import warnings
from textwrap import indent
import numpy as np
import astropy.units as u
from astropy.constants import c
from astropy.coordinates import (
ICRS,
CartesianDifferential,
CartesianRepresentation,
SkyCoord,
)
from astropy.coordinates.baseframe import BaseCoordinateFrame, frame_transform_graph
from astropy.coordinates.spectral_quantity import SpectralQuantity
from astropy.utils.exceptions import AstropyUserWarning
__all__ = ["SpectralCoord"]
class NoVelocityWarning(AstropyUserWarning):
pass
class NoDistanceWarning(AstropyUserWarning):
pass
KMS = u.km / u.s
ZERO_VELOCITIES = CartesianDifferential([0, 0, 0] * KMS)
# Default distance to use for target when none is provided
DEFAULT_DISTANCE = 1e6 * u.kpc
# We don't want to run doctests in the docstrings we inherit from Quantity
__doctest_skip__ = ["SpectralCoord.*"]
def _apply_relativistic_doppler_shift(scoord, velocity):
"""
Given a `SpectralQuantity` and a velocity, return a new `SpectralQuantity`
that is Doppler shifted by this amount.
Note that the Doppler shift applied is the full relativistic one, so
`SpectralQuantity` currently expressed in velocity and not using the
relativistic convention will temporarily be converted to use the
relativistic convention while the shift is applied.
Positive velocities are assumed to redshift the spectral quantity,
while negative velocities blueshift the spectral quantity.
"""
# NOTE: we deliberately don't keep sub-classes of SpectralQuantity intact
# since we can't guarantee that their metadata would be correct/consistent.
squantity = scoord.view(SpectralQuantity)
beta = velocity / c
doppler_factor = np.sqrt((1 + beta) / (1 - beta))
if squantity.unit.is_equivalent(u.m): # wavelength
return squantity * doppler_factor
elif (
squantity.unit.is_equivalent(u.Hz)
or squantity.unit.is_equivalent(u.eV)
or squantity.unit.is_equivalent(1 / u.m)
):
return squantity / doppler_factor
elif squantity.unit.is_equivalent(KMS): # velocity
return (squantity.to(u.Hz) / doppler_factor).to(squantity.unit)
else: # pragma: no cover
raise RuntimeError(
f"Unexpected units in velocity shift: {squantity.unit}. This should not"
" happen, so please report this in the astropy issue tracker!"
)
def update_differentials_to_match(
original, velocity_reference, preserve_observer_frame=False
):
"""
Given an original coordinate object, update the differentials so that
the final coordinate is at the same location as the original coordinate
but co-moving with the velocity reference object.
If preserve_original_frame is set to True, the resulting object will be in
the frame of the original coordinate, otherwise it will be in the frame of
the velocity reference.
"""
if not velocity_reference.data.differentials:
raise ValueError("Reference frame has no velocities")
# If the reference has an obstime already defined, we should ignore
# it and stick with the original observer obstime.
if "obstime" in velocity_reference.frame_attributes and hasattr(
original, "obstime"
):
velocity_reference = velocity_reference.replicate(obstime=original.obstime)
# We transform both coordinates to ICRS for simplicity and because we know
# it's a simple frame that is not time-dependent (it could be that both
# the original and velocity_reference frame are time-dependent)
original_icrs = original.transform_to(ICRS())
velocity_reference_icrs = velocity_reference.transform_to(ICRS())
differentials = velocity_reference_icrs.data.represent_as(
CartesianRepresentation, CartesianDifferential
).differentials
data_with_differentials = original_icrs.data.represent_as(
CartesianRepresentation
).with_differentials(differentials)
final_icrs = original_icrs.realize_frame(data_with_differentials)
if preserve_observer_frame:
final = final_icrs.transform_to(original)
else:
final = final_icrs.transform_to(velocity_reference)
return final.replicate(
representation_type=CartesianRepresentation,
differential_type=CartesianDifferential,
)
def attach_zero_velocities(coord):
"""
Set the differentials to be stationary on a coordinate object.
