def Jz(self, *args, **kwargs):
"""
NAME:
Jz
PURPOSE:
evaluate the action jz
INPUT:
Either:
a) R,vR,vT,z,vz
b) Orbit instance: initial condition used if that's it, orbit(t)
if there is a time given as well
scipy.integrate.quadrature keywords
OUTPUT:
jz
HISTORY:
2012-07-30 - Written - Bovy (IAS@MPIA)
"""
meta = actionAngle(*args)
Phi = galpy.potential.evaluatePotentials(meta._R, meta._z, self._pot)
Phio = galpy.potential.evaluatePotentials(meta._R, 0.0, self._pot)
Ez = Phi - Phio + meta._vz ** 2.0 / 2.0
# Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(meta._R))
if (
meta._R > self._Rmax or meta._R < self._Rmin or (Ez != 0.0 and numpy.log(Ez) > thisEzZmax)
): # Outside of the grid
if _PRINTOUTSIDEGRID:
print "Outside of grid in Ez"
jz = self._aA.Jz(meta._R, 0.0, 1.0, 0.0, math.sqrt(2.0 * Ez), **kwargs)[0] # these two r dummies
else:
jz = (self._jzInterp(meta._R, Ez / thisEzZmax) * (numpy.exp(self._jzEzmaxInterp(meta._R)) - 10.0 ** -5.0))[
0
][0]
return jz
def Jz(self, *args, **kwargs):
"""
NAME:
Jz
PURPOSE:
evaluate the action jz
INPUT:
Either:
a) R,vR,vT,z,vz
b) Orbit instance: initial condition used if that's it, orbit(t)
if there is a time given as well
scipy.integrate.quadrature keywords
OUTPUT:
jz
HISTORY:
2012-07-30 - Written - Bovy (IAS@MPIA)
"""
meta = actionAngle(*args)
Phi = galpy.potential.evaluatePotentials(meta._R, meta._z, self._pot)
Phio = galpy.potential.evaluatePotentials(meta._R, 0., self._pot)
Ez = Phi - Phio + meta._vz**2. / 2.
#Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(meta._R))
if meta._R > self._Rmax or meta._R < self._Rmin or (
Ez != 0. and numpy.log(Ez) > thisEzZmax): #Outside of the grid
if _PRINTOUTSIDEGRID:
print "Outside of grid in Ez"
jz = self._aA.Jz(
meta._R,
0.,
1., #these two r dummies
0.,
math.sqrt(2. * Ez),
**kwargs)[0]
else:
jz= (self._jzInterp(meta._R,Ez/thisEzZmax)\
*(numpy.exp(self._jzEzmaxInterp(meta._R))-10.**-5.))[0][0]
return jz
def __call__(self, *args, **kwargs):
"""
NAME:
__call__
PURPOSE:
evaluate the actions (jr,lz,jz)
INPUT:
Either:
a) R,vR,vT,z,vz
b) Orbit instance: initial condition used if that's it, orbit(t)
if there is a time given as well
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-07-27 - Written - Bovy (IAS@MPIA)
NOTE:
For a Miyamoto-Nagai potential, this seems accurate to 0.1% and takes ~0.13 ms
For a MWPotential, this takes ~ 0.17 ms
"""
if len(args) == 5: #R,vR.vT, z, vz
R, vR, vT, z, vz = args
elif len(args) == 6: #R,vR.vT, z, vz, phi
R, vR, vT, z, vz, phi = args
else:
meta = actionAngle(*args)
R = meta._R
vR = meta._vR
vT = meta._vT
z = meta._z
vz = meta._vz
#First work on the vertical action
Phi = galpy.potential.evaluatePotentials(R, z, self._pot)
Phio = galpy.potential.evaluatePotentials(R, 0., self._pot)
Ez = Phi - Phio + vz**2. / 2.
#Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(R))
if isinstance(R, numpy.ndarray):
indx = (R > self._Rmax)
indx += (R < self._Rmin)
indx += (Ez != 0.) * (numpy.log(Ez) > thisEzZmax)
indxc = True - indx
jz = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jz[indxc]= (self._jzInterp.ev(R[indxc],Ez[indxc]/thisEzZmax[indxc])\
*(numpy.exp(self._jzEzmaxInterp(R[indxc]))-10.**-5.))
if numpy.sum(indx) > 0:
jzindiv = numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
jzindiv[ii] = self._aA.Jz(
R[indx][ii],
0.,
1., #these two r dummies
0.,
numpy.sqrt(2. * Ez[indx][ii]),
**kwargs)[0]
except UnboundError:
jzindiv[ii] = numpy.nan
jz[indx] = jzindiv
else:
if R > self._Rmax or R < self._Rmin or (
Ez != 0
and numpy.log(Ez) > thisEzZmax): #Outside of the grid
if _PRINTOUTSIDEGRID:
print "Outside of grid in Ez", R > self._Rmax, R < self._Rmin, (
Ez != 0 and numpy.log(Ez) > thisEzZmax)
jz = self._aA.Jz(
R,
0.,
1., #these two r dummies
0.,
math.sqrt(2. * Ez),
**kwargs)[0]
else:
jz= (self._jzInterp(R,Ez/thisEzZmax)\
*(numpy.exp(self._jzEzmaxInterp(R))-10.**-5.))[0][0]
#Radial action
ERLz = numpy.fabs(R * vT) + self._gamma * jz
ER = Phio + vR**2. / 2. + ERLz**2. / 2. / R**2.
thisRL = self._RLInterp(ERLz)
thisERRL = -numpy.exp(self._ERRLInterp(ERLz)) + self._ERRLmax
thisERRa = -numpy.exp(self._ERRaInterp(ERLz)) + self._ERRamax
if isinstance(R, numpy.ndarray):
indx= ((ER-thisERRa)/(thisERRL-thisERRa) > 1.)\
*(((ER-thisERRa)/(thisERRL-thisERRa)-1.) < 10.**-2.)
ER[indx] = thisERRL[indx]
indx= ((ER-thisERRa)/(thisERRL-thisERRa) < 0.)\
*((ER-thisERRa)/(thisERRL-thisERRa) > -10.**-2.)
ER[indx] = thisERRa[indx]
indx = (ERLz < self._Lzmin)
indx += (ERLz > self._Lzmax)
indx += ((ER - thisERRa) / (thisERRL - thisERRa) > 1.)
indx += ((ER - thisERRa) / (thisERRL - thisERRa) < 0.)
indxc = True - indx
jr = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jr[indxc]= (self._jrInterp.ev(ERLz[indxc],
(ER[indxc]-thisERRa[indxc])/(thisERRL[indxc]-thisERRa[indxc]))\
*(numpy.exp(self._jrERRaInterp(ERLz[indxc]))-10.**-5.))
if numpy.sum(indx) > 0:
jrindiv = numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
jrindiv[ii] = self._aA.JR(
thisRL[indx][ii],
numpy.sqrt(2. *
(ER[indx][ii] -
galpy.potential.evaluatePotentials(
thisRL[indx][ii], 0., self._pot)) -
ERLz[indx][ii]**2. /
thisRL[indx][ii]**2.),
ERLz[indx][ii] / thisRL[indx][ii], 0., 0.,
**kwargs)[0]
except (UnboundError, OverflowError):
jrindiv[ii] = numpy.nan
jr[indx] = jrindiv
else:
if (ER-thisERRa)/(thisERRL-thisERRa) > 1. \
and ((ER-thisERRa)/(thisERRL-thisERRa)-1.) < 10.**-2.:
ER = thisERRL
elif (ER-thisERRa)/(thisERRL-thisERRa) < 0. \
and (ER-thisERRa)/(thisERRL-thisERRa) > -10.**-2.:
ER = thisERRa
#Outside of grid?
