weak convergence

test/runtests.jl

@@ -2,14 +2,15 @@ using StochasticDiffEq, DiffEqDevTools, DiffEqProblemLibrary
 using Base.Test
 
 const TEST_PLOT = false
-
+const LONGER_TESTS = false
 #SDE
 @time @testset "Linear SDE Tests" begin include("sde/sde_linear_tests.jl") end
 @time @testset "Two-dimensional Linear SDE Tests" begin include("sde/sde_twodimlinear_tests.jl") end
 @time @testset "Additive SDE Tests" begin include("sde/sde_additive_tests.jl") end
 @time @testset "Rossler Order Tests" begin include("sde/sde_rosslerorder_tests.jl") end
-@time @testset "SDE Convergence Tests" begin include("sde/sde_convergence_tests.jl") end
-@time @testset "SDE Number Type Tests" begin include("sde/sde_numbertype_tests.jl") end
+@time @testset "Convergence Tests" begin include("sde/sde_convergence_tests.jl") end
+LONGER_TESTS && @time @testset "Weak Convergence Tests" begin include("weak_convergence.jl") end
+@time @testset "Number Type Tests" begin include("sde/sde_numbertype_tests.jl") end
 @time @testset "Oval2" begin include("oval2_test.jl") end
 
 #Adaptive SDE

test/sde/sde_convergence_tests.jl

@@ -1,6 +1,6 @@
 @everywhere using StochasticDiffEq, DiffEqProblemLibrary, DiffEqDevTools
 srand(100)
-dts = 1./2.^(10:-1:4) #14->7 good plot
+dts = 1./2.^(10:-1:2) #14->7 good plot
 
 prob = prob_sde_wave
 sim  = test_convergence(dts,prob,EM(),numMonte=Int(1e1))

test/sde/sde_twodimlinear_tests.jl

@@ -18,13 +18,14 @@ sol = solve(prob,SRIW1(),dt=1/2^(3),progress=true,progress_steps=1)
 #Now do the simulation 5 times in parallel. Return an array
 solArr = monte_carlo_simulation(prob,SRIW1(),dt=1//2^(3),numMonte=5)
 
-TEST_PLOT && plot(sol,plot_analytic=true)
+#TEST_PLOT && plot(sol,plot_analytic=true)
 
 ## Convergence Testing
 println("Convergence Test on 2D Linear")
 dts = 1./2.^(7:-1:4) #14->7 good plot
 
 sim = test_convergence(dts,prob,EM(),numMonte=10)
+
 @test abs(sim.𝒪est[:l2]-.5) < 0.1
 
 sim2 = test_convergence(dts,prob,RKMil(),numMonte=10)

test/weak_convergence.jl

@@ -0,0 +1,65 @@
+@everywhere using StochasticDiffEq, DiffEqProblemLibrary, DiffEqDevTools, Base.Test
+srand(100)
+dts = 1./2.^(10:-1:2) #14->7 good plot
+
+prob = prob_sde_linear
+sim  = test_convergence(dts,prob,EM(),numMonte=Int(1e4))
+@test abs(sim.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l∞]-1) < 0.3
+sim2 = test_convergence(dts,prob,RKMil(),numMonte=Int(1e4))
+@test abs(sim2.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l∞]-1) < 0.3
+sim3 = test_convergence(dts,prob,SRI(),numMonte=Int(1e4))
+@test abs(sim3.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l∞]-2) < 0.3
+sim4 = test_convergence(dts,prob,SRIW1(),numMonte=Int(1e4))
+@test abs(sim4.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l∞]-2) < 0.3
+
+prob = prob_sde_2Dlinear
+sim  = test_convergence(dts,prob,EM(),numMonte=Int(1e4))
+@test abs(sim.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l∞]-1) < 0.3
+sim2 = test_convergence(dts,prob,RKMil(),numMonte=Int(1e4))
+@test abs(sim2.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l∞]-1) < 0.3
+sim3 = test_convergence(dts,prob,SRI(),numMonte=Int(1e4))
+@test abs(sim3.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l∞]-2) < 0.3
+sim4 = test_convergence(dts,prob,SRIW1(),numMonte=Int(1e4))
+@test abs(sim4.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l∞]-2) < 0.35
+
+prob = prob_sde_additive
+sim  = test_convergence(dts,prob,EM(),numMonte=Int(1e4))
+@test abs(sim.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim.𝒪est[:weak_l∞]-1) < 0.3
+sim2 = test_convergence(dts,prob,RKMil(),numMonte=Int(1e4))
+@test abs(sim2.𝒪est[:weak_final]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l2]-1) < 0.3
+@test abs(sim2.𝒪est[:weak_l∞]-1) < 0.3
+sim3 = test_convergence(dts,prob,SRI(),numMonte=Int(1e4))
+@test abs(sim3.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim3.𝒪est[:weak_l∞]-2) < 0.3
+sim4 = test_convergence(dts,prob,SRIW1(),numMonte=Int(1e4))
+@test abs(sim4.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim4.𝒪est[:weak_l∞]-2) < 0.35
+sim5 = test_convergence(dts,prob,SRA(),numMonte=Int(1e4))
+@test abs(sim5.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim5.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim5.𝒪est[:weak_l∞]-2) < 0.3
+sim6 = test_convergence(dts,prob,SRA1(),numMonte=Int(1e4))
+@test abs(sim6.𝒪est[:weak_final]-2) < 0.3
+@test abs(sim6.𝒪est[:weak_l2]-2) < 0.3
+@test abs(sim6.𝒪est[:weak_l∞]-2) < 0.3