq 28 in Wright & Eastmann (2014),
              # neglecting Shapiro delay and effects of the star's own motion
              zb = gamma_obs * (1 + beta_obs.dot(targcart)) / (1 + gr/speed_of_light)
              # try and get terms corresponding to stellar motion.
              if icrs_cart.differentials:
                  try:
                      ro = self.icrs.cartesian
                      beta_star = ro.differentials['s'].to_cartesian() / speed_of_light
                      # ICRS unit vector at coordinate epoch
                      ro = ro.without_differentials()
                      ro /= ro.norm()
                      zb *= (1 + beta_star.dot(ro)) / (1 + beta_star.dot(targcart))
                  except u.UnitConversionError:
                      warnings.warn("SkyCoord contains some velocity information, but not enough to "
                                    "calculate the full space motion of the source, and so this has "
                                    "been ignored for the purposes of calculating the radial velocity "
                                    "correction. This can lead to errors on the order of metres/second.",
                                    AstropyUserWarning)
  
              zb = zb - 1
              return zb * speed_of_light
          else:
              # do a simpler correction ignoring time dilation and gravitational redshift
              # this is adequate since Heliocentric corrections shouldn't be used if
              # cm/s precision is required.
              return targcart.dot(v_origin_to_earth + gcrs_v)
  
      # Table interactions
      @classmethod
      def guess_from_table(cls, table, **coord_kwargs):
          r"""
          A convenience method to create and return a new `SkyCoord` from the data
          in an astropy Table.
  
          This method matches table columns that start with the case-insensitive
          names of the the components of the requested frames, if they are also
          followed by a non-alphanumeric character. It will also match columns
          that *end* with the component name if a non-alphanumeric character is
          *before* it.
  
          For example, the first rule means columns with names like
          ``'RA[J2000]'`` or ``'ra'`` will be interpreted as ``ra`` attributes for
          `~astropy.coordinates.ICRS` frames, but ``'RAJ2000'`` or ``'radius'``
          are *not*. Similarly, the second rule applied to the
          `~astropy.coordinates.Galactic` frame means that a column named
          ``'gal_l'`` will be used as the the ``l`` component, but ``gall`` or
          ``'fill'`` will not.
  
          The definition of alphanumeric here is based on Unicode's definition
          of alphanumeric, except without ``_`` (which is normally considered
          alphanumeric).  So for ASCII, this means the non-alphanumeric characters
          are ``<space>_!"#$%&'()*+,-./\:;<=>?@[]^`{|}~``).
  
          Parameters
          ----------
          table : astropy.Table
              The table to load data from.
          coord_kwargs
              Any additional keyword arguments are passed directly to this class's
              constructor.
  
          Returns
          -------
          newsc : same as this class
              The new `SkyCoord` (or subclass) object.
          """
          _frame_cls, _frame_kwargs = _get_frame_without_data([], coord_kwargs)
          frame = _frame_cls(**_frame_kwargs)
          coord_kwargs['frame'] = coord_kwargs.get('frame', frame)
  
          comp_kwargs = {}
          for comp_name in frame.representation_component_names:
              # this matches things like 'ra[...]'' but *not* 'rad'.
              # note that the "_" must be in there explicitly, because
              # "alphanumeric" usually includes underscores.
              starts_with_comp = comp_name + r'(\W|\b|_)'
              # this part matches stuff like 'center_ra', but *not*
              # 'aura'
              ends_with_comp = r'.*(\W|\b|_)' + comp_name + r'\b'
              # the final regex ORs together the two patterns
              rex = re.compile('(' + starts_with_comp + ')|(' + ends_with_comp + ')',
                               re.IGNORECASE | re.UNICODE)
  
              for col_name in table.colnames:
                  if rex.match(col_name):
                      if comp_name in comp_kwargs:
                          oldname = comp_kwargs[comp_name].name
                          msg = ('Found at least two matches for  component "{0}"'
                                 ': "{1}" and "{2}". Cannot continue with this '
                                 'ambiguity.')
                          raise ValueError(msg.format(comp_name, oldname, col_name))
                      comp_kwargs[comp_name] = table[col_name]
  
          for k, v in comp_kwargs.items():
              if k in coord_kwargs:
                  raise ValueError('Found column "{}" in table, but it was '
                                   'already provided as "{}" keyword to '
                                   'guess_from_table function.'.format(v.name, k))
              else:
                  coord_kwargs[k] = v
  
          return cls(**coord_kwargs)
  
      # Name resolve
      @classmethod
      def from_name(cls, name, frame='icrs', parse=False, cache=True):
          """
          Given a name, query the CDS name resolver to attempt to retrieve
          coordinate information for that object. The search database, sesame
          url, and  query timeout can be set through configuration items in
          ``astropy.coordinates.name_resolve`` -- see docstring for
          `~astropy.coordinates.get_icrs_coordinates` for more
          information.
  
          Parameters
          ----------
          name : str
              The name of the object to get coordinates for, e.g. ``'M42'``.
          frame : str or `BaseCoordinateFrame` class or instance
              The frame to transform the object to.
          parse: bool
              Whether to attempt extracting the coordinates from the name by
              parsing with a regex. For objects catalog names that have
              J-coordinates embedded in their names, e.g.,
              'CRTS SSS100805 J194428-420209', this may be much faster than a
              Sesame query for the same object name. The coordinates extracted
              in this way may differ from the database coordinates by a few
              deci-arcseconds, so only use this option if you do not need
              sub-arcsecond accuracy for coordinates.
          cache : bool, optional
              Determines whether to cache the results or not. To update or
              overwrite an existing value, pass ``cache='update'``.
  
          Returns
          -------
          coord : SkyCoord
              Instance of the SkyCoord class.
          """
  
          from .name_resolve import get_icrs_coordinates
  
          icrs_coord = get_icrs_coordinates(name, parse, cache=cache)
          icrs_sky_coord = cls(icrs_coord)
          if frame in ('icrs', icrs_coord.__class__):
              return icrs_sky_coord
          else:
              return icrs_sky_coord.transform_to(frame)
  
apis: numpy.zeros numpy.logical_not numpy.all numpy.array numpy.isscalar