def modified_power_spectrum(b_1,
f_nl,
cosmo,
redshift=0.,
tracer_p=1.,
nbar=None,
contrast=None):
r"""Return the tracer power spectrum modified by primordial
non-Gaussianity.
Parameters
----------
b_1 : float
Scale-independent linear bias at input redshift.
f_nl : float
Local primordial non-Gaussianity.
cosmo : :class:`nbodykit.cosmology.cosmology.Cosmology`
Cosmological model.
redshift : float, optional
Redshift at which quantities are evaluated (default is 0.).
tracer_p : float, optional
Tracer-dependent parameter :math:`p` (default is 1.).
nbar : float or None, optional
If not `None` (default), add ``1/nbar`` as shot noise to the
resulting power spectrum.
contrast : float or None, optional
If not `None` (default), add additional ``1/(contrast*nbar)``
as shot noise to the resulting power spectrum.
Returns
-------
callable
Tracer power spectrum modified by primordial non-Gaussianity as a
function of wavenumber (in :math:`h`/Mpc).
"""
bias = scale_dependent_bias(b_1,
f_nl,
cosmo,
redshift=redshift,
tracer_p=tracer_p)
power_spectrum = cosmology.LinearPower(cosmo, redshift=redshift)
alpha = 0. if contrast is None else 1 / contrast
shot_noise = 0. if nbar is None else (1 + alpha) / nbar
return lambda k: bias(k)**2 * power_spectrum(k) + shot_noise
def __init__(self,
h=0.67556,
T0_cmb=2.7255,
Omega0_b=0.0482754208891869,
Omega0_cdm=0.26377065934278865,
N_ur=None,
m_ncdm=[0.06],
P_k_max=10.0,
P_z_max=100.0,
sigma8=0.8225,
gauge='synchronous',
n_s=0.9667,
nonlinear=False):
# input parameters
kw_cosmo = locals()
kw_cosmo.pop('self')
for kw, val in kw_cosmo.items():
print(f'{kw:10s}: {val}')
sigma8 = kw_cosmo.pop('sigma8')
cosmo = cosmology.Cosmology(**kw_cosmo).match(sigma8=sigma8)
# --- cosmology calculators
redshift = 0.0
delta_crit = 1.686 # critical overdensity for collapse from Press-Schechter
DH = (
cosmo.H0 / cosmo.C
) # in units of h/Mpc, eq. 4 https://arxiv.org/pdf/astro-ph/9905116.pdf
Omega0_m = cosmo.Omega0_m
k_ = np.logspace(-10, 10, 10000)
Plin_ = cosmology.LinearPower(cosmo, redshift,
transfer='CLASS') # P(k) in (Mpc/h)^3
self.Plin = IUS(k_, Plin_(k_), ext=1)
Tlin_ = cosmology.transfers.CLASS(
cosmo, redshift) # T(k), normalized to one at k=0
tk_ = Tlin_(k_)
is_good = np.isfinite(tk_)
self.Tlin = IUS(k_[is_good], tk_[is_good], ext=1)
self.Dlin = cosmo.scale_independent_growth_factor # D(z), normalized to one at z=0
self.f = cosmo.scale_independent_growth_rate # dlnD/dlna
self.Dc = cosmo.comoving_distance
self.h = cosmo.efunc
self.inv_pi = 2.0 / np.pi
# alpha_fnl: equation 2 of Mueller et al 2017
self.alpha_fnl = 3.0 * delta_crit * Omega0_m * (DH**2)
def generate_data(x):
redshift = 0.0
r_vals = np.linspace(50, 140, 10)
extra_input = {'redshift': redshift, 'r_vals': r_vals}
n_data = x.shape[1]
y = np.empty((len(r_vals), n_data))
for i in range(n_data):
print(i)
om, s8, ob = x[:, i]
ocdm = om - ob
m_ncdm = [] #no massive neutrinos
cosmo = cosmology.Cosmology(Omega0_b=ob,
Omega0_cdm=ocdm,
m_ncdm=m_ncdm)
cosmo = cosmo.match(sigma8=s8)
plin = cosmology.LinearPower(cosmo, redshift, transfer='EisensteinHu')
cf = cosmology.correlation.CorrelationFunction(plin)
y[:, i] = cf(r_vals)
return y, extra_input
print(r"Nmesh = {:.0f}, a_sqrt = {:.0f}, BoxSize = {:.0f}".format(
grid_mesh, a_sqrt, Boxsize))
mesh_6411 = cata_6411.to_mesh(Nmesh=grid_mesh,
BoxSize=Boxsize,
resampler='cic')
mesh_6411 = mesh_6411.compute()
print(mesh_6411.shape)
# xi_6411 = FFTCorr(mesh_6411, mode='1d')
redshift = cata_6411.attrs['Redshift']
cosmo = cosmology.Cosmology(
h=cata_6411.attrs['HubbleParam'],
P_k_max=200).match(Omega0_m=cata_6411.attrs['Omega0'])
pk_cosmo = cosmology.LinearPower(cosmo, redshift, transfer='EisensteinHu')
def VectorProjection(vector, direction):
r"""
Vector components of given vectors in a given direction.
.. math::
\mathbf{v}_\mathbf{d} &= (\mathbf{v} \cdot \hat{\mathbf{d}}) \hat{\mathbf{d}} \\
\hat{\mathbf{d}} &= \frac{\mathbf{d}}{\|\mathbf{d}\|}
Parameters
----------
vector : array_like, (..., D)
array of vectors to be projected