def reference_to_skyoffset_matrix(skyoffset_frame):
"""Make rotation matrix from reference frame and a skyoffset frame.
this function is useful after using astropy to make a rotation matrix
*modified from reference_to_skyoffset function in astropy
Parameters
----------
skyoffset_frame : SkyCoord frame
the rotated frame
note: SkyCoords are compatible
Returns
-------
R : numpy array
a 3d rotation matrix
"""
origin = skyoffset_frame.origin.spherical
mat1 = rotation_matrix(-skyoffset_frame.rotation, "x")
mat2 = rotation_matrix(-origin.lat, "y")
mat3 = rotation_matrix(origin.lon, "z")
R = matrix_product(mat1, mat2, mat3)
return R
def reference_to_greatcircle(reference_frame, greatcircle_frame):
"""Convert a reference coordinate to a great circle frame."""
# Define rotation matrices along the position angle vector, and
# relative to the origin.
pole = greatcircle_frame.pole.transform_to(coord.ICRS)
ra0 = greatcircle_frame.ra0
R_rot = rotation_matrix(greatcircle_frame.rotation, 'z')
if np.isnan(ra0):
R2 = rotation_matrix(pole.dec, 'y')
R1 = rotation_matrix(pole.ra, 'z')
R = matrix_product(R2, R1)
else:
xaxis = np.array([np.cos(ra0), np.sin(ra0), 0.])
zaxis = pole.cartesian.xyz.value
xaxis[2] = -(zaxis[0] * xaxis[0] +
zaxis[1] * xaxis[1]) / zaxis[2] # what?
xaxis = xaxis / np.sqrt(np.sum(xaxis**2))
yaxis = np.cross(zaxis, xaxis)
R = np.stack((xaxis, yaxis, zaxis))
return matrix_product(R_rot, R)
def camera_to_altaz(camera, altaz):
if camera.pointing_direction is None:
raise ValueError('Pointing Direction must not be None')
x = camera.x.copy()
y = camera.y.copy()
if camera.rotated is True:
x, y = y, -x
z = 1 / np.sqrt(1 + (x / focal_length)**2 + (y / focal_length)**2)
x *= z / focal_length
y *= z / focal_length
cartesian = CartesianRepresentation(x, y, z, copy=False)
rot_z_az = rotation_matrix(-camera.pointing_direction.az, 'z')
rot_y_zd = rotation_matrix(-camera.pointing_direction.zen, 'y')
cartesian = cartesian.transform(rot_y_zd)
cartesian = cartesian.transform(rot_z_az)
altitude = 90 * u.deg - np.arccos(cartesian.z)
azimuth = np.arctan2(cartesian.y, cartesian.x)
return AltAz(
alt=altitude,
az=azimuth,
location=camera.location,
obstime=camera.obstime,
)
def fk4_to_gal(fk4coords, galframe):
mat1 = rotation_matrix(180 - Galactic._lon0_B1950.degree, 'z')
mat2 = rotation_matrix(90 - Galactic._ngp_B1950.dec.degree, 'y')
mat3 = rotation_matrix(Galactic._ngp_B1950.ra.degree, 'z')
matprec = fk4coords._precession_matrix(fk4coords.equinox, EQUINOX_B1950)
return matrix_product(mat1, mat2, mat3, matprec)
def fk4_to_gal(fk4coords, galframe):
mat1 = rotation_matrix(180 - Galactic._lon0_B1950.degree, 'z')
mat2 = rotation_matrix(90 - Galactic._ngp_B1950.dec.degree, 'y')
mat3 = rotation_matrix(Galactic._ngp_B1950.ra.degree, 'z')
matprec = fk4coords._precession_matrix(fk4coords.equinox, EQUINOX_B1950)
return matrix_product(mat1, mat2, mat3, matprec)
def altaz_to_camera(altaz, camera):
if camera.pointing_direction is None:
raise ValueError('Pointing Direction must not be None')
cartesian = altaz.cartesian
rot_z_az = rotation_matrix(camera.pointing_direction.az, 'z')
rot_y_zd = rotation_matrix(camera.pointing_direction.zen, 'y')
cartesian = cartesian.transform(rot_z_az)
cartesian = cartesian.transform(rot_y_zd)
x = (cartesian.x * focal_length / cartesian.z).copy()
y = (cartesian.y * focal_length / cartesian.z).copy()
if camera.rotated is True:
x, y = -y, x
return CameraFrame(
x=x,
y=y,
pointing_direction=camera.pointing_direction,
obstime=altaz.obstime,
location=camera.location,
)
def get_ksi_eta(self, time, star):
""" Calculates relative position to star in the orthographic projection.
Parameters:
time (str, Time): Reference time to calculate the position.
It can be a string in the format "yyyy-mm-dd hh:mm:ss.s" or an astropy Time object
star (str, SkyCoord): The coordinate of the star in the same reference frame as the ephemeris.
It can be a string in the format "hh mm ss.s +dd mm ss.ss"
or an astropy SkyCoord object.
Returns:
ksi, eta (float): on-sky orthographic projection of the observer relative to a star
Ksi is in the North-South direction (North positive)
Eta is in the East-West direction (East positive)
"""
time = test_attr(time, Time, 'time')
try:
star = SkyCoord(star, unit=(u.hourangle, u.deg))
except:
raise ValueError(
'star is not an astropy object or a string in the format "hh mm ss.s +dd mm ss.ss"'
)
itrs = self.site.get_itrs(obstime=time)
gcrs = itrs.transform_to(GCRS(obstime=time))
rz = rotation_matrix(star.ra, 'z')
ry = rotation_matrix(-star.dec, 'y')
cp = gcrs.cartesian.transform(rz).transform(ry)
return cp.y.to(u.km).value, cp.z.to(u.km).value
def reference_plane(self, time):
"""Compute the orbit at specified times in the two-body barycentric
frame aligned with the reference plane coordinate system (XYZ).
