# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Implements rotations, including spherical rotations as defined in WCS Paper II
[1]_
`RotateNative2Celestial` and `RotateCelestial2Native` follow the convention in
WCS Paper II to rotate to/from a native sphere and the celestial sphere.
The implementation uses `EulerAngleRotation`. The model parameters are
three angles: the longitude (``lon``) and latitude (``lat``) of the fiducial point
in the celestial system (``CRVAL`` keywords in FITS), and the longitude of the celestial
pole in the native system (``lon_pole``). The Euler angles are ``lon+90``, ``90-lat``
and ``-(lon_pole-90)``.
References
----------
.. [1] Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II)
"""
import math
import numpy as np
from .core import Model
from .parameters import Parameter
from astropy.coordinates.matrix_utilities import rotation_matrix, matrix_product
from astropy import units as u
from astropy.utils.decorators import deprecated
from .utils import _to_radian, _to_orig_unit
__all__ = ['RotateCelestial2Native', 'RotateNative2Celestial', 'Rotation2D',
'EulerAngleRotation']
class _EulerRotation:
"""
Base class which does the actual computation.
"""
_separable = False
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
@staticmethod
def spherical2cartesian(alpha, delta):
alpha = np.deg2rad(alpha)
delta = np.deg2rad(delta)
x = np.cos(alpha) * np.cos(delta)
y = np.cos(delta) * np.sin(alpha)
z = np.sin(delta)
return np.array([x, y, z])
@staticmethod
def cartesian2spherical(x, y, z):
h = np.hypot(x, y)
alpha = np.rad2deg(np.arctan2(y, x))
delta = np.rad2deg(np.arctan2(z, h))
return alpha, delta
@deprecated(2.0)
@staticmethod
def rotation_matrix_from_angle(angle):
"""
Clockwise rotation matrix.
Parameters
----------
angle : float
Rotation angle in radians.
"""
return np.array([[math.cos(angle), math.sin(angle)],
[-math.sin(angle), math.cos(angle)]])
def evaluate(self, alpha, delta, phi, theta, psi, axes_order):
shape = None
if isinstance(alpha, np.ndarray) and alpha.ndim == 2:
alpha = alpha.flatten()
delta = delta.flatten()
shape = alpha.shape
inp = self.spherical2cartesian(alpha, delta)
matrix = self._create_matrix(phi, theta, psi, axes_order)
result = np.dot(matrix, inp)
a, b = self.cartesian2spherical(*result)
if shape is not None:
a.shape = shape
b.shape = shape
return a, b
_input_units_strict = True
_input_units_allow_dimensionless = True
@property
def input_units(self):
""" Input units. """
return {'alpha': u.deg, 'delta': u.deg}
@property
def return_units(self):
""" Output units. """
return {'alpha': u.deg, 'delta': u.deg}
[docs]class EulerAngleRotation(_EulerRotation, Model):
"""
Implements Euler angle intrinsic rotations.
Rotates one coordinate system into another (fixed) coordinate system.
All coordinate systems are right-handed. The sign of the angles is
determined by the right-hand rule..
Parameters
----------
phi, theta, psi : float or `~astropy.units.Quantity`
"proper" Euler angles in deg.
If floats, they should be in deg.
axes_order : str
A 3 character string, a combination of 'x', 'y' and 'z',
where each character denotes an axis in 3D space.
