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# Source code for astropy.coordinates.builtin_frames.galactocentric

    # Licensed under a 3-clause BSD style license - see LICENSE.rst

    import copy
    from collections.abc import MappingView
    from types import MappingProxyType

    import numpy as np

    from astropy import units as u
    from astropy.coordinates import representation as r
    from astropy.coordinates.angles import Angle
    from astropy.coordinates.attributes import (
        CoordinateAttribute,
        DifferentialAttribute,
        QuantityAttribute,
    )
    from astropy.coordinates.baseframe import (
        BaseCoordinateFrame,
        base_doc,
        frame_transform_graph,
    )
    from astropy.coordinates.errors import ConvertError
    from astropy.coordinates.matrix_utilities import matrix_transpose, rotation_matrix
    from astropy.coordinates.transformations import AffineTransform
    from astropy.utils.decorators import classproperty, deprecated, format_doc
    from astropy.utils.state import ScienceState

    from .icrs import ICRS

    __all__ = ["Galactocentric"]

    # Measured by minimizing the difference between a plane of coordinates along
    #   l=0, b=[-90,90] and the Galactocentric x-z plane
    # This is not used directly, but accessed via `get_roll0`.  We define it here to
    # prevent having to create new Angle objects every time `get_roll0` is called.
    _ROLL0 = Angle(58.5986320306 * u.degree)

    class _StateProxy(MappingView):
        """
        `~collections.abc.MappingView` with a read-only ``getitem`` through
        `~types.MappingProxyType`.

        """

        def __init__(self, mapping):
            super().__init__(mapping)
            self._mappingproxy = MappingProxyType(self._mapping)  # read-only

        def __getitem__(self, key):
            """Read-only ``getitem``."""
            return self._mappingproxy[key]

        def __deepcopy__(self, memo):
            return copy.deepcopy(self._mapping, memo=memo)

    class galactocentric_frame_defaults(ScienceState):
        """Global setting of default values for the frame attributes in the `~astropy.coordinates.Galactocentric` frame.

        These constancts may be updated in future versions of ``astropy``. Note
        that when using `~astropy.coordinates.Galactocentric`, changing values
        here will not affect any attributes that are set explicitly by passing
        values in to the `~astropy.coordinates.Galactocentric`
        initializer. Modifying these defaults will only affect the frame attribute
        values when using the frame as, e.g., ``Galactocentric`` or
        ``Galactocentric()`` with no explicit arguments.

        This class controls the parameter settings by specifying a string name,
        with the following pre-specified options:

        - 'pre-v4.0': The current default value, which sets the default frame
          attribute values to their original (pre-astropy-v4.0) values.
        - 'v4.0': The attribute values as updated in Astropy version 4.0.
        - 'latest': An alias of the most recent parameter set (currently: 'v4.0')

        Alternatively, user-defined parameter settings may be registered, with
        :meth:`~astropy.coordinates.galactocentric_frame_defaults.register`,
        and used identically as pre-specified parameter sets. At minimum,
        registrations must have unique names and a dictionary of parameters
        with keys "galcen_coord", "galcen_distance", "galcen_v_sun", "z_sun",
        "roll". See examples below.

        This class also tracks the references for all parameter values in the
        attribute ``references``, as well as any further information the registry.
        The pre-specified options can be extended to include similar
        state information as user-defined parameter settings -- for example, to add
        parameter uncertainties.

        The preferred method for getting a parameter set and metadata, by name, is
        :meth:`~astropy.coordinates.galactocentric_frame_defaults.get_from_registry`
        since it ensures the immutability of the registry.

        See :ref:`astropy:astropy-coordinates-galactocentric-defaults` for more
        information.