Parameters
----------
time : array_like, `astropy.time.Time`
Array of times as barycentric MJD values, or an Astropy
`~astropy.time.Time` object containing the times to evaluate at.
"""
xyz = self.orbital_plane(time)
vxyz = xyz.differentials['s']
xyz = xyz.without_differentials()
# Construct rotation matrix to take the orbit from the orbital plane
# system (xyz) to the reference plane system (XYZ):
R1 = rotation_matrix(-self.omega, axis='z')
R2 = rotation_matrix(self.i, axis='x')
R3 = rotation_matrix(self.Omega, axis='z')
Rot = matrix_product(R3, R2, R1)
# Rotate to the reference plane system
XYZ = coord.CartesianRepresentation(matrix_product(Rot, xyz.xyz))
VXYZ = coord.CartesianDifferential(matrix_product(Rot, vxyz.d_xyz))
XYZ = XYZ.with_differentials(VXYZ)
kw = dict()
if self.barycenter is not None:
kw['origin'] = self.barycenter.origin
return ReferencePlaneFrame(XYZ, **kw)
def add_detector_on_earth(name,
longitude,
latitude,
yangle=0,
xangle=None,
height=0):
""" Add a new detector on the earth
Parameters
----------
name: str
two-letter name to identify the detector
longitude: float
Longitude in radians using geodetic coordinates of the detector
latitude: float
Latitude in radians using geodetic coordinates of the detector
yangle: float
Azimuthal angle of the y-arm (angle drawn from pointing north)
xangle: float
Azimuthal angle of the x-arm (angle drawn from point north). If not set
we assume a right angle detector following the right-hand rule.
height: float
The height in meters of the detector above the standard
reference ellipsoidal earth
"""
if xangle is None:
# assume right angle detector if no separate xarm direction given
xangle = yangle + np.pi / 2.0
# Calculate response in earth centered coordinates
# by rotation of response in coordinates aligned
# with the detector arms
a, b = cos(2 * xangle), sin(2 * xangle)
xresp = np.array([[-a, b, 0], [b, a, 0], [0, 0, 0]])
a, b = cos(2 * yangle), sin(2 * yangle)
yresp = np.array([[-a, b, 0], [b, a, 0], [0, 0, 0]])
resp = (yresp - xresp) / 4.0
rm1 = rotation_matrix(longitude * units.rad, 'z')
rm2 = rotation_matrix((np.pi / 2.0 - latitude) * units.rad, 'y')
rm = np.matmul(rm2, rm1)
resp = np.matmul(resp, rm)
resp = np.matmul(rm.T, resp)
loc = coordinates.EarthLocation.from_geodetic(longitude * units.rad,
latitude * units.rad,
height=height * units.meter)
loc = np.array([loc.x.value, loc.y.value, loc.z.value])
_custom_ground_detectors[name] = {
'location': loc,
'response': resp,
'yangle': yangle,
'xangle': xangle,
'height': height,
'xaltitude': 0.0,
'yaltitude': 0.0,
}
def fk5_to_gal(fk5coord, galframe):
# need precess to J2000 first
pmat = fk5coord._precession_matrix(fk5coord.equinox, EQUINOX_J2000)
mat1 = rotation_matrix(180 - Galactic._lon0_J2000.degree, 'z')
mat2 = rotation_matrix(90 - Galactic._ngp_J2000.dec.degree, 'y')
mat3 = rotation_matrix(Galactic._ngp_J2000.ra.degree, 'z')
return matrix_product(mat1, mat2, mat3, pmat)
def fk5_to_gal(fk5coord, galframe):
# need precess to J2000 first
pmat = fk5coord._precession_matrix(fk5coord.equinox, EQUINOX_J2000)
mat1 = rotation_matrix(180 - Galactic._lon0_J2000.degree, 'z')
mat2 = rotation_matrix(90 - Galactic._ngp_J2000.dec.degree, 'y')
mat3 = rotation_matrix(Galactic._ngp_J2000.ra.degree, 'z')
return matrix_product(mat1, mat2, mat3, pmat)
def reference_to_skyoffset_matrix(
lon: T.Union[float, u.Quantity],
lat: T.Union[float, u.Quantity],
rotation: T.Union[float, u.Quantity],
) -> T.Sequence:
"""Convert a reference coordinate to an sky offset frame [astropy].
Cartesian to Cartesian matrix transform.
Parameters
----------
lon : float or |AngleType| or |Quantity| instance
For ICRS, the right ascension.
If float, assumed degrees.
lat : |AngleType| or |Quantity| instance
For ICRS, the declination.
If float, assumed degrees.
rotation : |AngleType| or |Quantity| instance
The final rotation of the frame about the ``origin``. The sign of
the rotation is the left-hand rule. That is, an object at a
particular position angle in the un-rotated system will be sent to
the positive latitude (z) direction in the final frame.
If float, assumed degrees.
Returns
-------
ndarray
(3x3) matrix. rotates reference Cartesian to skyoffset Cartesian.
