Source code for halotools.mock_observables.two_point_clustering.tpcf_one_two_halo_decomp

r"""
Module containing the `~halotools.mock_observables.tpcf` function used to
calculate the 1-halo, 2-halo decomposition of the
two-point correlation function in 3d.
"""



import numpy as np
from math import gamma

from .clustering_helpers import (process_optional_input_sample2, verify_tpcf_estimator)

from ..mock_observables_helpers import (enforce_sample_has_correct_shape,
    get_separation_bins_array, get_period, get_num_threads)
from ..pair_counters.mesh_helpers import _enforce_maximum_search_length

from .tpcf_estimators import _TP_estimator, _TP_estimator_requirements
from ..pair_counters import npairs_3d
from ..pair_counters import marked_npairs_3d

from ...custom_exceptions import HalotoolsError

__all__ = ['tpcf_one_two_halo_decomp']
__author__ = ['Duncan Campbell']


np.seterr(divide='ignore', invalid='ignore')  # ignore divide by zero in e.g. DD/RR


[docs]def 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): r""" Calculate the real space one-halo and two-halo decomposed two-point correlation functions, :math:`\xi^{1h}(r)` and :math:`\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 :ref:`mock_obs_pos_formatting` documentation page for instructions on how to transform your coordinate position arrays into the format accepted by the ``sample1`` and ``sample2`` arguments. See also :ref:`galaxy_catalog_analysis_tutorial2`. Parameters ---------- sample1 : array_like Npts1 x 3 numpy array containing 3-D positions of points. See the :ref:`mock_obs_pos_formatting` 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_id : array_like, optional *len(sample1)* integer array of host halo ids. 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. sample2_host_halo_id : array_like, optional *len(sample2)* integer array of host halo ids. 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. seed : int, 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, :math:`\xi^{1h}(r)` and :math:`\xi^{2h}(r)`, computed in each of the radial bins defined by input ``rbins``. .. math:: 1 + \xi(r) \equiv \mathrm{DD} / \mathrm{RR}, if ``estimator`` is set to 'Natural', where :math:`\mathrm{DD}` is calculated by the pair counter, and :math:`\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: .. math:: \xi^{1h}_{11}(r), \ \xi^{2h}_{11}(r), .. math:: \xi^{1h}_{12}(r), \ \xi^{2h}_{12}(r), .. math:: \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. Examples -------- For demonstration purposes, we'll use the `~halotools.sim_manager.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) See also ----------- :ref:`galaxy_catalog_analysis_tutorial3`. """ # check input arguments using clustering helper functions function_args = (sample1, sample1_host_halo_id, rbins, sample2, sample2_host_halo_id, randoms, period, do_auto, do_cross, estimator, num_threads, approx_cell1_size, approx_cell2_size, approx_cellran_size, seed) # pass arguments in, and get out processed arguments, plus some control flow variables sample1, sample1_host_halo_id, rbins, sample2, sample2_host_halo_id, randoms, period,\ do_auto, do_cross, num_threads, _sample1_is_sample2, PBCs =\ _tpcf_one_two_halo_decomp_process_args(*function_args) # What needs to be done? do_DD, do_DR, do_RR = _TP_estimator_requirements(estimator) # How many points are there (for normalization purposes)? N1 = len(sample1) N2 = len(sample2) if randoms is not None: NR = len(randoms) else: # set the number of randoms equal to the number of points in sample1 # this is arbitrarily set, but must remain consistent! NR = N1 # calculate 1-halo pairs weight_func_id = 3 one_halo_D1D1, one_halo_D1D2, one_halo_D2D2 = marked_pair_counts( sample1, sample2, rbins, period, num_threads, do_auto, do_cross, sample1_host_halo_id, sample2_host_halo_id, weight_func_id, _sample1_is_sample2) # calculate 