Floyd-Warshall #70
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,60 @@ | ||
| using DiagrammaticEquations | ||
| using SymbolicUtils | ||
| using SymbolicUtils.Rewriters | ||
| using SymbolicUtils.Code | ||
| using MLStyle | ||
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| const DECA_EQUALITY_SYMBOL = (==) | ||
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| to_symbolics(d::SummationDecapode, node::TraversalNode) = to_symbolics(d, node.index, Val(node.name)) | ||
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| function to_symbolics(d::SummationDecapode, op_index::Int, ::Val{:Op1}) | ||
| input_sym = SymbolicUtils.Sym{Number}(d[d[op_index, :src], :name]) | ||
| output_sym = SymbolicUtils.Sym{Number}(d[d[op_index, :tgt], :name]) | ||
| op_sym = SymbolicUtils.Sym{(SymbolicUtils.FnType){Tuple{Number}, Number}}(d[op_index, :op1]) | ||
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| rhs = SymbolicUtils.Term{Number}(op_sym, [input_sym]) | ||
| SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [output_sym, rhs]) | ||
| end | ||
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| function to_symbolics(d::SummationDecapode, op_index::Int, ::Val{:Op2}) | ||
| input1_sym = SymbolicUtils.Sym{Number}(d[d[op_index, :proj1], :name]) | ||
| input2_sym = SymbolicUtils.Sym{Number}(d[d[op_index, :proj2], :name]) | ||
| output_sym = SymbolicUtils.Sym{Number}(d[d[op_index, :res], :name]) | ||
| op_sym = SymbolicUtils.Sym{(SymbolicUtils.FnType){Tuple{Number, Number}, Number}}(d[op_index, :op2]) | ||
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| rhs = SymbolicUtils.Term{Number}(op_sym, [input1_sym, input2_sym]) | ||
| SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [output_sym, rhs]) | ||
| end | ||
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| #XXX: Always converting + -> .+ here since summation doesn't store the style of addition | ||
| # function to_symbolics(d::SummationDecapode, op_index::Int, ::Val{:Σ}) | ||
| # Expr(EQUALITY_SYMBOL, c.output, Expr(:call, Expr(:., :+), c.inputs...)) | ||
| # end | ||
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| function extract_symexprs(d::SummationDecapode) | ||
| topo_list = topological_sort_edges(d) | ||
| sym_list = [] | ||
| for node in topo_list | ||
| retrieve_name(d, node) != DerivOp || continue | ||
| push!(sym_list, to_symbolics(d, node)) | ||
| end | ||
| sym_list | ||
| end | ||
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| function apply_rewrites(d::SummationDecapode, rewriter) | ||
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| rewritten_list = [] | ||
| for sym in extract_symexprs(d) | ||
| res_sym = rewriter(sym) | ||
| rewritten_sym = isnothing(res_sym) ? sym : res_sym | ||
| push!(rewritten_list, rewritten_sym) | ||
| end | ||
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| rewritten_list | ||
| end | ||
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| # TODO: We need a way to get information like the d and ⋆ even when not in the ACSet | ||
| # @syms Δ(x) d(x) ⋆(x) | ||
| # lap_0_rule = @rule Δ(~x) => ⋆(d(⋆(d(~x)))) | ||
| # rewriter = Postwalk(RestartedChain([lap_0_rule])) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,104 @@ | ||
| using DiagrammaticEquations | ||
| using ACSets | ||
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| export TraversalNode, topological_sort_edges, number_of_ops, retrieve_name | ||
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| struct TraversalNode{T} | ||
| index::Int | ||
| name::T | ||
| dom::AbstractVector | ||
| cod::Int | ||
| end | ||
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| TraversalNode(i, d::SummationDecapode, ::Val{:Op1}) = | ||
| TraversalNode{Symbol}(i, d[i,:op1], [d[i,:src]], d[i,:tgt]) | ||
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| TraversalNode(i, d::SummationDecapode, ::Val{:Op2}) = | ||
| TraversalNode{Symbol}(i, d[i,:op2], [d[i,:proj1],d[i,:proj2]], d[i,:res]) | ||
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| TraversalNode(i, d::SummationDecapode, ::Val{:Σ}) = | ||
| TraversalNode{Symbol}(i, :+, d[incident(d,i,:summation),:summand], d[i,:sum]) | ||