        Examples
        --------
        The default `~astropy.coordinates.Galactocentric` frame parameters can be
        modified globally::

            >>> from astropy.coordinates import galactocentric_frame_defaults
            >>> _ = galactocentric_frame_defaults.set('v4.0') # doctest: +SKIP
            >>> Galactocentric() # doctest: +SKIP
            <Galactocentric Frame (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.122 kpc, galcen_v_sun=(12.9, 245.6, 7.78) km / s, z_sun=20.8 pc, roll=0.0 deg)>
            >>> _ = galactocentric_frame_defaults.set('pre-v4.0') # doctest: +SKIP
            >>> Galactocentric() # doctest: +SKIP
            <Galactocentric Frame (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.3 kpc, galcen_v_sun=(11.1, 232.24, 7.25) km / s, z_sun=27.0 pc, roll=0.0 deg)>

        The default parameters can also be updated by using this class as a context
        manager::

            >>> with galactocentric_frame_defaults.set('pre-v4.0'):
            ...     print(Galactocentric()) # doctest: +FLOAT_CMP
            <Galactocentric Frame (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.3 kpc, galcen_v_sun=(11.1, 232.24, 7.25) km / s, z_sun=27.0 pc, roll=0.0 deg)>

        Again, changing the default parameter values will not affect frame
        attributes that are explicitly specified::

            >>> import astropy.units as u
            >>> with galactocentric_frame_defaults.set('pre-v4.0'):
            ...     print(Galactocentric(galcen_distance=8.0*u.kpc)) # doctest: +FLOAT_CMP
            <Galactocentric Frame (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.0 kpc, galcen_v_sun=(11.1, 232.24, 7.25) km / s, z_sun=27.0 pc, roll=0.0 deg)>

        Additional parameter sets may be registered, for instance to use the
        Dehnen & Binney (1998) measurements of the solar motion. We can also
        add metadata, such as the 1-sigma errors. In this example we will modify
        the required key "parameters", change the recommended key "references" to
        match "parameters", and add the extra key "error" (any key can be added)::

            >>> state = galactocentric_frame_defaults.get_from_registry("v4.0")
            >>> state["parameters"]["galcen_v_sun"] = (10.00, 225.25, 7.17) * (u.km / u.s)
            >>> state["references"]["galcen_v_sun"] = "https://ui.adsabs.harvard.edu/full/1998MNRAS.298..387D"
            >>> state["error"] = {"galcen_v_sun": (0.36, 0.62, 0.38) * (u.km / u.s)}
            >>> galactocentric_frame_defaults.register(name="DB1998", **state)

        Just as in the previous examples, the new parameter set can be retrieved with::

            >>> state = galactocentric_frame_defaults.get_from_registry("DB1998")
            >>> print(state["error"]["galcen_v_sun"])  # doctest: +FLOAT_CMP
            [0.36 0.62 0.38] km / s

        """

        _latest_value = "v4.0"
        _value = None
        _references = None
        _state = dict()  # all other data

