hmf¶

This is the primary module for user-interaction with the hmf package.

The module contains a single class, MassFunction, which wraps almost all the functionality of hmf in an easy-to-use way.

class hmf.hmf.MassFunction(Mmin=10, Mmax=15, dlog10m=0.01, mf_fit=<class 'hmf.fitting_functions.Tinker08'>, delta_h=200.0, delta_wrt='mean', cut_fit=True, z2=None, nz=None, _fsig_params={}, delta_c=1.686, filter=<class 'hmf.filters.TopHat'>, filter_params={}, **transfer_kwargs)¶

An object containing all relevant quantities for the mass function.

The purpose of this class is to calculate many quantities associated with the dark matter halo mass function (HMF). The class is initialized to form a cosmology and takes in various options as to how to calculate all further quantities.

All required outputs are provided as @property attributes for ease of access.

Contains an update() method which can be passed arguments to update, in the most optimal manner. All output quantities are calculated only when needed (but stored after first calculation for quick access).

Quantities related to the transfer function can be accessed through the transfer property of this object.

Parameters:

Mmin : float Minimum mass at which to perform analysis [units \(\log_{10}M_\odot h^{-1}\)]. Mmax : float Maximum mass at which to perform analysis [units \(\log_{10}M_\odot h^{-1}\)]. dlog10m : float log10 interval between mass bins mf_fit : str or callable, optional, default "SMT" A string indicating which fitting function to use for \(f(\sigma)\) Available options: 'PS': Press-Schechter form from 1974 'ST': Sheth-Mo-Tormen empirical fit 2001 (deprecated!) 'SMT': Sheth-Mo-Tormen empirical fit from 2001 'Jenkins': Jenkins empirical fit from 2001 'Warren': Warren empirical fit from 2006 'Reed03': Reed empirical from 2003 'Reed07': Reed empirical from 2007 'Tinker': Tinker empirical from 2008 'Watson': Watson empirical 2012 'Watson_FoF': Watson Friend-of-friend fit 2012 'Crocce': Crocce 2010 'Courtin': Courtin 2011 'Angulo': Angulo 2012 'Angulo_Bound': Angulo sub-halo function 2012 'Bhattacharya': Bhattacharya empirical fit 2011 'Behroozi': Behroozi extension to Tinker for high-z 2013 Alternatively, one may define a callable function, with the signature func(self), where self is a MassFunction object (and has access to all its attributes). This may be passed here. delta_wrt : str, {"mean", "crit"} Defines what the overdensity of a halo is with respect to, mean density of the universe, or critical density. delta_h : float, optional, default 200.0 The overdensity for the halo definition, with respect to delta_wrt user_fit : str, optional, default "" A string defining a mathematical function in terms of x, used as the fitting function, where x is taken as \(\( \sigma \)\). Will only be applicable if mf_fit == "user_model". cut_fit : bool, optional, default True Whether to forcibly cut \(f(\sigma)\) at bounds in literature. If false, will use whole range of M. delta_c : float, default 1.686 The critical overdensity for collapse, \(\delta_c\) kwargs : keywords These keyword arguments are sent to the hmf.transfer.Transfer class. Included are all the cosmological parameters (see the docs for details).

