VineCopulas.jl

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Structure API ​

The structure API gives vine-specific algorithms a small, stable handle for the part of a vine that is not a pair-copula family or parameter.

AbstractVineStructure ​

AbstractVineStructure{p} is the abstract supertype for p-dimensional vine structures. Concrete public structures are:

  • CVineStructure{p,q};

  • DVineStructure{p,q};

  • RVineStructure{p,q}.

Here p is the dimension and q is the active truncation depth.

Do not store the same invariant twice

Structure truncation is encoded by q. Do not add a separate mutable or runtime truncation field to structure objects. A duplicated q/trunc representation can create inconsistent states and ambiguous traversal behavior.

CVineStructure and DVineStructure ​

CVineStructure and DVineStructure store only an order:

julia
CVineStructure{p,q}(order::NTuple{p,Int})
DVineStructure{p,q}(order::NTuple{p,Int})

Public constructors accept vectors or tuples and normalize to NTuple{p,Int}:

julia
st = CVineStructure((1, 2, 3, 4); trunc=2)
CVineStructure(order(st); trunc=truncation(st))

RVineStructure ​

RVineStructure stores order, structure array, and an optional matrix exchange representation:

julia
RVineStructure{p,q}(
    order::NTuple{p,Int},
    struct_array::NTuple{q,Vector{Int}},
    matrix::Union{Nothing,Matrix{Int}},
)

For R-vines, the invariant is especially direct:

Public operations ​

The public structural operations are:

julia
structure(vine)
order(vine_or_structure)
edges(vine)
struct_array(rvine_or_structure)
truncation(vine_or_structure)
truncate(vine_or_structure, level)
rvine_matrix(vine)

These methods are defined only for supported concrete types. There is no catch-all fallback for AbstractVineCopula or AbstractVineStructure.

Capability checks

Because unsupported abstract subtypes do not receive generic throwing fallbacks, applicable(structure, x) and applicable(truncation, x) are meaningful capability checks.

Truncation invariants ​

truncate(vine, level) and truncate(structure, level) return new objects. They do not mutate the input.

Truncating from level 4 to level 2 is valid. Truncating that result back to level 3 is not valid because the missing pair-copulas are no longer present.

The current public level range is 1:p-1. Level-zero truncation is mathematically meaningful as multivariate independence, but it requires a deliberate engine/API pass and is therefore tracked as future work.

Developer guidance ​

Add structure methods when they simplify a real algorithm: serialization, plotting, fitting, diagnostics, conditional simulation, or truncation. Avoid creating parallel structure abstractions that duplicate the public vine model objects without a concrete use.