# -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import (absolute_import, unicode_literals, division,
print_function)
import numpy as np
from ... import units as u
from ..representation import (SphericalRepresentation, CartesianRepresentation,
UnitSphericalRepresentation)
from ..baseframe import (BaseCoordinateFrame, frame_transform_graph,
TimeFrameAttribute, RepresentationMapping)
from ..transformations import FunctionTransform, DynamicMatrixTransform
from .. import earth_orientation as earth
from .utils import EQUINOX_B1950
[docs]class FK4(BaseCoordinateFrame):
"""
A coordinate or frame in the FK4 system.
Parameters
----------
representation : `BaseRepresentation` or None
A representation object or None to have no data (or use the other keywords)
ra : `Angle`, optional, must be keyword
The RA for this object (``dec`` must also be given and ``representation``
must be None).
dec : `Angle`, optional, must be keyword
The Declination for this object (``ra`` must also be given and
``representation`` must be None).
distance : :class:`~astropy.units.Quantity`, optional, must be keyword
The Distance for this object along the line-of-sight.
(``representation`` must be None).
equinox : astropy.time.Time, optional, must be keyword
The equinox of this frame.
obstime : astropy.time.Time, optional, must be keyword
The time this frame was observed. If None, will be the same as
``equinox``.
"""
frame_specific_representation_info = {
'spherical': [RepresentationMapping('lon', 'ra'),
RepresentationMapping('lat', 'dec')]
}
frame_specific_representation_info['unitspherical'] = \
frame_specific_representation_info['spherical']
default_representation = SphericalRepresentation
equinox = TimeFrameAttribute(default=EQUINOX_B1950)
obstime = TimeFrameAttribute(default=None, secondary_attribute='equinox')
# the "self" transform
@frame_transform_graph.transform(FunctionTransform, FK4, FK4)
def fk4_to_fk4(fk4coord1, fk4frame2):
# deceptively complicated: need to transform to No E-terms FK4, precess, and
# then come back, because precession is non-trivial with E-terms
fnoe_w_eqx1 = fk4coord1.transform_to(FK4NoETerms(equinox=fk4coord1.equinox))
fnoe_w_eqx2 = fnoe_w_eqx1.transform_to(FK4NoETerms(equinox=fk4frame2.equinox))
return fnoe_w_eqx2.transform_to(fk4frame2)
[docs]class FK4NoETerms(BaseCoordinateFrame):
"""
A coordinate or frame in the FK4 system, but with the E-terms of aberration
removed.
Parameters
----------
representation : `BaseRepresentation` or None
A representation object or None to have no data (or use the other keywords)
ra : `Angle`, optional, must be keyword
The RA for this object (``dec`` must also be given and ``representation``
must be None).
dec : `Angle`, optional, must be keyword
The Declination for this object (``ra`` must also be given and
``representation`` must be None).
distance : :class:`~astropy.units.Quantity`, optional, must be keyword
The Distance for this object along the line-of-sight.
(``representation`` must be None).
obstime : astropy.time.Time, optional, must be keyword
The time this frame was observed. If None, will be the same as
``equinox``.
"""
frame_specific_representation_info = {
'spherical': [RepresentationMapping('lon', 'ra'),
RepresentationMapping('lat', 'dec')]
}
frame_specific_representation_info['unitspherical'] = \
frame_specific_representation_info['spherical']
default_representation = SphericalRepresentation
equinox = TimeFrameAttribute(default=EQUINOX_B1950)
obstime = TimeFrameAttribute(default=None, secondary_attribute='equinox')
@staticmethod
def _precession_matrix(oldequinox, newequinox):
"""
Compute and return the precession matrix for FK4 using Newcomb's method.
Used inside some of the transformation functions.
Parameters
----------
oldequinox : `~astropy.time.Time`
The equinox to precess from.
newequinox : `~astropy.time.Time`
The equinox to precess to.
