# Source code for halotools.mock_observables.large_scale_density.large_scale_density_spherical_annulus

```
"""
Module containing functions used to determine various ways of quantifying
the large-scale density of a set of points.
"""
import numpy as np
from ..pair_counters import npairs_per_object_3d
from ...custom_exceptions import HalotoolsError
__all__ = ('large_scale_density_spherical_annulus', )
__author__ = ('Andrew Hearin', )
np.seterr(divide='ignore', invalid='ignore') # ignore divide by zero in e.g. DD/RR
[docs]def large_scale_density_spherical_annulus(sample, tracers, inner_radius, outer_radius,
period=None, sample_volume=None, num_threads=1, approx_cell1_size=None,
norm_by_mean_density=False):
"""
Calculate the mean density of the input ``sample``
from an input set of tracer particles using a spherical annulus
centered on each point in the input ``sample`` as the tracer volume.
Around each point in the input ``sample``, an annulus with input
``inner_radius`` and ``outer_radius``
is placed and the number of points in the input ``tracers`` is counted,
optionally accounting for box periodicity.
The `large_scale_density_spherical_annulus` function returns the mean number density
of tracer particles in each such sphere, optionally normalizing this result
by the global mean number density of tracer particles in the entire sample volume.
Parameters
------------
sample : array_like
Npts1 x 3 numpy array 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 ``sample`` and ``tracers`` arguments.
tracers : array_like
Npts2 x 3 numpy array containing 3-D positions of tracers.
inner_radius, outer_radius : float, float
Radii of the annulus used to define the volume inside which the
number density of tracers is calculated.
Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.
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,
and an input ``sample_volume`` must be provided.
Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.
sample_volume : float, optional
If period is set to None, you must specify the effective volume of the sample.
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.
norm_by_mean_density : bool, optional
If set to True, the returned number density will be normalized by
the global number density of tracer particles averaged across the
entire ``sample_volume``. Default is False.
Returns
--------
number_density : array_like
Length-Npts1 array of number densities
Examples
---------
>>> npts1, npts2 = 100, 200
>>> sample = np.random.random((npts1, 3))
>>> tracers = np.random.random((npts2, 3))
>>> inner_radius, outer_radius = 0.1, 0.2
>>> result = large_scale_density_spherical_annulus(sample, tracers, inner_radius, outer_radius, period=1)
"""
sample, tracers, rbins, period, sample_volume, num_threads, approx_cell1_size = (
_large_scale_density_spherical_annulus_process_args(
sample, tracers, inner_radius, outer_radius,
period, sample_volume, num_threads, approx_cell1_size)
)
result = npairs_per_object_3d(sample, tracers, rbins, period=period,
num_threads=num_threads, approx_cell1_size=approx_cell1_size)
result = np.diff(result, axis=1)
environment_volume = (4/3.)*np.pi*(outer_radius**3 - inner_radius**3)
number_density = result/environment_volume
if norm_by_mean_density is True:
mean_rho = tracers.shape[0]/sample_volume
return number_density/mean_rho
else:
return number_density
def _large_scale_density_spherical_annulus_process_args(
sample, tracers, inner_radius, outer_radius,
period, sample_volume, num_threads, approx_cell1_size):
"""
"""
sample = np.atleast_1d(sample)
tracers = np.atleast_1d(tracers)
try:
assert outer_radius > inner_radius
except AssertionError:
msg = ("Input ``outer_radius`` must be larger than input ``inner_radius``")
raise HalotoolsError(msg)
rbins = np.array([inner_radius, outer_radius])
if period is None:
if sample_volume is None:
msg = ("If period is None, you must pass in ``sample_volume``.")
raise HalotoolsError(msg)
else:
sample_volume = float(sample_volume)
else:
period = np.atleast_1d(period)
if len(period) == 1:
period = np.array([period, period, period])
elif len(period) == 3:
pass
else:
msg = ("\nInput ``period`` must either be a float or length-3 sequence")
raise HalotoolsError(msg)
if sample_volume is None:
sample_volume = period.prod()
else:
msg = ("If period is not None, do not pass in sample_volume")
raise HalotoolsError(msg)
return sample, tracers, rbins, period, sample_volume, num_threads, approx_cell1_size
```