Reference

The density and velocity fields of an N-body simulation are estimated with the Phase-Space Delaunay Tessellation Field Estimator implemented in Julia. This code accompanies the publication "Phase-Space Delaunay Tesselation Field Estimator", by Job Feldbrugge, 2024. (https://academic.oup.com/mnras/article/536/1/807/7915986).

BVH(data, box, depth, left, right)

A Bounding Volume Hierarchy (BVH) tree structure on a set of geometric objects.

BVH(data, box::Matrix{Float64}, points::Matrix{Float64}, simplices, depth::Int)

Generates a Bounding Volume Hierarchy (BVH) tree structure.

PS_DTFE(positions_initial, positions, velocities, m, depth, box)

Generates an Phase-Space DTFE object given the initial positions, final positions and velocities of an N-body simulation. The Boundary Volume Hirarchy goes depth levels deep. The PS_DTFE-object contains:

rho::Vector{Float64}
Drho::Matrix{Float64}
Dv::Array{Float64}
tree::BVH
simplices::Matrix{Int}
positions::Matrix{Float64}
velocities::Matrix{Float64}
positions_initial::Matrix{Float64}

PS_DTFE_subbox

Phase-Space DTFE subbox object containing

N_sub::Int64
N_target::Int64
m::Float64
depth::Int64
dir::String
L::Float64
Ni::Int64

SimBox(L, Ni)

Holds the size L of the simulation box and the particle number Ni per side length.

Examples

julia> SimBox(100, 64)
SimBox(100.0, 64)

DTFE_periodic(coords_q, coords_x, m, depth, sim_box; pad=0.05)

Constructs the DTFE-object from the final positions coords_x assuming periodic boundary conditions. These are Float64 matrices of size (N,3). m is the particle mass, a single Float64 or a matching matrix (N, 3). pad specifies the framing width in units of L.

DTFE_periodic(coords_q, coords_x, velocities, m, depth, sim_box; pad=0.05)

Constructs the DTFE-object from the final positions coords_x and velocities velocities assuming periodic boundary conditions. These are Float64 matrices of size (N,3). m is the particle mass, a single Float64 or a matching matrix (N, 3). pad specifies the framing width in units of L.

PS_DTFE_periodic(coords_q, coords_x, m, depth, sim_box; pad=0.05)

Constructs the PS-DTFE-object from the initial positions coords_q and final positions coords_x assuming periodic boundary conditions. These are Float64 matrices of size (N,3). m is the particle mass, a single Float64 or a matching matrix (N, 3). pad specifies the framing width in units of L.

PS_DTFE_periodic(coords_q, coords_x, velocities, m, depth, sim_box; pad=0.05)

Constructs the PS-DTFE-object from the initial positions coords_q, final positions coords_x and velocities velocities assuming periodic boundary conditions. These are Float64 matrices of size (N,3). m is the particle mass, a single Float64 or a matching matrix (N, 3). pad specifies the framing width in units of L.

density(p::Vector{Float64}, estimator::PS_DTFE)

Evaluate the Phase-Space DTFE density estimate in the point p.

density_subbox(coords_arr, ps_dtfe_sb)

Evaluate the Phase-Space DTFE density estimates in given coordinates coords_arr from the PS_DTFE_subbox object ps_dtfe_sb. coords_arr can be of any shape (..., 3).

findBox(p::Vector{Float64}, BVH_tree::BVH)

Find the box in the Bounding Volume Hierarchy containing the point p.

findCandidateSimplices(p::Vector{Float64}, BVH_tree::BVH)

Given a Bounding Volume Hierarchy, find a set candidate simplices that may contain the point p. The function outputs the indices of the candidate simplices.

findIntersections(p::Vector{Float64}, BVH_tree::BVH, points, simplices)

Find the indices of the simplices that intersect the point p.

frame(coords_q, coords_x, L, pad=0.05)

Cosmological N-body simulations normally work with periodic boundary conditions. This function adds a frame of periodic particle positions around the simulation box to implement periodicity in the Delaunay tesselation. pad specifies the width of the frame in units of the simulation box size L.

frame_velocities(coords_x, velocities, L, pad=0.05)

Cosmological N-body simulations normally work with periodic boundary conditions. This function adds a frame of velocities (corresponding to the periodic particle positions) around the simulation box to implement periodicity in the Delaunay tesselation. pad specifies the width of the frame in units of the simulation box size L.

