# Source code for halotools.mock_observables.ia_correlations.ed_3d_one_two_halo_decomp

r"""
Module containing the ~halotools.mock_observables.alignments.ed_3d_one_two_halo_decomp function used to
calculate the 1-halo and 2-halo contributions to the ellipticity-direction (ED) 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,
from ..pair_counters.mesh_helpers import _enforce_maximum_search_length
from ..pair_counters import positional_marked_npairs_3d, npairs_3d, marked_npairs_3d
from .ed_3d import _ed_3d_process_args

__all__ = ['ed_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 ed_3d_one_two_halo_decomp(sample1, orientations1, sample1_host_halo_id,
sample2, sample2_host_halo_id, rbins,
weights1=None, weights2=None,
approx_cell1_size=None, approx_cell2_size=None):
r"""
Calculate the one and two halo componenents of the 3-D ellipticity-direction
correlation function (ED), :math:\omega_{\rm 1h}(r), and :math:\omega_{\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 3 numpy array containing orientation vectors for each point in sample1.
these will be normalized if not already.

sample1_host_halo_id : array_like
Npts1 length integer array of host halo ids.

sample2 : array_like, optional
Npts2 x 3 array containing 3-D positions of points.

sample2_host_halo_id : array_like
Npts2 length 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 weights.  If this parameter is not specified, it is set to numpy.ones(Npts1).

weights2 : array_like, optional
Npts2 array of weights.  If this parameter is not specified, it is set to numpy.ones(Npts2).

Npts1 boolean array indicating which galaxies in sample1 contributes to the ED correlation function.
The default is np.array([True]*Npts1).

Npts2 boolean array indicating which galaxies in sample2 contributes to the ED correlation function.
The default is np.array([True]*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.

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_functions : numpy.array
Two *len(rbins)-1* length array containing the correlation function :math:\omega_{1\rm h}(r)
and :math:\omega_{2\rm h}(r) computed in each of the bins defined by input rbins.

Notes
-----
The ellipticity-direction 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}{3}

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,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-ED correlation between these points:

>>> rbins = np.logspace(-1,1,10)
>>> result = ed_3d_one_two_halo_decomp(sample1, random_orientations,  halo_ids, sample1, halo_ids, rbins, 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_3d_alignment_args(*alignment_args)

function_args = (sample1, rbins, sample2, period, num_threads)
sample1, rbins, sample2, period, num_threads, PBCs = _ed_3d_process_args(*function_args)

# How many points are there (for normalization purposes)?
N1 = len(sample1)
N2 = len(sample2)

else:
msg = ('mask1 is not the correct shape.')
raise ValueError(msg)

else:
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, 2))
marks2[:,0] = weights2
marks2[:,1] = sample2_host_halo_id

approx_cell1_size=approx_cell1_size,
approx_cell2_size=approx_cell2_size)
marked_counts_1h = np.diff(marked_counts_1h)

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,
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,
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

approx_cell1_size=approx_cell1_size,
approx_cell2_size=approx_cell2_size)
counts_1h = np.diff(counts_1h)