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_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 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_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_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_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_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_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
def test_scf_compute_nbody_twopowertriaxial():
N = int(1e5)
Mh = 11.
ah = 50. / 8.
m = Mh / N
yfactor = 1.5
zfactor = 2.5
nsamp = 10
Norder = 10
Lorder = 10
hern = potential.HernquistPotential(amp=2 * Mh, a=ah)
hern.turn_physical_off()
hdf = df.isotropicHernquistdf(hern)
numpy.random.seed(2)
samp = [hdf.sample(n=N) for i in range(nsamp)]
positions = numpy.array(
[[samp[i].x(), samp[i].y() * yfactor, samp[i].z() * zfactor]
for i in range(nsamp)])
# This is an triaxial Hernquist profile with the same mass as the above
tptp = potential.TwoPowerTriaxialPotential(amp=2. * Mh / yfactor / zfactor,
a=ah,
alpha=1.,
beta=4.,
b=yfactor,
c=zfactor)
tptp.turn_physical_off()
cc, ss = potential.scf_compute_coeffs(tptp.dens, Norder, Lorder, a=ah)
c, s = numpy.zeros((2, nsamp, Norder, Lorder, Lorder))
for i, p in enumerate(positions):
c[i], s[i] = potential.scf_compute_coeffs_nbody(p,
Norder,
Lorder,
mass=m * numpy.ones(N),
a=ah)
# Check that the difference between the coefficients is within two standard deviations
assert (cc - (numpy.mean(c, axis=0)) <= (2. * numpy.std(c, axis=0))).all()
# Repeat test for single mass
c, s = numpy.zeros((2, nsamp, Norder, Lorder, Lorder))
for i, p in enumerate(positions):
c[i], s[i] = potential.scf_compute_coeffs_nbody(p,
Norder,
Lorder,
mass=m,
a=ah)
assert (cc - (numpy.mean(c, axis=0)) <= (2. * numpy.std(c, axis=0))).all()
return None
def test_isotropic_hernquist_givenr_are_atgivenr():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
r= numpy.linspace(0.1,10.,1001)
theta= numpy.random.uniform(size=len(r))*numpy.pi
# n should be ignored in the following
samp= dfh.sample(R=r*numpy.sin(theta),z=r*numpy.cos(theta),n=100000)
assert len(samp) == len(r), 'Length of sample with given r array is not equal to length of r'
assert numpy.all(numpy.fabs(samp.r()-r) < 1e-8), 'Sampling a spherical distribution function at given r does not produce orbits at these given r'
assert numpy.all(numpy.fabs(samp.R()-r*numpy.sin(theta)) < 1e-8), 'Sampling a spherical distribution function at given R does not produce orbits at these given R'
assert numpy.all(numpy.fabs(samp.z()-r*numpy.cos(theta)) < 1e-8), 'Sampling a spherical distribution function at given z does not produce orbits at these given z'
return None
def test_isotropic_hernquist_diffcalls():
from galpy.orbit import Orbit
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
# R,vR... vs. E
R,vR,vT,z,vz,phi= 1.1,0.3,0.2,0.9,-0.2,2.4
# Calculate E directly
assert numpy.fabs(dfh(R,vR,vT,z,vz,phi)-dfh((pot(R,z)+0.5*(vR**2.+vT**2.+vz**2.),))) < 1e-8, 'Calling the isotropic Hernquist DF with R,vR,... or E[R,vR,...] does not give the same answer'
# Also L
assert numpy.fabs(dfh(R,vR,vT,z,vz,phi)-dfh((pot(R,z)+0.5*(vR**2.+vT**2.+vz**2.),numpy.sqrt(numpy.sum(Orbit([R,vR,vT,z,vz,phi]).L()**2.))))) < 1e-8, 'Calling the isotropic Hernquist DF with R,vR,... or E[R,vR,...] does not give the same answer'
# Also as orbit
assert numpy.fabs(dfh(R,vR,vT,z,vz,phi)-dfh(Orbit([R,vR,vT,z,vz,phi]))) < 1e-8, 'Calling the isotropic Hernquist DF with R,vR,... or E[R,vR,...] does not give the same answer'
return None
def test_isotropic_hernquist_singler_is_atrandomphi():
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.,n=100000)
tol= 1e-2
check_azimuthal_symmetry(samp,0,tol)
check_azimuthal_symmetry(samp,1,tol)
check_azimuthal_symmetry(samp,2,tol)
check_azimuthal_symmetry(samp,3,tol)
check_azimuthal_symmetry(samp,4,tol)
check_azimuthal_symmetry(samp,5,tol)
check_azimuthal_symmetry(samp,6,tol)
return None
def setup_class(cls):
"""Setup fixtures for testing."""
