def cross(a, b):
"""
Compute cross product of two CartesianRepresentations.
Parameters
----------
a : `CartesianRepresentation`
First CartesianRepresentation, e.g directions to earth
b : `CartesianRepresentation`
Second CartesianRepresentation, e.g directions of tiles
Returns
-------
cross_product : `CartesianRepresentation`
array of cross products. If `a` has shape (N, M) and `b` has shape (K,L)
returned Quantity has shape (N, M, K, L)
"""
# since the data can be n-dimensional, reshape
# to a 2-d (3, N) array
xyz_a, xyz_b = a.xyz, b.xyz
orig_shape_a = xyz_a.shape
orig_shape_b = xyz_b.shape
xyz_a = xyz_a.reshape((3, xyz_a.size // 3))
xyz_b = xyz_b.reshape((3, xyz_b.size // 3))
# take the cross product
cross_product = np.cross(xyz_a[:, :, np.newaxis], xyz_b,
axisa=0, axisb=0, axisc=0)
cross_product_unit = xyz_a.unit * xyz_b.unit
cross_product = u.Quantity(cross_product, unit=cross_product_unit)
cartrep = CartesianRepresentation(cross_product)
return cartrep.reshape(orig_shape_a[1:] + orig_shape_b[1:])
def test_creation_cartesian():
rep = CartesianRepresentation([10, 0., 0.]*u.pc)
dif = CartesianDifferential([0, 100, 0.]*u.pc/u.Myr)
rep = rep.with_differentials(dif)
c = SkyCoord(rep)
sdif = dif.represent_as(SphericalCosLatDifferential, rep)
assert_quantity_allclose(c.pm_ra_cosdec, sdif.d_lon_coslat)
def setup(self):
# Avoid top-level module import to make sure that the benchmarks are
# compatible with versions of astropy that did not have this functionality.
from astropy.coordinates import CartesianDifferential
self.scalar_rep = CartesianRepresentation([1., 2, 3] * u.kpc)
self.scalar_dif = CartesianDifferential([1, 2, 3.] * u.km/u.s)
self.array_rep = CartesianRepresentation(np.ones((3, 1000)) * u.kpc)
self.array_dif = CartesianDifferential(np.ones((3, 1000)) * u.km/u.s)
def test_plot_ephem_different_plane_raises_error():
unused_epochs = Time.now().reshape(-1)
unused_coordinates = CartesianRepresentation(
[(1, 0, 0)] * u.au,
xyz_axis=1,
differentials=CartesianDifferential([(0, 1, 0)] * (u.au / u.day),
xyz_axis=1),
)
op = StaticOrbitPlotter(plane=Planes.EARTH_ECLIPTIC)
op.set_attractor(Sun)
op.set_body_frame(Earth)
with pytest.raises(ValueError) as excinfo:
op.plot_ephem(
Ephem(unused_epochs, unused_coordinates, Planes.EARTH_EQUATOR))
assert (
"sample the ephemerides using a different plane or create a new plotter"
in excinfo.exconly())
def altaz_interpolate(self, time):
"""Interpolate pointing for a given time."""
t_new = time.mjd
t = self.time.mjd
xyz = self.altaz.cartesian
x_new = interp1d(t, xyz.x)(t_new)
y_new = interp1d(t, xyz.y)(t_new)
z_new = interp1d(t, xyz.z)(t_new)
xyz_new = CartesianRepresentation(x_new, y_new, z_new)
altaz_frame = AltAz(obstime=time, location=self.location)
# FIXME: an API change in Astropy in 3.1 broke this
# See https://github.com/gammapy/gammapy/pull/1906
if astropy_version >= "3.1":
kwargs = {"representation_type": "unitspherical"}
else:
kwargs = {"representation": "unitspherical"}
return SkyCoord(xyz_new, frame=altaz_frame, unit="deg", **kwargs)
def for_coords(cls, coords):
"""Create a coordinate frame that has its axes aligned with the
principal components of a cloud of points.