"""
new_data = coord.cartesian.with_differentials(ZERO_VELOCITIES)
return coord.realize_frame(new_data)
def _get_velocities(coord):
if "s" in coord.data.differentials:
return coord.velocity
else:
return ZERO_VELOCITIES
[docs]
class SpectralCoord(SpectralQuantity):
"""
A spectral coordinate with its corresponding unit.
.. note:: The |SpectralCoord| class is new in Astropy v4.1 and should be
considered experimental at this time. Note that we do not fully
support cases where the observer and target are moving
relativistically relative to each other, so care should be taken
in those cases. It is possible that there will be API changes in
future versions of Astropy based on user feedback. If you have
specific ideas for how it might be improved, please let us know
on the `astropy-dev mailing list`_ or at
http://feedback.astropy.org.
Parameters
----------
value : ndarray or `~astropy.units.Quantity` or `SpectralCoord`
Spectral values, which should be either wavelength, frequency,
energy, wavenumber, or velocity values.
unit : unit-like
Unit for the given spectral values.
observer : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`, optional
The coordinate (position and velocity) of observer. If no velocities
are present on this object, the observer is assumed to be stationary
relative to the frame origin.
target : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`, optional
The coordinate (position and velocity) of target. If no velocities
are present on this object, the target is assumed to be stationary
relative to the frame origin.
radial_velocity : `~astropy.units.Quantity` ['speed'], optional
The radial velocity of the target with respect to the observer. This
can only be specified if ``redshift`` is not specified.
redshift : float, optional
The relativistic redshift of the target with respect to the observer.
This can only be specified if ``radial_velocity`` cannot be specified.
doppler_rest : `~astropy.units.Quantity`, optional
The rest value to use when expressing the spectral value as a velocity.
doppler_convention : str, optional
The Doppler convention to use when expressing the spectral value as a velocity.
"""
@u.quantity_input(radial_velocity=u.km / u.s)
def __new__(
cls,
value,
unit=None,
observer=None,
target=None,
radial_velocity=None,
redshift=None,
**kwargs,
):
obj = super().__new__(cls, value, unit=unit, **kwargs)
# There are two main modes of operation in this class. Either the
# observer and target are both defined, in which case the radial
# velocity and redshift are automatically computed from these, or
# only one of the observer and target are specified, along with a
# manually specified radial velocity or redshift. So if a target and
# observer are both specified, we can't also accept a radial velocity
# or redshift.
if target is not None and observer is not None:
if radial_velocity is not None or redshift is not None:
raise ValueError(
"Cannot specify radial velocity or redshift if both "
"target and observer are specified"
)
# We only deal with redshifts here and in the redshift property.
# Otherwise internally we always deal with velocities.
if redshift is not None:
if radial_velocity is not None:
raise ValueError("Cannot set both a radial velocity and redshift")
redshift = u.Quantity(redshift)
# For now, we can't specify redshift=u.one in quantity_input above
# and have it work with plain floats, but if that is fixed, for
# example as in https://github.com/astropy/astropy/pull/10232, we
# can remove the check here and add redshift=u.one to the decorator
if not redshift.unit.is_equivalent(u.one):
raise u.UnitsError("redshift should be dimensionless")
radial_velocity = redshift.to(u.km / u.s, u.doppler_redshift())
# If we're initializing from an existing SpectralCoord, keep any
# parameters that aren't being overridden
if observer is None:
observer = getattr(value, "observer", None)
if target is None:
target = getattr(value, "target", None)
# As mentioned above, we should only specify the radial velocity
# manually if either or both the observer and target are not
# specified.
if observer is None or target is None:
if radial_velocity is None:
radial_velocity = getattr(value, "radial_velocity", None)
obj._radial_velocity = radial_velocity
obj._observer = cls._validate_coordinate(observer, label="observer")
obj._target = cls._validate_coordinate(target, label="target")
return obj
def __array_finalize__(self, obj):
super().__array_finalize__(obj)
self._radial_velocity = getattr(obj, "_radial_velocity", None)
self._observer = getattr(obj, "_observer", None)
self._target = getattr(obj, "_target", None)
@staticmethod
def _validate_coordinate(coord, label=""):
"""
Checks the type of the frame and whether a velocity differential and a
distance has been defined on the frame object.
