def xi_einasto_at_r(r, M, conc, alpha, om, delta=200, rhos=-1.):
"""Einasto halo profile.
Args:
r (float or array like): 3d distances from halo center in Mpc/h comoving
M (float): Mass in Msun/h; not used if rhos is specified
conc (float): Concentration
alpha (float): Profile exponent
om (float): Omega_matter, matter fraction of the density
delta (int): Overdensity, default is 200
rhos (float): Scale density in Msun h^2/Mpc^3 comoving; optional
Returns:
float or array like: Einasto halo profile.
"""
r = np.asarray(r)
scalar_input = False
if r.ndim == 0:
r = r[None] #makes r 1D
scalar_input = True
if r.ndim > 1:
raise Exception("r cannot be a >1D array.")
xi = np.zeros_like(r)
cluster_toolkit._lib.calc_xi_einasto(_dcast(r), len(r), M, rhos, conc,
alpha, delta, om, _dcast(xi))
if scalar_input:
return np.squeeze(xi)
return xi
def rho_nfw_at_r(r, M, c, Omega_m, delta=200):
"""NFW halo density profile.
Args:
r (float or array like): 3d distances from halo center in Mpc/h comoving.
M (float): Mass in Msun/h.
c (float): Concentration.
Omega_m (float): Omega_matter, matter fraction of the density.
delta (int; optional): Overdensity, default is 200.
Returns:
float or array like: NFW halo density profile in Msun h^2/Mpc^3 comoving.
"""
r = np.asarray(r)
scalar_input = False
if r.ndim == 0:
r = r[None] #makes r 1D
scalar_input = True
if r.ndim > 1:
raise Exception("r cannot be a >1D array.")
rho = np.zeros_like(r)
cluster_toolkit._lib.calc_rho_nfw(_dcast(r), len(r), M, c, delta,
Omega_m, _dcast(rho))
if scalar_input:
return np.squeeze(rho)
return rho
def xi_hm(xi_1halo, xi_2halo, combination="max"):
"""Halo-matter correlation function
Note: at the moment you can combine the 1-halo and 2-halo terms by either taking the max of the two or the sum of the two. The 'combination' field must be set to either 'max' (default) or 'sum'.
Args:
xi_1halo (float or array like): 1-halo term
xi_2halo (float or array like, same size as xi_1halo): 2-halo term
combination (string; optional): specifies how the 1-halo and 2-halo terms are combined, default is 'max' which takes the max of the two
Returns:
float or array like: Halo-matter correlation function
"""
if combination == "max":
switch = 0
elif combination == 'sum':
switch = 1
else:
raise Exception("Combinations other than maximum not implemented yet")
xi = np.zeros_like(xi_1halo)
cluster_toolkit._lib.calc_xi_hm(len(xi_1halo), _dcast(xi_1halo),
_dcast(xi_2halo), _dcast(xi), switch)
return xi
def G_at_sigma(sigma, d=1.97, e=1.0, f=0.51, g=1.228):
"""Tinker et al. 2008 appendix C multiplicity funciton G(sigma) as
a function of sigma.
NOTE: by default, this function is only valid at :math:`z=0`. For use
at higher redshifts either recompute the parameters yourself, or
wait for this behavior to be patched.
Args:
sigma (float or array like): RMS variance of the matter density field.
d (float; optional): First Tinker parameter. Default is 1.97.
e (float; optional): Second Tinker parameter. Default is 1.
f (float; optional): Third Tinker parameter. Default is 0.51.
g (float; optional): Fourth Tinker parameter. Default is 1.228.
Returns:
float or array like: Halo multiplicity G(sigma).
"""
sigma = np.asarray(sigma)
scalar_input = False
if sigma.ndim == 0:
sigma = sigma[None]
scalar_input = True
if sigma.ndim > 1:
raise Exception("sigma cannot be a >1D array.")
G = np.zeros_like(sigma)
cluster_toolkit._lib.G_at_sigma_arr(_dcast(sigma), len(sigma), d, e, f, g,
_dcast(G))
if scalar_input:
return np.squeeze(G)
return G
def DeltaSigma_mis_at_R(R, Rsigma, Sigma_mis):
"""Miscentered excess surface mass density profile at R. Units are Msun h/pc^2 comoving.
