def calcRapRperi(self, *args, **kwargs):
"""
NAME:
calcRapRperi
PURPOSE:
calculate the apocenter and pericenter radii
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:
(rperi,rap)
HISTORY:
2013-11-27 - Written - Bovy (IAS)
"""
#Set up the actionAngleAxi object
if isinstance(self._pot, list):
thispot = [
p.toPlanar() for p in self._pot
if not isinstance(p, planarPotential)
]
thispot.extend(
[p for p in self._pot if isinstance(p, planarPotential)])
elif not isinstance(self._pot, planarPotential):
thispot = self._pot.toPlanar()
else:
thispot = self._pot
aAAxi = actionAngleAxi(*args, pot=thispot, gamma=self._gamma)
return aAAxi.calcRapRperi(**kwargs)
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
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(self._eval_R)
aAAxi= actionAngleAxi(*args,pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
return aAAxi.calczmax(**kwargs)
def calczmax(self,*args,**kwargs): #pragma: no cover
"""
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)
"""
warnings.warn("actionAngleAdiabatic.calczmax function will soon be deprecated; please contact galpy's maintainer if you require this function")
#Set up the actionAngleAxi object
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(self._eval_R)
aAAxi= actionAngleAxi(*args,pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
return aAAxi.calczmax(**kwargs)
def calcRapRperi(self,*args,**kwargs):
"""
NAME:
calcRapRperi
PURPOSE:
calculate the apocenter and pericenter radii
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:
(rperi,rap)
HISTORY:
2013-11-27 - Written - Bovy (IAS)
"""
#Set up the actionAngleAxi object
if isinstance(self._pot,list):
thispot= [p.toPlanar() for p in self._pot if not isinstance(p,planarPotential)]
thispot.extend([p for p in self._pot if isinstance(p,planarPotential)])
elif not isinstance(self._pot,planarPotential):
thispot= self._pot.toPlanar()
else:
thispot= self._pot
aAAxi= actionAngleAxi(*args,pot=thispot,
gamma=self._gamma)
return aAAxi.calcRapRperi(**kwargs)
def calczmax(self, *args, **kwargs): #pragma: no cover
"""
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)
"""
warnings.warn(
"actionAngleAdiabatic.calczmax function will soon be deprecated; please contact galpy's maintainer if you require this function"
)
#Set up the actionAngleAxi object
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot = self._pot.toVertical(self._eval_R)
aAAxi = actionAngleAxi(*args,
pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
return aAAxi.calczmax(**kwargs)
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
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot = self._pot.toVertical(self._eval_R)
aAAxi = actionAngleAxi(*args,
pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
return aAAxi.calczmax(**kwargs)
def _EccZmaxRperiRap(self, *args, **kwargs):
"""
NAME:
EccZmaxRperiRap (_EccZmaxRperiRap)
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter for a spherical potential
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:
2017-12-22 - 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
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
L = nu.sqrt(L2)
#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
rperi, rap = [], []
for ii in range(len(axiR)):
axiaA = actionAngleAxi(axiR[ii],
axivR[ii],
axivT[ii],
pot=self._2dpot)
trperi, trap = axiaA.calcRapRperi()
rperi.append(trperi)
rap.append(trap)
rperi = nu.array(rperi)
rap = nu.array(rap)
return ((rap - rperi) / (rap + rperi),
rap * nu.sqrt(1. - Lz**2. / L2), rperi, rap)
def _EccZmaxRperiRap(self,*args,**kwargs):
"""
NAME:
EccZmaxRperiRap (_EccZmaxRperiRap)
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter for a spherical potential
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:
2017-12-22 - 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
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
L= nu.sqrt(L2)
#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
rperi, rap= [], []
for ii in range(len(axiR)):
axiaA= actionAngleAxi(axiR[ii],axivR[ii],axivT[ii],
pot=self._2dpot)
trperi,trap= axiaA.calcRapRperi()
rperi.append(trperi)
rap.append(trap)
rperi= nu.array(rperi)
rap= nu.array(rap)
return ((rap-rperi)/(rap+rperi),rap*nu.sqrt(1.-Lz**2./L2),
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
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:
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
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
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(self._eval_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
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:
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 = evaluatePotentials(
R, z, self._pot) + 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:
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 = evaluatePotentials(
R, z, self._pot) + 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]))
Op.append(omegac(self._pot, axiR[ii]))
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 _EccZmaxRperiRap(self,*args,**kwargs):
"""
NAME:
EccZmaxRperiRap (_EccZmaxRperiRap)
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter in the adiabatic 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
c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-21 - Written - Bovy (UofT)
"""
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])
rperi,Rap,zmax, err= actionAngleAdiabatic_c.actionAngleRperiRapZmaxAdiabatic_c(\
self._pot,self._gamma,R,vR,vT,z,vz)
if err == 0:
rap= nu.sqrt(Rap**2.+zmax**2.)
