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)
"""
self._parse_eval_args(*args)
Phi= _evaluatePotentials(self._pot,self._eval_R,self._eval_z)
Phio= _evaluatePotentials(self._pot,self._eval_R,0.)
Ez= Phi-Phio+self._eval_vz**2./2.
#Bigger than Ezzmax?
thisEzZmax= numpy.exp(self._EzZmaxsInterp(self._eval_R))
if self._eval_R > self._Rmax or self._eval_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(self._eval_R,0.,1.,#these two r dummies
0.,math.sqrt(2.*Ez),
_justjz=True,
**kwargs)[2]
else:
jz= (self._jzInterp(self._eval_R,Ez/thisEzZmax)\
*(numpy.exp(self._jzEzmaxInterp(self._eval_R))-10.**-5.))[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)
"""
self._parse_eval_args(*args)
Phi= _evaluatePotentials(self._pot,self._eval_R,self._eval_z)
Phio= _evaluatePotentials(self._pot,self._eval_R,0.)
Ez= Phi-Phio+self._eval_vz**2./2.
#Bigger than Ezzmax?
thisEzZmax= numpy.exp(self._EzZmaxsInterp(self._eval_R))
if self._eval_R > self._Rmax or self._eval_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(self._eval_R,0.,1.,#these two r dummies
0.,math.sqrt(2.*Ez),
_justjz=True,
**kwargs)[2]
else:
jz= (self._jzInterp(self._eval_R,Ez/thisEzZmax)\
*(numpy.exp(self._jzEzmaxInterp(self._eval_R))-10.**-5.))[0][0]
return jz
def calcELStaeckel(R,vR,vT,z,vz,pot,vc=1.,ro=1.):
"""
NAME:
calcELStaeckel
PURPOSE:
calculate the energy and angular momentum
INPUT:
R - Galactocentric radius (/ro)
vR - radial part of the velocity (/vc)
vT - azimuthal part of the velocity (/vc)
vc - circular velocity
ro - reference radius
OUTPUT:
(E,L)
HISTORY:
2012-11-30 - Written - Bovy (IAS)
"""
return (_evaluatePotentials(pot,R,z)+vR**2./2.+vT**2./2.+vz**2./2.,R*vT)
def potentialStaeckel(u,v,pot,delta):
"""
NAME:
potentialStaeckel
PURPOSE:
return the potential
INPUT:
u - confocal u
v - confocal v
pot - potential
delta - focus
OUTPUT:
Phi(u,v)
HISTORY:
2012-11-29 - Written - Bovy (IAS)
"""
R,z= bovy_coords.uv_to_Rz(u,v,delta=delta)
return _evaluatePotentials(pot,R,z)
def potentialStaeckel(u, v, pot, delta):
"""
NAME:
potentialStaeckel
PURPOSE:
return the potential
INPUT:
u - confocal u
v - confocal v
pot - potential
delta - focus
OUTPUT:
Phi(u,v)
HISTORY:
2012-11-29 - Written - Bovy (IAS)
"""
R, z = bovy_coords.uv_to_Rz(u, v, delta=delta)
return _evaluatePotentials(pot, R, z)
def calcELStaeckel(R,vR,vT,z,vz,pot,vc=1.,ro=1.):
"""
NAME:
calcELStaeckel
PURPOSE:
calculate the energy and angular momentum
INPUT:
R - Galactocentric radius (/ro)
vR - radial part of the velocity (/vc)
vT - azimuthal part of the velocity (/vc)
vc - circular velocity
ro - reference radius
OUTPUT:
(E,L)
HISTORY:
2012-11-30 - Written - Bovy (IAS)
"""
return (_evaluatePotentials(pot,R,z)+vR**2./2.+vT**2./2.+vz**2./2.,R*vT)
def _evaluate(self,*args,**kwargs):
"""
NAME:
_evaluate
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_vz
#First work on the vertical action
Phi= _evaluatePotentials(self._pot,R,z)
try:
Phio= _evaluatePotentials(self._pot,R,numpy.zeros(len(R)))
except TypeError:
Phio= _evaluatePotentials(self._pot,R,0.)
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]-_evaluatePotentials(self._pot,thisRL[indx],0.))-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-_evaluatePotentials(self._pot,thisRL,0.))-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 _evaluate(self, *args, **kwargs):
"""
NAME:
__call__ (_evaluate)
PURPOSE:
evaluate the actions (jr,lz,jz)
INPUT:
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
delta= (object-wide default) can be used to override the object-wide focal length; can also be an array with length N to allow different delta for different phase-space points
u0= (None) if object-wide option useu0 is set, u0 to use (if useu0 and useu0 is None, a good value will be computed)
c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation
order= (object-wide default, int) number of points to use in the Gauss-Legendre numerical integration of the relevant action integrals
When not using C:
fixed_quad= (False) if True, use Gaussian quadrature (scipy.integrate.fixed_quad instead of scipy.integrate.quad)
scipy.integrate.fixed_quad or .quad keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2012-11-27 - Written - Bovy (IAS)
2017-12-27 - Allowed individual delta for each point - Bovy (UofT)
"""
delta = kwargs.pop('delta', self._delta)
order = kwargs.get('order', self._order)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_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(self._pot, R[ii], z[ii]) +
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,delta)[0]
kwargs.pop('u0', None)
else:
u0 = None
jr, jz, err= actionAngleStaeckel_c.actionAngleStaeckel_c(\
self._pot,delta,R,vR,vT,z,vz,u0=u0,order=order)
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])
tkwargs = copy.copy(kwargs)
try:
tkwargs['delta'] = delta[ii]
except TypeError:
tkwargs['delta'] = delta
tjr, tlz, tjz = self(*targs, **tkwargs)
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=delta)
return (aASingle.JR(**copy.copy(kwargs)),
aASingle._R * aASingle._vT,
aASingle.Jz(**copy.copy(kwargs)))
def _uminumaxvmin(self, *args, **kwargs):
"""
NAME:
_uminumaxvmin
PURPOSE:
evaluate u_min, u_max, and v_min
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
OUTPUT:
(umin,umax,vmin)
HISTORY:
2017-12-12 - Written - Bovy (UofT)
"""
delta = kwargs.pop('delta', self._delta)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_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(self._pot, R[ii], z[ii]) +
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,delta)[0]
kwargs.pop('u0', None)
else:
u0 = None
umin, umax, vmin, err= \
actionAngleStaeckel_c.actionAngleUminUmaxVminStaeckel_c(\
self._pot,delta,R,vR,vT,z,vz,u0=u0)
if err == 0:
return (umin, umax, vmin)
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):
oumin = nu.zeros((len(args[0])))
oumax = nu.zeros((len(args[0])))
ovmin = 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])
tkwargs = copy.copy(kwargs)
try:
tkwargs['delta'] = delta[ii]
except TypeError:
tkwargs['delta'] = delta
tumin,tumax,tvmin= self._uminumaxvmin(\
*targs,**tkwargs)
oumin[ii] = tumin
oumax[ii] = tumax
ovmin[ii] = tvmin
return (oumin, oumax, ovmin)
else:
#Set up the actionAngleStaeckelSingle object
aASingle = actionAngleStaeckelSingle(*args,
pot=self._pot,
delta=delta)
umin, umax = aASingle.calcUminUmax()
vmin = aASingle.calcVmin()
return (umin, umax, vmin)
def _actionsFreqs(self,*args,**kwargs):
"""
NAME:
actionsFreqs (_actionsFreqs)
PURPOSE:
evaluate the actions and frequencies (jr,lz,jz,Omegar,Omegaphi,Omegaz)
INPUT:
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature or .fixed_quad keywords
OUTPUT:
(jr,lz,jz,Omegar,Omegaphi,Omegaz)
HISTORY:
2013-12-28 - Written - Bovy (IAS)
"""
fixed_quad= kwargs.pop('fixed_quad',False)
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_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= _evaluatePotentials(self._pot,R,z)+vR**2./2.+vT**2./2.+vz**2./2.