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| retrieve_name(d::SummationDecapode, tsr::TraversalNode) = tsr.name | ||
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| # Induce a topological ordering of operations from a topological ordering of variables. | ||
| # Taking Vᵢ(dom(e)ᵢ) like so is a structure preserving map. | ||
| edge2cost(tsv, tsr::TraversalNode) = maximum(tsv[tsr.dom]) | ||
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| number_of_ops(d::SummationDecapode) = nparts(d, :Op1) + nparts(d, :Op2) + nparts(d, :Σ) | ||
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| start_nodes(d::SummationDecapode) = vcat(infer_states(d), incident(d, :Literal, :type)) | ||
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| # TODO: This could be Catlab'd. Hypergraph category? Migration to a DWD? | ||
| """ function hyper_edge_list(d::SummationDecapode) | ||
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| Represent a Decapode as a directed hyper-edge list. | ||
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| Interpret a: | ||
| - unary operation as a hyperedge of order (1,1) , | ||
| - binary operation as a hyperedge of order (2,1) , and | ||
| - summation as a hyperedge of order (|summands|,1) . | ||
| """ | ||
| function hyper_edge_list(d::SummationDecapode) | ||
| [map(e -> TraversalNode(e, d, Val(:Op1)), parts(d, :Op1))..., | ||
| map(e -> TraversalNode(e, d, Val(:Op2)), parts(d, :Op2))..., | ||
| map(e -> TraversalNode(e, d, Val(:Σ )), parts(d, :Σ ))...] | ||
| end | ||
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There was a problem hiding this comment. Have a function that returns all of the "edge" symbols, so in this case |
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| """ function floyd_warshall(d::SummationDecapode) | ||
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| Return a |variable| × |variable| matrix of shortest paths via the Floyd-Warshall algorithm. | ||
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| Taking the maximum of the non-infinite short paths from state variables induces a topological ordering. | ||
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| https://en.wikipedia.org/wiki/Floyd–Warshall_algorithm | ||
| """ | ||
| function floyd_warshall(d::SummationDecapode) | ||
| # Define weights. | ||
| w(e) = (length(e.dom) == 1 && e.name ∈ [:∂ₜ,:dt]) ? -Inf : -1 | ||
| # Init dists | ||
| V = nparts(d, :Var) | ||
| dist = fill(Inf, (V, V)) | ||
| foreach(hyper_edge_list(d)) do e | ||
| dist[(e.dom), e.cod] .= w(e) | ||
| end | ||
| for v in 1:V | ||
| dist[v,v] = 0 | ||
| end | ||
| # Floyd-Warshall | ||
| for k in 1:V | ||
| for i in 1:V | ||
| for j in 1:V | ||
| if dist[i,j] > dist[i,k] + dist[k,j] | ||
| dist[i,j] = dist[i,k] + dist[k,j] | ||
| end | ||
| end | ||
| end | ||
| end | ||
| dist | ||
| end | ||
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| """ function topological_sort_verts(d::SummationDecapode) | ||
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| Topologically sort the variables in a Decapode. | ||
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| The vector returned by this function maps each vertex to the order that it would be traversed in a topological sort traversal. If you want a list of vertices in the order of traversal, call `sortperm` on the output. | ||
| """ | ||
| function topological_sort_verts(d::SummationDecapode) | ||
| m = floyd_warshall(d) | ||
| map(parts(d,:Var)) do v | ||
| minimum(filter(!isinf, m[v,infer_terminals(d)])) | ||
| end | ||
| end | ||
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| # TODO: Add in-place version for sorting a given hyperedge list. | ||
| """ function topological_sort_edges(d::SummationDecapode) | ||
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| Topologically sort the edges in a Decapode. | ||
| """ | ||
| function topological_sort_edges(d::SummationDecapode) | ||
| tsv = topological_sort_verts(d) | ||
| op_order = hyper_edge_list(d) | ||
| sort(op_order, by = x -> edge2cost(tsv,x)) | ||
| end | ||
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Call these src/tgt since we're talking about hypergraphs.