Warren¶

class hmf.core.fits.Warren(*, A=0.7234, b=1.625, c=0.2538, d=1.1982, e=1.0)[source]¶

The Warren et al. (2006) mass function.

\[f(\sigma) = A\left[\left(\frac{e}{\sigma}\right)^b + c\right] \exp\left(-\frac{d}{\sigma^2}\right).\]

The paper’s (A, a, b, c) are hmf’s (A, b, c, d), with e = 1.

Parameters:

A (float, default 0.7234) – The amplitude A.
b (float, default 1.625) – The exponent b of e/sigma.
c (float, default 0.2538) – The constant c added to (e/sigma)^b.
d (float, default 1.1982) – The exponential cut-off d.
e (float, default 1.0) – The scale e of sigma.

Model metadata

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

calibration_domain: ClassVar[Domain | None] = Domain(bounds=(('m', Interval(lower=10000000000.0, upper=1000000000000000.0, unit=Unit("solMass / littleh"), lower_open=False, upper_open=False)), ('z', Interval(lower=0.0, upper=0.0, unit=None, lower_open=False, upper_open=False))), source="Warren et al. 2006 state only 'over five orders of magnitude' in mass (Sec. 2); the range 1e10-1e15 Msun/h is Bhattacharya et al. 2011, Table 3. z: not stated, a single epoch, presumably z = 0. One cosmology: (Omega_m, Omega_b, n, h, sigma_8) = (0.3, 0.04, 1, 0.7, 0.9) (eq. 1).")¶: Where the fit was calibrated against simulations, with its source; None for a fit that was not calibrated (e.g. an analytic one).

measured_mass_definition: ClassVar[MeasuredMassDefinition] = MeasuredMassDefinition(kind='fof', linking_length=0.2, overdensity=None, preferred=None, note='Warren et al. 2006, Sec. 2, with the N(1 - N^-0.6) correction (eq. 3).')¶: 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] = 'Warren et al. 2006 (arXiv v1), eq. 8.'¶: 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, ...]] = ('Warren, M. S., et al., 2006. ApJ 646, 881. https://doi.org/10.1086/504962',)¶: References to cite when the model is used, each a formatted citation.

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

simulations: ClassVar[SimulationDetails | None] = SimulationDetails(box_size=<Quantity [ 96., 135., 192., 272., 384., 543., 768., 1086., 1536., 2172., 2583., 3072.] Mpc / littleh>, n_particles=(1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824, 1073741824), omega_m=(0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3), omega_b=(0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04, 0.04), sigma_8=(0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9), h=(0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7), n_s=(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), softening=None, transfer=('CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST', 'CMBFAST'), z_start=None, initial_conditions=None, halo_finder=None, n_min=400, z_range=None, names=None, notes='16 runs in all (three 384, two 272 and two 3072 Mpc/h boxes). Softening: 2.1 kpc/h (physical) in the highest-resolution run to 98 kpc/h (comoving) in the largest; not stated for the others. Redshift: not stated (a single epoch, presumably z = 0). FoF masses corrected by N(1 - N^-0.6) (eq. 3); fit by maximum likelihood on Poisson counts.', source='Warren et al. 2006 (arXiv v1), Sec. 2 and eq. 1.')¶: The simulations the fit was calibrated on (None for a fit to no simulations).

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