L= nu.sqrt(L2)
#Actions
Jphi= Lz
Jz= L-nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR= nu.sqrt(R**2.+z**2.)
axivT= L/axiR
axivR= (R*vR+z*vz)/axiR
Jr= []
Or= []
Op= []
for ii in range(len(axiR)):
axiaA= actionAngleAxi(axiR[ii],axivR[ii],axivT[ii],
pot=self._2dpot)
(rperi,rap)= axiaA.calcRapRperi()
EL= axiaA.calcEL()
E, L= EL
Jr.append(self._calc_jr(rperi,rap,E,L,fixed_quad,**kwargs))
#Radial period
if Jr[-1] < 10.**-9.: #Circular orbit
Or.append(epifreq(self._pot,axiR[ii],use_physical=False))
Op.append(omegac(self._pot,axiR[ii],use_physical=False))
continue
Rmean= m.exp((m.log(rperi)+m.log(rap))/2.)
Or.append(self._calc_or(Rmean,rperi,rap,E,L,fixed_quad,**kwargs))
Op.append(self._calc_op(Or[-1],Rmean,rperi,rap,E,L,fixed_quad,**kwargs))
Op= nu.array(Op)
Oz= copy.copy(Op)
Op[vT < 0.]*= -1.
return (nu.array(Jr),Jphi,Jz,nu.array(Or),Op,Oz)
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_vz
phi= self._eval_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(self._pot,R[ii],z[ii])
+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,use_physical=False) for r in R[indx]]
Omegaphi[indx]= [omegac(self._pot,r,use_physical=False) for r in R[indx]]
Omegaz[indx]= [verticalfreq(self._pot,r,use_physical=False) 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 _EccZmaxRperiRap(self,*args,**kwargs):
"""
NAME:
EccZmaxRperiRap (_EccZmaxRperiRap)
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter in the Staeckel approximation
INPUT:
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-15 - Written - Bovy (UofT)
"""
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_vz
Lz= R*vT
Phi= _evaluatePotentials(self._pot,R,z)
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
ecc= numpy.empty(R.shape)
zmax= numpy.empty(R.shape)
rperi= numpy.empty(R.shape)
rap= 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.)
ecc[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._eccFiltered,
coords,
order=3,
prefilter=False))-10.**-10.)
rperi[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._rperiFiltered,
coords,
order=3,
prefilter=False))-10.**-10.)*(numpy.exp(self._rperiLzInterp(Lz[indxc]))-10.**-5.)
# We do rap below with zmax
#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.)
zmax[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._zmaxFiltered,
newcoords,
order=3,
prefilter=False))-10.**-10.)*(numpy.exp(self._zmaxLzInterp(Lz[indxc]))-10.**-5.)
rap[indxc]= (numpy.exp(ndimage.interpolation.map_coordinates(self._rapFiltered,
newcoords,
order=3,
prefilter=False))-10.**-10.)*(numpy.exp(self._rapLzInterp(Lz[indxc]))-10.**-5.)
if numpy.sum(indx) > 0:
eccindiv, zmaxindiv, rperiindiv, rapindiv=\
self._aA.EccZmaxRperiRap(R[indx],
vR[indx],
vT[indx],
z[indx],
vz[indx],
**kwargs)
ecc[indx]= eccindiv
zmax[indx]= zmaxindiv
rperi[indx]= rperiindiv
rap[indx]= rapindiv
else:
ecc,zmax,rperi,rap= self.EccZmaxRperiRap(numpy.array([R]),
numpy.array([vR]),
numpy.array([vT]),
numpy.array([z]),
numpy.array([vz]),
**kwargs)
return (ecc[0],zmax[0],rperi[0],rap[0])
ecc[ecc < 0.]= 0.
zmax[zmax < 0.]= 0.
rperi[rperi < 0.]= 0.
rap[rap < 0.]= 0.
return (ecc,zmax,rperi,rap)
def _evaluate(self, *args, **kwargs):
"""
NAME:
_evaluate
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
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2013-12-28 - Written - Bovy (IAS)
"""
fixed_quad = kwargs.pop('fixed_quad', False)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_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= _evaluatePotentials(self._pot,R,z)\
+vR**2./2.+vT**2./2.+vz**2./2.
