def test_actionAngleTorus_interppot_freqs():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import LogarithmicHaloPotential, interpRZPotential
lp = LogarithmicHaloPotential(normalize=1.)
ip = interpRZPotential(RZPot=lp,
interpPot=True,
interpDens=True,
interpRforce=True,
interpzforce=True,
enable_c=True)
aAT = actionAngleTorus(pot=lp)
aATi = actionAngleTorus(pot=ip)
jr, jphi, jz = 0.05, 1.1, 0.02
om = aAT.Freqs(jr, jphi, jz)
omi = aATi.Freqs(jr, jphi, jz)
assert numpy.fabs(
(om[0] - omi[0]) / om[0]
) < 0.2, 'Radial frequency computed using the torus machine does not agree between potential and interpolated potential'
assert numpy.fabs(
(om[1] - omi[1]) / om[1]
) < 0.2, 'Azimuthal frequency computed using the torus machine does not agree between potential and interpolated potential'
assert numpy.fabs(
(om[2] - omi[2]) / om[2]
) < 0.8, 'Vertical frequency computed using the torus machine does not agree between potential and interpolated potential'
return None
def test_actionAngleTorus_basic():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential, rl, vcirc, \
FlattenedPowerPotential, PlummerPotential
tol= -4.
jr= 10.**-10.
jz= 10.**-10.
aAT= actionAngleTorus(pot=MWPotential)
# at R=1, Lz=1
jphi= 1.
angler= numpy.linspace(0.,2.*numpy.pi,101)
anglephi= numpy.linspace(0.,2.*numpy.pi,101)+1.
anglez= numpy.linspace(0.,2.*numpy.pi,101)+2.
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(MWPotential,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(MWPotential,rl(MWPotential,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
# at Lz=1.5, using Plummer
tol= -3.25
pp= PlummerPotential(normalize=1.)
aAT= actionAngleTorus(pot=pp)
jphi= 1.5
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(pp,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(pp,rl(pp,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
# at Lz=0.5, using FlattenedPowerPotential
tol= -4.
fp= FlattenedPowerPotential(normalize=1.)
aAT= actionAngleTorus(pot=fp)
jphi= 0.5
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(fp,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(fp,rl(fp,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
return None
def test_actionAngleTorus_basic():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential, rl, vcirc, \
FlattenedPowerPotential, PlummerPotential
tol= -4.
jr= 10.**-10.
jz= 10.**-10.
aAT= actionAngleTorus(pot=MWPotential)
# at R=1, Lz=1
jphi= 1.
angler= numpy.linspace(0.,2.*numpy.pi,101)
anglephi= numpy.linspace(0.,2.*numpy.pi,101)+1.
anglez= numpy.linspace(0.,2.*numpy.pi,101)+2.
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(MWPotential,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(MWPotential,rl(MWPotential,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
# at Lz=1.5, using Plummer
tol= -3.25
pp= PlummerPotential(normalize=1.)
aAT= actionAngleTorus(pot=pp)
jphi= 1.5
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(pp,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(pp,rl(pp,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
# at Lz=0.5, using FlattenedPowerPotential
tol= -4.
fp= FlattenedPowerPotential(normalize=1.)
aAT= actionAngleTorus(pot=fp)
jphi= 0.5
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
assert numpy.all(numpy.fabs(RvR[0]-rl(fp,jphi)) < 10.**tol), \
'circular orbit does not have constant radius for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[1]) < 10.**tol), \
'circular orbit does not have zero radial velocity for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[2]-vcirc(fp,rl(fp,jphi))) < 10.**tol), \
'circular orbit does not have constant vT=vc for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[3]) < 10.**tol), \
'circular orbit does not have zero vertical height for actionAngleTorus'
assert numpy.all(numpy.fabs(RvR[4]) < 10.**tol), \
'circular orbit does not have zero vertical velocity for actionAngleTorus'
return None
def test_actionAngleTorus_Isochrone_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochrone
ip = IsochronePotential(normalize=1., b=1.2)
aAI = actionAngleIsochrone(ip=ip)
tol = -6.
aAT = actionAngleTorus(pot=ip, tol=tol)
jr, jphi, jz = 0.075, 1.1, 0.05
angler = numpy.array([0.])
anglephi = numpy.array([numpy.pi])
anglez = numpy.array([numpy.pi / 2.])
# Calculate position from aAT
RvR = aAT(jr, jphi, jz, angler, anglephi, anglez).T
# Calculate actions from aAI
ji = aAI(*RvR)
djr = numpy.fabs((ji[0] - jr) / jr)
dlz = numpy.fabs((ji[1] - jphi) / jphi)
djz = numpy.fabs((ji[2] - jz) / jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (
djr * 100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (
dlz * 100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (
djz * 100.)
return None
def test_actionAngleTorus_Staeckel_actions():
from galpy.potential import KuzminKutuzovStaeckelPotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleStaeckel
delta = 1.2
kp = KuzminKutuzovStaeckelPotential(normalize=1., Delta=delta)
aAS = actionAngleStaeckel(pot=kp, delta=delta, c=True)
tol = -3.
aAT = actionAngleTorus(pot=kp, tol=tol)
jr, jphi, jz = 0.075, 1.1, 0.05
angler = numpy.array([0.])
anglephi = numpy.array([numpy.pi])
anglez = numpy.array([numpy.pi / 2.])
# Calculate position from aAT
RvR = aAT(jr, jphi, jz, angler, anglephi, anglez).T
# Calculate actions from aAI
ji = aAS(*RvR)
djr = numpy.fabs((ji[0] - jr) / jr)
dlz = numpy.fabs((ji[1] - jphi) / jphi)
djz = numpy.fabs((ji[2] - jz) / jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (
djr * 100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (
dlz * 100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (
djz * 100.)
return None
def test_actionAngleTorus_isochroneApprox_actions():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochroneApprox
aAIA = actionAngleIsochroneApprox(pot=MWPotential2014, b=0.8)
tol = -2.5
aAT = actionAngleTorus(pot=MWPotential2014, tol=tol)
jr, jphi, jz = 0.075, 1.1, 0.05
angler = numpy.array([0.])
anglephi = numpy.array([numpy.pi])
anglez = numpy.array([numpy.pi / 2.])
