def test_call_marginalizevperp():
from galpy.orbit import Orbit
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot[0], to=-10.) #one with just one potential
#l=0
R, phi, vR = 0.8, 0., 0.4
vts = numpy.linspace(0., 1.5, 51)
pvts = numpy.array(
[edf(Orbit([R, vR, vt, phi]), integrate_method='rk6_c') for vt in vts])
assert numpy.fabs(numpy.sum(pvts)*(vts[1]-vts[0])\
-edf(Orbit([R,vR,0.,phi]),marginalizeVperp=True,integrate_method='rk6_c')) < 10.**-3.5, 'evolveddiskdf call w/ marginalizeVperp does not work'
#l=270
edf = evolveddiskdf(idf, pot=pot, to=-10.)
R, phi, vT = numpy.sin(numpy.pi / 6.), -numpy.pi / 3., 0.7 #l=30 degree
vrs = numpy.linspace(-1., 1., 101)
pvrs = numpy.array(
[edf(Orbit([R, vr, vT, phi]), integrate_method='rk6_c') for vr in vrs])
assert numpy.fabs(numpy.log(numpy.sum(pvrs)*(vrs[1]-vrs[0]))\
-edf(Orbit([R,0.,vT,phi]),
marginalizeVperp=True,
integrate_method='rk6_c',log=True,
nsigma=4)) < 10.**-2.5, 'evolveddiskdf call w/ marginalizeVperp does not work'
return None
def peculiar(ra, dec, d, pm_ra, pm_dec, V):
o = Orbit([ra * u.deg, dec * u.deg, d * u.kpc, pm_ra * u.mas / u.yr, pm_dec * u.mas / u.yr, V * u.km / u.s],
radec=True)
o2 = Orbit(vxvv=[o.R(0.) / 8.0, 0., 1., 0., 0., o.phi(0.)], ro=8., vo=220.)
current_vel = np.sqrt(
(o.U(0.) - o2.U(0) + 11.1) ** 2 + (o.V(0.) - o2.V(0) + 12.24) ** 2 + (o.W(0.) - o2.W(0) + 7.25) ** 2)
return current_vel
def test_qdf():
from galpy.df import quasiisothermaldf
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleStaeckel
# Setup actionAngle instance for action calcs
aAS= actionAngleStaeckel(pot=MWPotential2014,delta=0.45,
c=True)
# Quasi-iso df w/ hr=1/3, hsr/z=1, sr(1)=0.2, sz(1)=0.1
df= quasiisothermaldf(1./3.,0.2,0.1,1.,1.,aA=aAS,
pot=MWPotential2014)
# Evaluate DF w/ R,vR,vT,z,vz
df(0.9,0.1,0.8,0.05,0.02)
assert numpy.fabs(df(0.9,0.1,0.8,0.05,0.02)-numpy.array([ 123.57158928])) < 10.**-4., 'qdf does not behave as expected'
# Evaluate DF w/ Orbit instance, return ln
from galpy.orbit import Orbit
df(Orbit([0.9,0.1,0.8,0.05,0.02]),log=True)
assert numpy.fabs(df(Orbit([0.9,0.1,0.8,0.05,0.02]),log=True)-numpy.array([ 4.81682066])) < 10.**-4., 'qdf does not behave as expected'
# Evaluate DF marginalized over vz
df.pvRvT(0.1,0.9,0.9,0.05)
assert numpy.fabs(df.pvRvT(0.1,0.9,0.9,0.05)-23.273310451852243) < 10.**-4., 'qdf does not behave as expected'
# Evaluate DF marginalized over vR,vT
df.pvz(0.02,0.9,0.05)
assert numpy.fabs(df.pvz(0.02,0.9,0.05)-50.949586235238172) < 10.**-4., 'qdf does not behave as expected'
# Calculate the density
df.density(0.9,0.05)
assert numpy.fabs(df.density(0.9,0.05)-12.73725936526167) < 10.**-4., 'qdf does not behave as expected'
# Estimate the DF's actual density scale length at z=0
df.estimate_hr(0.9,0.)
