Irreflexive Binary Relations
A binary relation R is irreflexive (or antireflexive), iff for all x we have !xRx.
rel_is_irreflexive(R)
R |
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set. |
rel_is_irreflexive finds out if a given binary relation
is irreflexive. The function just checks whether all elements
on the diagonal of R are zeros,
i.e., it has O(n) time complexity,
where n is the number of rows in R.
Missing values on the diagonal may result in NA.
When dealing with a graph's loops,
i.e., elements related to themselves, you may be interested
in finding a reflexive closure,
see rel_closure_reflexive,
or a reflexive reduction,
see rel_reduction_reflexive.
rel_is_irreflexive returns
a single logical value.
Other binary_relations: check_comonotonicity,
pord_nd, pord_spread,
pord_weakdom, rel_graph,
rel_is_antisymmetric,
rel_is_asymmetric,
rel_is_cyclic,
rel_is_reflexive,
rel_is_symmetric,
rel_is_total,
rel_is_transitive,
rel_reduction_hasse
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