Args:
R (float or array like): Projected radii to evaluate profile.
Rsigma (array like): Projected radii of miscentered Sigma profile.
Sigma_mis (array like): Miscentered Sigma profile.
Returns:
float array like: Miscentered excess surface mass density profile.
"""
R = np.asarray(R)
scalar_input = False
if R.ndim == 0:
R = R[None] #makes R 1D
scalar_input = True
if R.ndim > 1:
raise Exception("R cannot be a >1D array.")
if np.min(R) < np.min(Rsigma):
raise Exception("Minimum R must be >= min(R_Sigma)")
if np.max(R) > np.max(Rsigma):
raise Exception("Maximum R must be <= max(R_Sigma)")
DeltaSigma_mis = np.zeros_like(R)
cluster_toolkit._lib.DeltaSigma_mis_at_R_arr(_dcast(R), len(R),
_dcast(Rsigma),
_dcast(Sigma_mis),
len(Rsigma),
_dcast(DeltaSigma_mis))
if scalar_input:
return np.squeeze(DeltaSigma_mis)
return DeltaSigma_mis
def _calc_nu_at_M(M, k, P, Omega_m, nu):
"""Direct call to vectorized version of peak height of M.
"""
cluster_toolkit._lib.nu_at_M_arr(_dcast(M), len(M), _dcast(k), _dcast(P),
len(k), Omega_m, _dcast(nu))
return
def rho_einasto_at_r(r, M, rs, alpha, Omega_m, delta=200, rhos=-1.):
"""Einasto halo density profile. Distances are Mpc/h comoving.
Args:
r (float or array like): 3d distances from halo center.
M (float): Mass in Msun/h; not used if rhos is specified.
rhos (float): Scale density in Msun h^2/Mpc^3 comoving; optional.
rs (float): Scale radius.
alpha (float): Profile exponent.
Omega_m (float): Omega_matter, matter fraction of the density.
delta (int): Overdensity, default is 200.
Returns:
float or array like: Einasto halo density profile in Msun h^2/Mpc^3 comoving.
"""
r = np.asarray(r)
scalar_input = False
if r.ndim == 0:
r = r[None] #makes r 1D
scalar_input = True
if r.ndim > 1:
raise Exception("r cannot be a >1D array.")
rho = np.zeros_like(r)
cluster_toolkit._lib.calc_rho_einasto(_dcast(r), len(r), M, rhos, rs,
alpha, delta, Omega_m, _dcast(rho))
if scalar_input:
return np.squeeze(rho)
return rho
def _calc_Sigma_nfw_at_R(R, mass, concentration, Omega_m, Sigma, delta=200):
"""Direct call to vectorized surface mass density of NFW.
"""
return cluster_toolkit._lib.Sigma_nfw_at_R_arr(_dcast(R), len(R), mass,
concentration, delta,
Omega_m, _dcast(Sigma))
def bias_at_R(R, k, P, delta=200):
"""Tinker 2010 bais at mass M [Msun/h] corresponding to radius R [Mpc/h comoving].
Args:
R (float or array like): Lagrangian radius in Mpc/h comoving.
k (array like): Wavenumbers of power spectrum in h/Mpc comoving.
P (array like): Power spectrum in (Mpc/h)^3 comoving.
delta (int; optional): Overdensity, default is 200.
Returns:
float or array like: Halo bias.
"""
R = np.asarray(R)
scalar_input = False
if R.ndim == 0:
R = R[None] #makes r 1D
scalar_input = True
if R.ndim > 1:
raise Exception("R cannot be a >1D array.")
R = np.require(R, dtype=np.float64, requirements=["C"])
k = np.require(k, dtype=np.float64, requirements=["C"])
P = np.require(P, dtype=np.float64, requirements=["C"])
bias = np.zeros_like(R)
cluster_toolkit._lib.bias_at_R_arr(_dcast(R), len(R), delta, _dcast(k), _dcast(P), len(k), _dcast(bias))
if scalar_input:
return np.squeeze(bias)
return bias
def G_at_M(M, k, P, Omega_m, d=1.97, e=1.0, f=0.51, g=1.228):
"""Tinker et al. 2008 appendix C multiplicity funciton G(M) as
a function of mass. Default behavior is for :math:`M_{200m}` mass
definition.
