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test_actionAngle.py
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test_actionAngle.py
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from __future__ import print_function, division
import os
import sys
import pytest
import warnings
import numpy
from galpy.util import galpyWarning
_TRAVIS= bool(os.getenv('TRAVIS'))
PY2= sys.version < '3'
# Print all galpyWarnings always for tests of warnings
warnings.simplefilter("always",galpyWarning)
#Basic sanity checking of the actionAngleIsochrone actions
def test_actionAngleIsochrone_basic_actions():
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
aAI= actionAngleIsochrone(b=1.2)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAI(R,vR,vT,z,vz)
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the isochrone potential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the isochrone potential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAI(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the isochrone potential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-4., 'Close-to-circular orbit in the isochrone potential does not have small Jz'
#Close-to-circular orbit, called with time
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAI(Orbit([R,vR,vT,z,vz]),0.)
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the isochrone potential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-4., 'Close-to-circular orbit in the isochrone potential does not have small Jz'
return None
#Basic sanity checking of the actionAngleIsochrone actions
def test_actionAngleIsochrone_basic_freqs():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
jos= aAI.actionsFreqs(R,vR,vT,z,vz)
assert numpy.fabs((jos[3]-ip.epifreq(1.))/ip.epifreq(1.)) < 10.**-12., 'Circular orbit in the isochrone potential does not have Or=kappa at %g%%' % (100.*numpy.fabs((jos[3]-ip.epifreq(1.))/ip.epifreq(1.)))
assert numpy.fabs((jos[4]-ip.omegac(1.))/ip.omegac(1.)) < 10.**-12., 'Circular orbit in the isochrone potential does not have Op=Omega at %g%%' % (100.*numpy.fabs((jos[4]-ip.omegac(1.))/ip.omegac(1.)))
assert numpy.fabs((jos[5]-ip.verticalfreq(1.))/ip.verticalfreq(1.)) < 10.**-12., 'Circular orbit in the isochrone potential does not have Oz=nu at %g%%' % (100.*numpy.fabs((jos[5]-ip.verticalfreq(1.))/ip.verticalfreq(1.)))
#close-to-circular orbit
R,vR,vT,z,vz= 1.,0.01,1.01,0.01,0.01
jos= aAI.actionsFreqs(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs((jos[3]-ip.epifreq(1.))/ip.epifreq(1.)) < 10.**-2., 'Close-to-circular orbit in the isochrone potential does not have Or=kappa at %g%%' % (100.*numpy.fabs((jos[3]-ip.epifreq(1.))/ip.epifreq(1.)))
assert numpy.fabs((jos[4]-ip.omegac(1.))/ip.omegac(1.)) < 10.**-2., 'Close-to-circular orbit in the isochrone potential does not have Op=Omega at %g%%' % (100.*numpy.fabs((jos[4]-ip.omegac(1.))/ip.omegac(1.)))
assert numpy.fabs((jos[5]-ip.verticalfreq(1.))/ip.verticalfreq(1.)) < 10.**-2., 'Close-to-circular orbit in the isochrone potential does not have Oz=nu at %g%%' % (100.*numpy.fabs((jos[5]-ip.verticalfreq(1.))/ip.verticalfreq(1.)))
return None
# Test that EccZmaxRperiRap for an IsochronePotential are correctly computed
# by comparing to a numerical orbit integration
def test_actionAngleIsochrone_EccZmaxRperiRap_againstOrbit():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
o= Orbit([1.,0.1,1.1,0.2,0.03,0.])
ecc, zmax, rperi, rap= aAI.EccZmaxRperiRap(o)
ts= numpy.linspace(0.,100.,100001)
o.integrate(ts,ip)
assert numpy.fabs(ecc-o.e()) < 1e-10, 'Analytically calculated eccentricity does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(zmax-o.zmax()) < 1e-5, 'Analytically calculated zmax does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(rperi-o.rperi()) < 1e-10, 'Analytically calculated rperi does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(rap-o.rap()) < 1e-10, 'Analytically calculated rap does not agree with numerically calculated one for an IsochronePotential'
# Another one
o= Orbit([1.,0.1,1.1,0.2,-0.3,0.])
ecc, zmax, rperi, rap= aAI.EccZmaxRperiRap(o.R(),o.vR(),o.vT(),
o.z(),o.vz(),o.phi())
ts= numpy.linspace(0.,100.,100001)
o.integrate(ts,ip)
assert numpy.fabs(ecc-o.e()) < 1e-10, 'Analytically calculated eccentricity does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(zmax-o.zmax()) < 1e-3, 'Analytically calculated zmax does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(rperi-o.rperi()) < 1e-10, 'Analytically calculated rperi does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(rap-o.rap()) < 1e-10, 'Analytically calculated rap does not agree with numerically calculated one for an IsochronePotential'
return None
# Test that EccZmaxRperiRap for an IsochronePotential are correctly computed
# by comparing to a numerical orbit integration for a Kepler potential
def test_actionAngleIsochrone_EccZmaxRperiRap_againstOrbit_kepler():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=0)
aAI= actionAngleIsochrone(ip=ip)
o= Orbit([1.,0.1,1.1,0.2,0.03,0.])