ecc= (rap-rperi)/(rap+rperi)
return (ecc,zmax,rperi,rap)
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):
oecc= nu.zeros((len(args[0])))
orperi= nu.zeros((len(args[0])))
orap= nu.zeros((len(args[0])))
ozmax= 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])
tecc, tzmax, trperi,trap= self._EccZmaxRperiRap(\
*targs,**copy.copy(kwargs))
oecc[ii]= tecc
ozmax[ii]= tzmax
orperi[ii]= trperi
orap[ii]= trap
return (oecc,ozmax,orperi,orap)
else:
#Set up the actionAngleAxi object
self._parse_eval_args(*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(self._eval_R) for p in self._pot]
else:
thisverticalpot= self._pot.toVertical(self._eval_R)
aAAxi= actionAngleAxi(*args,pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
rperi,Rap= aAAxi.calcRapRperi(**kwargs)
zmax= aAAxi.calczmax(**kwargs)
rap= nu.sqrt(Rap**2.+zmax**2.)
return ((rap-rperi)/(rap+rperi),zmax,rperi,rap)
def _EccZmaxRperiRap(self, *args, **kwargs):
"""
NAME:
EccZmaxRperiRap (_EccZmaxRperiRap)
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter in the adiabatic 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
c= (object-wide default, bool) True/False to override the object-wide setting for whether or not to use the C implementation
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-21 - Written - Bovy (UofT)
"""
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])
rperi,Rap,zmax, err= actionAngleAdiabatic_c.actionAngleRperiRapZmaxAdiabatic_c(\
self._pot,self._gamma,R,vR,vT,z,vz)
if err == 0:
rap = nu.sqrt(Rap**2. + zmax**2.)
ecc = (rap - rperi) / (rap + rperi)
return (ecc, zmax, rperi, rap)
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):
oecc = nu.zeros((len(args[0])))
orperi = nu.zeros((len(args[0])))
orap = nu.zeros((len(args[0])))
ozmax = 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])
tecc, tzmax, trperi,trap= self._EccZmaxRperiRap(\
*targs,**copy.copy(kwargs))
oecc[ii] = tecc
ozmax[ii] = tzmax
orperi[ii] = trperi
orap[ii] = trap
return (oecc, ozmax, orperi, orap)
else:
#Set up the actionAngleAxi object
self._parse_eval_args(*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(self._eval_R) for p in self._pot
]
else:
thisverticalpot = self._pot.toVertical(self._eval_R)
aAAxi = actionAngleAxi(*args,
pot=thispot,
verticalPot=thisverticalpot,
gamma=self._gamma)
rperi, Rap = aAAxi.calcRapRperi(**kwargs)
zmax = aAAxi.calczmax(**kwargs)
rap = nu.sqrt(Rap**2. + zmax**2.)
return ((rap - rperi) / (rap + rperi), zmax, rperi, rap)
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 _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 _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
_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:
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
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
self._parse_eval_args(*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(self._eval_R) for p in self._pot
]
else:
thisverticalpot = self._pot.toVertical(self._eval_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 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:
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 = evaluatePotentials(
R, z, self._pot) + 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]))
Op.append(omegac(self._pot, axiR[ii]))
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)