import astropy.units as u
import numpy as np
from einsteinpy.coordinates.conversion import (
BoyerLindquistConversion,
CartesianConversion,
SphericalConversion,
)
[docs]class Cartesian(CartesianConversion):
"""
Class for Cartesian Coordinates and related transformations.
"""
@u.quantity_input(x=u.km, y=u.km, z=u.km)
def __init__(self, x, y, z):
"""
Constructor.
Parameters
----------
x : ~astropy.units.quantity.Quantity
y : ~astropy.units.quantity.Quantity
z : ~astropy.units.quantity.Qauntity
"""
self.x = x
self.y = y
self.z = z
super().__init__(x.si.value, y.si.value, z.si.value)
self.system = "Cartesian"
self._dimension = {"x": self.x, "y": self.y, "z": self.z, "system": self.system}
self._dimension_order = ("x", "y", "z")
def __repr__(self):
return "Cartesian x: {}, y: {}, z: {}".format(self.x, self.y, self.z)
def __str__(self):
return self.__repr__()
def __getitem__(self, item):
"""
Method to return coordinates.
Objects are subsctiptable with both explicit names of parameters
and integer indices.
Parameters
----------
item : str or int
Name of the parameter or its index.
If ``'system'``, Name of coordinate is returned.
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, m, m)
"""
element_list = [self.x.to(u.m), self.y.to(u.m), self.z.to(u.m)]
return np.array([e.value for e in element_list], dtype=float)
[docs] def norm(self):
"""
Function for finding euclidean norm of a vector.
Returns
-------
~astropy.units.quantity.Quantity
Euclidean norm with units.
"""
return np.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
[docs] def dot(self, target):
"""
Dot product of two vectors.
Parameters
----------
target: ~einsteipy.coordinates.core.Cartesian
Returns
-------
~astropy.units.quantity.Quantity
Dot product with units
"""
x = self.x * target.x
y = self.y * target.y
z = self.z * target.z
return x + y + z
[docs] def to_spherical(self):
"""
Method for conversion to spherical coordinates.
Returns
-------
~einsteinpy.coordinates.core.Spherical
Spherical representation of the Cartesian Coordinates.
"""
r, theta, phi = self.convert_spherical()
return Spherical(r * u.m, theta * u.rad, phi * u.rad)
[docs] @u.quantity_input(a=u.km)
def to_bl(self, a):
"""
Method for conversion to boyer-lindquist coordinates.
Parameters
----------
a : ~astropy.units.quantity.Quantity
a = J/Mc , the angular momentum per unit mass of the black hole per speed of light.
Returns
-------
~einsteinpy.coordinates.core.BoyerLindquist
BL representation of the Cartesian Coordinates.
"""
r, theta, phi, a = self.convert_bl(a.si.value)
return BoyerLindquist(r * u.m, theta * u.rad, phi * u.rad, a * u.m)
[docs]class Spherical(SphericalConversion):
"""
Class for Spherical Coordinates and related transformations.
"""
@u.quantity_input(r=u.km, theta=u.rad, phi=u.rad)
def __init__(self, r, theta, phi):
"""
Constructor.
Parameters
----------
r : ~astropy.units.quantity.Quantity
theta : ~astropy.units.quantity.Quantity
phi : ~astropy.units.quantity.Quantity
"""
self.r = r
self.theta = theta
self.phi = phi
super().__init__(r.si.value, theta.si.value, phi.si.value)
self.system = "Spherical"
self._dimension = {
"r": self.r,
"theta": self.theta,
"phi": self.phi,
"system": self.system,
}
self._dimension_order = ("r", "theta", "phi")
def __repr__(self):
return "Spherical r: {}, theta: {}, phi: {}".format(
self.r, self.theta, self.phi
)
def __str__(self):
return self.__repr__()
def __getitem__(self, item):
"""
Method to return coordinates.
Objects are subsctiptable with both explicit names of parameters
and integer indices.
Parameters
----------
item : str or int
Name of the parameter or its index.
If ``'system'``, Name of coordinate is returned.
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, rad, rad)
"""
element_list = [self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad)]
return np.array([e.value for e in element_list], dtype=float)
[docs] def to_cartesian(self):
"""
Method for conversion to cartesian coordinates.
Returns
-------
~einsteinpy.coordinates.core.Cartesian
Cartesian representation of the Spherical Coordinates.
"""
x, y, z = self.convert_cartesian()
return Cartesian(x * u.m, y * u.m, z * u.m)
[docs] @u.quantity_input(a=u.km)
def to_bl(self, a):
"""
Method for conversion to boyer-lindquist coordinates.
Parameters
----------
a : ~astropy.units.quantity.Quantity
a = J/Mc , the angular momentum per unit mass of the black hole per speed of light.
Returns
-------
~einsteinpy.coordinates.core.BoyerLindquist
BL representation of the Spherical Coordinates.
"""
r, theta, phi, a = self.convert_bl(a.si.value)
return BoyerLindquist(r * u.m, theta * u.rad, phi * u.rad, a * u.m)
[docs]class BoyerLindquist(BoyerLindquistConversion):
"""
Class for Spherical Coordinates and related transformations.
"""
@u.quantity_input(r=u.km, theta=u.rad, phi=u.rad, a=u.km)
def __init__(self, r, theta, phi, a):
"""
Constructor.
Parameters
----------
r : ~astropy.units.quantity.Quantity
theta : ~astropy.units.quantity.Quantity
phi : ~astropy.units.quantity.Quantity
a : ~astropy.units.quantity.Quantity
"""
self.r = r
self.theta = theta
self.phi = phi
self.a = a
super().__init__(r.si.value, theta.si.value, phi.si.value, a=a.si.value)
self.system = "BoyerLindquist"
self._dimension = {
"r": self.r,
"theta": self.theta,
"phi": self.phi,
"a": self.a,
"system": self.system,
}
self._dimension_order = ("r", "theta", "phi")
def __repr__(self):
return "Boyer-Lindquist r: {}, theta: {}, phi: {} | a: {}".format(
self.r, self.theta, self.phi, self.a
)
def __str__(self):
return self.__repr__()
def __getitem__(self, item):
"""
Method to return coordinates.
Objects are subsctiptable with both explicit names of parameters
and integer indices.
Parameters
----------
item : str or int
Name of the parameter or its index.
If ``'system'``, Name of coordinate is returned.
If ``'a'``, spin factor of the body, ``self.a`` is returned.
"""
if isinstance(item, (int, np.integer)):
return self._dimension[self._dimension_order[item]]
return self._dimension[item]
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, rad, rad)
"""
element_list = [self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad)]
return np.array([e.value for e in element_list], dtype=float)
[docs] def to_cartesian(self):
"""
Method for conversion to cartesian coordinates.
Returns
-------
~einsteinpy.coordinates.core.Cartesian
Cartesian representation of the BL Coordinates.
"""
x, y, z = self.convert_cartesian()
return Cartesian(x * u.m, y * u.m, z * u.m)
[docs] def to_spherical(self):
"""
Method for conversion to spherical coordinates.
Returns
-------
~einsteinpy.coordinates.core.Spherical
Spherical representation of the BL Coordinates.
"""
r, theta, phi = self.convert_spherical()
return Spherical(r * u.m, theta * u.rad, phi * u.rad)