L = nu.sqrt(L2)
#Actions
Jphi = Lz
Jz = L - nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR = nu.sqrt(R**2. + z**2.)
axivT = L / axiR
axivR = (R * vR + z * vz) / axiR
Jr = []
for ii in range(len(axiR)):
axiaA = actionAngleAxi(axiR[ii],
axivR[ii],
axivT[ii],
pot=self._2dpot)
(rperi, rap) = axiaA.calcRapRperi()
EL = axiaA.calcEL()
E, L = EL
Jr.append(self._calc_jr(rperi, rap, E, L, fixed_quad,
**kwargs))
return (nu.array(Jr), Jphi, Jz)
def _actionsFreqsAngles(self, *args, **kwargs):
"""
NAME:
_actionsFreqsAngles
PURPOSE:
evaluate the actions, frequencies, and angles
(jr,lz,jz,Omegar,Omegaphi,Omegaz,ar,ap,az)
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
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz,Omegar,Omegaphi,Omegaz,ar,aphi,az)
HISTORY:
2013-12-29 - Written - Bovy (IAS)
"""
fixed_quad = kwargs.pop('fixed_quad', False)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_vz
phi = self._eval_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 = _evaluatePotentials(
self._pot, R, z) + vR**2. / 2. + vT**2. / 2. + vz**2. / 2.
L = nu.sqrt(L2)
#Actions
Jphi = Lz
Jz = L - nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR = nu.sqrt(R**2. + z**2.)
axivT = L / axiR #these are really spherical coords, called axi bc they go in actionAngleAxi
axivR = (R * vR + z * vz) / axiR
axivz = (z * vR - R * vz) / axiR
Jr = []
Or = []
Op = []
ar = []
az = []
#Calculate the longitude of the ascending node
asc = self._calc_long_asc(z, R, axivz, phi, Lz, L)
for ii in range(len(axiR)):
axiaA = actionAngleAxi(axiR[ii],
axivR[ii],
axivT[ii],
pot=self._2dpot)
(rperi, rap) = axiaA.calcRapRperi()
EL = axiaA.calcEL()
E, L = EL
Jr.append(self._calc_jr(rperi, rap, E, L, fixed_quad,
**kwargs))
#Radial period
Rmean = m.exp((m.log(rperi) + m.log(rap)) / 2.)
if Jr[-1] < 10.**-9.: #Circular orbit
Or.append(epifreq(self._pot, axiR[ii], use_physical=False))
Op.append(omegac(self._pot, axiR[ii], use_physical=False))
else:
Or.append(
self._calc_or(Rmean, rperi, rap, E, L, fixed_quad,
**kwargs))
Op.append(
self._calc_op(Or[-1], Rmean, rperi, rap, E, L,
fixed_quad, **kwargs))
#Angles
ar.append(
self._calc_angler(Or[-1], axiR[ii], Rmean, rperi, rap, E,
L, axivR[ii], fixed_quad, **kwargs))
az.append(
self._calc_anglez(Or[-1], Op[-1], ar[-1], z[ii], axiR[ii],
Rmean, rperi, rap, E, L, Lz[ii],
axivR[ii], axivz[ii], fixed_quad,
**kwargs))
Op = nu.array(Op)
Oz = copy.copy(Op)
Op[vT < 0.] *= -1.
ap = copy.copy(asc)
ar = nu.array(ar)
az = nu.array(az)
ap[vT < 0.] -= az[vT < 0.]
ap[vT >= 0.] += az[vT >= 0.]
ar = ar % (2. * nu.pi)
ap = ap % (2. * nu.pi)
az = az % (2. * nu.pi)
return (nu.array(Jr), Jphi, Jz, nu.array(Or), Op, Oz, ar, ap, az)
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
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz,Omegar,Omegaphi,Omegaz)
HISTORY:
2013-12-28 - Written - Bovy (IAS)
"""
fixed_quad = kwargs.pop('fixed_quad', False)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_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 = _evaluatePotentials(
self._pot, R, z) + vR**2. / 2. + vT**2. / 2. + vz**2. / 2.
L = nu.sqrt(L2)
#Actions
Jphi = Lz
Jz = L - nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR = nu.sqrt(R**2. + z**2.)
axivT = L / axiR
axivR = (R * vR + z * vz) / axiR
Jr = []
Or = []
Op = []
for ii in range(len(axiR)):
axiaA = actionAngleAxi(axiR[ii],
axivR[ii],
axivT[ii],
pot=self._2dpot)
(rperi, rap) = axiaA.calcRapRperi()
EL = axiaA.calcEL()
E, L = EL
Jr.append(self._calc_jr(rperi, rap, E, L, fixed_quad,
**kwargs))
#Radial period
if Jr[-1] < 10.**-9.: #Circular orbit
Or.append(epifreq(self._pot, axiR[ii], use_physical=False))
Op.append(omegac(self._pot, axiR[ii], use_physical=False))
continue
Rmean = m.exp((m.log(rperi) + m.log(rap)) / 2.)
Or.append(
self._calc_or(Rmean, rperi, rap, E, L, fixed_quad,
**kwargs))
Op.append(
self._calc_op(Or[-1], Rmean, rperi, rap, E, L, fixed_quad,
**kwargs))
Op = nu.array(Op)
Oz = copy.copy(Op)
Op[vT < 0.] *= -1.
return (nu.array(Jr), Jphi, Jz, nu.array(Or), Op, Oz)
def _evaluate(self,*args,**kwargs):
"""
NAME:
__call__ (_evaluate)
PURPOSE:
evaluate the actions (jr,lz,jz)
INPUT:
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature or .fixed_quad keywords
OUTPUT:
(jr,lz,jz)
HISTORY:
2013-12-28 - Written - Bovy (IAS)
"""
fixed_quad= kwargs.pop('fixed_quad',False)
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_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= _evaluatePotentials(self._pot,R,z)\
+vR**2./2.+vT**2./2.+vz**2./2.