Parameters
----------
coords : `astropy.coordinates.SkyCoord`
A cloud of points
Returns
-------
frame : `EigenFrame`
A new coordinate frame
"""
v = coords.icrs.cartesian.xyz.value
_, r = np.linalg.eigh(np.dot(v, v.T))
r = r[:, ::-1] # Order by descending eigenvalue
e_x, e_y, e_z = CartesianRepresentation(r, unit=dimensionless_unscaled)
return cls(e_x=e_x, e_y=e_y, e_z=e_z)
def test_hgs_hcc_sunspice():
# Compare our HGS->HCC transformation against SunSPICE
# "HEQ" is another name for HEEQ, which is equivalent to Heliographic Stonyhurst
# "HGRTN" is equivalent to our Heliocentric, but with the axes permuted
# SunSPICE, like us, assumes an Earth observer if not explicitly specified
#
# IDL> coord = [7d5, 8d5, 9d5]
# IDL> convert_sunspice_coord, '2019-06-01', coord, 'HEQ', 'HGRTN'
# Assuming Earth observation
# IDL> print, coord
# 688539.32 800000.00 908797.89
old = SkyCoord(CartesianRepresentation([7e5, 8e5, 9e5]*u.km),
frame=HeliographicStonyhurst(obstime='2019-06-01'))
new = old.heliocentric
assert_quantity_allclose(new.x, 800000.00*u.km, atol=1e-2*u.km)
assert_quantity_allclose(new.y, 908797.89*u.km, atol=1e-2*u.km)
assert_quantity_allclose(new.z, 688539.32*u.km, atol=1e-2*u.km)
def __call__(self, t):
"""
Computes the interpolated coordinates at the given time(s).
Parameters
----------
t : Time
Time or list of times where an interpolated coordinate is required
Returns
-------
coords : SkyCoord
A `SkyCoord` object with the requested coordinate(s), in the
original frame
Raises
------
ValueError
If the requested `t` value is out of bounds for the interpolator
"""
if not self._interpolators_initialised:
# Lazy init interpolators only when required
self._init_interpolators()
# **** get coords at requested time ****
# compute raw r and v vectors and
# fill Astropy cartesian vectors (with velocities if available)
if t.isscalar:
# there is a single time instance
coords = CartesianRepresentation(self._compute_pos(t), copy=False)
if self._has_velocity:
v = CartesianDifferential(self._compute_vel(t), copy=False)
coords = coords.with_differentials(v)
else:
# there is more than one time instance
r = [self._compute_pos(time) for time in t]
coords = CartesianRepresentation(
np.asarray(r), unit=r[0].unit, copy=False, xyz_axis=1
)
if self._has_velocity:
v = [self._compute_vel(time) for time in t]
v = CartesianDifferential(
np.asarray(v), unit=v[0].unit, copy=False, xyz_axis=1
)
coords = coords.with_differentials(v)
return init_pvt(self._frame_name, t, coords)
def represent_as(self, representation):
"""Converts the orbit to a specific representation.
.. versionadded:: 0.11.0
Parameters
----------
representation : ~astropy.coordinates.BaseRepresentation
Representation object to use. It must be a class, not an instance.
Examples
--------
>>> from poliastro.examples import iss
>>> from astropy.coordinates import CartesianRepresentation, SphericalRepresentation
>>> iss.represent_as(CartesianRepresentation)
<CartesianRepresentation (x, y, z) in km
(859.07256, -4137.20368, 5295.56871)
(has differentials w.r.t.: 's')>
>>> iss.represent_as(CartesianRepresentation).xyz
<Quantity [ 859.07256, -4137.20368, 5295.56871] km>
>>> iss.represent_as(CartesianRepresentation).differentials['s']
<CartesianDifferential (d_x, d_y, d_z) in km / s
(7.37289205, 2.08223573, 0.43999979)>
>>> iss.represent_as(CartesianRepresentation).differentials['s'].d_xyz
<Quantity [7.37289205, 2.08223573, 0.43999979] km / s>
>>> iss.represent_as(SphericalRepresentation)
<SphericalRepresentation (lon, lat, distance) in (rad, rad, km)
(4.91712525, 0.89732339, 6774.76995296)
(has differentials w.r.t.: 's')>
"""
# As we do not know the differentials, we first convert to cartesian,
# then let the frame represent_as do the rest
# TODO: Perhaps this should be public API as well?
cartesian = CartesianRepresentation(
*self.r, differentials=CartesianDifferential(*self.v))
# See the propagate function for reasoning about the usage of a
# protected method
coords = self.frame._replicate(cartesian,
representation_type="cartesian")
return coords.represent_as(representation)
def _interpolate_sinc(epochs, reference_epochs, coordinates):
def _interp_1d(arr):
return _sinc_interp(arr, reference_epochs.jd, epochs.jd)
xyz_unit = coordinates.xyz.unit
d_xyz_unit = coordinates.differentials["s"].d_xyz.unit
x = _interp_1d(coordinates.x.value) * xyz_unit
y = _interp_1d(coordinates.y.value) * xyz_unit
z = _interp_1d(coordinates.z.value) * xyz_unit
d_x = _interp_1d(coordinates.differentials["s"].d_x.value) * d_xyz_unit
d_y = _interp_1d(coordinates.differentials["s"].d_y.value) * d_xyz_unit
d_z = _interp_1d(coordinates.differentials["s"].d_z.value) * d_xyz_unit
return CartesianRepresentation(x,
y,
z,
differentials=CartesianDifferential(
d_x, d_y, d_z))
def test_orbit_creation_using_skycoord(attractor):
vel = [0, 2, 0] * u.km / u.s
cartdiff = CartesianDifferential(*vel)
pos = [30_000, 0, 0] * u.km
cartrep = CartesianRepresentation(*pos, differentials=cartdiff)
coord = SkyCoord(cartrep, frame="icrs")
o = Orbit.from_coords(attractor, coord)
inertial_frame_at_body_centre = get_frame(
attractor, Planes.EARTH_EQUATOR, obstime=coord.obstime
)
coord_transformed_to_irf = coord.transform_to(inertial_frame_at_body_centre)
pos_transformed_to_irf = coord_transformed_to_irf.cartesian.xyz
vel_transformed_to_irf = coord_transformed_to_irf.cartesian.differentials["s"].d_xyz
assert (o.r == pos_transformed_to_irf).all()
assert (o.v == vel_transformed_to_irf).all()
def _create_coord_from_offset(observer, radial_velocity):
"""
Generates a default target or observer from a provided observer or
target with an offset defined such as to create the provided radial
velocity.
