Source code for halotools.mock_observables.pairwise_velocities.mean_los_velocity_vs_rp

Module containing the `~halotools.mock_observables.mean_los_velocity_vs_rp` function
used to calculate the pairwise mean line-of-sight velocity
as a function of projected distance between the pairs.
from __future__ import absolute_import, division, print_function, unicode_literals

import numpy as np

from .pairwise_velocities_helpers import (_pairwise_velocity_stats_process_args,

from .velocity_marked_npairs_xy_z import velocity_marked_npairs_xy_z

__all__ = ('mean_los_velocity_vs_rp', )
__author__ = ['Duncan Campbell']

np.seterr(divide='ignore', invalid='ignore')  # ignore divide by zero

[docs] def mean_los_velocity_vs_rp(sample1, velocities1, rp_bins, pi_max, sample2=None, velocities2=None, period=None, do_auto=True, do_cross=True, num_threads=1, approx_cell1_size=None, approx_cell2_size=None, seed=None): r""" Calculate the mean pairwise line-of-sight (LOS) velocity as a function of projected separation, :math:`\bar{v}_{z,12}(r_p)`. Example calls to this function appear in the documentation below. Parameters ---------- sample1 : array_like Npts x 3 numpy array containing 3-D positions of points. velocities1 : array_like N1pts x 3 array containing the 3-D components of the velocities. rp_bins : array_like array of boundaries defining the radial bins perpendicular to the LOS in which pairs are counted. pi_max : float maximum LOS separation sample2 : array_like, optional Npts x 3 array containing 3-D positions of points. velocities2 : array_like, optional N2pts x 3 array containing the 3-D components of the velocities. period : array_like, optional Length-3 array defining periodic boundary conditions. If only one number, Lbox, is specified, period is assumed to be [Lbox, Lbox, Lbox]. do_auto : boolean, optional caclulate the auto-pairwise velocities? do_cross : boolean, optional caclulate the cross-pairwise velocities? num_threads : int, optional number of threads to use in calculation. Default is 1. 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 *max(rbins)* 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. seed : int, optional Random number seed used to randomly downsample data, if applicable. Default is None, in which case downsampling will be stochastic. Returns ------- vz_12 : numpy.array *len(rbins)-1* length array containing the mean pairwise LOS velocity, :math:`\bar{v}_{z12}(r)`, computed in each of the bins defined by ``rp_bins``. Notes ----- The pairwise LOS velocity, :math:`v_{z12}(r)`, is defined as: .. math:: v_{z12} = |\vec{v}_{\rm 1, pec} \cdot \hat{z}-\vec{v}_{\rm 2, pec}\cdot\hat{z}| where :math:`\vec{v}_{\rm 1, pec}` is the peculiar velocity of object 1, and :math:`\hat{z}` is the unit-z vector. :math:`\bar{v}_{z12}(r_p)` is the mean of this quantity in projected radial bins. Pairs and radial velocities are calculated using `~halotools.mock_observables.pair_counters.velocity_marked_npairs_xy_z`. Examples -------- For demonstration purposes we will work with halos in the `~halotools.sim_manager.FakeSim`. >>> from halotools.sim_manager import FakeSim >>> halocat = FakeSim() >>> x = halocat.halo_table['halo_x'] >>> y = halocat.halo_table['halo_y'] >>> z = halocat.halo_table['halo_z'] 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((x,y,z)).T We will do the same to get a random set of velocities. >>> vx = halocat.halo_table['halo_vx'] >>> vy = halocat.halo_table['halo_vy'] >>> vz = halocat.halo_table['halo_vz'] >>> velocities = np.vstack((vx,vy,vz)).T >>> rp_bins = np.logspace(-2,-1,10) >>> pi_max = 0.3 >>> vz_12 = mean_los_velocity_vs_rp(sample1, velocities, rp_bins, pi_max, period=halocat.Lbox) """ function_args = (sample1, velocities1, sample2, velocities2, period, do_auto, do_cross, num_threads, approx_cell1_size, approx_cell2_size, seed) sample1, velocities1, sample2, velocities2, period, do_auto, do_cross,\ num_threads, _sample1_is_sample2, PBCs = _pairwise_velocity_stats_process_args(*function_args) rp_bins, pi_max = _process_rp_bins(rp_bins, pi_max, period, PBCs) pi_bins = np.array([0.0, pi_max]) # create marks for the marked pair counter. marks1 = np.vstack((sample1.T, velocities1.T)).T marks2 = np.vstack((sample2.T, velocities2.T)).T def marked_pair_counts(sample1, sample2, rp_bins, pi_bins, period, num_threads, do_auto, do_cross, marks1, marks2, weight_func_id, _sample1_is_sample2, approx_cell1_size, approx_cell2_size): """ Count velocity weighted data pairs. """ if do_auto is True: D1D1, dummy, N1N1 = velocity_marked_npairs_xy_z( sample1, sample1, rp_bins, pi_bins, weights1=marks1, weights2=marks1, weight_func_id=weight_func_id, period=period, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell1_size) D1D1 = np.diff(D1D1, axis=1)[:, 0] D1D1 = np.diff(D1D1) N1N1 = np.diff(N1N1, axis=1)[:, 0] N1N1 = np.diff(N1N1) else: D1D1 = None D2D2 = None N1N1 = None N2N2 = None if _sample1_is_sample2: D1D2 = D1D1 D2D2 = D1D1 N1N2 = N1N1 N2N2 = N1N1 else: if do_cross is True: D1D2, dummy, N1N2 = velocity_marked_npairs_xy_z( sample1, sample2, rp_bins, pi_bins, weights1=marks1, weights2=marks2, weight_func_id=weight_func_id, period=period, num_threads=num_threads, approx_cell1_size=approx_cell1_size, approx_cell2_size=approx_cell2_size) D1D2 = np.diff(D1D2, axis=1)[:, 0] D1D2 = np.diff(D1D2) N1N2 = np.diff(N1N2, axis=1)[:, 0] N1N2 = np.diff(N1N2) else: D1D2 = None N1N2 = None if do_auto is True: D2D2, dummy, N2N2 = velocity_marked_npairs_xy_z( sample2, sample2, rp_bins, pi_bins, weights1=marks2, weights2=marks2, weight_func_id=weight_func_id, period=period, num_threads=num_threads, approx_cell1_size=approx_cell2_size, approx_cell2_size=approx_cell2_size) D2D2 = np.diff(D2D2, axis=1)[:, 0] D2D2 = np.diff(D2D2) N2N2 = np.diff(N2N2, axis=1)[:, 0] N2N2 = np.diff(N2N2) else: D2D2 = None N2N2 = None return D1D1, D1D2, D2D2, N1N1, N1N2, N2N2 # count the sum of radial velocities and number of pairs weight_func_id = 3 V1V1, V1V2, V2V2, N1N1, N1N2, N2N2 =\ marked_pair_counts(sample1, sample2, rp_bins, pi_bins, period, num_threads, do_auto, do_cross, marks1, marks2, weight_func_id, _sample1_is_sample2, approx_cell1_size, approx_cell2_size) # return results: the sum of radial velocities divided by the number of pairs if _sample1_is_sample2: M_11 = V1V1/N1N1 return np.where(np.isfinite(M_11), M_11, 0.) else: if (do_auto is True) & (do_cross is True): M_11 = V1V1/N1N1 M_12 = V1V2/N1N2 M_22 = V2V2/N2N2 return (np.where(np.isfinite(M_11), M_11, 0.), np.where(np.isfinite(M_12), M_12, 0.), np.where(np.isfinite(M_22), M_22, 0.)) elif (do_cross is True): M_12 = V1V2/N1N2 return np.where(np.isfinite(M_12), M_12, 0.) elif (do_auto is True): M_11 = V1V1/N1N1 M_22 = V2V2/N2N2 return np.where(np.isfinite(M_11), M_11, 0.), np.where(np.isfinite(M_22), M_22, 0.)