L= nu.sqrt(L2)
#Actions
Jphi= Lz
Jz= L-nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR= nu.sqrt(R**2.+z**2.)
axivT= L/axiR
axivR= (R*vR+z*vz)/axiR
Jr= []
for ii in range(len(axiR)):
axiaA= actionAngleAxi(axiR[ii],axivR[ii],axivT[ii],
pot=self._2dpot)
(rperi,rap)= axiaA.calcRapRperi()
EL= axiaA.calcEL()
E, L= EL
Jr.append(self._calc_jr(rperi,rap,E,L,fixed_quad,**kwargs))
return (nu.array(Jr),Jphi,Jz)
def _actionsFreqsAngles(self,*args,**kwargs):
"""
NAME:
actionsFreqsAngles (_actionsFreqsAngles)
PURPOSE:
evaluate the actions, frequencies, and angles
(jr,lz,jz,Omegar,Omegaphi,Omegaz,ar,ap,az)
INPUT:
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
fixed_quad= (False) if True, use n=10 fixed_quad integration
scipy.integrate.quadrature or .fixed_quad keywords
OUTPUT:
(jr,lz,jz,Omegar,Omegaphi,Omegaz,ar,aphi,az)
HISTORY:
2013-12-29 - Written - Bovy (IAS)
"""
fixed_quad= kwargs.pop('fixed_quad',False)
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_vz
phi= self._eval_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= _evaluatePotentials(self._pot,R,z)+vR**2./2.+vT**2./2.+vz**2./2.
L= nu.sqrt(L2)
#Actions
Jphi= Lz
Jz= L-nu.fabs(Lz)
#Jr requires some more work
#Set up an actionAngleAxi object for EL and rap/rperi calculations
axiR= nu.sqrt(R**2.+z**2.)
axivT= L/axiR #these are really spherical coords, called axi bc they go in actionAngleAxi
axivR= (R*vR+z*vz)/axiR
axivz= (z*vR-R*vz)/axiR
Jr= []
Or= []
Op= []
ar= []
az= []
#Calculate the longitude of the ascending node
asc= self._calc_long_asc(z,R,axivz,phi,Lz,L)
for ii in range(len(axiR)):
axiaA= actionAngleAxi(axiR[ii],axivR[ii],axivT[ii],
pot=self._2dpot)
(rperi,rap)= axiaA.calcRapRperi()
EL= axiaA.calcEL()
E, L= EL
Jr.append(self._calc_jr(rperi,rap,E,L,fixed_quad,**kwargs))
#Radial period
Rmean= m.exp((m.log(rperi)+m.log(rap))/2.)
if Jr[-1] < 10.**-9.: #Circular orbit
Or.append(epifreq(self._pot,axiR[ii],use_physical=False))
Op.append(omegac(self._pot,axiR[ii],use_physical=False))
else:
Or.append(self._calc_or(Rmean,rperi,rap,E,L,fixed_quad,**kwargs))
Op.append(self._calc_op(Or[-1],Rmean,rperi,rap,E,L,fixed_quad,**kwargs))
#Angles
ar.append(self._calc_angler(Or[-1],axiR[ii],Rmean,rperi,rap,
E,L,axivR[ii],fixed_quad,**kwargs))
az.append(self._calc_anglez(Or[-1],Op[-1],ar[-1],
z[ii],axiR[ii],
Rmean,rperi,rap,E,L,Lz[ii],
axivR[ii],axivz[ii],
fixed_quad,**kwargs))
Op= nu.array(Op)
Oz= copy.copy(Op)
Op[vT < 0.]*= -1.
ap= copy.copy(asc)
ar= nu.array(ar)
az= nu.array(az)
ap[vT < 0.]-= az[vT < 0.]
ap[vT >= 0.]+= az[vT >= 0.]
ar= ar % (2.*nu.pi)
ap= ap % (2.*nu.pi)
az= az % (2.*nu.pi)
return (nu.array(Jr),Jphi,Jz,nu.array(Or),Op,Oz,
ar,ap,az)
def __init__(self,pot=None,zmax=1.,gamma=1.,Rmax=5.,
nR=16,nEz=16,nEr=31,nLz=31,numcores=1,
**kwargs):
"""
NAME:
__init__
PURPOSE:
initialize an actionAngleAdiabaticGrid object
INPUT:
pot= potential or list of potentials
zmax= zmax for building Ez grid
Rmax = Rmax for building grids
gamma= (default=1.) replace Lz by Lz+gamma Jz in effective potential
nEz=, nEr=, nLz, nR= grid size
numcores= number of cpus to use to parallellize
c= if True, use C to calculate actions
ro= distance from vantage point to GC (kpc; can be Quantity)
vo= circular velocity at ro (km/s; can be Quantity)
+scipy.integrate.quad keywords
OUTPUT:
instance
HISTORY:
2012-07-27 - Written - Bovy (IAS@MPIA)
"""
actionAngle.__init__(self,
ro=kwargs.get('ro',None),vo=kwargs.get('vo',None))
if pot is None: #pragma: no cover
raise IOError("Must specify pot= for actionAngleAxi")
self._c= kwargs.pop('c',False)
self._gamma= gamma
self._pot= pot
self._zmax= zmax
self._Rmax= Rmax
self._Rmin= 0.01
#Set up the actionAngleAdiabatic object that we will use to interpolate
self._aA= actionAngleAdiabatic(pot=self._pot,gamma=self._gamma,
c=self._c)
#Build grid for Ez, first calculate Ez(zmax;R) function
self._Rs= numpy.linspace(self._Rmin,self._Rmax,nR)
self._EzZmaxs= _evaluatePotentials(self._pot,self._Rs,
self._zmax*numpy.ones(nR))\
-_evaluatePotentials(self._pot,self._Rs,numpy.zeros(nR))
self._EzZmaxsInterp= interpolate.InterpolatedUnivariateSpline(self._Rs,numpy.log(self._EzZmaxs),k=3)
y= numpy.linspace(0.,1.,nEz)
jz= numpy.zeros((nR,nEz))
jzEzzmax= numpy.zeros(nR)
thisRs= (numpy.tile(self._Rs,(nEz,1)).T).flatten()
thisEzZmaxs= (numpy.tile(self._EzZmaxs,(nEz,1)).T).flatten()
thisy= (numpy.tile(y,(nR,1))).flatten()
if self._c:
jz= self._aA(thisRs,
numpy.zeros(len(thisRs)),
numpy.ones(len(thisRs)),#these two r dummies
numpy.zeros(len(thisRs)),
numpy.sqrt(2.*thisy*thisEzZmaxs),
**kwargs)[2]
jz= numpy.reshape(jz,(nR,nEz))
jzEzzmax[0:nR]= jz[:,nEz-1]
else:
if numcores > 1:
jz= multi.parallel_map((lambda x: self._aA(thisRs[x],0.,1.,#these two r dummies
0.,math.sqrt(2.*thisy[x]*thisEzZmaxs[x]),
_justjz=True,
**kwargs)[2]),
range(nR*nEz),numcores=numcores)
jz= numpy.reshape(jz,(nR,nEz))
jzEzzmax[0:nR]= jz[:,nEz-1]
else:
for ii in range(nR):
for jj in range(nEz):
#Calculate Jz
jz[ii,jj]= self._aA(self._Rs[ii],0.,1.,#these two r dummies
0.,numpy.sqrt(2.*y[jj]*self._EzZmaxs[ii]),
_justjz=True,**kwargs)[2]
if jj == nEz-1:
jzEzzmax[ii]= jz[ii,jj]
for ii in range(nR): jz[ii,:]/= jzEzzmax[ii]
#First interpolate Ez=Ezmax
self._jzEzmaxInterp= interpolate.InterpolatedUnivariateSpline(self._Rs,numpy.log(jzEzzmax+10.**-5.),k=3)
self._jz= jz
self._jzInterp= interpolate.RectBivariateSpline(self._Rs,
y,
jz,
kx=3,ky=3,s=0.)