ecc, zmax, rperi, rap= aAI.EccZmaxRperiRap(o.R(),o.vR(),o.vT(),o.z(),o.vz())
ts= numpy.linspace(0.,100.,100001)
o.integrate(ts,ip)
assert numpy.fabs(ecc-o.e()) < 1e-10, 'Analytically calculated eccentricity does not agree with numerically calculated one for an IsochronePotential'
# Don't do zmax, because zmax for Kepler is approximate
assert numpy.fabs(rperi-o.rperi()) < 1e-10, 'Analytically calculated rperi does not agree with numerically calculated one for an IsochronePotential'
assert numpy.fabs(rap-o.rap()) < 1e-10, 'Analytically calculated rap does not agree with numerically calculated one for an IsochronePotential'
return None
#Test the actions of an actionAngleIsochrone
def test_actionAngleIsochrone_conserved_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_conserved_actions(aAI,obs,ip,-5.,-5.,-5.)
else:
check_actionAngle_conserved_actions(aAI,obs,ip,-8.,-8.,-8.)
return None
#Test that the angles of an actionAngleIsochrone increase linearly
def test_actionAngleIsochrone_linear_angles():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_linear_angles(aAI,obs,ip,
-5.,-5.,-5.,
-6.,-6.,-6.,
-5.,-5.,-5.)
else:
check_actionAngle_linear_angles(aAI,obs,ip,
-6.,-6.,-6.,
-8.,-8.,-8.,
-8.,-8.,-8.)
return None
#Test that the Kelperian limit of the isochrone actions/angles works
def test_actionAngleIsochrone_kepler_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=0.)
aAI= actionAngleIsochrone(ip=ip)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
times= numpy.linspace(0.,100.,101)
obs.integrate(times,ip,method='dopr54_c')
jrs,jps,jzs= aAI(obs.R(times),obs.vR(times),obs.vT(times),
obs.z(times),obs.vz(times),obs.phi(times))
jc= ip._amp/numpy.sqrt(-2.*obs.E())
L= numpy.sqrt(numpy.sum(obs.L()**2.))
# Jr = Jc-L
assert numpy.all(numpy.fabs(jrs-(jc-L)) < 10.**-5.), 'Radial action for the Kepler potential not correct'
assert numpy.all(numpy.fabs(jps-obs.R()*obs.vT()) < 10.**-10.), 'Azimuthal action for the Kepler potential not correct'
assert numpy.all(numpy.fabs(jzs-(L-numpy.fabs(obs.R()*obs.vT()))) < 10.**-10.), 'Vertical action for the Kepler potential not correct'
return None
def test_actionAngleIsochrone_kepler_freqs():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=0.)
aAI= actionAngleIsochrone(ip=ip)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
times= numpy.linspace(0.,100.,101)
obs.integrate(times,ip,method='dopr54_c')
_, _, _, ors,ops,ozs= aAI.actionsFreqs(obs.R(times),obs.vR(times),
obs.vT(times),obs.z(times),
obs.vz(times),obs.phi(times))
jc= ip._amp/numpy.sqrt(-2.*obs.E())
oc= ip._amp**2./jc**3. # (BT08 eqn. E4)
assert numpy.all(numpy.fabs(ors-oc) < 10.**-10.), 'Radial frequency for the Kepler potential not correct'
assert numpy.all(numpy.fabs(ops-oc) < 10.**-10.), 'Azimuthal frequency for the Kepler potential not correct'
assert numpy.all(numpy.fabs(ozs-numpy.sign(obs.R()*obs.vT())*oc) < 10.**-10.), 'Vertical frequency for the Kepler potential not correct'
return None
def test_actionAngleIsochrone_kepler_angles():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=0.)
aAI= actionAngleIsochrone(ip=ip)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
times= numpy.linspace(0.,100.,101)
obs.integrate(times,ip,method='dopr54_c')
_, _, _, _, _, _,ars,aps,azs= \
aAI.actionsFreqsAngles(obs.R(times),obs.vR(times),
obs.vT(times),obs.z(times),
obs.vz(times),obs.phi(times))
jc= ip._amp/numpy.sqrt(-2.*obs.E())
oc= ip._amp**2./jc**3. # (BT08 eqn. E4)
# theta_r = Or x times + theta_r,0
assert numpy.all(numpy.fabs(ars-oc*times-ars[0]) < 10.**-10.), 'Radial angle for the Kepler potential not correct'
assert numpy.all(numpy.fabs(aps-oc*times-aps[0]) < 10.**-10.), 'Azimuthal angle for the Kepler potential not correct'
assert numpy.all(numpy.fabs(azs-oc*times-azs[0]) < 10.**-10.), 'Vertical angle for the Kepler potential not correct'
return None
#Basic sanity checking of the actionAngleSpherical actions
def test_actionAngleSpherical_basic_actions():
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
from galpy.potential import LogarithmicHaloPotential
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(Orbit([R,vR,vT]))
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the spherical LogarithmicHaloPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the spherical LogarithmicHaloPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz])._orb) #with OrbitTop
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-4., 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleSpherical actions
def test_actionAngleSpherical_basic_freqs():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=[lp])
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
jos= aAS.actionsFreqs(R,vR,vT,z,vz)
assert numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)) < 10.**-12., 'Circular orbit in the spherical LogarithmicHaloPotential does not have Or=kappa at %g%%' % (100.*numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)))
assert numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)) < 10.**-12., 'Circular orbit in the spherical LogarithmicHaloPotential does not have Op=Omega at %g%%' % (100.*numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)))
assert numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)) < 10.**-12., 'Circular orbit in the spherical LogarithmicHaloPotential does not have Oz=nu at %g%%' % (100.*numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)))
#close-to-circular orbit
R,vR,vT,z,vz= 1.,0.01,1.01,0.01,0.01
jos= aAS.actionsFreqs(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Or=kappa at %g%%' % (100.*numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)))
assert numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Op=Omega at %g%%' % (100.*numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)))
assert numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Oz=nu at %g%%' % (100.*numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)))
#Basic sanity checking of the actionAngleSpherical actions
def test_actionAngleSpherical_basic_freqsAngles():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
#v. close-to-circular orbit using actionsFreqsAngles
R,vR,vT,z,vz= 1.,10.**-8.,1.,10.**-8.,0.
