Result containers

AbstractStructureFunction

Abstract base type for all structure function result containers.

HelmholtzDecomposition2D(distance_bins, rotational_sums, rotational_counts,
                         divergent_sums, divergent_counts,
                         longitudinal_values, transverse_values)

Result of the 2D isotropic Helmholtz decomposition computed from binned longitudinal/transverse second-order structure functions. Rotational and divergent components are derived quantities, not pairwise operators.

StructureFunction{FT, OT, BT, VT}

Metadata-rich result object for structure function calculations.

• operator: The specific operator used (e.g., L2SF).
• distance: The coordinate container (can be bin midpoints, edges, or point distances).
• values: The computed structure function values.

StructureFunction2DSumsAndCounts{FT, OT, BT, VT, MT}

2D Joint-Probability intermediate result container containing raw sums and counts matrices. Useful for analyzing the PDF of structure function values across separation distance bins.

• operator: The specific operator used (e.g., L2SF).
• distance_bins: 1D container of distance bin edges.
• value_bins: 1D container of structure function value bin edges.
• sums: 2D matrix of accumulated exact values of shape (Ndistancebins, Nvaluebins).
• counts: 2D matrix of accumulated contribution counts of shape (Ndistancebins, Nvaluebins).

StructureFunctionSumsAndCounts{FT, OT, BT, VT}

Intermediate result object containing raw sums and per-bin pair counts (integer). Useful for aggregating measurements before final averaging.

StructureFunctionTensor(order, distance_bins, values)

Averaged binned tensor structure function — the mean tensor $D_{i…}(r)$ per distance bin (the sums ./ counts reduction of a StructureFunctionTensorSumsAndCounts, with the empty-bin guard count == 0 → NaN). For tensor order P and spatial dimension D, values has leading axes (D, D, ..., D, n_bins, auxiliary...) with P repeated component axes. This is the default result of calculate_structure_function_tensor; pass output_type = StructureFunctionTensorSumsAndCounts for the raw accumulator.

StructureFunctionTensor2DSumsAndCounts(order, distance_bins, axis_bins, sums, counts)

Raw tensor structure function joint in separation and a second axis: sums has shape (D, …, D, n_bins, n_axis) with P component axes, counts (n_bins, n_axis), axis_bins the edges of the second axis.

StructureFunctionTensorSumsAndCounts(order, distance_bins, sums, counts)

Raw binned tensor structure-function result. For tensor order P and spatial dimension D, sums has leading axes (D, D, ..., D, n_bins, auxiliary...) with P repeated component axes. counts has shape (n_bins, auxiliary...).

marginalize(sf2d::StructureFunction2DSumsAndCounts)

Sum $sums$ and $counts$ over the value-bin axis to produce a 1D $StructureFunctionSumsAndCounts$ (mass-conserving reduction of a 2D joint histogram).