Attributes

H0
M
Mmax
Mmin
N_nu
N_nu_massive
cosmolopy_dict	Collect parameters into a dictionary suitable for cosmolopy.
cs2_lam
cut_fit
delta_c
delta_h
delta_halo	Overdensity of a halo w.r.t mean density
delta_k	Dimensionless power spectrum, \(\Delta_k = \frac{k^3 P(k)}{2\pi^2}\)
delta_wrt
dlnk
dlog10m
dndlnm	The differential mass function in terms of natural log of M, len=len(M) [units \(h^3 Mpc^{-3}\)]
dndlog10m	The differential mass function in terms of log of M, len=len(M) [units \(h^3 Mpc^{-3}\)]
dndm	The number density of haloes, len=len(M) [units \(h^4 M_\odot^{-1} Mpc^{-3}\)]
filter
filter_mod
filter_params
force_flat
fsigma	The multiplicity function, \(f(\sigma)\), for mf_fit.
growth	The growth factor \(d(z)\)
h
how_big	Size of simulation volume in which to expect one halo of mass M, len=len(M) [units \(Mpch^{-1}\)]
kr_warning
lnk
lnk_max
lnk_min
lnsigma	Natural log of inverse mass variance, len=len(M)
mean_dens
mean_dens_z	Mean density of universe at redshift z
mf_fit
n
n_eff	Effective spectral index at scale of halo radius, len=len(M)
ngtm	The cumulative mass function above M, len=len(M) [units \(h^3 Mpc^{-3}\)]
nonlinear_delta_k	Dimensionless nonlinear power spectrum, \(\Delta_k = \frac{k^3 P_{\rm nl}(k)}{2\pi^2}\)
nonlinear_power	Non-linear log power [units \(Mpc^3/h^3\)]
nu	The parameter :math:`
nz
omegab
omegab_h2
omegac
omegac_h2
omegak
omegam
omegam_z	Density parameter at redshift of this instance.
omegan
omegav
power	Normalised log power spectrum [units \(Mpc^3/h^3\)]
pycamb_dict	Collect parameters into a dictionary suitable for pycamb.
radii	The radii corresponding to the masses M
rho_gtm	Mass density in haloes >M, len=len(M) [units \(M_\odot h^2 Mpc^{-3}\)]
rho_ltm	Mass density in haloes <M, len=len(M) [units \(M_\odot h^2 Mpc^{-3}\)]
sigma	The mass variance at z, len=len(M)
sigma_8
t_cmb
takahashi
tau
transfer_fit
transfer_options
w
y_he
z
z2
z_reion

Methods

cosmo_update(**kwargs)
update(**kwargs)	Update the class optimally with given arguments.

delta_halo¶

Overdensity of a halo w.r.t mean density

dndlnm¶

The differential mass function in terms of natural log of M, len=len(M) [units \(h^3 Mpc^{-3}\)]

dndlog10m¶

The differential mass function in terms of log of M, len=len(M) [units \(h^3 Mpc^{-3}\)]

dndm¶

The number density of haloes, len=len(M) [units \(h^4 M_\odot^{-1} Mpc^{-3}\)]

fsigma¶

The multiplicity function, \(f(\sigma)\), for mf_fit. len=len(M)

how_big¶

Size of simulation volume in which to expect one halo of mass M, len=len(M) [units \(Mpch^{-1}\)]

lnsigma¶

Natural log of inverse mass variance, len=len(M)

mean_dens_z¶

Mean density of universe at redshift z

n_eff¶

Effective spectral index at scale of halo radius, len=len(M)

Notes

This function, and any derived quantities, can show small non-physical ‘wiggles’ at the 0.1% level, if too coarse a grid in ln(k) is used. If applications are sensitive at this level, please use a very fine k-space grid.

Uses eq. 42 in Lukic et. al 2007.

ngtm¶

The cumulative mass function above M, len=len(M) [units \(h^3 Mpc^{-3}\)]

In the case that M does not extend to sufficiently high masses, this routine will auto-generate dndm for an extended mass range. If cut_fit is True, and this extension is invalid, then a power-law fit is applied to extrapolate to sufficient mass.

In the case of the Behroozi fit, it is impossible to auto-extend the mass range except by the power-law fit, thus one should be careful to supply appropriate mass ranges in this case.

nu¶

The parameter :math:`

u = left( rac{delta_c}{sigma} ight)^2`, len=len(M)

omegam_z¶

Density parameter at redshift of this instance.

radii¶

The radii corresponding to the masses M

rho_gtm¶

Mass density in haloes >M, len=len(M) [units \(M_\odot h^2 Mpc^{-3}\)]

In the case that M does not extend to sufficiently high masses, this routine will auto-generate dndm for an extended mass range. If cut_fit is True, and this extension is invalid, then a power-law fit is applied to extrapolate to sufficient mass.

In the case of the Behroozi fit, it is impossible to auto-extend the mass range except by the power-law fit, thus one should be careful to supply appropriate mass ranges in this case.

rho_ltm¶

Mass density in haloes <M, len=len(M) [units \(M_\odot h^2 Mpc^{-3}\)]

Note

As of v1.6.2, this assumes that the entire mass density of halos is encoded by the mean_density parameter (ie. all mass is found in halos). This is not explicitly true of all fitting functions (eg. Warren), in which case the definition of this property is somewhat inconsistent, but will still work.

