Merge pull request #317 from isaacsas/jumpsystems

JumpSystems for constant and variable rate jumps

Author: ChrisRackauckas

Project.toml

@@ -6,6 +6,7 @@ version = "3.1.1"
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+DiffEqJump = "c894b116-72e5-5b58-be3c-e6d8d4ac2b12"
 DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"

src/ModelingToolkit.jl

@@ -5,6 +5,7 @@ using StaticArrays, LinearAlgebra, SparseArrays
 using Latexify, Unitful, ArrayInterface
 using MacroTools
 using UnPack: @unpack
+using DiffEqJump
 
 using Base.Threads
 import MacroTools: splitdef, combinedef, postwalk, striplines
@@ -86,6 +87,8 @@ include("systems/diffeqs/first_order_transform.jl")
 include("systems/diffeqs/modelingtoolkitize.jl")
 include("systems/diffeqs/validation.jl")
 
+include("systems/jumps/jumpsystem.jl")
+
 include("systems/nonlinear/nonlinearsystem.jl")
 
 include("systems/optimization/optimizationsystem.jl")
@@ -99,7 +102,8 @@ include("build_function.jl")
 
 export ODESystem, ODEFunction
 export SDESystem, SDEFunction
-export ODEProblem, SDEProblem, NonlinearProblem, OptimizationProblem
+export JumpSystem
+export ODEProblem, SDEProblem, NonlinearProblem, OptimizationProblem, JumpProblem
 export NonlinearSystem, OptimizationSystem
 export ode_order_lowering
 export PDESystem

src/build_function.jl

@@ -56,11 +56,50 @@ function build_function(args...;target = JuliaTarget(),kwargs...)
   _build_function(target,args...;kwargs...)
 end
 
+function addheader(ex, fargs, iip; X=gensym(:MTIIPVar))
+  if iip  
+    wrappedex = :(
+        ($X,$(fargs.args...)) -> begin
+        $ex
+        nothing
+      end
+    )
+  else
+    wrappedex = :(
+      ($(fargs.args...),) -> begin
+        $ex
+      end
+    )  
+  end
+  wrappedex
+end
+
+function add_integrator_header(ex, fargs, iip; X=gensym(:MTIIPVar))
+  integrator = gensym(:MTKIntegrator)
+  if iip  
+    wrappedex = :(
+        $integrator -> begin 
+        ($X,$(fargs.args...)) = (($integrator).u,($integrator).u,($integrator).p,($integrator).t)
+        $ex
+        nothing
+      end
+    )
+  else
+    wrappedex = :(
+      $integrator -> begin 
+      ($(fargs.args...),) = (($integrator).u,($integrator).p,($integrator).t)
+        $ex
+      end
+    )  
+  end
+  wrappedex
+end
+
 # Scalar output
 function _build_function(target::JuliaTarget, op::Operation, args...;
                          conv = simplified_expr, expression = Val{true},
                          checkbounds = false, constructor=nothing,
-                         linenumbers = true)
+                         linenumbers = true, headerfun=addheader)
 
     argnames = [gensym(:MTKArg) for i in 1:length(args)]
     arg_pairs = map(vars_to_pairs,zip(argnames,args))
@@ -74,13 +113,8 @@ function _build_function(target::JuliaTarget, op::Operation, args...;
     bounds_block = checkbounds ? let_expr : :(@inbounds begin $let_expr end)
 
     fargs = Expr(:tuple,argnames...)
-
-    oop_ex = :(
-        ($(fargs.args...),) -> begin
-            $bounds_block
-        end
-    )
-
+    oop_ex = headerfun(bounds_block, fargs, false)
+        
     if !linenumbers
         oop_ex = striplines(oop_ex)
     end
@@ -95,8 +129,8 @@ end
 function _build_function(target::JuliaTarget, rhss, args...;
                          conv = simplified_expr, expression = Val{true},
                          checkbounds = false, constructor=nothing,
-                         linenumbers = false, multithread=false)
-
+                         linenumbers = false, multithread=false, 
+                         headerfun=addheader, outputidxs=nothing)
     argnames = [gensym(:MTKArg) for i in 1:length(args)]
     arg_pairs = map(vars_to_pairs,zip(argnames,args))
     ls = reduce(vcat,first.(arg_pairs))
@@ -106,6 +140,8 @@ function _build_function(target::JuliaTarget, rhss, args...;
     fname = gensym(:ModelingToolkitFunction)
     fargs = Expr(:tuple,argnames...)
 