# Calculate position from aAT
RvR = aAT(jr, jphi, jz, angler, anglephi, anglez).T
# Calculate actions from aAIA
ji = aAIA(*RvR)
djr = numpy.fabs((ji[0] - jr) / jr)
dlz = numpy.fabs((ji[1] - jphi) / jphi)
djz = numpy.fabs((ji[2] - jz) / jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleIsochroneApprox applied to MWPotential2014 potential disagree for Jr at %f%%' % (
djr * 100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleIsochroneApprox applied to MWPotential2014 potential disagree for Jr at %f%%' % (
dlz * 100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleMWPotential2014 applied to MWPotential2014 potential disagree for Jr at %f%%' % (
djz * 100.)
return None
def test_actionAngleTorus_hessian_symm():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
h= aAT.hessianFreqs(jr,jphi,jz,tol=0.0001,nosym=True)[0]
assert numpy.all(numpy.fabs((h-h.T)/h) < 0.03), 'actionAngleTorus Hessian is not symmetric'
return None
def test_actionAngleTorus_interppot_freqs():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import LogarithmicHaloPotential, interpRZPotential
lp= LogarithmicHaloPotential(normalize=1.)
ip= interpRZPotential(RZPot=lp,
interpPot=True,
interpDens=True,interpRforce=True,interpzforce=True,
enable_c=True)
aAT= actionAngleTorus(pot=lp)
aATi= actionAngleTorus(pot=ip)
jr,jphi,jz= 0.05,1.1,0.02
om= aAT.Freqs(jr,jphi,jz)
omi= aATi.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-omi[0])/om[0]) < 0.2, 'Radial frequency computed using the torus machine does not agree between potential and interpolated potential'
assert numpy.fabs((om[1]-omi[1])/om[1]) < 0.2, 'Azimuthal frequency computed using the torus machine does not agree between potential and interpolated potential'
assert numpy.fabs((om[2]-omi[2])/om[2]) < 0.8, 'Vertical frequency computed using the torus machine does not agree between potential and interpolated potential'
return None
def test_actionAngleTorus_hessian_symm():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
h= aAT.hessianFreqs(jr,jphi,jz,tol=0.0001,nosym=True)[0]
assert numpy.all(numpy.fabs((h-h.T)/h) < 0.03), 'actionAngleTorus Hessian is not symmetric'
return None
def setup_sdf(pot,prog,sigv,td,ro,vo,multi=None,nTrackChunks=8,isob=None,
trailing_only=False,verbose=True,useTM=True,logpot=False):
"""Simple function to setup the stream model"""
if isob is None:
if True or logpot:
isob= 0.75
if False:
# Determine good one
ts= numpy.linspace(0.,15.,1001)
# Hack!
epot= copy.deepcopy(pot)
epot[2]._b= 1.
epot[2]._b2= 1.
epot[2]._isNonAxi= False
epot[2]._aligned= True
prog.integrate(ts,pot)
estb= estimateBIsochrone(epot,
prog.R(ts,use_physical=False),
prog.z(ts,use_physical=False),
phi=prog.phi(ts,use_physical=False))
if estb[1] < 0.3: isob= 0.3
elif estb[1] > 1.5: isob= 1.5
else: isob= estb[1]
if verbose: print(pot[2]._c, isob,estb)
if not logpot and numpy.fabs(pot[2]._b-1.) > 0.05:
aAI= actionAngleIsochroneApprox(pot=pot,b=isob,tintJ=1000.,
ntintJ=30000)
else:
ts= numpy.linspace(0.,100.,10000)
aAI= actionAngleIsochroneApprox(pot=pot,b=isob,tintJ=100.,
ntintJ=10000,dt=ts[1]-ts[0])
if useTM:
aAT= actionAngleTorus(pot=pot,tol=0.001,dJ=0.0001)
else:
aAT= False
try:
sdf=\
streamdf(sigv/vo,progenitor=prog,pot=pot,aA=aAI,
useTM=aAT,approxConstTrackFreq=True,
leading=True,nTrackChunks=nTrackChunks,
tdisrupt=td/bovy_conversion.time_in_Gyr(vo,ro),
ro=ro,vo=vo,R0=ro,
vsun=[-11.1,vo+24.,7.25],
custom_transform=_TKOP,
multi=multi,
nospreadsetup=True)
except numpy.linalg.LinAlgError:
sdf=\
streamdf(sigv/vo,progenitor=prog,pot=pot,aA=aAI,
useTM=aAT,approxConstTrackFreq=True,
leading=True,nTrackChunks=nTrackChunks,
nTrackIterations=0,
tdisrupt=td/bovy_conversion.time_in_Gyr(vo,ro),
ro=ro,vo=vo,R0=ro,
vsun=[-11.1,vo+24.,7.25],
custom_transform=_TKOP,
multi=multi)
return sdf
def test_actionAngleTorus_AutoFitWarning():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleTorus
lp= LogarithmicHaloPotential(normalize=1.,q=0.9)
aAT= actionAngleTorus(pot=lp,tol=10.**-8.)