In the case that M does not extend to sufficiently high masses, this routine will auto-generate dndm for an extended mass range. If cut_fit is True, and this extension is invalid, then a power-law fit is applied to extrapolate to sufficient mass.

In the case of the Behroozi fit, it is impossible to auto-extend the mass range except by the power-law fit, thus one should be careful to supply appropriate mass ranges in this case.

sigma¶

The mass variance at z, len=len(M)

transfer¶

This module contains a single class, Transfer, which provides methods to calculate the transfer function, matter power spectrum and several other related quantities.

class hmf.transfer.Transfer(z=0.0, lnk_min=-18.420680743952367, lnk_max=9.9034875525361272, dlnk=0.05, transfer_fit=<class 'hmf.transfer.CAMB'>, transfer_options={}, takahashi=True, **kwargs)¶

Neatly deals with different transfer functions and their routines.

The purpose of this class is to calculate transfer functions, power spectra and several tightly associated quantities using many of the available fits from the literature.

Importantly, it contains the means to calculate the transfer function using the popular CAMB code, the Eisenstein-Hu fit (1998), the BBKS fit or the Bond and Efstathiou fit (1984). Furthermore, it can calculate non-linear corrections using the halofit model (with updated parameters from Takahashi2012).

The primary feature of this class is to wrap all the methods into a unified interface. On top of this, the class implements optimized updates of parameters which is useful in, for example, MCMC code which covers a large parameter-space. Calling the nonlinear_power does not re-evaluate the entire transfer function, rather it just calculates the corrections, improving performance.

To update parameters optimally, use the update() method. All output quantities are calculated only when needed (but stored after first calculation for quick access).

Parameters:

lnk_min : float Defines min log wavenumber, k [units \(h Mpc^{-1}\)]. lnk_max : float Defines max log wavenumber, k [units \(h Mpc^{-1}\)]. dlnk : float Defines log interval between wavenumbers z : float, optional, default 0.0 The redshift of the analysis. wdm_mass : float, optional, default None The warm dark matter particle size in keV, or None for CDM. transfer_fit : str, { "CAMB", "EH", "bbks", "bond_efs"} Defines which transfer function fit to use. If not defined from the listed options, it will be treated as a filename to be read in. In this case the file must contain a transfer function in CAMB output format. Scalar_initial_condition : int, {1,2,3,4,5} (CAMB-only) Initial scalar perturbation mode (adiabatic=1, CDM iso=2, Baryon iso=3,neutrino density iso =4, neutrino velocity iso = 5) lAccuracyBoost : float, optional, default 1.0 (CAMB-only) Larger to keep more terms in the hierarchy evolution AccuracyBoost : float, optional, default 1.0 (CAMB-only) Increase accuracy_boost to decrease time steps, use more k values, etc.Decrease to speed up at cost of worse accuracy. Suggest 0.8 to 3. w_perturb : bool, optional, default False (CAMB-only) transfer__k_per_logint : int, optional, default 11 (CAMB-only) Number of wavenumbers estimated per log interval by CAMB Default of 11 gets best performance for requisite accuracy of mass function. transfer__kmax : float, optional, default 0.25 (CAMB-only) Maximum value of the wavenumber. Default of 0.25 is high enough for requisite accuracy of mass function. ThreadNum : int, optional, default 0 (CAMB-only) Number of threads to use for calculation of transfer function by CAMB. Default 0 automatically determines the number. takahashi : bool, default True Whether to use updated HALOFIT coefficients from Takahashi+12 wdm_model : WDM subclass or string The WDM transfer function model to use kwargs : keywords The **kwargs take any cosmological parameters desired, which are input to the hmf.cosmo.Cosmology class. hmf.Perturbations uses a default parameter set from the first-year PLANCK mission, with optional modifications by the user. Here is a list of parameters currently available (and their defaults in Transfer): sigma_8: [0.8344] The normalisation. Mass variance in top-hat spheres with \(R=8Mpc h^{-1}\) n: [0.9624] The spectral index w: [-1] The dark-energy equation of state cs2_lam: [1] The constant comoving sound speed of dark energy t_cmb: [2.725] Temperature of the CMB y_he: [0.24] Helium fraction N_nu: [3.04] Number of massless neutrino species N_nu_massive: [0] Number of massive neutrino species delta_c: [1.686] The critical overdensity for collapse H0: [67.11] The hubble constant h: [H0/100.0] The hubble parameter omegan: [0] The normalised density of neutrinos omegab_h2: [0.022068] The normalised baryon density by h**2 omegac_h2: [0.12029] The normalised CDM density by h**2 omegav: [0.6825] The normalised density of dark energy omegab: [omegab_h2/h**2] The normalised baryon density omegac: [omegac_h2/h**2] The normalised CDM density force_flat: [False] Whether to force the cosmology to be flat (affects only omegav) default: ["planck1_base"] A default set of cosmological parameters