#JR grid
self._Lzmin= 0.01
self._Lzs= numpy.linspace(self._Lzmin,
self._Rmax\
*galpy.potential.vcirc(self._pot,
self._Rmax),
nLz)
self._Lzmax= self._Lzs[-1]
#Calculate ER(vr=0,R=RL)
self._RL= numpy.array([galpy.potential.rl(self._pot,l) for l in self._Lzs])
self._RLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
self._RL,k=3)
self._ERRL= _evaluatePotentials(self._pot,self._RL,numpy.zeros(nLz)) +self._Lzs**2./2./self._RL**2.
self._ERRLmax= numpy.amax(self._ERRL)+1.
self._ERRLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(-(self._ERRL-self._ERRLmax)),k=3)
self._Ramax= 99.
self._ERRa= _evaluatePotentials(self._pot,self._Ramax,0.) +self._Lzs**2./2./self._Ramax**2.
self._ERRamax= numpy.amax(self._ERRa)+1.
self._ERRaInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(-(self._ERRa-self._ERRamax)),k=3)
y= numpy.linspace(0.,1.,nEr)
jr= numpy.zeros((nLz,nEr))
jrERRa= numpy.zeros(nLz)
thisRL= (numpy.tile(self._RL,(nEr-1,1)).T).flatten()
thisLzs= (numpy.tile(self._Lzs,(nEr-1,1)).T).flatten()
thisERRL= (numpy.tile(self._ERRL,(nEr-1,1)).T).flatten()
thisERRa= (numpy.tile(self._ERRa,(nEr-1,1)).T).flatten()
thisy= (numpy.tile(y[0:-1],(nLz,1))).flatten()
if self._c:
mjr= self._aA(thisRL,
numpy.sqrt(2.*(thisERRa+thisy*(thisERRL-thisERRa)-_evaluatePotentials(self._pot,thisRL,numpy.zeros((nEr-1)*nLz)))-thisLzs**2./thisRL**2.),
thisLzs/thisRL,
numpy.zeros(len(thisRL)),
numpy.zeros(len(thisRL)),
**kwargs)[0]
jr[:,0:-1]= numpy.reshape(mjr,(nLz,nEr-1))
jrERRa[0:nLz]= jr[:,0]
else:
if numcores > 1:
mjr= multi.parallel_map((lambda x: self._aA(thisRL[x],
numpy.sqrt(2.*(thisERRa[x]+thisy[x]*(thisERRL[x]-thisERRa[x])-_evaluatePotentials(self._pot,thisRL[x],0.))-thisLzs[x]**2./thisRL[x]**2.),
thisLzs[x]/thisRL[x],
0.,0.,
_justjr=True,
**kwargs)[0]),
range((nEr-1)*nLz),
numcores=numcores)
jr[:,0:-1]= numpy.reshape(mjr,(nLz,nEr-1))
jrERRa[0:nLz]= jr[:,0]
else:
for ii in range(nLz):
for jj in range(nEr-1): #Last one is zero by construction
try:
jr[ii,jj]= self._aA(self._RL[ii],
numpy.sqrt(2.*(self._ERRa[ii]+y[jj]*(self._ERRL[ii]-self._ERRa[ii])-_evaluatePotentials(self._pot,self._RL[ii],0.))-self._Lzs[ii]**2./self._RL[ii]**2.),
self._Lzs[ii]/self._RL[ii],
0.,0.,
_justjr=True,
**kwargs)[0]
except UnboundError: #pragma: no cover
raise
if jj == 0:
jrERRa[ii]= jr[ii,jj]
for ii in range(nLz): jr[ii,:]/= jrERRa[ii]
#First interpolate Ez=Ezmax
self._jr= jr
self._jrERRaInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(jrERRa+10.**-5.),k=3)
self._jrInterp= interpolate.RectBivariateSpline(self._Lzs,
y,
jr,
kx=3,ky=3,s=0.)
# Check the units
self._check_consistent_units()
return None
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_vz
phi = self._eval_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(self._pot, R[ii], z[ii]) +
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, use_physical=False) for r in R[indx]
]
Omegaphi[indx] = [
omegac(self._pot, r, use_physical=False) for r in R[indx]
]
Omegaz[indx] = [
verticalfreq(self._pot, r, use_physical=False)
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 _evaluate(self, *args, **kwargs):
"""
NAME:
_evaluate
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_vz
#First work on the vertical action
Phi = _evaluatePotentials(self._pot, R, z)
try:
Phio = _evaluatePotentials(self._pot, R, numpy.zeros(len(R)))
except TypeError:
Phio = _evaluatePotentials(self._pot, R, 0.)