        # Note: _StateProxy() produces read-only view of enclosed mapping.
        _registry = {
            "v4.0": {
                "parameters": _StateProxy(
                    {
                        "galcen_coord": ICRS(
                            ra=266.4051 * u.degree, dec=-28.936175 * u.degree
                        ),
                        "galcen_distance": 8.122 * u.kpc,
                        "galcen_v_sun": r.CartesianDifferential(
                            [12.9, 245.6, 7.78] * (u.km / u.s)
                        ),
                        "z_sun": 20.8 * u.pc,
                        "roll": 0 * u.deg,
                    }
                ),
                "references": _StateProxy(
                    {
                        "galcen_coord": (
                            "https://ui.adsabs.harvard.edu/abs/2004ApJ...616..872R"
                        ),
                        "galcen_distance": (
                            "https://ui.adsabs.harvard.edu/abs/2018A%26A...615L..15G"
                        ),
                        "galcen_v_sun": [
                            "https://ui.adsabs.harvard.edu/abs/2018RNAAS...2..210D",
                            "https://ui.adsabs.harvard.edu/abs/2018A%26A...615L..15G",
                            "https://ui.adsabs.harvard.edu/abs/2004ApJ...616..872R",
                        ],
                        "z_sun": "https://ui.adsabs.harvard.edu/abs/2019MNRAS.482.1417B",
                        "roll": None,
                    }
                ),
            },
            "pre-v4.0": {
                "parameters": _StateProxy(
                    {
                        "galcen_coord": ICRS(
                            ra=266.4051 * u.degree, dec=-28.936175 * u.degree
                        ),
                        "galcen_distance": 8.3 * u.kpc,
                        "galcen_v_sun": r.CartesianDifferential(
                            [11.1, 220 + 12.24, 7.25] * (u.km / u.s)
                        ),
                        "z_sun": 27.0 * u.pc,
                        "roll": 0 * u.deg,
                    }
                ),
                "references": _StateProxy(
                    {
                        "galcen_coord": (
                            "https://ui.adsabs.harvard.edu/abs/2004ApJ...616..872R"
                        ),
                        "galcen_distance": (
                            "https://ui.adsabs.harvard.edu/#abs/2009ApJ...692.1075G"
                        ),
                        "galcen_v_sun": [
                            "https://ui.adsabs.harvard.edu/#abs/2010MNRAS.403.1829S",
                            "https://ui.adsabs.harvard.edu/#abs/2015ApJS..216...29B",
                        ],
                        "z_sun": "https://ui.adsabs.harvard.edu/#abs/2001ApJ...553..184C",
                        "roll": None,
                    }
                ),
            },
        }

        @classproperty  # read-only
        def parameters(cls):
            return cls._value

        @classproperty  # read-only
        def references(cls):
            return cls._references

        @classmethod
        def get_from_registry(cls, name: str):
            """
            Return Galactocentric solar parameters and metadata given string names
            for the parameter sets. This method ensures the returned state is a
            mutable copy, so any changes made do not affect the registry state.

            Returns
            -------
            state : dict
                Copy of the registry for the string name.
                Should contain, at minimum:

                - "parameters": dict
                    Galactocentric solar parameters
                - "references" : Dict[str, Union[str, Sequence[str]]]
                    References for "parameters".
                    Fields are str or sequence of str.

            Raises
            ------
            KeyError
                If invalid string input to registry
                to retrieve solar parameters for Galactocentric frame.

            """
            # Resolve the meaning of 'latest': latest parameter set is from v4.0
            # - update this as newer parameter choices are added
            if name == "latest":
                name = cls._latest_value

            # Get the state from the registry.
            # Copy to ensure registry is immutable to modifications of "_value".
            # Raises KeyError if `name` is invalid string input to registry
            # to retrieve solar parameters for Galactocentric frame.
            state = copy.deepcopy(cls._registry[name])  # ensure mutable

            return state

        @deprecated("v4.2", alternative="`get_from_registry`")
        @classmethod
        def get_solar_params_from_string(cls, arg):
            """
            Return Galactocentric solar parameters given string names
            for the parameter sets.

            Returns
            -------
            parameters : dict
                Copy of Galactocentric solar parameters from registry

            Raises
            ------
            KeyError
                If invalid string input to registry
                to retrieve solar parameters for Galactocentric frame.

            """
            return cls.get_from_registry(arg)["parameters"]

        @classmethod
        def validate(cls, value):
            if value is None:
                value = cls._latest_value

            if isinstance(value, str):
                state = cls.get_from_registry(value)
                cls._references = state["references"]
                cls._state = state
                parameters = state["parameters"]

            elif isinstance(value, dict):
                parameters = value

            elif isinstance(value, Galactocentric):
                # turn the frame instance into a dict of frame attributes
                parameters = dict()
                for k in value.frame_attributes:
                    parameters[k] = getattr(value, k)
                cls._references = value.frame_attribute_references.copy()
                cls._state = dict(parameters=parameters, references=cls._references)

            else:
                raise ValueError(
                    "Invalid input to retrieve solar parameters for Galactocentric frame:"
                    " input must be a string, dict, or Galactocentric instance"
                )

            return parameters

        @classmethod
        def register(cls, name: str, parameters: dict, references=None, **meta: dict):
            """Register a set of parameters.

