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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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, optionalA cosmology. Default is the default provided by the
cosmo.Cosmology
class. Not required ifomegam_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 ofcosmo
.**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)