Topologically sort sccs before attempting codegen

Author: Keno

src/bipartite_graph.jl

@@ -2,7 +2,7 @@ module BipartiteGraphs
 
 export BipartiteEdge, BipartiteGraph, DiCMOBiGraph, Unassigned, unassigned,
         Matching, ResidualCMOGraph, InducedCondensationGraph, maximal_matching,
-        construct_augmenting_path!
+        construct_augmenting_path!, MatchedCondensationGraph
 
 export 𝑠vertices, 𝑑vertices, has_𝑠vertex, has_𝑑vertex, 𝑠neighbors, 𝑑neighbors,
        𝑠edges, 𝑑edges, nsrcs, ndsts, SRC, DST, set_neighbors!, invview,
@@ -516,4 +516,80 @@ end
 Graphs.has_edge(g::DiCMOBiGraph{true}, a, b) = a in inneighbors(g, b)
 Graphs.has_edge(g::DiCMOBiGraph{false}, a, b) = b in outneighbors(g, a)
 
+# Condensation Graphs
+abstract type AbstractCondensationGraph <: AbstractGraph{Int}; end
+function (T::Type{<:AbstractCondensationGraph})(g, sccs::Vector{Union{Int, Vector{Int}}})
+    scc_assignment = Vector{Int}(undef, isa(g, BipartiteGraph) ? ndsts(g) : nv(g))
+    for (i, c) in enumerate(sccs)
+        for v in c
+            scc_assignment[v] = i
+        end
+    end
+    T(g, sccs, scc_assignment)
+end
+(T::Type{<:AbstractCondensationGraph})(g, sccs::Vector{Vector{Int}}) =
+    T(g, Vector{Union{Int, Vector{Int}}}(sccs))
+
+Graphs.is_directed(::Type{<:AbstractCondensationGraph}) = true
+Graphs.nv(icg::AbstractCondensationGraph) = length(icg.sccs)
+Graphs.vertices(icg::AbstractCondensationGraph) = Base.OneTo(nv(icg))
+
+"""
+    struct MatchedCondensationGraph
+
+For some bipartite-graph and an orientation induced on its destination contraction,
+records the condensation DAG of the digraph formed by the orientation. I.e. this
+is a DAG of connected components formed by the destination vertices of some
+underlying bipartite graph.
+N.B.: This graph does not store explicit neighbor relations of the sccs.
+Therefor, the edge multiplicity is derived from the underlying bipartite graph,
+i.e. this graph is not strict.
+"""
+struct MatchedCondensationGraph{G <: DiCMOBiGraph} <: AbstractCondensationGraph
+    graph::G
+    # Records the members of a strongly connected component. For efficiency,
+    # trivial sccs (with one vertex member) are stored inline. Note: the sccs
+    # here need not be stored in topological order.
+    sccs::Vector{Union{Int, Vector{Int}}}
+    # Maps the vertices back to the scc of which they are a part
+    scc_assignment::Vector{Int}
+end
+
+
+Graphs.outneighbors(mcg::MatchedCondensationGraph, cc::Integer) =
+    Iterators.flatten((mcg.scc_assignment[v′] for v′ in outneighbors(mcg.graph, v)) for v in mcg.sccs[cc])
+
+Graphs.inneighbors(mcg::MatchedCondensationGraph, cc::Integer) =
+    Iterators.flatten((mcg.scc_assignment[v′] for v′ in inneighbors(mcg.graph, v)) for v in mcg.sccs[cc])
+
+"""
+    struct InducedCondensationGraph
+
+For some bipartite-graph and a topologicall sorted list of connected components,
+represents the condensation DAG of the digraph formed by the orientation. I.e. this
+is a DAG of connected components formed by the destination vertices of some
+underlying bipartite graph.
+N.B.: This graph does not store explicit neighbor relations of the sccs.
+Therefor, the edge multiplicity is derived from the underlying bipartite graph,
+i.e. this graph is not strict.
+"""
+struct InducedCondensationGraph{G <: BipartiteGraph} <: AbstractCondensationGraph
+    graph::G
+    # Records the members of a strongly connected component. For efficiency,
+    # trivial sccs (with one vertex member) are stored inline. Note: the sccs
+    # here are stored in topological order.
+    sccs::Vector{Union{Int, Vector{Int}}}
+    # Maps the vertices back to the scc of which they are a part
+    scc_assignment::Vector{Int}
+end
+
+_neighbors(icg::InducedCondensationGraph, cc::Integer) =
+    Iterators.flatten(Iterators.flatten(icg.graph.fadjlist[vsrc] for vsrc in icg.graph.badjlist[v]) for v in icg.sccs[cc])
+
+Graphs.outneighbors(icg::InducedCondensationGraph, v::Integer) =
+    (icg.scc_assignment[n] for n in _neighbors(icg, v) if icg.scc_assignment[n] > v)
+
+Graphs.inneighbors(icg::InducedCondensationGraph, v::Integer) =
+    (icg.scc_assignment[n] for n in _neighbors(icg, v) if icg.scc_assignment[n] < v)
+
 end # module

src/compat/incremental_cycles.jl

@@ -1,4 +1,5 @@
 using Base.Iterators: repeated
+import Graphs.Experimental.Traversals: topological_sort
 
 # Abstract Interface
 

src/structural_transformation/codegen.jl

@@ -175,6 +175,10 @@ function build_torn_function(
     s = structure(sys)
     @unpack fullvars = s
     var_eq_matching, var_sccs = algebraic_variables_scc(sys)
+    condensed_graph = MatchedCondensationGraph(
+        DiCMOBiGraph{true}(complete(s.graph), complete(var_eq_matching)), var_sccs)
+    toporder = topological_sort_by_dfs(condensed_graph)
+    var_sccs = var_sccs[toporder]
 
     states = map(i->s.fullvars[i], diffvars_range(s))
     mass_matrix_diag = ones(length(states))