2-halo pairs weight_func_id = 4 two_halo_D1D1, two_halo_D1D2, two_halo_D2D2 = marked_pair_counts( sample1, sample2, rbins, period, num_threads, do_auto, do_cross, sample1_host_halo_id, sample2_host_halo_id, weight_func_id, _sample1_is_sample2) # count random pairs D1R, D2R, RR = random_counts(sample1, sample2, randoms, rbins, period, PBCs, num_threads, do_RR, do_DR, _sample1_is_sample2, approx_cell1_size, approx_cell2_size, approx_cellran_size) # run results through the estimator and return relavent/user specified results. if _sample1_is_sample2: one_halo_xi_11 = _TP_estimator(one_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) two_halo_xi_11 = _TP_estimator(two_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) return one_halo_xi_11, two_halo_xi_11 else: if (do_auto is True) & (do_cross is True): one_halo_xi_11 = _TP_estimator(one_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) one_halo_xi_12 = _TP_estimator(one_halo_D1D2, D1R, RR, N1, N2, NR, NR, estimator) one_halo_xi_22 = _TP_estimator(one_halo_D2D2, D2R, RR, N2, N2, NR, NR, estimator) two_halo_xi_11 = _TP_estimator(two_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) two_halo_xi_12 = _TP_estimator(two_halo_D1D2, D1R, RR, N1, N2, NR, NR, estimator) two_halo_xi_22 = _TP_estimator(two_halo_D2D2, D2R, RR, N2, N2, NR, NR, estimator) return one_halo_xi_11, two_halo_xi_11, one_halo_xi_12,\ two_halo_xi_12, one_halo_xi_22, two_halo_xi_22 elif (do_cross is True): one_halo_xi_12 = _TP_estimator(one_halo_D1D2, D1R, RR, N1, N2, NR, NR, estimator) two_halo_xi_12 = _TP_estimator(two_halo_D1D2, D1R, RR, N1, N2, NR, NR, estimator) return one_halo_xi_12, two_halo_xi_12 elif (do_auto is True): one_halo_xi_11 = _TP_estimator(one_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) one_halo_xi_22 = _TP_estimator(one_halo_D2D2, D2R, RR, N2, N2, NR, NR, estimator) two_halo_xi_11 = _TP_estimator(two_halo_D1D1, D1R, RR, N1, N1, NR, NR, estimator) two_halo_xi_22 = _TP_estimator(two_halo_D2D2, D2R, RR, N2, N2, NR, NR, estimator) return one_halo_xi_11, two_halo_xi_11, one_halo_xi_22, two_halo_xi_22
def nball_volume(R, k=3): """ Calculate the volume of a n-shpere. This is used for the analytical randoms. """ return (np.pi**(k/2.0)/gamma(k/2.0+1.0))*R**k def random_counts(sample1, sample2, randoms, rbins, period, PBCs, num_threads, do_RR, do_DR, _sample1_is_sample2, approx_cell1_size, approx_cell2_size, approx_cellran_size): r""" Count random pairs. There are two high level branches: 1. w/ or wo/ PBCs and randoms. 2. PBCs and analytical randoms There are also logical bits to do RR and DR pair counts, as not all estimators need one or the other, and not doing these can save a lot of calculation. Analytical counts are N**2*dv*rho, where dv can is the volume of the spherical shells, which is the correct volume to use for a continious cubic volume with PBCs """ # randoms provided, so calculate random pair counts. if randoms is not None: if do_RR is True: RR = npairs_3d(randoms, randoms, rbins, period=period, num_threads=num_threads, approx_cell1_size=approx_cellran_size, approx_cell2_size=approx_cellran_size) RR = np.diff(RR) else: RR = None if do_DR is True: D1R = npairs_3d(sample1, randoms, rbins, period=period, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cellran_size ) D1R = np.diff(D1R) else: D1R = None if _sample1_is_sample2: D2R = None else: if do_DR is True: D2R = npairs_3d(sample2, randoms, rbins, period=period, num_threads=num_threads, approx_cell1_size=approx_cell2_size, approx_cell2_size=approx_cellran_size) D2R = np.diff(D2R) else: D2R = None return D1R, D2R, RR # PBCs and no randoms--calculate randoms analytically. elif randoms is None: # set the number of randoms