# These should give warnings
jr, jp, jz= 0.27209033, 1.80253892, 0.6078445
ar, ap, az= numpy.array([1.95732492]), numpy.array([6.16753224]), \
numpy.array([4.08233059])
#Turn warnings into errors to test for them
import warnings
with warnings.catch_warnings(record=True) as w:
if PY2: reset_warning_registry('galpy')
warnings.simplefilter("always",galpyWarning)
aAT(jr,jp,jz,ar,ap,az)
# Should raise warning bc of Autofit, might raise others
raisedWarning= False
for wa in w:
raisedWarning= (str(wa.message) == "actionAngleTorus' AutoFit exited with non-zero return status -3: Fit failed the goal by more than 2")
if raisedWarning: break
assert raisedWarning, "actionAngleTorus with flattened LogarithmicHaloPotential and a particular orbit should have thrown a warning, but didn't"
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always",galpyWarning)
aAT.xvFreqs(jr,jp,jz,ar,ap,az)
# Should raise warning bc of Autofit, might raise others
raisedWarning= False
for wa in w:
raisedWarning= (str(wa.message) == "actionAngleTorus' AutoFit exited with non-zero return status -3: Fit failed the goal by more than 2")
if raisedWarning: break
assert raisedWarning, "actionAngleTorus with flattened LogarithmicHaloPotential and a particular orbit should have thrown a warning, but didn't"
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always",galpyWarning)
aAT.Freqs(jr,jp,jz)
# Should raise warning bc of Autofit, might raise others
raisedWarning= False
for wa in w:
raisedWarning= (str(wa.message) == "actionAngleTorus' AutoFit exited with non-zero return status -3: Fit failed the goal by more than 2")
if raisedWarning: break
assert raisedWarning, "actionAngleTorus with flattened LogarithmicHaloPotential and a particular orbit should have thrown a warning, but didn't"
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always",galpyWarning)
aAT.hessianFreqs(jr,jp,jz)
# Should raise warning bc of Autofit, might raise others
raisedWarning= False
for wa in w:
raisedWarning= (str(wa.message) == "actionAngleTorus' AutoFit exited with non-zero return status -3: Fit failed the goal by more than 2")
if raisedWarning: break
assert raisedWarning, "actionAngleTorus with flattened LogarithmicHaloPotential and a particular orbit should have thrown a warning, but didn't"
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always",galpyWarning)
aAT.xvJacobianFreqs(jr,jp,jz,ar,ap,az)
# Should raise warning bc of Autofit, might raise others
raisedWarning= False
for wa in w:
raisedWarning= (str(wa.message) == "actionAngleTorus' AutoFit exited with non-zero return status -3: Fit failed the goal by more than 2")
if raisedWarning: break
assert raisedWarning, "actionAngleTorus with flattened LogarithmicHaloPotential and a particular orbit should have thrown a warning, but didn't"
return None
def test_actionAngleTorus_Staeckel_freqsAngles():
from galpy.potential import KuzminKutuzovStaeckelPotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleStaeckel
delta = 1.2
kp = KuzminKutuzovStaeckelPotential(normalize=1., Delta=delta)
aAS = actionAngleStaeckel(pot=kp, delta=delta, c=True)
tol = -3.
aAT = actionAngleTorus(pot=kp, tol=tol)
jr, jphi, jz = 0.075, 1.1, 0.05
angler = numpy.array([0.1]) + numpy.linspace(0., numpy.pi, 101)
angler = angler % (2. * numpy.pi)
anglephi = numpy.array([numpy.pi]) + numpy.linspace(0., numpy.pi, 101)
anglephi = anglephi % (2. * numpy.pi)
anglez = numpy.array([numpy.pi / 2.]) + numpy.linspace(0., numpy.pi, 101)
anglez = anglez % (2. * numpy.pi)
# Calculate position from aAT
RvRom = aAT.xvFreqs(jr, jphi, jz, angler, anglephi, anglez)
# Calculate actions, frequencies, and angles from aAI
ws = aAS.actionsFreqsAngles(*RvRom[0].T)
dOr = numpy.fabs((ws[3] - RvRom[1]))
dOp = numpy.fabs((ws[4] - RvRom[2]))
dOz = numpy.fabs((ws[5] - RvRom[3]))
dar = numpy.fabs((ws[6] - angler))
dap = numpy.fabs((ws[7] - anglephi))
daz = numpy.fabs((ws[8] - anglez))
dar[dar > numpy.pi] -= 2. * numpy.pi
dar[dar < -numpy.pi] += 2. * numpy.pi
dap[dap > numpy.pi] -= 2. * numpy.pi
dap[dap < -numpy.pi] += 2. * numpy.pi
daz[daz > numpy.pi] -= 2. * numpy.pi
daz[daz < -numpy.pi] += 2. * numpy.pi
assert numpy.all(
dOr < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Or at %f%%' % (
numpy.nanmax(dOr) * 100.)
assert numpy.all(
dOp < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Ophi at %f%%' % (
numpy.nanmax(dOp) * 100.)
assert numpy.all(
dOz < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Oz at %f%%' % (
numpy.nanmax(dOz) * 100.)
assert numpy.all(
dar < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for ar at %f' % (
numpy.nanmax(dar))
assert numpy.all(
dap < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for aphi at %f' % (
numpy.nanmax(dap))
assert numpy.all(
daz < 10.**tol
), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for az at %f' % (
numpy.nanmax(daz))
return None
def test_actionAngleTorus_hessian_freqs():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
fO= aAT.Freqs(jr,jphi,jz)[:3]
hO= aAT.hessianFreqs(jr,jphi,jz)[1:4]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods Freqs and hessianFreqs return different frequencies'
return None
def test_actionAngleTorus_hessian_freqs():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
fO= aAT.Freqs(jr,jphi,jz)[:3]
hO= aAT.hessianFreqs(jr,jphi,jz)[1:4]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods Freqs and hessianFreqs return different frequencies'
return None
def test_actionAngleTorus_Isochrone_freqsAngles():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochrone
ip = IsochronePotential(normalize=1., b=1.2)
aAI = actionAngleIsochrone(ip=ip)
tol = -6.
