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# Source code for astropy.coordinates.angles

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

    """
    This module contains the fundamental classes used for representing
    coordinates in astropy.
    """

    import functools
    from collections import namedtuple

    import numpy as np

    from astropy import units as u
    from astropy.utils import isiterable

    from . import angle_formats as form

    __all__ = ["Angle", "Latitude", "Longitude"]

    # these are used by the `hms` and `dms` attributes
    hms_tuple = namedtuple("hms_tuple", ("h", "m", "s"))
    dms_tuple = namedtuple("dms_tuple", ("d", "m", "s"))
    signed_dms_tuple = namedtuple("signed_dms_tuple", ("sign", "d", "m", "s"))

    class Angle(u.SpecificTypeQuantity):
        """
        One or more angular value(s) with units equivalent to radians or degrees.

        An angle can be specified either as an array, scalar, tuple (see
        below), string, `~astropy.units.Quantity` or another
        :class:`~astropy.coordinates.Angle`.

        The input parser is flexible and supports a variety of formats.
        The examples below illustrate common ways of initializing an
        `~astropy.coordinates.Angle` object. First some imports::

          >>> from astropy.coordinates import Angle
          >>> from astropy import units as u

        The angle values can now be provided::

          >>> Angle('10.2345d')
          <Angle 10.2345 deg>
          >>> Angle(['10.2345d', '-20d'])
          <Angle [ 10.2345, -20.    ] deg>
          >>> Angle('1:2:30.43 degrees')
          <Angle 1.04178611 deg>
          >>> Angle('1 2 0 hours')
          <Angle 1.03333333 hourangle>
          >>> Angle(np.arange(1, 8), unit=u.deg)
          <Angle [1., 2., 3., 4., 5., 6., 7.] deg>
          >>> Angle('1°2′3″')
          <Angle 1.03416667 deg>
          >>> Angle('1°2′3″N')
          <Angle 1.03416667 deg>
          >>> Angle('1d2m3.4s')
          <Angle 1.03427778 deg>
          >>> Angle('1d2m3.4sS')
          <Angle -1.03427778 deg>
          >>> Angle('-1h2m3s')
          <Angle -1.03416667 hourangle>
          >>> Angle('-1h2m3sE')
          <Angle -1.03416667 hourangle>
          >>> Angle('-1h2.5m')
          <Angle -1.04166667 hourangle>
          >>> Angle('-1h2.5mW')
          <Angle 1.04166667 hourangle>
          >>> Angle('-1:2.5', unit=u.deg)
          <Angle -1.04166667 deg>
          >>> Angle(10.2345 * u.deg)
          <Angle 10.2345 deg>
          >>> Angle(Angle(10.2345 * u.deg))
          <Angle 10.2345 deg>

        Parameters
        ----------
        angle : `~numpy.array`, scalar, `~astropy.units.Quantity`, `~astropy.coordinates.Angle`
            The angle value. If a tuple, will be interpreted as ``(h, m,
            s)`` or ``(d, m, s)`` depending on ``unit``. If a string, it
            will be interpreted following the rules described above.

            If ``angle`` is a sequence or array of strings, the resulting
            values will be in the given ``unit``, or if `None` is provided,
            the unit will be taken from the first given value.

        unit : unit-like, optional
            The unit of the value specified for the angle.  This may be
            any string that `~astropy.units.Unit` understands, but it is
            better to give an actual unit object.  Must be an angular
            unit.

        dtype : `~numpy.dtype`, optional
            See `~astropy.units.Quantity`.

        copy : bool, optional
            See `~astropy.units.Quantity`.

