The halo mass function calculator.

hmf is a python application that provides a flexible and simple way to calculate the Halo Mass Function for a range of varying parameters. It is also the backend to HMFcalc, the online HMF calculator.


Due to the general trend of moving to Python 3 by important projects such as IPython and astropy, from version 3.0, hmf is compatible with Python 3, and from version 3.1, it will drop (official) support for Python 2.


Read the docs.


Please cite Murray, Power and Robotham (2013) if you find this code useful in your research.


  • Calculate mass functions and related quantities extremely easily.
  • Very simple to start using, but wide-ranging flexibility.
  • Caching system for optimal parameter updates, for efficient iteration over parameter space.
  • Support for all LambdaCDM cosmologies.
  • Focus on flexibility in models. Each “Component”, such as fitting functions, filter functions, growth factor models and transfer function fits are implemented as generic classes that can easily be altered by the user without touching the source code.
  • Focus on simplicity in frameworks. Each “Framework” mixes available “Components” to derive useful quantities – all given as attributes of the Framework.
  • Comprehensive in terms of output quantities: access differential and cumulative mass functions, mass variance, effective spectral index, growth rate, cosmographic functions and more.
  • Comprehensive in terms of implemented Component models
    • 5+ models of transfer functions including directly from CAMB
    • 4 filter functions
    • 20 hmf fitting functions
  • Includes models for Warm Dark Matter
  • Nonlinear power spectra via HALOFIT
  • Functions for sampling the mass function.
  • CLI scripts both for producing any quantity included, or fitting any quantity.
  • Python 2 and 3 compatible


hmf is built on several other packages, most of which will be familiar to the scientific python programmer. All of these dependencies should be automatically installed when installing hmf. Explicitly, the dependencies are numpy, scipy, astropy and camb.

You will only need emcee if you are going to be using the fitting capabilities of hmf.

Finally the hmf package needs to be installed: pip install hmf.

To go really bleeding edge, install the develop branch using pip install git+git://


Once you have hmf installed, you can quickly generate a mass function by opening an interpreter (e.g. IPython) and doing:

>>> from hmf import MassFunction
>>> hmf = MassFunction()
>>> mass_func = hmf.dndlnm

Note that all parameters have (what I consider reasonable) defaults. In particular, this will return a Tinker (2008) mass function between \(10^{10}-10^{15} M_\odot\), at \(z=0\) for the default PLANCK15 cosmology. Nevertheless, there are several parameters which can be input, either cosmological or otherwise. The best way to see these is to do

>>> MassFunction.parameter_info()

We can also check which parameters have been set in our “default” instance:

>>> hmf.parameter_values

To change the parameters (cosmological or otherwise), one should use the update() method, if a MassFunction() object already exists. For example

>>> hmf = MassFunction()
>>> hmf.update(Ob0 = 0.05, z=10) #update baryon density and redshift
>>> cumulative_mass_func = hmf.ngtm

For a more involved introduction to hmf, check out the tutorials, which are currently under construction, or the API docs.


Steven Murray: @steven-murray


Jordan Mirocha (UCLA): @mirochaj

Comments, corrections and suggestions

Chris Power (UWA) Aaron Robotham (UWA): @asgr Alexander Knebe (UAMadrid) Peter Behroozi (UC Berkeley)