If no distance is defined, the target is assumed to be "really far
away", and the observer is assumed to be "in the solar system".
Parameters
----------
coord : `~astropy.coordinates.BaseCoordinateFrame`
The new frame to be used for target or observer.
label : str, optional
The name of the object being validated (e.g. 'target' or 'observer'),
which is then used in error messages.
"""
if coord is None:
return
if not issubclass(coord.__class__, BaseCoordinateFrame):
if isinstance(coord, SkyCoord):
coord = coord.frame
else:
raise TypeError(
f"{label} must be a SkyCoord or coordinate frame instance"
)
# If the distance is not well-defined, ensure that it works properly
# for generating differentials
# TODO: change this to not set the distance and yield a warning once
# there's a good way to address this in astropy.coordinates
# https://github.com/astropy/astropy/issues/10247
with np.errstate(all="ignore"):
distance = getattr(coord, "distance", None)
if distance is not None and distance.unit.physical_type == "dimensionless":
coord = SkyCoord(coord, distance=DEFAULT_DISTANCE)
warnings.warn(
"Distance on coordinate object is dimensionless, an "
f"arbitrary distance value of {DEFAULT_DISTANCE} will be set instead.",
NoDistanceWarning,
)
# If the observer frame does not contain information about the
# velocity of the system, assume that the velocity is zero in the
# system.
if "s" not in coord.data.differentials:
warnings.warn(
f"No velocity defined on frame, assuming {ZERO_VELOCITIES}.",
NoVelocityWarning,
)
coord = attach_zero_velocities(coord)
return coord
[docs]
def replicate(
self,
value=None,
unit=None,
observer=None,
target=None,
radial_velocity=None,
redshift=None,
doppler_convention=None,
doppler_rest=None,
copy=False,
):
"""
Return a replica of the `SpectralCoord`, optionally changing the
values or attributes.
Note that no conversion is carried out by this method - this keeps
all the values and attributes the same, except for the ones explicitly
passed to this method which are changed.
If ``copy`` is set to `True` then a full copy of the internal arrays
will be made. By default the replica will use a reference to the
original arrays when possible to save memory.
Parameters
----------
value : ndarray or `~astropy.units.Quantity` or `SpectralCoord`, optional
Spectral values, which should be either wavelength, frequency,
energy, wavenumber, or velocity values.
unit : unit-like
Unit for the given spectral values.
observer : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`, optional
The coordinate (position and velocity) of observer.
target : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`, optional
The coordinate (position and velocity) of target.
radial_velocity : `~astropy.units.Quantity` ['speed'], optional
The radial velocity of the target with respect to the observer.
redshift : float, optional
The relativistic redshift of the target with respect to the observer.
doppler_rest : `~astropy.units.Quantity`, optional
The rest value to use when expressing the spectral value as a velocity.
doppler_convention : str, optional
The Doppler convention to use when expressing the spectral value as a velocity.
copy : bool, optional
If `True`, and ``value`` is not specified, the values are copied to
the new `SkyCoord` - otherwise a reference to the same values is used.
Returns
-------
sc : `SpectralCoord` object
Replica of this object
"""
if isinstance(value, u.Quantity):
if unit is not None:
raise ValueError(
"Cannot specify value as a Quantity and also specify unit"
)
else:
value, unit = value.value, value.unit
value = value if value is not None else self.value
unit = unit or self.unit
observer = self._validate_coordinate(observer) or self.observer
target = self._validate_coordinate(target) or self.target
doppler_convention = doppler_convention or self.doppler_convention
doppler_rest = doppler_rest or self.doppler_rest
# If value is being taken from self and copy is Tru
if copy:
value = value.copy()
# Only include radial_velocity if it is not auto-computed from the
# observer and target.
if (
(self.observer is None or self.target is None)
and radial_velocity is None
and redshift is None
):
radial_velocity = self.radial_velocity
with warnings.catch_warnings():
warnings.simplefilter("ignore", NoVelocityWarning)
return self.__class__(
value=value,
unit=unit,
observer=observer,
target=target,
radial_velocity=radial_velocity,
redshift=redshift,
doppler_convention=doppler_convention,
doppler_rest=doppler_rest,
copy=False,
)
@property
def quantity(self):
"""
Convert the ``SpectralCoord`` to a `~astropy.units.Quantity`.
