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: #pragma: no cover
print "Outside of grid in Ez"
jz= self._aA(meta._R,0.,1.,#these two r dummies
0.,math.sqrt(2.*Ez),
_justjz=True,
**kwargs)[2]
else:
jz= (self._jzInterp(meta._R,Ez/thisEzZmax)\
*(numpy.exp(self._jzEzmaxInterp(meta._R))-10.**-5.))[0][0]
return jz
def calczmax(self,*args,**kwargs):
"""
NAME:
calczmax
PURPOSE:
calculate the maximum height
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
OUTPUT:
zmax
HISTORY:
2012-06-01 - Written - Bovy (IAS)
"""
#Set up the actionAngleAxi object
meta= actionAngle(*args)
if isinstance(self._pot,list):
thispot= [p.toPlanar() for p in self._pot]
else:
thispot= self._pot.toPlanar()
if isinstance(self._pot,list):
thisverticalpot= [p.toVertical(meta._R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(meta._R)
aAAxi= actionAngleAxi(*args,pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
return aAAxi.calczmax(**kwargs)
def actionsFreqs(self,*args,**kwargs):
"""
NAME:
actionsFreqs
PURPOSE:
evaluate the actions and frequencies (jr,lz,jz,Omegar,Omegaphi,Omegaz)
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,Omegar,Omegaphi,Omegaz)
HISTORY:
2013-09-08 - Written - Bovy (IAS)
"""
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
if isinstance(R,float):
R= nu.array([R])
vR= nu.array([vR])
vT= nu.array([vT])
z= nu.array([z])
vz= nu.array([vz])
if self._c: #pragma: no cover
pass
else:
Lz= R*vT
Lx= -z*vT
Ly= z*vR-R*vz
L2= Lx*Lx+Ly*Ly+Lz*Lz
E= self._ip(R,z)+vR**2./2.+vT**2./2.+vz**2./2.
L= nu.sqrt(L2)
#Actions
Jphi= Lz
Jz= L-nu.fabs(Lz)
Jr= self.amp/nu.sqrt(-2.*E)\
-0.5*(L+nu.sqrt((L2+4.*self.amp*self.b)))
#Frequencies
Omegar= (-2.*E)**1.5/self.amp
Omegaz= 0.5*(1.+L/nu.sqrt(L2+4.*self.amp*self.b))*Omegar
Omegaphi= copy.copy(Omegaz)
indx= Lz < 0.
Omegaphi[indx]*= -1.
return (Jr,Jphi,Jz,Omegar,Omegaphi,Omegaz)
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: #pragma: no cover
print("Outside of grid in Ez")
jz = self._aA(
meta._R,
0.,
1., #these two r dummies
0.,
math.sqrt(2. * Ez),
_justjz=True,
**kwargs)[2]
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)
try:
Phio= galpy.potential.evaluatePotentials(R,numpy.zeros(len(R)),self._pot)
except TypeError:
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:
jz[indx]= self._aA(R[indx],
numpy.zeros(numpy.sum(indx)),
numpy.ones(numpy.sum(indx)),#these two r dummies
numpy.zeros(numpy.sum(indx)),
numpy.sqrt(2.*Ez[indx]),
_justjz=True,
**kwargs)[2]
else:
if R > self._Rmax or R < self._Rmin or (Ez != 0 and numpy.log(Ez) > thisEzZmax): #Outside of the grid
if _PRINTOUTSIDEGRID: #pragma: no cover
print "Outside of grid in Ez", R > self._Rmax , R < self._Rmin , (Ez != 0 and numpy.log(Ez) > thisEzZmax)
jz= self._aA(R,0.,1.,#these two r dummies
0.,math.sqrt(2.*Ez),
_justjz=True,
**kwargs)[2]
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:
jr[indx]= self._aA(thisRL[indx],
numpy.sqrt(2.*(ER[indx]-galpy.potential.evaluatePotentials(thisRL[indx],0.,self._pot))-ERLz[indx]**2./thisRL[indx]**2.),
ERLz[indx]/thisRL[indx],
numpy.zeros(len(thisRL)),
numpy.zeros(len(thisRL)),
_justjr=True,
**kwargs)[0]
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: #pragma: no cover
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(thisRL[0],
numpy.sqrt(2.*(ER-galpy.potential.evaluatePotentials(thisRL,0.,self._pot))-ERLz**2./thisRL**2.)[0],
(ERLz/thisRL)[0],
0.,0.,
_justjr=True,
**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)
try:
Phio = galpy.potential.evaluatePotentials(R, numpy.zeros(len(R)),
self._pot)
except TypeError:
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:
jz[indx] = self._aA(
R[indx],
numpy.zeros(numpy.sum(indx)),
numpy.ones(numpy.sum(indx)), #these two r dummies
numpy.zeros(numpy.sum(indx)),
numpy.sqrt(2. * Ez[indx]),
_justjz=True,
**kwargs)[2]
else:
if R > self._Rmax or R < self._Rmin or (
Ez != 0
and numpy.log(Ez) > thisEzZmax): #Outside of the grid
if _PRINTOUTSIDEGRID: #pragma: no cover
print("Outside of grid in Ez", R > self._Rmax,
R < self._Rmin,
(Ez != 0 and numpy.log(Ez) > thisEzZmax))
jz = self._aA(
R,
0.,
1., #these two r dummies
0.,
math.sqrt(2. * Ez),
_justjz=True,
**kwargs)[2]
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:
jr[indx] = self._aA(
thisRL[indx],
numpy.sqrt(2. *
(ER[indx] - galpy.potential.evaluatePotentials(
thisRL[indx], 0., self._pot)) -
ERLz[indx]**2. / thisRL[indx]**2.),
ERLz[indx] / thisRL[indx],
numpy.zeros(len(thisRL)),
numpy.zeros(len(thisRL)),
_justjr=True,
**kwargs)[0]
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: #pragma: no cover
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(
thisRL[0],
numpy.sqrt(2. * (ER - galpy.potential.evaluatePotentials(
thisRL, 0., self._pot)) - ERLz**2. / thisRL**2.)[0],
(ERLz / thisRL)[0],
0.,
0.,
_justjr=True,
**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:
R,vR,vT,z,vz
scipy.integrate.quadrature keywords (for off-the-grid calcs)
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-11-29 - Written - Bovy (IAS)
"""
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
Lz= R*vT
Phi= galpy.potential.evaluatePotentials(R,z,self._pot)
E= Phi+vR**2./2.+vT**2./2.+vz**2./2.
thisRL= self._RLInterp(Lz)
thisERL= -numpy.exp(self._ERLInterp(Lz))+self._ERLmax
thisERa= -numpy.exp(self._ERaInterp(Lz))+self._ERamax
if isinstance(R,numpy.ndarray):
if len(R) == 1 and not isinstance(thisERL,numpy.ndarray):
thisERL= numpy.array([thisERL])
thisERa= numpy.array([thisERa])
indx= ((E-thisERa)/(thisERL-thisERa) > 1.)\
*(((E-thisERa)/(thisERL-thisERa)-1.) < 10.**-2.)
E[indx]= thisERL[indx]
indx= ((E-thisERa)/(thisERL-thisERa) < 0.)\
*((E-thisERa)/(thisERL-thisERa) > -10.**-2.)
E[indx]= thisERa[indx]
indx= (Lz < self._Lzmin)
indx+= (Lz > self._Lzmax)
indx+= ((E-thisERa)/(thisERL-thisERa) > 1.)
indx+= ((E-thisERa)/(thisERL-thisERa) < 0.)
indxc= True-indx
jr= numpy.empty(R.shape)
jz= numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
u0= numpy.exp(self._logu0Interp.ev(Lz[indxc],
(_Efunc(E[indxc],thisERL[indxc])-_Efunc(thisERa[indxc],thisERL[indxc]))/(_Efunc(thisERL[indxc],thisERL[indxc])-_Efunc(thisERa[indxc],thisERL[indxc]))))
# (E[indxc]-thisERa[indxc])/(thisERL[indxc]-thisERa[indxc])))
sinh2u0= numpy.sinh(u0)**2.
thisEr= self.Er(R[indxc],z[indxc],vR[indxc],vz[indxc],
E[indxc],Lz[indxc],sinh2u0,u0)
thisEz= self.Ez(R[indxc],z[indxc],vR[indxc],vz[indxc],
E[indxc],Lz[indxc],sinh2u0,u0)
thisv2= self.vatu0(E[indxc],Lz[indxc],u0,self._delta*numpy.sinh(u0),retv2=True)
cos2psi= 2.*thisEr/thisv2/(1.+sinh2u0) #latter is cosh2u0
cos2psi[(cos2psi > 1.)*(cos2psi < 1.+10.**-5.)]= 1.
indxCos2psi= (cos2psi > 1.)
indxCos2psi+= (cos2psi < 0.)
indxc[indxc]= True-indxCos2psi#Handle these two cases as off-grid
indx= True-indxc
psi= numpy.arccos(numpy.sqrt(cos2psi[True-indxCos2psi]))
coords= numpy.empty((3,numpy.sum(indxc)))
coords[0,:]= (Lz[indxc]-self._Lzmin)/(self._Lzmax-self._Lzmin)*(self._nLz-1.)