See Also
--------
:func:`~astropy.coordinates.builtin.skyoffset.reference_to_skyoffset`
References
----------
.. [astropy] Astropy Collaboration, Robitaille, T., Tollerud, E.,
Greenfield, P., Droettboom, M., Bray, E., Aldcroft, T., Davis,
M., Ginsburg, A., Price-Whelan, A., Kerzendorf, W., Conley, A.,
Crighton, N., Barbary, K., Muna, D., Ferguson, H., Grollier, F.,
Parikh, M., Nair, P., Unther, H., Deil, C., Woillez, J.,
Conseil, S., Kramer, R., Turner, J., Singer, L., Fox, R.,
Weaver, B., Zabalza, V., Edwards, Z., Azalee Bostroem, K.,
Burke, D., Casey, A., Crawford, S., Dencheva, N., Ely, J.,
Jenness, T., Labrie, K., Lim, P., Pierfederici, F., Pontzen, A.,
Ptak, A., Refsdal, B., Servillat, M., & Streicher, O. (2013).
Astropy: A community Python package for astronomy.
Astronomy and Astrophysics, 558, A33.
"""
# Define rotation matrices along the position angle vector, and
# relative to the origin.
mat1 = rotation_matrix(-rotation, "x")
mat2 = rotation_matrix(-lat, "y")
mat3 = rotation_matrix(lon, "z")
M = matrix_product(mat1, mat2, mat3)
return M
def reference_to_skyoffset(reference_frame, telescope_frame):
'''Convert a reference coordinate to an sky offset frame.'''
# Define rotation matrices along the position angle vector, and
# relative to the telescope_pointing.
telescope_pointing = telescope_frame.telescope_pointing.spherical
mat1 = rotation_matrix(-telescope_pointing.lat, 'y')
mat2 = rotation_matrix(telescope_pointing.lon, 'z')
return matrix_product(mat1, mat2)
def reference_to_skyoffset(reference_frame, telescope_frame):
"""Convert a reference coordinate to an sky offset frame."""
# Define rotation matrices along the position angle vector, and
# relative to the origin.
origin = telescope_frame.origin.spherical
mat1 = rotation_matrix(-origin.lat, 'y')
mat2 = rotation_matrix(origin.lon, 'z')
return matrix_product(mat1, mat2)
def reference_to_skyoffset(reference_frame, telescope_frame):
"""Convert a reference coordinate to an sky offset frame."""
# Define rotation matrices along the position angle vector, and
# relative to the origin.
origin = telescope_frame.origin.spherical
mat1 = rotation_matrix(-origin.lat, "y")
mat2 = rotation_matrix(origin.lon, "z")
return matrix_product(mat1, mat2)
def reference_to_skyoffset(reference_frame, skyoffset_frame):
"""Convert a reference coordinate to an sky offset frame."""
# Define rotation matrices along the position angle vector, and
# relative to the origin.
origin = skyoffset_frame.origin.spherical
mat1 = rotation_matrix(-skyoffset_frame.rotation, 'x')
mat2 = rotation_matrix(-origin.lat, 'y')
mat3 = rotation_matrix(origin.lon, 'z')
return matrix_product(mat1, mat2, mat3)
def cb_crs_to_cb_j2000_eq(cb_crs_coord, _):
"""Conversion from Celestial Reference System of a Central Body
to its Local Equatorial at J2000 Epoch Reference System."""
ra, dec, w = celestial_body_rot_params(None, cb_crs_coord.body_name)
body_crs_to_body_eq = matrix_product(
rotation_matrix(90 * u.deg - dec, "x"),
rotation_matrix(90 * u.deg + ra, "z"))
return body_crs_to_body_eq
def body_crs_to_body_eq_matrix(obstime, body_name):
"""Computes the rotation matrix from Celestial Body CRS to
Local Equatorial True-of-Date Reference System."""
ra, dec, w = celestial_body_rot_params(obstime, body_name)
body_crs_to_body_eq = matrix_product(
rotation_matrix(90 * u.deg - dec, "x"),
rotation_matrix(90 * u.deg + ra, "z"),
)
return body_crs_to_body_eq
def body_crs_to_body_fixed_matrix(obstime, body_name):
"""Computes the rotation matrix from Celestial Body CRS to
Body Fixed Reference System."""
ra, dec, w = celestial_body_rot_params(obstime, body_name)
body_crs_to_body_fixed = matrix_product(
rotation_matrix(w, "z"),
rotation_matrix(90 * u.deg - dec, "x"),
rotation_matrix(90 * u.deg + ra, "z"),
)
return body_crs_to_body_fixed
def test_angle_axis():
m1 = rotation_matrix(35*u.deg, 'x')
an1, ax1 = angle_axis(m1)
assert an1 - 35*u.deg < 1e-10*u.deg
assert_allclose(ax1, [1, 0, 0])
m2 = rotation_matrix(-89*u.deg, [1, 1, 0])
an2, ax2 = angle_axis(m2)
assert an2 - 89*u.deg < 1e-10*u.deg
assert_allclose(ax2, [-2**-0.5, -2**-0.5, 0])
def test_angle_axis():
m1 = rotation_matrix(35 * u.deg, 'x')
an1, ax1 = angle_axis(m1)
assert an1 - 35 * u.deg < 1e-10 * u.deg
assert_allclose(ax1, [1, 0, 0])
m2 = rotation_matrix(-89 * u.deg, [1, 1, 0])
an2, ax2 = angle_axis(m2)
assert an2 - 89 * u.deg < 1e-10 * u.deg
assert_allclose(ax2, [-2**-0.5, -2**-0.5, 0])
def topo_frame_def(latitude, longitude, moon=True):
"""
Make a list of strings defining a topocentric frame. This can then be loaded
with spiceypy.lmpool.
