def test_nfw_sphericalOrder():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 10)
Acos2, Asin2 = potential.scf_compute_coeffs_spherical(rho_NFW,
10,
radial_order=50)
assert numpy.all(numpy.fabs(Acos - Acos2) < EPS), \
"Increasing the radial order fails for scf_compute_coeffs_spherical"
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_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_scf_ZeeuwCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 5)
Aaxi = potential.scf_compute_coeffs(rho_Zeeuw,
5,
5,
radial_order=20,
costheta_order=20)
reducesto_spherical(Aspherical, Aaxi, "Zeeuw Potential")
def test_scf_compute_spherical_hernquist():
Acos, Asin = potential.scf_compute_coeffs_spherical(
sphericalHernquistDensity, 10)
spherical_coeffsTest(Acos, Asin)
assert numpy.fabs(
Acos[0, 0, 0] - 1.
) < EPS, "Acos(n=0,l=0,m=0) = 1 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(
Acos[0, 0, 0])
assert numpy.all(
numpy.fabs(Acos[1:, 0, 0]) < EPS), "Acos(n>0,l=0,m=0) = 0 fails."
def test_scf_compute_spherical_zeeuw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 10)
spherical_coeffsTest(Acos, Asin)
assert numpy.fabs(
Acos[0, 0, 0] - 2 * 3. / 4
) < EPS, "Acos(n=0,l=0,m=0) = 3/2 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(
Acos[0, 0, 0])
assert numpy.fabs(
Acos[1, 0, 0] - 2 * 1. / 12
) < EPS, "Acos(n=1,l=0,m=0) = 1/6 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(
Acos[0, 0, 0])
assert numpy.all(
numpy.fabs(Acos[2:, 0, 0]) < EPS), "Acos(n>1,l=0,m=0) = 0 fails."
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_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_scf_compute_nfw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 10)
spherical_coeffsTest(Acos, Asin)
def test_scf_ZeeuwCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 5)
Aaxi = potential.scf_compute_coeffs(rho_Zeeuw, 5,5,radial_order=20,
costheta_order=20)
reducesto_spherical(Aspherical,Aaxi, "Zeeuw Potential")
def test_potentialMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 50, a=50)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin, a=50)
assertmsg = "Comparing nfw with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw, scf, assertmsg, eps=1e-4)
def test_densMatches_zeeuw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 10)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing the density of Zeeuw's perfect ellipsoid with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(rho_Zeeuw, scf.dens, assertmsg)
def test_zforceMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 50, a=50)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin, a=50)
assertmsg = "Comparing the vertical force of NFW Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw.zforce, scf.zforce, assertmsg, eps=1e-3)
def test_zforceMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW,50, a=50)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin, a=50)
assertmsg = "Comparing the vertical force of NFW Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw.zforce,scf.zforce, assertmsg, eps=1e-3)
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_potentialMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW,50, a=50)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin, a=50)
assertmsg = "Comparing nfw with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw,scf, assertmsg, eps=1e-4)
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_densMatches_zeeuw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_Zeeuw,10)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing the density of Zeeuw's perfect ellipsoid with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(rho_Zeeuw,scf.dens, assertmsg)
def test_scf_HernquistCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(
sphericalHernquistDensity, 5)
Aaxi = potential.scf_compute_coeffs(sphericalHernquistDensity, 5, 5)
reducesto_spherical(Aspherical, Aaxi, "Hernquist Potential")
def test_nfw_sphericalOrder():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 10)
Acos2, Asin2 = potential.scf_compute_coeffs_spherical(rho_NFW, 10, radial_order=50)
assert numpy.all(numpy.fabs(Acos - Acos2) < EPS), \
"Increasing the radial order fails for scf_compute_coeffs_spherical"
def test_scf_compute_spherical_zeeuw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_Zeeuw, 10)
spherical_coeffsTest(Acos, Asin)
assert numpy.fabs(Acos[0,0,0] - 2*3./4) < EPS, "Acos(n=0,l=0,m=0) = 3/2 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(Acos[0,0,0])
assert numpy.fabs(Acos[1,0,0] - 2*1./12) < EPS, "Acos(n=1,l=0,m=0) = 1/6 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(Acos[0,0,0])
assert numpy.all(numpy.fabs(Acos[2:,0,0]) < EPS), "Acos(n>1,l=0,m=0) = 0 fails."
def test_scf_compute_nfw():
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 10)
spherical_coeffsTest(Acos, Asin)
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_phiforceMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW,10)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing the azimuth force of NFW Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw.phiforce,scf.phiforce, assertmsg)
def test_scf_HernquistCoeffs_ReducesToSpherical():
Aspherical = potential.scf_compute_coeffs_spherical(sphericalHernquistDensity, 5)
Aaxi = potential.scf_compute_coeffs(sphericalHernquistDensity, 5,5)
reducesto_spherical(Aspherical,Aaxi, "Hernquist Potential")
def test_phiforceMatches_nfw():
nfw = potential.NFWPotential()
Acos, Asin = potential.scf_compute_coeffs_spherical(rho_NFW, 10)
scf = SCFPotential(amp=1, Acos=Acos, Asin=Asin)
assertmsg = "Comparing the azimuth force of NFW Potential with SCF fails at R={0}, Z={1}, phi={2}"
compareFunctions(nfw.phiforce, scf.phiforce, assertmsg)
def test_scf_compute_spherical_hernquist():
Acos, Asin = potential.scf_compute_coeffs_spherical(sphericalHernquistDensity, 10)
spherical_coeffsTest(Acos, Asin)
assert numpy.fabs(Acos[0,0,0] - 1.) < EPS, "Acos(n=0,l=0,m=0) = 1 fails. Found to be Acos(n=0,l=0,m=0) = {0}".format(Acos[0,0,0])
assert numpy.all(numpy.fabs(Acos[1:,0,0]) < EPS), "Acos(n>0,l=0,m=0) = 0 fails."