equal to the number of points in sample1 NR = len(sample1) # do volume calculations v = nball_volume(rbins) # volume of spheres dv = np.diff(v) # volume of shells global_volume = period.prod() # volume of simulation # calculate randoms for sample1 N1 = np.shape(sample1)[0] # number of points in sample1 rho1 = N1/global_volume # number density of points D1R = (NR)*(dv*rho1) # random counts are N**2*dv*rho # calculate randoms for sample2 N2 = np.shape(sample2)[0] # number of points in sample2 rho2 = N2/global_volume # number density of points D2R = (NR)*(dv*rho2) # random counts are N**2*dv*rho # calculate the random-random pairs. rhor = (NR**2)/global_volume RR = (dv*rhor) return D1R, D2R, RR def marked_pair_counts(sample1, sample2, rbins, period, num_threads, do_auto, do_cross, marks1, marks2, weight_func_id, _sample1_is_sample2): """ Count weighted data pairs. """ # add ones to weights, so returned value is return 1.0*1.0 marks1 = np.vstack((marks1, np.ones(len(marks1)))).T marks2 = np.vstack((marks2, np.ones(len(marks2)))).T if do_auto is True: D1D1 = marked_npairs_3d(sample1, sample1, rbins, weights1=marks1, weights2=marks1, weight_func_id=weight_func_id, period=period, num_threads=num_threads) D1D1 = np.diff(D1D1) else: D1D1 = None D2D2 = None if _sample1_is_sample2: D1D2 = D1D1 D2D2 = D1D1 else: if do_cross is True: D1D2 = marked_npairs_3d(sample1, sample2, rbins, weights1=marks1, weights2=marks2, weight_func_id=weight_func_id, period=period, num_threads=num_threads) D1D2 = np.diff(D1D2) else: D1D2 = None if do_auto is True: D2D2 = marked_npairs_3d(sample2, sample2, rbins, weights1=marks2, weights2=marks2, weight_func_id=weight_func_id, period=period, num_threads=num_threads) D2D2 = np.diff(D2D2) else: D2D2 = None return D1D1, D1D2, D2D2 def _tpcf_one_two_halo_decomp_process_args(sample1, sample1_host_halo_id, rbins, sample2, sample2_host_halo_id, randoms, period, do_auto, do_cross, estimator, num_threads, approx_cell1_size, approx_cell2_size, approx_cellran_size, seed): """ Private method to do bounds-checking on the arguments passed to `~halotools.mock_observables.tpcf_one_two_halo_decomp`. """ sample1 = enforce_sample_has_correct_shape(sample1) sample1_host_halo_id = np.atleast_1d(sample1_host_halo_id).astype(np.int64) sample2, _sample1_is_sample2, do_cross = process_optional_input_sample2( sample1, sample2, do_cross) if _sample1_is_sample2 is True: sample2_host_halo_id = sample1_host_halo_id else: if sample2_host_halo_id is None: msg = ("If passing an input ``sample2``, must also pass sample2_host_halo_id") raise ValueError(msg) else: sample2_host_halo_id = np.atleast_1d(sample2_host_halo_id).astype(np.int64) if randoms is not None: randoms = np.atleast_1d(randoms) # test to see if halo ids are the same length as samples if np.shape(sample1_host_halo_id) != (len(sample1),): msg = ("\n `sample1_host_halo_id` must be a 1-D \n" "array the same length as `sample1`.") raise HalotoolsError(msg) if np.shape(sample2_host_halo_id) != (len(sample2),): msg = ("\n `sample2_host_halo_id` must be a 1-D \n" "array the same length as `sample2`.") raise HalotoolsError(msg) rbins = get_separation_bins_array(rbins) rmax = np.max(rbins) period, PBCs = get_period(period) _enforce_maximum_search_length(rmax, period) if (randoms is None) & (PBCs is False): msg = ('\n If no PBCs are specified, randoms must be provided.') raise HalotoolsError(msg) try: assert do_auto == bool(do_auto) assert do_cross == bool(do_cross) except: msg = "`do_auto` and `do_cross` keywords must be boolean-valued." raise ValueError(msg) num_threads = get_num_threads(num_threads) verify_tpcf_estimator(estimator) return sample1, sample1_host_halo_id, rbins, sample2, sample2_host_halo_id,\ randoms, period, do_auto, do_cross, num_threads, _sample1_is_sample2, PBCs