rel_is_reflexive {agop} | R Documentation |

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`

[Package *agop* version 0.2-3 Index]