# Source code for halotools.mock_observables.pair_counters.positional_marked_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 .npairs_3d import _npairs_3d_process_args
from .mesh_helpers import _set_approximate_cell_sizes, _cell1_parallelization_indices
from .rectangular_mesh import RectangularDoubleMesh
from .marked_cpairs import positional_marked_npairs_3d_engine
from ...custom_exceptions import HalotoolsError
__author__ = ('Duncan Campbell', 'Andrew Hearin')
__all__ = ('positional_marked_npairs_3d', )
[docs]
def positional_marked_npairs_3d(sample1, sample2, rbins,
period=None, weights1=None, weights2=None,
weight_func_id=0, verbose=False, num_threads=1,
approx_cell1_size=None, approx_cell2_size=None):
r"""
Calculate the number of weighted pairs with separations greater than or equal to r, :math:`W(>r)`,
where the weight of each pair is given by soe function of a
N-d array stored in each input weight and the separation vector of the pair.
Note that if sample1 == sample2 that the `positional_marked_npairs` function double-counts pairs.
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
numpy array of length *Nrbins+1* defining the boundaries of 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.
weights1 : array_like, optional
Either a 1-D array of length *N1*, or a 2-D array of length *N1* x *N_weights1*,
containing the weights used for the weighted pair counts. If this parameter is
None, the weights are set to np.ones(*(N1, N_weights1)*).
weights2 : array_like, optional
Either a 1-D array of length *N2*, or a 2-D array of length *N2* x *N_weights2*,
containing the weights used for the weighted pair counts. If this parameter is
None, the weights are set to np.ones(*(N2, N_weights2)*).
weight_func_id : int, optional
weighting function integer ID. Each weighting function requires a specific
number of weights per point, *N_weights1*, *N_weights2*. See the Notes for a description of
available weighting functions.
verbose : Boolean, optional
If True, print out information and progress.
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
-------
wN_pairs : numpy.array
Numpy array of shape (Nrbins, ) containing the weighted number counts of pairs
N_pairs : numpy.array
Numpy array of shape (Nrbins, ) containing the number counts of pairs
Notes
-----
There are multiple marking functions available. In general, each requires a different
number of marks per point, N_marks. The marking function gets passed three vectors
per pair: :math:`w_1` and :math:`w_2` of length N_marks, and :math:`s_{12}`,
the length 3 vector between points 1 and 2. Each function returns a float.
The available marking functions, ``weight_func_id`` and the associated integer ID numbers are:
#. position-shape dot product (N_marks = 4,1)
.. math::
\begin{array}{ll}
\cos\theta = (w_1[1]\times s_{12}[0] + w_1[2]\times s_{12}[1] + w_1[3]\times s_{12}[2])/\sqrt{|s_{12}|} \\
f(w_1,w_2) = w_1[0]\times w_2[0]\times \cos\theta
\end{array}
#. gamma plus (N_marks = 4,1)
.. math::
\begin{array}{ll}
\cos\theta = (w_1[1]\times s_{12}[0] + w_1[2]\times s_{12}[1] + w_1[3]\times s_{12}[2])/\sqrt{|s_{12}|} \\
\theta = \cos^{-1}(\cos\theta) \\
f(w_1,w_2) = w_1[0]\times w_2[0]\times \cos(2\theta)
\end{array}
#. gamma minus (N_marks = 4,1)
.. math::
\begin{array}{ll}
\cos\theta = (w_1[1]\times s_{12}[0] + w_1[2]\times s_{12}[1] + w_1[3]\times s_{12}[2])/\sqrt{|s_{12}|} \\
\theta = \cos^{-1}(\cos\theta) \\
f(w_1,w_2) = w_1[0]\times w_2[0]\times \sin(2\theta)
\end{array}
#. position-shape dot product squared (N_marks = 4,1)
.. math::
\begin{array}{ll}
\cos\theta = (w_1[1]\times s_{12}[0] + w_1[2]\times s_{12}[1] + w_1[3]\times s_{12}[2])/\sqrt{|s_{12}|} \\
f(w_1,w_2) = w_1[0]\times w_2[0]\times \cos\theta\cos\theta
\end{array}
Examples
--------
For demonstration purposes we create randomly distributed sets of points within a
periodic unit cube, using random weights.