Parameters
----------
observer : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
Observer frame off which to base the target frame.
radial_velocity : `~astropy.units.Quantity`
Radial velocity used to calculate appropriate offsets between
provided observer and generated target.
Returns
-------
target : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
Generated target frame.
"""
# The generated observer or target will be set up along the same y and z
# coordinates as the target or observer, but offset along the x direction
observer_icrs = observer.transform_to(ICRS)
d = observer_icrs.cartesian.norm()
drep = CartesianRepresentation(
[DEFAULT_DISTANCE.to(d.unit), 0 * d.unit, 0 * d.unit])
obs_vel = observer_icrs.cartesian.differentials['s']
target = (observer_icrs.cartesian.without_differentials() +
drep).with_differentials(
CartesianDifferential([
_relativistic_velocity_addition(
obs_vel.d_x, radial_velocity),
obs_vel.d_y.to(radial_velocity.unit),
obs_vel.d_z.to(radial_velocity.unit)
]))
return observer_icrs.realize_frame(target)
def teme_to_tirs(teme_coord, tirs_frame):
# TEME to TIRS basic rotation matrix
teme_to_pef_mat = rotation_matrix(_gmst82_angle(teme_coord.obstime),
axis='z')
# rotate position vector: TEME to TIRS
r_tirs = teme_coord.cartesian.transform(teme_to_pef_mat)
# prepare rotation offset: w x r_TIRS
wxr = CartesianRepresentation(_w).cross(r_tirs)
# do the velocity rotation and then add rotation offset
v_tirs = teme_coord.velocity.to_cartesian().transform(
teme_to_pef_mat) - wxr
v_tirs = CartesianDifferential.from_cartesian(v_tirs)
# Prepare final coord vector with velocity
tirs_coord = r_tirs.with_differentials(v_tirs)
# Add coord data to the existing frame
return tirs_frame.realize_frame(tirs_coord)
def translate(cls, translation_vector):
"""
Apply a coordinate translation.
Parameters
----------
cls : astropy.coordinates.CartesianRepresentation
Equivalent to the 'self' argument for methods.
translation_vector : astropy.units.Quantity, with dimensions of length
3-vector by which to translate.
Returns
-------
out : astropy.coordinates.CartesianRepresentation
A new CartesianRepresentation instance with translation applied.
"""
return CartesianRepresentation(cls.__class__.get_xyz(cls) +
translation_vector.reshape(3, 1),
differentials=cls.differentials)
def test_orbit_creation_using_frame_obj(attractor, frame, obstime):
vel = [0, 2, 0] * u.km / u.s
cartdiff = CartesianDifferential(*vel)
pos = [30_000, 0, 0] * u.km
cartrep = CartesianRepresentation(*pos, differentials=cartdiff)
coord = frame(cartrep, obstime=obstime)
o = Orbit.from_coords(attractor, coord)
inertial_frame_at_body_centre = get_frame(
attractor, Planes.EARTH_EQUATOR, obstime=coord.obstime
)
coord_transformed_to_irf = coord.transform_to(inertial_frame_at_body_centre)
pos_transformed_to_irf = coord_transformed_to_irf.cartesian.xyz
vel_transformed_to_irf = coord_transformed_to_irf.cartesian.differentials["s"].d_xyz
assert_quantity_allclose(o.r, pos_transformed_to_irf, atol=1e-5 * u.km)
assert_quantity_allclose(o.v, vel_transformed_to_irf, atol=1e-5 * u.km / u.s)
def _sample(self, time_values, method=mean_motion):
positions = method(self, time_values.to(u.s).value)
data = CartesianRepresentation(positions[0] * u.km, xyz_axis=1)
# If the frame supports obstime, set the time values
kwargs = {}
if "obstime" in self.frame.frame_attributes:
kwargs["obstime"] = self.epoch + time_values
else:
warn(
"Frame {} does not support 'obstime', time values were not returned".format(
self.frame.__class__
)
)
