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 setup_potential_kuepper(Mhalo: float, a: float) -> List[Potential]:
"""Set up Kuepper et al. (2015) Potential.
Parameters
----------
Mhalo: float
mass / 10^12 Msun
a: float
scale length / kpc,
Returns
-------
potential : list
HernquistPotential + MiyamotoNagaiPotential + NFWPotential
"""
pot: List[Potential] = [
potential.HernquistPotential(amp=3.4e10 * u.Msun, a=0.7 * u.kpc),
potential.MiyamotoNagaiPotential(amp=1e11 * u.Msun,
a=6.5 * u.kpc,
b=0.26 * u.kpc),
potential.NFWPotential(amp=Mhalo * 1e12 * u.Msun, a=a * u.kpc),
]
return pot
def test_isotropic_hernquist_singlerphi_is_atsinglephi():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp= dfh.sample(R=1.3,z=0.,phi=numpy.pi-0.3,n=100000)
assert numpy.all(numpy.fabs(samp.phi()-numpy.pi+0.3) < 1e-8), 'Sampling a spherical distribution function at a single r and phi oes not produce orbits at a single phi'
return None
def compare_dens_nbody_spherical():
N = int(1e6)
Mh = 11.
ah = 50. / 8.
m = Mh / N
factor = 1.
nsamp = 10
Norder = 10
hern = potential.HernquistPotential(amp=2 * Mh, a=ah)
hern.turn_physical_off()
hdf = df.isotropicHernquistdf(hern)
samples = [hdf.sample(n=N) for i in range(nsamp)]
positions = numpy.array(
[[samples[i].x(), samples[i].y(), samples[i].z() * factor]
for i in range(nsamp)])
c = numpy.zeros((nsamp, Norder, 1, 1))
s = numpy.zeros((nsamp, Norder, 1, 1))
for i in range(nsamp):
c[i], s[i] = potential.scf_compute_coeffs_spherical_nbody(
m=m * numpy.ones(N), pos=positions[i], N=Norder, a=ah)
cc, ss = potential.scf_compute_coeffs_spherical(N=Norder,
a=ah,
dens=hern.dens)
# Check that the difference between the coefficients is within the standard deviation
assert (cc - numpy.mean(c, axis=0) < numpy.std(c, axis=0)).all()
def test_isotropic_hernquist_meanvr_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
tol= 1e-8
check_meanvr_directint(dfh,pot,tol,beta=0.,rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=31)
return None
def setup_class(cls):
"""Setup fixtures for testing."""
super().setup_class()
nx = ny = nz = 76 # must be int and even
nxr0 = nyr0 = nzr0 = 2.3 * 2
X, Y, Z = (np.array(
np.meshgrid(
np.linspace(-nxr0 / 2, nxr0 / 2, nx),
np.linspace(-nyr0 / 2, nyr0 / 2, ny),
np.linspace(-nzr0 / 2, nzr0 / 2, nz),
indexing="ij",
), ) * 1)
XYZ = coord.CartesianRepresentation(X, Y, Z, unit=u.kpc)
# THIRD PARTY
import galpy.potential as gpot
cls.potential = gpot.HernquistPotential()
cls.meshgrid = XYZ
cls.inst = cls.obj(
PotentialWrapper(cls.potential),
cls.meshgrid,
total_mass=10 * u.solMass,
)
def test_potentialMatches_hernquist():
h = potential.HernquistPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(
sphericalHernquistDensity, 10)
scf = SCFPotential()
assertmsg = "Comparing the potential of Hernquist Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(h, scf, assertmsg)
def test_phiforceMatches_hernquist():
h = potential.HernquistPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(
sphericalHernquistDensity, 1)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing the azimuth force of Hernquist Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(h.phiforce, scf.phiforce, assertmsg)
def test_anisotropic_hernquist_energyoutofbounds():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
assert numpy.all(numpy.fabs(dfh((numpy.arange(0.1,10.,0.1),1.1))) < 1e-8), 'Evaluating the isotropic Hernquist DF at E > 0 does not give zero'
assert numpy.all(numpy.fabs(dfh((pot(0,0)-1e-4,1.1))) < 1e-8), 'Evaluating the isotropic Hernquist DF at E < -GM/a does not give zero'
return None
def test_isotropic_hernquist_unittransfer():
from galpy.util import conversion
ro, vo= 9., 210.
pot= potential.HernquistPotential(amp=2.,a=1.3,ro=ro,vo=vo)
dfh= isotropicHernquistdf(pot=pot)
phys= conversion.get_physical(dfh,include_set=True)
assert phys['roSet'], "sphericaldf's ro not set when that of the underlying potential is set"
assert phys['voSet'], "sphericaldf's vo not set when that of the underlying potential is set"
assert numpy.fabs(phys['ro']-ro) < 1e-8, "Potential's unit system not correctly transfered to sphericaldf's"
assert numpy.fabs(phys['vo']-vo) < 1e-8, "Potential's unit system not correctly transfered to sphericaldf's"
# Following should not be on
pot= potential.HernquistPotential(amp=2.,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
phys= conversion.get_physical(dfh,include_set=True)
assert not phys['roSet'], "sphericaldf's ro set when that of the underlying potential is not set"
assert not phys['voSet'], "sphericaldf's vo set when that of the underlying potential is not set"
return None
def test_isotropic_hernquist_unitsofsamples():
from galpy.util import conversion
ro, vo= 9., 210.