Args:
M (float or array like): Mass in Msun/h.
k (array like): Wavenumbers of the matter power spectrum in h/Mpc comoving.
P_lin (array like): Linear matter power spectrum in (Mpc/h)^3 comoving.
Omega_m (float): Matter density fraction.
d (float; optional): First Tinker parameter. Default is 1.97.
e (float; optional): Second Tinker parameter. Default is 1.
f (float; optional): Third Tinker parameter. Default is 0.51.
g (float; optional): Fourth Tinker parameter. Default is 1.228.
Returns:
float or array like: Halo multiplicity :math:`G(M)`.
"""
M = np.asarray(M)
scalar_input = False
if M.ndim == 0:
M = M[None] #makes M 1D
scalar_input = True
if M.ndim > 1:
raise Exception("M cannot be a >1D array.")
M = np.require(M, dtype=np.float64, requirements=["C"])
k = np.require(k, dtype=np.float64, requirements=["C"])
P = np.require(P, dtype=np.float64, requirements=["C"])
G = np.zeros_like(M)
cluster_toolkit._lib.G_at_M_arr(_dcast(M), len(M), _dcast(k), _dcast(P),
len(k), Omega_m, d, e, f, g, _dcast(G))
if scalar_input:
return np.squeeze(G)
return G
def xi_mm_at_R(R, k, P, N=500, step=0.005, exact=False):
"""Matter-matter correlation function.
Args:
R (float or array like): 3d distances from halo center in Mpc/h comoving
k (array like): Wavenumbers of power spectrum in h/Mpc comoving
P (array like): Matter power spectrum in (Mpc/h)^3 comoving
N (int; optional): Quadrature step count, default is 500
step (float; optional): Quadrature step size, default is 5e-3
exact (boolean): Use the slow, exact calculation; default is False
Returns:
float or array like: Matter-matter correlation function
"""
if type(R) is list or type(R) is np.ndarray:
xi = np.zeros_like(R)
if not exact:
cluster_toolkit._lib.calc_xi_mm(_dcast(R), len(R), _dcast(k), _dcast(P), len(k), _dcast(xi), N, step)
else:
cluster_toolkit._lib.calc_xi_mm_exact(_dcast(R), len(R), _dcast(k), _dcast(P), len(k), _dcast(xi))
return xi
if not exact:
return cluster_toolkit._lib.xi_mm_at_R(R, _dcast(k), _dcast(P), len(k), N, step)
else:
return cluster_toolkit._lib.xi_mm_at_R_exact(R, _dcast(k), _dcast(P), len(k))
def _calc_sigma2_at_R(R, k, P, s2):
"""Direct call to vectorized version of RMS variance in top hat sphere of radius R [Mpc/h comoving] of linear power spectrum.
"""
cluster_toolkit._lib.sigma2_at_R_arr(_dcast(R), len(R), _dcast(k),
_dcast(P), len(k), _dcast(s2))
return
def _calc_bias_at_R(R, k, P, bias, delta=200):
"""Direct call to vectorized version of Tinker 2008 bias at R.
"""
cluster_toolkit._lib.bias_at_R_arr(_dcast(R), len(R), delta, _dcast(k),
_dcast(P), len(k), _dcast(bias))
return
def Sigma_nfw_at_R(R, mass, concentration, Omega_m, delta=200):
"""Surface mass density of an NFW profile [Msun h/pc^2 comoving].
Args:
R (float or array like): Projected radii Mpc/h comoving.
mass (float): Halo mass Msun/h.
concentration (float): concentration.
Omega_m (float): Matter density fraction.
delta (int; optional): Overdensity, default is 200.
Returns:
float or array like: Surface mass density Msun h/pc^2 comoving.
"""
R = np.asarray(R)
scalar_input = False
if R.ndim == 0:
R = R[None] #makes R 1D
scalar_input = True
if R.ndim > 1:
raise Exception("R cannot be a >1D array.")
Sigma = np.zeros_like(R)
cluster_toolkit._lib.Sigma_nfw_at_R_arr(_dcast(R), len(R), mass,
concentration, delta, Omega_m,
_dcast(Sigma))
if scalar_input:
return np.squeeze(Sigma)
return Sigma
def _calc_nu_at_R(R, k, P, nu):
"""Direct call to vectorized version of peak height of R.