aAT = actionAngleTorus(pot=ip, tol=tol)
jr, jphi, jz = 0.075, 1.1, 0.05
angler = numpy.array([0.1]) + numpy.linspace(0., numpy.pi, 101)
angler = angler % (2. * numpy.pi)
anglephi = numpy.array([numpy.pi]) + numpy.linspace(0., numpy.pi, 101)
anglephi = anglephi % (2. * numpy.pi)
anglez = numpy.array([numpy.pi / 2.]) + numpy.linspace(0., numpy.pi, 101)
anglez = anglez % (2. * numpy.pi)
# Calculate position from aAT
RvRom = aAT.xvFreqs(jr, jphi, jz, angler, anglephi, anglez)
# Calculate actions, frequencies, and angles from aAI
ws = aAI.actionsFreqsAngles(*RvRom[0].T)
dOr = numpy.fabs((ws[3] - RvRom[1]))
dOp = numpy.fabs((ws[4] - RvRom[2]))
dOz = numpy.fabs((ws[5] - RvRom[3]))
dar = numpy.fabs((ws[6] - angler))
dap = numpy.fabs((ws[7] - anglephi))
daz = numpy.fabs((ws[8] - anglez))
dar[dar > numpy.pi] -= 2. * numpy.pi
dar[dar < -numpy.pi] += 2. * numpy.pi
dap[dap > numpy.pi] -= 2. * numpy.pi
dap[dap < -numpy.pi] += 2. * numpy.pi
daz[daz > numpy.pi] -= 2. * numpy.pi
daz[daz < -numpy.pi] += 2. * numpy.pi
assert numpy.all(
dOr < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Or at %f%%' % (
numpy.nanmax(dOr) * 100.)
assert numpy.all(
dOp < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Ophi at %f%%' % (
numpy.nanmax(dOp) * 100.)
assert numpy.all(
dOz < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Oz at %f%%' % (
numpy.nanmax(dOz) * 100.)
assert numpy.all(
dar < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for ar at %f' % (
numpy.nanmax(dar))
assert numpy.all(
dap < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for aphi at %f' % (
numpy.nanmax(dap))
assert numpy.all(
daz < 10.**tol
), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for az at %f' % (
numpy.nanmax(daz))
return None
def test_actionAngleTorus_nocerr():
from galpy.actionAngle import actionAngleTorus
from test_potential import BurkertPotentialNoC
bp= BurkertPotentialNoC()
try:
aAT= actionAngleTorus(pot=bp)
except RuntimeError: pass
else:
raise AssertionError("actionAngleTorus initialization with potential w/o C should have given a RuntimeError, but didn't")
return None
def test_actionAngleTorus_nonaxierr():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import TriaxialNFWPotential
np= TriaxialNFWPotential(normalize=1.,b=0.9)
try:
aAT= actionAngleTorus(pot=np)
except RuntimeError: pass
else:
raise AssertionError("actionAngleTorus initialization with non-axisymmetric potential should have given a RuntimeError, but didn't")
return None
def test_actionAngleTorus_nocerr():
from galpy.actionAngle import actionAngleTorus
from test_potential import BurkertPotentialNoC
bp= BurkertPotentialNoC()
try:
aAT= actionAngleTorus(pot=bp)
except RuntimeError: pass
else:
raise AssertionError("actionAngleTorus initialization with potential w/o C should have given a RuntimeError, but didn't")
return None
def test_actionAngleTorus_nonaxierr():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import TriaxialNFWPotential
np= TriaxialNFWPotential(normalize=1.,b=0.9)
try:
aAT= actionAngleTorus(pot=np)
except RuntimeError: pass
else:
raise AssertionError("actionAngleTorus initialization with non-axisymmetric potential should have given a RuntimeError, but didn't")
return None
def test_actionAngleTorus_basic_freqs():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import epifreq, omegac, verticalfreq, rl, \
JaffePotential, PowerSphericalPotential, HernquistPotential
tol= -3.
jr= 10.**-6.
jz= 10.**-6.
jp= JaffePotential(normalize=1.)
aAT= actionAngleTorus(pot=jp)
# at Lz=1
jphi= 1.
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(jp,rl(jp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(jp,rl(jp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(jp,rl(jp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
# at Lz=1.5, w/ different potential
pp= PowerSphericalPotential(normalize=1.)
aAT= actionAngleTorus(pot=pp)
jphi= 1.5
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(pp,rl(pp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(pp,rl(pp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(pp,rl(pp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
# at Lz=0.5, w/ different potential
tol= -2.5 # appears more difficult
hp= HernquistPotential(normalize=1.)
aAT= actionAngleTorus(pot=hp)
jphi= 0.5
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(hp,rl(hp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(hp,rl(hp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(hp,rl(hp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
return None
def test_actionAngleTorus_basic_freqs():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import epifreq, omegac, verticalfreq, rl, \
JaffePotential, PowerSphericalPotential, HernquistPotential
tol= -3.
jr= 10.**-6.
jz= 10.**-6.
jp= JaffePotential(normalize=1.)
aAT= actionAngleTorus(pot=jp)
# at Lz=1
jphi= 1.
