| rel_is_reflexive {agop} | R Documentation |
Reflexive Binary Relations
Description
A binary relation R is reflexive, iff
for all x we have xRx.
Usage
rel_is_reflexive(R)
rel_closure_reflexive(R)
rel_reduction_reflexive(R)
Arguments
R |
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set. |
Details
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.
Value
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.
See Also
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()