rel_is_irreflexive {agop} | R Documentation |
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