Reference

A simple two-dimensional cosmological N-body code.

The cosmological box, setting the volume of the box L^2 and the number of particles N^2.

Caustic skeleton

The cosmological background in which the N-body simulation runs with the current Hubble rate H0, the matter density OmegaM, dark energy density OmegaL and the curvature component OmegaK.

The state of the N-body simulation in phase-space.

Constrained Gaussian random field object

Gridcell with attributes

Cloud-in-Cell density estimator.

Compute the caustics

A drift step.

Push the skeleton from Lagrangian to Eulerian space

Push the skeleton from Lagrangian to Eulerian space

Push the skeleton from Lagrangian to Eulerian space

Push the skeleton from Lagrangian to Eulerian space

Push the skeleton from Lagrangian to Eulerian space

Generate an unconstrained Gaussian random field.

Generate an unconstrained Gaussian random field.

Finite diference gradient

Two dimensional interpolation.

A kick step.

Lagrangian grid

The Leap Frog integrator.

The Leap Frog integrator.

Compute the cusp (A3), swallowtail (A4) and butterfly (A5) caustics

Compute the cusp (A3), swallowtail (A4) and butterfly (A5) caustics

Compute the fold (A2) caustics

Compute the fold (A2) caustics

Compute the umbilic (D4) caustics

Compute the umbilic (D4) caustics

Interpolate a vertex along a line

Evaluate the Zel'dovich approximation.

The derivative of the scale factor.

Generate an unconstrained, constrained Gaussian random field pair.

Convolution.

Finite difference order dx^4

Finite difference order dx^6

Finite difference order dx^2

Evaluate the first order directional derivative v₁⋅∇λ₁

Evaluate the second order directional derivative v₁⋅∇(v₁⋅∇λ₁)

Evaluate first eigenvalue and eigenvector field

Evaluate first eigenvalue and eigenvector

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.

Generalzed moments.

Gradient of a scalar field

The growing mode.

The normalization of the growing mode.

Hessian of a scalar field

Cubic interpolation of a regular grid

Laplace operator.

Mean of an Array.

The mean field given the constraints c.

Measure the constraints.

Mesh plot of the N-body simulation

Mesh plot of the N-body simulation

Plot Caustic Skeleton

Plot Caustic Skeleton

Smooth an Array.

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.

The variance field of the constraints.