# Two-Point Correlation Functions¶

All of these can be imported from halotools.mock_observables.

 tpcf(sample1, rbins[, sample2, randoms, ...]) Calculate the real space two-point correlation function, $$\xi(r)$$. wp(sample1, rp_bins, pi_max[, sample2, ...]) Calculate the projected two point correlation function, $$w_{p}(r_p)$$, where $$r_p$$ is the separation perpendicular to the line-of-sight (LOS). rp_pi_tpcf(sample1, rp_bins, pi_bins[, ...]) Calculate the redshift space correlation function, $$\xi(r_{p}, \pi)$$ tpcf_multipole(s_mu_tcpf_result, mu_bins[, ...]) Calculate the multipoles of the two point correlation function after first computing s_mu_tpcf. s_mu_tpcf(sample1, s_bins, mu_bins[, ...]) Calculate the redshift space correlation function, $$\xi(s, \mu)$$ tpcf_jackknife(sample1, randoms, rbins[, ...]) Calculate the two-point correlation function, $$\xi(r)$$ and the covariance matrix, $${C}_{ij}$$, between ith and jth radial bin. tpcf_one_two_halo_decomp(sample1, ...[, ...]) Calculate the real space one-halo and two-halo decomposed two-point correlation functions, $$\xi^{1h}(r)$$ and $$\xi^{2h}(r)$$. mean_delta_sigma(galaxies, particles, ...[, ...]) Calculate $$\Delta\Sigma(r_p)$$, the galaxy-galaxy lensing signal as a function of projected distance. marked_tpcf(sample1, rbins[, sample2, ...]) Calculate the real space marked two-point correlation function, $$\mathcal{M}(r)$$.

# Calculating the HOD¶

 hod_from_mock(haloprop_galaxies, haloprop_halos) Calculate the HOD of a mock galaxy sample.

# Galaxy Group Statistics¶

 FoFGroups(positions, b_perp, b_para[, ...]) Friends-of-friends (FoF) groups class.

# Isolation Criteria¶

 spherical_isolation(sample1, sample2, r_max) Determine whether a set of points, sample1, is isolated, i.e. does not have a neighbor in sample2 within an user specified spherical volume centered at each point in sample1. cylindrical_isolation(sample1, sample2, ...) Determine whether a set of points, sample1, is isolated, i.e. does not have a neighbor in sample2 within an user specified cylindrical volume centered at each point in sample1. conditional_spherical_isolation(sample1, ...) Determine whether a set of points, sample1, is isolated, i.e. does not have a neighbor in sample2 within an user specified spherical volume centered at each point in sample1, where various additional conditions may be applied to judge whether a matching point is considered to be a neighbor. conditional_cylindrical_isolation(sample1, ...) Determine whether a set of points, sample1, is isolated, i.e. does not have a neighbor in sample2 within an user specified cylindrical volume centered at each point in sample1, where various additional conditions may be applied to judge whether a matching point is considered to be a neighbor.

# Pairwise Velocities¶

 mean_radial_velocity_vs_r(sample1, velocities1) Calculate the mean pairwise velocity, $$\bar{v}_{12}(r)$$. mean_los_velocity_vs_rp(sample1, ...[, ...]) Calculate the mean pairwise line-of-sight (LOS) velocity as a function of projected separation, $$\bar{v}_{z,12}(r_p)$$. radial_pvd_vs_r(sample1, velocities1[, ...]) Calculate the pairwise radial velocity dispersion as a function of absolute distance, or as a function of $$s = r / R_{\rm vir}$$. los_pvd_vs_rp(sample1, velocities1, rp_bins, ...) Calculate the pairwise line-of-sight (LOS) velocity dispersion (PVD), as a function of radial distance from sample1 $$\sigma_{z12}(r_p)$$.

 radial_profile_3d(sample1, sample2, ...[, ...]) Function used to calculate the mean value of some quantity in sample2 as a function of 3d distance from the points in sample1.

# Void Statistics¶

 void_prob_func(sample1, rbins[, n_ran, ...]) Calculate the void probability function (VPF), $$P_0(r)$$, defined as the probability that a random sphere of radius r contains zero points in the input sample. underdensity_prob_func(sample1, rbins[, ...]) Calculate the underdensity probability function (UPF), $$P_U(r)$$.

# Large Scale Density¶

 large_scale_density_spherical_volume(sample, ...) Calculate the mean density of the input sample from an input set of tracer particles using a sphere centered on each point in the input sample as the tracer volume. large_scale_density_spherical_annulus(...[, ...]) 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.

# Tensor Calculations¶

 inertia_tensor_per_object(sample1, sample2, ...) For each point in sample1, identify all sample2 points within the input smoothing_scale; using those points together with the input weights2, the inertia_tensor_per_object function calculates the inertia tensor of the mass distribution surrounding each point in sample1. Calculate the principal eigenvector of each of the input inertia tensors.