r"""
Module containing the `~halotools.mock_observables.alignments.ed_projected` function used to
calculate the ellipticity-direction (ED) 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 positional_marked_npairs_xy_z, npairs_xy_z, marked_npairs_xy_z
__all__ = ['ed_projected`']
__author__ = ['Duncan Campbell']
np.seterr(divide='ignore', invalid='ignore') # ignore divide by zero in e.g. DD/RR
[docs]
def ed_projected(sample1, orientations1, sample2, rp_bins, pi_max, weights1=None, weights2=None,
period=None, num_threads=1, approx_cell1_size=None, approx_cell2_size=None):
r"""
Calculate the ellipticity-direction projected correlation function (ED), :math:`\omega(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.
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(rp_bins)-1* length array containing the correlation function :math:`\omega(r_p)`
computed in each of the bins defined by input ``rp_bins``.
Notes
-----
The ellipticity-direction projected correlation function is defined as:
.. math::
\omega = \frac{\sum_{i \neq j}w_iw_j|\hat{e}_i \cdot \hat{r}_{ij}|^2}{\sum_{i \neq j} w_iw_j} - \frac{1}{2}
where e.g. :math:`\hat{e}_i` is the orientation of the :math:`i`-th galaxy, and
:math:`\hat{r}_{ij}` is the normalized vector in the direction of the :math:`j`-th galaxy
from 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-ED correlation between these points:
>>> rp_bins = np.logspace(-1,1,10)
>>> pi_max = 0.2
>>> result = ed_projected(sample1, random_orientations, sample1, rp_bins, pi_max, period=Lbox)
"""
# process arguments
alignment_args = (sample1, orientations1, None, weights1,
sample2, None, None, weights2,
None, None, None, None)
dum = 0.0 # dummy variable to store arguments not needed for this function
sample1, orientations1, dum, weights1,\
sample2, dum, 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 = _ed_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 = weights2
marked_counts, counts = positional_marked_npairs_xy_z(sample1, sample2, rp_bins, pi_bins,
period=period, weights1=marks1, weights2=marks2,
weight_func_id=4, 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-weihgted 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 _ed_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.ed_3d`.
"""
sample1 = enforce_sample_has_correct_shape(sample1)
sample2 = enforce_sample_has_correct_shape(sample2)
N1 = len(sample1)
N2 = len(sample2)
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