"""
if moon:
idnum = 1301000
station_name = 'LUNAR-TOPO'
relative = 'MOON_ME'
else:
idnum = 1399000
station_name = 'EARTH-TOPO'
relative = 'ITRF93'
# The DSS stations are built into SPICE, and they number up to 66.
# We will call this station number 98.
station_num = 98
idnum += station_num
fm_center_id = idnum - 1000000
ecef_to_enu = np.matmul(
rotation_matrix(-longitude, 'z', unit='deg'), rotation_matrix(latitude, 'y', unit='deg')
).T
# Reorder the axes so that X,Y,Z = E,N,U
ecef_to_enu = ecef_to_enu[[2, 1, 0]]
mat = " ".join(map("{:.7f}".format, ecef_to_enu.flatten()))
fmt_strs = [
"FRAME_{1} = {0}",
"FRAME_{0}_NAME = '{1}'",
"FRAME_{0}_CLASS = 4",
"FRAME_{0}_CLASS_ID = {0}",
"FRAME_{0}_CENTER = {2}",
"OBJECT_{2}_FRAME = '{1}'",
"TKFRAME_{0}_RELATIVE = '{3}'",
"TKFRAME_{0}_SPEC = 'MATRIX'",
"TKFRAME_{0}_MATRIX = {4}"
]
frame_specs = [s.format(idnum, station_name, fm_center_id, relative, mat) for s in fmt_strs]
frame_dict = {}
for spec in frame_specs:
k, v = map(str.strip, spec.split('='))
frame_dict[k] = v
latlon = ["{:.4f}".format(l) for l in [latitude, longitude]]
return station_name, idnum, frame_dict, latlon
def icrs_to_arbpole(icrs_coord, arbpole_frame):
roll = arbpole_frame.roll
pole = arbpole_frame.pole
# Align z(new) with direction to M31
mat1 = rotation_matrix(-pole.dec, 'y')
mat2 = rotation_matrix(pole.ra, 'z')
mat3 = rotation_matrix(roll, 'z')
mat4 = rotation_matrix(90 * u.degree, 'y')
R = matrix_product(mat4, mat1, mat2, mat3)
return R
def _get_matrix_vectors(gal_frame, inverse=False):
"""
Utility function: use the ``inverse`` argument to get the inverse transformation, matrix and
offsets to go from external galaxy frame to ICRS.
"""
# this is based on the astropy Galactocentric class code
# shorthand
gcf = gal_frame
# rotation matrix to align x(ICRS) with the vector to the galaxy center
mat0 = np.array([[0., 1., 0.],
[0., 0., 1.],
[1., 0., 0.]]) # relabel axes so x points in RA, y in dec, z away from us
mat1 = rotation_matrix(-gcf.gal_coord.dec, 'y')
mat2 = rotation_matrix(gcf.gal_coord.ra, 'z')
# construct transformation matrix and use it
R = matrix_product(mat0, mat1, mat2)
# Now define translation by distance to galaxy center - best defined in current sky coord system defined by R
translation = r.CartesianRepresentation(gcf.gal_distance * [0., 0., 1.])
# Now rotate galaxy to right orientation
pa_rot = rotation_matrix(-gcf.PA, 'z')
inc_rot = rotation_matrix(gcf.inclination, 'y')
H = matrix_product(inc_rot, pa_rot)
# compute total matrices
A = matrix_product(H, R)
# Now we transform the translation vector between sky-aligned and galaxy-aligned frames
offset = -translation.transform(H)
if inverse:
# the inverse of a rotation matrix is a transpose, which is much faster
# and more stable to compute
A = matrix_transpose(A)
offset = (-offset).transform(A)
# galvel is given in sky-aligned coords, need to transform to ICRS, so use R transpose
R = matrix_transpose(R)
offset_v = r.CartesianDifferential.from_cartesian(
(gcf.galvel_heliocentric).to_cartesian().transform(R))
offset = offset.with_differentials(offset_v)
else:
# galvel is given in sky-aligned coords, need to transform to gal frame, so use H
offset_v = r.CartesianDifferential.from_cartesian(
(-gcf.galvel_heliocentric).to_cartesian().transform(H))
offset = offset.with_differentials(offset_v)
return A, offset
def get_rot(fr, x0=0.):
origin = get_origin(fr)
usph_band = coord.UnitSphericalRepresentation(
np.random.uniform(0, 360, 10000) * u.deg,
np.random.uniform(-1, 1, size=10000) * u.deg)
band_icrs = fr.realize_frame(usph_band).transform_to(coord.ICRS)
R1 = rotation_matrix(origin.ra, 'z')
R2 = rotation_matrix(-origin.dec, 'y')
Rtmp = R2 @ R1
roll = get_roll(band_icrs, Rtmp, x0)
return [origin.ra.degree, origin.dec.degree, roll.degree]
def _rotation_matrix_hcc_to_hgs(longitude, latitude):
# Returns the rotation matrix from HCC to HGS based on the observer longitude and latitude
# Permute the axes of HCC to match HGS Cartesian equivalent
# HGS_X = HCC_Z
# HGS_Y = HCC_X
# HGS_Z = HCC_Y
axes_matrix = np.array([[0, 0, 1], [1, 0, 0], [0, 1, 0]])
# Rotate in latitude and longitude (sign difference because of direction difference)
lat_matrix = rotation_matrix(latitude, 'y')
lon_matrix = rotation_matrix(-longitude, 'z')
return lon_matrix @ lat_matrix @ axes_matrix
def rotate(self, axis_angle=None, rotmat=None, L_coords=None):
"""
Rotate the source.