Attributes

H0
N_nu
N_nu_massive
cosmolopy_dict	Collect parameters into a dictionary suitable for cosmolopy.
cs2_lam
delta_k	Dimensionless power spectrum, \(\Delta_k = \frac{k^3 P(k)}{2\pi^2}\)
dlnk
force_flat
growth	The growth factor \(d(z)\)
h
lnk
lnk_max
lnk_min
mean_dens
n
nonlinear_delta_k	Dimensionless nonlinear power spectrum, \(\Delta_k = \frac{k^3 P_{\rm nl}(k)}{2\pi^2}\)
nonlinear_power	Non-linear log power [units \(Mpc^3/h^3\)]
omegab
omegab_h2
omegac
omegac_h2
omegak
omegam
omegan
omegav
power	Normalised log power spectrum [units \(Mpc^3/h^3\)]
pycamb_dict	Collect parameters into a dictionary suitable for pycamb.
sigma_8
t_cmb
takahashi
tau
transfer_fit
transfer_options
w
y_he
z
z_reion

Methods

cosmo_update(**kwargs)
update(**kwargs)	Update the class optimally with given arguments.

delta_k¶

Dimensionless power spectrum, \(\Delta_k = \frac{k^3 P(k)}{2\pi^2}\)

growth¶

The growth factor \(d(z)\)

This is calculated (see Lukic 2007) as

\[d(z) = \frac{D^+(z)}{D^+(z=0)}\]

where

\[D^+(z) = \frac{5\Omega_m}{2}\frac{H(z)}{H_0}\int_z^{\infty}{\frac{(1+z')dz'}{[H(z')/H_0]^3}}\]

and

\[H(z) = H_0\sqrt{\Omega_m (1+z)^3 + (1-\Omega_m)}\]

nonlinear_delta_k¶

Dimensionless nonlinear power spectrum, \(\Delta_k = \frac{k^3 P_{\rm nl}(k)}{2\pi^2}\)

nonlinear_power¶

Non-linear log power [units \(Mpc^3/h^3\)]

Non-linear corrections come from HALOFIT (Smith2003) with updated parameters from Takahashi2012.

This code was heavily influenced by the HaloFit class from the chomp python package by Christopher Morrison, Ryan Scranton and Michael Schneider (https://code.google.com/p/chomp/). It has been modified to improve its integration with this package.

power¶

Normalised log power spectrum [units \(Mpc^3/h^3\)]

update(**kwargs)¶

Update the class optimally with given arguments.

Accepts any argument that the constructor takes

hmf.transfer.get_transfer(name, t)¶

A function that chooses the correct Profile class and returns it

cosmo¶

class hmf.cosmo.Cosmology(default='planck1_base', force_flat=False, **kwargs)¶

A class that nicely deals with cosmological parameters.

Most cosmological parameters are merely input and exposed as attributes in the class. However, more complicated relations such as the interrelation of omegab, omegac, omegam, omegav for example are dealt with in a more robust manner.

The secondary purpose of this class is to provide simple mappings of the parameters to common python cosmology libraries (for now just cosmolopy and pycamb). It has been found by the authors that using more than one library becomes confusing in terms of naming all the parameters, so this class helps deal with that.

Note

There are an incredible number of possible combinations of input parameters, many of which could easily be inconsistent. To this end, this class raises an exception if an inconsistent parameter combination is input, eg. h = 1.0, omegab = 0.05, omegab_h2 = 0.06.

Note

force_flat is provided for convenience to ensure a flat cosmology. In nearly all cases (except where it would be quite perverse to do so) this will modify omegav if it is otherwise inconsistent. Eg. if omegam = 0.3, omegav = 0.8, force_flat = True is passed, the omegav will modified to 0.7.

