A binary relation \(R\) is reflexive, iff for all \(x\) we have \(xRx\).
rel_is_reflexive(R)rel_closure_reflexive(R)
rel_reduction_reflexive(R)
The rel_closure_reflexive and
rel_reduction_reflexive functions
return a logical square matrix. dimnames
of R are preserved.
On the other hand, rel_is_reflexive returns
a single logical value.
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.
rel_is_reflexive finds out if a given binary relation
is reflexive. The function just checks whether all elements
on the diagonal of R are non-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.
A reflexive closure of a binary relation \(R\),
determined by rel_closure_reflexive,
is the minimal reflexive superset \(R'\) of \(R\).
A reflexive reduction of a binary relation \(R\),
determined by rel_reduction_reflexive,
is the minimal subset \(R'\) of \(R\),
such that the reflexive closures of \(R\) and \(R'\) are equal
i.e., the largest irreflexive relation contained in \(R\).
Other binary_relations:
check_comonotonicity(),
pord_nd(),
pord_spread(),
pord_weakdom(),
rel_graph(),
rel_is_antisymmetric(),
rel_is_asymmetric(),
rel_is_cyclic(),
rel_is_irreflexive(),
rel_is_symmetric(),
rel_is_total(),
rel_is_transitive(),
rel_reduction_hasse()