npairs_jackknife_3d

halotools.mock_observables.pair_counters.npairs_jackknife_3d(sample1, sample2, rbins, jtags1, jtags2, N_samples, period=None, weights1=None, weights2=None, num_threads=1, approx_cell1_size=None, approx_cell2_size=None)

Pair counter used to make jackknife error estimates of real-space pair counter npairs.

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. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

rbinsarray_like

Boundaries defining the bins in which pairs are counted. Length units are comoving and assumed to be in Mpc/h, here and throughout Halotools.

jtags1array_like

Numpy array of shape (Npts1, ) containing integer tags used to define jackknife sample membership. Tags are in the range [1, N_samples]. The tag ‘0’ is a reserved tag and should not be used.

jtags2array_like

Numpy array of shape (Npts2, ) containing integer tags used to define jackknife sample membership. Tags are in the range [1, N_samples]. The tag ‘0’ is a reserved tag and should not be used.

N_samplesint

Total number of jackknife samples. All values of jtags1 and jtags2 should be in the range [1, N_samples].

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

Numpy array of shape (Npts1, ) containing weights used for weighted pair counts.

weights2array_like, optional

Numpy array of shape (Npts2, ) containing weights used for weighted pair counts.

num_threadsint, 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_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:

N_pairsarray_like

Numpy array of shape (N_samples+1,len(rbins)). The sub-array N_pairs[0, :] stores numbers of pairs in the input bins for the entire sample. The sub-array N_pairs[i, :] stores numbers of pairs in the input bins for the \(i^{\rm th}\) jackknife sub-sample.

Notes

Jackknife weights are calculated using a weighting function.

If both points are outside the sample, the weighting function returns 0. If both points are inside the sample, the weighting function returns (w1 * w2) If one point is inside, and the other is outside, the weighting function returns (w1 * w2)/2

Examples

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

>>> from halotools.mock_observables.pair_counters import npairs_jackknife_3d
>>> 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 mock_observables sub-package:

>>> sample1 = np.vstack([x1, y1, z1]).T
>>> sample2 = np.vstack([x2, y2, z2]).T

Ordinarily, you would create jtags for the points by properly subdivide the points into spatial sub-volumes. For illustration purposes, we’ll simply use randomly assigned sub-volumes as this has no impact on the calling signature:

>>> N_samples = 10
>>> jtags1 = np.random.randint(1, N_samples+1, Npts1)
>>> jtags2 = np.random.randint(1, N_samples+1, Npts2)

>>> result = npairs_jackknife_3d(sample1, sample2, rbins, period = period, jtags1=jtags1, jtags2=jtags2, N_samples = N_samples)