simplified continuous adjoints

REQUIRE

@@ -4,3 +4,4 @@ Compat 0.17.0
 ForwardDiff
 DiffEqDiffTools
 DiffEqCallbacks
+QuadGK

src/DiffEqSensitivity.jl

@@ -2,7 +2,7 @@ __precompile__()
 
 module DiffEqSensitivity
 
-using DiffEqBase, Compat, ForwardDiff, DiffEqDiffTools, DiffEqCallbacks
+using DiffEqBase, Compat, ForwardDiff, DiffEqDiffTools, DiffEqCallbacks, QuadGK
 
 abstract type SensitivityFunction end
 
@@ -13,5 +13,6 @@ include("adjoint_sensitivity.jl")
 export extract_local_sensitivities
 
 export ODELocalSensitvityFunction, ODELocalSensitivityProblem, SensitivityFunction,
-       ODEAdjointSensitivityProblem, ODEAdjointProblem, AdjointSensitivityIntegrand
+       ODEAdjointSensitivityProblem, ODEAdjointProblem, AdjointSensitivityIntegrand,
+       adjoint_sensitivities
 end # module

src/adjoint_sensitivity.jl

@@ -94,7 +94,7 @@ function ODEAdjointProblem(sol,g,t=nothing,dg=nothing,
   end
 
   u0 = zeros(sol.prob.u0)'
-  y = sol(tspan[1]) # TODO: Has to start at interpolation value!
+  y = copy(sol(tspan[1])) # TODO: Has to start at interpolation value!
   λ = similar(u0)
   sense = ODEAdjointSensitvityFunction(f,uf,pg,u0,jac_config,pg_config,p,
                                        λ,alg,discrete,
@@ -177,3 +177,17 @@ function (S::AdjointSensitivityIntegrand)(t)
   out = similar(S.p)
   S(out,t)
 end
+
+
+function adjoint_sensitivities(sol,alg,g,t=nothing,dg=nothing;
+                               abstol=1e-6,reltol=1e-3,
+                               iabstol = abstol, ireltol=reltol,
+                               kwargs...)
+
+  adj_prob = ODEAdjointProblem(sol,g,t,dg)
+  adj_sol = solve(adj_prob,alg,abstol=abstol,reltol=reltol)
+  integrand = AdjointSensitivityIntegrand(sol,adj_sol)
+  res,err = quadgk(integrand,sol.prob.tspan[1],sol.prob.tspan[2],
+                   abstol=iabstol,reltol=ireltol)
+  res
+end

test/adjoint.jl

@@ -14,21 +14,22 @@ sol = solve(prob,Vern9(),abstol=1e-14,reltol=1e-14)
 
 t = 0.0:0.5:10.0 # TODO: Add end point handling for callback
 # g(t,u,i) = (1-u)^2/2, L2 away from 1
-dg(out,u,i) = (out.=1.-u)
+dg(out,u,i) = (out.=1.0.-u)
+
+easy_res = adjoint_sensitivities(sol,Vern9(),dg,t,abstol=1e-14,
+                                 reltol=1e-14,iabstol=1e-14,ireltol=1e-12)
 
 adj_prob = ODEAdjointProblem(sol,dg,t)
 adj_sol = solve(adj_prob,Vern9(),abstol=1e-14,reltol=1e-14)
 integrand = AdjointSensitivityIntegrand(sol,adj_sol)
-res,err = quadgk(integrand,0.0,10.0,abstol=1e-14,reltol=1e-10)
+res,err = quadgk(integrand,0.0,10.0,abstol=1e-14,reltol=1e-12)
 
-using Plots
-gr()
-plot(adj_sol,tspan=(0.0,10.0))
+@test norm(res - easy_res) < 1e-14
 
 t_short = 0.5:0.5:10.0
 function G(p)
   tmp_prob = problem_new_parameters(prob,p)
-  sol = solve(tmp_prob,Vern9(),abstol=1e-14,reltol=1e-14,saveat=t_short,save_start=false)
+  sol = solve(tmp_prob,Vern9(),abstol=1e-14,reltol=1e-14,saveat=t)
   A = convert(Array,sol)
   sum(((1-A).^2)./2)
 end
@@ -42,37 +43,31 @@ res3 = Calculus.gradient(G,[1.5,1.0,3.0])
 # Do a continuous adjoint problem
 
 # Energy calculation
-g(t,u,p) = (out.=(sum(u).^2) ./ 2)
+g(t,u,p) = (sum(u).^2) ./ 2
 # Gradient of (u1 + u2)^2 / 2
 function dg(out,t,u,p)
   out[1]= u[1] + u[2]
   out[2]= u[1] + u[2]
 end
 
 adj_prob = ODEAdjointProblem(sol,g,nothing,dg)
-adj_sol = solve(adj_prob,Vern9(),abstol=1e-14,reltol=1e-14)
+adj_sol = solve(adj_prob,Vern9(),abstol=1e-14,reltol=1e-10)
 integrand = AdjointSensitivityIntegrand(sol,adj_sol)
 res,err = quadgk(integrand,0.0,10.0,abstol=1e-14,reltol=1e-10)
 
+easy_res = adjoint_sensitivities(sol,Vern9(),g,nothing,dg,abstol=1e-14,
+                                 reltol=1e-14,iabstol=1e-14,ireltol=1e-12)
 
-function G(p)
-  tmp_prob = problem_new_parameters(prob,p)
-  sol = solve(tmp_prob,Vern9(),abstol=1e-14,reltol=1e-14,saveat=0.0:0.00001:10.0)
-  # Trapezoidal rule since quadgk can't autodiff
-  A = convert(Array,sol)
-  sum((sum(A,1).^2)./2)* 0.00001
-  end
-G([1.5,1.0,3.0])
-res2 = ForwardDiff.gradient(G,[1.5,1.0,3.0])
+@test norm(easy_res - res) < 1e-8
 
-function G_calc(p)
+function G(p)
   tmp_prob = problem_new_parameters(prob,p)
   sol = solve(tmp_prob,Vern9(),abstol=1e-14,reltol=1e-14)
   res,err = quadgk((t)-> (sum(sol(t)).^2)./2,0.0,10.0,abstol=1e-14,reltol=1e-10)
   res
 end
+res2 = ForwardDiff.gradient(G,[1.5,1.0,3.0])
+res3 = Calculus.gradient(G,[1.5,1.0,3.0])
 
-res3 = Calculus.gradient(G_calc,[1.5,1.0,3.0])
-
-@test norm(res' - res2) < 1e-4
+@test norm(res' - res2) < 1e-8
 @test norm(res' - res3) < 1e-6

test/runtests.jl

@@ -2,3 +2,4 @@ using DiffEqSensitivity
 using Base.Test
 
 @testset "Local Sensitivity" begin include("local.jl") end
+@testset "Adjoint Sensitivity" begin include("adjoint.jl") end