assert numpy.fabs(df.estimate_hr(0.9,0.)-0.322420336223) < 10.**-2., 'qdf does not behave as expected'
# Estimate the DF's actual surface-density scale length
df.estimate_hr(0.9,None)
assert numpy.fabs(df.estimate_hr(0.9,None)-0.38059909132766462) < 10.**-4., 'qdf does not behave as expected'
# Estimate the DF's density scale height
df.estimate_hz(0.9,0.02)
assert numpy.fabs(df.estimate_hz(0.9,0.02)-0.064836202345657207) < 10.**-4., 'qdf does not behave as expected'
# Calculate the mean velocities
df.meanvR(0.9,0.05), df.meanvT(0.9,0.05),
df.meanvz(0.9,0.05)
assert numpy.fabs(df.meanvR(0.9,0.05)-3.8432265354618213e-18) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(df.meanvT(0.9,0.05)-0.90840425173325279) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(df.meanvz(0.9,0.05)+4.3579787517991084e-19) < 10.**-4., 'qdf does not behave as expected'
# Calculate the velocity dispersions
from numpy import sqrt
sqrt(df.sigmaR2(0.9,0.05)), sqrt(df.sigmaz2(0.9,0.05))
assert numpy.fabs(sqrt(df.sigmaR2(0.9,0.05))-0.22695537077102387) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(sqrt(df.sigmaz2(0.9,0.05))-0.094215523962105044) < 10.**-4., 'qdf does not behave as expected'
# Calculate the tilt of the velocity ellipsoid
# 2017/10-28: CHANGED bc tilt now returns angle in rad, no longer in deg
df.tilt(0.9,0.05)
assert numpy.fabs(df.tilt(0.9,0.05)-2.5166061974413765/180.*numpy.pi) < 10.**-4., 'qdf does not behave as expected'
# Calculate a higher-order moment of the velocity DF
df.vmomentdensity(0.9,0.05,6.,2.,2.,gl=True)
assert numpy.fabs(df.vmomentdensity(0.9,0.05,6.,2.,2.,gl=True)-0.0001591100892366438) < 10.**-4., 'qdf does not behave as expected'
# Sample velocities at given R,z, check mean
numpy.random.seed(1)
vs= df.sampleV(0.9,0.05,n=500); mvt= numpy.mean(vs[:,1])
assert numpy.fabs(numpy.mean(vs[:,0])) < 0.05 # vR
assert numpy.fabs(mvt-df.meanvT(0.9,0.05)) < 0.01 #vT
assert numpy.fabs(numpy.mean(vs[:,2])) < 0.05 # vz
return None
def test_surfacesection():
#Preliminary code
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz= -1.25, 0.6
o1= Orbit([0.8,0.,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(MWPotential2014,0.8,0.)-(Lz/0.8)**2./2.)),0.])
ts= numpy.linspace(0.,100.,2001)
o1.integrate(ts,MWPotential2014)
o2= Orbit([0.8,0.3,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(MWPotential2014,0.8,0.)-(Lz/0.8)**2./2.-0.3**2./2.)),0.])
o2.integrate(ts,MWPotential2014)
def surface_section(Rs,zs,vRs):
# Find points where the orbit crosses z from - to +
shiftzs= numpy.roll(zs,-1)
indx= (zs[:-1] < 0.)*(shiftzs[:-1] > 0.)
return (Rs[:-1][indx],vRs[:-1][indx])
# Calculate and plot the surface of section
ts= numpy.linspace(0.,1000.,20001) # long integration
o1.integrate(ts,MWPotential2014)
o2.integrate(ts,MWPotential2014)
sect1Rs,sect1vRs=surface_section(o1.R(ts),o1.z(ts),o1.vR(ts))
sect2Rs,sect2vRs=surface_section(o2.R(ts),o2.z(ts),o2.vR(ts))
from matplotlib.pyplot import plot, xlim, ylim
plot(sect1Rs,sect1vRs,'bo',mec='none')
xlim(0.3,1.); ylim(-0.69,0.69)
plot(sect2Rs,sect2vRs,'yo',mec='none')
return None
def test_call_marginalizevlos():
from galpy.orbit import Orbit
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot[0], to=-10.) #one with just one potential
#l=0
R, phi, vT = 0.8, 0., 0.7
vrs = numpy.linspace(-1., 1., 101)
pvrs = numpy.array(
[edf(Orbit([R, vr, vT, phi]), integrate_method='rk6_c') for vr in vrs])
assert numpy.fabs(numpy.log(numpy.sum(pvrs)*(vrs[1]-vrs[0]))\
-edf(Orbit([R,0.,vT,phi]),marginalizeVlos=True,integrate_method='rk6_c',log=True)) < 10.**-4., 'diskdf call w/ marginalizeVlos does not work'
#l=270, this DF has some issues, but it suffices to test the mechanics of the code
edf = evolveddiskdf(idf, pot=pot, to=-10.)