            Parameters
            ----------
            name : str
                The registration name for the parameter and metadata set.
            parameters : dict
                The solar parameters for Galactocentric frame.
            references : dict or None, optional
                References for contents of `parameters`.
                None becomes empty dict.
            **meta : dict, optional
                Any other properties to register.

            """
            # check on contents of `parameters`
            must_have = {"galcen_coord", "galcen_distance", "galcen_v_sun", "z_sun", "roll"}
            missing = must_have.difference(parameters)
            if missing:
                raise ValueError(f"Missing parameters: {missing}")

            references = references or {}  # None -> {}

            state = dict(parameters=parameters, references=references)
            state.update(meta)  # meta never has keys "parameters" or "references"

            cls._registry[name] = state

    doc_components = """
        x : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`x` position component.
        y : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`y` position component.
        z : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`z` position component.

        v_x : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`v_x` velocity component.
        v_y : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`v_y` velocity component.
        v_z : `~astropy.units.Quantity`, optional
            Cartesian, Galactocentric :math:`v_z` velocity component.
    """

    doc_footer = """
        Other parameters
        ----------------
        galcen_coord : `~astropy.coordinates.ICRS`, optional, keyword-only
            The ICRS coordinates of the Galactic center.
        galcen_distance : `~astropy.units.Quantity`, optional, keyword-only
            The distance from the sun to the Galactic center.
        galcen_v_sun : `~astropy.coordinates.CartesianDifferential`, `~astropy.units.Quantity` ['speed'], optional, keyword-only
            The velocity of the sun *in the Galactocentric frame* as Cartesian
            velocity components.
        z_sun : `~astropy.units.Quantity` ['length'], optional, keyword-only
            The distance from the sun to the Galactic midplane.
        roll : `~astropy.coordinates.Angle`, optional, keyword-only
            The angle to rotate about the final x-axis, relative to the
            orientation for Galactic. For example, if this roll angle is 0,
            the final x-z plane will align with the Galactic coordinates x-z
            plane. Unless you really know what this means, you probably should
            not change this!

        Examples
        --------

        To transform to the Galactocentric frame with the default
        frame attributes, pass the uninstantiated class name to the
        ``transform_to()`` method of a `~astropy.coordinates.SkyCoord` object::

            >>> import astropy.units as u
            >>> import astropy.coordinates as coord
            >>> c = coord.SkyCoord(ra=[158.3122, 24.5] * u.degree,
            ...                    dec=[-17.3, 81.52] * u.degree,
            ...                    distance=[11.5, 24.12] * u.kpc,
            ...                    frame='icrs')
            >>> c.transform_to(coord.Galactocentric) # doctest: +FLOAT_CMP
            <SkyCoord (Galactocentric: galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.122 kpc, galcen_v_sun=(12.9, 245.6, 7.78) km / s, z_sun=20.8 pc, roll=0.0 deg): (x, y, z) in kpc
                [( -9.43489286, -9.40062188, 6.51345359),
                 (-21.11044918, 18.76334013, 7.83175149)]>

        To specify a custom set of parameters, you have to include extra keyword
        arguments when initializing the Galactocentric frame object::

            >>> c.transform_to(coord.Galactocentric(galcen_distance=8.1*u.kpc)) # doctest: +FLOAT_CMP
            <SkyCoord (Galactocentric: galcen_coord=<ICRS Coordinate: (ra, dec) in deg
                (266.4051, -28.936175)>, galcen_distance=8.1 kpc, galcen_v_sun=(12.9, 245.6, 7.78) km / s, z_sun=20.8 pc, roll=0.0 deg): (x, y, z) in kpc
                [( -9.41284763, -9.40062188, 6.51346272),
                 (-21.08839478, 18.76334013, 7.83184184)]>

        Similarly, transforming from the Galactocentric frame to another coordinate frame::