>>> 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
We create a set of random weights:
>>> weights1 = np.random.random((Npts1, 4))
>>> weights2 = np.random.random((Npts2, 1))
The weighted counts are calculated by:
>>> weighted_counts, counts = positional_marked_npairs_3d(sample1, sample2, rbins, period=period, weights1=weights1, weights2=weights2, weight_func_id=1)
"""
result = _npairs_3d_process_args(sample1, sample2, rbins, period,
num_threads, approx_cell1_size, approx_cell2_size)
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
# Process the input weights and with the helper function
weights1, weights2 = _marked_npairs_process_weights(sample1, sample2,
weights1, weights2, weight_func_id)
# 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(positional_marked_npairs_3d_engine, double_mesh,
x1in, y1in, z1in, x2in, y2in, z2in,
weights1, weights2, weight_func_id, rbins)
# Calculate the cell1 indices that will be looped over by the engine
num_threads, cell1_tuples = _cell1_parallelization_indices(
double_mesh.mesh1.ncells, num_threads)
if num_threads > 1:
pool = multiprocessing.Pool(num_threads)
result = np.array(pool.map(engine, cell1_tuples))
counts, marked_counts = result[:, 0, :], result[:, 1, :]
marked_counts = np.sum(np.array(marked_counts), axis=0)
counts = np.sum(np.array(counts), axis=0)
pool.close()
else:
counts, marked_counts = engine(cell1_tuples[0])
return np.array(marked_counts), np.array(counts)
def _marked_npairs_process_weights(sample1, sample2, weights1, weights2, weight_func_id):
"""
check weights arguments for consistency
"""
correct_num_weights1, correct_num_weights2 = _func_signature_int_from_wfunc(weight_func_id)
npts_sample1 = np.shape(sample1)[0]
npts_sample2 = np.shape(sample2)[0]
correct_shape1 = (npts_sample1, correct_num_weights1)
correct_shape2 = (npts_sample2, correct_num_weights2)
# Process the input weights1
_converted_to_2d_from_1d = False
# First convert weights1 into a 2-d ndarray
if weights1 is None:
weights1 = np.ones(correct_shape1, dtype=np.float64)
else:
weights1 = np.atleast_1d(weights1)
weights1 = weights1.astype("float64")
if weights1.ndim == 1:
_converted_to_2d_from_1d = True
npts1 = len(weights1)
weights1 = weights1.reshape((npts1, 1))
elif weights1.ndim == 2:
pass
else:
ndim1 = weights1.ndim
msg = ("\n You must either pass in a 1-D or 2-D array \n"
"for the input `weights1`. Instead, an array of \n"
"dimension %i was received.")
raise HalotoolsError(msg % ndim1)
npts_weights1 = np.shape(weights1)[0]
num_weights1 = np.shape(weights1)[1]
# At this point, weights1 is guaranteed to be a 2-d ndarray
# now we check its shape
if np.shape(weights1) != correct_shape1:
if _converted_to_2d_from_1d is True:
msg = ("\n You passed in a 1-D array for `weights1` that \n"
"does not have the correct length. The number of \n"
"points in `sample1` = %i, while the number of points \n"
"in your input 1-D `weights1` array = %i")
raise HalotoolsError(msg % (npts_sample1, npts_weights1))
else:
msg = ("\n You passed in a 2-D array for `weights1` that \n"
"does not have a consistent shape with `sample1`. \n"
"`sample1` has length %i. The input value of `weight_func_id` = %i \n"
"For this value of `weight_func_id`, there should be %i weights \n"
"per point. The shape of your input `weights1` is (%i, %i)\n")
raise HalotoolsError(msg %
(npts_sample1, weight_func_id, correct_num_weights1, npts_weights1, num_weights1))
# Process the input weights2
_converted_to_2d_from_1d = False
# Now convert weights2 into a 2-d ndarray
if weights2 is None:
weights2 = np.ones(correct_shape2, dtype=np.float64)
else:
weights2 = np.atleast_1d(weights2)
weights2 = weights2.astype("float64")
if weights2.ndim == 1:
_converted_to_2d_from_1d = True
npts2 = len(weights2)
weights2 = weights2.reshape((npts2, 1))
elif weights2.ndim == 2:
pass
else:
ndim2 = weights2.ndim
msg = ("\n You must either pass in a 1-D or 2-D array \n"
"for the input `weights2`. Instead, an array of \n"
"dimension %i was received.")
raise HalotoolsError(msg % ndim2)
npts_weights2 = np.shape(weights2)[0]
num_weights2 = np.shape(weights2)[1]
# At this point, weights2 is guaranteed to be a 2-d ndarray
# now we check its shape
if np.shape(weights2) != correct_shape2:
if _converted_to_2d_from_1d is True:
msg = ("\n You passed in a 1-D array for `weights2` that \n"
"does not have the correct length. The number of \n"
"points in `sample2` = %i, while the number of points \n"
"in your input 1-D `weights2` array = %i")
raise HalotoolsError(msg % (npts_sample2, npts_weights2))
else:
msg = ("\n You passed in a 2-D array for `weights2` that \n"
"does not have a consistent shape with `sample2`. \n"
"`sample2` has length %i. The input value of `weight_func_id` = %i \n"
"For this value of `weight_func_id`, there should be %i weights \n"
"per point. The shape of your input `weights2` is (%i, %i)\n")
raise HalotoolsError(msg %
(npts_sample2, weight_func_id, correct_num_weights2, npts_weights2, num_weights2))
return weights1, weights2
def _func_signature_int_from_wfunc(weight_func_id):
"""
Return the function signature for available weighting functions.
"""
if type(weight_func_id) != int:
msg = "\n weight_func_id parameter must be an integer ID of a weighting function."
raise ValueError(msg)
if weight_func_id == 1:
return (4, 1)
elif weight_func_id == 2:
return (4, 1)
elif weight_func_id == 3:
return (4, 1)
elif weight_func_id == 4:
return (4, 1)
elif weight_func_id == 5:
return (4, 4)
elif weight_func_id == 6:
return (4, 4)
elif weight_func_id == 7:
return (5, 2)
elif weight_func_id == 8:
return (5, 2)
else:
msg = ("The value ``weight_func_id`` = %i is not recognized")
raise HalotoolsError(msg % weight_func_id)
```