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(jp,rl(jp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(jp,rl(jp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(jp,rl(jp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
# at Lz=1.5, w/ different potential
pp= PowerSphericalPotential(normalize=1.)
aAT= actionAngleTorus(pot=pp)
jphi= 1.5
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(pp,rl(pp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(pp,rl(pp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(pp,rl(pp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
# at Lz=0.5, w/ different potential
tol= -2.5 # appears more difficult
hp= HernquistPotential(normalize=1.)
aAT= actionAngleTorus(pot=hp)
jphi= 0.5
om= aAT.Freqs(jr,jphi,jz)
assert numpy.fabs((om[0]-epifreq(hp,rl(hp,jphi)))/om[0]) < 10.**tol, \
'Close-to-circular orbit does not have Or=kappa for actionAngleTorus'
assert numpy.fabs((om[1]-omegac(hp,rl(hp,jphi)))/om[1]) < 10.**tol, \
'Close-to-circular orbit does not have Ophi=omega for actionAngleTorus'
assert numpy.fabs((om[2]-verticalfreq(hp,rl(hp,jphi)))/om[2]) < 10.**tol, \
'Close-to-circular orbit does not have Oz=nu for actionAngleTorus'
return None
def test_actionAngleTorus_jacobian_hessian():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
fO= aAT.hessianFreqs(jr,jphi,jz)[0]
hO= aAT.xvJacobianFreqs(jr,jphi,jz,
numpy.array([0.]),numpy.array([1.]),
numpy.array([2.]))[2]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods hessianFreqs and xvJacobianFreqs return different Hessians'
return None
def test_actionAngleTorus_jacobian_hessian():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
fO= aAT.hessianFreqs(jr,jphi,jz)[0]
hO= aAT.xvJacobianFreqs(jr,jphi,jz,
numpy.array([0.]),numpy.array([1.]),
numpy.array([2.]))[2]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods hessianFreqs and xvJacobianFreqs return different Hessians'
return None
def test_actionAngleTorus_hessian_linear():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
h= aAT.hessianFreqs(jr,jphi,jz,tol=0.0001,nosym=True)[0]
dj= numpy.array([0.02,0.005,-0.01])
do_fromhessian= numpy.dot(h,dj)
O= numpy.array(aAT.Freqs(jr,jphi,jz)[:3])
do= numpy.array(aAT.Freqs(jr+dj[0],jphi+dj[1],jz+dj[2])[:3])-O
assert numpy.all(numpy.fabs((do_fromhessian-do)/O)< 0.001), 'actionAngleTorus Hessian does not return good approximation to dO/dJ'
return None
def test_actionAngleTorus_hessian_linear():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
h= aAT.hessianFreqs(jr,jphi,jz,tol=0.0001,nosym=True)[0]
dj= numpy.array([0.02,0.005,-0.01])
do_fromhessian= numpy.dot(h,dj)
O= numpy.array(aAT.Freqs(jr,jphi,jz)[:3])
do= numpy.array(aAT.Freqs(jr+dj[0],jphi+dj[1],jz+dj[2])[:3])-O
assert numpy.all(numpy.fabs((do_fromhessian-do)/O)< 0.001), 'actionAngleTorus Hessian does not return good approximation to dO/dJ'
return None
def test_actionAngleTorus_jacobian_xv():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.,1.])
anglephi= numpy.array([1.,2.])
anglez= numpy.array([2.,3.])
fO= aAT(jr,jphi,jz,angler,anglephi,anglez)
hO= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)[0]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods __call__ and xvJacobianFreqs return different xv'
return None
def test_actionAngleTorus_jacobian_detone():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014,dJ=0.0001)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.,1.])
anglephi= numpy.array([1.,2.])
anglez= numpy.array([2.,3.])
jf= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)
assert numpy.fabs(jf[0][0,0]*numpy.fabs(numpy.linalg.det(jf[1][0]))-1) < 0.01, 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not have the expected determinant'
assert numpy.fabs(jf[0][1,0]*numpy.fabs(numpy.linalg.det(jf[1][1]))-1) < 0.01, 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not have the expected determinant'
return None
def test_actionAngleTorus_jacobian_xv():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.,1.])
anglephi= numpy.array([1.,2.])
anglez= numpy.array([2.,3.])
fO= aAT(jr,jphi,jz,angler,anglephi,anglez)
hO= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)[0]
assert numpy.all(numpy.fabs(numpy.array(fO)-numpy.array(hO)) < 10.**-8.), 'actionAngleTorus methods __call__ and xvJacobianFreqs return different xv'
return None
def test_actionAngleTorus_jacobian_detone():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014,dJ=0.0001)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.,1.])
anglephi= numpy.array([1.,2.])
anglez= numpy.array([2.,3.])
jf= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)
assert numpy.fabs(jf[0][0,0]*numpy.fabs(numpy.linalg.det(jf[1][0]))-1) < 0.01, 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not have the expected determinant'
assert numpy.fabs(jf[0][1,0]*numpy.fabs(numpy.linalg.det(jf[1][1]))-1) < 0.01, 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not have the expected determinant'
return None
def test_MWPotential_warning_torus():
# Test that using MWPotential throws a warning, see #229
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential
warnings.simplefilter("error",galpyWarning)
try:
aAA= actionAngleTorus(pot=MWPotential)
except: pass
else:
raise AssertionError("actionAngleTorus with MWPotential should have thrown a warning, but didn't")
#Turn warnings back into warnings
warnings.simplefilter("always",galpyWarning)
return None
def test_MWPotential_warning_torus():
# Test that using MWPotential throws a warning, see #229
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential
if PY2: reset_warning_registry('galpy')
warnings.simplefilter("error",galpyWarning)
try:
aAA= actionAngleTorus(pot=MWPotential)
except: pass
else:
raise AssertionError("actionAngleTorus with MWPotential should have thrown a warning, but didn't")
#Turn warnings back into warnings
warnings.simplefilter("always",galpyWarning)
return None
def test_actionAngleTorus_jacobian_linear():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.5])
anglephi= numpy.array([1.])
anglez= numpy.array([2.])
