import astropy.units as u
import numpy as np
from einsteinpy.coordinates.conversion import (
BoyerLindquistConversion,
CartesianConversion,
SphericalConversion,
)
[docs]class CartesianDifferential(CartesianConversion):
"""
Class for calculating and transforming the velocity in Cartesian coordinates.
"""
@u.quantity_input(
x=u.km, y=u.km, z=u.km, v_x=u.km / u.s, v_y=u.km / u.s, v_z=u.km / u.s
)
def __init__(self, x, y, z, v_x, v_y, v_z):
"""
Constructor.
Parameters
----------
x : ~astropy.units.quantity.Quantity
y : ~astropy.units.quantity.Quantity
z : ~astropy.units.quantity.Quantity
v_x : ~astropy.units.quantity.Quantity
v_y : ~astropy.units.quantity.Quantity
v_z : ~astropy.units.quantity.Quantity
"""
self.x = x
self.y = y
self.z = z
self.v_x = v_x
self.v_y = v_y
self.v_z = v_z
super().__init__(
x.si.value, y.si.value, z.si.value, v_x.si.value, v_y.si.value, v_z.si.value
)
self.system = "Cartesian"
def __repr__(self):
return "Cartesian x: {}, y: {}, z: {}\n" "vx: {}, vy: {}, vz: {}".format(
self.x, self.y, self.z, self.v_x, self.v_y, self.v_z
)
def __str__(self):
return self.__repr__()
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, m, m, m/s, m/s, m/s)
"""
element_list = [
self.x.to(u.m),
self.y.to(u.m),
self.z.to(u.m),
self.v_x.to(u.m / u.s),
self.v_y.to(u.m / u.s),
self.v_z.to(u.m / u.s),
]
return np.array([e.value for e in element_list], dtype=float)
[docs] def velocities(self, return_np=False):
"""
Function for returning velocity.
Parameters
----------
return_np : bool
True for numpy array with SI values, False for list with astropy units.
Defaults to False
Returns
-------
~numpy.ndarray or list
Array or list containing velocity.
"""
if return_np:
return self.si_values()[3:]
return [self.v_x, self.v_y, self.v_z]
[docs] def spherical_differential(self):
"""
Function to convert velocity to spherical coordinates velocity
Returns
-------
~einsteinpy.coordinates.velocity.SphericalDifferential
Spherical representation of the velocity in Cartesian Coordinates.
"""
r, theta, phi, v_r, v_t, v_p = self.convert_spherical()
return SphericalDifferential(
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_t * u.rad / u.s,
v_p * u.rad / u.s,
)
[docs] @u.quantity_input(a=u.km)
def bl_differential(self, a):
"""
Function to convert velocity 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.velocity.BoyerLindquistDifferential
Boyer-Lindquist representation of the velocity in Cartesian Coordinates.
"""
r, theta, phi, v_r, v_t, v_p, a = self.convert_bl(a.si.value)
return BoyerLindquistDifferential(
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_t * u.rad / u.s,
v_p * u.rad / u.s,
a * u.m,
)
[docs]class SphericalDifferential(SphericalConversion):
"""
Class for calculating and transforming the velocity in Spherical coordinates.
"""
@u.quantity_input(
r=u.km, theta=u.rad, phi=u.rad, v_r=u.km / u.s, v_t=u.rad / u.s, v_p=u.rad / u.s
)
def __init__(self, r, theta, phi, v_r, v_t, v_p):
"""
Constructor.
Parameters
----------
r : ~astropy.units.quantity.Quantity
theta : ~astropy.units.quantity.Quantity
phi : ~astropy.units.quantity.Quantity
v_r : ~astropy.units.quantity.Quantity
v_t : ~astropy.units.quantity.Quantity
v_p : ~astropy.units.quantity.Quantity
"""
self.r = r
self.theta = theta
self.phi = phi
self.v_r = v_r
self.v_t = v_t
self.v_p = v_p
super().__init__(
r.si.value,
theta.si.value,
phi.si.value,
v_r.si.value,
v_t.si.value,
v_p.si.value,
)
self.system = "Spherical"
def __repr__(self):
return "Spherical r: {}, theta: {}, phi: {}\n" "vr: {}, vt: {}, vp: {}".format(
self.r, self.theta, self.phi, self.v_r, self.v_t, self.v_p
)
def __str__(self):
return self.__repr__()
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, rad, rad, m/s, rad/s, rad/s)
"""
element_list = [
self.r.to(u.m),
self.theta.to(u.rad),
self.phi.to(u.rad),
self.v_r.to(u.m / u.s),
self.v_t.to(u.rad / u.s),
self.v_p.to(u.rad / u.s),
]
return np.array([e.value for e in element_list], dtype=float)
[docs] def velocities(self, return_np=False):
"""
Function for returning velocity.