R, phi, vR = numpy.sin(numpy.pi / 6.), -numpy.pi / 3., 0.4 #l=30 degree
vts = numpy.linspace(0.3, 1.5, 101)
pvts = numpy.array(
[edf(Orbit([R, vR, vt, phi]), integrate_method='rk6_c') for vt in vts])
assert numpy.fabs(numpy.sum(pvts)*(vts[1]-vts[0])\
-edf(Orbit([R,vR,0.,phi]),
marginalizeVlos=True,
integrate_method='rk6_c',
nsigma=4)) < 10.**-3.5, 'diskdf call w/ marginalizeVlos does not work'
return None
def test_leapfrog_nfw_galpy(self): # Compare a more complicated set of initial conditions to the galpy # outputs (which are slow but known to work). # Set the parameters for a slightly offset circular orbit rho_0 = 0.1 r_scale = 1 G = 0.8962419740798497 dt = 0.001 num_dt = int(5e4) pos_nfw_array = np.tile(np.zeros(3,dtype=np.float64),(num_dt,1)) save_pos = np.zeros((num_dt+1,3)) save_vel = np.zeros((num_dt+1,3)) # Change the rho_0 and r_scale to a fixed array in time rho_0_array = rho_0*np.ones(num_dt,dtype=np.float64) r_scale_array = r_scale*np.ones(num_dt,dtype=np.float64) r_init = 20 pos_init = np.array([r_init,0,0],dtype=np.float64) M_r = 4*np.pi*rho_0*r_scale**3*(np.log((r_scale+r_init)/r_scale)+ r_scale/(r_scale+r_init) - 1) v_r = np.sqrt(G*M_r/r_init) v_kick = 1e-1 vel_init = np.array([v_kick,v_r,0],dtype=np.float64) integrator.leapfrog_int_nfw(pos_init,vel_init,rho_0_array, r_scale_array,pos_nfw_array,dt,save_pos,save_vel) # Compare to galpy orbits o=Orbit([r_init,v_kick,v_r,0,0,0]) nfw = NFWPotential(a=r_scale,amp=rho_0*G*4*np.pi*r_scale**3) ts = np.linspace(0,dt*num_dt,num_dt+1) o.integrate(ts,nfw,method='leapfrog',dt=dt) np.testing.assert_almost_equal(o.x(ts),save_pos[:,0]) np.testing.assert_almost_equal(o.y(ts),save_pos[:,1]) np.testing.assert_almost_equal(o.z(ts),save_pos[:,2]) # Make the kick bigger and see what happens v_kick = 5e-1 pos_init = np.array([r_init,0,0],dtype=np.float64) vel_init = np.array([v_kick,v_r,v_kick],dtype=np.float64) integrator.leapfrog_int_nfw(pos_init,vel_init,rho_0_array, r_scale_array,pos_nfw_array,dt,save_pos,save_vel) # Do the same for galpy o=Orbit([r_init,v_kick,v_r,0,v_kick,0]) nfw = NFWPotential(a=r_scale,amp=rho_0*G*4*np.pi*r_scale**3) ts = np.linspace(0,dt*num_dt,num_dt+1) o.integrate(ts,nfw,method='leapfrog',dt=dt) np.testing.assert_almost_equal(o.x(ts),save_pos[:,0]) np.testing.assert_almost_equal(o.y(ts),save_pos[:,1]) np.testing.assert_almost_equal(o.z(ts),save_pos[:,2])
def sample_spraydf_pal5_spiral(Nsamples,
spiralpot,
fo='blah_trailing.dat',
trailing=True):
p5 = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24., 7.25])
#convert to galpy units
pal5 = Orbit(p5._orb.vxvv)
if trailing:
spdft = streamspraydf.streamspraydf(50000. * u.Msun,
progenitor=pal5,
pot=spiralpot,
leading=False,
tdisrupt=5. * u.Gyr)
RvR, dt = spdft.sample(n=Nsamples, returndt=True, integrate=True)
R = RvR[0]
vR = RvR[1]
vT = RvR[2]
z = RvR[3]
vz = RvR[4]
phi = RvR[5]
fo = open(fo, 'w')
else:
spdf = streamspraydf.streamspraydf(50000. * u.Msun,
progenitor=pal5,
pot=spiralpot,
tdisrupt=5. * u.Gyr)
RvR, dt = spdf.sample(n=Nsamples, returndt=True, integrate=True)
R = RvR[0]
vR = RvR[1]
vT = RvR[2]
z = RvR[3]
vz = RvR[4]
phi = RvR[5]
fo_lead = fo.replace('trailing', 'leading')
fo = open(fo_lead, 'w')
fo.write("#R phi z vR vT vz ts" + "\n")
for jj in range(Nsamples):
fo.write(
str(R[jj]) + " " + str(phi[jj]) + " " + str(z[jj]) + " " +
str(vR[jj]) + " " + str(vT[jj]) + " " + str(vz[jj]) + " " +
str(dt[jj]) + "\n")
fo.close()
return None
def test_careful_traceback_and_forward():
"""Step by step, project orbit forward, then backward"""
bovy_times = np.array([0., np.pi / 3.])
chron_times = torb.convert_bovytime2myr(bovy_times)
init_pos_chron = np.array([
4000, 8000. * np.sqrt(3) / 2, 0,
np.sin(np.pi / 3) * 220., -np.cos(np.pi / 3) * 220., 0
])
init_pos_galpy = torb.convert_cart2galpycoords(init_pos_chron, ts=0.)
assert np.allclose(np.array([1., 0, 1, 0, 0, np.pi / 3.]), init_pos_galpy)
o = Orbit(vxvv=init_pos_galpy, ro=8., vo=220.)
