r"""
Module containing the `~halotools.mock_observables.alignments.ee_3d` function used to
calculate the ellipticity-ellipticity (EE) 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_3d_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_3d, npairs_3d, marked_npairs_3d
from .ee_3d import _ee_3d_process_args
__all__ = ['ee_3d_one_two_halo_decomp']
__author__ = ['Duncan Campbell']
np.seterr(divide='ignore', invalid='ignore') # ignore divide by zero in e.g. DD/RR
[docs]
def ee_3d_one_two_halo_decomp(sample1, orientations1, sample1_host_halo_id,
sample2, orientations2, sample2_host_halo_id,
rbins,
weights1=None, weights2=None,
mask1=None, mask2=None,
period=None, num_threads=1,
approx_cell1_size=None, approx_cell2_size=None):
r"""
Calculate the one and two halo componenents of the 3-D ellipticity-ellipticity
correlation function (EE), :math:`\eta_{\rm 1h}(r)`, and :math:`\eta_{\rm 2h}(r)`.
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.
sample1_host_halo_id : array_like
*len(sample1)* integer array of host halo ids.
sample2 : array_like, optional
Npts2 x 3 array containing 3-D positions of points.
orientations2 : array_like
Npts1 x 3 numpy array containing orientation vectors for each point in ``sample2``.
these will be normalized if not already.
sample2_host_halo_id : array_like
*len(sample2)* integer array of host halo ids.
rbins : array_like
array of boundaries defining the radial bins in which pairs are counted.
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)`
computed in each of the bins defined by input ``rbins``.
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} w_i w_j} - \frac{1}{3}
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,3))
And a set of random halo ids for each point
>>> halo_ids = np.random.randint(1, 10, Npts)
We can the calculate the auto-EE correlation between these points:
>>> rbins = np.logspace(-1,1,10)
>>> result_1h, result_2h = ee_3d_one_two_halo_decomp(sample1, random_orientations, halo_ids, sample1, random_orientations, halo_ids, rbins, 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_3d_alignment_args(*alignment_args)
function_args = (sample1, rbins, sample2, period, num_threads)
sample1, rbins, sample2, period, num_threads, PBCs = _ee_3d_process_args(*function_args)
# How many points are there (for normalization purposes)?
N1 = len(sample1)
N2 = len(sample2)
# process mask1
if mask1 is None:
mask1 = np.array([True]*N1)
else:
mask1 = np.atleast_1d(mask1).astype('bool')
if np.shape(mask1) != (N1,):
msg = ('`mask1` is not the correct shape.')
raise ValueError(msg)
# process mask2
if mask2 is None:
mask2 = np.array([True]*N2)
else:
mask2 = np.atleast_1d(mask2).astype('bool')
if np.shape(mask2) != (N2,):
msg = ('`mask2` is not the correct shape.')
raise ValueError(msg)
# process halo ids
sample1_host_halo_id = np.atleast_1d(sample1_host_halo_id).astype('int')
sample2_host_halo_id = np.atleast_1d(sample2_host_halo_id).astype('int')
if np.shape(sample1_host_halo_id) != (N1,):
msg = ('`sample1_host_halo_id` is not a 1D array of length ``len(samnple1)``.')
raise ValueError(msg)
if np.shape(sample2_host_halo_id) != (N2,):
msg = ('`sample2_host_halo_id` is not a 1D array of length ``len(samnple2)``.')
raise ValueError(msg)
marks1 = np.zeros((N1, 5))
marks1[:,0] = weights1
marks1[:,1] = orientations1[:,0]
marks1[:,2] = orientations1[:,1]
marks1[:,3] = orientations1[:,2]
marks1[:,4] = sample1_host_halo_id
marks2 = np.zeros((N2, 5))
marks2[:,0] = weights2
marks2[:,1] = orientations2[:,0]
marks2[:,2] = orientations2[:,1]
marks2[:,3] = orientations2[:,2]
marks2[:,4] = sample2_host_halo_id
marked_counts_1h = marked_npairs_3d(sample1[mask1], sample2[mask2], rbins,
period=period, weights1=marks1[mask1], weights2=marks2[mask2],
weight_func_id=16, num_threads=num_threads,
approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size)
marked_counts_1h = np.diff(marked_counts_1h)
marked_counts_2h = marked_npairs_3d(sample1[mask1], sample2[mask2], rbins,
period=period, weights1=marks1[mask1], weights2=marks2[mask2],
weight_func_id=17, num_threads=num_threads,
approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size)
marked_counts_2h = np.diff(marked_counts_2h)
# if no weights, use fast un-weighted pair counter
if np.all(weights1==1.0) & np.all(weights2==1.0):
counts = npairs_3d(sample1, sample2, rbins,
period=period, num_threads=num_threads,
approx_cell1_size=approx_cell1_size,
approx_cell2_size=approx_cell2_size)
else:
counts = marked_npairs_3d(sample1, sample2, rbins,
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(counts)
# get 1-halo and 2-halo pair counts
marks1 = np.zeros((N1, 2))
marks1[:,0] = sample1_host_halo_id
marks1[:,1] = weights1
marks2 = np.zeros((N2, 2))
marks2[:,0] = sample2_host_halo_id
marks2[:,1] = weights2
counts_1h = marked_npairs_3d(sample1[mask1], sample2[mask2], rbins,
weights1=marks1[mask1], weights2=marks2[mask2], weight_func_id=3,
period=period, num_threads=num_threads,
approx_cell1_size=approx_cell1_size,
approx_cell2_size=approx_cell2_size)
counts_1h = np.diff(counts_1h)
counts_2h = marked_npairs_3d(sample1[mask1], sample2[mask2], rbins,
weights1=marks1[mask1], weights2=marks2[mask2], weight_func_id=4,
period=period, num_threads=num_threads,
approx_cell1_size=approx_cell1_size,
approx_cell2_size=approx_cell2_size)
counts_2h = np.diff(counts_2h)
#counts = counts_1h + counts_2h
result_1h = marked_counts_1h/counts - 1.0/3.0*(counts_1h/counts)
result_2h = marked_counts_2h/counts - 1.0/3.0*(counts_2h/counts)
return result_1h, result_2h