jos= aAS.actionsFreqsAngles(R,vR,vT,z,vz,0.)
assert numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Or=kappa at %g%%' % (100.*numpy.fabs((jos[3]-lp.epifreq(1.))/lp.epifreq(1.)))
assert numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Op=Omega at %g%%' % (100.*numpy.fabs((jos[4]-lp.omegac(1.))/lp.omegac(1.)))
assert numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)) < 10.**-1.9, 'Close-to-circular orbit in the spherical LogarithmicHaloPotential does not have Oz=nu at %g%%' % (100.*numpy.fabs((jos[5]-lp.verticalfreq(1.))/lp.verticalfreq(1.)))
return None
# Test that EccZmaxRperiRap for a spherical potential are correctly computed
# by comparing to a numerical orbit integration
def test_actionAngleSpherical_EccZmaxRperiRap_againstOrbit():
from galpy.potential import LogarithmicHaloPotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleSpherical
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
o= Orbit([1.,0.1,1.1,0.2,0.03,0.])
ecc, zmax, rperi, rap= aAS.EccZmaxRperiRap(o)
ts= numpy.linspace(0.,100.,100001)
o.integrate(ts,lp)
assert numpy.fabs(ecc-o.e()) < 1e-9, 'Analytically calculated eccentricity does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(zmax-o.zmax()) < 1e-4, 'Analytically calculated zmax does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(rperi-o.rperi()) < 1e-8, 'Analytically calculated rperi does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(rap-o.rap()) < 1e-8, 'Analytically calculated rap does not agree with numerically calculated one for a spherical potential'
# Another one
o= Orbit([1.,0.1,1.1,0.2,-0.3,0.])
ecc, zmax, rperi, rap= aAS.EccZmaxRperiRap(o.R(),o.vR(),o.vT(),
o.z(),o.vz())
ts= numpy.linspace(0.,100.,100001)
o.integrate(ts,lp)
assert numpy.fabs(ecc-o.e()) < 1e-9, 'Analytically calculated eccentricity does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(zmax-o.zmax()) < 1e-3, 'Analytically calculated zmax does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(rperi-o.rperi()) < 1e-8, 'Analytically calculated rperi does not agree with numerically calculated one for a spherical potential'
assert numpy.fabs(rap-o.rap()) < 1e-8, 'Analytically calculated rap does not agree with numerically calculated one for a spherical potential'
return None
#Test the actions of an actionAngleSpherical
def test_actionAngleSpherical_conserved_actions():
from galpy import potential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= potential.LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_conserved_actions(aAS,obs,lp,-5.,-5.,-5.,ntimes=101)
else:
check_actionAngle_conserved_actions(aAS,obs,lp,-8.,-8.,-8.,ntimes=101)
return None
#Test the actions of an actionAngleSpherical
def test_actionAngleSpherical_conserved_actions_fixed_quad():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_conserved_actions(aAS,obs,lp,-5.,-5.,-5.,ntimes=101,
fixed_quad=True)
else:
check_actionAngle_conserved_actions(aAS,obs,lp,-8.,-8.,-8.,ntimes=101,
fixed_quad=True)
return None
#Test that the angles of an actionAngleIsochrone increase linearly
def test_actionAngleSpherical_linear_angles():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_linear_angles(aAS,obs,lp,
-4.,-4.,-4.,
-4.,-4.,-4.,
-4.,-4.,-4.,
ntimes=501) #need fine sampling for de-period
else:
check_actionAngle_linear_angles(aAS,obs,lp,
-6.,-6.,-6.,
-8.,-8.,-8.,
-8.,-8.,-8.,
ntimes=501) #need fine sampling for de-period
return None
#Test that the angles of an actionAngleIsochrone increase linearly
def test_actionAngleSpherical_linear_angles_fixed_quad():
from galpy.potential import LogarithmicHaloPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
lp= LogarithmicHaloPotential(normalize=1.,q=1.)
aAS= actionAngleSpherical(pot=lp)
obs= Orbit([1.1, 0.3, 1.2, 0.2,0.5,2.])
from galpy.orbit.FullOrbit import ext_loaded
if not ext_loaded: #odeint is not as accurate as dopr54_c
check_actionAngle_linear_angles(aAS,obs,lp,
-4.,-4.,-4.,
-4.,-4.,-4.,
-4.,-4.,-4.,
ntimes=501, #need fine sampling for de-period
fixed_quad=True)
else:
check_actionAngle_linear_angles(aAS,obs,lp,
-6.,-6.,-6.,
-8.,-8.,-8.,
-8.,-8.,-8.,
ntimes=501, #need fine sampling for de-period
fixed_quad=True)
return None
#Test the conservation of ecc, zmax, rperi, rap of an actionAngleSpherical
def test_actionAngleSpherical_conserved_EccZmaxRperiRap_ecc():
from galpy.potential import NFWPotential
from galpy.actionAngle import actionAngleSpherical
from galpy.orbit import Orbit
np= NFWPotential(normalize=1.,a=2.)