o.integrate(bovy_times, MWPotential2014, method='odeint')
orbit_galpy = o.getOrbit()
assert np.allclose(init_pos_galpy, orbit_galpy[0])
assert np.allclose(
init_pos_galpy + np.array([0., 0., 0., 0., 0., bovy_times[-1]]),
orbit_galpy[-1])
orbit_chron = torb.convert_galpycoords2cart(orbit_galpy, ts=bovy_times)
assert np.allclose(init_pos_chron, orbit_chron[0])
assert np.allclose(init_pos_chron, orbit_chron[-1])
# Setup for backwards time integration
# Currently at time of PI/3
back_init_pos_chron = orbit_chron[-1]
back_init_pos_galpy = torb.convert_cart2galpycoords(
back_init_pos_chron,
bovy_times=bovy_times[-1],
)
assert np.allclose(
back_init_pos_galpy,
torb.convert_cart2galpycoords(back_init_pos_chron,
bovy_times=bovy_times[-1]))
back_o = Orbit(vxvv=back_init_pos_galpy, ro=8., vo=220.)
back_o.integrate(-1 * bovy_times, MWPotential2014, method='odeint')
back_orbit_galpy = back_o.getOrbit()
assert np.allclose(back_init_pos_galpy, back_orbit_galpy[0])
assert np.allclose(
back_init_pos_galpy - np.array([0., 0., 0., 0., 0., bovy_times[-1]]),
back_orbit_galpy[-1])
assert np.allclose(init_pos_galpy, back_orbit_galpy[-1])
back_orbit_chron = torb.convert_galpycoords2cart(
back_orbit_galpy,
ts=bovy_times[::-1],
)
assert np.allclose(init_pos_chron, back_orbit_chron[-1])
def test_call_special():
from galpy.orbit import Orbit
idf= dehnendf(beta=0.)
pot= [LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)] #very mild non-axi
edf= evolveddiskdf(idf,pot=pot,to=-10.)
o= Orbit([0.9,0.1,1.1,2.])
#call w/ and w/o explicit t
assert numpy.fabs(numpy.log(edf(o,0.))-numpy.log(edf(o))) < 10.**-10., 'edf.__call__ w/ explicit t=0. and w/o t do not give the same answer'
#call must get Orbit, otherwise error
try: edf(0.9,0.1,1.1,2.)
except IOError: pass
else: raise AssertionError('edf.__call__ w/o Orbit input did not raise IOError')
#Call w/ list, but just to
assert numpy.fabs(numpy.log(edf(o,[-10.]))-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF'
#Call w/ just to
assert numpy.fabs(numpy.log(edf(o,-10.))-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF'
#also w/ log
assert numpy.fabs(edf(o,[-10.],log=True)-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF (log)'
assert numpy.fabs(edf(o,-10.,log=True)-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF (log)'
# Tests w/ odeint: tlist
codeint= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='odeint',log=True)
crk6c= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='rk6_c',log=True)
assert numpy.all(numpy.fabs(codeint-crk6c) < 10.**-4.), 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Crazy orbit w/ tlist
crk6c= edf(Orbit([3.,1.,-1.,2.]),[0.],integrate_method='odeint',log=True)
assert crk6c < -20., 'crazy orbit does not have DF equal to zero'
# deriv w/ odeint
codeint= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='odeint',
deriv='R')
crk6c= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='rk6_c',deriv='R')
assert numpy.all(numpy.fabs(codeint-crk6c) < 10.**-4.), 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c (deriv=R)'
# deriv w/ len(tlist)=1
crk6c= edf(o,[0.],integrate_method='rk6_c',deriv='R')
crk6c2= edf(o,0.,integrate_method='rk6_c',deriv='R')
assert numpy.all(numpy.fabs(crk6c-crk6c2) < 10.**-4.), 'edf.__call__ w/ tlist consisting of one time and just a scalar time do not agree'
#Call w/ just to and deriv
assert numpy.fabs(edf(o,-10.,deriv='R')-idf(o)*idf._dlnfdR(o._orb.vxvv[0],o._orb.vxvv[1],o._orb.vxvv[2])) < 10.**-10., 'edf.__call__ w/ to did not return initial DF (deriv=R)'
assert numpy.fabs(edf(o,-10.,deriv='phi')) < 10.**-10., 'edf.__call__ w/ to did not return initial DF (deriv=phi)'
# Call w/ just one t and odeint
codeint= edf(o,0,integrate_method='odeint',log=True)
crk6c= edf(o,0.,integrate_method='rk6_c',log=True)
assert numpy.fabs(codeint-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Call w/ just one t and fallback to odeint
# turn off C
edf._pot[0].hasC= False
edf._pot[0].hasC_dxdv= False
codeint= edf(o,0,integrate_method='dopr54_c',log=True)
assert numpy.fabs(codeint-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Call w/ just one t and fallback to leaprog
cleapfrog= edf(o,0,integrate_method='leapfrog_c',log=True)
