Source code for halotools.mock_observables.pair_counters.npairs_3d

```""" Module containing the `~halotools.mock_observables.npairs_3d` function
used to count pairs as a function of separation.
"""
from __future__ import (absolute_import, division, print_function, unicode_literals)
import numpy as np
import multiprocessing
from functools import partial

from .rectangular_mesh import RectangularDoubleMesh
from .mesh_helpers import _set_approximate_cell_sizes, _enclose_in_box, _cell1_parallelization_indices
from .cpairs import npairs_3d_engine
from ...utils.array_utils import array_is_monotonic, custom_len

__author__ = ('Andrew Hearin', 'Duncan Campbell')

__all__ = ('npairs_3d', )

[docs]
def npairs_3d(sample1, sample2, rbins, period=None,
"""
Function counts the number of pairs of points separated by
a three-dimensional distance smaller than the input ``rbins``.

Note that if sample1 == sample2 that the
`~halotools.mock_observables.npairs_3d` function double-counts pairs.
If your science application requires sample1==sample2 inputs and also pairs
to not be double-counted, simply divide the final counts by 2.

A common variation of pair-counting calculations is to count pairs with
separations *between* two different distances *r1* and *r2*. You can retrieve
this information from the `~halotools.mock_observables.npairs_3d`
by taking `numpy.diff` of the returned array.

Parameters
----------
sample1 : array_like
Numpy array of shape (Npts1, 3) 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.

sample2 : array_like
Numpy array of shape (Npts2, 3) containing 3-D positions of points.
Should be identical to sample1 for cases of auto-sample pair counts.

rbins : array_like
Boundaries defining the bins in which pairs are counted.

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.

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
-------
num_pairs : numpy.array
Numpy array of length len(rbins) storing the numbers of pairs in the input bins.

Examples
--------
For demonstration purposes we create randomly distributed sets of points within a
periodic unit cube.

>>> Npts1, Npts2, Lbox = 1000, 1000, 250.
>>> period = [Lbox, Lbox, Lbox]
>>> rbins = np.logspace(-1, 1.5, 15)

>>> x1 = np.random.uniform(0, Lbox, Npts1)
>>> y1 = np.random.uniform(0, Lbox, Npts1)
>>> z1 = np.random.uniform(0, Lbox, Npts1)
>>> x2 = np.random.uniform(0, Lbox, Npts2)
>>> y2 = np.random.uniform(0, Lbox, Npts2)
>>> z2 = np.random.uniform(0, Lbox, Npts2)

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([x1, y1, z1]).T
>>> sample2 = np.vstack([x2, y2, z2]).T

>>> result = npairs_3d(sample1, sample2, rbins, period = period)

"""

# Process the inputs with the helper function
result = _npairs_3d_process_args(sample1, sample2, rbins, period,
x1in, y1in, z1in, x2in, y2in, z2in = result[0:6]
rbins, period, num_threads, PBCs, approx_cell1_size, approx_cell2_size = result[6:]
xperiod, yperiod, zperiod = period

rmax = np.max(rbins)
search_xlength, search_ylength, search_zlength = rmax, rmax, rmax

# Compute the estimates for the cell sizes
approx_cell1_size, approx_cell2_size = (
_set_approximate_cell_sizes(approx_cell1_size, approx_cell2_size, period)
)
approx_x1cell_size, approx_y1cell_size, approx_z1cell_size = approx_cell1_size
approx_x2cell_size, approx_y2cell_size, approx_z2cell_size = approx_cell2_size

# Build the rectangular mesh
double_mesh = RectangularDoubleMesh(x1in, y1in, z1in, x2in, y2in, z2in,
approx_x1cell_size, approx_y1cell_size, approx_z1cell_size,
approx_x2cell_size, approx_y2cell_size, approx_z2cell_size,
search_xlength, search_ylength, search_zlength, xperiod, yperiod, zperiod, PBCs)

# Create a function object that has a single argument, for parallelization purposes
engine = partial(npairs_3d_engine,
double_mesh, x1in, y1in, z1in, x2in, y2in, z2in, rbins)

# Calculate the cell1 indices that will be looped over by the engine

result = pool.map(engine, cell1_tuples)
counts = np.sum(np.array(result), axis=0)
pool.close()
else:
counts = engine(cell1_tuples[0])

return np.array(counts)

def _npairs_3d_process_args(sample1, sample2, rbins, period,
"""
"""
msg = "Input ``num_threads`` argument must be an integer or the string 'max'"
raise ValueError(msg)

# Passively enforce that we are working with ndarrays
x1 = sample1[:, 0]
y1 = sample1[:, 1]
z1 = sample1[:, 2]
x2 = sample2[:, 0]
y2 = sample2[:, 1]
z2 = sample2[:, 2]
rbins = np.atleast_1d(rbins).astype('f8')

rmax = np.max(rbins)

try:
assert rbins.ndim == 1
assert len(rbins) > 1
if len(rbins) > 2:
assert array_is_monotonic(rbins, strict=True) == 1
except AssertionError:
msg = "Input ``rbins`` must be a monotonically increasing 1D array with at least two entries"
raise ValueError(msg)

# Set the boolean value for the PBCs variable
if period is None:
PBCs = False
x1, y1, z1, x2, y2, z2, period = (
_enclose_in_box(x1, y1, z1, x2, y2, z2,
min_size=[rmax*3.0, rmax*3.0, rmax*3.0]))
else:
PBCs = True
period = np.atleast_1d(period).astype(float)
if len(period) == 1:
period = np.array([period[0]]*3)
try:
assert np.all(period < np.inf)
assert np.all(period > 0)
except AssertionError:
msg = "Input ``period`` must be a bounded positive number in all dimensions"
raise ValueError(msg)

if approx_cell1_size is None:
approx_cell1_size = [rmax, rmax, rmax]
elif custom_len(approx_cell1_size) == 1:
approx_cell1_size = [approx_cell1_size, approx_cell1_size, approx_cell1_size]
if approx_cell2_size is None:
approx_cell2_size = [rmax, rmax, rmax]
elif custom_len(approx_cell2_size) == 1:
approx_cell2_size = [approx_cell2_size, approx_cell2_size, approx_cell2_size]

return (x1, y1, z1, x2, y2, z2,