Equivalent to ``self.view(u.Quantity)``.
Returns
-------
`~astropy.units.Quantity`
This object viewed as a `~astropy.units.Quantity`.
"""
return self.view(u.Quantity)
@property
def observer(self):
"""
The coordinates of the observer.
If set, and a target is set as well, this will override any explicit
radial velocity passed in.
Returns
-------
`~astropy.coordinates.BaseCoordinateFrame`
The astropy coordinate frame representing the observation.
"""
return self._observer
@observer.setter
def observer(self, value):
if self.observer is not None:
raise ValueError("observer has already been set")
self._observer = self._validate_coordinate(value, label="observer")
# Switch to auto-computing radial velocity
if self._target is not None:
self._radial_velocity = None
@property
def target(self):
"""
The coordinates of the target being observed.
If set, and an observer is set as well, this will override any explicit
radial velocity passed in.
Returns
-------
`~astropy.coordinates.BaseCoordinateFrame`
The astropy coordinate frame representing the target.
"""
return self._target
@target.setter
def target(self, value):
if self.target is not None:
raise ValueError("target has already been set")
self._target = self._validate_coordinate(value, label="target")
# Switch to auto-computing radial velocity
if self._observer is not None:
self._radial_velocity = None
@property
def radial_velocity(self):
"""
Radial velocity of target relative to the observer.
Returns
-------
`~astropy.units.Quantity` ['speed']
Radial velocity of target.
Notes
-----
This is different from the ``.radial_velocity`` property of a
coordinate frame in that this calculates the radial velocity with
respect to the *observer*, not the origin of the frame.
"""
if self._observer is None or self._target is None:
if self._radial_velocity is None:
return 0 * KMS
else:
return self._radial_velocity
else:
return self._calculate_radial_velocity(
self._observer, self._target, as_scalar=True
)
@property
def redshift(self):
"""
Redshift of target relative to observer. Calculated from the radial
velocity.
Returns
-------
`astropy.units.Quantity`
Redshift of target.
"""
return self.radial_velocity.to(u.dimensionless_unscaled, u.doppler_redshift())
@staticmethod
def _calculate_radial_velocity(observer, target, as_scalar=False):
"""
Compute the line-of-sight velocity from the observer to the target.
Parameters
----------
observer : `~astropy.coordinates.BaseCoordinateFrame`
The frame of the observer.
target : `~astropy.coordinates.BaseCoordinateFrame`
The frame of the target.
as_scalar : bool
If `True`, the magnitude of the velocity vector will be returned,
otherwise the full vector will be returned.
Returns
-------
`~astropy.units.Quantity` ['speed']
The radial velocity of the target with respect to the observer.
"""
# Convert observer and target to ICRS to avoid finite differencing
# calculations that lack numerical precision.
observer_icrs = observer.transform_to(ICRS())
target_icrs = target.transform_to(ICRS())
pos_hat = SpectralCoord._normalized_position_vector(observer_icrs, target_icrs)
d_vel = target_icrs.velocity - observer_icrs.velocity
vel_mag = pos_hat.dot(d_vel)
if as_scalar:
return vel_mag
else:
return vel_mag * pos_hat
@staticmethod
def _normalized_position_vector(observer, target):
"""
Calculate the normalized position vector between two frames.
Parameters
----------
observer : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
The observation frame or coordinate.
target : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
The target frame or coordinate.
Returns
-------
pos_hat : `BaseRepresentation`
Position representation.
"""
d_pos = (
target.cartesian.without_differentials()
- observer.cartesian.without_differentials()
)
dp_norm = d_pos.norm()
# Reset any that are 0 to 1 to avoid nans from 0/0
dp_norm[dp_norm == 0] = 1 * dp_norm.unit
pos_hat = d_pos / dp_norm
return pos_hat
[docs]
@u.quantity_input(velocity=u.km / u.s)
def with_observer_stationary_relative_to(
self, frame, velocity=None, preserve_observer_frame=False
):
"""
A new `SpectralCoord` with the velocity of the observer altered,
but not the position.