assert numpy.fabs(cleapfrog-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
def sample_streamdf_pal5_noprog(N,barpot,nobarpot,fo='blah_trailing.dat',trailing=True):
if trailing :
sdf_trailing= pal5_util.setup_pal5model(pot=nobarpot)
R,vR,vT,z,vz,phi,dt= sdf_trailing.sample(n=N,returndt=True)
fo=open(fo,'w')
else :
sdf_leading= pal5_util.setup_pal5model(pot=nobarpot,leading=True)
R,vR,vT,z,vz,phi,dt= sdf_leading.sample(n=N,returndt=True)
fo_lead=fo.replace('trailing','leading')
fo=open(fo_lead,'w')
finalR= numpy.empty(N)
finalvR=numpy.empty(N)
finalvT=numpy.empty(N)
finalvz=numpy.empty(N)
finalphi= numpy.empty(N)
finalz= numpy.empty(N)
tt=numpy.empty(N)
for ii in range(N):
o= Orbit([R[ii],vR[ii],vT[ii],z[ii],vz[ii],phi[ii]])
o.turn_physical_off()
ts= numpy.linspace(0.,-dt[ii],1001)
o.integrate(ts,nobarpot)
orb=Orbit([o.R(ts[-1]),o.vR(ts[-1]),o.vT(ts[-1]),o.z(ts[-1]),o.vz(ts[-1]),o.phi(ts[-1])])
ts_future= numpy.linspace(-dt[ii],0.,1001)
#forward integrate in barred potential
orb.integrate(ts_future,barpot)
finalR[ii]= orb.R(ts_future[-1])
finalphi[ii]= orb.phi(ts_future[-1])
finalz[ii]= orb.z(ts_future[-1])
finalvR[ii]=orb.vR(ts_future[-1])
finalvT[ii]=orb.vT(ts_future[-1])
finalvz[ii]=orb.vz(ts_future[-1])
tt[ii]=dt[ii]
fo.write("#R phi z vR vT vz ts" + "\n")
for jj in range(N):
fo.write(str(finalR[jj]) + " " + str(finalphi[jj]) + " " + str(finalz[jj]) + " " + str(finalvR[jj]) + " " + str(finalvT[jj]) + " " + str(finalvz[jj]) + " " + str(tt[jj]) + "\n")
fo.close()
return None
def test_orbitint():
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz= -1.25, 0.6
o1= Orbit([0.8,0.,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(MWPotential2014,0.8,0.)-(Lz/0.8)**2./2.)),0.])
ts= numpy.linspace(0.,100.,2001)
o1.integrate(ts,MWPotential2014)
o1.plot(xrange=[0.3,1.],yrange=[-0.2,0.2],color='k')
o2= Orbit([0.8,0.3,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(MWPotential2014,0.8,0.)-(Lz/0.8)**2./2.-0.3**2./2.)),0.])
o2.integrate(ts,MWPotential2014)
o2.plot(xrange=[0.3,1.],yrange=[-0.2,0.2],color='k')
return None
def add_orbit_from_prev(self, pot=None, vxvv=None, **kw):
"""Add orbit from prev conditions.
Parameters
----------
pot: Potential
vxvv: list
Returns
-------
self
"""
# Checking integrated previous orbit (has non-zero time domain)
if not self._check_curr_orbit_integrated():
return
# Forward or Backwards?
drct = self._data.direction
if drct == "forward":
oldt = self._bounds[1] # getting current time
if vxvv is None: # use most recent orbit
orbit = Orbit(vxvv=self.o.SkyCoord(oldt))
elif isinstance(vxvv, Orbit):
orbit = vxvv
else:
orbit = Orbit(vxvv=vxvv, **kw)
self._data.append(oldt, orbit)
else:
oldt = self._bounds[0] # getting current time
if vxvv is None: # use most recent orbit
orbit = Orbit(vxvv=self.o.SkyCoord(oldt))
elif isinstance(vxvv, Orbit):
orbit = vxvv
else:
orbit = Orbit(vxvv=vxvv, **kw)
self._data.prepend(oldt, orbit)
# potential
if pot is not None:
self._pot = pot
return self
def test_nemo_MWPotential2014():
mp = potential.MWPotential2014
tmax = 3.5
vo, ro = 220., 8.
o = Orbit([1., 0.1, 1.1, 0.2, 0.1, 1.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, mp, tmax, vo, ro, isList=True)
return None
def test_nemo_PlummerPotential():
pp = potential.PlummerPotential(normalize=1., b=2.)
tmax = 3.
vo, ro = 213., 8.23
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, pp, tmax, vo, ro, tol=0.03)
return None
def test_nemo_LogarithmicHaloPotential():
lp = potential.LogarithmicHaloPotential(normalize=1.)
tmax = 2.
vo, ro = 210., 8.5
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, lp, tmax, vo, ro, tol=0.03)
return None
def test_nemo_HernquistPotential():
hp = potential.HernquistPotential(normalize=1., a=3.)
tmax = 3.
vo, ro = 210., 7.5
o = Orbit([1., 0.25, 1.4, 0.3, -0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, hp, tmax, vo, ro)
return None
def test_nemo_NFWPotential():
np = potential.NFWPotential(normalize=1., a=3.)
tmax = 3.
vo, ro = 200., 7.
o = Orbit([1., 0.5, 1.3, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, np, tmax, vo, ro)
return None
def observed_to_xyzuvw_orbit(obs, ts, lsr_orbit=None):
"""
Convert six-parameter astrometric solution to XYZUVW orbit.