Returns
-------
newcoord : array
The precession matrix to transform to the new equinox
"""
return earth._precession_matrix_besselian(oldequinox.byear, newequinox.byear)
# the "self" transform
@frame_transform_graph.transform(DynamicMatrixTransform, FK4NoETerms, FK4NoETerms)
def fk4noe_to_fk4noe(fk4necoord1, fk4neframe2):
return fk4necoord1._precession_matrix(fk4necoord1.equinox, fk4neframe2.equinox)
# FK4-NO-E to/from FK4 ----------------------------->
# Unlike other frames, this module include *two* frame classes for FK4
# coordinates - one including the E-terms of aberration (FK4), and
# one not including them (FK4NoETerms). The following functions
# implement the transformation between these two.
def fk4_e_terms(equinox):
"""
Return the e-terms of aberation vector
Parameters
----------
equinox : Time object
The equinox for which to compute the e-terms
"""
# Constant of aberration at J2000
k = 0.0056932
# Eccentricity of the Earth's orbit
e = earth.eccentricity(equinox.jd)
e = np.radians(e)
# Mean longitude of perigee of the solar orbit
g = earth.mean_lon_of_perigee(equinox.jd)
g = np.radians(g)
# Obliquity of the ecliptic
o = earth.obliquity(equinox.jd, algorithm=1980)
o = np.radians(o)
return e * k * np.sin(g), \
-e * k * np.cos(g) * np.cos(o), \
-e * k * np.cos(g) * np.sin(o)
@frame_transform_graph.transform(FunctionTransform, FK4, FK4NoETerms)
def fk4_to_fk4_no_e(fk4coord, fk4noeframe):
# Extract cartesian vector
c = fk4coord.cartesian.xyz
r = np.asarray(c.reshape((3, c.size // 3)))
# Find distance (for re-normalization)
d_orig = np.sqrt(np.sum(r ** 2))
# Apply E-terms of aberration. Note that this depends on the equinox (not
# the observing time/epoch) of the coordinates. See issue #1496 for a
# discussion of this.
eterms_a = np.asarray(fk4_e_terms(fk4coord.equinox))
r = r - eterms_a.reshape(3, 1) + np.dot(eterms_a, r) * r
# Find new distance (for re-normalization)
d_new = np.sqrt(np.sum(r ** 2))
# Renormalize
r = r * d_orig / d_new
subshape = c.shape[1:]
x = r[0].reshape(subshape)
y = r[1].reshape(subshape)
z = r[2].reshape(subshape)
#now re-cast into an appropriate Representation, and precess if need be
if isinstance(fk4coord.data, UnitSphericalRepresentation):
representation = CartesianRepresentation(x=x*u.one, y=y*u.one, z=z*u.one)
representation = representation.represent_as(UnitSphericalRepresentation)
else:
representation = CartesianRepresentation(x=x*c.unit, y=y*c.unit, z=z*c.unit)
# if no obstime was given in the new frame, use the old one for consistency
newobstime = fk4coord._obstime if fk4noeframe._obstime is None else fk4noeframe._obstime
fk4noe = FK4NoETerms(representation, equinox=fk4coord.equinox,
obstime=newobstime)
if fk4coord.equinox != fk4noeframe.equinox:
#precession
fk4noe = fk4noe.transform_to(fk4noeframe)
return fk4noe
@frame_transform_graph.transform(FunctionTransform, FK4NoETerms, FK4)
def fk4_no_e_to_fk4(fk4noecoord, fk4frame):
#first precess, if necessary
if fk4noecoord.equinox != fk4frame.equinox:
fk4noe_w_fk4equinox = FK4NoETerms(equinox=fk4frame.equinox,
obstime=fk4noecoord.obstime)
fk4noecoord = fk4noecoord.transform_to(fk4noe_w_fk4equinox)
# Extract cartesian vector
c = fk4noecoord.cartesian.xyz
r = np.asarray(c.reshape((3, c.size // 3)))
# Find distance (for re-normalization)
d_orig = np.sqrt(np.sum(r ** 2))
# Apply E-terms of aberration. Note that this depends on the equinox (not
# the observing time/epoch) of the coordinates. See issue #1496 for a
# discussion of this.
eterms_a = np.asarray(fk4_e_terms(fk4noecoord.equinox))
r0 = r.copy()
for _ in range(10):
r = (eterms_a.reshape(3, 1) + r0) / (1. + np.dot(eterms_a, r))
# Find new distance (for re-normalization)
d_new = np.sqrt(np.sum(r ** 2))
# Renormalize
r = r * d_orig / d_new
subshape = c.shape[1:]
x = r[0].reshape(subshape)
y = r[1].reshape(subshape)
z = r[2].reshape(subshape)
#now re-cast into an appropriate Representation, and precess if need be
if isinstance(fk4noecoord.data, UnitSphericalRepresentation):
representation = CartesianRepresentation(x=x*u.one, y=y*u.one, z=z*u.one)
representation = representation.represent_as(UnitSphericalRepresentation)
else:
representation = CartesianRepresentation(x=x*c.unit, y=y*c.unit, z=z*c.unit)
return fk4frame.realize_frame(representation)