pot= potential.HernquistPotential(amp=2.,a=1.3,ro=ro,vo=vo)
dfh= isotropicHernquistdf(pot=pot)
samp= dfh.sample(n=100)
assert conversion.get_physical(samp,include_set=True)['roSet'], 'Orbit samples from spherical DF with units on do not have units on'
assert conversion.get_physical(samp,include_set=True)['voSet'], 'Orbit samples from spherical DF with units on do not have units on'
assert numpy.fabs(conversion.get_physical(samp,include_set=True)['ro']-ro) < 1e-8, 'Orbit samples from spherical DF with units on do not have correct ro'
assert numpy.fabs(conversion.get_physical(samp,include_set=True)['vo']-vo) < 1e-8, 'Orbit samples from spherical DF with units on do not have correct vo'
# Also test a case where they should be off
pot= potential.HernquistPotential(amp=2.,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
samp= dfh.sample(n=100)
assert not conversion.get_physical(samp,include_set=True)['roSet'], 'Orbit samples from spherical DF with units off do not have units off'
assert not conversion.get_physical(samp,include_set=True)['voSet'], 'Orbit samples from spherical DF with units off do not have units off'
return None
def test_isotropic_hernquist_sigmar():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp= dfh.sample(n=300000)
tol= 0.05
check_sigmar_against_jeans(samp,pot,tol,beta=0.,
rmin=pot._scale/10.,rmax=pot._scale*10.,bins=31)
return None
def test_isotropic_hernquist_sigmar_directint_forcevmoment():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
tol= 1e-5
check_sigmar_against_jeans_directint_forcevmoment(dfh,pot,tol,beta=0.,
rmin=pot._scale/10.,
rmax=pot._scale*10.,
bins=31)
return None
def test_isotropic_hernquist_dens_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
tol= 1e-8
check_dens_directint(dfh,pot,tol,
lambda r: pot.dens(r,0)/(2.3/2.), # need to divide by mass
rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=31)
return None
def test_isotropic_hernquist_beta():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp= dfh.sample(n=1000000)
tol= 6*1e-2
check_beta(samp,pot,tol,beta=0.,
rmin=pot._scale/10.,rmax=pot._scale*10.,bins=31)
return None
def test_osipkovmerritt_hernquist_meanvr_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
ras= [0.3,2.3,5.7]
for ra in ras:
dfh= osipkovmerrittHernquistdf(pot=pot,ra=ra)
tol= 1e-8
check_meanvr_directint(dfh,pot,tol,rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=6)
return None
def test_staeckel_fudge_delta():
import galpy.potential as galpy_pot
from galpy.actionAngle import estimateDeltaStaeckel
ro = 8.1 * u.kpc
vo = 229 * u.km / u.s
paired_potentials = []
# Miyamoto-Nagai
potential = gp.MiyamotoNagaiPotential(m=6e10 * u.Msun,
a=3 * u.kpc,
b=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['a'].to_value(ro)
b = potential.parameters['b'].to_value(ro)
galpy_potential = galpy_pot.MiyamotoNagaiPotential(amp=amp,
a=a,
b=b,
ro=ro,
vo=vo)
paired_potentials.append((potential, galpy_potential))
# Hernquist
potential = gp.HernquistPotential(m=6e10 * u.Msun,
c=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['c'].to_value(ro)
galpy_potential = galpy_pot.HernquistPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# NFW
potential = gp.NFWPotential(m=6e11 * u.Msun,
r_s=15.6 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['r_s'].to_value(ro)
galpy_potential = galpy_pot.NFWPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# TEST:
N = 1024
rnd = np.random.default_rng(42)
w = PhaseSpacePosition(pos=rnd.uniform(-10, 10, size=(3, N)) * u.kpc,
vel=rnd.uniform(-100, 100, size=(3, N)) * u.km /
u.s)
R = w.cylindrical.rho.to_value(ro)
z = w.z.to_value(ro)
for p, galpy_p in paired_potentials:
galpy_deltas = estimateDeltaStaeckel(galpy_p, R, z, no_median=True)
gala_deltas = get_staeckel_fudge_delta(p, w).value
print(p, np.allclose(gala_deltas, galpy_deltas))
assert np.allclose(gala_deltas, galpy_deltas, atol=1e-6)
def test_isotropic_hernquist_incompatibleunits():
pot= potential.HernquistPotential(amp=2.,a=1.3,ro=9.,vo=210.)
with pytest.raises(RuntimeError):
dfh= isotropicHernquistdf(pot=pot,ro=8.,vo=210.)
with pytest.raises(RuntimeError):
dfh= isotropicHernquistdf(pot=pot,ro=9.,vo=230.)
