Merge pull request #353 from isaacsas/depgraphs

dependency graphs for JumpSystems

Author: ChrisRackauckas

Project.toml

@@ -12,6 +12,7 @@ Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 GeneralizedGenerated = "6b9d7cbe-bcb9-11e9-073f-15a7a543e2eb"
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"

src/ModelingToolkit.jl

@@ -18,6 +18,8 @@ using RecursiveArrayTools
 import SymbolicUtils
 import SymbolicUtils: to_symbolic, FnType
 
+import LightGraphs: SimpleDiGraph, add_edge!
+
 import TreeViews
 
 """
@@ -101,6 +103,7 @@ include("systems/optimization/optimizationsystem.jl")
 include("systems/pde/pdesystem.jl")
 
 include("systems/reaction/reactionsystem.jl")
+include("systems/dependency_graphs.jl")
 
 include("latexify_recipes.jl")
 include("build_function.jl")
@@ -118,7 +121,7 @@ export Differential, expand_derivatives, @derivatives
 export IntervalDomain, ProductDomain, ⊗, CircleDomain
 export Equation, ConstrainedEquation
 export Operation, Expression, Variable
-export independent_variable, states, parameters, equations
+export independent_variable, states, parameters, equations 
 
 export calculate_jacobian, generate_jacobian, generate_function
 export calculate_tgrad, generate_tgrad
@@ -127,6 +130,10 @@ export calculate_factorized_W, generate_factorized_W
 export calculate_hessian, generate_hessian
 export calculate_massmatrix, generate_diffusion_function
 
+export BipartiteGraph, equation_dependencies, variable_dependencies
+export eqeq_dependencies, varvar_dependencies
+export asgraph, asdigraph
+
 export simplified_expr, rename, get_variables
 export simplify, substitute
 export build_function

src/systems/dependency_graphs.jl

@@ -0,0 +1,114 @@
+# variables equations depend on as a vector of vectors of variables
+# each system type should define extract_variables! for a single equation
+function equation_dependencies(sys::AbstractSystem; variables=states(sys))
+    eqs  = equations(sys)
+    deps = Set{Variable}()
+    depeqs_to_vars = Vector{Vector{Variable}}(undef,length(eqs))
+
+    for (i,eq) in enumerate(eqs)      
+        depeqs_to_vars[i] = collect(get_variables!(deps, eq, variables))
+        empty!(deps)
+    end
+
+    depeqs_to_vars
+end
+
+# modeled on LightGraphs SimpleGraph
+mutable struct BipartiteGraph{T <: Integer}
+    ne::Int
+    fadjlist::Vector{Vector{T}}  # fadjlist[src] = [dest1,dest2,...]
+    badjlist::Vector{Vector{T}}  # badjlist[dst] = [src1,src2,...]
+end
+
+# convert equation-variable dependencies to a bipartite graph
+function asgraph(eqdeps, vtois)    
+    fadjlist = Vector{Vector{Int}}(undef, length(eqdeps))
+    for (i,dep) in enumerate(eqdeps)
+        fadjlist[i] = sort!([vtois[var] for var in dep])
+    end
+
+    badjlist = [Vector{Int}() for i = 1:length(vtois)]
+    ne = 0
+    for (eqidx,vidxs) in enumerate(fadjlist)
+        foreach(vidx -> push!(badjlist[vidx], eqidx), vidxs)
+        ne += length(vidxs)
+    end
+
+    BipartiteGraph(ne, fadjlist, badjlist)
+end
+
+function Base.isequal(bg1::BipartiteGraph{T}, bg2::BipartiteGraph{T}) where {T<:Integer} 
+    iseq = (bg1.ne == bg2.ne)
+    iseq &= (bg1.fadjlist == bg2.fadjlist) 
+    iseq &= (bg1.badjlist == bg2.badjlist) 
+    iseq
+end
+
+# could be made to directly generate graph and save memory
+function asgraph(sys::AbstractSystem; variables=nothing, variablestoids=nothing)
+    vs     = isnothing(variables) ? states(sys) : variables    
+    eqdeps = equation_dependencies(sys, variables=vs)
+    vtois  = isnothing(variablestoids) ? Dict(convert(Variable, v) => i for (i,v) in enumerate(vs)) : variablestoids
+    asgraph(eqdeps, vtois)
+end
+
+# for each variable determine the equations that modify it
+function variable_dependencies(sys::AbstractSystem; variables=states(sys), variablestoids=nothing)
+    eqs   = equations(sys)
+    vtois = isnothing(variablestoids) ? Dict(convert(Variable, v) => i for (i,v) in enumerate(variables)) : variablestoids
+
+    deps = Set{Variable}()
+    badjlist = Vector{Vector{Int}}(undef, length(eqs))    
+    for (eidx,eq) in enumerate(eqs)
+        modified_states!(deps, eq, variables)
+        badjlist[eidx] = sort!([vtois[var] for var in deps])
+        empty!(deps)
+    end
+
+    fadjlist = [Vector{Int}() for i = 1:length(variables)]
+    ne = 0
+    for (eqidx,vidxs) in enumerate(badjlist)
+        foreach(vidx -> push!(fadjlist[vidx], eqidx), vidxs)
+        ne += length(vidxs)
+    end
+
+    BipartiteGraph(ne, fadjlist, badjlist)
+end
+
+# convert BipartiteGraph to LightGraph.SimpleDiGraph
+function asdigraph(g::BipartiteGraph, sys::AbstractSystem; variables = states(sys), equationsfirst = true)
+    neqs     = length(equations(sys))
+    nvars    = length(variables)
+    fadjlist = deepcopy(g.fadjlist)
+    badjlist = deepcopy(g.badjlist)
+
+    # offset is for determining indices for the second set of vertices
+    offset = equationsfirst ? neqs : nvars
+    for i = 1:offset
+        fadjlist[i] .+= offset
+    end
+
+    # add empty rows for vertices without connections
+    append!(fadjlist, [Vector{Int}() for i=1:(equationsfirst ? nvars : neqs)])
+    prepend!(badjlist, [Vector{Int}() for i=1:(equationsfirst ? neqs : nvars)])
+
+    SimpleDiGraph(g.ne, fadjlist, badjlist)
+end
+
+# maps the i'th eq to equations that depend on it
+function eqeq_dependencies(eqdeps::BipartiteGraph{T}, vardeps::BipartiteGraph{T}) where {T <: Integer}
+    g = SimpleDiGraph{T}(length(eqdeps.fadjlist))
+    
+    for (eqidx,sidxs) in enumerate(vardeps.badjlist)
+        # states modified by eqidx
+        for sidx in sidxs
+            # equations depending on sidx
+            foreach(v -> add_edge!(g, eqidx, v), eqdeps.badjlist[sidx])
+        end
+    end
+
+    g
+end
+
+# maps the i'th variable to variables that depend on it
+varvar_dependencies(eqdeps::BipartiteGraph{T}, vardeps::BipartiteGraph{T}) where {T <: Integer} = eqeq_dependencies(vardeps, eqdeps)