jf= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)
xv= aAT(jr,jphi,jz,angler,anglephi,anglez)
dja= 2.*numpy.array([0.001,0.002,0.003,-0.002,0.004,0.002])
xv_direct= aAT(jr+dja[0],jphi+dja[1],jz+dja[2],
angler+dja[3],anglephi+dja[4],anglez+dja[5])
xv_fromjac= xv+numpy.dot(jf[1],dja)
assert numpy.all(numpy.fabs((xv_fromjac-xv_direct)/xv_direct) < 0.01), 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not appear to be correct'
return None
def test_actionAngleTorus_jacobian_linear():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
aAT= actionAngleTorus(pot=MWPotential2014)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.5])
anglephi= numpy.array([1.])
anglez= numpy.array([2.])
jf= aAT.xvJacobianFreqs(jr,jphi,jz,angler,anglephi,anglez)
xv= aAT(jr,jphi,jz,angler,anglephi,anglez)
dja= 2.*numpy.array([0.001,0.002,0.003,-0.002,0.004,0.002])
xv_direct= aAT(jr+dja[0],jphi+dja[1],jz+dja[2],
angler+dja[3],anglephi+dja[4],anglez+dja[5])
xv_fromjac= xv+numpy.dot(jf[1],dja)
assert numpy.all(numpy.fabs((xv_fromjac-xv_direct)/xv_direct) < 0.01), 'Jacobian returned by actionAngleTorus method xvJacobianFreqs does not appear to be correct'
return None
def test_actionAngleTorus_Staeckel_freqsAngles():
from galpy.potential import KuzminKutuzovStaeckelPotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleStaeckel
delta= 1.2
kp= KuzminKutuzovStaeckelPotential(normalize=1.,Delta=delta)
aAS= actionAngleStaeckel(pot=kp,delta=delta,c=True)
tol= -3.
aAT= actionAngleTorus(pot=kp,tol=tol)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.1])+numpy.linspace(0.,numpy.pi,101)
angler= angler % (2.*numpy.pi)
anglephi= numpy.array([numpy.pi])+numpy.linspace(0.,numpy.pi,101)
anglephi= anglephi % (2.*numpy.pi)
anglez= numpy.array([numpy.pi/2.])+numpy.linspace(0.,numpy.pi,101)
anglez= anglez % (2.*numpy.pi)
# Calculate position from aAT
RvRom= aAT.xvFreqs(jr,jphi,jz,angler,anglephi,anglez)
# Calculate actions, frequencies, and angles from aAI
ws= aAS.actionsFreqsAngles(*RvRom[0].T)
dOr= numpy.fabs((ws[3]-RvRom[1]))
dOp= numpy.fabs((ws[4]-RvRom[2]))
dOz= numpy.fabs((ws[5]-RvRom[3]))
dar= numpy.fabs((ws[6]-angler))
dap= numpy.fabs((ws[7]-anglephi))
daz= numpy.fabs((ws[8]-anglez))
dar[dar > numpy.pi]-= 2.*numpy.pi
dar[dar < -numpy.pi]+= 2.*numpy.pi
dap[dap > numpy.pi]-= 2.*numpy.pi
dap[dap < -numpy.pi]+= 2.*numpy.pi
daz[daz > numpy.pi]-= 2.*numpy.pi
daz[daz < -numpy.pi]+= 2.*numpy.pi
assert numpy.all(dOr < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Or at %f%%' % (numpy.nanmax(dOr)*100.)
assert numpy.all(dOp < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Ophi at %f%%' % (numpy.nanmax(dOp)*100.)
assert numpy.all(dOz < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Oz at %f%%' % (numpy.nanmax(dOz)*100.)
assert numpy.all(dar < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for ar at %f' % (numpy.nanmax(dar))
assert numpy.all(dap < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for aphi at %f' % (numpy.nanmax(dap))
assert numpy.all(daz < 10.**tol), 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for az at %f' % (numpy.nanmax(daz))
return None
def test_actionAngleTorus_orbit():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential2014
from galpy.orbit import Orbit
# Set up instance
aAT= actionAngleTorus(pot=MWPotential2014,tol=10.**-5.)
jr,jphi,jz= 0.05,1.1,0.025
# First calculate frequencies and the initial RvR
RvRom= aAT.xvFreqs(jr,jphi,jz,
numpy.array([0.]),
numpy.array([1.]),
numpy.array([2.]))
om= RvRom[1:]
# Angles along an orbit
ts= numpy.linspace(0.,100.,1001)
angler= ts*om[0]
anglephi= 1.+ts*om[1]
anglez= 2.+ts*om[2]
# Calculate the orbit using actionAngleTorus
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate the orbit using orbit integration
orb= Orbit([RvRom[0][:,0],RvRom[0][:,1],RvRom[0][:,2],
RvRom[0][:,3],RvRom[0][:,4],RvRom[0][:,5]])
orb.integrate(ts,MWPotential2014)
# Compare
tol= -3.
assert numpy.all(numpy.fabs(orb.R(ts)-RvR[0]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in R'
assert numpy.all(numpy.fabs(orb.vR(ts)-RvR[1]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vR'
assert numpy.all(numpy.fabs(orb.vT(ts)-RvR[2]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vT'
assert numpy.all(numpy.fabs(orb.z(ts)-RvR[3]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in z'
assert numpy.all(numpy.fabs(orb.vz(ts)-RvR[4]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vz'
assert numpy.all(numpy.fabs(orb.phi(ts)-RvR[5]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in phi'
return None
def test_actionAngleTorus_isochroneApprox_actions():
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochroneApprox
aAIA= actionAngleIsochroneApprox(pot=MWPotential2014,b=0.8)
tol= -2.5
aAT= actionAngleTorus(pot=MWPotential2014,tol=tol)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.])
anglephi= numpy.array([numpy.pi])
anglez= numpy.array([numpy.pi/2.])