# Use of a protected method instead of frame.realize_frame
# because the latter does not let the user choose the representation type
# in one line despite its parameter names, see
# https://github.com/astropy/astropy/issues/7784
return self.frame._replicate(data, representation_type="cartesian", **kwargs)
def test_from_orbit_has_desired_properties(method, rtol):
epochs = Time(
[
"2020-02-01 12:00:00",
"2020-02-13 12:00:00",
"2020-03-04 12:00:00",
"2020-03-17 12:00:00",
]
)
expected_coordinates = CartesianRepresentation(
[
(336.77109079, -1447.38211842, -743.72094119),
(-1133.43957703, 449.41297342, 3129.10416554),
(201.42480053, -1978.64139325, -287.25776291),
(-1084.94556884, -1713.5357774, 3298.72284309),
]
* u.km,
xyz_axis=1,
differentials=CartesianDifferential(
[
(-2.68502706, -14.85798508, 9.66683585),
(1.36841306, 7.30080155, -4.88822441),
(-3.46999908, -10.04899184, 11.19715233),
(-1.46069855, 5.88696886, 3.28112281),
]
* (u.km / u.s),
xyz_axis=1,
),
)
r = [-1000, -2000, 3100] * u.km
v = [-1.836, 5.218, 4.433] * u.km / u.s
orb = Orbit.from_vectors(Earth, r, v)
unused_plane = Planes.EARTH_EQUATOR
ephem = Ephem.from_orbit(orbit=orb, epochs=epochs, plane=unused_plane)
coordinates = ephem.sample()
assert ephem.epochs is epochs
assert_coordinates_allclose(coordinates, expected_coordinates, rtol=rtol)
def tirs_to_teme(tirs_coord, teme_frame):
# TIRS to TEME basic rotation matrix
teme_to_pef_mat = rotation_matrix(_gmst82_angle(tirs_coord.obstime),
axis='z')
pef_to_teme_mat = teme_to_pef_mat.transpose()
# rotate position vector: TIRS to TEME
r_teme = tirs_coord.cartesian.transform(pef_to_teme_mat)
# prepare rotation offset: w x r_TIRS
wxr = CartesianRepresentation(_w).cross(tirs_coord.cartesian)
# add rotation offset and then do the velocity rotation
v_teme = (tirs_coord.velocity.to_cartesian() +
wxr).transform(pef_to_teme_mat)
v_teme = CartesianDifferential.from_cartesian(v_teme)
# Prepare final coord vector with velocity
teme_coord = r_teme.with_differentials(v_teme)
# Add coord data to the existing frame
return teme_frame.realize_frame(teme_coord)
def _target_from_observer(observer, radial_velocity):
"""
Generates a default target from a provided observer with an offset
defined such as to create the provided radial velocity.
Parameters
----------
observer : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
Observer frame off which to base the target frame.
radial_velocity : `~astropy.units.Quantity`
Radial velocity used to calculate appropriate offsets between
provided observer and generated target.
Returns
-------
target : `~astropy.coordinates.BaseCoordinateFrame` or `~astropy.coordinates.SkyCoord`
Generated target frame.
"""
observer = SpectralCoord._validate_coordinate(observer)
observer_icrs = observer.transform_to(ICRS)
d = observer_icrs.cartesian.norm()
drep = CartesianRepresentation(
[DEFAULT_DISTANCE.to(d.unit), 0 * d.unit, 0 * d.unit])
obs_vel = observer_icrs.cartesian.differentials['s']
tot_rv = radial_velocity # + observer_icrs.radial_velocity
target = (observer_icrs.cartesian.without_differentials() +
drep).with_differentials(
CartesianDifferential([
obs_vel.d_x + tot_rv,
obs_vel.d_y.to(tot_rv.unit),
obs_vel.d_z.to(tot_rv.unit)
]))
target = observer_icrs.realize_frame(target)
return target
def nominal_to_altaz(altaz_coord,norm_coord):
"""
Transformation from astropy AltAz system to nominal system
Parameters
----------
altaz_coord: AltAz system
norm_coord: nominal system
Returns
-------
nominal Coordinates
"""
alt_norm,az_norm = norm_coord.array_direction
az = altaz_coord.az
alt = altaz_coord.alt
x,y = altaz_to_offset(az,alt,az_norm,alt_norm)
x=x*u.rad
y=y*u.rad
representation = CartesianRepresentation(x.to(u.deg),y.to(u.deg),0*u.deg)
return norm_coord.realize_frame(representation)
def rotate(self, angle):
"""
Rotate the star, by moving the spots.
