/
actionAngleVertical.py
340 lines (317 loc) · 11.9 KB
/
actionAngleVertical.py
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###############################################################################
# actionAngle: a Python module to calculate actions, angles, and frequencies
#
# class: actionAngleVertical
#
# methods:
# __call__: returns (j)
# actionsFreqs: returns (j,omega)
# actionsFreqsAngles: returns (j,omega,a)
# calcxmax
###############################################################################
import numpy
from scipy import integrate, optimize
from ..potential.linearPotential import evaluatelinearPotentials
from .actionAngle import actionAngle
class actionAngleVertical(actionAngle):
"""Action-angle formalism for one-dimensional potentials (or of the vertical potential in a galactic disk in the adiabatic approximation, hence the name)"""
def __init__(self, *args, **kwargs):
"""
Initialize an actionAngleVertical object.
Parameters
----------
pot : potential or list of 1D potentials (linearPotential or verticalPotential)
Potential or list of 1D potentials.
ro : float or Quantity, optional
Distance scale for translation into internal units (default from configuration file).
vo : float or Quantity, optional
Velocity scale for translation into internal units (default from configuration file).
Notes
-----
- 2012-06-01 - Written - Bovy (IAS)
- 2018-05-19 - Conformed to the general actionAngle framework - Bovy (UofT)
"""
actionAngle.__init__(self, ro=kwargs.get("ro", None), vo=kwargs.get("vo", None))
if not "pot" in kwargs: # pragma: no cover
raise OSError("Must specify pot= for actionAngleVertical")
if not "pot" in kwargs: # pragma: no cover
raise OSError("Must specify pot= for actionAngleVertical")
self._pot = kwargs["pot"]
return None
def _evaluate(self, *args, **kwargs):
"""
Evaluate the action.
Parameters
----------
*args : tuple
Either:
a) x,vx:
1) floats: phase-space value for single object (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
Returns
-------
float or numpy.ndarray
action
Notes
-----
- 2018-05-19 - Written based on re-write of existing code - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x, vx = args
if isinstance(x, float):
x = numpy.array([x])
vx = numpy.array([vx])
J = numpy.empty(len(x))
for ii in range(len(x)):
E = vx[ii] ** 2.0 / 2.0 + evaluatelinearPotentials(
self._pot, x[ii], use_physical=False
)
xmax = self.calcxmax(x[ii], vx[ii], E)
if xmax == -9999.99:
J[ii] = 9999.99
else:
J[ii] = (
2.0
* integrate.quad(
lambda xi: numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xi, use_physical=False
)
)
),
0.0,
xmax,
)[0]
/ numpy.pi
)
return J
else: # pragma: no cover
raise ValueError("actionAngleVertical __call__ input not understood")
def _actionsFreqs(self, *args, **kwargs):
"""
Evaluate the action and frequency.
Parameters
----------
*args : tuple
Either:
a) x,vx:
1) floats: phase-space value for single object (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
Returns
-------
tuple
action,frequency
Notes
-----
- 2018-05-19 - Written based on re-write of existing code - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x, vx = args
if isinstance(x, float):
x = numpy.array([x])
vx = numpy.array([vx])
J = numpy.empty(len(x))
Omega = numpy.empty(len(x))
for ii in range(len(x)):
E = vx[ii] ** 2.0 / 2.0 + evaluatelinearPotentials(
self._pot, x[ii], use_physical=False
)
xmax = self.calcxmax(x[ii], vx[ii], E)
if xmax == -9999.99:
J[ii] = 9999.99
Omega[ii] = 9999.99
else:
J[ii] = (
2.0
* integrate.quad(
lambda xi: numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xi, use_physical=False
)
)
),
0.0,
xmax,
)[0]
/ numpy.pi
)
# Transformed x = xmax-t^2 for singularity
Omega[ii] = (
numpy.pi
/ 2.0
/ integrate.quad(
lambda t: 2.0
* t
/ numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xmax - t**2.0, use_physical=False
)
)
),
0,
numpy.sqrt(xmax),
)[0]
)
return (J, Omega)
else: # pragma: no cover
raise ValueError("actionAngleVertical actionsFreqs input not understood")
def _actionsFreqsAngles(self, *args, **kwargs):
"""
Evaluate the action, frequency, and angle.
Parameters
----------
*args : tuple
Either:
a) x,vx:
1) floats: phase-space value for single object (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
Returns
-------
tuple
action,frequency,angle
Notes
-----
- 2018-05-19 - Written based on re-write of existing code - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x, vx = args
if isinstance(x, float):
x = numpy.array([x])
vx = numpy.array([vx])
J = numpy.empty(len(x))
Omega = numpy.empty(len(x))
angle = numpy.empty(len(x))
for ii in range(len(x)):
E = vx[ii] ** 2.0 / 2.0 + evaluatelinearPotentials(
self._pot, x[ii], use_physical=False
)
xmax = self.calcxmax(x[ii], vx[ii], E)
if xmax == -9999.99:
J[ii] = 9999.99
Omega[ii] = 9999.99
angle[ii] = 9999.99
else:
J[ii] = (
2.0
* integrate.quad(
lambda xi: numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xi, use_physical=False
)
)
),
0.0,
xmax,
)[0]
/ numpy.pi
)
Omega[ii] = (
numpy.pi
/ 2.0
/ integrate.quad(
lambda t: 2.0
* t
/ numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xmax - t**2.0, use_physical=False
)
)
),
0,
numpy.sqrt(xmax),
)[0]
)
angle[ii] = integrate.quad(
lambda xi: 1.0
/ numpy.sqrt(
2.0
* (
E
- evaluatelinearPotentials(
self._pot, xi, use_physical=False
)
)
),
0,
numpy.fabs(x[ii]),
)[0]
angle *= Omega
angle[(x >= 0.0) * (vx < 0.0)] = numpy.pi - angle[(x >= 0.0) * (vx < 0.0)]
angle[(x < 0.0) * (vx <= 0.0)] = numpy.pi + angle[(x < 0.0) * (vx <= 0.0)]
angle[(x < 0.0) * (vx > 0.0)] = (
2.0 * numpy.pi - angle[(x < 0.0) * (vx > 0.0)]
)
return (J, Omega, angle % (2.0 * numpy.pi))
else: # pragma: no cover
raise ValueError(
"actionAngleVertical actionsFreqsAngles input not understood"
)
def calcxmax(self, x, vx, E=None):
"""
Calculate the maximum height
Parameters
----------
x : float
Position
vx : float
Velocity
E : float, optional
Energy (default is None)
Returns
-------
float
Maximum height
Notes
-----
- 2012-06-01 - Written - Bovy (IAS)
- 2018-05-19 - Re-written for new framework - Bovy (UofT)
"""
if E is None:
E = E = vx**2.0 / 2.0 + evaluatelinearPotentials(
self._pot, x, use_physical=False
)
if vx == 0.0: # We are exactly at the maximum height
xmax = numpy.fabs(x)
else:
xstart = x
try:
if x == 0.0:
xend = 0.00001
else:
xend = 2.0 * numpy.fabs(x)
while (
E - evaluatelinearPotentials(self._pot, xend, use_physical=False)
) > 0.0:
xend *= 2.0
if xend > 100.0: # pragma: no cover
raise OverflowError
except OverflowError: # pragma: no cover
xmax = -9999.99
else:
xmax = optimize.brentq(
lambda xm: E
- evaluatelinearPotentials(self._pot, xm, use_physical=False),
xstart,
xend,
xtol=1e-14,
)
while (
E - evaluatelinearPotentials(self._pot, xmax, use_physical=False)
) < 0:
xmax -= 1e-14
return xmax