# Calculate position from aAT
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate actions from aAIA
ji= aAIA(*RvR)
djr= numpy.fabs((ji[0]-jr)/jr)
dlz= numpy.fabs((ji[1]-jphi)/jphi)
djz= numpy.fabs((ji[2]-jz)/jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleIsochroneApprox applied to MWPotential2014 potential disagree for Jr at %f%%' % (djr*100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleIsochroneApprox applied to MWPotential2014 potential disagree for Jr at %f%%' % (dlz*100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleMWPotential2014 applied to MWPotential2014 potential disagree for Jr at %f%%' % (djz*100.)
return None
def test_actionAngleTorus_orbit():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential2014
from galpy.orbit import Orbit
# Set up instance
aAT= actionAngleTorus(pot=MWPotential2014,tol=10.**-5.)
jr,jphi,jz= 0.05,1.1,0.025
# First calculate frequencies and the initial RvR
RvRom= aAT.xvFreqs(jr,jphi,jz,
numpy.array([0.]),
numpy.array([1.]),
numpy.array([2.]))
om= RvRom[1:]
# Angles along an orbit
ts= numpy.linspace(0.,100.,1001)
angler= ts*om[0]
anglephi= 1.+ts*om[1]
anglez= 2.+ts*om[2]
# Calculate the orbit using actionAngleTorus
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate the orbit using orbit integration
orb= Orbit([RvRom[0][:,0],RvRom[0][:,1],RvRom[0][:,2],
RvRom[0][:,3],RvRom[0][:,4],RvRom[0][:,5]])
orb.integrate(ts,MWPotential2014)
# Compare
tol= -3.
assert numpy.all(numpy.fabs(orb.R(ts)-RvR[0]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in R'
assert numpy.all(numpy.fabs(orb.vR(ts)-RvR[1]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vR'
assert numpy.all(numpy.fabs(orb.vT(ts)-RvR[2]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vT'
assert numpy.all(numpy.fabs(orb.z(ts)-RvR[3]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in z'
assert numpy.all(numpy.fabs(orb.vz(ts)-RvR[4]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vz'
assert numpy.all(numpy.fabs(orb.phi(ts)-RvR[5]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in phi'
return None
def test_actionAngleTorus_Isochrone_freqsAngles():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
tol= -6.
aAT= actionAngleTorus(pot=ip,tol=tol)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.1])+numpy.linspace(0.,numpy.pi,101)
angler= angler % (2.*numpy.pi)
anglephi= numpy.array([numpy.pi])+numpy.linspace(0.,numpy.pi,101)
anglephi= anglephi % (2.*numpy.pi)
anglez= numpy.array([numpy.pi/2.])+numpy.linspace(0.,numpy.pi,101)
anglez= anglez % (2.*numpy.pi)
# Calculate position from aAT
RvRom= aAT.xvFreqs(jr,jphi,jz,angler,anglephi,anglez)
# Calculate actions, frequencies, and angles from aAI
ws= aAI.actionsFreqsAngles(*RvRom[0].T)
dOr= numpy.fabs((ws[3]-RvRom[1]))
dOp= numpy.fabs((ws[4]-RvRom[2]))
dOz= numpy.fabs((ws[5]-RvRom[3]))
dar= numpy.fabs((ws[6]-angler))
dap= numpy.fabs((ws[7]-anglephi))
daz= numpy.fabs((ws[8]-anglez))
dar[dar > numpy.pi]-= 2.*numpy.pi
dar[dar < -numpy.pi]+= 2.*numpy.pi
dap[dap > numpy.pi]-= 2.*numpy.pi
dap[dap < -numpy.pi]+= 2.*numpy.pi
daz[daz > numpy.pi]-= 2.*numpy.pi
daz[daz < -numpy.pi]+= 2.*numpy.pi
assert numpy.all(dOr < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Or at %f%%' % (numpy.nanmax(dOr)*100.)
assert numpy.all(dOp < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Ophi at %f%%' % (numpy.nanmax(dOp)*100.)
assert numpy.all(dOz < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Oz at %f%%' % (numpy.nanmax(dOz)*100.)
assert numpy.all(dar < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for ar at %f' % (numpy.nanmax(dar))
assert numpy.all(dap < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for aphi at %f' % (numpy.nanmax(dap))
assert numpy.all(daz < 10.**tol), 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for az at %f' % (numpy.nanmax(daz))
return None
def test_actionAngleTorus_Isochrone_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
tol= -6.
aAT= actionAngleTorus(pot=ip,tol=tol)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.])
anglephi= numpy.array([numpy.pi])
anglez= numpy.array([numpy.pi/2.])
# Calculate position from aAT
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate actions from aAI
ji= aAI(*RvR)
djr= numpy.fabs((ji[0]-jr)/jr)
dlz= numpy.fabs((ji[1]-jphi)/jphi)
djz= numpy.fabs((ji[2]-jz)/jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (djr*100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (dlz*100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleIsochrone applied to isochrone potential disagree for Jr at %f%%' % (djz*100.)
return None
def test_actionAngleTorus_Staeckel_actions():
from galpy.potential import KuzminKutuzovStaeckelPotential
from galpy.actionAngle import actionAngleTorus, \
actionAngleStaeckel
delta= 1.2
kp= KuzminKutuzovStaeckelPotential(normalize=1.,Delta=delta)
aAS= actionAngleStaeckel(pot=kp,delta=delta,c=True)
tol= -3.
aAT= actionAngleTorus(pot=kp,tol=tol)
jr,jphi,jz= 0.075,1.1,0.05
angler= numpy.array([0.])
anglephi= numpy.array([numpy.pi])
anglez= numpy.array([numpy.pi/2.])