Parameters
----------
obs : [RA (deg), DEC (deg), pi (mas),
mu_ra (mas/yr), mu_dec (mas/yr), vlos (km/s)]
Current kinematics
ts : [ntimes] array
times (in Myr) to traceback to
lsr_orbit : Orbit
the orbit of the local standard of rest for comparison, if None can
calculate on the fly
XYZUVW : [ntimes, 6] array
The space position and velocities of the star in a co-rotating frame
centred on the LSR
"""
#convert times from Myr into bovy_time
bovy_ts = ts / (bovy_conversion.time_in_Gyr(220., 8.) * 1000
) # bovy-time/Myr
logging.info("max time in Myr: {}".format(np.max(ts)))
logging.info("max time in Bovy time: {}".format(np.max(bovy_ts)))
o = Orbit(vxvv=obs, radec=True, solarmotion='schoenrich')
o.integrate(bovy_ts, mp, method='odeint')
data = o.getOrbit()
XYZUVW = galpy_coords_to_xyzuvw(data, bovy_ts)
return XYZUVW
def pass_v(ra, dec, d, pm_ra, pm_dec, V, time, numpoints):
o = Orbit([ra * u.deg, dec * u.deg, d * u.kpc, pm_ra * u.mas / u.yr, pm_dec * u.mas / u.yr, V * u.km / u.s],
radec=True)
lp = MWPotential2014
ts = np.linspace(0, time, numpoints) * u.Gyr
o.integrate(ts, lp)
pass_t_array = ts[np.where(np.sign(o.z(ts)[:-1]) - np.sign(o.z(ts)[1:]) != 0)[0]]
results = []
for pass_t in pass_t_array:
o2 = Orbit(vxvv=[o.R(pass_t) / 8.0, 0., 1., 0., 0., o.phi(pass_t)], ro=8., vo=220.)
# results.append(np.sqrt((o.U(pass_t)-o2.U(0)+11.1)**2 + (o.V(pass_t)-o2.V(0)+12.24)**2 + (o.W(pass_t)-o2.W(0)+7.25)**2))
results.append(
np.sqrt((o.U(pass_t) - o2.U(0)) ** 2 + (o.V(pass_t) - o2.V(0)) ** 2 + (o.W(pass_t) - o2.W(0)) ** 2))
return results
def test_actionConservation():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20., Delta=Delta, normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1., 0.1, 1.1, 0.01, 0.1]
o = Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts = numpy.linspace(0, 101, 100)
o.integrate(ts, pot, method='leapfrog_c')
#_____Setup ActionAngle object and calculate actions (Staeckel approximation)_____
aAS = actionAngleStaeckel(pot=pot, delta=Delta, c=True)
jrs, lzs, jzs = aAS(o.R(ts), o.vR(ts), o.vT(ts), o.z(ts), o.vz(ts))
assert numpy.all(numpy.fabs(jrs - jrs[0]) < 10.**-8.), \
'Radial action is not conserved along orbit.'
assert numpy.all(numpy.fabs(lzs - lzs[0]) < 10.**-8.), \
'Angular momentum is not conserved along orbit.'
assert numpy.all(numpy.fabs(jzs - jzs[0]) < 10.**-8.), \
'Vertical action is not conserved along orbit.'
return None
def test_estimateDelta():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20., Delta=Delta, normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1., 0.1, 1.1, 0.01, 0.1]
o = Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts = numpy.linspace(0, 101, 100)
o.integrate(ts, pot, method='leapfrog_c')
#____estimate Focal length Delta_____
#for each time step individually:
deltas_estimate = numpy.zeros(len(ts))
for ii in range(len(ts)):
deltas_estimate[ii] = estimateDeltaStaeckel(pot, o.R(ts[ii]),
o.z(ts[ii]))
assert numpy.all(numpy.fabs(deltas_estimate - Delta) < 10.**-8), \
'Focal length Delta estimated along the orbit is not constant.'
#for all time steps together:
delta_estimate = estimateDeltaStaeckel(pot, o.R(ts), o.z(ts))
assert numpy.fabs(delta_estimate - Delta) < 10.**-8, \
'Focal length Delta estimated from the orbit is not the same as the input focal length.'
