Check If Two Vectors Are Comonotonic
This functions determines if two vectors have a common ordering permutation.
check_comonotonicity(x, y, incompatible_lengths = NA)
x |
numeric vector |
y |
numeric vector |
incompatible_lengths |
single logical value,
value to return iff lengths of |
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
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