conditional_abunmatch_bin_based¶

halotools.empirical_models.
conditional_abunmatch_bin_based
(haloprop, galprop, sigma=0.0, npts_lookup_table=1000, seed=None)[source] [edit on github]¶ Function used to model a correlation between two variables,
haloprop
andgalprop
, using conditional abundance matching (CAM).The input
galprop
defines a PDF of the desired galaxy property being modeled. We will use themonte_carlo_from_cdf_lookup
function to generate Monte Carlo realizations of this input PDF. If there arenum_halos
in the inputhaloprop
array, we will drawnum_halos
times from this input PDF, and we will do so in such a way that larger values ofgalprop
will be associated with larger values ofhaloprop
. The returned array will thus be a Monte Carlo realization of the inputgalprop
distribution, but a correlation between the halo property and galaxy property has been introduced. The strength of this correlation can be controlled with the inputsigma
.An example application of this technique is age matching, in which it is supposed that earlier forming halos host earlier forming galaxies (See Hearin and Watson 2013). Alternative applications are numerous. For example, conditional abundance matching could be used to model a correlation between galaxy disk size and halo spin, or to model intrinsic alignments by introducing a correlation between halo and galaxy orientation.
Parameters:  haloprop : ndarray
Numpy array of shape (num_halos, ) typically storing a halo property
 galprop : ndarray
Numpy array of shape (num_gals, ) typically storing a galaxy property
 sigma : float, optional
Level of Gaussian noise that will be introduced to the haloprop–galprop correlation.
Default is 0, for a perfect monotonic relation between haloprop and galprop.
 npts_lookup_table : int, optional
Size of the lookup table used to approximate the
galprop
distribution.Default is 1000.
 seed : int, optional
Random number seed used to introduce noise in the haloprop–galprop correlation.
Default is None for stochastic results.
Returns:  model_galprop : ndarray
Numpy array of shape (num_halos, ) storing the modeled galpropvalues associated with each value of the input
haloprop
.
Notes
To approximate the input
galprop
distribution, the implementation ofconditional_abunmatch_bin_based
builds a lookup table for the CDF of the inputgalprop
using a simple call tonumpy.interp
, which can result in undesired edge case behavior if a large fraction of model galaxies lie outside the range of the data. To ensure your results are not impacted by this, make sure that num_gals >> npts_lookup_table. It is recommended that you always visually check histograms of the distribution of returned values against the desired distribution defined bygalprop
.This function is not really intended for traditional abundance matching applications involving Schechterlike abundance functions such as the stellartohalo mass relation, where extrapolation at the exponentially decaying highmass end requires special care. For code that provides careful treatment of this extrapolation in such cases, see the deconvolution abundance matching code written by YaoYuan Mao.
With the release of Halotools v0.7, this function had its name changed. The previous name given to this function was “conditional_abunmatch”. Halotools v0.7 has a new function
conditional_abunmatch
with this name that largely replaces the functionality here. See Tutorial on Conditional Abundance Matching demonstrating how to use the new function in galaxyhalo modeling with several worked examples.Examples
Suppose we would like to do some CAMstyle modeling of a correlation between some halo property
haloprop
and some galaxy propertygalprop
. Theconditional_abunmatch_bin_based
function can be used to map values of the galaxy property onto the halos in such a way that the PDF ofgalprop
is preserved and a correlation (of variable strength) betweenhaloprop
andgalprop
is introduced.>>> num_halos_in_mpeak_bin = int(1e4) >>> mean, size, std = 1.5, num_halos_in_mpeak_bin, 0.3 >>> spin_at_fixed_mpeak = 10**np.random.normal(loc=mean, size=size, scale=std) >>> num_gals_in_mstar_bin = int(1e3) >>> some_galprop_at_fixed_mstar = np.random.power(2.5, size=num_gals_in_mstar_bin) >>> modeled_galprop = conditional_abunmatch_bin_based(spin_at_fixed_mpeak, some_galprop_at_fixed_mstar)