def test_setup_diffsetups():
#Test the different ways to setup a qdf object
#Test errors
try:
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
aA=aAS,cutcounter=True)
except IOError: pass
else: raise AssertionError("qdf setup w/o pot set did not raise exception")
try:
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=MWPotential,cutcounter=True)
except IOError: pass
else: raise AssertionError("qdf setup w/o aA set did not raise exception")
from galpy.potential import LogarithmicHaloPotential
try:
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=LogarithmicHaloPotential(),
aA=aAS,cutcounter=True)
except IOError: pass
else: raise AssertionError("qdf setup w/ aA potential different from pot= did not raise exception")
#qdf setup with an actionAngleIsochrone instance (issue #190)
from galpy.potential import IsochronePotential
from galpy.actionAngle import actionAngleIsochrone
ip= IsochronePotential(normalize=1.,b=2.)
try:
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=ip,
aA=actionAngleIsochrone(ip=ip),cutcounter=True)
except:
raise
raise AssertionError('quasi-isothermaldf setup w/ an actionAngleIsochrone instance failed')
#qdf setup with an actionAngleIsochrone instance should raise error if potentials are not the same
ip= IsochronePotential(normalize=1.,b=2.)
try:
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=ip,
aA=actionAngleIsochrone(ip=IsochronePotential(normalize=1.,b=2.5)),
cutcounter=True)
except IOError: pass
else: raise AssertionError("qdf setup w/ aA potential different from pot= did not raise exception")
#precompute
qdf= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=MWPotential,aA=aAS,cutcounter=True,
_precomputerg=True)
qdfnpc= quasiisothermaldf(1./4.,0.2,0.1,1.,1.,
pot=MWPotential,aA=aAS,cutcounter=True,
_precomputerg=False)
assert numpy.fabs(qdf.rg(1.1)-qdfnpc.rg(1.1)) < 10.**-5., 'rg calculated from qdf instance w/ precomputerg set is not the same as that computed from an instance w/o it set'
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_adinvariance():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
# Initialize two different IsochronePotentials
ip1= IsochronePotential(normalize=1.,b=1.)
ip2= IsochronePotential(normalize=0.5,b=1.)
# Use TimeInterpPotential to interpolate smoothly
tip= TimeInterpPotential(ip1,ip2,dt=100.,tform=50.)
# Integrate: 1) Orbit in the first isochrone potential
o1= Orbit([1.,0.1,1.1,0.0,0.1,0.])
ts= numpy.linspace(0.,50.,1001)
o1.integrate(ts,tip)
o1.plot(d1='x',d2='y',xrange=[-1.6,1.6],yrange=[-1.6,1.6],
color='b')
# 2) Orbit in the transition
o2= o1(ts[-1]) # Last time step => initial time step
ts2= numpy.linspace(50.,150.,1001)
o2.integrate(ts2,tip)
o2.plot(d1='x',d2='y',overplot=True,color='g')
# 3) Orbit in the second isochrone potential
o3= o2(ts2[-1])
ts3= numpy.linspace(150.,200.,1001)
o3.integrate(ts3,tip)
o3.plot(d1='x',d2='y',overplot=True,color='r')
# Now we calculate energy, maximum height, and mean radius
print(o1.E(pot=ip1), (o1.rperi()+o1.rap())/2, o1.zmax())
assert numpy.fabs(o1.E(pot=ip1)+2.79921356237) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o1.rperi()+o1.rap())/2-1.07854158141) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o1.zmax()-0.106331362938) < 10.**-4., 'zmax in the adiabatic invariance test is different'
print(o3.E(pot=ip2), (o3.rperi()+o3.rap())/2, o3.zmax())
assert numpy.fabs(o3.E(pot=ip2)+1.19677002624) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o3.rperi()+o3.rap())/2-1.39962036137) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o3.zmax()-0.138364269321) < 10.**-4., 'zmax in the adiabatic invariance test is different'
# The orbit has clearly moved to larger radii,
# the actions are however conserved from beginning to end
aAI1= actionAngleIsochrone(ip=ip1); print(aAI1(o1))
js= aAI1(o1)
assert numpy.fabs(js[0]-numpy.array([ 0.00773779])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
aAI2= actionAngleIsochrone(ip=ip2); print(aAI2(o3))
js= aAI2(o3)
assert numpy.fabs(js[0]-numpy.array([ 0.00773812])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
return None
def test_adinvariance():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
# Initialize two different IsochronePotentials
ip1= IsochronePotential(normalize=1.,b=1.)
ip2= IsochronePotential(normalize=0.5,b=1.)
