3.2.11.7. dg/VertexMapper.hpp

3.2.11.7.1. Class dg::VertexMapper

class dg::VertexMapper

A class for enumerating all valid vertex maps for a given dg::DG::HyperEdge. That is, for such a hyperedge, collect the graphs associated with respectively the source and target vertices, and create the disjoint union of those graphs. Let the result be the graphs \(G'\) and \(H'\). Then each rule \(p = (L\leftarrow K\rightarrow R)\) associated with the hyperedge, generate direct derivations \(G\overset{p, m}{\Rightarrow} H\) where \(G\) is isomorphic to \(G'\) and \(H\) is isomorphic to \(H'\).

Each recorded vertex map is a map \(V(G) \rightarrow V(H)\). Those maps are available in this class.

3.2.11.7.1.1. Synopsis

using Map = VertexMap<graph::Union, graph::Union>;
class Result
class iterator
using const_iterator = iterator
VertexMapper(DG::HyperEdge e)
VertexMapper(DG::HyperEdge e, bool upToIsomorphismG, int leftLimit, int rightLimit, int verbosity)
DG::HyperEdge getEdge() const
graph::Union getLeft() const
graph::Union getRight() const
const_iterator begin() const
const_iterator end() const
std::size_t size() const
Result operator[](std::size_t i) const

3.2.11.7.1.2. Details

using Map = VertexMap<graph::Union, graph::Union>;

The vertex map type.

class Result

The value type returned for each vertex map. the rule used to generate the map, and then the actual map.

std::shared_ptr<rule::Rule> r

The rule used to generate the map.

Map map

The actual vertex map \(V(G) \rightarrow V(H)\).

class iterator

A random-access iterator over Results.

using const_iterator = iterator
VertexMapper(DG::HyperEdge e)
VertexMapper(DG::HyperEdge e, bool upToIsomorphismG, int leftLimit, int rightLimit, int verbosity)

Construct a vertex map holder. It will immediately calculate all vertex maps for the derivations underlying the given hyperedge. By default all maps \(V(G) \rightarrow V(H)\) are enumerated. To only enumerate a singular vertex map per rule, use upToIsomorphismG = true and leftLimit = rightLimit = 1.

Parameters:

  • e – the hyperedge to construct vertex maps for.

  • upToIsomrophismG – whether to enumerate all \(m\), or just those such that all bottom spans \((G\leftarrow D\rightarrow H)\) up to isomorphism are generated. Defaults to true.

  • leftLimit – after bottom span generation, find this many isomorphisms back to the sources of the hyperedge. Defaults to 1.

  • rightLimit – after bottom span generation, find this many isomorphisms back to the targets of the hyperedge. Defaults to \(2^{30}\).

  • verbosity –

    the level of debug information to print. Defaults to 0.

    • 0 (or less): print no information.

    • 1: print debug information within the vertex mapping, but not debug information related to rule composition.

    • 10: also print information for morphism generation for rule composition.

    • 20: also print rule composition information.

Throws:

LogicError if !e.

DG::HyperEdge getEdge() const
Returns:

the hyperedge for which the mapper calculates vertex maps.

graph::Union getLeft() const
graph::Union getRight() const
Returns:

the disjoint union of graphs from respectively the source and target vertices of the hyperedge. That is, the graphs \(G\) and \(H\) that are the domain and codomain graphs of the calculated vertex maps.

const_iterator begin() const
const_iterator end() const
Returns:

iterators for the range of vertex maps calculated by the mapper.

std::size_t size() const
Returns:

end() - begin()

Result operator[](std::size_t i) const
Returns:

begin()[i]

Throws:

LogicError if i >= size().