rel_reduction_hasse {agop} | R Documentation |
This function computes the reflexive reduction and a kind of transitive reduction which is useful for drawing Hasse diagrams.
rel_reduction_hasse(R)
R |
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set. |
The input matrix R might not necessarily be acyclic/asymmetric, i.e.,
it may represent any totally preordered set (which induces an equivalence
relation on the underlying preordered set).
The implemented algorithm runs in O(n^3) time
and first determines the transitive closure of R.
If an irreflexive R is given, then the transitive closures
of R and of the resulting matrix are identical.
Moreover, if R is additionally acyclic, then this function
is equivalent to rel_reduction_transitive
.
The rel_reduction_hasse
function
returns a logical square matrix. dimnames
of R
are preserved.
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_reflexive
,
rel_is_symmetric
,
rel_is_total
,
rel_is_transitive
## Not run: # Let ord be a total preorder (a total and transitive binary relation) # === Plot the Hasse diagram of ord === # === requires the igraph package === library("igraph") hasse <- graph.adjacency(rel_reduction_transitive(ord)) plot(hasse, layout=layout.fruchterman.reingold(hasse, dim=2)) ## End(Not run)