The arguments correspond to different rotation types. If supplied
together in one function call, they are applied in order: axis_angle,
then rotmat, then L_coords.
Parameters
----------
axis_angle : 2-tuple
First element one of 'x', 'y', 'z' for the axis to rotate about,
second element an astropy.units.Quantity with dimensions of angle,
indicating the angle to rotate through.
rotmat : (3, 3) array-like
Rotation matrix.
L_coords : 2-tuple
First element containing an inclination and second element an
azimuthal angle (both astropy.units.Quantity instances with
dimensions of angle). The routine will first attempt to identify
a preferred plane based on the angular momenta of the central 1/3
of particles in the source. This plane will then be rotated to lie
in the 'y-z' plane, followed by a rotation by the azimuthal angle
about its angular momentum pole (rotation about 'x'), and finally
inclined (rotation about 'y').
"""
do_rot = np.eye(3)
if axis_angle is not None:
do_rot = rotation_matrix(axis_angle[1],
axis=axis_angle[0]).dot(do_rot)
if rotmat is not None:
do_rot = rotmat.dot(do_rot)
if L_coords is not None:
incl, az_rot = L_coords
do_rot = L_align(self.coordinates_g.get_xyz(),
self.coordinates_g.differentials['s'].get_d_xyz(),
self.mHI_g,
frac=.3,
Laxis='x').dot(do_rot)
do_rot = rotation_matrix(az_rot, axis='x').dot(do_rot)
do_rot = rotation_matrix(incl, axis='y').dot(do_rot)
self.current_rotation = do_rot.dot(self.current_rotation)
self.coordinates_g = self.coordinates_g.transform(do_rot)
return
def _icrs_to_fk5_matrix():
"""
B-matrix from USNO circular 179. Used by the ICRS->FK5 transformation
functions.
"""
eta0 = -19.9 / 3600000.
xi0 = 9.1 / 3600000.
da0 = -22.9 / 3600000.
m1 = rotation_matrix(-eta0, 'x')
m2 = rotation_matrix(xi0, 'y')
m3 = rotation_matrix(da0, 'z')
return matrix_product(m1, m2, m3)
def tip_axis(coord: UnitSphericalRepresentation, axis_lon: Angle,
rot_angle: Angle) -> UnitSphericalRepresentation:
"""Perform a rotation about an axis perpendicular to the Z-axis.
The purpose of this rotation is to move the pole of the coordinate system from one place to
another. For example, transforming from a coordinate system where the pole is aligned with the
physical pole of a mount to a topocentric coordinate system where the pole is aligned with
zenith.
Note that this is a true rotation, and the same rotation is applied to all coordinates in the
originating coordinate system equally. It is not equivalent to using SkyCoord
directional_offset_by() with a fixed position angle and separation since the direction and
magnitude of the offset depend on the value of coord.
Args:
coord: Coordinate to be transformed.
axis_lon: Longitude angle of the axis of rotation.
rot_angle: Angle of rotation.
Returns:
Coordinate after transformation.
"""
rot = rotation_matrix(rot_angle,
axis=SkyCoord(axis_lon, 0 *
u.deg).represent_as('cartesian').xyz)
coord_cart = coord.represent_as(CartesianRepresentation)
coord_rot_cart = coord_cart.transform(rot)
return coord_rot_cart.represent_as(UnitSphericalRepresentation)
def wcs(target, xobj, yobj, pattern, a = 0, p = 0.25):
from astropy.wcs import WCS
from astropy.coordinates.matrix_utilities import rotation_matrix
from astropy import units as u
from astropy.coordinates import SkyCoord
header = get_header(pattern)
for filename in pattern:
angle = a * u.deg
plate = p * header['CCDXBIN']*u.arcsec
rot_matrix = plate.to(u.deg) * rotation_matrix(angle)[:-1,:-1]
#questa matrice orienta l'immagine in modo diverso!