aAS= actionAngleSpherical(pot=np)
obs= Orbit([1.1,0.2, 1.3, 0.1,0.,2.])
check_actionAngle_conserved_EccZmaxRperiRap(aAS,obs,np,
-1.1,-0.4,-1.8,-1.8,ntimes=101,
inclphi=True)
return None
#Test the actionAngleSpherical against an isochrone potential: actions
def test_actionAngleSpherical_otherIsochrone_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleSpherical, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAS= actionAngleSpherical(pot=ip)
R,vR,vT,z,vz,phi= 1.1, 0.3, 1.2, 0.2,0.5,2.
ji= aAI(R,vR,vT,z,vz,phi)
jia= aAS(R,vR,vT,z,vz,phi)
djr= numpy.fabs((ji[0]-jia[0])/ji[0])
dlz= numpy.fabs((ji[1]-jia[1])/ji[1])
djz= numpy.fabs((ji[2]-jia[2])/ji[2])
assert djr < 10.**-10., 'actionAngleSpherical applied to isochrone potential fails for Jr at %g%%' % (djr*100.)
#Lz and Jz are easy, because ip is a spherical potential
assert dlz < 10.**-10., 'actionAngleSpherical applied to isochrone potential fails for Lz at %g%%' % (dlz*100.)
assert djz < 10.**-10., 'actionAngleSpherical applied to isochrone potential fails for Jz at %g%%' % (djz*100.)
return None
#Test the actionAngleSpherical against an isochrone potential: frequencies
def test_actionAngleSpherical_otherIsochrone_freqs():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleSpherical, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAS= actionAngleSpherical(pot=ip)
R,vR,vT,z,vz,phi= 1.1, 0.3, 1.2, 0.2,0.5,2.
jiO= aAI.actionsFreqs(R,vR,vT,z,vz,phi)
jiaO= aAS.actionsFreqs(R,vR,vT,z,vz,phi)
dOr= numpy.fabs((jiO[3]-jiaO[3])/jiO[3])
dOp= numpy.fabs((jiO[4]-jiaO[4])/jiO[4])
dOz= numpy.fabs((jiO[5]-jiaO[5])/jiO[5])
assert dOr < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Or at %g%%' % (dOr*100.)
assert dOp < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Op at %g%%' % (dOp*100.)
assert dOz < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Oz at %g%%' % (dOz*100.)
return None
#Test the actionAngleSpherical against an isochrone potential: frequencies
def test_actionAngleSpherical_otherIsochrone_freqs_fixed_quad():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleSpherical, \
actionAngleIsochrone
from galpy.orbit import Orbit
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAS= actionAngleSpherical(pot=ip)
R,vR,vT,z,vz,phi= 1.1, 0.3, 1.2, 0.2,0.5,2.
jiO= aAI.actionsFreqs(R,vR,vT,z,vz,phi)
jiaO= aAS.actionsFreqs(Orbit([R,vR,vT,z,vz,phi]),fixed_quad=True)
dOr= numpy.fabs((jiO[3]-jiaO[3])/jiO[3])
dOp= numpy.fabs((jiO[4]-jiaO[4])/jiO[4])
dOz= numpy.fabs((jiO[5]-jiaO[5])/jiO[5])
assert dOr < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Or at %g%%' % (dOr*100.)
assert dOp < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Op at %g%%' % (dOp*100.)
assert dOz < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for Oz at %g%%' % (dOz*100.)
return None
#Test the actionAngleSpherical against an isochrone potential: angles
def test_actionAngleSpherical_otherIsochrone_angles():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleSpherical, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAS= actionAngleSpherical(pot=ip,b=0.8)
R,vR,vT,z,vz,phi= 1.1, 0.3, 1.2, 0.2,0.5,2.
jiO= aAI.actionsFreqsAngles(R,vR,vT,z,vz,phi)
jiaO= aAS.actionsFreqsAngles(R,vR,vT,z,vz,phi)
dar= numpy.fabs((jiO[6]-jiaO[6])/jiO[6])
dap= numpy.fabs((jiO[7]-jiaO[7])/jiO[7])
daz= numpy.fabs((jiO[8]-jiaO[8])/jiO[8])
assert dar < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for ar at %g%%' % (dar*100.)
assert dap < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for ap at %g%%' % (dap*100.)
assert daz < 10.**-6., 'actionAngleSpherical applied to isochrone potential fails for az at %g%%' % (daz*100.)
return None
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabatic_basic_actions():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAA= actionAngleAdiabatic(pot=MWPotential,gamma=1.)
#circular orbit
R,vR,vT,phi= 1.,0.,1.,2.
js= aAA(Orbit([R,vR,vT,phi]))
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,0.99,0.0,0.0
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,1.01,0.0,0.0
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
return None
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabatic_basic_actions_gamma0():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAA= actionAngleAdiabatic(pot=[MWPotential[0],MWPotential[1:]],gamma=0.)
