# tpcf¶

halotools.mock_observables.tpcf(sample1, rbins, sample2=None, randoms=None, period=None, do_auto=True, do_cross=True, estimator=u'Natural', num_threads=1, approx_cell1_size=None, approx_cell2_size=None, approx_cellran_size=None, RR_precomputed=None, NR_precomputed=None, seed=None)[source] [edit on github]

Calculate the real space two-point correlation function, $$\xi(r)$$.

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 for example usage on a mock galaxy catalog.

Parameters: sample1 : array_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. rbins : array_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. sample2 : array_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. randoms : array_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). period : array_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_auto : boolean, optional Boolean determines whether the auto-correlation function will be calculated and returned. Default is True. do_cross : boolean, 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. estimator : string, optional Statistical estimator for the tpcf. Options are ‘Natural’, ‘Davis-Peebles’, ‘Hewett’ , ‘Hamilton’, ‘Landy-Szalay’ Default is Natural. num_threads : int, 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_size : array_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_size : array_like, optional Analogous to approx_cell1_size, but for sample2. See comments for approx_cell1_size for details. approx_cellran_size : array_like, optional Analogous to approx_cell1_size, but for randoms. See comments for approx_cell1_size for details. RR_precomputed : array_like, optional Array storing the number of RR-counts calculated in advance during a pre-processing phase. Must have the same length as len(rbins). If the RR_precomputed argument is provided, you must also provide the NR_precomputed argument. Default is None. NR_precomputed : int, optional Number of points in the random sample used to calculate RR_precomputed. If the NR_precomputed argument is provided, you must also provide the RR_precomputed argument. Default is None. seed : int, optional Random number seed used to randomly downsample data, if applicable. Default is None, in which case downsampling will be stochastic. correlation_function(s) : numpy.array len(rbins)-1 length array containing the correlation function $$\xi(r)$$ computed in each of the bins defined by input rbins. $1 + \xi(r) \equiv \mathrm{DD}(r) / \mathrm{RR}(r),$ If estimator is set to ‘Natural’. $$\mathrm{DD}(r)$$ is the number of sample pairs with separations equal to $$r$$, calculated by the pair counter. $$\mathrm{RR}(r)$$ is the number of random pairs with separations equal to $$r$$, and is counted internally using “analytic randoms” if randoms is set to None (see notes for an explanation), otherwise it is calculated using the pair counter. If sample2 is passed as input (and if sample2 is not exactly the same as sample1), then three arrays of length len(rbins)-1 are returned: $\xi_{11}(r), \xi_{12}(r), \xi_{22}(r),$ the autocorrelation of sample1, the cross-correlation between sample1 and sample2, and the autocorrelation of sample2, respectively. If do_auto or do_cross is set to False, the appropriate sequence of results is returned.

Notes

For a higher-performance implementation of the tpcf function written in C, see the Corrfunc code written by Manodeep Sinha, available at https://github.com/manodeep/Corrfunc.

Examples

For demonstration purposes we calculate the tpcf for halos in the FakeSim.

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

>>> x = halocat.halo_table['halo_x']
>>> y = halocat.halo_table['halo_y']
>>> z = halocat.halo_table['halo_z']


We transform our x, y, z points into the array shape used by the pair-counter by taking the transpose of the result of numpy.vstack. This boilerplate transformation is used throughout the mock_observables sub-package:

>>> sample1 = np.vstack((x,y,z)).T


Alternatively, you may use the return_xyz_formatted_array convenience function for this same purpose, which provides additional wrapper behavior around numpy.vstack such as placing points into redshift-space.

>>> rbins = np.logspace(-1, 1, 10)
>>> xi = tpcf(sample1, rbins, period=halocat.Lbox)