# Calculate position from aAT
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate actions from aAI
ji= aAS(*RvR)
djr= numpy.fabs((ji[0]-jr)/jr)
dlz= numpy.fabs((ji[1]-jphi)/jphi)
djz= numpy.fabs((ji[2]-jz)/jz)
assert djr < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (djr*100.)
assert dlz < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (dlz*100.)
assert djz < 10.**tol, 'actionAngleTorus and actionAngleStaeckel applied to Staeckel potential disagree for Jr at %f%%' % (djz*100.)
return None
def setup_sdf(
pot: Sequence[Potential],
prog: Orbit,
sigv: float,
td: float,
ro: float = REFR0,
vo: float = REFV0,
multi: Optional[Any] = None,
nTrackChunks: int = 8,
isob: Optional[bool] = None,
trailing_only: bool = False,
verbose: bool = True,
useTM: bool = True,
logpot: bool = False,
):
"""Simple function to setup the stream model."""
if isob is None:
if True or logpot: # FIXME, "if True"
isob = 0.75
if isob is False: # FIXME, was "if False"
# Determine good one
ts = np.linspace(0.0, 15.0, 1001)
# Hack!
epot = copy.deepcopy(pot)
epot[2]._b = 1.0
epot[2]._b2 = 1.0
epot[2]._isNonAxi = False
epot[2]._aligned = True
prog.integrate(ts, pot)
estb = estimateBIsochrone(
epot,
prog.R(ts, use_physical=False),
prog.z(ts, use_physical=False),
phi=prog.phi(ts, use_physical=False),
)
if estb[1] < 0.3:
isob = 0.3
elif estb[1] > 1.5:
isob = 1.5
else:
isob = estb[1]
if verbose:
print(pot[2]._c, isob, estb)
if not logpot and np.fabs(pot[2]._b - 1.0) > 0.05:
aAI = actionAngleIsochroneApprox(pot=pot, b=isob, tintJ=1000.0, ntintJ=30000)
else:
ts = np.linspace(0.0, 100.0, 10000)
aAI = actionAngleIsochroneApprox(
pot=pot, b=isob, tintJ=100.0, ntintJ=10000, dt=ts[1] - ts[0]
)
if useTM:
aAT = actionAngleTorus(pot=pot, tol=0.001, dJ=0.0001)
else:
aAT = False
try:
sdf = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TKOP,
multi=multi,
nospreadsetup=True,
)
except np.linalg.LinAlgError:
sdf = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
nTrackIterations=0,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TKOP,
multi=multi,
)
return sdf
def setup_sdf(
pot: potential.Potential,
prog: Orbit,
sigv: float,
td: float,
ro: float = REFR0,
vo: float = REFV0,
multi: Optional[bool] = None,
nTrackChunks: float = 8,
isob=None,
trailing_only: bool = False,
verbose: bool = True,
useTM: bool = True,
) -> Tuple[Optional[streamdf], Optional[streamdf]]:
"""Setup Stream Distribution Function.
Parameters
----------
pot : Potential
prog : Orbit
Progenitor
sigv : float
td : float
ro : float
vo : float
multi
default None
nTrackChunks: float
default 8
isob
default None
trailing_only: bool
default False
verbose: bool
default True
useTM: bool
default True
Returns
-------
sdf_trailing, sdf_leading: streamdf or None
"""
if isob is None:
# Determine good one
ts = np.linspace(0.0, 150.0, 1001)
# Hack!
epot = copy.deepcopy(pot)
epot[2]._b = 1.0
epot[2]._b2 = 1.0
epot[2]._isNonAxi = False
epot[2]._aligned = True
prog.integrate(ts, pot)
estb = estimateBIsochrone(
epot,
prog.R(ts, use_physical=False),
prog.z(ts, use_physical=False),
phi=prog.phi(ts, use_physical=False),
)
if estb[1] < 0.3:
isob = 0.3
elif estb[1] > 1.5:
isob = 1.5
else:
isob = estb[1]
if verbose:
print(pot[2]._c, isob)
if np.fabs(pot[2]._b - 1.0) > 0.05:
aAI = actionAngleIsochroneApprox(pot=pot,
b=isob,
tintJ=1000.0,
ntintJ=30000)
else:
aAI = actionAngleIsochroneApprox(pot=pot, b=isob)
if useTM:
aAT = actionAngleTorus(pot=pot, tol=0.001, dJ=0.0001)
else:
aAT = False
trailing_kwargs = dict(
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=False,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TPAL5,
multi=multi,
)
try:
sdf_trailing = streamdf(sigv / vo, **trailing_kwargs)
except np.linalg.LinAlgError:
sdf_trailing = streamdf(sigv / vo,
nTrackIterations=0,
**trailing_kwargs)
if trailing_only:
sdf_leading = None
else:
leading_kwargs = dict(
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TPAL5,
multi=multi,
)
try:
sdf_leading = streamdf(sigv / vo, **leading_kwargs)
except np.linalg.LinAlgError:
sdf_leading = streamdf(sigv / vo,
nTrackIterations=0,
**leading_kwargs)
return sdf_trailing, sdf_leading
- https://galpy.readthedocs.io/en/v1.4.0/actionAngle.html#actionanglestaeckel
- https://galpy.readthedocs.io/en/v1.4.0/orbit.html#fastchar
- https://galpy.readthedocs.io/en/v1.4.0/actionAngle.html#accessing-action-angle-coordinates-for-orbit-instances
"""
import numpy as np
from galpy.orbit import Orbit
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential2014
import sys
sys.path.insert(0, '..')
import chronostar.traceorbit as torb
xyzuvw_start = [0., 0., 25., 0., 0., 0.]
print('xyzuvw start: {}'.format(xyzuvw_start))
galpy_coords = torb.convert_cart2galpycoords(xyzuvw_start)
print('galpy start: {}'.format(galpy_coords))
aAT = actionAngleTorus(pot=MWPotential2014)
o = Orbit(vxvv=galpy_coords, ro=8., vo=220.)
o.e(analytic=True, type='staeckel', pot=MWPotential2014)
aAS = actionAngleStaeckel(pot=mp, delta=0.4)
# Om= aAT.Freqs(jr,lz,jz)