# marked_npairs_xy_z¶

halotools.mock_observables.pair_counters.marked_npairs_xy_z(sample1, sample2, rp_bins, pi_bins, period=None, weights1=None, weights2=None, weight_func_id=0, num_threads=1, approx_cell1_size=None, approx_cell2_size=None)[source]

Calculate the number of weighted pairs with separations greater than or equal to $$r_{\perp}$$ and $$r_{\parallel}$$, $$W(>r_{\perp},>r_{\parallel})$$.

$$r_{\perp}$$ and $$r_{\parallel}$$ are defined wrt the z-direction.

The weight given to each pair is determined by the weights for a pair, $$w_1$$, $$w_2$$, and a user-specified “weighting function”, indicated by the wfunc parameter, $$f(w_1,w_2)$$.

Parameters:
sample1array_like

Numpy array of shape (Npts1, 3) containing 3-D positions of points. See the Formatting your xyz coordinates for Mock Observables calculations 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.

sample2array_like, optional

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

rp_binsarray_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_binsarray_like

array of boundaries defining the p radial bins parallel to the LOS in which pairs are counted. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

periodarray_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.

weights1array_like, optional

Either a 1-D array of length N1, or a 2-D array of length N1 x N_weights, containing the weights used for the weighted pair counts. If this parameter is None, the weights are set to np.ones((N1,N_weights)).

weights2array_like, optional

Either a 1-D array of length N1, or a 2-D array of length N1 x N_weights, containing the weights used for the weighted pair counts. If this parameter is None, the weights are set to np.ones((N1,N_weights)).

wfuncint, optional

weighting function integer ID. Each weighting function requires a specific number of weights per point, N_weights. See the Notes for a description of available weighting functions.

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_sizearray_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_sizearray_like, optional

Analogous to approx_cell1_size, but for sample2. See comments for approx_cell1_size for details.

Returns:
wN_pairsnumpy.ndarray

2-D array of shape (Nrp_bins,Npi_bins) containing the weighted number counts of pairs

Notes

See the docstring of the marked_tpcf function for a description of the available marking functions that can be passed in via the wfunc optional argument.

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]
>>> rp_bins = np.logspace(-1, 1.5, 15)
>>> pi_bins = [20, 40, 60]

>>> 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 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, 1))
>>> weights2 = np.random.random((Npts2, 1))


The weighted counts are calculated by:

>>> weighted_counts = marked_npairs_xy_z(sample1, sample2, rp_bins, pi_bins, period=period, weights1=weights1, weights2=weights2, weight_func_id=1)