        Raises
        ------
        `~astropy.units.UnitsError`
            If a unit is not provided or it is not an angular unit.
        """

        _equivalent_unit = u.radian
        _include_easy_conversion_members = True

        def __new__(cls, angle, unit=None, dtype=np.inexact, copy=True, **kwargs):
            if not isinstance(angle, u.Quantity):
                if unit is not None:
                    unit = cls._convert_unit_to_angle_unit(u.Unit(unit))

                if isinstance(angle, tuple):
                    angle = cls._tuple_to_float(angle, unit)

                elif isinstance(angle, str):
                    angle, angle_unit = form.parse_angle(angle, unit)
                    if angle_unit is None:
                        angle_unit = unit

                    if isinstance(angle, tuple):
                        if angle_unit == u.hourangle:
                            form._check_hour_range(angle[0])
                        form._check_minute_range(angle[1])
                        a = np.abs(angle[0]) + angle[1] / 60.0
                        if len(angle) == 3:
                            form._check_second_range(angle[2])
                            a += angle[2] / 3600.0

                        angle = np.copysign(a, angle[0])

                    if angle_unit is not unit:
                        # Possible conversion to `unit` will be done below.
                        angle = u.Quantity(angle, angle_unit, copy=False)

                elif isiterable(angle) and not (
                    isinstance(angle, np.ndarray) and angle.dtype.kind not in "SUVO"
                ):
                    angle = [Angle(x, unit, copy=False) for x in angle]

            return super().__new__(cls, angle, unit, dtype=dtype, copy=copy, **kwargs)

        @staticmethod
        def _tuple_to_float(angle, unit):
            """
            Converts an angle represented as a 3-tuple or 2-tuple into a floating
            point number in the given unit.
            """
            # TODO: Numpy array of tuples?
            if unit == u.hourangle:
                return form.hms_to_hours(*angle)
            elif unit == u.degree:
                return form.dms_to_degrees(*angle)
            else:
                raise u.UnitsError(f"Can not parse '{angle}' as unit '{unit}'")

        @staticmethod
        def _convert_unit_to_angle_unit(unit):
            return u.hourangle if unit == u.hour else unit

        def _set_unit(self, unit):
            super()._set_unit(self._convert_unit_to_angle_unit(unit))

        @property
        def hour(self):
            """
            The angle's value in hours (read-only property).
            """
            return self.hourangle

        @property
        def hms(self):
            """
            The angle's value in hours, as a named tuple with ``(h, m, s)``
            members.  (This is a read-only property.)
            """
            return hms_tuple(*form.hours_to_hms(self.hourangle))

        @property
        def dms(self):
            """
            The angle's value in degrees, as a named tuple with ``(d, m, s)``
            members.  (This is a read-only property.)
            """
            return dms_tuple(*form.degrees_to_dms(self.degree))

        @property
        def signed_dms(self):
            """
            The angle's value in degrees, as a named tuple with ``(sign, d, m, s)``
            members.  The ``d``, ``m``, ``s`` are thus always positive, and the sign of
            the angle is given by ``sign``. (This is a read-only property.)

            This is primarily intended for use with `dms` to generate string
            representations of coordinates that are correct for negative angles.
            """
            return signed_dms_tuple(
                np.sign(self.degree), *form.degrees_to_dms(np.abs(self.degree))
            )

        def to_string(
            self,
            unit=None,
            decimal=False,
            sep="fromunit",
            precision=None,
            alwayssign=False,
            pad=False,
            fields=3,
            format=None,
        ):
            """A string representation of the angle.

            Parameters
            ----------
            unit : `~astropy.units.UnitBase`, optional
                Specifies the unit.  Must be an angular unit.  If not
                provided, the unit used to initialize the angle will be
                used.

            decimal : bool, optional
                If `False`, the returned string will be in sexagesimal form
                if possible (for units of degrees or hourangle).  If `True`,
                a decimal representation will be used. In that case, no unit
                will be appended if ``format`` is not explicitly given.

            sep : str, optional
                The separator between numbers in a sexagesimal
                representation.  E.g., if it is ':', the result is
                ``'12:41:11.1241'``. Also accepts 2 or 3 separators. E.g.,
                ``sep='hms'`` would give the result ``'12h41m11.1241s'``, or
                sep='-:' would yield ``'11-21:17.124'``.  Alternatively, the
                special string 'fromunit' means 'dms' if the unit is
                degrees, or 'hms' if the unit is hours.