# Use TimeInterpPotential to interpolate smoothly
tip= TimeInterpPotential(ip1,ip2,dt=100.,tform=50.)
# Integrate: 1) Orbit in the first isochrone potential
o1= Orbit([1.,0.1,1.1,0.0,0.1,0.])
ts= numpy.linspace(0.,50.,1001)
o1.integrate(ts,tip)
o1.plot(d1='x',d2='y',xrange=[-1.6,1.6],yrange=[-1.6,1.6],
color='b')
# 2) Orbit in the transition
o2= o1(ts[-1]) # Last time step => initial time step
ts2= numpy.linspace(50.,150.,1001)
o2.integrate(ts2,tip)
o2.plot(d1='x',d2='y',overplot=True,color='g')
# 3) Orbit in the second isochrone potential
o3= o2(ts2[-1])
ts3= numpy.linspace(150.,200.,1001)
o3.integrate(ts3,tip)
o3.plot(d1='x',d2='y',overplot=True,color='r')
# Now we calculate energy, maximum height, and mean radius
print(o1.E(pot=ip1), (o1.rperi()+o1.rap())/2, o1.zmax())
assert numpy.fabs(o1.E(pot=ip1)+2.79921356237) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o1.rperi()+o1.rap())/2-1.07854158141) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o1.zmax()-0.106331362938) < 10.**-4., 'zmax in the adiabatic invariance test is different'
print(o3.E(pot=ip2), (o3.rperi()+o3.rap())/2, o3.zmax())
assert numpy.fabs(o3.E(pot=ip2)+1.19677002624) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o3.rperi()+o3.rap())/2-1.39962036137) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o3.zmax()-0.138364269321) < 10.**-4., 'zmax in the adiabatic invariance test is different'
# The orbit has clearly moved to larger radii,
# the actions are however conserved from beginning to end
aAI1= actionAngleIsochrone(ip=ip1); print(aAI1(o1))
js= aAI1(o1)
assert numpy.fabs(js[0]-numpy.array([ 0.00773779])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
aAI2= actionAngleIsochrone(ip=ip2); print(aAI2(o3))
js= aAI2(o3)
assert numpy.fabs(js[0]-numpy.array([ 0.00773812])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
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 illustrate_adiabatic_invariance(plotfilename1,plotfilename2):
# Initialize two different IsochronePotentials
ip1= IsochronePotential(normalize=1.,b=1.)
ip2= IsochronePotential(normalize=0.5,b=1.)
# Use TimeInterpPotential to interpolate smoothly between the two
tip= TimeInterpPotential(ip1,ip2,dt=100.,tform=50.)
# Integrate the orbit, in three parts
# 1) Orbit in the first isochrone potential
o1= Orbit([1.,0.1,1.1,0.0,0.1,0.])