Parameters
----------
return_np : bool
True for numpy array with SI values, False for list with astropy units.
Defaults to False
Returns
-------
~numpy.ndarray or list
Array or list containing velocity.
"""
if return_np:
return self.si_values()[3:]
return [self.v_r, self.v_t, self.v_p]
[docs] def cartesian_differential(self):
"""
Function to convert velocity to cartesian coordinates
Returns
-------
~einsteinpy.coordinates.velocity.CartesianDifferential
Cartesian representation of the velocity in Spherical Coordinates.
"""
x, y, z, v_x, v_y, v_z = self.convert_cartesian()
return CartesianDifferential(
x * u.m, y * u.m, z * u.m, v_x * u.m / u.s, v_y * u.m / u.s, v_z * u.m / u.s
)
[docs] @u.quantity_input(a=u.km)
def bl_differential(self, a):
"""
Function to convert velocity 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.velocity.BoyerLindquistDifferential
Boyer-Lindquist representation of the velocity in Spherical Coordinates.
"""
r, theta, phi, v_r, v_t, v_p, a = self.convert_bl(a.si.value)
return BoyerLindquistDifferential(
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_t * u.rad / u.s,
v_p * u.rad / u.s,
a * u.m,
)
[docs]class BoyerLindquistDifferential(BoyerLindquistConversion):
"""
Class for calculating and transforming the velocity in Boyer-Lindquist coordinates
"""
@u.quantity_input(
r=u.km,
theta=u.rad,
phi=u.rad,
v_r=u.km / u.s,
v_t=u.rad / u.s,
v_p=u.rad / u.s,
a=u.km,
)
def __init__(self, r, theta, phi, v_r, v_t, v_p, a):
"""
Constructor.
Parameters
----------
r : ~astropy.units.quantity.Quantity
theta : ~astropy.units.quantity.Quantity
phi : ~astropy.units.quantity.Quantity
v_r : ~astropy.units.quantity.Quantity
v_t : ~astropy.units.quantity.Quantity
v_p : ~astropy.units.quantity.Quantity
a : ~astropy.units.quantity.Quantity
"""
self.r = r
self.theta = theta
self.phi = phi
self.a = a
self.v_r = v_r
self.v_t = v_t
self.v_p = v_p
super().__init__(
r.si.value,
theta.si.value,
phi.si.value,
v_r.si.value,
v_t.si.value,
v_p.si.value,
a.si.value,
)
self.system = "BoyerLindquist"
def __repr__(self):
return (
"Boyer-Lindquist r: {}, theta: {}, phi: {}\n"
"vr: {}, vt: {}, vp: {}\n"
"a: {}".format(
self.r, self.theta, self.phi, self.v_r, self.v_t, self.v_p, self.a
)
)
def __str__(self):
return self.__repr__()
[docs] def si_values(self):
"""
Function for returning values in SI units.
Returns
-------
~numpy.ndarray
Array containing values in SI units (m, rad, rad, m/s, rad/s, rad/s)
"""
element_list = [
self.r.to(u.m),
self.theta.to(u.rad),
self.phi.to(u.rad),
self.v_r.to(u.m / u.s),
self.v_t.to(u.rad / u.s),
self.v_p.to(u.rad / u.s),
]
return np.array([e.value for e in element_list], dtype=float)
[docs] def velocities(self, return_np=False):
"""
Function for returning velocity.
Parameters
----------
return_np : bool
True for numpy array with SI values, False for list with astropy units.
Defaults to False
Returns
-------
~numpy.ndarray or list
Array or list containing velocity.
"""
if return_np:
return self.si_values()[3:6]
return [self.v_r, self.v_t, self.v_p]
[docs] def cartesian_differential(self):
"""
Function to convert velocity to cartesian coordinates
Returns
-------
~einsteinpy.coordinates.velocity.CartesianDifferential
Cartesian representation of the velocity in Boyer-Lindquist Coordinates.
"""
x, y, z, v_x, v_y, v_z = self.convert_cartesian()
return CartesianDifferential(
x * u.m, y * u.m, z * u.m, v_x * u.m / u.s, v_y * u.m / u.s, v_z * u.m / u.s
)
[docs] def spherical_differential(self):
"""
Function to convert velocity to spherical coordinates
Returns
-------
~einsteinpy.coordinates.velocity.SphericalDifferential
Spherical representation of the velocity in Boyer-Lindquist Coordinates.
"""
r, theta, phi, v_r, v_t, v_p = self.convert_spherical()
return SphericalDifferential(
r * u.m,
theta * u.rad,
phi * u.rad,
v_r * u.m / u.s,
v_t * u.rad / u.s,
v_p * u.rad / u.s,
)