Parameters
----------
angle : `~astropy.units.Quantity`
"""
remove_is = rotation_matrix(-self.inclination, axis='x')
rotate = rotation_matrix(angle, axis='z')
add_is = rotation_matrix(self.inclination, axis='x')
transform_matrix = matrix_product(remove_is, rotate, add_is)
for spot in self.spots:
cartesian = CartesianRepresentation(
x=spot.x, y=spot.y, z=spot.z).transform(transform_matrix)
spot.x = cartesian.x.value
spot.y = cartesian.y.value
spot.z = cartesian.z.value
self.rotations_applied += angle
def select_tidal_annulus(w0,\
ann_low = 0.0,\
ann_high = 0.5,\
sat_mass=1e8,\
mw_mass=130.0075e10,\
mw_c=32.089):
com_p, com_v, com_index = calc_com(w0)
distances_to_com =\
np.linalg.norm((w0.pos - CartesianRepresentation(com_p)).xyz, axis=0)
tidal_radius = r_tidal(sat_mass, mw_mass, mw_c, np.linalg.norm(com_p))
selected_indices = []
for p_index in range(len(distances_to_com)):
curr_dist = distances_to_com[p_index]
if (ann_low * tidal_radius) <= curr_dist < (ann_high * tidal_radius):
selected_indices.append(p_index)
return w0[selected_indices]
def telescope_to_camera(telescope_coord, camera_frame):
'''
Transformation between TelescopeFrame and CameraFrame
Is called when a SkyCoord is transformed from TelescopeFrame into CameraFrame
'''
x_pos = telescope_coord.delta_alt
y_pos = telescope_coord.delta_az
# reverse the rotation applied to get to this system
rot = -camera_frame.rotation
if rot.value == 0.0: # if no rotation applied save a few cycles
x_rotated = x_pos
y_rotated = y_pos
else: # or else rotate all positions around the camera centre
cosrot = np.cos(rot)
sinrot = np.sin(rot)
x_rotated = x_pos * cosrot - y_pos * sinrot
y_rotated = x_pos * sinrot + y_pos * cosrot
focal_length = camera_frame.focal_length
# this assumes an equidistant mapping function of the telescope optics
# or a small angle approximation of most other mapping functions
# this could be replaced by actually defining the mapping function
# as an Attribute of `CameraFrame` that maps f(theta, focal_length) -> r,
# where theta is the angle to the optical axis and r is the distance
# to the camera center in the focal plane
x_rotated = x_rotated.to_value(u.rad) * focal_length
y_rotated = y_rotated.to_value(u.rad) * focal_length
representation = CartesianRepresentation(
x_rotated,
y_rotated,
0 * u.m
)
return camera_frame.realize_frame(representation)
def interpolate(self, epochs, reference_epochs, coordinates):
xyz_unit = coordinates.xyz.unit
d_xyz_unit = coordinates.differentials["s"].d_xyz.unit
result_xyz = (
spline_interp(
coordinates.xyz.value, reference_epochs.jd, epochs.jd, kind=self._kind
)
<< xyz_unit
)
result_d_xyz = (
spline_interp(
coordinates.differentials["s"].d_xyz.value,
reference_epochs.jd,
epochs.jd,
kind=self._kind,
)
<< d_xyz_unit
)
return CartesianRepresentation(
result_xyz, differentials=CartesianDifferential(result_d_xyz)
)
def propagation_engine(line1, line2, time_list):
"""Tests the interpolation accuracy for a given TLE."""
# Init satellite object from the TLE
sat = Satrec.twoline2rv(line1, line2)
# ****** Generate the pos, vel vectors for each time instant ******
# Run the propagation and init pos and vel vectors in TEME
e, r_list, v_list = sat.sgp4_array(time_list.jd1, time_list.jd2)
# Load the time, pos, vel info into astropy objects (shallow copied)
vel_list = CartesianDifferential(v_list, unit=u.km / u.s, xyz_axis=1)
pos_list = CartesianRepresentation(r_list, unit=u.km,
xyz_axis=1).with_differentials(vel_list)
# trajectory in astropy
traj_astropy = init_pvt(TEME, time_list, pos_list)
# Init trajectory in Trajectory object
trajectory = Trajectory(traj_astropy)
return {"traj": trajectory, "sat": sat}
def test_teme_itrf():
"""
Test case transform from TEME to ITRF.
Test case derives from example on appendix C of Vallado, Crawford, Hujsak & Kelso (2006).