#coords[1,:]= (E[indxc]-thisERa[indxc])/(thisERL[indxc]-thisERa[indxc])*(self._nE-1.)
y= (_Efunc(E[indxc],thisERL[indxc])-_Efunc(thisERa[indxc],thisERL[indxc]))/(_Efunc(thisERL[indxc],thisERL[indxc])-_Efunc(thisERa[indxc],thisERL[indxc]))
coords[1,:]= y*(self._nE-1.)
coords[2,:]= psi/numpy.pi*2.*(self._npsi-1.)
jr[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._jrFiltered,
coords,
order=3,
prefilter=False))-10.**-10.)*(numpy.exp(self._jrLzInterp(Lz[indxc]))-10.**-5.)
#Switch to Ez-calculated psi
sin2psi= 2.*thisEz[True-indxCos2psi]/thisv2[True-indxCos2psi]/(1.+sinh2u0[True-indxCos2psi]) #latter is cosh2u0
sin2psi[(sin2psi > 1.)*(sin2psi < 1.+10.**-5.)]= 1.
indxSin2psi= (sin2psi > 1.)
indxSin2psi+= (sin2psi < 0.)
indxc[indxc]= True-indxSin2psi#Handle these two cases as off-grid
indx= True-indxc
psiz= numpy.arcsin(numpy.sqrt(sin2psi[True-indxSin2psi]))
newcoords= numpy.empty((3,numpy.sum(indxc)))
newcoords[0:2,:]= coords[0:2,True-indxSin2psi]
newcoords[2,:]= psiz/numpy.pi*2.*(self._npsi-1.)
jz[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._jzFiltered,
newcoords,
order=3,
prefilter=False))-10.**-10.)*(numpy.exp(self._jzLzInterp(Lz[indxc]))-10.**-5.)
if numpy.sum(indx) > 0:
jrindiv, lzindiv, jzindiv= self._aA(R[indx],
vR[indx],
vT[indx],
z[indx],
vz[indx],
**kwargs)
jr[indx]= jrindiv
jz[indx]= jzindiv
"""
jrindiv= numpy.empty(numpy.sum(indx))
jzindiv= numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
thisaA= actionAngleStaeckel.actionAngleStaeckelSingle(\
R[indx][ii], #R
vR[indx][ii], #vR
vT[indx][ii], #vT
z[indx][ii], #z
vz[indx][ii], #vz
pot=self._pot,delta=self._delta)
jrindiv[ii]= thisaA.JR(fixed_quad=True)[0]
jzindiv[ii]= thisaA.Jz(fixed_quad=True)[0]
except (UnboundError,OverflowError):
jrindiv[ii]= numpy.nan
jzindiv[ii]= numpy.nan
jr[indx]= jrindiv
jz[indx]= jzindiv
"""
else:
jr,Lz, jz= self(numpy.array([R]),
numpy.array([vR]),
numpy.array([vT]),
numpy.array([z]),
numpy.array([vz]),
**kwargs)
return (jr[0],Lz[0],jz[0])
return (jr,R*vT,jz)
def __call__(self, *args, **kwargs):
"""
NAME:
__call__
PURPOSE:
evaluate the actions (jr,lz,jz)
INPUT:
Either:
R,vR,vT,z,vz
scipy.integrate.quadrature keywords (for off-the-grid calcs)
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-11-29 - Written - Bovy (IAS)
"""
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
Lz = R * vT
Phi = galpy.potential.evaluatePotentials(R, z, self._pot)
E = Phi + vR**2. / 2. + vT**2. / 2. + vz**2. / 2.
thisERL = -numpy.exp(self._ERLInterp(Lz)) + self._ERLmax
thisERa = -numpy.exp(self._ERaInterp(Lz)) + self._ERamax
if isinstance(R, numpy.ndarray):
indx= ((E-thisERa)/(thisERL-thisERa) > 1.)\
*(((E-thisERa)/(thisERL-thisERa)-1.) < 10.**-2.)
