#include <vinecopulib/include/vinecopulib/misc/triangular_array.hpp>
template<typename T>
vinecopulib::TriangularArray class

Triangular arrays.

A triangular array behaves like a matrix with the structure

x x x x x
x x x x
x x x
x x
x

and all other elements omitted. This structure appears naturally in the representation of a vine copula model and related algorithms. Each row corresponds to one tree in the vine, starting from the top. In each tree (=row), each column represents an edge.

For truncated vine models the last few trees are omitted. For example, a 3-truncated version of the above array contains the elements

x x x x x
x x x x
x x x

Only the elements indicated by xs are stored and can be accessed.

The data structure is templated and any type or class can be used to fill the entries (xs) of the triangular array.

Constructors, destructors, conversion operators

TriangularArray() defaulted
TriangularArray(size_t d) explicit
Construct a triangular array of dimension d.
TriangularArray(size_t d, size_t trunc_lvl)
Construct a truncated triangular array.
TriangularArray(const std::vector<std::vector<T>>& rows) explicit
Construct a truncated triangular array from nested vector.
template<typename Json, typename std::enable_if<std::is_same<typename std::decay<Json>::type, nlohmann::json>::value, int>::type = 0>
TriangularArray(const Json& input) explicit
Constructs a triangular array from a nlohmann::json object.

Public functions

auto operator()(size_t row, size_t column) -> T&
Access one element of the trapezoid (writable).
auto operator()(size_t row, size_t column) const -> T
Access one element of the trapezoid (non-writable).
auto operator==(const TriangularArray<T>& rhs) const -> bool
Equality operator to compare two TriangularArray objects.
auto operator<(const TriangularArray<T>& rhs) const -> bool
Lexicographic comparison operator for sorting.
auto truncate(size_t trunc_lvl) -> void
Truncates the trapezoid. If the trapezoid is already truncated at a level less than trunc_lvl, the function does nothing.
auto get_trunc_lvl() const -> size_t
Gets the truncation level of the underlying vine..
auto get_dim() const -> size_t
Gets the dimension of the underlying vine (the matrix has d-1 columns and. min(trunv_lvl, d-1) rows).
auto to_json() const -> nlohmann::json
Converts the triangular array to a nlohmann::json object.
auto to_list() const -> std::vector<std::vector<T>>
Converts the triangular array to a nested vector of rows.
auto str() const -> std::string
represent triangular array as a string.

Function documentation

template<typename T _1>
vinecopulib::TriangularArray<_1>::TriangularArray(size_t d) explicit

Construct a triangular array of dimension d.

Parameters
d The dimension of the underlying vine.

The array has d-1 columns and d-1 rows.

template<typename T _1>
vinecopulib::TriangularArray<_1>::TriangularArray(size_t d, size_t trunc_lvl)

Construct a truncated triangular array.

Parameters
d The dimension of the vine.
trunc_lvl The truncation level.

The array has d-1 columns and min(trunc_lvl, d-1) rows.

template<typename T _1>
vinecopulib::TriangularArray<_1>::TriangularArray(const std::vector<std::vector<T>>& rows) explicit

Construct a truncated triangular array from nested vector.

Parameters
rows A vector of rows; the length of the first row defines the dimension of the triangular array. The number of rows defines the truncation level.

An arrax of dimension d has d-1 columns and min(trunc_lvl, d-1) rows.

template<typename T _1> template<typename Json, typename std::enable_if<std::is_same<typename std::decay<Json>::type, nlohmann::json>::value, int>::type = 0>
vinecopulib::TriangularArray<_1>::TriangularArray(const Json& input) explicit

Constructs a triangular array from a nlohmann::json object.

Parameters
input The nlohmann::json object to convert from.

The "data" field must contain the rows of the array (as written by to_json()); the dimension and truncation level are derived from the rows. Templated so that brace-enclosed initializer lists keep selecting the nested-vector constructor.

template<typename T _1>
T& vinecopulib::TriangularArray<_1>::operator()(size_t row, size_t column)

Access one element of the trapezoid (writable).

Parameters
row The row level.
column The column in this row.

template<typename T _1>
T vinecopulib::TriangularArray<_1>::operator()(size_t row, size_t column) const

Access one element of the trapezoid (non-writable).

Parameters
row The row level.
column The column in this row.

template<typename T _1>
bool vinecopulib::TriangularArray<_1>::operator==(const TriangularArray<T>& rhs) const

Equality operator to compare two TriangularArray objects.

Parameters
rhs Right-hand-side of the equality operator.

template<typename T _1>
bool vinecopulib::TriangularArray<_1>::operator<(const TriangularArray<T>& rhs) const

Lexicographic comparison operator for sorting.

Parameters
rhs Right-hand-side of the less-than operator.

template<typename T _1>
void vinecopulib::TriangularArray<_1>::truncate(size_t trunc_lvl)

Truncates the trapezoid. If the trapezoid is already truncated at a level less than trunc_lvl, the function does nothing.

Parameters
trunc_lvl The truncation level.

template<typename T _1>
nlohmann::json vinecopulib::TriangularArray<_1>::to_json() const

Converts the triangular array to a nlohmann::json object.

Returns The nlohmann::json object containing the array.

The result contains the fields "d" (dimension), "t" (truncation level), and "data" (the rows of the array); it can be converted back with the JSON constructor.

template<typename T _1>
std::vector<std::vector<T>> vinecopulib::TriangularArray<_1>::to_list() const

Converts the triangular array to a nested vector of rows.

Returns The rows of the array.

Row i holds the d - 1 - i entries of tree i; the result can be converted back with the nested-vector constructor.