def test_axi_density1_axiOrder():
Acos, Asin = potential.scf_compute_coeffs_axi(axi_density1, 10, 10)
Acos2, Asin2 = potential.scf_compute_coeffs_axi(axi_density1,
10,
10,
radial_order=50,
costheta_order=50)
assert numpy.all(numpy.fabs(Acos - Acos2) < 1e-10), \
"Increasing the radial and costheta order fails for scf_compute_coeffs_axi"
def make_McMillan2017(ro=8.21, vo=233.1):
'''
make_McMillan2017:
Make the McMillan 2017 potential using SCF basis expansion:
No arguments, but could change ro, vo if desired. ro is from the Gravity
Collaboration (2018). vo is from Eilers (2018) and Schonrich (2010)
Args:
None
'''
#dicts used in DiskSCFPotential
sigmadict = [{'type':'exp','h':Rd_HI,'amp':Sigma0_HI, 'Rhole':Rm_HI},
{'type':'exp','h':Rd_H2,'amp':Sigma0_H2, 'Rhole':Rm_H2},
{'type':'exp','h':Rd_thin,'amp':Sigma0_thin, 'Rhole':0.},
{'type':'exp','h':Rd_thick,'amp':Sigma0_thick, 'Rhole':0.}]
hzdict = [{'type':'sech2', 'h':zd_HI},
{'type':'sech2', 'h':zd_H2},
{'type':'exp', 'h':0.3/ro},
{'type':'exp', 'h':0.9/ro}]
McMillan_bulge=\
mySCFPotential(Acos=potential.scf_compute_coeffs_axi(bulge_dens,20,10,a=0.1)[0],
a=0.1,ro=ro,vo=vo)
McMillan_disk = myDiskSCFPotential(dens=lambda R,z: gas_stellar_dens(R,z),
Sigma=sigmadict, hz=hzdict,
a=2.5, N=30, L=30,ro=ro,vo=vo)
McMillan_halo = potential.NFWPotential(amp = rho0_halo*(4*np.pi*rh**3),
a = rh,ro=ro,vo=vo)
McMillan2017 = [McMillan_disk,McMillan_halo,McMillan_bulge]
return McMillan2017
def test_scf_compute_axi_density2():
A = potential.scf_compute_coeffs_axi(axi_density2,
10,
10,
radial_order=30,
costheta_order=12)
axi_coeffsTest(A[0], A[1])
analytically_calculated = 2 * numpy.array([
[1., 7. * 3**(-3 / 2.) / 4., 3 * 11 * 5**(-5. / 2) / 2., 0],
[0, 0, 0, 0], ##I never did analytically solve for n=1
[
0, 11. / (7 * 5 * 3**(3. / 2) * 2**(3.)),
(7 * 5**(.5) * 2**3.)**-1., 0
]
])
numerically_calculated = A[0][:3, :4, 0]
shape = numerically_calculated.shape
for n in range(shape[0]):
if n == 1: continue
for l in range(shape[1]):
assert numpy.fabs(numerically_calculated[n,l] - analytically_calculated[n,l]) < EPS, \
"Acos(n={0},l={1},0) = {2}, whereas it was analytically calculated to be {3}".format(n,l, numerically_calculated[n,l], analytically_calculated[n,l])
#Checks that A at l != 0,1,2 are always zero
assert numpy.all(
numpy.fabs(A[0][:, 3:, 0]) < 1e-10), "Acos(n,l>2,m=0) = 0 fails."
#Checks that A = 0 when n = 2,4,..,2*n and l = 0
assert numpy.all(
numpy.fabs(A[0][2::2, 0,
0]) < 1e-10), "Acos(n > 1,l = 0,m=0) = 0 fails."
def test_scf_compute_axi_nbody_twopowertriaxial():
N = int(1e5)
Mh = 11.
ah = 50. / 8.