#mi pare che, per essere "in linea" con il catalogo, debba ruotare attorno all'asse x
w = WCS(header)
if 'CTYPE' in header and 'CRVAL' in header and 'CRPIX' in header and 'CD1_1 CD1_2' in header and 'CD2_1 CD2_2' in header and 'NAXIS' in header: #cerco WCS in header
pass
else:
w.wcs.ctype = ["RA---TAN", "DEC--TAN"]
w.wcs.cd = w.wcs.cd = [[0, 0.00013888888888888889], [0.00013888888888888889, 0]]
if 'RA' in header and 'DEC' in header:
c = SkyCoord(header['RA'], header['DEC'], unit=(u.hourangle, u.deg),equinox="J2019.9")
w.wcs.crval = [c.ra.degree, c.dec.degree]
w.wcs.crpix = [header['NAXIS1']/2, header['NAXIS2']/2]
else:
o = get_obj(target, xobj, yobj, pattern)
c = SkyCoord.from_name(o['obj'],equinox="J2019.9")
w.wcs.crval = [c.ra.degree, c.dec.degree]
w.wcs.crpix = [header['NAXIS1']/2, header['NAXIS2']/2] #o, in alternativa, xobj e yobj date in input
header.extend(w.to_header(), update=True)
return(w)
def test_varying_transform_pc():
varying_matrix_lt = [
rotation_matrix(a)[:2, :2] for a in np.linspace(0, 90, 10)
] * u.arcsec
vct = VaryingCelestialTransform(crpix=(5, 5) * u.pix,
cdelt=(1, 1) * u.arcsec / u.pix,
crval_table=(0, 0) * u.arcsec,
pc_table=varying_matrix_lt,
lon_pole=180 * u.deg)
trans5 = vct.transform_at_index(5)
assert isinstance(trans5, CompoundModel)
# Verify that we have the 5th matrix in the series
affine = trans5.left.left.right
assert isinstance(affine, m.AffineTransformation2D)
assert u.allclose(affine.matrix, varying_matrix_lt[5])
# x.shape=(1,), y.shape=(1,), z.shape=(1,)
pixel = (0 * u.pix, 0 * u.pix, 5 * u.pix)
world = vct(*pixel)
assert np.array(world[0]).shape == ()
assert u.allclose(world, (359.99804329 * u.deg, 0.00017119 * u.deg))
assert u.allclose(vct.inverse(*world, 5 * u.pix),
pixel[:2],
atol=0.01 * u.pix)
def test_vct_shape_errors():
pc_table = [rotation_matrix(a)[:2, :2]
for a in np.linspace(0, 90, 15)] * u.arcsec
pc_table = pc_table.reshape((5, 3, 2, 2))
crval_table = list(zip(np.arange(1, 16), np.arange(16, 31))) * u.arcsec
crval_table = crval_table.reshape((5, 3, 2))
kwargs = dict(crpix=(5, 5) * u.pix,
cdelt=(1, 1) * u.arcsec / u.pix,
lon_pole=180 * u.deg)
with pytest.raises(ValueError,
match="only be constructed with a one dimensional"):
VaryingCelestialTransform(crval_table=crval_table,
pc_table=pc_table,
**kwargs)
with pytest.raises(ValueError,
match="only be constructed with a one dimensional"):
VaryingCelestialTransformSlit(crval_table=crval_table,
pc_table=pc_table,
**kwargs)
with pytest.raises(ValueError,
match="only be constructed with a two dimensional"):
VaryingCelestialTransform2D(crval_table=crval_table[0],
pc_table=pc_table[0],
**kwargs)
with pytest.raises(ValueError,
match="only be constructed with a two dimensional"):
VaryingCelestialTransformSlit2D(crval_table=crval_table[0],
pc_table=pc_table[0],
**kwargs)
def test_vct_dispatch():
varying_matrix_lt = [
rotation_matrix(a)[:2, :2] for a in np.linspace(0, 90, 15)
] * u.arcsec
varying_matrix_lt = varying_matrix_lt.reshape((5, 3, 2, 2))
crval_table = list(zip(np.arange(1, 16), np.arange(16, 31))) * u.arcsec
crval_table = crval_table.reshape((5, 3, 2))
kwargs = dict(crpix=(5, 5) * u.pix,
cdelt=(1, 1) * u.arcsec / u.pix,
lon_pole=180 * u.deg)
vct_3d = varying_celestial_transform_from_tables(
pc_table=varying_matrix_lt[0], crval_table=crval_table[0], **kwargs)
assert isinstance(vct_3d, VaryingCelestialTransform)
vct_2d = varying_celestial_transform_from_tables(
pc_table=varying_matrix_lt, crval_table=crval_table, **kwargs)
assert isinstance(vct_2d, VaryingCelestialTransform2D)
with pytest.raises(
ValueError,
match="Only one or two dimensional lookup tables are supported"):
varying_celestial_transform_from_tables(
pc_table=varying_matrix_lt[1:].reshape((3, 2, 2, 2, 2)),
crval_table=crval_table[1:].reshape((3, 2, 2, 2)),
**kwargs)
def from_equatorial(equatorial_coo, fixed_frame):
# TODO replace w/ something smart (Sun/Earth special cased)
if fixed_frame.body == Sun:
assert type(equatorial_coo) == HCRS
else:
assert equatorial_coo.body == fixed_frame.body
r = equatorial_coo.cartesian
ra, dec, W = fixed_frame.rot_elements_at_epoch(fixed_frame.obstime)
r_trans2 = r.transform(rotation_matrix(90 * u.deg + ra, "z"))
r_f = r_trans2.transform(rotation_matrix(90 * u.deg - dec, "x"))
r_f = r_f.transform(rotation_matrix(W, "z"))
return fixed_frame.realize_frame(r_f)
def test_static_matrix_combine_paths():
"""
Check that combined staticmatrixtransform matrices provide the same
transformation as using an intermediate transformation.
This is somewhat of a regression test for #7706
"""
from astropy.coordinates.baseframe import BaseCoordinateFrame
from astropy.coordinates.matrix_utilities import rotation_matrix
class AFrame(BaseCoordinateFrame):
default_representation = r.SphericalRepresentation
default_differential = r.SphericalCosLatDifferential
t1 = t.StaticMatrixTransform(rotation_matrix(30.*u.deg, 'z'),
ICRS, AFrame)
t1.register(frame_transform_graph)
t2 = t.StaticMatrixTransform(rotation_matrix(30.*u.deg, 'z').T,
AFrame, ICRS)
t2.register(frame_transform_graph)
class BFrame(BaseCoordinateFrame):
default_representation = r.SphericalRepresentation
default_differential = r.SphericalCosLatDifferential
t3 = t.StaticMatrixTransform(rotation_matrix(30.*u.deg, 'x'),
ICRS, BFrame)
t3.register(frame_transform_graph)
t4 = t.StaticMatrixTransform(rotation_matrix(30.*u.deg, 'x').T,
BFrame, ICRS)
t4.register(frame_transform_graph)
c = Galactic(123*u.deg, 45*u.deg)
c1 = c.transform_to(BFrame) # direct
c2 = c.transform_to(AFrame).transform_to(BFrame) # thru A
c3 = c.transform_to(ICRS).transform_to(BFrame) # thru ICRS
assert quantity_allclose(c1.lon, c2.lon)
assert quantity_allclose(c1.lat, c2.lat)
assert quantity_allclose(c1.lon, c3.lon)
assert quantity_allclose(c1.lat, c3.lat)
for t_ in [t1, t2, t3, t4]:
t_.unregister(frame_transform_graph)
def _create_matrix(self, phi, theta, psi, axes_order):
matrices = []
for angle, axis in zip([phi, theta, psi], axes_order):
if isinstance(angle, u.Quantity):
angle = angle.value
angle = angle.item()
matrices.append(rotation_matrix(angle, axis, unit=u.rad))
result = matrix_product(*matrices[::-1])
return result
def get_matrix_vectors(galactocentric_frame, inverse=False):
"""
Use the ``inverse`` argument to get the inverse transformation, matrix and
offsets to go from Galactocentric to ICRS.
