# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module contains the fundamental classes used for representing
coordinates in astropy.
"""
from __future__ import annotations
import functools
from typing import Any, NamedTuple
import numpy as np
from astropy import units as u
from astropy.units import SpecificTypeQuantity
from astropy.utils import isiterable
from astropy.utils.compat import COPY_IF_NEEDED, NUMPY_LT_2_0
from . import formats
__all__ = ["Angle", "Latitude", "Longitude"]
# these are used by the `hms` and `dms` attributes
class hms_tuple(NamedTuple):
"""A named tuple of (hour, minute, second) values."""
h: float | np.floating[Any]
"""The hour value."""
m: float | np.floating[Any]
"""The minute value."""
s: float | np.floating[Any]
"""The second value."""
class dms_tuple(NamedTuple):
"""A named tuple of (degree, minute, second) values."""
d: float | np.floating[Any]
"""The degree value."""
m: float | np.floating[Any]
"""The minute value."""
s: float | np.floating[Any]
"""The second value."""
class signed_dms_tuple(NamedTuple):
"""A named tuple of (sign, degree, minute, second) values."""
sign: float | np.integer[Any]
"""The sign of the angle, either -1 or +1."""
d: float | np.floating[Any]
"""The degree value."""
m: float | np.floating[Any]
"""The minute value."""
s: float | np.floating[Any]
"""The second value."""
[docs]
class Angle(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):
unit = cls._convert_unit_to_angle_unit(unit)
if isinstance(angle, tuple):
raise TypeError(
"Creating an Angle with a tuple of degrees (or hours), minutes, and seconds "
"is no longer supported, as it has ambiguous behavior when the degree "
"value is 0. Use another way of creating angles instead (e.g., a less "
"ambiguous string like '-0d1m2.3s'). In a future version of astropy, a tuple "
"will be interpreted simply as a sequence with the given unit."
)
if isinstance(angle, str):
angle, angle_unit = formats.parse_angle(angle, unit)
if angle_unit is None:
angle_unit = unit
if isinstance(angle, tuple):
if angle_unit == u.hourangle:
formats._check_hour_range(angle[0])
formats._check_minute_range(angle[1])
a = np.abs(angle[0]) + angle[1] / 60.0
if len(angle) == 3:
formats._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=COPY_IF_NEEDED)
elif isiterable(angle) and not (
isinstance(angle, np.ndarray) and angle.dtype.kind not in "SUVO"
):
angle = [Angle(x, unit, copy=COPY_IF_NEEDED) for x in angle]
return super().__new__(cls, angle, unit, dtype=dtype, copy=copy, **kwargs)
@staticmethod
@functools.cache
def _convert_unit_to_angle_unit(unit):
# using caching to return early when possible (unit comparison is expensive)
if unit is not None:
unit = u.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."""
return hms_tuple(*formats._decimal_to_sexagesimal(self.hourangle))
@property
def dms(self):
"""The angle's value in degrees, as a ``(d, m, s)`` named tuple."""
return dms_tuple(*formats._decimal_to_sexagesimal(self.degree))
@property
def signed_dms(self):
"""The angle's value in degrees, as a ``(sign, d, m, s)`` named tuple.
The ``d``, ``m``, ``s`` are thus always positive, and the sign of
the angle is given by ``sign``.
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), *formats._decimal_to_sexagesimal(np.abs(self.degree))
)
[docs]
def to_string(
self,
unit=None,
decimal: bool = False,
sep: str = "fromunit",
precision: int | None = None,
alwayssign: bool = False,
pad: bool = False,
fields: int = 3,
format: str | None = None,
) -> str:
"""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 decimal and sep != "fromunit":
raise ValueError(
f"With decimal=True, separator cannot be used (got {sep=!r})"
)
if unit is None:
if sep == "dms":
unit = u.degree
elif sep == "hms":
unit = u.hourangle
else:
unit = self.unit
else:
unit = self._convert_unit_to_angle_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 == 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(
formats._decimal_to_sexagesimal_string,
precision=precision,
sep=sep,
pad=pad,
fields=fields,
)
else:
func = ("{:g}" if precision is None else f"{{0:0.{precision}f}}").format
# Don't add unit by default for decimal.
# TODO: could we use Quantity.to_string() here?
if not (decimal and format is None):
unit_string = unit.to_string(format=format)
if format == "latex" or format == "latex_inline":
# Remove $ and add space in front if unit is not a superscript.
if "^" in unit_string:
unit_string = unit_string[1:-1]
else:
unit_string = r"\;" + unit_string[1:-1]
elif len(unit_string) > 1:
# Length one for angular units can only happen for
# superscript degree, arcmin, arcsec, hour, minute, second,
# and those should not get an extra space.
unit_string = " " + unit_string
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)
self_angle = self.view(np.ndarray)
if NUMPY_LT_2_0:
# Ensure ndim>=1 so that comparison is done using the angle dtype.
self_angle = self_angle[np.newaxis]
else:
# Use explicit float to ensure casting to self_angle.dtype (NEP 50).
wrap_angle = float(wrap_angle)
wrap_angle_floor = wrap_angle - a360
# Do the wrapping, but only if any angles need to be wrapped
#
# Catch any invalid warnings from the floor division.
# See if any wrapping is necessary and return early otherwise.
# It is useful to avoid this since the array may be read-only
# (e.g. due to broadcasting).
# Note that since comparisons with NaN always return False,
# this also ensures that no adjustments are made for a
# read-only array with some NaN but otherwise OK elements.
out_of_range = (self_angle < wrap_angle_floor) | (self_angle >= wrap_angle)
if not out_of_range.any():
return
wraps = (self_angle - wrap_angle_floor) // a360
self_angle -= wraps * a360
# Rounding errors can cause problems.
self_angle[self_angle >= wrap_angle] -= a360
self_angle[self_angle < wrap_angle_floor] += a360
[docs]
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
[docs]
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
[docs]
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 = 0.5 * np.pi
else:
limit = u.degree.to(angles.unit, 90.0)
angles_view = angles.view(np.ndarray)
if NUMPY_LT_2_0:
# Ensure ndim>=1 so that comparison is done using the angle dtype.
# Otherwise, e.g., np.array(np.pi/2, 'f4') > np.pi/2 will yield True.
angles_view = angles_view[np.newaxis]
if np.any(np.abs(angles_view) > limit):
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",)
[docs]
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)