Parameters:

default : str, {"planck1_base"} Defines a set of default parameters, based on a published set from WMAP or Planck. These defaults are applied in a smart way, so as not to override any user-set parameters. Current options are "planck1_base": The cosmology of first-year PLANCK mission (with no lensing or WP) force_flat : bool, default False If True, enforces a flat cosmology \((\Omega_m+\Omega_\lambda=1)\). This will modify omegav only, never omegam. **kwargs : The list of available keyword arguments is as follows: sigma_8: The normalisation. Mass variance in top-hat spheres with \(R=8Mpc h^{-1}\) n: The spectral index w: The dark-energy equation of state cs2_lam: The constant comoving sound speed of dark energy t_cmb: Temperature of the CMB y_he: Helium fraction N_nu: Number of massless neutrino species N_nu_massive:Number of massive neutrino species z_reion: Redshift of reionization tau: Optical depth at reionization delta_c: The critical overdensity for collapse h: The hubble parameter H0: The hubble constant omegan: The normalised density of neutrinos omegam: The normalised density of matter omegav: The normalised density of dark energy omegab: The normalised baryon density omegac: The normalised CDM density omegab_h2: The normalised baryon density by h**2 omegac_h2: The normalised CDM density by h**2 Note The reason these are implemented as kwargs rather than the usual arguments, is because the code can’t tell a priori which combination of density parameters the user will input.

Attributes

H0
N_nu
N_nu_massive
cosmolopy_dict	Collect parameters into a dictionary suitable for cosmolopy.
cs2_lam
force_flat
h
mean_dens
n
omegab
omegab_h2
omegac
omegac_h2
omegak
omegam
omegan
omegav
pycamb_dict	Collect parameters into a dictionary suitable for pycamb.
sigma_8
t_cmb
tau
w
y_he
z_reion

Methods

cosmo_update(**kwargs)

cosmolopy_dict¶

Collect parameters into a dictionary suitable for cosmolopy.

Returns:	dict Dictionary of values appropriate for cosmolopy

pycamb_dict¶

Collect parameters into a dictionary suitable for pycamb.

Returns:	dict Dictionary of values appropriate for pycamb

fitting_functions¶

class hmf.fitting_functions.Angulo(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Angulo mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Angulo [R1] form is:

\[f_{\rm Ang}(\sigma) = A\left[\left(\frac{e}{\sigma}\right)^b + c\right]\exp(\frac{d}{\sigma^2})\]

References

[R1]	(1, 2) Angulo, R. E., et al., 2012.

arXiv:1203.3216v1

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Bhattacharya(**model_parameters)¶

Class representing a Bhattacharya mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Bhattacharya [R2] form is:

\[f_{\rm Btc}(\sigma) = f_{\rm SMT}(\sigma) (\nu\sqrt{a})^q\]

References

[R2]	(1, 2) Bhattacharya, S., et al., May 2011. ApJ 732 (2), 122.

http://labs.adsabs.harvard.edu/ui/abs/2011ApJ...732..122B

Methods

fsigma(cut_fit)

Calculate \(f(\sigma)\) for Bhattacharya form.

fsigma(cut_fit)¶

Calculate \(f(\sigma)\) for Bhattacharya form.

Bhattacharya, S., et al., May 2011. ApJ 732 (2), 122. http://labs.adsabs.harvard.edu/ui/abs/2011ApJ...732..122B

Note

valid for \(10^{11.8}M_\odot < M <10^{15.5}M_\odot\)

Returns:	vfv : array_like, len=len(pert.M) The function :math:`f(sigma)equiv u f( u)` defined on pert.M

class hmf.fitting_functions.Courtin(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Courtin mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Courtin [R3] form is:

\[f_{\rm Ctn}(\sigma) = A\sqrt{2a/\pi}\nu\exp(-a\nu^2/2)(1+(a\nu^2)^{-p})\]

References

[R3]	(1, 2) Courtin, J., et al., Oct. 2010. MNRAS 1931

http://doi.wiley.com/10.1111/j.1365-2966.2010.17573.x

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Crocce(**model_parameters)¶

Class representing a Crocce mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Crocce [R4] form is:

\[f_{\rm Cro}(\sigma) = A\left[\left(\frac{e}{\sigma}\right)^b + c\right]\exp(\frac{d}{\sigma^2})\]

References

[R4]	(1, 2) Crocce, M., et al. MNRAS 403 (3), 1353-1367.

http://doi.wiley.com/10.1111/j.1365-2966.2009.16194.x

Methods

fsigma(cut_fit)

class hmf.fitting_functions.FittingFunction(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Base-class for a halo mass function fit

This class should not be called directly, rather use a subclass which is specific to a certain fitting formula.