E[indx] = thisERL[indx]
indx= ((E-thisERa)/(thisERL-thisERa) < 0.)\
*((E-thisERa)/(thisERL-thisERa) > -10.**-2.)
E[indx] = thisERa[indx]
indx = (Lz < self._Lzmin)
indx += (Lz > self._Lzmax)
indx += ((E - thisERa) / (thisERL - thisERa) > 1.)
indx += ((E - thisERa) / (thisERL - thisERa) < 0.)
indxc = True - indx
jr = numpy.empty(R.shape)
jz = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
u0 = numpy.exp(
self._logu0Interp.ev(
Lz[indxc], (_Efunc(E[indxc], thisERL[indxc]) -
_Efunc(thisERa[indxc], thisERL[indxc])) /
(_Efunc(thisERL[indxc], thisERL[indxc]) -
_Efunc(thisERa[indxc], thisERL[indxc]))))
sinh2u0 = numpy.sinh(u0)**2.
thisEr = self.Er(R[indxc], z[indxc], vR[indxc], vz[indxc],
E[indxc], Lz[indxc], sinh2u0, u0)
thisEz = self.Ez(R[indxc], z[indxc], vR[indxc], vz[indxc],
E[indxc], Lz[indxc], sinh2u0, u0)
thisv2 = self.vatu0(E[indxc],
Lz[indxc],
u0,
self._delta * numpy.sinh(u0),
retv2=True)
cos2psi = 2. * thisEr / thisv2 / (1. + sinh2u0
) #latter is cosh2u0
cos2psi[(cos2psi > 1.) * (cos2psi < 1. + 10.**-5.)] = 1.
indxCos2psi = (cos2psi > 1.)
indxCos2psi += (cos2psi < 0.)
indxc[
indxc] = True - indxCos2psi #Handle these two cases as off-grid
indx = True - indxc
psi = numpy.arccos(numpy.sqrt(cos2psi[True - indxCos2psi]))
coords = numpy.empty((3, numpy.sum(indxc)))
coords[0, :] = (Lz[indxc] - self._Lzmin) / (
self._Lzmax - self._Lzmin) * (self._nLz - 1.)
y = (_Efunc(E[indxc], thisERL[indxc]) -
_Efunc(thisERa[indxc], thisERL[indxc])) / (
_Efunc(thisERL[indxc], thisERL[indxc]) -
_Efunc(thisERa[indxc], thisERL[indxc]))
coords[1, :] = y * (self._nE - 1.)
coords[2, :] = psi / numpy.pi * 2. * (self._npsi - 1.)
jr[indxc] = (numpy.exp(
ndimage.interpolation.map_coordinates(
self._jrFiltered, coords, order=3, prefilter=False)) -
10.**-10.) * (numpy.exp(
self._jrLzInterp(Lz[indxc])) - 10.**-5.)
#Switch to Ez-calculated psi
sin2psi = 2. * thisEz[True - indxCos2psi] / thisv2[
True - indxCos2psi] / (1. + sinh2u0[True - indxCos2psi]
) #latter is cosh2u0
sin2psi[(sin2psi > 1.) * (sin2psi < 1. + 10.**-5.)] = 1.
indxSin2psi = (sin2psi > 1.)
indxSin2psi += (sin2psi < 0.)
indxc[
indxc] = True - indxSin2psi #Handle these two cases as off-grid
indx = True - indxc
psiz = numpy.arcsin(numpy.sqrt(sin2psi[True - indxSin2psi]))
newcoords = numpy.empty((3, numpy.sum(indxc)))
newcoords[0:2, :] = coords[0:2, True - indxSin2psi]
newcoords[2, :] = psiz / numpy.pi * 2. * (self._npsi - 1.)
jz[indxc] = (numpy.exp(
ndimage.interpolation.map_coordinates(
self._jzFiltered, newcoords, order=3,
prefilter=False)) - 10.**-10.) * (
numpy.exp(self._jzLzInterp(Lz[indxc])) - 10.**-5.)
