tpcf_one_two_halo_decomp

halotools.mock_observables.tpcf_one_two_halo_decomp(sample1, sample1_host_halo_id, rbins, sample2=None, sample2_host_halo_id=None, randoms=None, period=None, do_auto=True, do_cross=True, estimator='Natural', num_threads=1, approx_cell1_size=None, approx_cell2_size=None, approx_cellran_size=None, seed=None)

Calculate the real space one-halo and two-halo decomposed two-point correlation functions, \(\xi^{1h}(r)\) and \(\xi^{2h}(r)\).

This returns the correlation function for galaxies which reside in the same halo, and those that reside in separate halos, as indicated by a host halo ID.

Example calls to this function appear in the documentation below. See the Formatting your xyz coordinates for Mock Observables calculations documentation page for instructions on how to transform your coordinate position arrays into the format accepted by the sample1 and sample2 arguments.

See also Galaxy Catalog Analysis Example: Calculating galaxy clustering in 3d.

Parameters:

sample1array_like

Npts1 x 3 numpy array containing 3-D positions of points. See the Formatting your xyz coordinates for Mock Observables calculations documentation page, or the Examples section below, for instructions on how to transform your coordinate position arrays into the format accepted by the sample1 and sample2 arguments. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

sample1_host_halo_idarray_like, optional

len(sample1) integer array of host halo ids.

rbinsarray_like

array of boundaries defining the real space radial bins in which pairs are counted. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

sample2array_like, optional

Npts2 x 3 array containing 3-D positions of points. Passing sample2 as an input permits the calculation of the cross-correlation function. Default is None, in which case only the auto-correlation function will be calculated.

sample2_host_halo_idarray_like, optional

len(sample2) integer array of host halo ids.

randomsarray_like, optional

Nran x 3 array containing 3-D positions of randomly distributed points. If no randoms are provided (the default option), calculation of the tpcf can proceed using analytical randoms (only valid for periodic boundary conditions).

periodarray_like, optional

Length-3 sequence defining the periodic boundary conditions in each dimension. If you instead provide a single scalar, Lbox, period is assumed to be the same in all Cartesian directions. If set to None (the default option), PBCs are set to infinity, in which case randoms must be provided. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

do_autoboolean, optional

Boolean determines whether the auto-correlation function will be calculated and returned. Default is True.

do_crossboolean, optional

Boolean determines whether the cross-correlation function will be calculated and returned. Only relevant when sample2 is also provided. Default is True for the case where sample2 is provided, otherwise False.

estimatorstring, optional

Statistical estimator for the tpcf. Options are ‘Natural’, ‘Davis-Peebles’, ‘Hewett’ , ‘Hamilton’, ‘Landy-Szalay’ Default is Natural.

num_threadsint, optional

Number of threads to use in calculation, where parallelization is performed using the python multiprocessing module. Default is 1 for a purely serial calculation, in which case a multiprocessing Pool object will never be instantiated. A string ‘max’ may be used to indicate that the pair counters should use all available cores on the machine.

approx_cell1_sizearray_like, optional

Length-3 array serving as a guess for the optimal manner by how points will be apportioned into subvolumes of the simulation box. The optimum choice unavoidably depends on the specs of your machine. Default choice is to use Lbox/10 in each dimension, which will return reasonable result performance for most use-cases. Performance can vary sensitively with this parameter, so it is highly recommended that you experiment with this parameter when carrying out performance-critical calculations.

approx_cell2_sizearray_like, optional

Analogous to approx_cell1_size, but for sample2. See comments for approx_cell1_size for details.

approx_cellran_sizearray_like, optional

Analogous to approx_cell1_size, but for randoms. See comments for approx_cell1_size for details.

seedint, optional

Random number seed used to randomly downsample data, if applicable. Default is None, in which case downsampling will be stochastic.

Returns:

correlation_function(s)numpy.array

Two len(rbins)-1 length arrays containing the one and two halo correlation functions, \(\xi^{1h}(r)\) and \(\xi^{2h}(r)\), computed in each of the radial bins defined by input rbins.

\[1 + \xi(r) \equiv \mathrm{DD} / \mathrm{RR},\]

if estimator is set to ‘Natural’, where \(\mathrm{DD}\) is calculated by the pair counter, and \(\mathrm{RR}\) is counted internally using “analytic randoms” if no randoms are passed as an argument (see notes for an explanation). If a different estimator is specified, the appropiate formula is used.

If sample2 is passed as input, six arrays of length len(rbins)-1 are returned:

\[\xi^{1h}_{11}(r), \ \xi^{2h}_{11}(r),\]

\[\xi^{1h}_{12}(r), \ \xi^{2h}_{12}(r),\]

\[\xi^{1h}_{22}(r), \ \xi^{2h}_{22}(r),\]

the autocorrelation of one and two halo autocorrelation of sample1, the one and two halo cross-correlation between sample1 and sample2, and the one and two halo autocorrelation of sample2. If do_auto or do_cross is set to False, only the appropriate result(s) is returned.

See also

Galaxy Catalog Analysis Example: Galaxy-galaxy lensing

Examples

For demonstration purposes, we’ll use the FakeSim to demonstrate how to calculate the 1- and 2-halo term on a set of fake halos.

>>> from halotools.sim_manager import FakeSim
>>> halocat = FakeSim()

>>> x,y,z = halocat.halo_table['halo_x'], halocat.halo_table['halo_y'], halocat.halo_table['halo_z']
>>> sample1 = np.vstack((x,y,z)).T

>>> rbins = np.logspace(-2,-1,10)
>>> host_halo_IDs = halocat.halo_table['halo_hostid']
>>> xi_1h, xi_2h = tpcf_one_two_halo_decomp(sample1, host_halo_IDs, rbins, period=halocat.Lbox)