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] -
_evaluatePotentials(self._pot, thisRL[indx], 0.)) -
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 - _evaluatePotentials(self._pot, thisRL, 0.)) -
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 _evaluate(self,*args,**kwargs):
"""
NAME:
_evaluate
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_vz
Lz= R*vT
Phi= _evaluatePotentials(self._pot,R,z)
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 _evaluate(self, *args, **kwargs):
"""
NAME:
_evaluate
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_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(self._pot, R[ii], z[ii]) +
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 _evaluate(self,*args,**kwargs):
"""
NAME:
_evaluate
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:
self._parse_eval_args(*args)
R= self._eval_R
vR= self._eval_vR
vT= self._eval_vT
z= self._eval_z
vz= self._eval_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(self._pot,R[ii],z[ii])
+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 __init__(self,pot=None,delta=None,Rmax=5.,
nE=25,npsi=25,nLz=30,numcores=1,
**kwargs):
"""
NAME:
__init__
PURPOSE:
initialize an actionAngleStaeckelGrid object
INPUT:
pot= potential or list of potentials
delta= focus of prolate confocal coordinate system (can be Quantity)
Rmax = Rmax for building grids (natural units)
nE=, npsi=, nLz= grid size
numcores= number of cpus to use to parallellize
ro= distance from vantage point to GC (kpc; can be Quantity)
vo= circular velocity at ro (km/s; can be Quantity)
OUTPUT:
instance
HISTORY:
2012-11-29 - Written - Bovy (IAS)
"""
actionAngle.__init__(self,
ro=kwargs.get('ro',None),vo=kwargs.get('vo',None))
if pot is None:
raise IOError("Must specify pot= for actionAngleStaeckelGrid")
self._pot= pot
if delta is None:
raise IOError("Must specify delta= for actionAngleStaeckelGrid")
if ext_loaded and 'c' in kwargs and kwargs['c']:
self._c= True
else:
self._c= False
self._delta= delta
if _APY_LOADED and isinstance(self._delta,units.Quantity):
self._delta= self._delta.to(units.kpc).value/self._ro
self._Rmax= Rmax
self._Rmin= 0.01
#Set up the actionAngleStaeckel object that we will use to interpolate
self._aA= actionAngleStaeckel.actionAngleStaeckel(pot=self._pot,delta=self._delta,c=self._c)
#Build grid
self._Lzmin= 0.01
self._Lzs= numpy.linspace(self._Lzmin,
self._Rmax\
*galpy.potential.vcirc(self._pot,
self._Rmax),
nLz)
self._Lzmax= self._Lzs[-1]
self._nLz= nLz
#Calculate E_c(R=RL), energy of circular orbit
self._RL= numpy.array([galpy.potential.rl(self._pot,l) for l in self._Lzs])
self._RLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
self._RL,k=3)
self._ERL= _evaluatePotentials(self._pot,self._RL,
numpy.zeros(self._nLz))\
+self._Lzs**2./2./self._RL**2.
self._ERLmax= numpy.amax(self._ERL)+1.
self._ERLInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(-(self._ERL-self._ERLmax)),k=3)
self._Ramax= 200./8.
self._ERa= _evaluatePotentials(self._pot,self._Ramax,0.) +self._Lzs**2./2./self._Ramax**2.
#self._EEsc= numpy.array([self._ERL[ii]+galpy.potential.vesc(self._pot,self._RL[ii])**2./4. for ii in range(nLz)])
self._ERamax= numpy.amax(self._ERa)+1.
self._ERaInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(-(self._ERa-self._ERamax)),k=3)
y= numpy.linspace(0.,1.,nE)
self._nE= nE
psis= numpy.linspace(0.,1.,npsi)*numpy.pi/2.
self._npsi= npsi
jr= numpy.zeros((nLz,nE,npsi))
jz= numpy.zeros((nLz,nE,npsi))
u0= numpy.zeros((nLz,nE))
jrLzE= numpy.zeros((nLz))
jzLzE= numpy.zeros((nLz))
#First calculate u0
thisLzs= (numpy.tile(self._Lzs,(nE,1)).T).flatten()
thisERL= (numpy.tile(self._ERL,(nE,1)).T).flatten()
thisERa= (numpy.tile(self._ERa,(nE,1)).T).flatten()
thisy= (numpy.tile(y,(nLz,1))).flatten()
thisE= _invEfunc(_Efunc(thisERa,thisERL)+thisy*(_Efunc(thisERL,thisERL)-_Efunc(thisERa,thisERL)),thisERL)
if isinstance(self._pot,galpy.potential.interpRZPotential) and hasattr(self._pot,'_origPot'):
u0pot= self._pot._origPot
else:
u0pot= self._pot
if self._c:
mu0= actionAngleStaeckel_c.actionAngleStaeckel_calcu0(thisE,thisLzs,
u0pot,
self._delta)[0]
else:
if numcores > 1:
mu0= multi.parallel_map((lambda x: self.calcu0(thisE[x],
thisLzs[x])),
range(nE*nLz),
numcores=numcores)
else:
mu0= list(map((lambda x: self.calcu0(thisE[x],
thisLzs[x])),
range(nE*nLz)))
u0= numpy.reshape(mu0,(nLz,nE))
thisR= self._delta*numpy.sinh(u0)
thisv= numpy.reshape(self.vatu0(thisE.flatten(),thisLzs.flatten(),
u0.flatten(),
thisR.flatten()),(nLz,nE))
self.thisv= thisv
#reshape
thisLzs= numpy.reshape(thisLzs,(nLz,nE))
thispsi= numpy.tile(psis,(nLz,nE,1)).flatten()
thisLzs= numpy.tile(thisLzs.T,(npsi,1,1)).T.flatten()
thisR= numpy.tile(thisR.T,(npsi,1,1)).T.flatten()
thisv= numpy.tile(thisv.T,(npsi,1,1)).T.flatten()
mjr, mlz, mjz= self._aA(thisR, #R
thisv*numpy.cos(thispsi), #vR
thisLzs/thisR, #vT
numpy.zeros(len(thisR)), #z
thisv*numpy.sin(thispsi), #vz
fixed_quad=True)
if isinstance(self._pot,galpy.potential.interpRZPotential) and hasattr(self._pot,'_origPot'):
#Interpolated potentials have problems with extreme orbits
indx= (mjr == 9999.99)
indx+= (mjz == 9999.99)
#Re-calculate these using the original potential, hopefully not too slow
tmpaA= actionAngleStaeckel.actionAngleStaeckel(pot=self._pot._origPot,delta=self._delta,c=self._c)
mjr[indx], dum, mjz[indx]= tmpaA(thisR[indx], #R
thisv[indx]*numpy.cos(thispsi[indx]), #vR
thisLzs[indx]/thisR[indx], #vT
numpy.zeros(numpy.sum(indx)), #z
thisv[indx]*numpy.sin(thispsi[indx]), #vz
fixed_quad=True)
jr= numpy.reshape(mjr,(nLz,nE,npsi))
jz= numpy.reshape(mjz,(nLz,nE,npsi))
for ii in range(nLz):
jrLzE[ii]= numpy.nanmax(jr[ii,(jr[ii,:,:] != 9999.99)])#:,:])
jzLzE[ii]= numpy.nanmax(jz[ii,(jz[ii,:,:] != 9999.99)])#:,:])
jrLzE[(jrLzE == 0.)]= numpy.nanmin(jrLzE[(jrLzE > 0.)])