See https://celestrak.com/publications/AIAA/2006-6753/AIAA-2006-6753-Rev2.pdf
"""
v_itrf = CartesianDifferential(-3.225636520,
-2.872451450,
5.531924446,
unit=u.km / u.s)
p_itrf = CartesianRepresentation(-1033.479383,
7901.2952740,
6380.35659580,
unit=u.km,
differentials={'s': v_itrf})
t = Time("2004-04-06T07:51:28.386")
teme = ITRS(p_itrf, obstime=t).transform_to(TEME(obstime=t))
v_teme = CartesianDifferential(-4.746131487,
0.785818041,
5.531931288,
unit=u.km / u.s)
p_teme = CartesianRepresentation(5094.18016210,
6127.64465050,
6380.34453270,
unit=u.km,
differentials={'s': v_teme})
assert_allclose(teme.cartesian.without_differentials().xyz,
p_teme.without_differentials().xyz,
atol=30 * u.cm)
assert_allclose(teme.cartesian.differentials['s'].d_xyz,
p_teme.differentials['s'].d_xyz,
atol=1.0 * u.cm / u.s)
# test round trip
itrf = teme.transform_to(ITRS(obstime=t))
assert_allclose(itrf.cartesian.without_differentials().xyz,
p_itrf.without_differentials().xyz,
atol=100 * u.cm)
assert_allclose(itrf.cartesian.differentials['s'].d_xyz,
p_itrf.differentials['s'].d_xyz,
atol=1 * u.cm / u.s)
def test_regression_6300():
"""Check that importing old frame attribute names from astropy.coordinates
still works. See comments at end of #6300
"""
from astropy.utils.exceptions import AstropyDeprecationWarning
from astropy.coordinates import CartesianRepresentation
from astropy.coordinates import (TimeFrameAttribute,
QuantityFrameAttribute,
CartesianRepresentationFrameAttribute)
with catch_warnings() as found_warnings:
attr = TimeFrameAttribute(default=Time("J2000"))
for w in found_warnings:
if issubclass(w.category, AstropyDeprecationWarning):
break
else:
assert False, "Deprecation warning not raised"
with catch_warnings() as found_warnings:
attr = QuantityFrameAttribute(default=5 * u.km)
for w in found_warnings:
if issubclass(w.category, AstropyDeprecationWarning):
break
else:
assert False, "Deprecation warning not raised"
with catch_warnings() as found_warnings:
attr = CartesianRepresentationFrameAttribute(
default=CartesianRepresentation([5, 6, 7] * u.kpc))
for w in found_warnings:
if issubclass(w.category, AstropyDeprecationWarning):
break
else:
assert False, "Deprecation warning not raised"
def _interpolate_splines(epochs,
reference_epochs,
coordinates,
*,
kind="cubic"):
xyz_unit = coordinates.xyz.unit
d_xyz_unit = coordinates.differentials["s"].d_xyz.unit
# TODO: Avoid building interpolant every time?
# Does it have a performance impact?
interpolant_xyz = interp1d(reference_epochs.jd,
coordinates.xyz.value,
kind=kind)
interpolant_d_xyz = interp1d(
reference_epochs.jd,
coordinates.differentials["s"].d_xyz.value,
kind=kind,
)
result_xyz = interpolant_xyz(epochs.jd) * xyz_unit
result_d_xyz = interpolant_d_xyz(epochs.jd) * d_xyz_unit
return CartesianRepresentation(
result_xyz, differentials=CartesianDifferential(result_d_xyz))
def test_array_coordinates_creation():
"""
Test creating coordinates from arrays.
"""
c = ICRS(np.array([1, 2])*u.deg, np.array([3, 4])*u.deg)
assert not c.ra.isscalar
with pytest.raises(ValueError):
c = ICRS(np.array([1, 2])*u.deg, np.array([3, 4, 5])*u.deg)
with pytest.raises(ValueError):
c = ICRS(np.array([1, 2, 4, 5])*u.deg, np.array([[3, 4], [5, 6]])*u.deg)
# make sure cartesian initialization also works
cart = CartesianRepresentation(x=[1., 2.]*u.kpc, y=[3., 4.]*u.kpc, z=[5., 6.]*u.kpc)
c = ICRS(cart)
# also ensure strings can be arrays
c = SkyCoord(['1d0m0s', '2h02m00.3s'], ['3d', '4d'])
# but invalid strings cannot
with pytest.raises(ValueError):
c = SkyCoord(Angle(['10m0s', '2h02m00.3s']), Angle(['3d', '4d']))
with pytest.raises(ValueError):
c = SkyCoord(Angle(['1d0m0s', '2h02m00.3s']), Angle(['3x', '4d']))
def earth_location_itrf(self, time=None):
'''Return NuSTAR spacecraft location in ITRF coordinates'''
if self.tt2tdb_mode.lower().startswith('pint'):
# log.warning('Using location=None for TT to TDB conversion')
return None
elif self.tt2tdb_mode.lower().startswith('astropy'):
