check_comonotonicity: Check If Two Vectors Are Comonotonic
In agop: Aggregation Operators and Preordered Sets

Description Usage Arguments Details Value References See Also

This functions determines if two vectors have a common ordering permutation.

1	check_comonotonicity(x, y, incompatible_lengths = NA)

`x`	numeric vector
`y`	numeric vector
`incompatible_lengths`	single logical value, value to return iff lengths of `x` and `y` differ

Two vectors x, y of equal length n are comonotonic, if and only if there exists a permutation σ such that x_{σ(1)}≤ … ≤ x_{σ(n)} and y_{σ(1)}≤ … ≤ y_{σ(n)}. Thus, σ orders x and y simultaneously. Equivalently, x and y are comonotonic, iff (x_i-x_j)(y_i-y_j)≥ 0 for every i,j.

If there are missing values in x or y, the function returns NA.

Currently, the implemented algorithm has O(n^2) time complexity.

Returns a single logical value.

Grabisch M., Marichal J.-L., Mesiar R., Pap E., Aggregation functions, Cambridge University Press, 2009.

Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7

Other binary_relations: pord_nd, pord_spread, pord_weakdom, rel_graph, rel_is_antisymmetric, rel_is_asymmetric, rel_is_cyclic, rel_is_irreflexive, rel_is_reflexive, rel_is_symmetric, rel_is_total, rel_is_transitive, rel_reduction_hasse