            precision : int, optional
                The level of decimal precision.  If ``decimal`` is `True`,
                this is the raw precision, otherwise it gives the
                precision of the last place of the sexagesimal
                representation (seconds).  If `None`, or not provided, the
                number of decimal places is determined by the value, and
                will be between 0-8 decimal places as required.

            alwayssign : bool, optional
                If `True`, include the sign no matter what.  If `False`,
                only include the sign if it is negative.

            pad : bool, optional
                If `True`, include leading zeros when needed to ensure a
                fixed number of characters for sexagesimal representation.

            fields : int, optional
                Specifies the number of fields to display when outputting
                sexagesimal notation.  For example:

                    - fields == 1: ``'5d'``
                    - fields == 2: ``'5d45m'``
                    - fields == 3: ``'5d45m32.5s'``

                By default, all fields are displayed.

            format : str, optional
                The format of the result.  If not provided, an unadorned
                string is returned.  Supported values are:

                - 'latex': Return a LaTeX-formatted string

                - 'latex_inline': Return a LaTeX-formatted string which is the
                  same as with ``format='latex'`` for |Angle| instances

                - 'unicode': Return a string containing non-ASCII unicode
                  characters, such as the degree symbol

            Returns
            -------
            strrepr : str or array
                A string representation of the angle. If the angle is an array, this
                will be an array with a unicode dtype.

            """
            if unit is None:
                unit = self.unit
            else:
                unit = self._convert_unit_to_angle_unit(u.Unit(unit))

            separators = {
                "generic": {u.degree: "dms", u.hourangle: "hms"},
                "latex": {
                    u.degree: [r"^\circ", r"{}^\prime", r"{}^{\prime\prime}"],
                    u.hourangle: [r"^{\mathrm{h}}", r"^{\mathrm{m}}", r"^{\mathrm{s}}"],
                },
                "unicode": {u.degree: "°′″", u.hourangle: "ʰᵐˢ"},
            }
            # 'latex_inline' provides no functionality beyond what 'latex' offers,
            # but it should be implemented to avoid ValueErrors in user code.
            separators["latex_inline"] = separators["latex"]
            # Default separators are as for generic.
            separators[None] = separators["generic"]

            # Create an iterator so we can format each element of what
            # might be an array.
            if not decimal and (unit_is_deg := unit == u.degree or unit == u.hourangle):
                # Sexagesimal.
                if sep == "fromunit":
                    if format not in separators:
                        raise ValueError(f"Unknown format '{format}'")
                    sep = separators[format][unit]
                func = functools.partial(
                    form.degrees_to_string if unit_is_deg else form.hours_to_string,
                    precision=precision,
                    sep=sep,
                    pad=pad,
                    fields=fields,
                )
            else:
                if sep != "fromunit":
                    raise ValueError(
                        f"'{unit}' can not be represented in sexagesimal notation"
                    )
                func = ("{:g}" if precision is None else f"{{0:0.{precision}f}}").format
                # Don't add unit by default for decimal.
                if not (decimal and format is None):
                    unit_string = unit.to_string(format=format)
                    if format == "latex" or format == "latex_inline":
                        unit_string = unit_string[1:-1]
                    format_func = func
                    func = lambda x: format_func(x) + unit_string

            def do_format(val):
                # Check if value is not nan to avoid ValueErrors when turning it into
                # a hexagesimal string.
                if not np.isnan(val):
                    s = func(float(val))
                    if alwayssign and not s.startswith("-"):
                        s = "+" + s
                    if format == "latex" or format == "latex_inline":
                        s = f"${s}$"
                    return s
                s = f"{val}"
                return s

            values = self.to_value(unit)
            format_ufunc = np.vectorize(do_format, otypes=["U"])
            result = format_ufunc(values)

            if result.ndim == 0:
                result = result[()]
            return result