+
+    oidx = isnothing(outputidxs) ? (i -> i) : (i -> outputidxs[i])
     X = gensym(:MTIIPVar)
 	if eltype(eltype(rhss)) <: AbstractArray # Array of arrays of arrays
 		ip_sys_exprs = reduce(vcat,[vec(reduce(vcat,[vec([:($X[$i][$j][$k] = $(conv(rhs))) for (k, rhs) ∈ enumerate(rhsel2)]) for (j, rhsel2) ∈ enumerate(rhsel)],init=Expr[])) for (i,rhsel) ∈ enumerate(rhss)],init=Expr[])
@@ -118,7 +154,7 @@ function _build_function(target::JuliaTarget, rhss, args...;
     elseif rhss isa SparseMatrixCSC
         ip_sys_exprs = [:($X.nzval[$i] = $(conv(rhs))) for (i, rhs) ∈ enumerate(rhss.nzval)]
     else
-        ip_sys_exprs = [:($X[$i] = $(conv(rhs))) for (i, rhs) ∈ enumerate(rhss)]
+        ip_sys_exprs = [:($X[$(oidx(i))] = $(conv(rhs))) for (i, rhs) ∈ enumerate(rhss)]
     end
 
     ip_let_expr = Expr(:let, var_eqs, build_expr(:block, ip_sys_exprs))
@@ -165,26 +201,20 @@ function _build_function(target::JuliaTarget, rhss, args...;
     arr_bounds_block = checkbounds ? arr_let_expr : :(@inbounds begin $arr_let_expr end)
     ip_bounds_block = checkbounds ? ip_let_expr : :(@inbounds begin $ip_let_expr end)
 
-    oop_ex = :(
-        ($(fargs.args...),) -> begin
-            # If u is a weird non-StaticArray type and we want a sparse matrix, just do the optimized sparse anyways
-            if $(fargs.args[1]) isa Array || (!(typeof($(fargs.args[1])) <: StaticArray) && $(rhss isa SparseMatrixCSC))
-                return $arr_bounds_block
-            else
-                X = $bounds_block
-                construct = $_constructor
-                return construct(X)
-            end
-        end
-    )
-
-    iip_ex = :(
-        ($X,$(fargs.args...)) -> begin
-            $ip_bounds_block
-            nothing
-        end
+    oop_body_block = :(
+      # If u is a weird non-StaticArray type and we want a sparse matrix, just do the optimized sparse anyways
+      if $(fargs.args[1]) isa Array || (!(typeof($(fargs.args[1])) <: StaticArray) && $(rhss isa SparseMatrixCSC))
+          return $arr_bounds_block
+      else
+          X = $bounds_block
+          construct = $_constructor
+          return construct(X)
+      end
     )
 
+    oop_ex = headerfun(oop_body_block, fargs, false)
+    iip_ex = headerfun(ip_bounds_block, fargs, true; X=X)
+    
     if !linenumbers
         oop_ex = striplines(oop_ex)
         iip_ex = striplines(iip_ex)

src/systems/jumps/jumpsystem.jl

@@ -0,0 +1,68 @@
+JumpType = Union{VariableRateJump, ConstantRateJump, MassActionJump}
+
+struct JumpSystem <: AbstractSystem
+    eqs::Vector{JumpType}
+    iv::Variable
+    states::Vector{Variable}
+    ps::Vector{Variable}
+    name::Symbol
+    systems::Vector{JumpSystem}
+end
+
+function JumpSystem(eqs, iv, states, ps; systems = JumpSystem[], 
+                                          name = gensym(:JumpSystem))
+    JumpSystem(eqs, iv, convert.(Variable, states), convert.(Variable, ps), name, systems)
+end
+
+
+
+generate_rate_function(js, rate) = build_function(rate, states(js), parameters(js), 
+                                                  independent_variable(js), 
+                                                  expression=Val{false})
+
+generate_affect_function(js, affect, outputidxs) = build_function(affect, states(js), 
+                                                      parameters(js), 
+                                                      independent_variable(js),
+                                                      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!)
+    outputidxs = ((statetoid[var] for var in outputvars)...,)
+    affect = generate_affect_function(js, vrj.affect!, outputidxs)
+    VariableRateJump(rate, affect)
+end
+
+function assemble_crj(js, crj, statetoid)
+    rate   = generate_rate_function(js, crj.rate)
+    outputvars = (convert(Variable,affect.lhs) for affect in crj.affect!)
+    outputidxs = ((statetoid[var] for var in outputvars)...,)
+    affect = generate_affect_function(js, crj.affect!, outputidxs)
+    ConstantRateJump(rate, affect)
+end
+
+"""
+```julia
+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}()
+    statetoid = Dict(convert(Variable,state) => i for (i,state) in enumerate(states(js)))
+    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))
+        else
+            (j isa MassActionJump) && error("Generation of JumpProblems with MassActionJumps is not yet supported.")
+        end
+    end
+    ((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, nothing)
+    JumpProblem(prob, aggregator, jset)
+end