            >>> c = coord.SkyCoord(x=[-8.3, 4.5] * u.kpc,
            ...                    y=[0., 81.52] * u.kpc,
            ...                    z=[0.027, 24.12] * u.kpc,
            ...                    frame=coord.Galactocentric)
            >>> c.transform_to(coord.ICRS) # doctest: +FLOAT_CMP
            <SkyCoord (ICRS): (ra, dec, distance) in (deg, deg, kpc)
                [( 88.22423301, 29.88672864,  0.17813456),
                 (289.72864549, 49.9865043 , 85.93949064)]>

        Or, with custom specification of the Galactic center::

            >>> c = coord.SkyCoord(x=[-8.0, 4.5] * u.kpc,
            ...                    y=[0., 81.52] * u.kpc,
            ...                    z=[21.0, 24120.0] * u.pc,
            ...                    frame=coord.Galactocentric,
            ...                    z_sun=21 * u.pc, galcen_distance=8. * u.kpc)
            >>> c.transform_to(coord.ICRS) # doctest: +FLOAT_CMP
            <SkyCoord (ICRS): (ra, dec, distance) in (deg, deg, kpc)
                [( 86.2585249 , 28.85773187, 2.75625475e-05),
                 (289.77285255, 50.06290457, 8.59216010e+01)]>

    """

    @format_doc(base_doc, components=doc_components, footer=doc_footer)
    class Galactocentric(BaseCoordinateFrame):
        r"""
        A coordinate or frame in the Galactocentric system.

        This frame allows specifying the Sun-Galactic center distance, the height of
        the Sun above the Galactic midplane, and the solar motion relative to the
        Galactic center. However, as there is no modern standard definition of a
        Galactocentric reference frame, it is important to pay attention to the
        default values used in this class if precision is important in your code.
        The default values of the parameters of this frame are taken from the
        original definition of the frame in 2014. As such, the defaults are somewhat
        out of date relative to recent measurements made possible by, e.g., Gaia.
        The defaults can, however, be changed at runtime by setting the parameter
        set name in `~astropy.coordinates.galactocentric_frame_defaults`.

        The current default parameter set is ``"pre-v4.0"``, indicating that the
        parameters were adopted before ``astropy`` version 4.0. A regularly-updated
        parameter set can instead be used by setting
        ``galactocentric_frame_defaults.set ('latest')``, and other parameter set
        names may be added in future versions. To find out the scientific papers
        that the current default parameters are derived from, use
        ``galcen.frame_attribute_references`` (where ``galcen`` is an instance of
        this frame), which will update even if the default parameter set is changed.

        The position of the Sun is assumed to be on the x axis of the final,
        right-handed system. That is, the x axis points from the position of
        the Sun projected to the Galactic midplane to the Galactic center --
        roughly towards :math:`(l,b) = (0^\circ,0^\circ)`. For the default
        transformation (:math:`{\rm roll}=0^\circ`), the y axis points roughly
        towards Galactic longitude :math:`l=90^\circ`, and the z axis points
        roughly towards the North Galactic Pole (:math:`b=90^\circ`).

        For a more detailed look at the math behind this transformation, see
        the document :ref:`astropy:coordinates-galactocentric`.

        The frame attributes are listed under **Other Parameters**.
        """

        default_representation = r.CartesianRepresentation
        default_differential = r.CartesianDifferential

        # frame attributes
        galcen_coord = CoordinateAttribute(frame=ICRS)
        galcen_distance = QuantityAttribute(unit=u.kpc)

        galcen_v_sun = DifferentialAttribute(allowed_classes=[r.CartesianDifferential])

        z_sun = QuantityAttribute(unit=u.pc)
        roll = QuantityAttribute(unit=u.deg)

        def __init__(self, *args, **kwargs):
            # Set default frame attribute values based on the ScienceState instance
            # for the solar parameters defined above
            default_params = galactocentric_frame_defaults.get()
            self.frame_attribute_references = (
                galactocentric_frame_defaults.references.copy()
            )

            for k in default_params:
                if k in kwargs:
                    # If a frame attribute is set by the user, remove its reference
                    self.frame_attribute_references.pop(k, None)

