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
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
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-12 - Written - Bovy (UofT)
"""
delta = kwargs.get('delta', self._delta)
umin, umax, vmin = self._uminumaxvmin(*args, **kwargs)
rperi = bovy_coords.uv_to_Rz(umin, nu.pi / 2., delta=delta)[0]
rap_tmp, zmax = bovy_coords.uv_to_Rz(umax, vmin, delta=delta)
rap = nu.sqrt(rap_tmp**2. + zmax**2.)
e = (rap - rperi) / (rap + rperi)
return (e, 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 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
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
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-12 - Written - Bovy (UofT)
"""
delta= kwargs.get('delta',self._delta)
umin, umax, vmin= self._uminumaxvmin(*args,**kwargs)
rperi= bovy_coords.uv_to_Rz(umin,nu.pi/2.,delta=delta)[0]
rap_tmp, zmax= bovy_coords.uv_to_Rz(umax,vmin,delta=delta)
rap= nu.sqrt(rap_tmp**2.+zmax**2.)
e= (rap-rperi)/(rap+rperi)
return (e,zmax,rperi,rap)
def test_Rz_to_uv():
u, v= numpy.arccosh(5./3.), numpy.pi/6.
ut,vt= bovy_coords.Rz_to_uv(*bovy_coords.uv_to_Rz(u,v,delta=3.),delta=3.)
assert numpy.fabs(ut-u) < 10.**-10., 'Rz_to_uvz conversion did not work as expected'
assert numpy.fabs(vt-vt) < 10.**-10., 'Rz_to_uv conversion did not work as expected'
#Also test for arrays
os= numpy.ones(2)
ut,vt= bovy_coords.Rz_to_uv(*bovy_coords.uv_to_Rz(u*os,v*os,delta=3.),delta=3.)
assert numpy.all(numpy.fabs(ut-u) < 10.**-10.), 'Rz_to_uvz conversion did not work as expected'
assert numpy.all(numpy.fabs(vt-vt) < 10.**-10.), 'Rz_to_uv conversion did not work as expected'
return None
def test_uv_to_Rz():
u, v= numpy.arccosh(5./3.), numpy.pi/6.
R,z= bovy_coords.uv_to_Rz(u,v,delta=3.)
assert numpy.fabs(R-2.) < 10.**-10., 'uv_to_Rz conversion did not work as expected'
assert numpy.fabs(z-2.5*numpy.sqrt(3.)) < 10.**-10., 'uv_to_Rz conversion did not work as expected'
#Also test for arrays
os= numpy.ones(2)
R,z= bovy_coords.uv_to_Rz(os*u,os*v,delta=3.)
assert numpy.all(numpy.fabs(R-2.) < 10.**-10.), 'uv_to_Rz conversion did not work as expected'
assert numpy.all(numpy.fabs(z-2.5*numpy.sqrt(3.)) < 10.**-10.), 'uv_to_Rz conversion did not work as expected'
return None
def test_Rz_to_coshucosv():
u, v= numpy.arccosh(5./3.), numpy.pi/3.
R,z= bovy_coords.uv_to_Rz(u,v,delta=3.)
coshu,cosv= bovy_coords.Rz_to_coshucosv(R,z,delta=3.)
assert numpy.fabs(coshu-5./3.) < 10.**-10., 'Rz_to_coshucosv conversion did notwork as expected'
assert numpy.fabs(cosv-0.5) < 10.**-10., 'Rz_to_coshucosv conversion did notwork as expected'
#Also test for arrays
os= numpy.ones(2)
coshu,cosv= bovy_coords.Rz_to_coshucosv(R*os,z*os,delta=3.)
assert numpy.all(numpy.fabs(coshu-5./3.) < 10.**-10.), 'Rz_to_coshucosv conversion did notwork as expected'
assert numpy.all(numpy.fabs(cosv-0.5) < 10.**-10.), 'Rz_to_coshucosv conversion did notwork as expected'
return None
def estimate_orbit_params(orbit, pot=MWPotential2014, delta=0.375, c=True):
'''
use the staeckel approximation to estimate orbital parameters for an orbit
'''
try:
if not c:
aASS = actionAngleStaeckelSingle(orbit, pot=pot, delta=delta)
umin, umax = aASS.calcUminUmax()
vmin = aASS.calcVmin()
rperi = bovy_coords.uv_to_Rz(umin,
numpy.pi / 2.,
delta=aASS._delta)[0]
rap_tmp, zmax = bovy_coords.uv_to_Rz(umax, vmin, delta=aASS._delta)
rap = numpy.sqrt(rap_tmp**2. + zmax**2.)
e = (rap - rperi) / (rap + rperi)
return [rperi, rap, zmax, e]
else:
aAS = actionAngleStaeckel(pot=pot, delta=delta)
e, zmax, rperi, rap = aAS.EccZmaxRperiRap(orbit)
return [rperi, rap, zmax, e]
except UnboundError:
return [np.nan, np.nan, np.nan, np.nan]
def FZStaeckel(u,v,pot,delta): #pragma: no cover because unused
"""
NAME:
FZStaeckel
PURPOSE:
return the vertical force
INPUT:
u - confocal u
v - confocal v
pot - potential
delta - focus
OUTPUT:
FZ(u,v)
HISTORY:
2012-11-30 - Written - Bovy (IAS)
"""
R,z= bovy_coords.uv_to_Rz(u,v,delta=delta)
return _evaluatezforces(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 FRStaeckel(u, v, pot, delta): #pragma: no cover because unused
"""
NAME:
FRStaeckel
PURPOSE:
return the radial force
INPUT:
u - confocal u
v - confocal v
pot - potential
delta - focus
OUTPUT:
FR(u,v)
HISTORY:
2012-11-30 - Written - Bovy (IAS)
"""
R, z = bovy_coords.uv_to_Rz(u, v, delta=delta)
return _evaluateRforces(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 FRStaeckel(u,v,pot,delta):
"""
NAME:
FRStaeckel
PURPOSE:
return the radial force
INPUT:
u - confocal u
v - confocal v
pot - potential
delta - focus
OUTPUT:
FR(u,v)
HISTORY:
2012-11-30 - Written - Bovy (IAS)
"""
R,z= bovy_coords.uv_to_Rz(u,v,delta=delta)
return evaluateRforces(R,z,pot)