# First, interpolate ECI geocentric location from orbit file.
# These are inertial coorinates aligned with ICRF
log.warning('Performing GCRS to ITRS transformation')
pos_gcrs = GCRS(CartesianRepresentation(self.X(time.tt.mjd)*u.m,
self.Y(time.tt.mjd)*u.m,
self.Z(time.tt.mjd)*u.m),
obstime=time)
# Now transform ECI (GCRS) to ECEF (ITRS)
# By default, this uses the WGS84 ellipsoid
pos_ITRS = pos_gcrs.transform_to(ITRS(obstime=time))
# Return geocentric ITRS coordinates as an EarthLocation object
return pos_ITRS.earth_location
else:
log.error('Unknown tt2tdb_mode %s, using None' % self.tt2tdb_mode)
return None
def telescope_to_nominal(tel_coord,norm_frame):
"""
Coordinate transformation from telescope frame to nominal frame
Parameters
----------
tel_coord: TelescopeFrame system
norm_frame: NominalFrame system
Returns
-------
NominalFrame coordinates
"""
alt_tel,az_tel = tel_coord.pointing_direction
alt_norm,az_norm = norm_frame.array_direction
alt_trans,az_trans = offset_to_altaz(tel_coord.x,tel_coord.y,az_tel,alt_tel)
x,y = altaz_to_offset(az_trans,alt_trans,az_norm,alt_norm)
x = x*u.rad
y = y*u.rad
representation = CartesianRepresentation(x.to(tel_coord.x.unit),y.to(tel_coord.x.unit),0*tel_coord.x.unit)
return norm_frame.realize_frame(representation)
def test_ephem_from_horizons_calls_horizons_with_correct_parameters(
horizons_mock, attractor, location_str, plane, refplane_str):
unused_name = "Strange Object"
unused_id_type = "id_type"
epochs = Time(["2020-03-01 12:00:00"], scale="tdb")
horizons_mock().vectors.return_value = {
"x": [1] * u.au,
"y": [0] * u.au,
"z": [0] * u.au,
"vx": [0] * (u.au / u.day),
"vy": [1] * (u.au / u.day),
"vz": [0] * (u.au / u.day),
}
expected_coordinates = CartesianRepresentation(
[(1, 0, 0)] * u.au,
xyz_axis=1,
differentials=CartesianDifferential([(0, 1, 0)] * (u.au / u.day),
xyz_axis=1),
)
ephem = Ephem.from_horizons(unused_name,
epochs,
attractor=attractor,
plane=plane,
id_type=unused_id_type)
horizons_mock.assert_called_with(id=unused_name,
location=location_str,
epochs=epochs.jd,
id_type=unused_id_type)
horizons_mock().vectors.assert_called_once_with(refplane=refplane_str)
coordinates = ephem.sample()
assert_coordinates_allclose(coordinates, expected_coordinates)
def telescope_to_camera(telescope_coord, camera_frame):
"""
Transformation between TelescopeFrame and CameraFrame
Parameters
----------
telescope_coord: `astropy.coordinates.SkyCoord`
TelescopeFrame system
camera_frame: `astropy.coordinates.SkyCoord`
CameraFrame system
Returns
-------
CameraFrame Coordinates
"""
x_pos = telescope_coord.cartesian.x
y_pos = telescope_coord.cartesian.y
# reverse the rotation applied to get to this system
rot = camera_frame.rotation * -1
if rot == 0: # if no rotation applied save a few cycles
x_rotated = x_pos
y_rotated = y_pos
else: # or else rotate all positions around the camera centre
x_rotated = x_pos * cos(rot) - y_pos * sin(rot)
y_rotated = x_pos * sin(rot) + y_pos * cos(rot)
focal_length = camera_frame.focal_length
# Remove distance units here as we are using small angle approx
x_rotated = x_rotated.to(u.rad) * (focal_length / u.m)
y_rotated = y_rotated.to(u.rad) * (focal_length / u.m)
representation = CartesianRepresentation(x_rotated.value * u.m,
y_rotated.value * u.m, 0 * u.m)
return camera_frame.realize_frame(representation)
def add_oriented_radecs(elvis_tab, hostidx=0, targetidx=1,
target_coord=SkyCoord(0*u.deg, 0*u.deg),
earth_distance=8.5*u.kpc, earth_vrot=220*u.km/u.s,
roll_angle=0*u.deg):
"""
Computes a spherical coordinate system centered on the `hostidx` halo,
re-oriented so that `targetidx` is at the `target_coord` coordinate
location.
Note that this adds columns 'host<n>_*' to
`elvis_tab`, and will *overwrite* them if they already exist.