                # Keep the frame attribute if it is set by the user, otherwise use
                # the default value
                kwargs[k] = kwargs.get(k, default_params[k])

            super().__init__(*args, **kwargs)

        @classmethod
        def get_roll0(cls):
            """The additional roll angle (about the final x axis) necessary to align the
            final z axis to match the Galactic yz-plane.  Setting the ``roll``
            frame attribute to -this method's return value removes this rotation,
            allowing the use of the `~astropy.coordinates.Galactocentric` frame
            in more general contexts.

            """
            # note that the actual value is defined at the module level.  We make at
            # a property here because this module isn't actually part of the public
            # API, so it's better for it to be accessible from Galactocentric
            return _ROLL0

    # ICRS to/from Galactocentric ----------------------->

    def get_matrix_vectors(galactocentric_frame, inverse=False):
        """
        Use the ``inverse`` argument to get the inverse transformation, matrix and
        offsets to go from Galactocentric to ICRS.
        """
        # shorthand
        gcf = galactocentric_frame

        # rotation matrix to align x(ICRS) with the vector to the Galactic center
        mat1 = rotation_matrix(-gcf.galcen_coord.dec, "y")
        mat2 = rotation_matrix(gcf.galcen_coord.ra, "z")
        # extra roll away from the Galactic x-z plane
        mat0 = rotation_matrix(gcf.get_roll0() - gcf.roll, "x")

        # construct transformation matrix and use it
        R = mat0 @ mat1 @ mat2

        # Now need to translate by Sun-Galactic center distance around x' and
        # rotate about y' to account for tilt due to Sun's height above the plane
        translation = r.CartesianRepresentation(gcf.galcen_distance * [1.0, 0.0, 0.0])
        z_d = gcf.z_sun / gcf.galcen_distance
        H = rotation_matrix(-np.arcsin(z_d), "y")

        # compute total matrices
        A = H @ R

        # Now we re-align the translation vector to account for the Sun's height
        # above the midplane
        offset = -translation.transform(H)

        if inverse:
            # the inverse of a rotation matrix is a transpose, which is much faster
            #   and more stable to compute
            A = matrix_transpose(A)
            offset = (-offset).transform(A)
            offset_v = r.CartesianDifferential.from_cartesian(
                (-gcf.galcen_v_sun).to_cartesian().transform(A)
            )
            offset = offset.with_differentials(offset_v)

        else:
            offset = offset.with_differentials(gcf.galcen_v_sun)

        return A, offset

    def _check_coord_repr_diff_types(c):
        if isinstance(c.data, r.UnitSphericalRepresentation):
            raise ConvertError(
                "Transforming to/from a Galactocentric frame requires a 3D coordinate, e.g."
                " (angle, angle, distance) or (x, y, z)."
            )

        if "s" in c.data.differentials and isinstance(
            c.data.differentials["s"],
            (
                r.UnitSphericalDifferential,
                r.UnitSphericalCosLatDifferential,
                r.RadialDifferential,
            ),
        ):
            raise ConvertError(
                "Transforming to/from a Galactocentric frame requires a 3D velocity, e.g.,"
                " proper motion components and radial velocity."
            )

    @frame_transform_graph.transform(AffineTransform, ICRS, Galactocentric)
    def icrs_to_galactocentric(icrs_coord, galactocentric_frame):
        _check_coord_repr_diff_types(icrs_coord)
        return get_matrix_vectors(galactocentric_frame)

    @frame_transform_graph.transform(AffineTransform, Galactocentric, ICRS)
    def galactocentric_to_icrs(galactocentric_coord, icrs_frame):
        _check_coord_repr_diff_types(galactocentric_coord)
        return get_matrix_vectors(galactocentric_coord, inverse=True)

    # Create loopback transformation
    frame_transform_graph._add_merged_transform(Galactocentric, ICRS, Galactocentric)