if numpy.sum(indx) > 0:
jrindiv, lzindiv, jzindiv = self._aA(R[indx], vR[indx],
vT[indx], z[indx],
vz[indx], **kwargs)
jr[indx] = jrindiv
jz[indx] = jzindiv
"""
jrindiv= numpy.empty(numpy.sum(indx))
jzindiv= numpy.empty(numpy.sum(indx))
for ii in range(numpy.sum(indx)):
try:
thisaA= actionAngleStaeckel.actionAngleStaeckelSingle(\
R[indx][ii], #R
vR[indx][ii], #vR
vT[indx][ii], #vT
z[indx][ii], #z
vz[indx][ii], #vz
pot=self._pot,delta=self._delta)
jrindiv[ii]= thisaA.JR(fixed_quad=True)[0]
jzindiv[ii]= thisaA.Jz(fixed_quad=True)[0]
except (UnboundError,OverflowError):
jrindiv[ii]= numpy.nan
jzindiv[ii]= numpy.nan
jr[indx]= jrindiv
jz[indx]= jzindiv
"""
else:
jr, Lz, jz = self(numpy.array([R]), numpy.array([vR]),
numpy.array([vT]), numpy.array([z]),
numpy.array([vz]), **kwargs)
return (jr[0], Lz[0], jz[0])
jr[jr < 0.] = 0.
jz[jz < 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
_justjr, _justjz= if True, only calculate the radial or vertical action (internal use)
OUTPUT:
(jr,lz,jz), where jr=[jr,jrerr], and jz=[jz,jzerr]
HISTORY:
2012-07-26 - Written - Bovy (IAS@MPIA)
"""
if ((self._c and not ('c' in kwargs and not kwargs['c']))\
or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \
and _check_c(self._pot):
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
if isinstance(R,float):
R= nu.array([R])
vR= nu.array([vR])
vT= nu.array([vT])
z= nu.array([z])
vz= nu.array([vz])
Lz= R*vT
jr, jz, err= actionAngleAdiabatic_c.actionAngleAdiabatic_c(\
self._pot,self._gamma,R,vR,vT,z,vz)
if err == 0:
return (jr,Lz,jz)
else: #pragma: no cover
raise RuntimeError("C-code for calculation actions failed; try with c=False")
else:
if 'c' in kwargs and kwargs['c'] and not self._c:
warnings.warn("C module not used because potential does not have a C implementation",galpyWarning) #pragma: no cover
kwargs.pop('c',None)
if (len(args) == 5 or len(args) == 6) \
and isinstance(args[0],nu.ndarray):
ojr= nu.zeros((len(args[0])))
olz= nu.zeros((len(args[0])))
ojz= nu.zeros((len(args[0])))
for ii in range(len(args[0])):
if len(args) == 5:
targs= (args[0][ii],args[1][ii],args[2][ii],
args[3][ii],args[4][ii])
elif len(args) == 6:
targs= (args[0][ii],args[1][ii],args[2][ii],
args[3][ii],args[4][ii],args[5][ii])
tjr,tlz,tjz= self(*targs,**copy.copy(kwargs))
ojr[ii]= tjr
ojz[ii]= tjz
olz[ii]= tlz
return (ojr,olz,ojz)
else:
#Set up the actionAngleAxi object
meta= actionAngle(*args)
if isinstance(self._pot,list):
thispot= [p.toPlanar() for p in self._pot]
else:
thispot= self._pot.toPlanar()
if isinstance(self._pot,list):
thisverticalpot= [p.toVertical(meta._R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(meta._R)
aAAxi= actionAngleAxi(*args,pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
if kwargs.get('_justjr',False):
kwargs.pop('_justjr')
return (aAAxi.JR(**kwargs),nu.nan,nu.nan)
elif kwargs.get('_justjz',False):
kwargs.pop('_justjz')
return (nu.nan,nu.nan,aAAxi.Jz(**kwargs))
else:
return (aAAxi.JR(**kwargs),aAAxi._R*aAAxi._vT,aAAxi.Jz(**kwargs))
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
c= True/False; overrides the object's c= keyword to use C or not
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-11-27 - Written - Bovy (IAS)
"""
if ((self._c and not ('c' in kwargs and not kwargs['c']))\
or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \
and _check_c(self._pot):
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
if isinstance(R, float):
R = nu.array([R])
vR = nu.array([vR])
vT = nu.array([vT])
z = nu.array([z])
vz = nu.array([vz])
Lz = R * vT
if self._useu0:
#First calculate u0
if 'u0' in kwargs:
u0 = nu.asarray(kwargs['u0'])
else:
E = nu.array([
evaluatePotentials(R[ii], z[ii], self._pot) +
vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2.
