# Source code for galpy.actionAngle.actionAngleHarmonic

###############################################################################
#   actionAngle: a Python module to calculate  actions, angles, and frequencies
#
#      class: actionAngleHarmonic
#
#             Calculate actions-angle coordinates for the harmonic-oscillator
#
#      methods:
#             __call__: returns (j)
#             actionsFreqs: returns (j,omega)
#             actionsFreqsAngles: returns (j,omega,a)
#
###############################################################################
import numpy
from .actionAngle import actionAngle
from ..util import conversion
[docs]class actionAngleHarmonic(actionAngle):
"""Action-angle formalism for the one-dimensional harmonic oscillator"""
[docs]    def __init__(self,*args,**kwargs):
"""
NAME:

__init__

PURPOSE:

initialize an actionAngleHarmonic object

INPUT:

omega= frequencies (can be Quantity)

ro= distance from vantage point to GC (kpc; can be Quantity)

vo= circular velocity at ro (km/s; can be Quantity)

OUTPUT:

instance

HISTORY:

2018-04-08 - Written - Bovy (Uoft)

"""
actionAngle.__init__(self,
ro=kwargs.get('ro',None),vo=kwargs.get('vo',None))
if not 'omega' in kwargs: #pragma: no cover
raise IOError("Must specify omega= for actionAngleHarmonic")
self._omega= conversion.parse_frequency(kwargs.get('omega'),
ro=self._ro,vo=self._vo)
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:
2018-04-08 - Written - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x,vx= args
return (vx**2./self._omega+self._omega*x**2.)/2.
else: # pragma: no cover
raise ValueError('actionAngleHarmonic __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:
2018-04-08 - Written - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x,vx= args
return ((vx**2./self._omega+self._omega*x**2.)/2.,
self._omega*numpy.ones_like(x))
else: # pragma: no cover
raise ValueError('actionAngleHarmonic __call__ 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:
2018-04-08 - Written - Bovy (UofT)
"""
if len(args) == 2: # x,vx
x,vx= args
return ((vx**2./self._omega+self._omega*x**2.)/2.,
self._omega*numpy.ones_like(x),
numpy.arctan2(self._omega*x,vx))
else: # pragma: no cover
raise ValueError('actionAngleHarmonic __call__ input not understood')