test/jumpsystem.jl

@@ -0,0 +1,106 @@
+using ModelingToolkit, DiffEqBase, DiffEqJump, Test, LinearAlgebra
+MT = ModelingToolkit
+
+# basic MT SIR model with tweaks
+@parameters β γ t
+@variables S I R
+rate₁   = β*S*I
+affect₁ = [S ~ S - 1, I ~ I + 1]
+rate₂   = γ*I+t
+affect₂ = [I ~ I - 1, R ~ R + 1]
+j₁      = ConstantRateJump(rate₁,affect₁)
+j₂      = VariableRateJump(rate₂,affect₂)
+js      = JumpSystem([j₁,j₂], t, [S,I,R], [β,γ])
+statetoid = Dict(convert(Variable,state) => i for (i,state) in enumerate(states(js)))
+mtjump1 = MT.assemble_crj(js, j₁, statetoid)
+mtjump2 = MT.assemble_vrj(js, j₂, statetoid)
+
+# doc version
+rate1(u,p,t) = (0.1/1000.0)*u[1]*u[2]
+function affect1!(integrator)
+  integrator.u[1] -= 1
+  integrator.u[2] += 1
+end
+jump1 = ConstantRateJump(rate1,affect1!)
+rate2(u,p,t) = 0.01u[2]+t
+function affect2!(integrator)
+  integrator.u[2] -= 1
+  integrator.u[3] += 1
+end
+jump2 = VariableRateJump(rate2,affect2!)
+
+# test crjs
+u = [100, 9, 5]
+p = (0.1/1000,0.01)
+tf = 1.0
+mutable struct TestInt{U,V,T}
+    u::U
+    p::V
+    t::T
+end
+mtintegrator = TestInt(u,p,tf)
+integrator   = TestInt(u,p,tf)
+@test abs(mtjump1.rate(u,p,tf) - jump1.rate(u,p,tf)) < 10*eps()
+@test abs(mtjump2.rate(u,p,tf) - jump2.rate(u,p,tf)) < 10*eps()
+mtjump1.affect!(mtintegrator)
+jump1.affect!(integrator)
+@test all(integrator.u .== mtintegrator.u) 
+mtintegrator.u .= u; integrator.u .= u
+mtjump2.affect!(mtintegrator)
+jump2.affect!(integrator)
+@test all(integrator.u .== mtintegrator.u)
+
+# test MT can make and solve a jump problem
+rate₃   = γ*I
+affect₃ = [I ~ I - 1, R ~ R + 1]
+j₃ = ConstantRateJump(rate₃,affect₃)
+js2 = JumpSystem([j₁,j₃], t, [S,I,R], [β,γ])
+u₀ = [999,1,0]; p = (0.1/1000,0.01); tspan = (0.,250.)
+dprob = DiscreteProblem(u₀,tspan,p)
+jprob = JumpProblem(js2, dprob, Direct(), save_positions=(false,false))
+Nsims = 10000
+function getmean(jprob,Nsims)
+  m = 0.0
+  for i = 1:Nsims
+    sol = solve(jprob, SSAStepper())
+    m += sol[end,end]
+  end
+  m/Nsims
+end
+m = getmean(jprob,Nsims)
+
+#test the MT JumpProblem rates/affects are correct
+rate2(u,p,t) = 0.01u[2]
+jump2 = ConstantRateJump(rate2,affect2!)
+mtjumps = jprob.discrete_jump_aggregation
+@test abs(mtjumps.rates[1](u,p,tf) - jump1.rate(u,p,tf)) < 10*eps()
+@test abs(mtjumps.rates[2](u,p,tf) - jump2.rate(u,p,tf)) < 10*eps()
+mtjumps.affects![1](mtintegrator)
+jump1.affect!(integrator)
+@test all(integrator.u .== mtintegrator.u) 
+mtintegrator.u .= u; integrator.u .= u
+mtjumps.affects![2](mtintegrator)
+jump2.affect!(integrator)
+@test all(integrator.u .== mtintegrator.u)
+
+# direct vers
+p = (0.1/1000,0.01)
+prob = DiscreteProblem([999,1,0],(0.0,250.0),p)
+r1(u,p,t) = (0.1/1000.0)*u[1]*u[2]
+function a1!(integrator)
+  integrator.u[1] -= 1
+  integrator.u[2] += 1
+end
+j1 = ConstantRateJump(r1,a1!)
+r2(u,p,t) = 0.01u[2]
+function a2!(integrator)
+  integrator.u[2] -= 1
+  integrator.u[3] += 1
+end
+j2 = ConstantRateJump(r2,a2!)
+jset = JumpSet((),(j1,j2),nothing,nothing)
+jprob = JumpProblem(prob,Direct(),jset, save_positions=(false,false))
+m2 = getmean(jprob,Nsims)
+
+# test JumpSystem solution agrees with direct version
+@test abs(m-m2) ./ m < .01