#circular orbit
R,vR,vT,phi= 1.,0.,1.,2.
js= aAA(Orbit([R,vR,vT,phi]))
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,0.99,0.0,0.0
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,1.01,0.0,0.0
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
return None
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabatic_basic_actions_c():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
from galpy.potential import MWPotential
# test nested list of potentials
aAA= actionAngleAdiabatic(pot=[MWPotential[0],MWPotential[1:]],c=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAA(R,vR,vT,z,vz)
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabatic_unboundz_actions_c():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.potential import MWPotential
aAA= actionAngleAdiabatic(pot=MWPotential,c=True,gamma=0.)
#Unbound in z, so jz should be very large
R,vR,vT,z,vz= 1.,0.,1.,0., 10.
js= aAA(R,vR,vT,z,vz)
assert js[2] > 1000., 'Unbound orbit in z in the MWPotential does not have large Jz'
return None
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabatic_zerolz_actions_c():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.potential import MWPotential
aAA= actionAngleAdiabatic(pot=MWPotential,c=True,gamma=0.)
#Zero angular momentum, so rperi=0, but should have finite jr
R,vR,vT,z,vz= 1.,0.,0.,0., 0.
js= aAA(R,vR,vT,z,vz)
R,vR,vT,z,vz= 1.,0.,0.0000001,0., 0.
js2= aAA(R,vR,vT,z,vz)
assert numpy.fabs(js[0]-js2[0]) < 10.**-6., 'Orbit with zero angular momentum does not have the correct Jr'
#Zero angular momentum, so rperi=0, but should have finite jr
R,vR,vT,z,vz= 1.,-0.5,0.,0., 0.
js= aAA(R,vR,vT,z,vz)
R,vR,vT,z,vz= 1.,-0.5,0.0000001,0., 0.
js2= aAA(R,vR,vT,z,vz)
assert numpy.fabs(js[0]-js2[0]) < 10.**-6., 'Orbit with zero angular momentum does not have the correct Jr'
return None
#Basic sanity checking of the actionAngleAdiabatic ecc, zmax, rperi, rap calc.
def test_actionAngleAdiabatic_basic_EccZmaxRperiRap():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.potential import MWPotential
aAA= actionAngleAdiabatic(pot=MWPotential,gamma=1.)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-16., 'Circular orbit in the MWPotential does not have e=0'
assert numpy.fabs(tzmax) < 10.**-16., 'Circular orbit in the MWPotential does not have zmax=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-2., 'Close-to-circular orbit in the MWPotential does not have small eccentricity'
assert numpy.fabs(tzmax) < 2.*10.**-2., 'Close-to-circular orbit in the MWPotential does not have small zmax'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,0.99,0.0,0.0
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-2., 'Close-to-circular orbit in the MWPotential does not have small eccentricity'
assert numpy.fabs(tzmax) < 2.*10.**-2., 'Close-to-circular orbit in the MWPotential does not have small zmax'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,1.,0.01,0.0
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-2., 'Close-to-circular orbit in the MWPotential does not have small eccentricity'
assert numpy.fabs(tzmax) < 2.*10.**-2., 'Close-to-circular orbit in the MWPotential does not have small zmax'
return None
#Basic sanity checking of the actionAngleAdiabatic ecc, zmax, rperi, rap calc.
def test_actionAngleAdiabatic_basic_EccZmaxRperiRap_gamma0():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.potential import MiyamotoNagaiPotential
mp= MiyamotoNagaiPotential(normalize=1.,a=1.5,b=0.3)
aAA= actionAngleAdiabatic(pot=mp,gamma=0.,c=False)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-16., 'Circular orbit in the MWPotential does not have e=0'
assert numpy.fabs(tzmax) < 10.**-16., 'Circular orbit in the MWPotential does not have zmax=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz)
assert numpy.fabs(te) < 10.**-2., 'Close-to-circular orbit in the MWPotential does not have small eccentricity'
assert numpy.fabs(tzmax) < 2.*10.**-2., 'Close-to-circular orbit in the MWPotential does not have small zmax'
return None
#Basic sanity checking of the actionAngleAdiabatic ecc, zmax, rperi, rap calc.
def test_actionAngleAdiabatic_basic_EccZmaxRperiRap_gamma_c():
from galpy.actionAngle import actionAngleAdiabatic
from galpy.potential import MWPotential
from galpy.orbit import Orbit
aAA= actionAngleAdiabatic(pot=MWPotential,gamma=1.,c=True)
#circular orbit
R,vR,vT,z,vz,phi= 1.,0.,1.,0.,0.,2.
te,tzmax,_,_= aAA.EccZmaxRperiRap(Orbit([R,vR,vT,z,vz,phi]))
assert numpy.fabs(te) < 10.**-16., 'Circular orbit in the MWPotential does not have e=0'
assert numpy.fabs(tzmax) < 10.**-16., 'Circular orbit in the MWPotential does not have zmax=0'
#Close-to-circular orbit
R,vR,vT,z,vz,phi= 1.01,0.01,1.,0.01,0.01,2.
te,tzmax,_,_= aAA.EccZmaxRperiRap(R,vR,vT,z,vz,phi)
assert numpy.fabs(te) < 10.**-2., 'Close-to-circular orbit in the MWPotential does not have small eccentricity'
assert numpy.fabs(tzmax) < 2.*10.**-2., 'Close-to-circular orbit in the MWPotential does not have small zmax'
return None
#Test the actions of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_actions():
from galpy.potential import MWPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
aAA= actionAngleAdiabatic(pot=MWPotential,c=False)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.])