If a coordinate frame is specified, the observer velocities will be
modified to be stationary in the specified frame. If a coordinate
instance is specified, optionally with non-zero velocities, the
observer velocities will be updated so that the observer is co-moving
with the specified coordinates.
Parameters
----------
frame : str, `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
The observation frame in which the observer will be stationary. This
can be the name of a frame (e.g. 'icrs'), a frame class, frame instance
with no data, or instance with data. This can optionally include
velocities.
velocity : `~astropy.units.Quantity` or `~astropy.coordinates.CartesianDifferential`, optional
If ``frame`` does not contain velocities, these can be specified as
a 3-element `~astropy.units.Quantity`. In the case where this is
also not specified, the velocities default to zero.
preserve_observer_frame : bool
If `True`, the final observer frame class will be the same as the
original one, and if `False` it will be the frame of the velocity
reference class.
Returns
-------
new_coord : `SpectralCoord`
The new coordinate object representing the spectral data
transformed based on the observer's new velocity frame.
"""
if self.observer is None or self.target is None:
raise ValueError(
"This method can only be used if both observer "
"and target are defined on the SpectralCoord."
)
# Start off by extracting frame if a SkyCoord was passed in
if isinstance(frame, SkyCoord):
frame = frame.frame
if isinstance(frame, BaseCoordinateFrame):
if not frame.has_data:
frame = frame.realize_frame(
CartesianRepresentation(0 * u.km, 0 * u.km, 0 * u.km)
)
if frame.data.differentials:
if velocity is not None:
raise ValueError(
"frame already has differentials, cannot also specify velocity"
)
# otherwise frame is ready to go
else:
if velocity is None:
differentials = ZERO_VELOCITIES
else:
differentials = CartesianDifferential(velocity)
frame = frame.realize_frame(
frame.data.with_differentials(differentials)
)
if isinstance(frame, (type, str)):
if isinstance(frame, type):
frame_cls = frame
elif isinstance(frame, str):
frame_cls = frame_transform_graph.lookup_name(frame)
if velocity is None:
velocity = 0 * u.m / u.s, 0 * u.m / u.s, 0 * u.m / u.s
elif velocity.shape != (3,):
raise ValueError("velocity should be a Quantity vector with 3 elements")
frame = frame_cls(
0 * u.m,
0 * u.m,
0 * u.m,
*velocity,
representation_type="cartesian",
differential_type="cartesian",
)
observer = update_differentials_to_match(
self.observer, frame, preserve_observer_frame=preserve_observer_frame
)
# Calculate the initial and final los velocity
init_obs_vel = self._calculate_radial_velocity(
self.observer, self.target, as_scalar=True
)
fin_obs_vel = self._calculate_radial_velocity(
observer, self.target, as_scalar=True
)
# Apply transformation to data
new_data = _apply_relativistic_doppler_shift(self, fin_obs_vel - init_obs_vel)
new_coord = self.replicate(value=new_data, observer=observer)
return new_coord
[docs]
def with_radial_velocity_shift(self, target_shift=None, observer_shift=None):
"""
Apply a velocity shift to this spectral coordinate.
The shift can be provided as a redshift (float value) or radial
velocity (`~astropy.units.Quantity` with physical type of 'speed').
Parameters
----------
target_shift : float or `~astropy.units.Quantity` ['speed']
Shift value to apply to current target.
observer_shift : float or `~astropy.units.Quantity` ['speed']
Shift value to apply to current observer.
Returns
-------
`SpectralCoord`
New spectral coordinate with the target/observer velocity changed
to incorporate the shift. This is always a new object even if
``target_shift`` and ``observer_shift`` are both `None`.
"""
if observer_shift is not None and (
self.target is None or self.observer is None
):
raise ValueError(
"Both an observer and target must be defined "
"before applying a velocity shift."
