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remove generate_weak_solution and instead use test_convergence #360

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Sep 17, 2020
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remove generate_weak_solution and instead use test_convergence #360

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125 changes: 68 additions & 57 deletions test/weak_convergence/PL1WM.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -7,18 +7,9 @@ import LinearAlgebra # for the normn
using StochasticDiffEq
using Test
using Random
using DiffEqDevTools
#using DiffEqGPU

function generate_weak_solutions(prob, alg, dts, numtraj; ensemblealg=EnsembleThreads())
sols = []
for i in 1:length(dts)
sol = solve(prob,alg;ensemblealg=ensemblealg,dt=dts[i],save_start=false,save_everystep=false,weak_timeseries_errors=false,weak_dense_errors=false,trajectories=Int(numtraj))
println(i)
push!(sols,sol)
end
return sols
end

function prob_func(prob, i, repeat)
remake(prob,seed=seeds[i])
end
Expand Down Expand Up @@ -50,15 +41,14 @@ ensemble_prob = EnsembleProblem(prob;
output_func = (sol,i) -> (h1(sol[end]),false),
prob_func = prob_func
)
_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u) .- u₀.*exp(1.0*(p[1]))) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.3

#using Plots; convergence_plot = plot(dts, errors, xaxis=:log, yaxis=:log)
#savefig(convergence_plot, "PL1WM-scalar.png")
println("PL1WM:", m)
sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)
@test abs(sim.𝒪est[:weak_final]-2) < 0.34 # order is 2.34
println("PL1WM:", sim.𝒪est[:weak_final])


"""
Expand Down Expand Up @@ -87,14 +77,13 @@ seed = 100
Random.seed!(seed)
seeds = rand(UInt, numtraj)


_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u) .- u₀.*exp(1.0*(p[1]))) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.3

println("PL1WM:", m)
sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)
@test abs(sim.𝒪est[:weak_final]-2) < 0.34 # order is 2.34
println("PL1WM:", sim.𝒪est[:weak_final])

"""
Test non-commutative noise SDEs (iip)
Expand Down Expand Up @@ -144,15 +133,13 @@ seed = 100
Random.seed!(seed)
seeds = rand(UInt, numtraj)


_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u)-u₀[1]*exp(2*1.0)) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.33

println("PL1WM:", m)

sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀[1]*exp(2*1.0)
)
@test abs(sim.𝒪est[:weak_final]-2) < 0.33 # order is 1.6748033428458136
println("PL1WM:", sim.𝒪est[:weak_final])


"""
Expand Down Expand Up @@ -186,14 +173,13 @@ seed = 100
Random.seed!(seed)
seeds = rand(UInt, numtraj)

_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u)-1//100*exp(301//100)) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.3

println("PL1WM:", m)

sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=1//100*exp(301//100)
)
@test abs(sim.𝒪est[:weak_final]-2) < 0.3
println("PL1WM:", sim.𝒪est[:weak_final])


"""
Expand All @@ -217,15 +203,26 @@ ensemble_prob = EnsembleProblem(prob;
output_func = (sol,i) -> (sol[end],false),
prob_func = prob_func
)
_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())
_solutions1 = @time generate_weak_solutions(ensemble_prob, PL1WMA(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u) .- u₀.*exp(1.0*(p[1]))) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.3
@test minimum(_solutions .≈ _solutions1)
sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)

@test abs(sim.𝒪est[:weak_final]-2) < 0.3
println("PL1WM:", sim.𝒪est[:weak_final])

println("PL1WM:", m)
sim1 = test_convergence(dts,ensemble_prob,PL1WMA(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)

@test abs(sim1.𝒪est[:weak_final]-2) < 0.3
println("PL1WMA:", sim1.𝒪est[:weak_final])

@test minimum(sim.solutions .≈ sim1.solutions)

#inplace

Expand All @@ -236,13 +233,27 @@ gadd!(du,u,p,t) = @.(du = p[2])

prob = SDEProblem(fadd!,gadd!,u₀,tspan,p)
ensemble_prob = EnsembleProblem(prob;
output_func = (sol,i) -> (sol[end],false),
output_func = (sol,i) -> (sol[end][1],false),
prob_func = prob_func
)
_solutions = @time generate_weak_solutions(ensemble_prob, PL1WM(), dts, numtraj, ensemblealg=EnsembleThreads())
_solutions1 = @time generate_weak_solutions(ensemble_prob, PL1WMA(), dts, numtraj, ensemblealg=EnsembleThreads())

errors = [LinearAlgebra.norm(Statistics.mean(sol.u) .- u₀.*exp(1.0*(p[1]))) for sol in _solutions]
m = log(errors[end]/errors[1])/log(dts[end]/dts[1])
@test -(m-2) < 0.3
@test minimum(_solutions .≈ _solutions1)

sim = test_convergence(dts,ensemble_prob,PL1WM(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)

@test abs(sim.𝒪est[:weak_final]-2) < 0.3
println("PL1WM:", sim.𝒪est[:weak_final])

sim1 = test_convergence(dts,ensemble_prob,PL1WMA(),
save_everystep=false,trajectories=numtraj,save_start=false,adaptive=false,
weak_timeseries_errors=false,weak_dense_errors=false,
expected_value=u₀.*exp(1.0*(p[1]))
)

@test abs(sim1.𝒪est[:weak_final]-2) < 0.3
println("PL1WMA:", sim1.𝒪est[:weak_final])

@test minimum(sim.solutions .≈ sim1.solutions)