Reflexive Binary Relations
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)
R |
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.
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.
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
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