Description Usage Arguments Details Value See Also
A binary relation R is reflexive, iff for all x we have xRx.
1 2 3 4 5 |
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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