for ii in range(len(R))
])
u0 = actionAngleStaeckel_c.actionAngleStaeckel_calcu0(
E, Lz, self._pot, self._delta)[0]
kwargs.pop('u0', None)
else:
u0 = None
jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\
self._pot,self._delta,R,vR,vT,z,vz,u0=u0)
if err == 0:
return (jr, Lz, jz)
else: #pragma: no cover
raise RuntimeError(
"C-code for calculation actions failed; try with c=False")
else:
if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover
warnings.warn(
"C module not used because potential does not have a C implementation",
galpyWarning)
kwargs.pop('c', None)
if (len(args) == 5 or len(args) == 6) \
and isinstance(args[0],nu.ndarray):
ojr = nu.zeros((len(args[0])))
olz = nu.zeros((len(args[0])))
ojz = nu.zeros((len(args[0])))
for ii in range(len(args[0])):
if len(args) == 5:
targs = (args[0][ii], args[1][ii], args[2][ii],
args[3][ii], args[4][ii])
elif len(args) == 6:
targs = (args[0][ii], args[1][ii], args[2][ii],
args[3][ii], args[4][ii], args[5][ii])
tjr, tlz, tjz = self(*targs, **copy.copy(kwargs))
ojr[ii] = tjr
ojz[ii] = tjz
olz[ii] = tlz
return (ojr, olz, ojz)
else:
#Set up the actionAngleStaeckelSingle object
aASingle = actionAngleStaeckelSingle(*args,
pot=self._pot,
delta=self._delta)
return (aASingle.JR(**copy.copy(kwargs)),
aASingle._R * aASingle._vT,
aASingle.Jz(**copy.copy(kwargs)))
def actionsFreqsAngles(self, *args, **kwargs):
"""
NAME:
actionsFreqsAngles
PURPOSE:
evaluate the actions, frequencies, and angles
(jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
INPUT:
Either:
a) R,vR,vT,z,vz,phi (MUST HAVE PHI)
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,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
if ((self._c and not ('c' in kwargs and not kwargs['c']))\
or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \
and _check_c(self._pot):
if len(args) == 5: #R,vR.vT, z, vz pragma: no cover
raise IOError("Must specify phi")
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
phi = meta._phi
if isinstance(R, float):
R = nu.array([R])
vR = nu.array([vR])
vT = nu.array([vT])
z = nu.array([z])
vz = nu.array([vz])
phi = nu.array([phi])
Lz = R * vT
if self._useu0:
#First calculate u0
if 'u0' in kwargs:
u0 = nu.asarray(kwargs['u0'])
else:
E = nu.array([
evaluatePotentials(R[ii], z[ii], self._pot) +
vR[ii]**2. / 2. + vz[ii]**2. / 2. + vT[ii]**2. / 2.
for ii in range(len(R))
])
u0 = actionAngleStaeckel_c.actionAngleStaeckel_calcu0(
E, Lz, self._pot, self._delta)[0]
kwargs.pop('u0', None)
else:
u0 = None
jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\
self._pot,self._delta,R,vR,vT,z,vz,phi,u0=u0)
# Adjustements for close-to-circular orbits
indx = nu.isnan(Omegar) * (jr < 10.**-3.) + nu.isnan(Omegaz) * (
jz < 10.**-3.
