PS¶

class hmf.core.fits.PS[source]¶

The Press & Schechter (1974) mass function.

\[f(\sigma) = \sqrt{2/\pi}\,\nu\exp(-\nu^2/2).\]

It follows from spherical collapse with the “fudge factor” of 2, which makes it normalised: all mass is in haloes. It has no free parameters.

Model metadata

alias: ClassVar[str | None] = 'PS'¶: The short name the model is registered under, if any. Set by the alias class keyword; never inherited.

calibration_domain: ClassVar[Domain | None] = None¶

not calibrated on simulations.

Type:: Analytic (spherical collapse)

measured_mass_definition: ClassVar[MeasuredMassDefinition] = MeasuredMassDefinition(kind='so_virial', linking_length=None, overdensity=None, preferred=None, note='Analytic: spherical collapse, i.e. virialised haloes.')¶: The halo mass definition the fit was measured in.

modifies_dndm: ClassVar[bool] = False¶: Whether modify_dndm_kernel() changes the mass function (see “Post-processing the mass function” in the module documentation); if False, it is the identity.

normalized¶: Whether \(f\) integrates to 1 over \(\ln\sigma^{-1}\) (all mass in haloes).

parameter_source: ClassVar[str] = 'Press & Schechter 1974: analytic, no free parameters.'¶: The exact source (paper, version, table or equation) of the parameter defaults, e.g. “Tinker et al. 2008, ApJ 688, 709 (published), Table 2”.

references: ClassVar[tuple[str, ...]] = ('Press, W. H., Schechter, P., 1974. ApJ 187, 425. https://doi.org/10.1086/152650',)¶: References to cite when the model is used, each a formatted citation.

requires: ClassVar[frozenset[str]] = frozenset({'delta_c'})¶: The inputs (from INPUTS) that fsigma() needs, besides sigma.

simulations: ClassVar[SimulationDetails | None] = None¶: The simulations the fit was calibrated on (None for a fit to no simulations).

valid_domain: ClassVar[Domain] = Domain(bounds=(('delta_c', Interval(lower=0.0, upper=inf, unit=None, lower_open=True, upper_open=True)), ('sigma', Interval(lower=0.0, upper=inf, unit=None, lower_open=True, upper_open=True))), source='sigma > 0 and delta_c > 0.')¶

fsigma() raises outside it.

Type:: Where the formula is defined or sensible

Methods

check_required(x: FitInputs) → None¶

Raise if an input needed to evaluate the fit is missing from x.

Raises:: ValueError – If an input in requires (or needed to check valid_domain) is missing.

check_valid(x: FitInputs) → None¶

Raise if any input is outside valid_domain.

Raises:: DomainError – Always, if any value is outside the valid domain: this does not depend on any policy.

classmethod coerce(value: object) → Self¶

Convert a value to a model of this kind: the converter of a model field.

Parameters:

value – An instance of cls, which is returned as it is; or a name, import path or class that get() accepts, which is looked up and instantiated with its default parameters.

Returns:

An instance of cls.

Return type:

Model

Raises:

ModelNotFoundError – If value is a name that no model of this kind is known by.
TypeError – If value is of any other type, or names a class that is not a concrete subclass of cls.

Examples

>>> from hmf.core.filters import Filter, TopHat
>>> Filter.coerce("TopHat") == TopHat()
True

classmethod domain_inputs() → frozenset[str]¶: The inputs (besides sigma) needed to evaluate the fit and check both domains.

classmethod fields_info() → tuple[FieldInfo, ...]¶

Describe this class’s fields, without creating an instance.

Returns:: The name, type, default and documentation of each field.
Return type:: tuple of FieldInfo

The multiplicity function, \(f(\sigma) = \nu f(\nu)\).

m must be a Quantity (see hmf.core.units); every other input is dimensionless. Code that already has plain arrays in canonical units calls fsigma_kernel() or evaluate_fsigma() instead (see “Evaluating a fit” in the module documentation). It applies no calibration policy (see evaluate_fsigma() for that), but always checks valid_domain.

Parameters:

sigma – \(\sigma(m, z)\).
z – Redshift.
omega_m_z – \(\Omega_m(z)\).
delta_halo – The halo overdensity relative to the mean density.
delta_c – The critical overdensity for collapse.
n_eff – The effective spectral index.
m – The halo mass, a Quantity (e.g. in Msun_h).

Returns:

\(f(\sigma)\) (dimensionless), broadcast over the inputs.

Return type:

numpy.ndarray

Raises:

ValueError – If an input the fit requires is not given.
UnitBoundaryError – If m is not a Quantity.
DomainError – If any input is outside valid_domain, or makes the fit’s parameters unphysical.

fsigma_kernel(x: FitInputs) → ndarray[tuple[Any, ...], dtype[float64]]¶

fsigma() at kernel level, from inputs that are plain arrays.