return None
def initialise_orbit(ID):
cand = gk_candidates[(gk_candidates.T[-1] == int(ID))]
cand = cand[0]
ra_mean = cand[0]
ra_err = 0 #unavailable
dec_mean = cand[1]
dec_err = 0
pmRA_mean = cand[3]
pmRA_err = cand[6]
pmDec_mean = cand[4]
pmDec_err = cand[7]
#calc a random value from gaussian
# ra = generate_rand(ra_mean, ra_err, measurement_type = 'mas')
# dec = generate_rand(dec_mean, dec_err, measurement_type = 'mas')
ra = ra_mean
dec = dec_mean
pmRA = generate_rand(pmRA_mean, pmRA_err)
if pmDec_mean == pmDec_err: #some issue with things being wrong just ignore it
pmDec = pmDec_mean
else:
pmDec = generate_rand(pmDec_mean, pmDec_err)
#no error for distance in this set
dist = cand[2]
#VLOS is reliable and stays as is
Vlos = cand[5]
orbit = Orbit(vxvv=[ra, dec, dist, pmRA, pmDec, Vlos],
radec=True,
ro=8.,
vo=220.,
solarmotion="schoenrich")
return orbit
def traceback2(params, times):
"""Trace forward a cluster. First column of returned array is the
position of the cluster at a given age.
Parameters
----------
times: float array
Times to trace forward, in Myr. Note that positive numbers are going
forward in time.
params: float array
[RA,DE,Plx,PM(RA),PM(DE),RV]
RA = Right Ascension (Deg)
DE = Declination (Deg)
Plx = Paralax (Mas)
PM(RA) = Proper motion (Right Ascension) (mas/yr)
PM(DE) = Proper motion (Declination) (mas/yr)
RV = Radial Velocity (km/s)
age: Age of cluster, in Myr
"""
#FIXME: This is very out of date and should be deleted!!!
#Times in Myr
ts = -(times / 1e3) / bovy_conversion.time_in_Gyr(220., 8.)
nts = len(times)
#Positions and velocities in the co-rotating solar reference frame.
xyzuvw = np.zeros((1, nts, 6))
#Trace forward the local standard of rest.
lsr_orbit = Orbit(vxvv=[1., 0, 1, 0, 0., 0], vo=220, ro=8)
lsr_orbit.integrate(ts, MWPotential2014) #,method='odeint')
xyzuvw = integrate_xyzuvw(params, ts, lsr_orbit, MWPotential2014)
return xyzuvw
def test_correctInitialSolarMotion():
age = np.pi # Half a galactic revolution
# For reference: the expected solar motion as provided by Schoenrich
REFERENCE_SCHOENRICH_SOLAR_MOTION = np.array([-11.1, -12.24, -7.25])
ntimesteps = 10
# vxvv is in cylindrical coordinates here. [R,vR,vT(,z,vz,phi)]
lsr_orbit = Orbit(vxvv=[1, 0, 1, 0, 0, 0],
vo=220,
ro=8,
solarmotion='schoenrich')
lsr_orbit.integrate(np.linspace(0., age, ntimesteps), MWPotential2014)
U = lsr_orbit.U(0)
V = lsr_orbit.V(0)
W = lsr_orbit.W(0)
results = np.array([U, V, W]).reshape(3)
for i, vel in enumerate('UVW'):
print("For velocity {}:".format(vel))
print(" expected: {}".format(REFERENCE_SCHOENRICH_SOLAR_MOTION[i]))
print(" received: {}".format(results[i]))
assert (np.allclose(REFERENCE_SCHOENRICH_SOLAR_MOTION, results)),\
'!!! Using galpy version {} Need galpy version 1.1 !!!'.format(
galpy.__version__
)
def make_nondefault_pal5stream(chain_ind,leading=False,timpact=None,b=0.8,hernquist=False,td=5.):
orb,pot,sigv,tvo=set_prog_potential(chain_ind)
try :
sdf= pal5_util.setup_pal5model_MWfit(ro=_REFR0,vo=tvo,timpact=timpact,pot=pot,orb=orb,hernquist=hernquist,leading=leading,age=td,sigv=sigv)
except numpy.linalg.LinAlgError:
print ("using estimateBIsochrone")
ts= numpy.linspace(0.,td,1001)/bovy_conversion.time_in_Gyr(_REFV0, _REFR0)
prog = Orbit(orb,radec=True,ro=_REFR0,vo=tvo,solarmotion=[-11.1,24.,7.25])
prog.integrate(ts,pot)
estb= estimateBIsochrone(pot,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]
print ("b=%f"%isob)
sdf=pal5_util.setup_pal5model_MWfit(ro=_REFR0,vo=tvo,leading=leading,pot=pot,orb=orb,timpact=timpact,b=isob,hernquist=hernquist,age=td,sigv=sigv)
return sdf
def test_amuse_PowerSphericalPotentialwCutoffPotential():
pp= potential.PowerSphericalPotentialwCutoff(normalize=1.,alpha=1.,rc=0.4)
tmax= 2.
vo,ro= 180., 9.
o= Orbit([1.,0.03,1.03,0.2,0.1,0.4],ro=ro,vo=vo)
run_orbitIntegration_comparison(o,pp,tmax,vo,ro)
return None
def test_orbmethods():
from galpy.orbit import Orbit
from galpy.potential import MWPotential2014
# 8/17/2019: added explicit z=0.025, because that was the default at the
# time of the galpy paper, but the default has been changed
o = Orbit([0.8, 0.3, 0.75, 0., 0.2, 0.],
zo=0.025) # setup R,vR,vT,z,vz,phi
times = numpy.linspace(0., 10., 1001) # Output times
o.integrate(times, MWPotential2014) # Integrate
o.E() # Energy
assert numpy.fabs(o.E() + 1.2547650648697966
) < 10.**-5., 'Orbit method does not work as expected'
o.L() # Angular momentum
assert numpy.all(
numpy.fabs(o.L() - numpy.array([[0., -0.16, 0.6]])) < 10.**-5.