with pytest.raises(RuntimeError):
dfh= isotropicHernquistdf(pot=pot,ro=8.,vo=230.)
return None
def test_anisotropic_hernquist_meanvr_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
tol= 1e-8
check_meanvr_directint(dfh,pot,tol,beta=beta,rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=31)
return None
def test_osipkovmerritt_hernquist_Qoutofbounds():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
ras= [0.3,2.3,5.7]
for ra in ras:
dfh= osipkovmerrittHernquistdf(pot=pot,ra=ra)
assert numpy.all(numpy.fabs(dfh((numpy.arange(0.1,10.,0.1),1.1))) < 1e-8), 'Evaluating the Osipkov-Merritt Hernquist DF at E > 0 does not give zero'
# The next one is not actually a physical orbit...
assert numpy.all(numpy.fabs(dfh((pot(0,0)-1e-1,0.1))) < 1e-8), 'Evaluating the Osipkov-Merritt Hernquist DF at E < -GM/a does not give zero'
assert numpy.all(numpy.fabs(dfh((-1e-4,1.1))) < 1e-8), 'Evaluating the Osipkov-Merritt Hernquist DF at Q < 0 does not give zero'
return None
def test_isotropic_hernquist_singler_sigmar():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
for r in [0.3,1.3,2.3]:
samp= dfh.sample(R=r,z=0.,n=100000)
tol= 0.01
check_sigmar_against_jeans(samp,pot,tol,beta=0.,
rmin=r-0.1,rmax=r+0.1,bins=1)
return None
def test_anisotropic_hernquist_beta():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
numpy.random.seed(10)
samp= dfh.sample(n=1000000)
tol= 8*1e-2 * (beta > -0.7) + 0.12 * (beta == -0.7)
check_beta(samp,pot,tol,beta=beta,
rmin=pot._scale/10.,rmax=pot._scale*10.,bins=31)
return None
def test_osipkovmerritt_hernquist_beta_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
ras= [0.3,2.3,5.7]
for ra in ras:
dfh= osipkovmerrittHernquistdf(pot=pot,ra=ra)
tol= 1e-8
check_beta_directint(dfh,tol,beta=lambda r: 1./(1.+ra**2./r**2.),
rmin=pot._scale/10.,
rmax=pot._scale*10.,
bins=6)
return None
def test_anisotropic_hernquist_negdf():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
# beta > 0.5 has negative DF parts
dfh= constantbetaHernquistdf(pot=pot,beta=0.7)
with pytest.warns(None) as record:
samp= dfh.sample(n=100)
raisedWarning= False
for rec in record:
# check that the message matches
raisedWarning+= (str(rec.message.args[0]) == "The DF appears to have negative regions; we'll try to ignore these for sampling the DF, but this may adversely affect the generated samples. Proceed with care!")
assert raisedWarning, "Using an anisotropic Hernquist DF that has negative parts should have raised a warning, but didn't"
def test_osipkovmerritt_hernquist_dens_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
ras= [0.3,2.3,5.7]
for ra in ras:
dfh= osipkovmerrittHernquistdf(pot=pot,ra=ra)
tol= 1e-5
check_dens_directint(dfh,pot,tol,
lambda r: pot.dens(r,0)/(2.3/2.), # need to divide by mass
rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=6)
return None
def test_anisotropic_hernquist_dens_directint():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
tol= 1e-7
check_dens_directint(dfh,pot,tol,
lambda r: pot.dens(r,0)/(2.3/2.), # need to divide by mass
rmin=pot._scale/10.,
rmax=pot._scale*10.,bins=31)
return None
def test_osipkovmerritt_hernquist_beta():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
ras= [0.3,2.3,5.7]
for ra in ras:
dfh= osipkovmerrittHernquistdf(pot=pot,ra=ra)
numpy.random.seed(10)
samp= dfh.sample(n=1000000)
tol= 0.06
check_beta(samp,pot,tol,beta=lambda r: 1./(1.+ra**2./r**2.),
rmin=pot._scale/10.,rmax=pot._scale*10.,bins=31)
return None
def test_anisotropic_hernquist_dens_massprofile():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
numpy.random.seed(10)
samp= dfh.sample(n=100000)
tol= 5*1e-3
check_spherical_massprofile(samp,lambda r: pot.mass(r)\
/pot.mass(numpy.amax(samp.r())),
tol,skip=1000)
return None
def test_anisotropic_hernquist_sigmar():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
betas= [-0.7,-0.5,-0.4,0.,0.3,0.5]
for beta in betas:
dfh= constantbetaHernquistdf(pot=pot,beta=beta)
numpy.random.seed(10)
samp= dfh.sample(n=100000)
tol= 0.05
check_sigmar_against_jeans(samp,pot,tol,beta=beta,
rmin=pot._scale/10.,rmax=pot._scale*10.,
bins=31)
return None
def test_isotropic_hernquist_dens_massprofile():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp= dfh.sample(n=100000)
tol= 5*1e-3
check_spherical_massprofile(samp,
lambda r: pot.mass(r)\
/pot.mass(numpy.amax(samp.r()),
),
tol,skip=1000)
return None