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actionAngleVertical.py
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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 optimize, integrate
from .actionAngle import actionAngle
from ..potential.linearPotential import evaluatelinearPotentials
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):
"""
NAME:
__init__
PURPOSE:
initialize an actionAngleVertical object
INPUT:
pot= potential or list of potentials (planarPotentials)
ro= distance from vantage point to GC (kpc; can be Quantity)
vo= circular velocity at ro (km/s; can be Quantity)
OUTPUT:
instance
HISTORY:
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 IOError("Must specify pot= for actionAngleVertical")
if not 'pot' in kwargs: #pragma: no cover
raise IOError("Must specify pot= for actionAngleVertical")
self._pot= kwargs['pot']
return None
"""
self._parse_eval_args(*args,_noOrbUnitsCheck=True,**kwargs)
self._z= self._eval_z
self._vz= self._eval_vz
self._verticalpot= kwargs['pot']
return None
"""
def _evaluate(self,*args,**kwargs):
"""
NAME:
__call__ (_evaluate)
PURPOSE:
evaluate the action
INPUT:
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)
OUTPUT:
action
HISTORY:
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./2.\
+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.*integrate.quad(\
lambda xi: numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,xi,
use_physical=False))),
0.,xmax)[0]/numpy.pi
return J
else: # pragma: no cover
raise ValueError('actionAngleVertical __call__ input not understood')
def _actionsFreqs(self,*args,**kwargs):
"""
NAME:
actionsFreqs (_actionsFreqs)
PURPOSE:
evaluate the action and frequency
INPUT:
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)
OUTPUT:
action,frequency
HISTORY:
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./2.\
+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.*integrate.quad(\
lambda xi: numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,xi,
use_physical=False))),
0.,xmax,)[0]/numpy.pi
# Transformed x = xmax-t^2 for singularity
Omega[ii]= numpy.pi/2./integrate.quad(\
lambda t: 2.*t/numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,
xmax-t**2.,
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):
"""
NAME:
actionsFreqsAngles (_actionsFreqsAngles)
PURPOSE:
evaluate the action, frequency, and angle
INPUT:
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)
OUTPUT:
action,frequency,angle
HISTORY:
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./2.\
+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.*integrate.quad(\
lambda xi: numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,xi,
use_physical=False))),
0.,xmax)[0]/numpy.pi
Omega[ii]= numpy.pi/2./integrate.quad(\
lambda t: 2.*t/numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,
xmax-t**2.,
use_physical=False))),
0,numpy.sqrt(xmax))[0]
angle[ii]= integrate.quad(\
lambda xi: 1./numpy.sqrt(2.*(E\
-evaluatelinearPotentials(self._pot,xi,
use_physical=False))),
0,numpy.fabs(x[ii]))[0]
angle*= Omega
angle[(x >= 0.)*(vx < 0.)]= numpy.pi-angle[(x >= 0.)*(vx < 0.)]
angle[(x < 0.)*(vx <= 0.)]= numpy.pi+angle[(x < 0.)*(vx <= 0.)]
angle[(x < 0.)*(vx > 0.)]= 2.*numpy.pi-angle[(x < 0.)*(vx > 0.)]
return (J,Omega,angle % (2.*numpy.pi))
else: # pragma: no cover
raise ValueError('actionAngleVertical actionsFreqsAngles input not understood')
def calcxmax(self,x,vx,E=None):
"""
NAME:
calcxmax
PURPOSE:
calculate the maximum height
INPUT:
x - position
vx - velocity
OUTPUT:
zmax
HISTORY:
2012-06-01 - Written - Bovy (IAS)
2018-05-19 - Re-written for new framework - Bovy (UofT)
"""
if E is None:
E= E= vx**2./2.\
+evaluatelinearPotentials(self._pot,x,use_physical=False)
if vx == 0.: #We are exactly at the maximum height
xmax= numpy.fabs(x)
else:
xstart= x
try:
if x == 0.: xend= 0.00001
else: xend= 2.*numpy.fabs(x)
while (E-evaluatelinearPotentials(self._pot,xend,
use_physical=False)) > 0.:
xend*= 2.
if xend > 100.: #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