        def _wrap_at(self, wrap_angle):
            """
            Implementation that assumes ``angle`` is already validated
            and that wrapping is inplace.
            """
            # Convert the wrap angle and 360 degrees to the native unit of
            # this Angle, then do all the math on raw Numpy arrays rather
            # than Quantity objects for speed.
            a360 = u.degree.to(self.unit, 360.0)
            wrap_angle = wrap_angle.to_value(self.unit)
            wrap_angle_floor = wrap_angle - a360
            self_angle = self.view(np.ndarray)
            # Do the wrapping, but only if any angles need to be wrapped
            #
            # Catch any invalid warnings from the floor division.
            with np.errstate(invalid="ignore"):
                wraps = (self_angle - wrap_angle_floor) // a360
            valid = np.isfinite(wraps) & (wraps != 0)
            if np.any(valid):
                self_angle -= wraps * a360
                # Rounding errors can cause problems.
                self_angle[self_angle >= wrap_angle] -= a360
                self_angle[self_angle < wrap_angle_floor] += a360

        def wrap_at(self, wrap_angle, inplace=False):
            """
            Wrap the `~astropy.coordinates.Angle` object at the given ``wrap_angle``.

            This method forces all the angle values to be within a contiguous
            360 degree range so that ``wrap_angle - 360d <= angle <
            wrap_angle``. By default a new Angle object is returned, but if the
            ``inplace`` argument is `True` then the `~astropy.coordinates.Angle`
            object is wrapped in place and nothing is returned.

            For instance::

              >>> from astropy.coordinates import Angle
              >>> import astropy.units as u
              >>> a = Angle([-20.0, 150.0, 350.0] * u.deg)

              >>> a.wrap_at(360 * u.deg).degree  # Wrap into range 0 to 360 degrees  # doctest: +FLOAT_CMP
              array([340., 150., 350.])

              >>> a.wrap_at('180d', inplace=True)  # Wrap into range -180 to 180 degrees  # doctest: +FLOAT_CMP
              >>> a.degree  # doctest: +FLOAT_CMP
              array([-20., 150., -10.])

            Parameters
            ----------
            wrap_angle : angle-like
                Specifies a single value for the wrap angle.  This can be any
                object that can initialize an `~astropy.coordinates.Angle` object,
                e.g. ``'180d'``, ``180 * u.deg``, or ``Angle(180, unit=u.deg)``.

            inplace : bool
                If `True` then wrap the object in place instead of returning
                a new `~astropy.coordinates.Angle`

            Returns
            -------
            out : Angle or None
                If ``inplace is False`` (default), return new
                `~astropy.coordinates.Angle` object with angles wrapped accordingly.
                Otherwise wrap in place and return `None`.
            """
            wrap_angle = Angle(wrap_angle, copy=False)  # Convert to an Angle
            if not inplace:
                self = self.copy()
            self._wrap_at(wrap_angle)
            return None if inplace else self

        def is_within_bounds(self, lower=None, upper=None):
            """
            Check if all angle(s) satisfy ``lower <= angle < upper``

            If ``lower`` is not specified (or `None`) then no lower bounds check is
            performed.  Likewise ``upper`` can be left unspecified.  For example::

              >>> from astropy.coordinates import Angle
              >>> import astropy.units as u
              >>> a = Angle([-20, 150, 350] * u.deg)
              >>> a.is_within_bounds('0d', '360d')
              False
              >>> a.is_within_bounds(None, '360d')
              True
              >>> a.is_within_bounds(-30 * u.deg, None)
              True

            Parameters
            ----------
            lower : angle-like or None
                Specifies lower bound for checking.  This can be any object
                that can initialize an `~astropy.coordinates.Angle` object, e.g. ``'180d'``,
                ``180 * u.deg``, or ``Angle(180, unit=u.deg)``.
            upper : angle-like or None
                Specifies upper bound for checking.  This can be any object
                that can initialize an `~astropy.coordinates.Angle` object, e.g. ``'180d'``,
                ``180 * u.deg``, or ``Angle(180, unit=u.deg)``.

            Returns
            -------
            is_within_bounds : bool
                `True` if all angles satisfy ``lower <= angle < upper``
            """
            ok = True
            if lower is not None:
                ok &= np.all(Angle(lower) <= self)
            if ok and upper is not None:
                ok &= np.all(self < Angle(upper))
            return bool(ok)

        def _str_helper(self, format=None):
            if self.isscalar:
                return self.to_string(format=format)

            def formatter(x):
                return x.to_string(format=format)

            return np.array2string(self, formatter={"all": formatter})

        def __str__(self):
            return self._str_helper()

        def _repr_latex_(self):
            return self._str_helper(format="latex")

    def _no_angle_subclass(obj):
        """Return any Angle subclass objects as an Angle objects.