m = Mh / N
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(1)
samp = [hdf.sample(n=N) for i in range(nsamp)]
positions = numpy.array([[samp[i].x(), samp[i].y(), samp[i].z() * zfactor]
for i in range(nsamp)])
# This is an axisymmtric Hernquist profile with the same mass as the above
tptp = potential.TwoPowerTriaxialPotential(amp=2. * Mh / zfactor,
a=ah,
alpha=1.,
beta=4.,
b=1.,
c=zfactor)
tptp.turn_physical_off()
cc, ss = potential.scf_compute_coeffs_axi(tptp.dens, Norder, Lorder, a=ah)
c, s = numpy.zeros((2, nsamp, Norder, Lorder, 1))
for i, p in enumerate(positions):
c[i], s[i] = potential.scf_compute_coeffs_axi_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, 1))
for i, p in enumerate(positions):
c[i], s[i] = potential.scf_compute_coeffs_axi_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_scf_compute_axi_density1():
A = potential.scf_compute_coeffs_axi(axi_density1, 10,10)
axi_coeffsTest(A[0], A[1])
analytically_calculated = numpy.array([[4./3, 7.* 3**(-5/2.), 2*11*5**(-5./2), 0],
[0, 0,0,0],
[0,11. / (3.**(5./2) * 5 * 7. * 2), 1. / (2*3.*5**.5*7.), 0]])
numerically_calculated = A[0][:3,:4,0]
shape = numerically_calculated.shape
for n in range(shape[0]):
for l in range(shape[1]):
assert numpy.fabs(numerically_calculated[n,l] - analytically_calculated[n,l]) < EPS, \
"Acos(n={0},l={1},0) = {2}, whereas it was analytically calculated to be {3}".format(n,l, numerically_calculated[n,l], analytically_calculated[n,l])
#Checks that A at l != 0,1,2 are always zero
assert numpy.all(numpy.fabs(A[0][:,3:,0]) < 1e-10), "Acos(n,l>2,m=0) = 0 fails."
#Checks that A at n odd is always zero
assert numpy.all(numpy.fabs(A[0][1::2,:,0]) < 1e-10), "Acos(n odd,l,m=0) = 0 fails."
#Checks that A = 0 when n != 0 and l = 0
assert numpy.all(numpy.fabs(A[0][1:,0,0]) < 1e-10), "Acos(n > 1,l=0,m=0) = 0 fails."
def test_scf_compute_axi_density2():
A = potential.scf_compute_coeffs_axi(axi_density2, 10,10,
radial_order=30,costheta_order=12)
axi_coeffsTest(A[0], A[1])
analytically_calculated = 2*numpy.array([[1., 7.* 3**(-3/2.) /4., 3*11*5**(-5./2)/2., 0],
[0,0,0,0], ##I never did analytically solve for n=1
[0, 11./(7*5*3**(3./2)*2**(3.)), (7 * 5**(.5)*2**3.)**-1., 0]])
numerically_calculated = A[0][:3,:4,0]
shape = numerically_calculated.shape
for n in range(shape[0]):
if n ==1: continue
for l in range(shape[1]):
assert numpy.fabs(numerically_calculated[n,l] - analytically_calculated[n,l]) < EPS, \
"Acos(n={0},l={1},0) = {2}, whereas it was analytically calculated to be {3}".format(n,l, numerically_calculated[n,l], analytically_calculated[n,l])
#Checks that A at l != 0,1,2 are always zero
assert numpy.all(numpy.fabs(A[0][:,3:,0]) < 1e-10), "Acos(n,l>2,m=0) = 0 fails."
#Checks that A = 0 when n = 2,4,..,2*n and l = 0
assert numpy.all(numpy.fabs(A[0][2::2,0,0]) < 1e-10), "Acos(n > 1,l = 0,m=0) = 0 fails."
def test_scf_compute_axi_density1():
A = potential.scf_compute_coeffs_axi(axi_density1, 10,10)
axi_coeffsTest(A[0], A[1])
analytically_calculated = numpy.array([[4./3, 7.* 3**(-5/2.), 2*11*5**(-5./2), 0],
[0, 0,0,0],
[0,11. / (3.**(5./2) * 5 * 7. * 2), 1. / (2*3.*5**.5*7.), 0]])
numerically_calculated = A[0][:3,:4,0]
shape = numerically_calculated.shape
for n in range(shape[0]):
for l in range(shape[1]):
assert numpy.fabs(numerically_calculated[n,l] - analytically_calculated[n,l]) < EPS, \
"Acos(n={0},l={1},0) = {2}, whereas it was analytically calculated to be {3}".format(n,l, numerically_calculated[n,l], analytically_calculated[n,l])
#Checks that A at l != 0,1,2 are always zero
assert numpy.all(numpy.fabs(A[0][:,3:,0]) < 1e-10), "Acos(n,l>2,m=0) = 0 fails."
