Source code for halotools.mock_observables.ia_correlations.ee_projected

Module containing the `~halotools.mock_observables.alignments.ee_projected` function used to
calculate the ellipticity-ellipticity (EE) projected correlation functon

from __future__ import absolute_import, division, print_function, unicode_literals

import numpy as np
from math import pi

from .alignment_helpers import process_projected_alignment_args
from ..mock_observables_helpers import (enforce_sample_has_correct_shape,
    get_separation_bins_array, get_line_of_sight_bins_array, get_period, get_num_threads)
from ..pair_counters.mesh_helpers import _enforce_maximum_search_length
from ..pair_counters import marked_npairs_xy_z, npairs_xy_z, marked_npairs_xy_z

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

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

[docs] def ee_projected(sample1, orientations1, sample2, orientations2, rp_bins, pi_max, weights1=None, weights2=None, period=None, num_threads=1, approx_cell1_size=None, approx_cell2_size=None): r""" Calculate the projected ellipticity-ellipticity projected correlation function (EE), :math:`\eta(r_p)`. Parameters ---------- sample1 : array_like Npts1 x 3 numpy array containing 3-D positions of points with associated orientations. 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. orientations1 : array_like Npts1 x 2 numpy array containing projected orientation vectors for each point in ``sample1``. these will be normalized if not already. sample2 : array_like, optional Npts2 x 3 array containing 3-D positions of points. orientations2 : array_like Npts1 x 2 numpy array containing orientation vectors for each point in ``sample2``. these will be normalized if not already. rp_bins : array_like array of boundaries defining the radial bins perpendicular to the LOS in which pairs are counted. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools. pi_max : float maximum LOS distance defining the projection integral length-scale in the z-dimension. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools. weights1 : array_like, optional Npts1 array of weghts. If this parameter is not specified, it is set to numpy.ones(Npts1). weights2 : array_like, optional Npts2 array of weghts. If this parameter is not specified, it is set to numpy.ones(Npts2). 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. 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. Returns ------- correlation_function : numpy.array *len(rbins)-1* length array containing the correlation function :math:`\eta(r_p)` computed in each of the bins defined by input ``rp_bins``. Notes ----- The ellipticity-ellipticity correlation function is defined as: .. math:: \eta = \frac{\sum_{i \neq j}w_iw_j|\hat{e}_i \cdot \hat{e}_j|^2}{\sum_{i \neq j}} - \frac{1}{2} where e.g. :math:`\hat{e}_i` is the orientation of the :math:`i`-th galaxy. :math:`w_i` and :math:`w_j` are the weights associated with the :math:`i`-th and :math:`j`-th galaxy. The weights default to 1 if not set. Example -------- For demonstration purposes we create a randomly distributed set of points within a periodic cube of Lbox = 250 Mpc/h. >>> Npts = 1000 >>> Lbox = 250 >>> x = np.random.uniform(0, Lbox, Npts) >>> y = np.random.uniform(0, Lbox, Npts) >>> z = np.random.uniform(0, Lbox, Npts) 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 `~halotools.mock_observables` sub-package: >>> sample1 = np.vstack((x,y,z)).T Alternatively, you may use the `~halotools.mock_observables.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. We then create a set of random orientation vectors for each point >>> random_orientations = np.random.random((Npts,2)) We can the calculate the auto-EE correlation between these points: >>> rp_bins = np.logspace(-1,1,10) >>> pi_max = 0.2 >>> result = ee_projected(sample1, random_orientations, sample1, random_orientations, rp_bins, pi_max, period=Lbox) """ # process arguments alignment_args = (sample1, orientations1, None, weights1, sample2, orientations2, None, weights2, None, None, None, None) dum = 0.0 # dummy variable to store arguments not needed for this function sample1, orientations1, dum, weights1,\ sample2, orientations2, dum, weights2,\ dum, dum, dum, dum = process_projected_alignment_args(*alignment_args) function_args = (sample1, rp_bins, pi_max, sample2, period, num_threads) sample1, rp_bins, pi_bins, sample2, period, num_threads, PBCs = _ee_projected_process_args(*function_args) # How many points are there (for normalization purposes)? N1 = len(sample1) N2 = len(sample2) marks1 = np.zeros((N1, 3)) marks1[:,0] = weights1 marks1[:,1] = orientations1[:,0] marks1[:,2] = orientations1[:,1] marks2 = np.zeros((N2, 3)) marks2[:,0] = weights2 marks2[:,1] = orientations2[:,0] marks2[:,2] = orientations2[:,1] marked_counts = marked_npairs_xy_z(sample1, sample2, rp_bins, pi_bins, period=period, weights1=marks1, weights2=marks2, weight_func_id=15, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size) marked_counts = np.diff(np.diff(marked_counts, axis=0), axis=1) # if no weights, use fast un-weighted pair counter if np.all(weights1==1.0) & np.all(weights2==1.0): counts = npairs_xy_z(sample1, sample2, rp_bins, pi_bins, period=period, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size) else: counts = marked_npairs_xy_z(sample1, sample2, rp_bins, pi_bins, weights1=weights1, weights2=weights2, weight_func_id=1, period=period, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size) counts = np.diff(np.diff(counts, axis=0), axis=1) return marked_counts/counts - 1.0/2.0
def _ee_projected_process_args(sample1, rp_bins, pi_max, sample2, period, num_threads): r""" Private method to do bounds-checking on the arguments passed to `~halotools.mock_observables.alignments.ee_projected`. """ sample1 = enforce_sample_has_correct_shape(sample1) rp_bins = get_separation_bins_array(rp_bins) rp_max = np.amax(rp_bins) pi_max = float(pi_max) pi_bins = np.array([0.0, pi_max]) period, PBCs = get_period(period) _enforce_maximum_search_length([rp_max, rp_max, pi_max], period) num_threads = get_num_threads(num_threads) return sample1, rp_bins, pi_bins, sample2, period, num_threads, PBCs