"""
cluster_toolkit._lib.nu_at_R_arr(_dcast(R), len(R), _dcast(k), _dcast(P),
len(k), _dcast(nu))
return
def dbiasdM_at_M(M, k, P, Omega_m, delta=200):
"""d/dM of Tinker et al. 2010 bais at mass M [Msun/h].
Args:
M (float or array like): Mass in Msun/h.
k (array like): Wavenumbers of power spectrum in h/Mpc comoving.
P (array like): Power spectrum in (Mpc/h)^3 comoving.
Omega_m (float): Matter density fraction.
delta (int; optional): Overdensity, default is 200.
Returns:
float or array like: Derivative of the halo bias.
"""
M = np.asarray(M)
scalar_input = False
if M.ndim == 0:
M = M[None] #makes M 1D
scalar_input = True
if M.ndim > 1:
raise Exception("M cannot be a >1D array.")
M = np.require(M, dtype=np.float64, requirements=["C"])
k = np.require(k, dtype=np.float64, requirements=["C"])
P = np.require(P, dtype=np.float64, requirements=["C"])
deriv = np.zeros_like(M)
cluster_toolkit._lib.dbiasdM_at_M_arr(_dcast(M), len(M), delta, _dcast(k),
_dcast(P), len(k), Omega_m,
_dcast(deriv))
if scalar_input:
return np.squeeze(deriv)
return deriv
def boost_nfw_at_R(R, B0, R_scale):
"""NFW boost factor model.
Args:
R (float or array like): Distances on the sky in the same units as R_scale. Mpc/h comoving suggested for consistency with other modules.
B0 (float): NFW profile amplitude.
R_scale (float): NFW profile scale radius.
Returns:
float or array like: NFW boost factor profile; B = (1-fcl)^-1.
"""
R = np.asarray(R)
scalar_input = False
if R.ndim == 0:
R = R[None] #makes R 1D
scalar_input = True
if R.ndim > 1:
raise Exception("R cannot be a >1D array.")
boost = np.zeros_like(R)
cluster_toolkit._lib.boost_nfw_at_R_arr(_dcast(R), len(R), B0, R_scale,
_dcast(boost))
if scalar_input:
return np.squeeze(boost)
return boost
def G_at_sigma(sigma, d=1.97, e=1.0, f=0.51, g=1.228):
"""Tinker et al. 2008 appendix C multiplicity funciton G(sigma) as
a function of sigma.
NOTE: by default, this function is only valid at :math:`z=0`. For use
at higher redshifts either recompute the parameters yourself, or
wait for this behavior to be patched.
Args:
sigma (float or array like): RMS variance of the matter density field.
d (float; optional): First Tinker parameter. Default is 1.97.
e (float; optional): Second Tinker parameter. Default is 1.
f (float; optional): Third Tinker parameter. Default is 0.51.
g (float; optional): Fourth Tinker parameter. Default is 1.228.
Returns:
float or array like: Halo multiplicity :math:`G(\sigma)`.
"""
if type(sigma) is list or type(sigma) is np.ndarray:
G = np.zeros_like(sigma)
cluster_toolkit._lib.G_at_sigma_arr(_dcast(sigma), len(sigma), d, e, f,
g, _dcast(G))
return G
else:
return cluster_toolkit._lib.G_at_sigma(sigma, d, e, f, g)
def _calc_bias_at_M(M, k, P, Omega_m, bias, delta=200):
"""Direct call to vectorized version of Tinker 2008 bias at M.
"""
cluster_toolkit._lib.bias_at_M_arr(_dcast(M), len(M), delta, _dcast(k),
_dcast(P), len(k), Omega_m,
_dcast(bias))
return
def _bias_at_nu_FREEPARAMS(nu, A, a, B, b, C, c, delta=200):
"""A special function used only for quickly computing best fit parameters
for the halo bias models.
"""
bias = np.zeros_like(nu)
cluster_toolkit._lib.bias_at_nu_arr_FREEPARAMS(_dcast(nu), len(nu), delta,
A, a, B, b, C, c, _dcast(bias))
return bias
def _calc_sigma2_at_M(M, k, P, Omega_m, s2):
"""Direct call to vectorized version of RMS variance in top hat sphere of lagrangian radius R [Mpc/h comoving] corresponding to a mass M [Msun/h] of linear power spectrum.