#Checks that A at n odd is always zero
assert numpy.all(numpy.fabs(A[0][1::2,:,0]) < 1e-10), "Acos(n odd,l,m=0) = 0 fails."
#Checks that A = 0 when n != 0 and l = 0
assert numpy.all(numpy.fabs(A[0][1:,0,0]) < 1e-10), "Acos(n > 1,l=0,m=0) = 0 fails."
def test_densMatches_axi_density2():
Acos, Asin = potential.scf_compute_coeffs_axi(axi_density2, 50, 3)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing axi_density2 with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(axi_density2, scf.dens, assertmsg, eps=1e-3)
def test_scf_axiZeeuwCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 10)
Aaxi = potential.scf_compute_coeffs_axi(rho_Zeeuw, 10, 10)
axi_reducesto_spherical(Aspherical, Aaxi, "Zeeuw Potential")
def test_scf_axiHernquistCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(
sphericalHernquistDensity, 10)
Aaxi = potential.scf_compute_coeffs_axi(sphericalHernquistDensity, 10, 10)
axi_reducesto_spherical(Aspherical, Aaxi, "Hernquist Potential")
def test_densMatches_axi_density2():
Acos, Asin = potential.scf_compute_coeffs_axi(axi_density2,50,3)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing axi_density2 with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(axi_density2,scf.dens, assertmsg, eps=1e-3)
def test_scf_axiZeeuwCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 10)
Aaxi = potential.scf_compute_coeffs_axi(rho_Zeeuw, 10,10)
axi_reducesto_spherical(Aspherical,Aaxi, "Zeeuw Potential")
def test_scf_axiHernquistCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(sphericalHernquistDensity, 10)
Aaxi = potential.scf_compute_coeffs_axi(sphericalHernquistDensity, 10,10)
axi_reducesto_spherical(Aspherical,Aaxi, "Hernquist Potential")
def test_axi_density1_axiOrder():
Acos, Asin = potential.scf_compute_coeffs_axi(axi_density1, 10,10)
Acos2, Asin2 = potential.scf_compute_coeffs_axi(axi_density1, 10, 10, radial_order=50, costheta_order=50)
assert numpy.all(numpy.fabs(Acos - Acos2) < 1e-10), \
"Increasing the radial and costheta order fails for scf_compute_coeffs_axi"
return gas_dens(R,z)+stellar_dens(R,z)+bulge_dens(R,z)+NFW_dens(R,z)
def sech(x):
return 1./np.cosh(x)
#dicts used in DiskSCFPotential
sigmadict = [{'type':'exp','h':Rd_HI,'amp':Sigma0_HI, 'Rhole':Rm_HI},
{'type':'exp','h':Rd_H2,'amp':Sigma0_H2, 'Rhole':Rm_H2},
{'type':'exp','h':Rd_thin,'amp':Sigma0_thin, 'Rhole':0.},
{'type':'exp','h':Rd_thick,'amp':Sigma0_thick, 'Rhole':0.}]
hzdict = [{'type':'sech2', 'h':zd_HI},
{'type':'sech2', 'h':zd_H2},
{'type':'exp', 'h':0.3/ro},
{'type':'exp', 'h':0.9/ro}]
#generate separate disk and halo potential - and combined potential
McMillan_bulge=\
mySCFPotential(Acos=scf_compute_coeffs_axi(bulge_dens,20,10,a=0.1)[0],
a=0.1,ro=ro,vo=vo)
McMillan_disk = myDiskSCFPotential(dens=lambda R,z: gas_stellar_dens(R,z),
Sigma=sigmadict, hz=hzdict,
a=2.5, N=30, L=30,ro=ro,vo=vo)
McMillan_halo = NFWPotential(amp = rho0_halo*(4*np.pi*rh**3),
a = rh,ro=ro,vo=vo)
McMillan2017 = [McMillan_disk,McMillan_halo,McMillan_bulge]