ts= numpy.linspace(0.,50.,1001)
o1.integrate(ts,tip)
bovy_plot.bovy_print()
o1.plot(d1='x',d2='y',xrange=[-1.6,1.6],yrange=[-1.6,1.6],color='b',
gcf=True)
# 2) Orbit in the transition
o2= o1(ts[-1]) # Last time step = initial time step of the next integration
ts2= numpy.linspace(50.,150.,1001)
o2.integrate(ts2,tip)
o2.plot(d1='x',d2='y',overplot=True,color='g')
# 3) Orbit in the second isochrone potential
o3= o2(ts2[-1])
ts3= numpy.linspace(150.,200.,1001)
o3.integrate(ts3,ip2)
o3.plot(d1='x',d2='y',overplot=True,color='r')
bovy_plot.bovy_end_print(plotfilename1)
# Also plot the R,z projection
bovy_plot.bovy_print(fig_height=2.3333)
o1.plot(d1='R',d2='z',xrange=[0.9,1.65],yrange=[-.175,.175],color='b',
gcf=True)
o2.plot(d1='R',d2='z',overplot=True,color='g')
o3.plot(d1='R',d2='z',overplot=True,color='r')
bovy_plot.bovy_end_print(plotfilename2)
# Now we calculate the energy, eccentricity, mean radius, and maximum height
print o1.E(pot=ip1), o1.e(), 0.5*(o1.rperi()+o1.rap()), o1.zmax()
print o3.E(pot=ip2), o3.e(), 0.5*(o3.rperi()+o3.rap()), o3.zmax()
# The orbit has clearly moved to larger radii, the actions are however conserved
aAI1= actionAngleIsochrone(ip=ip1)
aAI2= actionAngleIsochrone(ip=ip2)
print aAI1(o1)
print aAI2(o3)
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 plot_aaspher_conservation(plotfilename1,plotfilename2):
#Setup orbit
E, Lz= -1.25, 0.6
o= Orbit([0.8,0.3,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.-0.3**2./2.)),0.])
#Integrate the orbit to estimate an equivalent b
nt= 1001
ts= numpy.linspace(0.,20.,nt)
o.integrate(ts,MWPotential2014,method='symplec4_c')
b= estimateBIsochrone(o.R(ts),o.z(ts),pot=MWPotential2014)
print b
b= 0.3
#Now integrate the orbit in the isochronePotential
ip= IsochronePotential(normalize=1.,b=b)
aAI= actionAngleIsochrone(ip=ip)
orbt= 2.*numpy.pi/aAI.actionsFreqs(o)[4]
norb= 200.
nt= 20001
ts= numpy.linspace(0.,norb*orbt,nt)
o.integrate(ts,ip,method='symplec4_c')
#Calculate actions, frequencies, and angles
jfa= aAI.actionsFreqsAngles(o.R(ts),o.vR(ts),o.vT(ts),
o.z(ts),o.vz(ts),o.phi(ts))
dJs= numpy.fabs((jfa[0]-numpy.mean(jfa[0]))/numpy.mean(jfa[0]))
dOrs= numpy.fabs((jfa[3]-numpy.mean(jfa[3]))/numpy.mean(jfa[3]))
dOzs= numpy.fabs((jfa[5]-numpy.mean(jfa[5]))/numpy.mean(jfa[5]))
print "frequencies", numpy.mean(dOrs), numpy.mean(dOzs)
ar= dePeriod(numpy.reshape(jfa[6],(1,len(ts)))).flatten()
az= dePeriod(numpy.reshape(jfa[8],(1,len(ts)))).flatten()
danglers= numpy.fabs(ar-numpy.mean(jfa[3])*ts-jfa[6][0])/2./numpy.pi
danglezs= numpy.fabs(az-numpy.mean(jfa[5])*ts-jfa[8][0])/2./numpy.pi
#Break up
breakt= 50.
pts= parse_break(ts,ts < breakt)
pdJs= parse_break(dJs,ts < breakt)
pdanglers= parse_break(danglers,ts < breakt)
pdanglezs= parse_break(danglezs,ts < breakt)
#dAngles
bovy_plot.bovy_print()
pyplot.subplot(2,1,1)
bovy_plot.bovy_plot(pts/orbt,
pdJs,
color='k',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.])
bovy_plot.bovy_text(r'$\texttt{actionAngleIsochrone}$',
top_left=True,size=14.)
