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Compare colorings against values from papers (#3)
* Test against reference papers * Rng * Using * Rename * CSV * Add performance tests * Correct column intersection graph * Missing using
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,81 +1,129 @@ | ||
| ## Standard graph | ||
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| """ | ||
| Graph{T} | ||
| Undirected graph structure stored in Compressed Sparse Column (CSC) format. | ||
| # Fields | ||
| - `colptr::Vector{T}`: same as for `SparseMatrixCSC` | ||
| - `rowval::Vector{T}`: same as for `SparseMatrixCSC` | ||
| """ | ||
| struct Graph{T<:Integer} | ||
| colptr::Vector{T} | ||
| rowval::Vector{T} | ||
| end | ||
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| Graph(A::SparseMatrixCSC) = Graph(A.colptr, A.rowval) | ||
| Graph(A::AbstractMatrix) = Graph(sparse(A)) | ||
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| Base.length(g::Graph) = length(g.colptr) - 1 | ||
| SparseArrays.nnz(g::Graph) = length(g.rowval) | ||
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| vertices(g::Graph) = 1:length(g) | ||
| neighbors(g::Graph, v::Integer) = view(g.rowval, g.colptr[v]:(g.colptr[v + 1] - 1)) | ||
| degree(g::Graph, v::Integer) = length(g.colptr[v]:(g.colptr[v + 1] - 1)) | ||
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| ## Adjacency graph | ||
| maximum_degree(g::Graph) = maximum(Base.Fix1(degree, g), vertices(g)) | ||
| minimum_degree(g::Graph) = minimum(Base.Fix1(degree, g), vertices(g)) | ||
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| ## Bipartite graph | ||
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| """ | ||
| AdjacencyGraph | ||
| BipartiteGraph{T} | ||
| Undirected graph representing the nonzeros of a symmetrix matrix (typically a Hessian matrix). | ||
| Undirected bipartite graph structure stored in bidirectional Compressed Sparse Column format (redundancy allows for faster access). | ||
| The adjacency graph of a symmetrix matrix `A ∈ ℝ^{n × n}` is `G(A) = (V, E)` where | ||
| A bipartite graph has two "sides", which we number `1` and `2`. | ||
| - `V = 1:n` is the set of rows or columns | ||
| - `(i, j) ∈ E` whenever `A[i, j] ≠ 0` and `i ≠ j` | ||
| # Fields | ||
| - `g1::Graph{T}`: contains the neighbors for vertices on side `1` | ||
| - `g2::Graph{T}`: contains the neighbors for vertices on side `2` | ||
| """ | ||
| struct AdjacencyGraph{T} | ||
| g::Graph{T} | ||
| struct BipartiteGraph{T<:Integer} | ||
| g1::Graph{T} | ||
| g2::Graph{T} | ||
| end | ||
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| function AdjacencyGraph(H::SparseMatrixCSC) | ||
| g = Graph(H - Diagonal(H)) | ||
| return AdjacencyGraph(g) | ||
| end | ||
| Base.length(bg::BipartiteGraph, ::Val{1}) = length(bg.g1) | ||
| Base.length(bg::BipartiteGraph, ::Val{2}) = length(bg.g2) | ||
| SparseArrays.nnz(bg::BipartiteGraph) = nnz(bg.g1) | ||
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| Base.length(ag::AdjacencyGraph) = length(ag.g) | ||
| """ | ||
| vertices(bg::BipartiteGraph, Val(side)) | ||
| Return the list of vertices of `bg` from the specified `side` as a range `1:n`. | ||
| """ | ||
| neighbors(ag::AdjacencyGraph, v::Integer) | ||
| vertices(bg::BipartiteGraph, ::Val{side}) where {side} = 1:length(bg, Val(side)) | ||
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| Return the neighbors of `v` in the graph `ag`. | ||
| """ | ||
| neighbors(ag::AdjacencyGraph, v::Integer) = neighbors(ag.g, v) | ||
| neighbors(bg::BipartiteGraph, Val(side), v::Integer) | ||
| degree(ag::AdjacencyGraph, v::Integer) = length(neighbors(ag, v)) | ||
| Return the neighbors of `v` (a vertex from the specified `side`, `1` or `2`), in the graph `bg`. | ||
| """ | ||
| neighbors(bg::BipartiteGraph, ::Val{1}, v::Integer) = neighbors(bg.g1, v) | ||
| neighbors(bg::BipartiteGraph, ::Val{2}, v::Integer) = neighbors(bg.g2, v) | ||