jzLzE[(jzLzE == 0.)]= numpy.nanmin(jzLzE[(jzLzE > 0.)])
for ii in range(nLz):
jr[ii,:,:]/= jrLzE[ii]
jz[ii,:,:]/= jzLzE[ii]
#Deal w/ 9999.99
jr[(jr > 1.)]= 1.
jz[(jz > 1.)]= 1.
#Deal w/ NaN
jr[numpy.isnan(jr)]= 0.
jz[numpy.isnan(jz)]= 0.
#First interpolate the maxima
self._jr= jr
self._jz= jz
self._u0= u0
self._jrLzE= jrLzE
self._jzLzE= jzLzE
self._jrLzInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(jrLzE+10.**-5.),k=3)
self._jzLzInterp= interpolate.InterpolatedUnivariateSpline(self._Lzs,
numpy.log(jzLzE+10.**-5.),k=3)
#Interpolate u0
self._logu0Interp= interpolate.RectBivariateSpline(self._Lzs,
y,
numpy.log(u0),
kx=3,ky=3,s=0.)
#spline filter jr and jz, such that they can be used with ndimage.map_coordinates
self._jrFiltered= ndimage.spline_filter(numpy.log(self._jr+10.**-10.),order=3)
self._jzFiltered= ndimage.spline_filter(numpy.log(self._jz+10.**-10.),order=3)
# Check the units
self._check_consistent_units()
return None
def __init__(self,
pot=None,
zmax=1.,
gamma=1.,
Rmax=5.,
nR=16,
nEz=16,
nEr=31,
nLz=31,
numcores=1,
**kwargs):
"""
NAME:
__init__
PURPOSE:
initialize an actionAngleAdiabaticGrid object
INPUT:
pot= potential or list of potentials
zmax= zmax for building Ez grid
Rmax = Rmax for building grids
gamma= (default=1.) replace Lz by Lz+gamma Jz in effective potential
nEz=, nEr=, nLz, nR= grid size
numcores= number of cpus to use to parallellize
c= if True, use C to calculate actions
ro= distance from vantage point to GC (kpc; can be Quantity)
vo= circular velocity at ro (km/s; can be Quantity)
+scipy.integrate.quad keywords
OUTPUT:
instance
HISTORY:
2012-07-27 - Written - Bovy (IAS@MPIA)
"""
actionAngle.__init__(self,
ro=kwargs.get('ro', None),
vo=kwargs.get('vo', None))
if pot is None: #pragma: no cover
raise IOError("Must specify pot= for actionAngleAxi")
self._c = kwargs.pop('c', False)
self._gamma = gamma
self._pot = pot
self._zmax = zmax
self._Rmax = Rmax
self._Rmin = 0.01
#Set up the actionAngleAdiabatic object that we will use to interpolate
self._aA = actionAngleAdiabatic(pot=self._pot,
gamma=self._gamma,
c=self._c)
#Build grid for Ez, first calculate Ez(zmax;R) function
self._Rs = numpy.linspace(self._Rmin, self._Rmax, nR)
self._EzZmaxs= _evaluatePotentials(self._pot,self._Rs,
self._zmax*numpy.ones(nR))\
-_evaluatePotentials(self._pot,self._Rs,numpy.zeros(nR))
self._EzZmaxsInterp = interpolate.InterpolatedUnivariateSpline(
self._Rs, numpy.log(self._EzZmaxs), k=3)
y = numpy.linspace(0., 1., nEz)
jz = numpy.zeros((nR, nEz))
jzEzzmax = numpy.zeros(nR)
thisRs = (numpy.tile(self._Rs, (nEz, 1)).T).flatten()
thisEzZmaxs = (numpy.tile(self._EzZmaxs, (nEz, 1)).T).flatten()
thisy = (numpy.tile(y, (nR, 1))).flatten()
if self._c:
jz = self._aA(
thisRs,
numpy.zeros(len(thisRs)),
numpy.ones(len(thisRs)), #these two r dummies
numpy.zeros(len(thisRs)),
numpy.sqrt(2. * thisy * thisEzZmaxs),
**kwargs)[2]
jz = numpy.reshape(jz, (nR, nEz))
jzEzzmax[0:nR] = jz[:, nEz - 1]
else:
if numcores > 1:
jz = multi.parallel_map(
(
lambda x: self._aA(
thisRs[x],
0.,
1., #these two r dummies
0.,
math.sqrt(2. * thisy[x] * thisEzZmaxs[x]),
_justjz=True,
**kwargs)[2]),
range(nR * nEz),
numcores=numcores)
jz = numpy.reshape(jz, (nR, nEz))
jzEzzmax[0:nR] = jz[:, nEz - 1]
else:
for ii in range(nR):
for jj in range(nEz):
#Calculate Jz
jz[ii, jj] = self._aA(
self._Rs[ii],
0.,
1., #these two r dummies
0.,
numpy.sqrt(2. * y[jj] * self._EzZmaxs[ii]),
_justjz=True,
**kwargs)[2]
if jj == nEz - 1:
jzEzzmax[ii] = jz[ii, jj]
for ii in range(nR):
jz[ii, :] /= jzEzzmax[ii]
#First interpolate Ez=Ezmax
self._jzEzmaxInterp = interpolate.InterpolatedUnivariateSpline(
self._Rs, numpy.log(jzEzzmax + 10.**-5.), k=3)
self._jz = jz
self._jzInterp = interpolate.RectBivariateSpline(self._Rs,
y,
jz,
kx=3,
ky=3,
s=0.)