"""
cluster_toolkit._lib.sigma2_at_M_arr(_dcast(M), len(M),
_dcast(k), _dcast(P), len(k), Omega_m,
_dcast(s2))
return
def Sigma_mis_at_R(R,
Rsigma,
Sigma,
M,
conc,
Omega_m,
Rmis,
delta=200,
kernel="rayleigh"):
"""Miscentered surface mass density [Msun h/pc^2 comoving]
convolved with a distribution for Rmis. Units are Msun h/pc^2 comoving.
Args:
R (float or array like): Projected radii Mpc/h comoving.
Rsigma (array like): Projected radii of the centered surface mass density profile.
Sigma (float or array like): Surface mass density Msun h/pc^2 comoving.
M (float): Halo mass Msun/h.
conc (float): concentration.
Omega_m (float): Matter density fraction.
Rmis (float): Miscentered distance in Mpc/h comoving.
delta (int; optional): Overdensity, default is 200.
kernel (string; optional): Kernal for convolution. Options: rayleigh or gamma.
Returns:
float or array like: Miscentered projected surface mass density.
"""
R = np.asarray(R)
scalar_input = False
if R.ndim == 0:
R = R[None] #makes R 1D
scalar_input = True
#Exception checking
if R.ndim > 1:
raise Exception("R cannot be a >1D array.")
if np.min(R) < np.min(Rsigma):
raise Exception("Minimum R must be >= min(R_Sigma)")
if np.max(R) > np.max(Rsigma):
raise Exception("Maximum R must be <= max(R_Sigma)")
if kernel == "rayleigh":
integrand_switch = 0
elif kernel == "gamma":
integrand_switch = 1
else:
raise Exception("Miscentering kernel must be either " +
"'rayleigh' or 'gamma'")
Sigma_mis = np.zeros_like(R)
cluster_toolkit._lib.Sigma_mis_at_R_arr(_dcast(R), len(R), _dcast(Rsigma),
_dcast(Sigma), len(Rsigma), M,
conc, delta, Omega_m,
Rmis, integrand_switch,
_dcast(Sigma_mis))
if scalar_input:
return np.squeeze(Sigma_mis)
return Sigma_mis
def xi_DK_appendix1(r,
M,
conc,
be,
se,
k,
P,
om,
bias,
xi_mm,
delta=200,
rhos=-1.,
alpha=-1.,
beta=-1.,
gamma=-1.):
"""Diemer-Kravtsov 2014 profile, first form from the appendix, eq. A3.
Args:
r (float or array like): radii in Mpc/h comoving
M (float): mass in Msun/h
conc (float): Einasto concentration
be (float): DK transition parameter
se (float): DK transition parameter
k (array like): wavenumbers in h/Mpc
P (array like): matter power spectrum in [Mpc/h]^3
Omega_m (float): matter density fraction
bias (float): halo bias
xi_mm (float or array like): matter correlation function at r
delta (float): overdensity of matter. Optional, default is 200
rhos (float): Einasto density. Optional, default is compute from the mass
alpha (float): Einasto parameter. Optional, default is computed from peak height
beta (float): DK 2-halo parameter. Optional, default is 4
gamma (float): DK 2-halo parameter. Optional, default is 8
Returns:
float or array like: DK profile evaluated at the input radii
"""
r = np.asarray(r)
scalar_input = False
if r.ndim == 0:
r = r[None] #makes r 1D
scalar_input = True
if r.ndim > 1:
raise Exception("r cannot be a >1D array.")
xi = np.zeros_like(r)
cluster_toolkit._lib.calc_xi_DK_app1(_dcast(r), len(r), M, rhos, conc, be,
se, alpha, beta, gamma, delta,
_dcast(k), _dcast(P), len(k), om,
bias, _dcast(xi_mm), _dcast(xi))
if scalar_input:
return np.squeeze(xi)
return xi
def _calc_Sigma_mis_single_at_R(R,
Rsigma,
Sigma,
M,
conc,
Omega_m,
Rmis,
Sigma_mis,
delta=200):
return cluster_toolkit._lib.Sigma_mis_single_at_R_arr(
_dcast(R), len(R), _dcast(Rsigma), _dcast(Sigma), len(Rsigma), M, conc,
delta, Omega_m, Rmis, _dcast(Sigma_mis))
def _dndM_sigma2_precomputed(M,
sigma2,
dsigma2dM,
Omega_m,
d=1.97,
e=1.0,
f=0.51,
g=1.228):
dndM = np.zeros_like(M)
cluster_toolkit._lib.dndM_sigma2_precomputed(_dcast(M), _dcast(sigma2),
_dcast(dsigma2dM), len(M),
Omega_m, d, e, f, g,
_dcast(dndM))
return dndM
def n_in_bin(Mlo, Mhi, Marr, dndM):
"""Tinker et al. 2008 appendix C binned mass function.