"""
inputs = ('alpha', 'delta')
outputs = ('alpha', 'delta')
phi = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
theta = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
psi = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
def __init__(self, phi, theta, psi, axes_order, **kwargs):
self.axes = ['x', 'y', 'z']
if len(axes_order) != 3:
raise TypeError(
"Expected axes_order to be a character sequence of length 3,"
"got {0}".format(axes_order))
unrecognized = set(axes_order).difference(self.axes)
if unrecognized:
raise ValueError("Unrecognized axis label {0}; "
"should be one of {1} ".format(unrecognized, self.axes))
self.axes_order = axes_order
qs = [isinstance(par, u.Quantity) for par in [phi, theta, psi]]
if any(qs) and not all(qs):
raise TypeError("All parameters should be of the same type - float or Quantity.")
super().__init__(phi=phi, theta=theta, psi=psi, **kwargs)
def inverse(self):
return self.__class__(phi=-self.psi,
theta=-self.theta,
psi=-self.phi,
axes_order=self.axes_order[::-1])
[docs] def evaluate(self, alpha, delta, phi, theta, psi):
a, b = super().evaluate(alpha, delta, phi, theta, psi, self.axes_order)
return a, b
class _SkyRotation(_EulerRotation, Model):
"""
Base class for RotateNative2Celestial and RotateCelestial2Native.
"""
lon = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
lat = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
lon_pole = Parameter(default=0, getter=_to_orig_unit, setter=_to_radian)
def __init__(self, lon, lat, lon_pole, **kwargs):
qs = [isinstance(par, u.Quantity) for par in [lon, lat, lon_pole]]
if any(qs) and not all(qs):
raise TypeError("All parameters should be of the same type - float or Quantity.")
super().__init__(lon, lat, lon_pole, **kwargs)
self.axes_order = 'zxz'
def _evaluate(self, phi, theta, lon, lat, lon_pole):
alpha, delta = super().evaluate(phi, theta, lon, lat, lon_pole,
self.axes_order)
mask = alpha < 0
if isinstance(mask, np.ndarray):
alpha[mask] += 360
else:
alpha += 360
return alpha, delta
[docs]class RotateNative2Celestial(_SkyRotation):
"""
Transform from Native to Celestial Spherical Coordinates.
Parameters
----------
lon : float or or `~astropy.units.Quantity`
Celestial longitude of the fiducial point.
lat : float or or `~astropy.units.Quantity`
Celestial latitude of the fiducial point.
lon_pole : float or or `~astropy.units.Quantity`
Longitude of the celestial pole in the native system.
Notes
-----
If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg.
"""
#: Inputs are angles on the native sphere
inputs = ('phi_N', 'theta_N')
#: Outputs are angles on the celestial sphere
outputs = ('alpha_C', 'delta_C')
@property
def input_units(self):
""" Input units. """
return {'phi_N': u.deg, 'theta_N': u.deg}
@property
def return_units(self):
""" Output units. """
return {'alpha_C': u.deg, 'delta_C': u.deg}
def __init__(self, lon, lat, lon_pole, **kwargs):
super().__init__(lon, lat, lon_pole, **kwargs)
[docs] def evaluate(self, phi_N, theta_N, lon, lat, lon_pole):
"""
Parameters
----------
phi_N, theta_N : float (deg) or `~astropy.units.Quantity`
Angles in the Native coordinate system.
lon, lat, lon_pole : float (in deg) or `~astropy.units.Quantity`
Parameter values when the model was initialized.
Returns
-------
alpha_C, delta_C : float (deg) or `~astropy.units.Quantity`
Angles on the Celestial sphere.
"""
# The values are in radians since they have already been through the setter.
if isinstance(lon, u.Quantity):
lon = lon.value
lat = lat.value
lon_pole = lon_pole.value
# Convert to Euler angles
phi = lon_pole - np.pi / 2
theta = - (np.pi / 2 - lat)
psi = -(np.pi / 2 + lon)
alpha_C, delta_C = super()._evaluate(phi_N, theta_N, phi, theta, psi)
return alpha_C, delta_C
@property
def inverse(self):
# convert to angles on the celestial sphere
return RotateCelestial2Native(self.lon, self.lat, self.lon_pole)
[docs]class RotateCelestial2Native(_SkyRotation):
"""
Transform from Celestial to Native Spherical Coordinates.
