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:
2013-08-28 - Written - Bovy (IAS)
"""
if ((self._c and not (kwargs.has_key('c') and not kwargs['c']))\
or (ext_loaded and ((kwargs.has_key('c') 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 kwargs.has_key('u0'):
u0= 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]
if kwargs.has_key('u0'): kwargs.pop('u0')
else:
u0= None
jr, jz, Omegar, Omegaphi, Omegaz, err= actionAngleStaeckel_c.actionAngleFreqStaeckel_c(\
self._pot,self._delta,R,vR,vT,z,vz,u0=u0)
if err == 0:
return (jr,Lz,jz,Omegar,Omegaphi,Omegaz)
else:
raise RuntimeError("C-code for calculation actions failed; try with c=False")
else:
if kwargs.has_key('c') and kwargs['c'] and not self._c:
warnings.warn("C module not used because potential does not have a C implementation",galpyWarning)
raise NotImplementedError("actionsFreqs with c=False not implemented")
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 JR(self, *args, **kwargs):
"""
NAME:
JR
PURPOSE:
evaluate the action jr
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
HISTORY:
2012-07-30 - Written - Bovy (IAS@MPIA)
"""
#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()
aAAxi = actionAngleAxi(*args, pot=thispot, gamma=self._gamma)
return aAAxi.JR(**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
scipy.integrate.quadrature keywords
OUTPUT:
(jr,lz,jz), where jr=[jr,jrerr], and jz=[jz,jzerr]
HISTORY:
2012-07-26 - Written - Bovy (IAS@MPIA)
"""
#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.JR(**kwargs), aAAxi._R * aAAxi._vT, aAAxi.Jz(**kwargs))
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,jzerr
HISTORY:
2012-07-27 - Written - Bovy (IAS@MPIA)
"""
#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.Jz(**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:
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 __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:
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)))
return (Jr,Jphi,Jz)
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
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:
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)
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 (kwargs.has_key('c') and not kwargs['c']))\
or (ext_loaded and ((kwargs.has_key('c') 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 kwargs.has_key('c') 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
if kwargs.has_key('c'): kwargs.pop('c')
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 (kwargs.has_key('c') and not kwargs['c']))\
or (ext_loaded and ((kwargs.has_key('c') 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 kwargs.has_key('u0'):
u0= 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]
if kwargs.has_key('u0'): kwargs.pop('u0')
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:
raise RuntimeError("C-code for calculation actions failed; try with c=False")
else:
if kwargs.has_key('c') and kwargs['c'] and not self._c:
warnings.warn("C module not used because potential does not have a C implementation",galpyWarning)
if kwargs.has_key('c'): kwargs.pop('c')
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)))