Args:
Mlo (float): Lower mass edge.
Mhi (float): Upper mass edge.
Marr (array like): Array of locations that dndM has been evaluated at.
dndM (array like): Array of dndM.
Returns:
float: number density of halos in the mass bin.
"""
return cluster_toolkit._lib.n_in_bin(Mlo, Mhi, _dcast(Marr), _dcast(dndM),
len(Marr))
def xi_2halo(bias, xi_mm):
"""2-halo term in halo-matter correlation function
Args:
bias (float): Halo bias
xi_mm (float or array like): Matter-matter correlation function
Returns:
float or array like: 2-halo term in halo-matter correlation function
"""
NR = len(xi_mm)
xi = np.zeros_like(xi_mm)
cluster_toolkit._lib.calc_xi_2halo(NR, bias, _dcast(xi_mm), _dcast(xi))
return xi
def n_in_bins(edges, Marr, dndM):
"""Tinker et al. 2008 appendix C binned mass function.
Args:
edges (array like): Edges of the mass bins.
Marr (array like): Array of locations that dndM has been evaluated at.
dndM (array like): Array of dndM.
Returns:
numpy.ndarray: number density of halos in the mass bins. Length is :code:`len(edges)-1`.
"""
n = np.zeros(len(edges) - 1)
cluster_toolkit._lib.n_in_bins(_dcast(edges), len(edges), _dcast(Marr),
_dcast(dndM), len(Marr), _dcast(n))
return n
def _calc_Sigma_at_R(R,
Rxi,
xi,
mass,
concentration,
Omega_m,
Sigma,
delta=200):
"""Direct call to vectorized surface mass density given xi_hm
"""
return cluster_toolkit._lib.Sigma_at_R_full_arr(_dcast(R), len(R),
_dcast(Rxi), _dcast(xi),
len(Rxi), mass,
concentration, delta,
Omega_m, _dcast(Sigma))
def xi_DK_appendix2(R, M, conc, be, se, k, P, om, bias, xi_mm, delta=200, rhos=-1., alpha=-1., beta=-1., gamma=-1.):
"""Diemer-Kravtsov 2014 profile, second form from the appendix, eq. A4.
Args:
r (float or array like): radii in Mpc/h comoving
M (float): mass in Msun/h
conc (float): Einasto concentration
be (float): DK transition parameter
se (float): DK transition parameter
k (array like): wavenumbers in h/Mpc
P (array like): matter power spectrum in [Mpc/h]^3
Omega_m (float): matter density fraction
bias (float): halo bias
xi_mm (float or array like): matter correlation function at r
delta (float): overdensity of matter. Optional, default is 200
rhos (float): Einasto density. Optional, default is compute from the mass
alpha (float): Einasto parameter. Optional, default is computed from peak height
beta (float): DK 2-halo parameter. Optional, default is 4
gamma (float): DK 2-halo parameter. Optional, default is 8
Returns:
float or array like: DK profile evaluated at the input radii
"""
Nk = len(k)
if type(R) is list or type(R) is np.ndarray:
NR = len(R)
xi = np.zeros_like(R)
cluster_toolkit._lib.calc_xi_DK_app2(_dcast(R), NR, M, rhos, conc, be, se, alpha, beta, gamma, delta, _dcast(k), _dcast(P), Nk, om, bias, _dcast(xi_mm), _dcast(xi))
return xi
else:
return cluster_toolkit._lib.xi_DK_app2(R, M, rhos, conc, be, se, alpha, beta, gamma, delta, _dcast(k), _dcast(P), Nk, om, bias, _dcast(xi_mm))