check_actionAngle_conserved_actions(aAA,obs,MWPotential,
-1.2,-8.,-1.7,ntimes=101)
return None
#Test the actions of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_actions_c():
from galpy.potential import MWPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.])
aAA= actionAngleAdiabatic(pot=MWPotential,c=True)
check_actionAngle_conserved_actions(aAA,obs,MWPotential,
-1.4,-8.,-1.7,ntimes=101)
return None
#Test the actions of an actionAngleAdiabatic, single pot
def test_actionAngleAdiabatic_conserved_actions_singlepot():
from galpy.potential import MiyamotoNagaiPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
mp= MiyamotoNagaiPotential(normalize=1.)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,2.])
aAA= actionAngleAdiabatic(pot=mp,c=False)
check_actionAngle_conserved_actions(aAA,obs,mp,
-1.5,-8.,-2.,ntimes=101,
inclphi=True)
return None
#Test the actions of an actionAngleAdiabatic, single pot, C
def test_actionAngleAdiabatic_conserved_actions_singlepot_c():
from galpy.potential import MiyamotoNagaiPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
mp= MiyamotoNagaiPotential(normalize=1.)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,2.])
aAA= actionAngleAdiabatic(pot=mp,c=True)
check_actionAngle_conserved_actions(aAA,obs,mp,
-1.5,-8.,-2.,ntimes=101,
inclphi=True)
return None
#Test the actions of an actionAngleAdiabatic, interpolated pot
def test_actionAngleAdiabatic_conserved_actions_interppot_c():
from galpy.potential import MWPotential, interpRZPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
ip= interpRZPotential(RZPot=MWPotential,
rgrid=(numpy.log(0.01),numpy.log(20.),101),
zgrid=(0.,1.,101),logR=True,use_c=True,enable_c=True,
interpPot=True,interpRforce=True,interpzforce=True)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,2.])
aAA= actionAngleAdiabatic(pot=ip,c=True)
check_actionAngle_conserved_actions(aAA,obs,ip,
-1.4,-8.,-1.7,ntimes=101)
return None
#Test the conservation of ecc, zmax, rperi, rap of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_EccZmaxRperiRap():
from galpy.potential import MWPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
aAA= actionAngleAdiabatic(pot=MWPotential,c=False,gamma=1.)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,0.])
check_actionAngle_conserved_EccZmaxRperiRap(aAA,obs,MWPotential,
-1.7,-1.4,-2.,-2.,ntimes=101)
return None
#Test the conservation of ecc, zmax, rperi, rap of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_EccZmaxRperiRap_ecc():
from galpy.potential import MWPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
aAA= actionAngleAdiabatic(pot=MWPotential,c=False,gamma=1.)
obs= Orbit([1.1,0.2, 1.3, 0.1,0.,2.])
check_actionAngle_conserved_EccZmaxRperiRap(aAA,obs,MWPotential,
-1.1,-0.4,-1.8,-1.8,ntimes=101,
inclphi=True)
return None
#Test the conservation of ecc, zmax, rperi, rap of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_EccZmaxRperiRap_singlepot_c():
from galpy.potential import MiyamotoNagaiPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
mp= MiyamotoNagaiPotential(normalize=1.)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,2.])
aAA= actionAngleAdiabatic(pot=mp,c=True)
check_actionAngle_conserved_EccZmaxRperiRap(aAA,obs,mp,
-1.7,-1.4,-2.,-2.,ntimes=101)
return None
#Test the conservation of ecc, zmax, rperi, rap of an actionAngleAdiabatic
def test_actionAngleAdiabatic_conserved_EccZmaxRperiRa_interppot_c():
from galpy.potential import MWPotential, interpRZPotential
from galpy.actionAngle import actionAngleAdiabatic
from galpy.orbit import Orbit
ip= interpRZPotential(RZPot=MWPotential,
rgrid=(numpy.log(0.01),numpy.log(20.),101),
zgrid=(0.,1.,101),logR=True,use_c=True,enable_c=True,
interpPot=True,interpRforce=True,interpzforce=True)
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.,2.])
aAA= actionAngleAdiabatic(pot=ip,c=True)
check_actionAngle_conserved_EccZmaxRperiRap(aAA,obs,ip,
-1.7,-1.4,-2.,-2.,ntimes=101)
return None
#Test the actionAngleAdiabatic against an isochrone potential: actions
def test_actionAngleAdiabatic_Isochrone_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleAdiabatic, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAA= actionAngleAdiabatic(pot=ip,c=True)
R,vR,vT,z,vz,phi= 1.01, 0.05, 1.05, 0.05,0.,2.
ji= aAI(R,vR,vT,z,vz,phi)
jia= aAA(R,vR,vT,z,vz,phi)
djr= numpy.fabs((ji[0]-jia[0])/ji[0])
dlz= numpy.fabs((ji[1]-jia[1])/ji[1])
djz= numpy.fabs((ji[2]-jia[2])/ji[2])
assert djr < 10.**-1.2, 'actionAngleAdiabatic applied to isochrone potential fails for Jr at %f%%' % (djr*100.)