"""
# shorthand
gcf = galactocentric_frame
# rotation matrix to align x(ICRS) with the vector to the Galactic center
mat1 = rotation_matrix(-gcf.galcen_coord.dec, 'y')
mat2 = rotation_matrix(gcf.galcen_coord.ra, 'z')
# extra roll away from the Galactic x-z plane
mat0 = rotation_matrix(gcf.get_roll0() - gcf.roll, 'x')
# construct transformation matrix and use it
R = matrix_product(mat0, mat1, mat2)
# Now need to translate by Sun-Galactic center distance around x' and
# rotate about y' to account for tilt due to Sun's height above the plane
translation = r.CartesianRepresentation(gcf.galcen_distance * [1., 0., 0.])
z_d = gcf.z_sun / gcf.galcen_distance
H = rotation_matrix(-np.arcsin(z_d), 'y')
# compute total matrices
A = matrix_product(H, R)
# Now we re-align the translation vector to account for the Sun's height
# above the midplane
offset = -translation.transform(H)
if inverse:
# the inverse of a rotation matrix is a transpose, which is much faster
# and more stable to compute
A = matrix_transpose(A)
offset = (-offset).transform(A)
offset_v = r.CartesianDifferential.from_cartesian(
(-gcf.galcen_v_sun).to_cartesian().transform(A))
offset = offset.with_differentials(offset_v)
else:
offset = offset.with_differentials(gcf.galcen_v_sun)
return A, offset
def _ecliptic_rotation_matrix(equinox):
# This code calls pmat06 from ERFA, which retrieves the precession
# matrix (including frame bias) according to the IAU 2006 model, but
# leaves out the nutation. This matches what ERFA does in the ecm06
# function and also brings the results closer to what other libraries
# give (see https://github.com/astropy/astropy/pull/6508). However,
# notice that this makes the name "TrueEcliptic" misleading, and might
# be changed in the future (discussion in the same pull request)
jd1, jd2 = get_jd12(equinox, 'tt')
rbp = erfa.pmat06(jd1, jd2)
obl = erfa.obl06(jd1, jd2)*u.radian
return matrix_product(rotation_matrix(obl, 'x'), rbp)
def _make_rotation_matrix_from_reprs(start_representation, end_representation):
"""
Return the matrix for the direct rotation from one representation to a second representation.
The representations need not be normalized first.
"""
A = start_representation.to_cartesian()
B = end_representation.to_cartesian()
rotation_axis = A.cross(B)
rotation_angle = -np.arccos(A.dot(B) / (A.norm() * B.norm())) # negation is required
# This line works around some input/output quirks of Astropy's rotation_matrix()
matrix = np.array(rotation_matrix(rotation_angle, rotation_axis.xyz.value.tolist()))
return matrix
def _rotate_polygon(lon, lat, lon0, lat0):
"""
Given a polygon with vertices defined by (lon, lat), rotate the polygon
such that the North pole of the spherical coordinates is now at (lon0,
lat0). Therefore, to end up with a polygon centered on (lon0, lat0), the
polygon should initially be drawn around the North pole.
"""
# Create a representation object
polygon = UnitSphericalRepresentation(lon=lon, lat=lat)