ax= pyplot.gca()
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
nullfmt = NullFormatter() # no labels
ax.xaxis.set_major_formatter(nullfmt)
#Same for actionAngleSpherical
aAS= actionAngleSpherical(pot=ip)
tts= ts[::1]
jfa= aAS.actionsFreqsAngles(o.R(tts),o.vR(tts),o.vT(tts),
o.z(tts),o.vz(tts),o.phi(tts),
fixed_quad=True)
#dJr
dJs= numpy.fabs((jfa[0]-numpy.mean(jfa[0]))/numpy.mean(jfa[0]))
dOrs= numpy.fabs((jfa[3]-numpy.mean(jfa[3]))/numpy.mean(jfa[3]))
dOzs= numpy.fabs((jfa[5]-numpy.mean(jfa[5]))/numpy.mean(jfa[5]))
print "frequencies", numpy.mean(dOrs), numpy.mean(dOzs)
#dAngles
ar= dePeriod(numpy.reshape(jfa[6],(1,len(tts)))).flatten()
az= dePeriod(numpy.reshape(jfa[8],(1,len(tts)))).flatten()
danglers= numpy.fabs(ar-numpy.mean(jfa[3])*tts-jfa[6][0])/2./numpy.pi
danglezs= numpy.fabs(az-numpy.mean(jfa[5])*tts-jfa[8][0])/2./numpy.pi
print numpy.mean(danglers)
print numpy.mean(danglezs)
ptts= parse_break(tts,tts < breakt)
pdJs= parse_break(dJs,tts < breakt)
pyplot.subplot(2,1,2)
bovy_plot.bovy_plot(ptts/orbt,
pdJs,
color='k',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_text(r'$\texttt{actionAngleSpherical}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.175,10.**2.,r'$\left|\Delta J_R / J_R\right|$',
fontsize=16.,
rotation='vertical')
ax= pyplot.gca()
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter(r'$%0.f$'))
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
bovy_plot.bovy_end_print(plotfilename1)
#Now plot the deviations in the angles
bovy_plot.bovy_print()
pyplot.subplot(2,1,1)
liner= bovy_plot.bovy_plot(pts/orbt,
pdanglers,
color='k',ls='-',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.])
linez= bovy_plot.bovy_plot(pts/orbt,
pdanglezs,
color='k',ls='--',overplot=True)
legend1= pyplot.legend((liner[0],linez[0]),
(r'$\theta_R$',
r'$\theta_z$'),
loc='lower right',#bbox_to_anchor=(.91,.375),
numpoints=2,
prop={'size':14},
frameon=False)
bovy_plot.bovy_text(r'$\texttt{actionAngleIsochrone}$',
top_left=True,size=14.)
ax= pyplot.gca()
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
nullfmt = NullFormatter() # no labels
ax.xaxis.set_major_formatter(nullfmt)
#Same for Spherical
pdanglers= parse_break(danglers,tts < breakt)
pdanglezs= parse_break(danglezs,tts < breakt)
pyplot.subplot(2,1,2)
bovy_plot.bovy_plot(ptts/orbt,
pdanglers,
color='k',ls='-',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_plot(ptts/orbt,
pdanglezs,
color='k',ls='--',overplot=True)
bovy_plot.bovy_text(r'$\texttt{actionAngleSpherical}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.175,10.**4.,r'$\left|\Delta \theta_{R,z} / 2\,\pi\right|$',
fontsize=16.,
rotation='vertical')
ax= pyplot.gca()
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter(r'$%0.f$'))
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
bovy_plot.bovy_end_print(plotfilename2)
return None
def create_frames(basefilename):
"""Create Frames.