) #Close-to-circular and close-to-the-plane orbits
if nu.sum(indx) > 0:
Omegar[indx] = [epifreq(self._pot, r) for r in R[indx]]
Omegaphi[indx] = [omegac(self._pot, r) for r in R[indx]]
Omegaz[indx] = [verticalfreq(self._pot, r) for r in R[indx]]
if err == 0:
return (jr, Lz, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,
anglez)
else:
raise RuntimeError(
"C-code for calculation actions failed; try with c=False"
) #pragma: no cover
else: #pragma: no cover
if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover
warnings.warn(
"C module not used because potential does not have a C implementation",
galpyWarning)
raise NotImplementedError(
"actionsFreqs with c=False not implemented")
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
c= True/False; overrides the object's c= keyword to use C or not
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-11-27 - Written - Bovy (IAS)
"""
if ((self._c and not ('c' in kwargs and not kwargs['c']))\
or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \
and _check_c(self._pot):
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
if isinstance(R,float):
R= nu.array([R])
vR= nu.array([vR])
vT= nu.array([vT])
z= nu.array([z])
vz= nu.array([vz])
Lz= R*vT
if self._useu0:
#First calculate u0
if 'u0' in kwargs:
u0= nu.asarray(kwargs['u0'])
else:
E= nu.array([evaluatePotentials(R[ii],z[ii],self._pot) +vR[ii]**2./2.+vz[ii]**2./2.+vT[ii]**2./2. for ii in range(len(R))])
u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(E,Lz,
self._pot,
self._delta)[0]
kwargs.pop('u0',None)
else:
u0= None
jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\
self._pot,self._delta,R,vR,vT,z,vz,u0=u0)
if err == 0:
return (jr,Lz,jz)
else: #pragma: no cover
raise RuntimeError("C-code for calculation actions failed; try with c=False")
else:
if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover
warnings.warn("C module not used because potential does not have a C implementation",galpyWarning)
kwargs.pop('c',None)
if (len(args) == 5 or len(args) == 6) \
and isinstance(args[0],nu.ndarray):
ojr= nu.zeros((len(args[0])))
olz= nu.zeros((len(args[0])))
ojz= nu.zeros((len(args[0])))
for ii in range(len(args[0])):
if len(args) == 5:
targs= (args[0][ii],args[1][ii],args[2][ii],
args[3][ii],args[4][ii])
elif len(args) == 6:
targs= (args[0][ii],args[1][ii],args[2][ii],
args[3][ii],args[4][ii],args[5][ii])
tjr,tlz,tjz= self(*targs,**copy.copy(kwargs))
ojr[ii]= tjr
ojz[ii]= tjz
olz[ii]= tlz
return (ojr,olz,ojz)
else:
#Set up the actionAngleStaeckelSingle object
aASingle= actionAngleStaeckelSingle(*args,pot=self._pot,
delta=self._delta)
return (aASingle.JR(**copy.copy(kwargs)),
aASingle._R*aASingle._vT,
aASingle.Jz(**copy.copy(kwargs)))
def actionsFreqsAngles(self,*args,**kwargs):
"""
NAME:
actionsFreqsAngles
PURPOSE:
evaluate the actions, frequencies, and angles
(jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
INPUT:
Either:
a) R,vR,vT,z,vz,phi (MUST HAVE PHI)
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,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
if ((self._c and not ('c' in kwargs and not kwargs['c']))\
or (ext_loaded and (('c' in kwargs and kwargs['c'])))) \
and _check_c(self._pot):
if len(args) == 5: #R,vR.vT, z, vz pragma: no cover
raise IOError("Must specify phi")
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
phi= meta._phi
if isinstance(R,float):
R= nu.array([R])
vR= nu.array([vR])
vT= nu.array([vT])
z= nu.array([z])
vz= nu.array([vz])
phi= nu.array([phi])
Lz= R*vT
if self._useu0:
#First calculate u0
if 'u0' in kwargs:
u0= nu.asarray(kwargs['u0'])
else:
E= nu.array([evaluatePotentials(R[ii],z[ii],self._pot) +vR[ii]**2./2.+vz[ii]**2./2.+vT[ii]**2./2. for ii in range(len(R))])
u0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(E,Lz,
self._pot,
self._delta)[0]
kwargs.pop('u0',None)
else:
u0= None
jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\
self._pot,self._delta,R,vR,vT,z,vz,phi,u0=u0)
# Adjustements for close-to-circular orbits
indx= nu.isnan(Omegar)*(jr < 10.**-3.)+nu.isnan(Omegaz)*(jz < 10.**-3.) #Close-to-circular and close-to-the-plane orbits
if nu.sum(indx) > 0:
Omegar[indx]= [epifreq(self._pot,r) for r in R[indx]]
Omegaphi[indx]= [omegac(self._pot,r) for r in R[indx]]
Omegaz[indx]= [verticalfreq(self._pot,r) for r in R[indx]]
if err == 0:
return (jr,Lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
else:
raise RuntimeError("C-code for calculation actions failed; try with c=False") #pragma: no cover
else: #pragma: no cover
if 'c' in kwargs and kwargs['c'] and not self._c: #pragma: no cover
warnings.warn("C module not used because potential does not have a C implementation",galpyWarning)
raise NotImplementedError("actionsFreqs with c=False not implemented")
def actionsFreqsAngles(self,*args,**kwargs):
"""
NAME:
actionsFreqsAngles
PURPOSE:
evaluate the actions, frequencies, and angles
(jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
INPUT:
Either:
a) R,vR,vT,z,vz,phi (MUST HAVE PHI)
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,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
HISTORY:
2013-09-08 - Written - Bovy (IAS)
"""
if len(args) == 5: #R,vR.vT, z, vz pragma: no cover
raise IOError("You need to provide phi when calculating angles")
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
phi= meta._phi
if isinstance(R,float):
R= nu.array([R])
vR= nu.array([vR])
vT= nu.array([vT])
z= nu.array([z])
vz= nu.array([vz])
phi= nu.array([phi])
if self._c: #pragma: no cover
pass
else:
Lz= R*vT
Lx= -z*vT
Ly= z*vR-R*vz
L2= Lx*Lx+Ly*Ly+Lz*Lz
E= self._ip(R,z)+vR**2./2.+vT**2./2.+vz**2./2.