super().setup_class()
# make potential
cls.mass = 1e12 * u.solMass
hernquist_pot = HernquistPotential(amp=2 * cls.mass)
hernquist_pot.turn_physical_on() # force units
cls.potential = hernquist_pot
cls.df = isotropicHernquistdf(hernquist_pot)
cls.df.turn_physical_on()
cls.inst = cls.obj(GalpyPotentialWrapper(cls.potential))
def test_isotropic_hernquist_phasespacesamples_vs_orbitsamples():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp_orbits= dfh.sample(n=1000)
# Reset seed such that we should get the same
numpy.random.seed(10)
samp_RvR= dfh.sample(n=1000,return_orbit=False)
assert numpy.all(numpy.fabs(samp_orbits.R()-samp_RvR[0]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
assert numpy.all(numpy.fabs(samp_orbits.vR()-samp_RvR[1]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
assert numpy.all(numpy.fabs(samp_orbits.vT()-samp_RvR[2]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
assert numpy.all(numpy.fabs(samp_orbits.z()-samp_RvR[3]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
assert numpy.all(numpy.fabs(samp_orbits.vz()-samp_RvR[4]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
assert numpy.all(numpy.fabs(samp_orbits.phi()-samp_RvR[5]) < 1e-8), 'Sampling R,vR,... from spherical DF does not give the same as sampling equivalent orbits'
return None
def test_isotropic_hernquist_dens_spherically_symmetric():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
numpy.random.seed(10)
samp= dfh.sample(n=100000)
# Check spherical symmetry for different harmonics l,m
tol= 1e-2
check_spherical_symmetry(samp,0,0,tol)
check_spherical_symmetry(samp,1,0,tol)
check_spherical_symmetry(samp,1,-1,tol)
check_spherical_symmetry(samp,1,1,tol)
check_spherical_symmetry(samp,2,0,tol)
check_spherical_symmetry(samp,2,-1,tol)
check_spherical_symmetry(samp,2,-2,tol)
check_spherical_symmetry(samp,2,1,tol)
check_spherical_symmetry(samp,2,2,tol)
# and some higher order ones
check_spherical_symmetry(samp,3,1,tol)
check_spherical_symmetry(samp,9,-6,tol)
return None
def compare_dens_nbody():
N = int(1e5)
Mh = 11.
ah = 50. / 8.
m = Mh / N
factor = 1.
nsamp = 10
Norder = 10
Lorder = 10
hern = potential.HernquistPotential(amp=2 * Mh, a=ah)
hern.turn_physical_off()
hdf = df.isotropicHernquistdf(hern)
samp = [hdf.sample(n=N) for i in range(nsamp)]
positions = numpy.array([[samp[i].x(), samp[i].y(), samp[i].z() * factor]
for i in range(nsamp)])
tptp = potential.TwoPowerTriaxialPotential(amp=2. * Mh,
a=ah,
alpha=1.,
beta=4.,
b=1.,
c=factor)
tptp.turn_physical_off()
cc, ss = potential.scf_compute_coeffs(tptp.dens, Norder, Lorder, a=ah)
c, s = numpy.zeros((2, nsamp, Norder, Lorder, Lorder))
for i, p in enumerate(positions):
c[i], s[i] = potential.scf_compute_coeffs_nbody(p,
m * numpy.ones(N) *
factor,
Norder,
Lorder,
a=ah)
# Check that the difference between the coefficients is within two standard deviations
assert (cc - (numpy.mean(c, axis=0)) <= (2. * numpy.std(c, axis=0))).all()
def test_isotropic_hernquist_nopot():
with pytest.raises(AssertionError) as excinfo:
dfh= isotropicHernquistdf()
assert str(excinfo.value) == 'pot= must be potential.HernquistPotential', 'Error message when not supplying the potential is incorrect'
return None
def test_isotropic_hernquist_energyoutofbounds():
pot= potential.HernquistPotential(amp=2.3,a=1.3)
dfh= isotropicHernquistdf(pot=pot)
assert numpy.all(numpy.fabs(dfh((numpy.arange(0.1,10.,0.1),))) < 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,))) < 1e-8), 'Evaluating the isotropic Hernquist DF at E < -GM/a does not give zero'
return None
def test_isotropic_hernquist_wrongpot():
pot= potential.JaffePotential(amp=2.,a=1.3)
with pytest.raises(AssertionError) as excinfo:
dfh= isotropicHernquistdf(pot=pot)
assert str(excinfo.value) == 'pot= must be potential.HernquistPotential', 'Error message when not supplying the potential is incorrect'
return None