)
for arg in [x for x in [target_shift, observer_shift] if x is not None]:
if isinstance(arg, u.Quantity) and not arg.unit.is_equivalent((u.one, KMS)):
raise u.UnitsError(
"Argument must have unit physical type 'speed' for radial velocty"
" or 'dimensionless' for redshift."
)
# The target or observer value is defined but is not a quantity object,
# assume it's a redshift float value and convert to velocity
if target_shift is None:
if self._observer is None or self._target is None:
return self.replicate()
target_shift = 0 * KMS
else:
target_shift = u.Quantity(target_shift)
if target_shift.unit.physical_type == "dimensionless":
target_shift = target_shift.to(u.km / u.s, u.doppler_redshift())
if self._observer is None or self._target is None:
return self.replicate(
value=_apply_relativistic_doppler_shift(self, target_shift),
radial_velocity=self.radial_velocity + target_shift,
)
if observer_shift is None:
observer_shift = 0 * KMS
else:
observer_shift = u.Quantity(observer_shift)
if observer_shift.unit.physical_type == "dimensionless":
observer_shift = observer_shift.to(u.km / u.s, u.doppler_redshift())
target_icrs = self._target.transform_to(ICRS())
observer_icrs = self._observer.transform_to(ICRS())
pos_hat = SpectralCoord._normalized_position_vector(observer_icrs, target_icrs)
target_velocity = _get_velocities(target_icrs) + target_shift * pos_hat
observer_velocity = _get_velocities(observer_icrs) + observer_shift * pos_hat
target_velocity = CartesianDifferential(target_velocity.xyz)
observer_velocity = CartesianDifferential(observer_velocity.xyz)
new_target = target_icrs.realize_frame(
target_icrs.cartesian.with_differentials(target_velocity)
).transform_to(self._target)
new_observer = observer_icrs.realize_frame(
observer_icrs.cartesian.with_differentials(observer_velocity)
).transform_to(self._observer)
init_obs_vel = self._calculate_radial_velocity(
observer_icrs, target_icrs, as_scalar=True
)
fin_obs_vel = self._calculate_radial_velocity(
new_observer, new_target, as_scalar=True
)
new_data = _apply_relativistic_doppler_shift(self, fin_obs_vel - init_obs_vel)
return self.replicate(value=new_data, observer=new_observer, target=new_target)
[docs]
def to_rest(self):
"""
Transforms the spectral axis to the rest frame.
"""
if self.observer is not None and self.target is not None:
return self.with_observer_stationary_relative_to(self.target)
result = _apply_relativistic_doppler_shift(self, -self.radial_velocity)
return self.replicate(value=result, radial_velocity=0.0 * KMS, redshift=None)
def __repr__(self):
prefixstr = "<" + self.__class__.__name__ + " "
try:
radial_velocity = self.radial_velocity
redshift = self.redshift
except ValueError:
radial_velocity = redshift = "Undefined"
repr_items = [f"{prefixstr}"]
if self.observer is not None:
observer_repr = indent(repr(self.observer), 14 * " ").lstrip()
repr_items.append(f" observer: {observer_repr}")
if self.target is not None:
target_repr = indent(repr(self.target), 12 * " ").lstrip()
repr_items.append(f" target: {target_repr}")
if (
self._observer is not None and self._target is not None
) or self._radial_velocity is not None:
if self.observer is not None and self.target is not None:
repr_items.append(" observer to target (computed from above):")
else:
repr_items.append(" observer to target:")
repr_items.append(f" radial_velocity={radial_velocity}")
repr_items.append(f" redshift={redshift}")
if self.doppler_rest is not None or self.doppler_convention is not None:
repr_items.append(f" doppler_rest={self.doppler_rest}")
repr_items.append(f" doppler_convention={self.doppler_convention}")
arrstr = np.array2string(self.view(np.ndarray), separator=", ", prefix=" ")
if len(repr_items) == 1:
repr_items[0] += f"{arrstr}{self._unitstr:s}"
else:
repr_items[1] = " (" + repr_items[1].lstrip()
repr_items[-1] += ")"
repr_items.append(f" {arrstr}{self._unitstr:s}")
return "\n".join(repr_items) + ">"