#Lz and Jz are easy, because ip is a spherical potential
assert dlz < 10.**-10., 'actionAngleAdiabatic applied to isochrone potential fails for Lz at %f%%' % (dlz*100.)
assert djz < 10.**-1.2, 'actionAngleAdiabatic applied to isochrone potential fails for Jz at %f%%' % (djz*100.)
return None
#Basic sanity checking of the actionAngleAdiabatic actions (incl. conserved, bc takes a lot of time)
def test_actionAngleAdiabaticGrid_basicAndConserved_actions():
from galpy.actionAngle import actionAngleAdiabaticGrid
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAA= actionAngleAdiabaticGrid(pot=MWPotential,gamma=1.,c=False)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAA(R,vR,vT,z,vz,0.)
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(aAA.Jz(R,vR,vT,z,vz,0.)) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#setup w/ multi
aAA= actionAngleAdiabaticGrid(pot=MWPotential,gamma=1.,c=False,numcores=2)
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#Check that actions are conserved along the orbit
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.])
check_actionAngle_conserved_actions(aAA,obs,MWPotential,
-1.2,-8.,-1.7,ntimes=101)
return None
#Basic sanity checking of the actionAngleAdiabatic actions
def test_actionAngleAdiabaticGrid_basic_actions_c():
from galpy.actionAngle import actionAngleAdiabaticGrid
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAA= actionAngleAdiabaticGrid(pot=MWPotential,c=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAA(R,vR,vT,z,vz)
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAA(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 10.**-3., 'Close-to-circular orbit in the MWPotentialspherical LogarithmicHalo does not have small Jz'
#actionAngleAdiabaticGrid actions outside the grid
def test_actionAngleAdiabaticGrid_outsidegrid_c():
from galpy.actionAngle import actionAngleAdiabaticGrid, \
actionAngleAdiabatic
from galpy.potential import MWPotential
aA= actionAngleAdiabatic(pot=MWPotential,c=True)
aAA= actionAngleAdiabaticGrid(pot=MWPotential,c=True,Rmax=2.,zmax=0.2)
R,vR,vT,z,vz,phi= 3.,0.1,1.,0.1,0.1,2.
js= aA(R,vR,vT,z,vz,phi)
jsa= aAA(R,vR,vT,z,vz,phi)
assert numpy.fabs(js[0]-jsa[0]) < 10.**-8., 'actionAngleAdiabaticGrid evaluation outside of the grid fails'
assert numpy.fabs(js[2]-jsa[2]) < 10.**-8., 'actionAngleAdiabaticGrid evaluation outside of the grid fails'
assert numpy.fabs(js[2]-aAA.Jz(R,vR,vT,z,vz,phi)) < 10.**-8., 'actionAngleAdiabaticGrid evaluation outside of the grid fails'
#Also for array
s= numpy.ones(2)
js= aA(R,vR,vT,z,vz,phi)
jsa= aAA(R*s,vR*s,vT*s,z*s,vz*s,phi*s)
assert numpy.all(numpy.fabs(js[0]-jsa[0]) < 10.**-8.), 'actionAngleAdiabaticGrid evaluation outside of the grid fails'
assert numpy.all(numpy.fabs(js[2]-jsa[2]) < 10.**-8.), 'actionAngleAdiabaticGrid evaluation outside of the grid fails'
return None
#Test the actions of an actionAngleAdiabatic
def test_actionAngleAdiabaticGrid_conserved_actions_c():
from galpy.potential import MWPotential
from galpy.actionAngle import actionAngleAdiabaticGrid
from galpy.orbit import Orbit
obs= Orbit([1.05, 0.02, 1.05, 0.03,0.])
aAA= actionAngleAdiabaticGrid(pot=MWPotential,c=True)
check_actionAngle_conserved_actions(aAA,obs,MWPotential,
-1.4,-8.,-1.7,ntimes=101)
return None
#Test the actionAngleAdiabatic against an isochrone potential: actions
def test_actionAngleAdiabaticGrid_Isochrone_actions():
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleAdiabaticGrid, \
actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=1.2)
aAI= actionAngleIsochrone(ip=ip)
aAA= actionAngleAdiabaticGrid(pot=ip,c=True)
R,vR,vT,z,vz,phi= 1.01, 0.05, 1.05, 0.05,0.,2.
ji= aAI(R,vR,vT,z,vz,phi)
jia= aAA(R,vR,vT,z,vz,phi)
djr= numpy.fabs((ji[0]-jia[0])/ji[0])
dlz= numpy.fabs((ji[1]-jia[1])/ji[1])
djz= numpy.fabs((ji[2]-jia[2])/ji[2])
assert djr < 10.**-1.2, 'actionAngleAdiabatic applied to isochrone potential fails for Jr at %f%%' % (djr*100.)
#Lz and Jz are easy, because ip is a spherical potential
assert dlz < 10.**-10., 'actionAngleAdiabatic applied to isochrone potential fails for Lz at %f%%' % (dlz*100.)
assert djz < 10.**-1.2, 'actionAngleAdiabatic applied to isochrone potential fails for Jz at %f%%' % (djz*100.)