        This is used to ensure that Latitude and Longitude change to Angle
        objects when they are used in calculations (such as lon/2.)
        """
        if isinstance(obj, tuple):
            return tuple(_no_angle_subclass(_obj) for _obj in obj)

        return obj.view(Angle) if isinstance(obj, (Latitude, Longitude)) else obj

    class Latitude(Angle):
        """
        Latitude-like angle(s) which must be in the range -90 to +90 deg.

        A Latitude object is distinguished from a pure
        :class:`~astropy.coordinates.Angle` by virtue of being constrained
        so that::

          -90.0 * u.deg <= angle(s) <= +90.0 * u.deg

        Any attempt to set a value outside that range will result in a
        `ValueError`.

        The input angle(s) can be specified either as an array, list,
        scalar, tuple (see below), string,
        :class:`~astropy.units.Quantity` or another
        :class:`~astropy.coordinates.Angle`.

        The input parser is flexible and supports all of the input formats
        supported by :class:`~astropy.coordinates.Angle`.

        Parameters
        ----------
        angle : array, list, scalar, `~astropy.units.Quantity`, `~astropy.coordinates.Angle`
            The angle value(s). If a tuple, will be interpreted as ``(h, m, s)``
            or ``(d, m, s)`` depending on ``unit``. If a string, it will be
            interpreted following the rules described for
            :class:`~astropy.coordinates.Angle`.

            If ``angle`` is a sequence or array of strings, the resulting
            values will be in the given ``unit``, or if `None` is provided,
            the unit will be taken from the first given value.

        unit : unit-like, optional
            The unit of the value specified for the angle.  This may be
            any string that `~astropy.units.Unit` understands, but it is
            better to give an actual unit object.  Must be an angular
            unit.

        Raises
        ------
        `~astropy.units.UnitsError`
            If a unit is not provided or it is not an angular unit.
        `TypeError`
            If the angle parameter is an instance of :class:`~astropy.coordinates.Longitude`.
        """

        def __new__(cls, angle, unit=None, **kwargs):
            # Forbid creating a Lat from a Long.
            if isinstance(angle, Longitude):
                raise TypeError("A Latitude angle cannot be created from a Longitude angle")
            self = super().__new__(cls, angle, unit=unit, **kwargs)
            self._validate_angles()
            return self

        def _validate_angles(self, angles=None):
            """Check that angles are between -90 and 90 degrees.
            If not given, the check is done on the object itself"""
            # Convert the lower and upper bounds to the "native" unit of
            # this angle.  This limits multiplication to two values,
            # rather than the N values in `self.value`.  Also, the
            # comparison is performed on raw arrays, rather than Quantity
            # objects, for speed.
            if angles is None:
                angles = self

            # For speed, compare using "is", which is not strictly guaranteed to hold,
            # but if it doesn't we'll just convert correctly in the 'else' clause.
            if angles.unit is u.deg:
                limit = 90
            elif angles.unit is u.rad:
                limit = self.dtype.type(0.5 * np.pi)
            else:
                limit = u.degree.to(angles.unit, 90.0)

            invalid_angles = np.any(angles.value < -limit) or np.any(angles.value > limit)
            if invalid_angles:
                raise ValueError(
                    "Latitude angle(s) must be within -90 deg <= angle <= 90 deg, "
                    f"got {angles.to(u.degree)}"
                )

        def __setitem__(self, item, value):
            # Forbid assigning a Long to a Lat.
            if isinstance(value, Longitude):
                raise TypeError("A Longitude angle cannot be assigned to a Latitude angle")
            # first check bounds
            if value is not np.ma.masked:
                self._validate_angles(value)
            super().__setitem__(item, value)

        # Any calculation should drop to Angle
        def __array_ufunc__(self, *args, **kwargs):
            results = super().__array_ufunc__(*args, **kwargs)
            return _no_angle_subclass(results)

    class LongitudeInfo(u.QuantityInfo):
        _represent_as_dict_attrs = u.QuantityInfo._represent_as_dict_attrs + ("wrap_angle",)

    class Longitude(Angle):
        """
        Longitude-like angle(s) which are wrapped within a contiguous 360 degree range.