The inputs are in canonical units (the mass in Msun/h); see hmf.core._kernels. It checks the valid domain, as fsigma() does, and applies no calibration policy (see evaluate_fsigma()).

Parameters:

x – The inputs.

Return type:

numpy.ndarray

Raises:

ValueError – If an input the fit requires is not in x.
DomainError – As for fsigma().

classmethod get(name: str | type[Model]) → type[Self]¶

Look up a model of this kind.

Parameters:

name – An alias ("Tinker08"), a qualified name ("hmf.core.fits:Tinker08"), an import path to a class not yet imported ("pkg.mod:Cls" or "pkg.mod.Cls"), or a class.

Returns:

The model class (not an instance). It is always a subclass of cls.

Return type:

type

Raises:

ModelNotFoundError – If no model of this kind is known by name, even after loading the hmf.models entry points and trying name as an import path.
TypeError – If name resolves to something that is not a concrete subclass of cls.

classmethod get_aliases() → Mapping[str, str]¶: Return a read-only mapping from alias to qualified name, for this kind.

classmethod get_models() → Mapping[str, type[Self]]¶

Return the registered models of this kind, by qualified name.

Plugins advertised in the hmf.models entry-point group are loaded first.

Returns:: A read-only mapping from qualified name to class. Called on a kind, it is a live view of the registry. Called on a non-kind subclass, it holds only the models that subclass it.
Return type:: Mapping

in_calibration_domain(x: FitInputs) → bool | ndarray[tuple[Any, ...], dtype[bool]]¶

Whether each input is inside calibration_domain.

Parameters:: x – The inputs, from inputs().
Returns:: A bool if every input is a scalar, else the broadcast array. True if the fit has no calibration domain (it is None).
Return type:: bool or numpy.ndarray of bool
Raises:: ValueError – If an input needed to check the domain was not given.

Collect the inputs, checking that the required ones are given.

Parameters are as for fsigma() (m is a Quantity). Code that already has plain arrays in canonical units builds FitInputs directly (see “Evaluating a fit” in the module documentation).

Returns:: The inputs as plain arrays, in canonical units.
Return type:: FitInputs
Raises:: ValueError – If an input in requires (or needed to check valid_domain) is missing.

modify_dndm(m: Any, dndm: Any, *, z: ArrayLike, ngtm: Any, H0: Any, omega_m0: ArrayLike) → Any¶

Map the mass function computed from fsigma() to the fit’s.

The identity unless modifies_dndm (see “Post-processing the mass function” in the module documentation). Every fit takes the same arguments, whether it uses them or not. This method converts them and calls modify_dndm_kernel(), which a mass-function Stage calls directly.

Parameters:

m – Halo masses, a Quantity: in h-units, or physical units (converted with H0).
dndm – The mass function from fsigma(), a Quantity (number density per mass).
z – Redshift.
ngtm – The cumulative mass function n(>m) from fsigma(), a Quantity.
H0 – The Hubble constant, a scalar Quantity (e.g. 70 * H0_unit). It converts physical units, and gives h to fits whose formula is in physical units.
omega_m0 – The density parameter of CDM + baryons today.

Returns:

The fit’s mass function, in dndm_unit.

Return type:

Quantity

modify_dndm_kernel(m: ArrayLike, dndm: ArrayLike, *, z: ArrayLike, ngtm: ArrayLike, h: ArrayLike, omega_m0: ArrayLike) → ndarray[tuple[Any, ...], dtype[float64]]¶

modify_dndm() at kernel level, on plain arrays.

A pure kernel in canonical units (see hmf.core._kernels): the identity, unless the fit sets modifies_dndm (its class documentation describes the correction). All arguments broadcast. It checks the arguments that say where the mass function is evaluated (m, z, h, omega_m0), from their extent; dndm and ngtm are values it maps, and may be NaN (e.g. masked by a domain policy).

Parameters:

m – Halo masses, in Msun/h.
dndm – The mass function from fsigma(), in h^4 / (Msun Mpc^3).
z – Redshift.
ngtm – The cumulative mass function n(>m) from fsigma(), in h^3 / Mpc^3.
h – The dimensionless Hubble parameter, H0 / (100 km/s/Mpc).
omega_m0 – The density parameter of CDM + baryons today.

Returns:

The fit’s mass function, in h^4 / (Msun Mpc^3).

Return type:

numpy.ndarray

Raises:

DomainError – If an m, h or omega_m0 is not finite and > 0, or a z is not finite and >= 0.

classmethod qualified_name() → str¶: Return this class’s qualified name, package.module:Class.