return None
#Basic sanity checking of the actionAngleStaeckel actions
def test_actionAngleStaeckel_basic_actions():
from galpy.actionAngle import actionAngleStaeckel
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAS= actionAngleStaeckel(pot=MWPotential,delta=0.71,c=False)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,0.99,0.0,0.0
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
#Another close-to-circular orbit
R,vR,vT,z,vz= 1.0,0.0,1.,0.01,0.0
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleStaeckel actions
def test_actionAngleStaeckel_basic_actions_u0():
from galpy.actionAngle import actionAngleStaeckel
from galpy.orbit import Orbit
from galpy.potential import MWPotential
# test nested list of potentials
aAS= actionAngleStaeckel(pot=[MWPotential[0],MWPotential[1:]],
delta=0.71,c=False,useu0=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleStaeckel actions
def test_actionAngleStaeckel_basic_actions_u0_c():
from galpy.actionAngle import actionAngleStaeckel
from galpy.orbit import Orbit
from galpy.potential import MWPotential
# test nested list of potentials
aAS= actionAngleStaeckel(pot=[MWPotential[0],MWPotential[1:]],
delta=0.71,c=True,useu0=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz]),u0=1.15)
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleStaeckel actions, w/ u0, and interppot
def test_actionAngleStaeckel_basic_actions_u0_interppot_c():
from galpy.actionAngle import actionAngleStaeckel
from galpy.orbit import Orbit
from galpy.potential import MWPotential, interpRZPotential
ip= interpRZPotential(RZPot=MWPotential,
rgrid=(numpy.log(0.01),numpy.log(20.),101),
zgrid=(0.,1.,101),logR=True,use_c=True,enable_c=True,
interpPot=True)
aAS= actionAngleStaeckel(pot=ip,delta=0.71,c=True,useu0=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2][0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleStaeckel actions
def test_actionAngleStaeckel_basic_actions_c():
from galpy.actionAngle import actionAngleStaeckel
from galpy.orbit import Orbit
from galpy.potential import MWPotential
aAS= actionAngleStaeckel(pot=MWPotential,delta=0.71,c=True)
#circular orbit
R,vR,vT,z,vz= 1.,0.,1.,0.,0.
js= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jr=0'
assert numpy.fabs(js[2]) < 10.**-16., 'Circular orbit in the MWPotential does not have Jz=0'
#Close-to-circular orbit
R,vR,vT,z,vz= 1.01,0.01,1.,0.01,0.01
js= aAS(Orbit([R,vR,vT,z,vz]))
assert numpy.fabs(js[0]) < 10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jr'
assert numpy.fabs(js[2]) < 2.*10.**-4., 'Close-to-circular orbit in the MWPotential does not have small Jz'
return None
#Basic sanity checking of the actionAngleStaeckel actions, unbound
def test_actionAngleStaeckel_unboundr_actions_c():
from galpy.actionAngle import actionAngleStaeckel
from galpy.potential import MWPotential
aAS= actionAngleStaeckel(pot=MWPotential,delta=0.71,c=True)
#Unbound orbit, shouldn't fail
R,vR,vT,z,vz= 1.,0.,10.,0.1,0.
js= aAS(R,vR,vT,z,vz)
assert js[0] > 1000., 'Unbound in R orbit in the MWPotential does not have large Jr'
#Another unbound orbit, shouldn't fail
R,vR,vT,z,vz= 1.,0.1,10.,0.1,0.
js= aAS(R,vR,vT,z,vz)
assert js[0] > 1000., 'Unbound in R orbit in the MWPotential does not have large Jr'
return None
#Basic sanity checking of the actionAngleStaeckel actions
def test_actionAngleStaeckel_zerolz_actions_c():
from galpy.actionAngle import actionAngleStaeckel
from galpy.potential import MWPotential
aAS= actionAngleStaeckel(pot=MWPotential,c=True,delta=0.71)
#Zero angular momentum, so rperi=0, but should have finite jr
R,vR,vT,z,vz= 1.,0.,0.,0., 0.
js= aAS(R,vR,vT,z,vz)
R,vR,vT,z,vz= 1.,0.,0.0000001,0., 0.
js2= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0]-js2[0]) < 10.**-6., 'Orbit with zero angular momentum does not have the correct Jr'
#Zero angular momentum, so rperi=0, but should have finite jr
R,vR,vT,z,vz= 1.,-0.5,0.,0., 0.
js= aAS(R,vR,vT,z,vz)
R,vR,vT,z,vz= 1.,-0.5,0.0000001,0., 0.
js2= aAS(R,vR,vT,z,vz)
assert numpy.fabs(js[0]-js2[0]) < 10.**-6., 'Orbit with zero angular momentum does not have the correct Jr'
return None
# Check that precision increases with increasing Gauss-Legendre order
def test_actionAngleStaeckel_actions_order():
from galpy.potential import KuzminKutuzovStaeckelPotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleStaeckel
kksp= KuzminKutuzovStaeckelPotential(normalize=1.,ac=4.,Delta=1.4)
o= Orbit([1.,0.5,1.1,0.2,-0.3,0.4])
aAS= actionAngleStaeckel(pot=kksp,delta=kksp._Delta,c=False)
# We'll assume that order=10000 is the truth, so 50 should be better than 5
jrt,jpt,jzt= aAS(o,order=10000,fixed_quad=True)
jr1,jp1,jz1= aAS(o,order=5,fixed_quad=True)
jr2,jp2,jz2= aAS(o,order=50,fixed_quad=True)
assert numpy.fabs(jr1-jrt) > numpy.fabs(jr2-jrt), 'Accuracy of actionAngleStaeckel does not increase with increasing order of integration'
assert numpy.fabs(jz1-jzt) > numpy.fabs(jz2-jzt), 'Accuracy of actionAngleStaeckel does not increase with increasing order of integration'