if ERLz < self._Lzmin or ERLz > self._Lzmax \
or (ER-thisERRa)/(thisERRL-thisERRa) > 1. \
or (ER-thisERRa)/(thisERRL-thisERRa) < 0.:
if _PRINTOUTSIDEGRID:
print "Outside of grid in ER/Lz", ERLz < self._Lzmin , ERLz > self._Lzmax \
, (ER-thisERRa)/(thisERRL-thisERRa) > 1. \
, (ER-thisERRa)/(thisERRL-thisERRa) < 0., ER, thisERRL, thisERRa, (ER-thisERRa)/(thisERRL-thisERRa)
jr = self._aA.JR(
thisRL,
numpy.sqrt(2. * (ER - galpy.potential.evaluatePotentials(
thisRL, 0., self._pot)) - ERLz**2. / thisRL**2.),
ERLz / thisRL, 0., 0., **kwargs)[0]
else:
jr= (self._jrInterp(ERLz,
(ER-thisERRa)/(thisERRL-thisERRa))\
*(numpy.exp(self._jrERRaInterp(ERLz))-10.**-5.))[0][0]
return (jr, R * vT, jz)
def __call__(self, *args, **kwargs):
"""
NAME:
__call__
PURPOSE:
evaluate the actions (jr,lz,jz)
INPUT:
Either:
a) R,vR,vT,z,vz
b) Orbit instance: initial condition used if that's it, orbit(t)
if there is a time given as well
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-07-27 - Written - Bovy (IAS@MPIA)
NOTE:
For a Miyamoto-Nagai potential, this seems accurate to 0.1% and takes ~0.13 ms
For a MWPotential, this takes ~ 0.17 ms
"""
if len(args) == 5: # R,vR.vT, z, vz
R, vR, vT, z, vz = args
elif len(args) == 6: # R,vR.vT, z, vz, phi
R, vR, vT, z, vz, phi = args
else:
meta = actionAngle(*args)
R = meta._R
vR = meta._vR
vT = meta._vT
z = meta._z
vz = meta._vz
# First work on the vertical action
Phi = galpy.potential.evaluatePotentials(R, z, self._pot)
Phio = galpy.potential.evaluatePotentials(R, 0.0, self._pot)
Ez = Phi - Phio + vz ** 2.0 / 2.0
# Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(R))
if isinstance(R, numpy.ndarray):
indx = R > self._Rmax
indx += R < self._Rmin
indx += (Ez != 0.0) * (numpy.log(Ez) > thisEzZmax)
indxc = True - indx
jz = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jz[indxc] = self._jzInterp.ev(R[indxc], Ez[indxc] / thisEzZmax[indxc]) * (
numpy.exp(self._jzEzmaxInterp(R[indxc])) - 10.0 ** -5.0
)
if numpy.sum(indx) > 0:
jzindiv = numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
jzindiv[ii] = self._aA.Jz(
R[indx][ii], 0.0, 1.0, 0.0, numpy.sqrt(2.0 * Ez[indx][ii]), **kwargs # these two r dummies
)[0]
except UnboundError:
jzindiv[ii] = numpy.nan
jz[indx] = jzindiv
else:
if R > self._Rmax or R < self._Rmin or (Ez != 0 and numpy.log(Ez) > thisEzZmax): # Outside of the grid
if _PRINTOUTSIDEGRID:
print "Outside of grid in Ez", R > self._Rmax, R < self._Rmin, (
Ez != 0 and numpy.log(Ez) > thisEzZmax
)
jz = self._aA.Jz(R, 0.0, 1.0, 0.0, math.sqrt(2.0 * Ez), **kwargs)[0] # these two r dummies
else:
jz = (self._jzInterp(R, Ez / thisEzZmax) * (numpy.exp(self._jzEzmaxInterp(R)) - 10.0 ** -5.0))[0][0]
# Radial action
ERLz = numpy.fabs(R * vT) + self._gamma * jz
ER = Phio + vR ** 2.0 / 2.0 + ERLz ** 2.0 / 2.0 / R ** 2.0
thisRL = self._RLInterp(ERLz)
thisERRL = -numpy.exp(self._ERRLInterp(ERLz)) + self._ERRLmax
thisERRa = -numpy.exp(self._ERRaInterp(ERLz)) + self._ERRamax
if isinstance(R, numpy.ndarray):
indx = ((ER - thisERRa) / (thisERRL - thisERRa) > 1.0) * (
((ER - thisERRa) / (thisERRL - thisERRa) - 1.0) < 10.0 ** -2.0
)
ER[indx] = thisERRL[indx]
indx = ((ER - thisERRa) / (thisERRL - thisERRa) < 0.0) * (
(ER - thisERRa) / (thisERRL - thisERRa) > -10.0 ** -2.0
)
ER[indx] = thisERRa[indx]
indx = ERLz < self._Lzmin
indx += ERLz > self._Lzmax
indx += (ER - thisERRa) / (thisERRL - thisERRa) > 1.0
indx += (ER - thisERRa) / (thisERRL - thisERRa) < 0.0
indxc = True - indx
jr = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jr[indxc] = self._jrInterp.ev(
ERLz[indxc], (ER[indxc] - thisERRa[indxc]) / (thisERRL[indxc] - thisERRa[indxc])
) * (numpy.exp(self._jrERRaInterp(ERLz[indxc])) - 10.0 ** -5.0)
if numpy.sum(indx) > 0:
jrindiv = numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
jrindiv[ii] = self._aA.JR(
thisRL[indx][ii],
numpy.sqrt(
2.0
* (ER[indx][ii] - galpy.potential.evaluatePotentials(thisRL[indx][ii], 0.0, self._pot))
- ERLz[indx][ii] ** 2.0 / thisRL[indx][ii] ** 2.0
),
ERLz[indx][ii] / thisRL[indx][ii],
0.0,
0.0,
**kwargs
)[0]
except (UnboundError, OverflowError):
jrindiv[ii] = numpy.nan
jr[indx] = jrindiv
else:
if (ER - thisERRa) / (thisERRL - thisERRa) > 1.0 and (
(ER - thisERRa) / (thisERRL - thisERRa) - 1.0
) < 10.0 ** -2.0:
ER = thisERRL
elif (ER - thisERRa) / (thisERRL - thisERRa) < 0.0 and (ER - thisERRa) / (
thisERRL - thisERRa
) > -10.0 ** -2.0:
ER = thisERRa
# Outside of grid?
if (
ERLz < self._Lzmin
or ERLz > self._Lzmax
or (ER - thisERRa) / (thisERRL - thisERRa) > 1.0
or (ER - thisERRa) / (thisERRL - thisERRa) < 0.0
):
if _PRINTOUTSIDEGRID:
print "Outside of grid in ER/Lz", ERLz < self._Lzmin, ERLz > self._Lzmax, (ER - thisERRa) / (
thisERRL - thisERRa
) > 1.0, (ER - thisERRa) / (thisERRL - thisERRa) < 0.0, ER, thisERRL, thisERRa, (ER - thisERRa) / (
thisERRL - thisERRa
)
jr = self._aA.JR(
thisRL,
numpy.sqrt(
2.0 * (ER - galpy.potential.evaluatePotentials(thisRL, 0.0, self._pot))
- ERLz ** 2.0 / thisRL ** 2.0
),
ERLz / thisRL,
0.0,
0.0,
**kwargs
)[0]
else:
jr = (
self._jrInterp(ERLz, (ER - thisERRa) / (thisERRL - thisERRa))
* (numpy.exp(self._jrERRaInterp(ERLz)) - 10.0 ** -5.0)
)[0][0]
return (jr, R * vT, jz)