Examples

Runnable scripts live in examples/ and have their own environment:

julia --project=examples examples/simple_2d.jl

Script	Shows
`simple_2d.jl`	2D field, 2nd-order SF, K41 scaling, plotting
`threaded_calculation.jl`	`ThreadedBackend` (OhMyThreads), serial-vs-threaded speedup
`distributed_parallel.jl`	`DistributedBackend` across worker processes
`gpu_acceleration.jl`	`GPUBackend` + reusable `GPUSFWorkspace`
`gpu_time_slices.jl`	native batch over the trailing `(D, N, T)` axis
`single_pass.jl`	six invariants + Helmholtz in one pair pass

Featured snippets

Single pass: six invariants + Helmholtz

Single-pass invariants and Helmholtz decomposition

One O(N²) pair pass returns all six isotropic invariants (and, for point-field input, the rotational/divergent Helmholtz decomposition) as a NamedTuple keyed by invariant:

using StructureFunctions: Calculations as SFC, LogBinEdges

x = rand(2, 4096) .* 1.0e4          # (D, N) coordinates
u = randn(2, 4096)                  # (D, N) velocities
bins = LogBinEdges(collect(exp10.(range(log10(50.0), log10(5.0e3); length = 41))))

res = SFC.calculate_structure_functions_single_pass(x, u, bins; backend = CB.AutoBackend())
res.S2          # StructureFunction (averaged) for S2; also res.L2, res.T2, res.S3, res.L3, res.L1T2
res.helmholtz   # HelmholtzDecomposition2D (rotational/divergent), point-field input only

# Raw sums + counts instead of the averaged view:
raw = SFC.calculate_structure_functions_single_pass(
    x, u, bins; output_type = SFC.StructureFunctionObjects.StructureFunctionSumsAndCounts,
)
raw.L2.sums, raw.L2.counts

2D joint (distance × value) histogram

2D joint-probability binning across all invariants, with vs without a cascade

using StructureFunctions: Calculations as SFC, StructureFunctionTypes as SFT, LogBinEdges, LinearBinEdges

dist = LogBinEdges(collect(exp10.(range(log10(50.0), log10(5.0e3); length = 41))))
vbins = LinearBinEdges(collect(range(-5.0, 5.0; length = 51)))
sf2d = SFC.calculate_structure_function(SFT.L2SFType(), x, u, dist, vbins; backend = CB.AutoBackend())
sf2d.sums, sf2d.counts   # (n_dist, n_val) joint histogram

Native batch over time slices

Pass a (D, N, T) array (shared positions may be a single (D, N) matrix). Geometry is computed once per pair and the batch axis is vectorized — far faster than looping t:

sums  = zeros(SFC.SINGLE_PASS_N, length(dist) - 1, length(vbins) - 1, T)
counts = zeros(Int, size(sums))
SFC.calculate_structure_functions_single_pass_2d_batch!(sums, counts, x, u_batch, dist, vbins;
                                                        backend = CB.AutoBackend())

See Backends for choosing serial / threaded / distributed / GPU, and GPU Acceleration for the GPU batch path and GPUSFWorkspace.