"""
if hasattr(target_coord, 'spherical'):
target_lat = target_coord.spherical.lat
target_lon = target_coord.spherical.lon
else:
target_lat = target_coord.lat
target_lon = target_coord.lon
def offset_repr(rep, vector, newrep=None):
if newrep is None:
newrep = rep.__class__
newxyz = rep.to_cartesian().xyz + vector.reshape(3, 1)
return CartesianRepresentation(newxyz).represent_as(newrep)
def rotate_repr(rep, matrix, newrep=None):
if newrep is None:
newrep = rep.__class__
newxyz = np.dot(matrix.view(np.ndarray), rep.to_cartesian().xyz)
return CartesianRepresentation(newxyz).represent_as(newrep)
rep = CartesianRepresentation(elvis_tab['X'], elvis_tab['Y'], elvis_tab['Z'])
# first we offset the catalog to have its origin at host
rep = offset_repr(rep, -rep.xyz[:, hostidx])
# now rotate so that host1 is along the z-axis, and apply the arbitrary roll angle
usph = rep.represent_as(UnitSphericalRepresentation)
M1 = rotation_matrix(usph.lon[targetidx], 'z')
M2 = rotation_matrix(90*u.deg-usph.lat[targetidx], 'y')
M3 = rotation_matrix(roll_angle, 'z')
Mfirst = M3*M2*M1
rep = rotate_repr(rep, Mfirst)
# now determine the location of the earth in this system
# need diagram to explain this, but it uses SSA formula
theta = target_coord.separation(galactic_center) # target to GC angle
D = rep.z[targetidx] # distance to the target host
R = earth_distance
# srho = (R/D) * np.sin(theta)
# sdelta_p = (srho * np.cos(theta) + (1 - srho**2)**0.5)
# sdelta_m = (srho * np.cos(theta) - (1 - srho**2)**0.5)
d1, d2 = R * np.cos(theta), (D**2 - (R * np.sin(theta))**2)**0.5
dp, dm = d1 + d2, d1 - d2
sdelta = (dp/D) * np.sin(theta)
x = R * sdelta
z = R * (1-sdelta**2)**0.5
earth_location = u.Quantity([x, 0*u.kpc, z])
# now offset to put earth at the origin
rep = offset_repr(rep, -earth_location)
sph = rep.represent_as(SphericalRepresentation)
# rotate to put the target at its correct spot
# first sent the target host to 0,0
M1 = rotation_matrix(sph[targetidx].lon, 'z')
M2 = rotation_matrix(-sph[targetidx].lat, 'y')
# now rotate from origin to target lat,lon
M3 = rotation_matrix(target_lat, 'y')
M4 = rotation_matrix(-target_lon, 'z')
Mmiddle = M4*M3*M2*M1
rep = rotate_repr(rep, Mmiddle)
# now one more rotation about the target to stick the GC in the right place
def tomin(ang, inrep=rep[hostidx], axis=rep[targetidx].xyz, target=galactic_center.icrs):
newr = rotate_repr(inrep, rotation_matrix(ang[0]*u.deg, axis))
return ICRS(newr).separation(target).radian
rot_angle = optimize.minimize(tomin, np.array(0).ravel(), method='Nelder-Mead')['x'][0]
Mlast = rotation_matrix(rot_angle*u.deg, rep[targetidx].xyz)
rep = rotate_repr(rep, Mlast)
sph = rep.represent_as(SphericalRepresentation)
elvis_tab['host{}_lat'.format(hostidx)] = sph.lat.to(u.deg)
elvis_tab['host{}_lon'.format(hostidx)] = sph.lon.to(u.deg)
elvis_tab['host{}_dist'.format(hostidx)] = sph.distance
# now compute velocities
# host galactocentric
dvxg = u.Quantity((elvis_tab['Vx'])-elvis_tab['Vx'][hostidx])
dvyg = u.Quantity((elvis_tab['Vy'])-elvis_tab['Vy'][hostidx])
dvzg = u.Quantity((elvis_tab['Vz'])-elvis_tab['Vz'][hostidx])
earth_location_in_xyz = np.dot(Mfirst.T, earth_location)
dxg = elvis_tab['X'] - elvis_tab['X'][0] - earth_location_in_xyz[0]
dyg = elvis_tab['Y'] - elvis_tab['Y'][0] - earth_location_in_xyz[0]
dzg = elvis_tab['Z'] - elvis_tab['Z'][0] - earth_location_in_xyz[0]
vrg = (dvxg*dxg + dvyg*dyg + dvzg*dzg) * (dxg**2+dyg**2+dzg**2)**-0.5
elvis_tab['host{}_galvr'.format(hostidx)] = vrg.to(u.km/u.s)
# "vLSR-like"
# first figure out the rotation direction
earth_rotdir = SkyCoord(90*u.deg, 0*u.deg, frame='galactic').icrs
#now apply the component from that everywhere
offset_angle = earth_rotdir.separation(ICRS(sph))
vrlsr = vrg - earth_vrot*np.cos(offset_angle)
elvis_tab['host{}_vrlsr'.format(hostidx)] = vrlsr.to(u.km/u.s)