#JR grid
self._Lzmin = 0.01
self._Lzs= numpy.linspace(self._Lzmin,
self._Rmax\
*galpy.potential.vcirc(self._pot,
self._Rmax),
nLz)
self._Lzmax = self._Lzs[-1]
#Calculate ER(vr=0,R=RL)
self._RL = numpy.array(
[galpy.potential.rl(self._pot, l) for l in self._Lzs])
self._RLInterp = interpolate.InterpolatedUnivariateSpline(self._Lzs,
self._RL,
k=3)
self._ERRL = _evaluatePotentials(
self._pot, self._RL,
numpy.zeros(nLz)) + self._Lzs**2. / 2. / self._RL**2.
self._ERRLmax = numpy.amax(self._ERRL) + 1.
self._ERRLInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(-(self._ERRL - self._ERRLmax)), k=3)
self._Ramax = 99.
self._ERRa = _evaluatePotentials(
self._pot, self._Ramax, 0.) + self._Lzs**2. / 2. / self._Ramax**2.
self._ERRamax = numpy.amax(self._ERRa) + 1.
self._ERRaInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(-(self._ERRa - self._ERRamax)), k=3)
y = numpy.linspace(0., 1., nEr)
jr = numpy.zeros((nLz, nEr))
jrERRa = numpy.zeros(nLz)
thisRL = (numpy.tile(self._RL, (nEr - 1, 1)).T).flatten()
thisLzs = (numpy.tile(self._Lzs, (nEr - 1, 1)).T).flatten()
thisERRL = (numpy.tile(self._ERRL, (nEr - 1, 1)).T).flatten()
thisERRa = (numpy.tile(self._ERRa, (nEr - 1, 1)).T).flatten()
thisy = (numpy.tile(y[0:-1], (nLz, 1))).flatten()
if self._c:
mjr = self._aA(
thisRL,
numpy.sqrt(2. *
(thisERRa + thisy *
(thisERRL - thisERRa) - _evaluatePotentials(
self._pot, thisRL, numpy.zeros(
(nEr - 1) * nLz))) -
thisLzs**2. / thisRL**2.), thisLzs / thisRL,
numpy.zeros(len(thisRL)), numpy.zeros(len(thisRL)),
**kwargs)[0]
jr[:, 0:-1] = numpy.reshape(mjr, (nLz, nEr - 1))
jrERRa[0:nLz] = jr[:, 0]
else:
if numcores > 1:
mjr = multi.parallel_map((lambda x: self._aA(
thisRL[x],
numpy.sqrt(2. *
(thisERRa[x] + thisy[x] *
(thisERRL[x] - thisERRa[x]) -
_evaluatePotentials(self._pot, thisRL[
x], 0.)) - thisLzs[x]**2. / thisRL[x]**2.),
thisLzs[x] / thisRL[x],
0.,
0.,
_justjr=True,
**kwargs)[0]),
range((nEr - 1) * nLz),
numcores=numcores)
jr[:, 0:-1] = numpy.reshape(mjr, (nLz, nEr - 1))
jrERRa[0:nLz] = jr[:, 0]
else:
for ii in range(nLz):
for jj in range(nEr -
1): #Last one is zero by construction
try:
jr[ii, jj] = self._aA(
self._RL[ii],
numpy.sqrt(2. *
(self._ERRa[ii] + y[jj] *
(self._ERRL[ii] - self._ERRa[ii]) -
_evaluatePotentials(
self._pot, self._RL[ii], 0.)) -
self._Lzs[ii]**2. /
self._RL[ii]**2.),
self._Lzs[ii] / self._RL[ii],
0.,
0.,
_justjr=True,
**kwargs)[0]
except UnboundError: #pragma: no cover
raise
if jj == 0:
jrERRa[ii] = jr[ii, jj]
for ii in range(nLz):
jr[ii, :] /= jrERRa[ii]
#First interpolate Ez=Ezmax
self._jr = jr
self._jrERRaInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(jrERRa + 10.**-5.), k=3)
self._jrInterp = interpolate.RectBivariateSpline(self._Lzs,
y,
jr,
kx=3,
ky=3,
s=0.)
# Check the units
self._check_consistent_units()
return None
def _actionsFreqsAngles(self, *args, **kwargs):
"""
NAME:
actionsFreqsAngles (_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]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
delta= (object-wide default) can be used to override the object-wide focal length; can also be an array with length N to allow different delta for different phase-space points
u0= (None) if object-wide option useu0 is set, u0 to use (if useu0 and useu0 is None, a good value will be computed)
c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation
order= (10) number of points to use in the Gauss-Legendre numerical integration of the relevant action, frequency, and angle integrals
When not using C:
fixed_quad= (False) if True, use Gaussian quadrature (scipy.integrate.fixed_quad instead of scipy.integrate.quad)
scipy.integrate.fixed_quad or .quad keywords
OUTPUT:
(jr,lz,jz,Omegar,Omegaphi,Omegaz,angler,anglephi,anglez)
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
delta = kwargs.pop('delta', self._delta)
order = kwargs.get('order', self._order)
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:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_vz
phi = self._eval_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(self._pot, R[ii], z[ii]) +
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,delta)[0]
kwargs.pop('u0', None)
else:
u0 = None
jr, jz, Omegar, Omegaphi, Omegaz, angler, anglephi,anglez, err= actionAngleStaeckel_c.actionAngleFreqAngleStaeckel_c(\
self._pot,delta,R,vR,vT,z,vz,phi,u0=u0,order=order)
# 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, use_physical=False) for r in R[indx]
]
Omegaphi[indx] = [
omegac(self._pot, r, use_physical=False) for r in R[indx]
]
Omegaz[indx] = [
verticalfreq(self._pot, r, use_physical=False)
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")