get_coords_in_subbox(coords, idx, N_sub, L)

From a given coordinates array coords, get those coordinates contained in subbox number idx.

get_subbox_estimator(coords_q, coords_x, velocities, idx, N_sub, m, depth, sim_box::SimBox; pad=0.05, dir="./ps_dtfe")

Construct the Phase-Space DTFE object for given coordinates and velocities. Called for each subbox estimator construction.

get_subbox_estimator(coords_q, coords_x, idx, N_sub, m, depth, sim_box::SimBox; pad=0.05, dir="./ps_dtfe")

Obtain the subbox estimator associated to a given position.

get_subboxes(ps_dtfe_sub::PS_DTFE_subbox)

Get all subbox indices.

inSimplices(p::Vector{Float64}, estimator::PS_DTFE)

Find the simplices in the Eulerian-evolved tesselation that contain the point p.

intersection(p::Vector{Float64}, simplex)

Check whether the point p is contained in the simplex.

numberOfStreams(p::Vector{Float64}, estimator::PS_DTFE)

Evaluates the number of incoming streams in point in the point p.

numberOfStreams_subbox(coords_arr, ps_dtfe_sb)

Evaluate the number of streams field in given coordinates coords_arr from the PS_DTFE_subbox object ps_dtfe_sb. coords_arr can be of any shape (..., 3).

ps_dtfe_subbox(coords_q, coords_x, velocities, m, depth, sim_box::SimBox; N_target=128, pad=0.05, dir="./ps_dtfe")

Construct the Phase-Space DTFE subbox estimator given the initial positions coords_q, final positions coords_x and velocities velocities of an N-body simulation, assuming periodic boundary positions. The Boundary Volume Hirarchy goes depth levels deep. For data types, see documentation of PS_DTFE_periodic(). The keyword argument N_target=128 specifies the number of particles (N_target^3) per subbox. pad is the framing width in units of L. dir is the data storage directory.

ps_dtfe_subbox(coords_q, coords_x, m, depth, sim_box::SimBox; N_target=128, pad=0.05, dir="./ps_dtfe")

Construct the Phase-Space DTFE subbox estimator given the initial positions coords_q and final positions coords_x of an N-body simulation, assuming periodic boundary positions. The Boundary Volume Hirarchy goes depth levels deep. For data types, see documentation of PS_DTFE_periodic(). The keyword argument N_target=128 specifies the number of particles (N_target^3) per subbox. pad is the framing width in units of L. dir is the data storage directory.

translate(coords_q, coords_x, L)

Cosmological N-body simulations normally work with periodic boundary conditions. This function shifts both the initial and final positions of the particles such that they are located in the simulation box in Eulerian space.

unwrap_s(s, L)

Cosmological N-body simulations normally work with periodic boundary conditions. This function undoes the wrapping of particles around the box in the displacement field, assuming the particles did not travel more than half the size of the box.

unwrap_x_(q, x, L)

Cosmological N-body simulations normally work with periodic boundary conditions. This function undoes the wrapping of particles around the box, assuming the particles did not travel more than half the size of the box.

velocity(p::Vector{Float64}, estimator::PS_DTFE, single_stream=false)

Evaluate the Phase-Space DTFE velocity estimate in the point p. Returns a matrix of size (n, 3) for n stream velocities ((1,3) in single-stream regions, (n, 3) otherwise). If single_stream=true, returns [NaN NaN NaN] in multistream regions.

velocitySum(p::Vector{Float64}, estimator::PS_DTFE)

Evaluate the stream-mass weighted sum of the Phase-Space DTFE velocities estimates for the individual streams in the point p.

velocitySum_subbox(coords_arr, ps_dtfe_sb)

Evaluate the stream-mass weighted sum of the Phase-Space DTFE stream velocity estimates in given coordinates coords_arr from the PS_DTFE_subbox object ps_dtfe_sb. coords_arr can be of any shape (..., 3).

velocity_subbox(coords_arr, ps_dtfe_sb)

Evaluate the Phase-Space DTFE velocity estimates in given coordinates coords_arr from the PS_DTFE_subbox object ps_dtfe_sb. coords_arr can be of any shape (..., 3). In the current code release, [NaN NaN NaN] is returned in multistream regions, i.e. individual stream velocities are not supported.

volume(sim, points)

Evaluate the volume of the simplex sim.