src/systems/jumps/jumpsystem.jl

@@ -1,7 +1,7 @@
 JumpType = Union{VariableRateJump, ConstantRateJump, MassActionJump}
 
-struct JumpSystem <: AbstractSystem
-    eqs::Vector{JumpType}
+struct JumpSystem{U <: ArrayPartition} <: AbstractSystem
+    eqs::U
     iv::Variable
     states::Vector{Variable}
     ps::Vector{Variable}
@@ -11,9 +11,22 @@ end
 
 function JumpSystem(eqs, iv, states, ps; systems = JumpSystem[],
                                           name = gensym(:JumpSystem))
-    JumpSystem(eqs, iv, convert.(Variable, states), convert.(Variable, ps), name, systems)
-end
 
+    ap = ArrayPartition(MassActionJump[], ConstantRateJump[], VariableRateJump[])
+    for eq in eqs
+        if eq isa MassActionJump 
+            push!(ap.x[1], eq)
+        elseif eq isa ConstantRateJump
+            push!(ap.x[2], eq)
+        elseif eq isa VariableRateJump
+            push!(ap.x[3], eq)
+        else
+            error("JumpSystem equations must contain MassActionJumps, ConstantRateJumps, or VariableRateJumps.")
+        end
+    end
+
+    JumpSystem{typeof(ap)}(ap, convert(Variable,iv), convert.(Variable, states), convert.(Variable, ps), name, systems)
+end
 
