χ = Lgp!(dϕ,ϕ,sim,t)

In-place evaluation of Gross-Pitaevskii equation defined by nlin! and parameters in sim. Allows imaginary time γ, and evolves in rotating frame defined by chemical potential μ.

χ = Lgp(ϕ,sim,t)

Evaluate Gross-Pitaevskii equation defined by nlin and parameters in sim. Allows imaginary time γ, and evolves in rotating frame defined by chemical potential μ.

V(x,t) = ...

Define the system potential, with default zero. Should be defined as a scalar function (without .), suitable for broadcasting on spatial arrays via V.(...).

A = crandn_array(M)

Make placeholder 2x2x... complex randn() array of M dimensions.

A = crandnpartition(D,M)

Make placeholder ArrayPartition vector of length M, containing 2x2x... rank D complex matrices.

definetransforms(funcs,args,meas,kwargs)

Build all transforms for simulation.

Dx,Dk = dfft(x,k)

Measures that make fft, ifft 2-norm preserving. Correct measures for mapping between x- and k-space.

DX,DK = dfftall(X,K)

Evalutes tuple of measures that make fft, ifft 2-norm preserving for each x or k dimension.

initsim!(sim;flags=FFTW.MEASURE)

Initialize all arrays, measures and transform libraries for a particular simulation.

k² = k2(K)

Create the kinetic energy array k² on the k-grid defined by the tuple K.

kspace!(ψ,sim)

Mutating transform from x- to k-space using transforms packed into sim.

kspace(ψ,sim)

Transform from x- to k-space using transforms packed into sim.

k = kvec(λ,N)

Create k values with correct periodicity for box specified by length λ for number of points N.

K = kvecs(L,N)

Create a tuple containing the spatial coordinate array for each spatial dimension.

T = makeT(X,K,j)

Build FFTW transform library for the array tuples X, K. Defaults to a measure plan. j is number of scratch fields to initialize for in-place evaluation.

T = makeTMixed(X,K,j)

Build mixed transform library for the array tuples X, K. Defaults to a measure plan.

X,K,dX,dK = makearrays(L,N)

Create all x and k arrays for box specified by tuples L=(Lx,...) and N=(Nx,...). For convenience, differentials dX, dK are also reaturned. L and N must be tuples of equal length.

maketransarrays(L,N,j=1;flags=FFTW.MEASURE)

Make all transforms and arrays in one call.

nlin!(ϕ,sim::Sim{D},t)

Mutating evaluation of position space nonlinear terms. Dispatches on dimension D, using potential V(x...,t).

χ = nlin(ϕ,sim,t)

Evalutes nonlinear terms in x-space, returning to k-space.

runsim(sim,ϕ;info,tplot,nfiles)

Call DifferentialEquations to solve Gross-Pitaevskii equation.

xspace!(ϕ,sim)

Mutating transform from k- to x-space using transforms packed into sim.

ψ = xspace(ϕ,sim)

Transform from k- to x-space using transforms packed into sim.

x = xvec(λ,N)

Create x values with correct periodicity for box specified by length λ, using N points.

X = xvecs(L,N)

Create a tuple containing the spatial coordinate array for each spatial dimension.