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Methods

fsigma(cut_fit)

Calculate \(f(\sigma)\equiv\nu f(\nu)\).

fsigma(cut_fit)¶

Calculate \(f(\sigma)\equiv\nu f(\nu)\).

Parameters:	cut_fit : bool Whether to cut the fit at bounds corresponding to the fitted range (in mass or corresponding unit, not redshift). If so, values outside this range will be set to NaN.
Returns:	vfv : array_like, len=len(self.M) The function f(sigma).

class hmf.fitting_functions.Jenkins(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Jenkins mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Jenkins [R5] form is:

\[f_{\rm Jenkins}(\sigma) = A\exp(-|\ln\sigma^{-1}+b|^c)\]

References

[R5]	(1, 2) Jenkins, A. R., et al., Feb. 2001. MNRAS 321 (2), 372-384.

http://doi.wiley.com/10.1046/j.1365-8711.2001.04029.x

Methods

fsigma(cut_fit)

class hmf.fitting_functions.PS(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Press-Schechter mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Press-Schechter [R6] form is:

\[f_{\rm PS}(\sigma) = \sqrt{\frac{2}{\pi}}\nu\exp(-0.5\nu^2)\]

References

[R6]	(1, 2) Press, W. H., Schechter, P., 1974. ApJ 187, 425-438.

http://adsabs.harvard.edu/full/1974ApJ...187..425P

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Peacock(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Peacock mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Peacock [R7] form is:

\[f_{\rm Pck}(\sigma) = \nu\exp(-c\nu^2)(2cd\nu+ba\nu^{b-1})/d^2\]

References

[R7]	(1, 2) Peacock, J. A., Aug. 2007. MNRAS 379 (3), 1067-1074.

http://adsabs.harvard.edu/abs/2007MNRAS.379.1067P

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Reed03(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Reed03 mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Reed03 [R8] form is:

\[f_{\rm R03}(\sigma) = f_{\rm SMT}(\sigma)\exp\left(-\frac{c}{\sigma \cosh^5(2\sigma)}\right)\]

References

[R8]	(1, 2) Reed, D., et al., Dec. 2003. MNRAS 346 (2), 565-572.

http://adsabs.harvard.edu/abs/2003MNRAS.346..565R

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Reed07(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Reed07 mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Reed07 [R9] form is:

\[f_{\rm R07}(\sigma) = A\sqrt{2a/\pi}\left[1+(\frac{1}{a\nu^2})^p+0.6G_1+0.4G_2\right]\nu\exp(-ca\nu^2/2-\frac{0.03\nu^{0.6}}{(n_{\rm eff}+3)^2})\]

References

[R9]	(1, 2) Reed, D. S., et al., Jan. 2007. MNRAS 374 (1), 2-15.

http://adsabs.harvard.edu/abs/2007MNRAS.374....2R

Methods

fsigma(cut_fit)

class hmf.fitting_functions.SMT(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Sheth-Mo-Tormen mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Sheth-Mo-Tormen [R10] form is:

\[f_{\rm SMT}(\sigma) = A\sqrt{2a/\pi}\nu\exp(-a\nu^2/2)(1+(a\nu^2)^{-p})\]

References

[R10]

(1, 2) Sheth, R. K., Mo, H. J., Tormen, G., May 2001. MNRAS 323 (1), 1-12.

http://doi.wiley.com/10.1046/j.1365-8711.2001.04006.x

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Tinker08(**model_parameters)¶

Class representing a Tinker08 mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Tinker08 [R11] form is:

\[f_{\rm Tkr}(\sigma) = A(\frac{\sigma}{b}^{-a}+1)\exp(-c/\sigma^2)\]

References

[R11]

(1, 2) Tinker, J., et al., 2008. ApJ 688, 709-728.

http://iopscience.iop.org/0004-637X/688/2/709

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Warren(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Warren mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Warren [R12] form is:

\[f_{\rm Warren}(\sigma) = A\left[\left(\frac{e}{\sigma}\right)^b + c\right]\exp(\frac{d}{\sigma^2})\]