 
 generate_rate_function(js, rate) = build_function(rate, states(js), parameters(js),
@@ -26,6 +39,7 @@ generate_affect_function(js, affect, outputidxs) = build_function(affect, states
                                                       expression=Val{false},
                                                       headerfun=add_integrator_header,
                                                       outputidxs=outputidxs)[2]
+                                                      
 function assemble_vrj(js, vrj, statetoid)
     rate   = generate_rate_function(js, vrj.rate)
     outputvars = (convert(Variable,affect.lhs) for affect in vrj.affect!)
@@ -84,10 +98,13 @@ Generates a DiscreteProblem from an AbstractSystem
 function DiffEqBase.DiscreteProblem(sys::AbstractSystem, u0map, tspan::Tuple,
                                     parammap=DiffEqBase.NullParameters(); kwargs...)
     u0 = varmap_to_vars(u0map, states(sys))
-    p = varmap_to_vars(parammap, parameters(sys))
-    DiscreteProblem(u0, tspan, p; kwargs...)
+    p  = varmap_to_vars(parammap, parameters(sys))
+    f  = (du,u,p,t) -> du.=u    # identity function to make syms works
+    df = DiscreteFunction(f, syms=Symbol.(states(sys)))
+    DiscreteProblem(df, u0, tspan, p; kwargs...)
 end
 