L= nu.sqrt(L2)
#Actions
Jphi= Lz
Jz= L-nu.fabs(Lz)
Jr= self.amp/nu.sqrt(-2.*E)\
-0.5*(L+nu.sqrt((L2+4.*self.amp*self.b)))
#Frequencies
Omegar= (-2.*E)**1.5/self.amp
Omegaz= 0.5*(1.+L/nu.sqrt(L2+4.*self.amp*self.b))*Omegar
Omegaphi= copy.copy(Omegaz)
indx= Lz < 0.
Omegaphi[indx]*= -1.
#Angles
c= -self.amp/2./E-self.b
e2= 1.-L2/self.amp/c*(1.+self.b/c)
e= nu.sqrt(e2)
s= 1.+nu.sqrt(1.+(R**2.+z**2.)/self.b**2.)
coseta= 1/e*(1.-self.b/c*(s-2.))
pindx= (coseta > 1.)*(coseta < (1.+10.**-7.))
coseta[pindx]= 1.
pindx= (coseta < -1.)*(coseta > (-1.-10.**-7.))
coseta[pindx]= -1.
eta= nu.arccos(coseta)
costheta= z/nu.sqrt(R**2.+z**2.)
sintheta= R/nu.sqrt(R**2.+z**2.)
vrindx= (vR*sintheta+vz*costheta) < 0.
eta[vrindx]= 2.*nu.pi-eta[vrindx]
angler= eta-e*c/(c+self.b)*nu.sin(eta)
tan11= nu.arctan(nu.sqrt((1.+e)/(1.-e))*nu.tan(0.5*eta))
tan12= nu.arctan(nu.sqrt((1.+e+2.*self.b/c)/(1.-e+2.*self.b/c))*nu.tan(0.5*eta))
vzindx= (-vz*sintheta+vR*costheta) > 0.
tan11[tan11 < 0.]+= nu.pi
tan12[tan12 < 0.]+= nu.pi
pindx= (Lz/L > 1.)*(Lz/L < (1.+10.**-7.))
Lz[pindx]= L[pindx]
pindx= (Lz/L < -1.)*(Lz/L > (-1.-10.**-7.))
Lz[pindx]= -L[pindx]
i= nu.arccos(Lz/L)
sinpsi= costheta/nu.sin(i)
pindx= (sinpsi > 1.)*(sinpsi < (1.+10.**-7.))
sinpsi[pindx]= 1.
pindx= (sinpsi < -1.)*(sinpsi > (-1.-10.**-7.))
sinpsi[pindx]= -1.
psi= nu.arcsin(sinpsi)
psi[vzindx]= nu.pi-psi[vzindx]
psi= psi % (2.*nu.pi)
anglez= psi+Omegaz/Omegar*angler\
-tan11-1./nu.sqrt(1.+4*self.amp*self.b/L2)*tan12
sinu= z/R/nu.tan(i)
pindx= (sinu > 1.)*(sinu < (1.+10.**-7.))
sinu[pindx]= 1.
pindx= (sinu < -1.)*(sinu > (-1.-10.**-7.))
sinu[pindx]= -1.
u= nu.arcsin(sinu)
u[vzindx]= nu.pi-u[vzindx]
Omega= phi-u
anglephi= Omega
anglephi[indx]-= anglez[indx]
anglephi[True-indx]+= anglez[True-indx]
angler= angler % (2.*nu.pi)
anglephi= anglephi % (2.*nu.pi)
anglez= anglez % (2.*nu.pi)
return (Jr,Jphi,Jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