References

[R12]

(1, 2) Warren, M. S., et al., Aug. 2006. ApJ 646 (2), 881-885.

http://adsabs.harvard.edu/abs/2006ApJ...646..881W

Methods

fsigma(cut_fit)

class hmf.fitting_functions.Watson(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a Watson mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The Watson [R13] form is:

\[f_{\rm WatS}(\sigma) = \Gamma A \left((\frac{\beta}{\sigma}^\alpha+1\right)\exp(-\gamma/\sigma^2)\]

References

[R13]

(1, 2) Watson, W. A., et al., Dec. 2012.

http://arxiv.org/abs/1212.0095

Methods

fsigma(cut_fit)
gamma()	Calculate \(\Gamma\) for the Watson fit.

gamma()¶

Calculate \(\Gamma\) for the Watson fit.

class hmf.fitting_functions.Watson_FoF(M, nu2, delta_c, sigma=None, n_eff=None, lnsigma=None, z=0, delta_halo=200, cosmo=None, omegam_z=None, **model_parameters)¶

Class representing a WatsonFoF mass function fit

Parameters:

M : array A vector of halo masses [units M_sun/h] nu2 : array A vector of peak-heights, \(\delta_c^2/\sigma^2\) corresponding to M z : float, optional The redshift. delta_halo : float, optional The overdensity of the halo w.r.t. the mean density of the universe. cosmo : cosmo.Cosmology instance, optional A cosmology. Default is the default provided by the cosmo.Cosmology class. Not required if omegam_z is passed. omegam_z : float, optional A value for the mean matter density at the given redshift z. If not provided, will be calculated using the value of cosmo. **model_parameters : unpacked-dictionary These parameters are model-specific. For any model, list the available parameters (and their defaults) using <model>._defaults

Notes

The WatsonFoF [R14] form is:

\[f_{\rm WatF}(\sigma) = A\left[\left(\frac{e}{\sigma}\right)^b + c\right]\exp(\frac{d}{\sigma^2})\]

References

[R14]

(1, 2) Watson, W. A., et al., Dec. 2012.

http://arxiv.org/abs/1212.0095

Methods

fsigma(cut_fit)

hmf.fitting_functions.get_fit(name, **kwargs)¶

Returns the correct subclass of FittingFunction.

Parameters:	name : str The class name of the appropriate fit **kwargs : Any parameters for the instantiated fit (including model parameters)

tools¶

A collection of functions which do some of the core work of the HMF calculation.

The routines here could be made more ‘elegant’ by taking MassFunction or Transfer objects as arguments, but we keep them simple for the sake of flexibility.

hmf.tools.check_kr(min_m, max_m, mean_dens, mink, maxk)¶

Check the bounds of the product of k*r

If the bounds are not high/low enough, then there can be information loss in the calculation of the mass variance. This routine returns a warning indicating the necessary adjustment for requisite accuracy.

See http://arxiv.org/abs/1306.6721 for details.

hmf.tools.d_plus(z, cdict, getvec=False)¶

Finds the factor \(D^+(a)\), from Lukic et. al. 2007, eq. 8.

Uses simpson’s rule to integrate, with 1000 steps.

Parameters:	z : float The redshift cosmo : hmf.cosmo.Cosmology() object Cosmological parameters
Returns:	dplus : float The un-normalised growth factor.

hmf.tools.growth_factor(z, cdict, getvec=False)¶

Calculate \(d(a) = D^+(a)/D^+(a=1)\), from Lukic et. al. 2007, eq. 7.

Parameters:	z : float The redshift cosmo : hmf.cosmo.Cosmology() object Cosmological parameters
Returns:	growth : float The normalised growth factor.

hmf.tools.normalize(norm_sigma_8, unn_power, lnk, mean_dens)¶

Normalize the power spectrum to a given \(\sigma_8\)

Parameters:	norm_sigma_8 : float The value of \(\sigma_8\) to normalize to. unn_power : array_like The natural logarithm of the unnormalised power spectrum lnk : array_like The natural logarithm of the values of k/h at which unn_power is defined. mean_dens : float The mean density of the Universe.
Returns:	power : array_like An array of the same length as unn_power in which the values are normalised to :math:``sigma_8` normalisation : float The normalisation constant.