), 'Orbit method does not work as expected'
o.Jacobi(OmegaP=0.65) #Jacobi integral E-OmegaP Lz
assert numpy.fabs(o.Jacobi(OmegaP=0.65) - numpy.array([-1.64476506])
) < 10.**-5., 'Orbit method does not work as expected'
o.ER(times[-1]), o.Ez(times[-1]) # Rad. and vert. E at end
assert numpy.fabs(o.ER(times[-1]) + 1.27601734263047
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.Ez(times[-1]) - 0.021252201847851909
) < 10.**-5., 'Orbit method does not work as expected'
o.rperi(), o.rap(), o.zmax() # Peri-/apocenter r, max. |z|
assert numpy.fabs(o.rperi() - 0.44231993168097
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.rap() - 0.87769030382105
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.zmax() - 0.077452357289016
) < 10.**-5., 'Orbit method does not work as expected'
o.e() # eccentricity (rap-rperi)/(rap+rperi)
assert numpy.fabs(o.e() - 0.32982348199330563
) < 10.**-5., 'Orbit method does not work as expected'
o.R(2., ro=8.) # Cylindrical radius at time 2. in kpc
assert numpy.fabs(o.R(2., ro=8.) - 3.5470772876920007
) < 10.**-3., 'Orbit method does not work as expected'
o.vR(5., vo=220.) # Cyl. rad. velocity at time 5. in km/s
assert numpy.fabs(o.vR(5., vo=220.) - 45.202530965094553
) < 10.**-3., 'Orbit method does not work as expected'
o.ra(1.), o.dec(1.) # RA and Dec at t=1. (default settings)
# 5/12/2016: test weakened, because improved galcen<->heliocen
# transformation has changed these, but still close
assert numpy.fabs(o.ra(1.) - numpy.array([288.19277])
) < 10.**-1., 'Orbit method does not work as expected'
assert numpy.fabs(o.dec(1.) - numpy.array([18.98069155])
) < 10.**-1., 'Orbit method does not work as expected'
o.jr(type='adiabatic'), o.jz() # R/z actions (ad. approx.)
assert numpy.fabs(o.jr(type='adiabatic') - 0.05285302231137586
) < 10.**-3., 'Orbit method does not work as expected'
assert numpy.fabs(o.jz() - 0.006637988850751242
) < 10.**-3., 'Orbit method does not work as expected'
# Rad. period w/ Staeckel approximation w/ focal length 0.5,
o.Tr(type='staeckel', delta=0.5, ro=8., vo=220.) # in Gyr
assert numpy.fabs(
o.Tr(type='staeckel', delta=0.5, ro=8., vo=220.) - 0.1039467864018446
) < 10.**-3., 'Orbit method does not work as expected'
o.plot(d1='R', d2='z') # Plot the orbit in (R,z)
o.plot3d() # Plot the orbit in 3D, w/ default [x,y,z]
return None
def test_nemo_MN3ExponentialDiskPotential():
mn = potential.MN3ExponentialDiskPotential(normalize=1., hr=0.5, hz=0.1)
tmax = 3.
vo, ro = 215., 8.75
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, mn, tmax, vo, ro)
return None
def test_nemo_MiyamotoNagaiPotential():
mp = potential.MiyamotoNagaiPotential(normalize=1., a=0.5, b=0.1)
tmax = 4.
vo, ro = 220., 8.
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, mp, tmax, vo, ro)
return None
def initialise_orbit(ID):
cand = gk_candidates[(gk_candidates[-1] == ID)]
ra_mean = cand[0]
ra_err = 0 #unavailable
dec_mean = cand[1]
dec_err = 0
pmRA_mean = cand[3]
pmRA_err = cand[6]
pmDec_mean = cand[4]
pmDec_err = cand[7]
#calc a random value from gaussian
ra = generate_rand(ra_mean, ra_err, measurement_type='mas')
dec = generate_rand(dec_mean, dec_err, measurement_type='mas')
pmRA = generate_rand(pmRA_mean, pmRA_err)
pmDec = generate_rand(pmDec_mean, pmDec_err)
#no error for distance in this set
dist = cand[2]
#VLOS is reliable and stays as is
Vlos = cand[5]
orbit = Orbit(vxvv=[ra, dec, dist, pmRA, pmDec, Vlos],
radec=True,
ro=8.,
vo=220.,
solarmotion="schoenrich")
return orbit