# Determine rotation matrix to make it so that the circle is centered
# on the correct longitude/latitude.
m1 = rotation_matrix(-(0.5 * np.pi * u.radian - lat0), axis='y')
m2 = rotation_matrix(-lon0, axis='z')
transform_matrix = matrix_product(m2, m1)
# Apply 3D rotation
polygon = polygon.to_cartesian()
polygon = polygon.transform(transform_matrix)
polygon = UnitSphericalRepresentation.from_cartesian(polygon)
return polygon.lon, polygon.lat
def test_rotation_matrix():
assert_array_equal(rotation_matrix(0*u.deg, 'x'), np.eye(3))
assert_allclose(rotation_matrix(90*u.deg, 'y'), [[0, 0, -1],
[0, 1, 0],
[1, 0, 0]], atol=1e-12)
assert_allclose(rotation_matrix(-90*u.deg, 'z'), [[0, -1, 0],
[1, 0, 0],
[0, 0, 1]], atol=1e-12)
assert_allclose(rotation_matrix(45*u.deg, 'x'),
rotation_matrix(45*u.deg, [1, 0, 0]))
assert_allclose(rotation_matrix(125*u.deg, 'y'),
rotation_matrix(125*u.deg, [0, 1, 0]))
assert_allclose(rotation_matrix(-30*u.deg, 'z'),
rotation_matrix(-30*u.deg, [0, 0, 1]))
assert_allclose(np.dot(rotation_matrix(180*u.deg, [1, 1, 0]), [1, 0, 0]),
[0, 1, 0], atol=1e-12)
# make sure it also works for very small angles
assert_allclose(rotation_matrix(0.000001*u.deg, 'x'),
rotation_matrix(0.000001*u.deg, [1, 0, 0]))
def gal_to_mag():
mat1 = rotation_matrix(57.275785782128686*u.deg, 'z')
mat2 = rotation_matrix(90*u.deg - MagellanicStreamNidever08._ngp.b, 'y')
mat3 = rotation_matrix(MagellanicStreamNidever08._ngp.l, 'z')
return matrix_product(mat1, mat2, mat3)
# TODO: remove this. This is a hack required as of astropy v3.1 in order
# to have the longitude components wrap at the desired angle
def represent_as(self, base, s='base', in_frame_units=False):
r = super().represent_as(base, s=s, in_frame_units=in_frame_units)
r.lon.wrap_angle = self._default_wrap_angle
return r
represent_as.__doc__ = coord.BaseCoordinateFrame.represent_as.__doc__
# Define the Euler angles
phi = 128.79 * u.degree
theta = 54.39 * u.degree
psi = 90.70 * u.degree
# Generate the rotation matrix using the x-convention (see Goldstein)
D = rotation_matrix(phi, "z")
C = rotation_matrix(theta, "x")
B = rotation_matrix(psi, "z")
R = matrix_product(B, C, D)
@frame_transform_graph.transform(coord.StaticMatrixTransform, coord.Galactic,
OrphanNewberg10)
def galactic_to_orp():
""" Compute the transformation from Galactic spherical to
heliocentric Orphan coordinates.
"""
return R
# Oph to Galactic coordinates
@frame_transform_graph.transform(coord.StaticMatrixTransform, OrphanNewberg10,
coord.Galactic)
# In this case we override the names in the spherical representations but don't
# do anything with other representations like cartesian or cylindrical.
#
# Next we have to define the transformation from this coordinate system to some
# other built-in coordinate system; we will use Galactic coordinates. We can do
# this by defining functions that return transformation matrices, or by simply
# defining a function that accepts a coordinate and returns a new coordinate in
# the new system. We'll start by constructing the rotation matrix, using the
# ``rotation_matrix`` helper function:
SGR_PHI = np.radians(180+3.75) # Euler angles (from Law & Majewski 2010)
SGR_THETA = np.radians(90-13.46)
SGR_PSI = np.radians(180+14.111534)
# Generate the rotation matrix using the x-convention (see Goldstein)
D = rotation_matrix(SGR_PHI, "z", unit=u.radian)
C = rotation_matrix(SGR_THETA, "x", unit=u.radian)
B = rotation_matrix(SGR_PSI, "z", unit=u.radian)
SGR_MATRIX = np.array(B.dot(C).dot(D))
##############################################################################
# This is done at the module level, since it will be used by both the
# transformation from Sgr to Galactic as well as the inverse from Galactic to
# Sgr. Now we can define our first transformation function:
@frame_transform_graph.transform(coord.FunctionTransform, coord.Galactic, Sagittarius)
def galactic_to_sgr(gal_coord, sgr_frame):
""" Compute the transformation from Galactic spherical to
heliocentric Sgr coordinates.
"""
def _ecliptic_rotation_matrix():
jd1, jd2 = get_jd12(J2000, J2000.scale)
obl = erfa.obl80(jd1, jd2) * u.radian
assert obl.to(u.arcsec).value == 84381.448
return rotation_matrix(obl, "x")
def gal_to_supergal():
mat1 = rotation_matrix(90, 'z')
mat2 = rotation_matrix(90 - Supergalactic._nsgp_gal.b.degree, 'y')
mat3 = rotation_matrix(Supergalactic._nsgp_gal.l.degree, 'z')
return matrix_product(mat1, mat2, mat3)
# Next we have to define the transformation from this coordinate system to some
# other built-in coordinate system; we will use Galactic coordinates. We can do
# this by defining functions that return transformation matrices, or by simply
# defining a function that accepts a coordinate and returns a new coordinate in
# the new system. Because the transformation to the Sagittarius coordinate
# system is just a spherical rotation from Galactic coordinates, we'll just
# define a function that returns this matrix. We'll start by constructing the
# transformation matrix using pre-deteremined Euler angles and the
# ``rotation_matrix`` helper function:
SGR_PHI = (180 + 3.75) * u.degree # Euler angles (from Law & Majewski 2010)
SGR_THETA = (90 - 13.46) * u.degree
SGR_PSI = (180 + 14.111534) * u.degree
# Generate the rotation matrix using the x-convention (see Goldstein)
D = rotation_matrix(SGR_PHI, "z")
C = rotation_matrix(SGR_THETA, "x")
B = rotation_matrix(SGR_PSI, "z")
A = np.diag([1.,1.,-1.])
SGR_MATRIX = matrix_product(A, B, C, D)
##############################################################################
# Since we already constructed the transformation (rotation) matrix above, and
# the inverse of a rotation matrix is just its transpose, the required
# transformation functions are very simple:
@frame_transform_graph.transform(coord.StaticMatrixTransform, coord.Galactic, Sagittarius)
def galactic_to_sgr():
""" Compute the transformation matrix from Galactic spherical to
heliocentric Sgr coordinates.
"""
def _ecliptic_rotation_matrix_pulsar(obl):
"""Here we only do the obliquity angle rotation. Astropy will add the
precession-nutation correction.
"""
return rotation_matrix(obl, 'x')