Parameters
----------
basefilename : str
Returns
-------
None
"""
pot = IsochronePotential(normalize=1.0, b=1.2)
aAT = actionAngleIsochrone(ip=pot)
bmock = 0.8
aAF = actionAngleIsochrone(b=bmock)
o = Orbit([1.0, 0.3, 0.9, 0.2, 1.0, 0.1])
tfac, skip = 10, 1
ndesired = 30 * 25
times = numpy.linspace(0.0, 7.0, tfac * ndesired) * u.Gyr
# Subsample
otimesIndices = (numpy.arange(len(times)) /
float(len(times) - 1))**10 * (len(times) - 2)
otimesIndices = numpy.unique(numpy.floor(otimesIndices).astype("int"))
if len(otimesIndices) > ndesired:
sfac = int(numpy.floor(len(otimesIndices) / float(ndesired)))
otimesIndices = otimesIndices[::sfac]
otimes = times[otimesIndices]
o.integrate(times, pot)
# Compute all actions in the wrong potential
acfs = aAF.actionsFreqsAngles(
o.R(times),
o.vR(times),
o.vT(times),
o.z(times),
o.vz(times),
o.phi(times),
)
js = (acfs[0], acfs[1], acfs[2])
danglerI = ((numpy.roll(acfs[6], -1) - acfs[6]) % (2.0 * numpy.pi))[:-1]
jrC = numpy.cumsum(acfs[0][:-1] * danglerI) / numpy.cumsum(danglerI)
# And also the actions in the true potential
jsT = aAT(o.R(times), o.vR(times), o.vT(times), o.z(times), o.vz(times))
jrT = numpy.median(jsT[0]) * _RO * _VO
# ---------------------------------------------------------------
# Plotting
# Setup gridspec
gs = gridspec.GridSpec(1, 3, wspace=0.325, bottom=0.2, left=0.075)
# For each time step, plot: orbit, Jr, <Jr>
for ii in tqdm(range(len(otimes))):
bovy_plot.bovy_print(
fig_width=11.2,
fig_height=4.0,
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=13.0,
ytick_labelsize=13.0,
)
pyplot.figure()
pyplot.subplot(gs[0])
minIndx = otimesIndices[ii] - 100
if minIndx < 0:
minIndx = 0
bovy_plot.bovy_plot(
[o.x(otimes[ii:ii + 1]) * _RO],
[o.z(otimes[ii:ii + 1]) * _RO],
"o",
ms=15.0,
gcf=True,
xrange=[-19.0, 19.0],
yrange=[-19.0, 19.0],
xlabel=r"$X\,(\mathrm{kpc})$",
ylabel=r"$z\,(\mathrm{kpc})$",
)
if ii > 0:
bovy_plot.bovy_plot(
o.x(times[minIndx:otimesIndices[ii]:skip]) * _RO,
o.z(times[minIndx:otimesIndices[ii]:skip]) * _RO,
"-",
overplot=True,
)
pyplot.subplot(gs[1])
bovy_plot.bovy_plot(
[times[otimesIndices[ii]].value],
[js[0][otimesIndices[ii]] * _RO * _VO],
"o",
ms=15.0,
gcf=True,
xrange=[0.0, 1.0 + times[otimesIndices[ii]].value],
yrange=[0.0, 349.0],
xlabel=r"$\mathrm{time}\,(\mathrm{Gyr})$",
ylabel=r"$J_R\,(\mathrm{kpc\,km\,s}^{-1})$",
)
if ii > 0:
bovy_plot.bovy_plot(
times[:otimesIndices[ii]:skip].value,
js[0][:otimesIndices[ii]:skip] * _RO * _VO,
"-",
overplot=True,
)
pyplot.axhline(jrT, ls="--", color="k")
pyplot.subplot(gs[2])
bovy_plot.bovy_plot(
[otimes[ii].value],
[jrC[otimesIndices[ii]] * _RO * _VO],
"o",
ms=15.0,
gcf=True,
xrange=[0.0, 1.0 + times[otimesIndices[ii]].value],
yrange=[
(otimes[ii] / times[-1])**0.3 * (jrT - 3),
349.0 + (otimes[ii] / times[-1])**0.3 * (jrT + 3 - 349.0),
],
xlabel=r"$\mathrm{time}\,(\mathrm{Gyr})$",
ylabel=r"$J_R\,(\mathrm{kpc\,km\,s}^{-1})$",
)
if ii > 0:
bovy_plot.bovy_plot(
times[:otimesIndices[ii]:skip].value,
jrC[:otimesIndices[ii]:skip] * _RO * _VO,
"-",
overplot=True,
)
pyplot.axhline(jrT, ls="--", color="k")
bovy_plot.bovy_end_print(basefilename + "_%05d.png" % ii)
return None