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| ## Bipartite graph | ||
| degree(bg::BipartiteGraph, ::Val{1}, v::Integer) = degree(bg.g1, v) | ||
| degree(bg::BipartiteGraph, ::Val{2}, v::Integer) = degree(bg.g2, v) | ||
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| function maximum_degree(bg::BipartiteGraph, ::Val{side}) where {side} | ||
| return maximum(v -> degree(bg, Val(side), v), vertices(bg, Val(side))) | ||
| end | ||
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| function minimum_degree(bg::BipartiteGraph, ::Val{side}) where {side} | ||
| return minimum(v -> degree(bg, Val(side), v), vertices(bg, Val(side))) | ||
| end | ||
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| ## Construct from matrices | ||
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| """ | ||
| adjacency_graph(H::AbstractMatrix) | ||
| Return a [`Graph`](@ref) representing the nonzeros of a symmetric matrix (typically a Hessian matrix). | ||
| The adjacency graph of a symmetrix matric `A ∈ ℝ^{n × n}` is `G(A) = (V, E)` where | ||
| - `V = 1:n` is the set of rows or columns `i`/`j` | ||
| - `(i, j) ∈ E` whenever `A[i, j] ≠ 0` and `i ≠ j` | ||
| """ | ||
| adjacency_graph(H::SparseMatrixCSC) = Graph(H - Diagonal(H)) | ||
| adjacency_graph(H::AbstractMatrix) = adjacency_graph(sparse(H)) | ||
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| """ | ||
| BipartiteGraph | ||
| bipartite_graph(J::AbstractMatrix) | ||
| Undirected bipartite graph representing the nonzeros of a non-symmetric matrix (typically a Jacobian matrix). | ||
| Return a [`BipartiteGraph`](@ref) representing the nonzeros of a non-symmetric matrix (typically a Jacobian matrix). | ||
| The bipartite graph of a matrix `A ∈ ℝ^{m × n}` is `Gb(A) = (V₁, V₂, E)` where | ||
| - `V₁ = 1:m` is the set of rows `i` | ||
| - `V₂ = 1:n` is the set of columns `j` | ||
| - `(i, j) ∈ E` whenever `A[i, j] ≠ 0` | ||
| """ | ||
| struct BipartiteGraph{T} | ||
| g1::Graph{T} | ||
| g2::Graph{T} | ||
| end | ||
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| function BipartiteGraph(J::SparseMatrixCSC) | ||
| g1 = Graph(SparseMatrixCSC(transpose(J))) # rows to columns | ||
| function bipartite_graph(J::SparseMatrixCSC) | ||
| g1 = Graph(transpose(J)) # rows to columns | ||
| g2 = Graph(J) # columns to rows | ||
| return BipartiteGraph(g1, g2) | ||
| end | ||
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| Base.length(bg::BipartiteGraph, ::Val{1}) = length(bg.g1) | ||
| Base.length(bg::BipartiteGraph, ::Val{2}) = length(bg.g2) | ||
| bipartite_graph(J::AbstractMatrix) = bipartite_graph(sparse(J)) | ||
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| """ | ||
| neighbors(bg::BipartiteGraph, Val(side), v::Integer) | ||
| column_intersection_graph(J::AbstractMatrix) | ||
| Return the neighbors of `v`, which is a vertex from the specified `side` (`1` or `2`), in the graph `bg`. | ||
| """ | ||
| neighbors(bg::BipartiteGraph, ::Val{1}, v::Integer) = neighbors(bg.g1, v) | ||
| neighbors(bg::BipartiteGraph, ::Val{2}, v::Integer) = neighbors(bg.g2, v) | ||
| Return a [`Graph`](@ref) representing the column intersections of a non-symmetric matrix (typically a Jacobian matrix). | ||
| The column intersection graph of a matrix `A ∈ ℝ^{m × n}` is `Gc(A) = (V, E)` where | ||
| function degree(bg::BipartiteGraph, ::Val{side}, v::Integer) where {side} | ||
| return length(neighbors(bg, Val(side), v)) | ||
| - `V = 1:n` is the set of columns `j` | ||
| - `(j1, j2) ∈ E` whenever `A[:, j1] ∩ A[:, j2] ≠ ∅` | ||
| """ | ||
| function column_intersection_graph(J::SparseMatrixCSC) | ||
| A = transpose(J) * J | ||
| return adjacency_graph(A - Diagonal(A)) | ||
| end | ||
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| column_intersection_graph(J::AbstractMatrix) = column_intersection_graph(sparse(J)) |
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