Parameters
----------
lon : float or or `~astropy.units.Quantity`
Celestial longitude of the fiducial point.
lat : float or or `~astropy.units.Quantity`
Celestial latitude of the fiducial point.
lon_pole : float or or `~astropy.units.Quantity`
Longitude of the celestial pole in the native system.
Notes
-----
If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg.
"""
#: Inputs are angles on the celestial sphere
inputs = ('alpha_C', 'delta_C')
#: Outputs are angles on the native sphere
outputs = ('phi_N', 'theta_N')
@property
def input_units(self):
""" Input units. """
return {'alpha_C': u.deg, 'delta_C': u.deg}
@property
def return_units(self):
""" Output units. """
return {'phi_N': u.deg, 'theta_N': u.deg}
def __init__(self, lon, lat, lon_pole, **kwargs):
super().__init__(lon, lat, lon_pole, **kwargs)
[docs] def evaluate(self, alpha_C, delta_C, lon, lat, lon_pole):
"""
Parameters
----------
alpha_C, delta_C : float (deg) or `~astropy.units.Quantity`
Angles in the Celestial coordinate frame.
lon, lat, lon_pole : float (deg) or `~astropy.units.Quantity`
Parameter values when the model was initialized.
Returns
-------
phi_N, theta_N : float (deg) or `~astropy.units.Quantity`
Angles on the Native sphere.
"""
if isinstance(lon, u.Quantity):
lon = lon.value
lat = lat.value
lon_pole = lon_pole.value
# Convert to Euler angles
phi = (np.pi / 2 + lon)
theta = (np.pi / 2 - lat)
psi = -(lon_pole - np.pi / 2)
phi_N, theta_N = super()._evaluate(alpha_C, delta_C, phi, theta, psi)
return phi_N, theta_N
@property
def inverse(self):
return RotateNative2Celestial(self.lon, self.lat, self.lon_pole)
[docs]class Rotation2D(Model):
"""
Perform a 2D rotation given an angle.
Positive angles represent a counter-clockwise rotation and vice-versa.
Parameters
----------
angle : float or `~astropy.units.Quantity`
Angle of rotation (if float it should be in deg).
"""
inputs = ('x', 'y')
outputs = ('x', 'y')
_separable = False
angle = Parameter(default=0.0, getter=_to_orig_unit, setter=_to_radian)
@property
def inverse(self):
"""Inverse rotation."""
return self.__class__(angle=-self.angle)
[docs] @classmethod
def evaluate(cls, x, y, angle):
"""
Rotate (x, y) about ``angle``.
Parameters
----------
x, y : ndarray-like
Input quantities
angle : float (deg) or `~astropy.units.Quantity`
Angle of rotations.
"""
if x.shape != y.shape:
raise ValueError("Expected input arrays to have the same shape")
# If one argument has units, enforce they both have units and they are compatible.
x_unit = getattr(x, 'unit', None)
y_unit = getattr(y, 'unit', None)
has_units = x_unit is not None and y_unit is not None
if x_unit != y_unit:
if has_units and y_unit.is_equivalent(x_unit):
y = y.to(x_unit)
y_unit = x_unit
else:
raise u.UnitsError("x and y must have compatible units")
# Note: If the original shape was () (an array scalar) convert to a
# 1-element 1-D array on output for consistency with most other models
orig_shape = x.shape or (1,)
inarr = np.array([x.flatten(), y.flatten()])
if isinstance(angle, u.Quantity):
angle = angle.to_value(u.rad)
result = np.dot(cls._compute_matrix(angle), inarr)
x, y = result[0], result[1]
x.shape = y.shape = orig_shape
if has_units:
return u.Quantity(x, unit=x_unit), u.Quantity(y, unit=y_unit)
else:
return x, y
@staticmethod
def _compute_matrix(angle):
return np.array([[math.cos(angle), -math.sin(angle)],
[math.sin(angle), math.cos(angle)]],
dtype=np.float64)