+
 """
 ```julia
 function DiffEqBase.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)
@@ -96,25 +113,65 @@ function DiffEqBase.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)
 Generates a JumpProblem from a JumpSystem.
 """
 function DiffEqJump.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)
-    vrjs = Vector{VariableRateJump}()
-    crjs = Vector{ConstantRateJump}()
-    majs = Vector{MassActionJump}()
-    pvars = parameters(js)
+
     statetoid = Dict(convert(Variable,state) => i for (i,state) in enumerate(states(js)))
-    parammap = map((x,y)->Pair(x(),y),pvars,prob.p)
-
-    for j in equations(js)
-        if j isa ConstantRateJump
-            push!(crjs, assemble_crj(js, j, statetoid))
-        elseif j isa VariableRateJump
-            push!(vrjs, assemble_vrj(js, j, statetoid))
-        elseif j isa MassActionJump
-            push!(majs, assemble_maj(js, j, statetoid, parammap))
-        else
-            error("JumpSystems should only contain Constant, Variable or Mass Action Jumps.")
-        end
-    end
-    ((prob isa DiscreteProblem) && !isempty(vrjs)) && error("Use continuous problems such as an ODEProblem or a SDEProblem with VariableRateJumps")
+    parammap  = map((x,y)->Pair(x(),y), parameters(js), prob.p)
+    eqs       = equations(js)
+
+    majs = MassActionJump[assemble_maj(js, j, statetoid, parammap) for j in eqs.x[1]]
+    crjs = ConstantRateJump[assemble_crj(js, j, statetoid) for j in eqs.x[2]]
+    vrjs = VariableRateJump[assemble_vrj(js, j, statetoid) for j in eqs.x[3]]
+    ((prob isa DiscreteProblem) && !isempty(vrjs)) && error("Use continuous problems such as an ODEProblem or a SDEProblem with VariableRateJumps") 
     jset = JumpSet(Tuple(vrjs), Tuple(crjs), nothing, isempty(majs) ? nothing : majs)
-    JumpProblem(prob, aggregator, jset)
+
+    if needs_vartojumps_map(aggregator) || needs_depgraph(aggregator)
+        jdeps = asgraph(js)
+        vdeps = variable_dependencies(js)
+        vtoj = jdeps.badjlist
+        jtov = vdeps.badjlist
+        jtoj = needs_depgraph(aggregator) ? eqeq_dependencies(jdeps, vdeps).fadjlist : nothing
+    else
+        vtoj = nothing; jtov = nothing; jtoj = nothing
+    end
+
+    JumpProblem(prob, aggregator, jset; dep_graph=jtoj, vartojumps_map=vtoj, jumptovars_map=jtov)
 end
+
+
+### Functions to determine which states a jump depends on
+function get_variables!(dep, jump::Union{ConstantRateJump,VariableRateJump}, variables)
+    foreach(var -> (var in variables) && push!(dep, var), vars(jump.rate))
+    dep
+end
+
+function get_variables!(dep, jump::MassActionJump, variables)
+    jsr = jump.scaled_rates
+
+    if jsr isa Variable
+        (jsr in variables) && push!(dep, jsr)
+    elseif jsr isa Operation
+        foreach(var -> (var in variables) && push!(dep, var),  vars(jsr))            
+    end
+
+    for varasop in jump.reactant_stoch
+        var = convert(Variable, varasop[1])
+        (var in variables) && push!(dep, var)
+    end
+
+    dep
+end
+
+### Functions to determine which states are modified by a given jump
+function modified_states!(mstates, jump::Union{ConstantRateJump,VariableRateJump}, sts)
+    for eq in jump.affect!
+        st = convert(Variable, eq.lhs)
+        (st in sts) && push!(mstates, st)
+    end
+end
+
+function modified_states!(mstates, jump::MassActionJump, sts)
+    for (state,stoich) in jump.net_stoch
+        st = convert(Variable, state)
+        (st in sts) && push!(mstates, st)
+    end
+end

src/systems/reaction/reactionsystem.jl

@@ -149,7 +149,7 @@ function jumpratelaw(rx)
     @unpack rate, substrates, substoich, only_use_rate = rx
     rl = deepcopy(rate)
     for op in get_variables(rx.rate)
-        rl = substitute_expr!(rl,op=>var2op(op.op))
+        rl = substitute(rl,op=>var2op(op.op))
     end
     if !only_use_rate
         for (i,stoich) in enumerate(substoich)

test/dep_graphs.jl

@@ -0,0 +1,74 @@
+using ModelingToolkit, LightGraphs
+
+# use a ReactionSystem to generate systems for testing
+@parameters k1 k2 t
+@variables S(t) I(t) R(t)
+
+rxs = [Reaction(k1, nothing, [S]),
+       Reaction(k1, [S], nothing),
+       Reaction(k2, [S,I], [I], [1,1], [2]),
+       Reaction(k2, [S,R], [S], [2,1], [2]),
+       Reaction(k1*I, nothing, [R]),
+       Reaction(k1*k2/(1+t), [S], [R])]
+rs = ReactionSystem(rxs, t, [S,I,R], [k1,k2])
+
+
+################################# 
+#      testing for Jumps 
+#################################
+js = convert(JumpSystem, rs)
+S  = convert(Variable,S); I = convert(Variable,I); R = convert(Variable,R)
+k1 = convert(Variable,k1); k2 = convert(Variable,k2)
+
+# eq to vars they depend on
+eq_sdeps  = [Variable[], [S], [S,I], [S,R], [I], [S]]
+eq_sidepsf = [Int[], [1], [1,2], [1,3], [2], [1]]
+eq_sidepsb = [[2,3,4,6], [3,5],[4]]
+deps = equation_dependencies(js)
+@test all(i -> isequal(Set(eq_sdeps[i]),Set(deps[i])), 1:length(rxs))
+depsbg = asgraph(js)
+@test depsbg.fadjlist == eq_sidepsf
+@test depsbg.badjlist == eq_sidepsb
+
+# eq to params they depend on
+eq_pdeps    = [[k1],[k1],[k2],[k2],[k1],[k1,k2]]
+eq_pidepsf = [[1],[1],[2],[2],[1],[1,2]]
+eq_pidepsb = [[1,2,5,6],[3,4,6]]
+deps = equation_dependencies(js, variables=parameters(js))
+@test all(i -> isequal(Set(eq_pdeps[i]),Set(deps[i])), 1:length(rxs))
+depsbg2 = asgraph(js, variables=parameters(js))
+@test depsbg2.fadjlist == eq_pidepsf
+@test depsbg2.badjlist == eq_pidepsb
+
+# var to eqs that modify them
+s_eqdepsf = [[1,2,3,6],[3],[4,5,6]]
+s_eqdepsb = [[1],[1],[1,2],[3],[3],[1,3]]
+ne        = 8
+bg        = BipartiteGraph(ne, s_eqdepsf, s_eqdepsb)
+deps2     = variable_dependencies(js)
+@test isequal(bg,deps2)
+
+# eq to eqs that depend on them
+eq_eqdeps = [[2,3,4,6],[2,3,4,6],[2,3,4,5,6],[4],[4],[2,3,4,6]]
+dg = SimpleDiGraph(6)
+for (eqidx,eqdeps) in enumerate(eq_eqdeps)
+    for eqdepidx in eqdeps
+       add_edge!(dg, eqidx, eqdepidx)
+    end
+end
+dg3 = eqeq_dependencies(depsbg,deps2)
+@test dg == dg3
+
+# var to vars that depend on them
+var_vardeps = [[1,2,3],[1,2,3],[3]]
+ne = 7
+dg = SimpleDiGraph(3)
+for (vidx,vdeps) in enumerate(var_vardeps)
+    for vdepidx in vdeps
+       add_edge!(dg, vidx, vdepidx)
+    end
+end
+dg4 = varvar_dependencies(depsbg,deps2)
+@test dg == dg4
+
+