        A ``Longitude`` object is distinguished from a pure
        :class:`~astropy.coordinates.Angle` by virtue of a ``wrap_angle``
        property.  The ``wrap_angle`` specifies that all angle values
        represented by the object will be in the range::

          wrap_angle - 360 * u.deg <= angle(s) < wrap_angle

        The default ``wrap_angle`` is 360 deg.  Setting ``wrap_angle=180 *
        u.deg`` would instead result in values between -180 and +180 deg.
        Setting the ``wrap_angle`` attribute of an existing ``Longitude``
        object will result in re-wrapping the angle values in-place.

        The input angle(s) can be specified either as an array, list,
        scalar, tuple, string, :class:`~astropy.units.Quantity`
        or another :class:`~astropy.coordinates.Angle`.

        The input parser is flexible and supports all of the input formats
        supported by :class:`~astropy.coordinates.Angle`.

        Parameters
        ----------
        angle : tuple or angle-like
            The angle value(s). If a tuple, will be interpreted as ``(h, m s)`` or
            ``(d, m, s)`` depending on ``unit``. If a string, it will be interpreted
            following the rules described for :class:`~astropy.coordinates.Angle`.

            If ``angle`` is a sequence or array of strings, the resulting
            values will be in the given ``unit``, or if `None` is provided,
            the unit will be taken from the first given value.

        unit : unit-like ['angle'], optional
            The unit of the value specified for the angle.  This may be
            any string that `~astropy.units.Unit` understands, but it is
            better to give an actual unit object.  Must be an angular
            unit.

        wrap_angle : angle-like or None, optional
            Angle at which to wrap back to ``wrap_angle - 360 deg``.
            If ``None`` (default), it will be taken to be 360 deg unless ``angle``
            has a ``wrap_angle`` attribute already (i.e., is a ``Longitude``),
            in which case it will be taken from there.

        Raises
        ------
        `~astropy.units.UnitsError`
            If a unit is not provided or it is not an angular unit.
        `TypeError`
            If the angle parameter is an instance of :class:`~astropy.coordinates.Latitude`.
        """

        _wrap_angle = None
        _default_wrap_angle = Angle(360 * u.deg)
        info = LongitudeInfo()

        def __new__(cls, angle, unit=None, wrap_angle=None, **kwargs):
            # Forbid creating a Long from a Lat.
            if isinstance(angle, Latitude):
                raise TypeError(
                    "A Longitude angle cannot be created from a Latitude angle."
                )
            self = super().__new__(cls, angle, unit=unit, **kwargs)
            if wrap_angle is None:
                wrap_angle = getattr(angle, "wrap_angle", self._default_wrap_angle)
            self.wrap_angle = wrap_angle  # angle-like b/c property setter
            return self

        def __setitem__(self, item, value):
            # Forbid assigning a Lat to a Long.
            if isinstance(value, Latitude):
                raise TypeError("A Latitude angle cannot be assigned to a Longitude angle")
            super().__setitem__(item, value)
            self._wrap_at(self.wrap_angle)

        @property
        def wrap_angle(self):
            return self._wrap_angle

        @wrap_angle.setter
        def wrap_angle(self, value):
            self._wrap_angle = Angle(value, copy=False)
            self._wrap_at(self.wrap_angle)

        def __array_finalize__(self, obj):
            super().__array_finalize__(obj)
            self._wrap_angle = getattr(obj, "_wrap_angle", self._default_wrap_angle)

        # Any calculation should drop to Angle
        def __array_ufunc__(self, *args, **kwargs):
            results = super().__array_ufunc__(*args, **kwargs)
            return _no_angle_subclass(results)