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author title
Chris Rackauckas
Adaptive Efficiency Tests
 
using Distributed
addprocs(2)

p1 = Vector{Any}(undef,3)
p2 = Vector{Any}(undef,3)
p3 = Vector{Any}(undef,3)

@everywhere begin
  using DiffEqMonteCarlo, StochasticDiffEq, DiffEqProblemLibrary, DiffEqNoiseProcess, Plots, ParallelDataTransfer
  using DiffEqProblemLibrary.SDEProblemLibrary: importsdeproblems; importsdeproblems()
  import DiffEqProblemLibrary.SDEProblemLibrary: prob_sde_additive,
              prob_sde_linear, prob_sde_wave
end
Error: On worker 2:
ArgumentError: Package DiffEqMonteCarlo not found in current path:
- Run `import Pkg; Pkg.add("DiffEqMonteCarlo")` to install the DiffEqMonteC
arlo package.

require at ./loading.jl:892
top-level scope at none:3
eval at ./boot.jl:331
#101 at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1
.4/Distributed/src/process_messages.jl:290
run_work_thunk at /buildworker/worker/package_linux64/build/usr/share/julia
/stdlib/v1.4/Distributed/src/process_messages.jl:79
run_work_thunk at /buildworker/worker/package_linux64/build/usr/share/julia
/stdlib/v1.4/Distributed/src/process_messages.jl:88
#94 at ./task.jl:358

...and 5 more exception(s).

using DiffEqMonteCarlo, StochasticDiffEq, DiffEqProblemLibrary, DiffEqNoiseProcess, Plots, ParallelDataTransfer
using DiffEqProblemLibrary.SDEProblemLibrary: importsdeproblems; importsdeproblems()
import DiffEqProblemLibrary.SDEProblemLibrary: prob_sde_additive,
            prob_sde_linear, prob_sde_wave

probs = Matrix{SDEProblem}(undef,3,3)
## Problem 1
prob = prob_sde_linear
probs[1,1] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM1)))
probs[1,2] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM2)))
probs[1,3] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM3)))
## Problem 2
prob = prob_sde_wave
probs[2,1] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM1)))
probs[2,2] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM2)))
probs[2,3] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM3)))
## Problem 3
prob = prob_sde_additive
probs[3,1] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM1)))
probs[3,2] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM2)))
probs[3,3] = SDEProblem(prob.f,prob.g,prob.u0,prob.tspan,prob.p,noise=WienerProcess(0.0,0.0,0.0,rswm=RSWM(adaptivealg=:RSwM3)))

fullMeans = Vector{Array}(undef,3)
fullMedians = Vector{Array}(undef,3)
fullElapsed = Vector{Array}(undef,3)
fullTols = Vector{Array}(undef,3)
offset = 0

Ns = [17,23,
17]
3-element Array{Int64,1}:
 17
 23
 17

Timings are only valid if no workers die. Workers die if you run out of memory.

for k in 1:size(probs,1)
  global probs, Ns, fullMeans, fullMedians, fullElapsed, fullTols
  println("Problem $k")
  ## Setup
  N = Ns[k]

  msims = Vector{Any}(undef,N)
  elapsed = Array{Float64}(undef,N,3)
  medians = Array{Float64}(undef,N,3)
  means   = Array{Float64}(undef,N,3)
  tols    = Array{Float64}(undef,N,3)

  #Compile
  prob = probs[k,1]
  ParallelDataTransfer.sendto(workers(), prob=prob)
  monte_prob = MonteCarloProblem(prob)
  solve(monte_prob,SRIW1(),dt=1/2^(4),adaptive=true,num_monte=1000,abstol=2.0^(-1),reltol=0)

  println("RSwM1")
  for i=1+offset:N+offset
    tols[i-offset,1] = 2.0^(-i-1)
    msims[i-offset] = DiffEqBase.calculate_monte_errors(solve(monte_prob,SRIW1(),
                                            num_monte=1000,abstol=2.0^(-i-1),
                                            reltol=0,force_dtmin=true))
    elapsed[i-offset,1] = msims[i-offset].elapsedTime
    medians[i-offset,1] = msims[i-offset].error_medians[:final]
    means[i-offset,1]   = msims[i-offset].error_means[:final]
  end

  println("RSwM2")
  prob = probs[k,2]

  ParallelDataTransfer.sendto(workers(), prob=prob)
  monte_prob = MonteCarloProblem(prob)
  solve(monte_prob,SRIW1(),dt=1/2^(4),adaptive=true,num_monte=1000,abstol=2.0^(-1),reltol=0)

  for i=1+offset:N+offset
    tols[i-offset,2] = 2.0^(-i-1)
    msims[i-offset] = DiffEqBase.calculate_monte_errors(solve(monte_prob,SRIW1(),
                                            num_monte=1000,abstol=2.0^(-i-1),
                                            reltol=0,force_dtmin=true))
    elapsed[i-offset,2] = msims[i-offset].elapsedTime
    medians[i-offset,2] = msims[i-offset].error_medians[:final]
    means[i-offset,2]   = msims[i-offset].error_means[:final]
  end

  println("RSwM3")
  prob = probs[k,3]
  ParallelDataTransfer.sendto(workers(), prob=prob)
  monte_prob = MonteCarloProblem(prob)
  solve(monte_prob,SRIW1(),dt=1/2^(4),adaptive=true,num_monte=1000,abstol=2.0^(-1),reltol=0)

  for i=1+offset:N+offset
    tols[i-offset,3] = 2.0^(-i-1)
        msims[i-offset] = DiffEqBase.calculate_monte_errors(solve(monte_prob,SRIW1(),
                                    adaptive=true,num_monte=1000,abstol=2.0^(-i-1),
                                    reltol=0,force_dtmin=true))
    elapsed[i-offset,3] = msims[i-offset].elapsedTime
    medians[i-offset,3] = msims[i-offset].error_medians[:final]
    means[i-offset,3]   = msims[i-offset].error_means[:final]
  end

  fullMeans[k] = means
  fullMedians[k] =medians
  fullElapsed[k] = elapsed
  fullTols[k] = tols
end
Problem 1
Error: MethodError: no method matching append!(::Nothing, ::Array{RODESolut
ion{Float64,1,Array{Float64,1},Array{Float64,1},Dict{Symbol,Float64},Array{
Float64,1},NoiseProcess{Float64,1,Float64,Float64,Float64,Array{Float64,1},
typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST),typeof(DiffEqNoiseProcess.WHITE
_NOISE_BRIDGE),false,ResettableStacks.ResettableStack{Tuple{Float64,Float64
,Float64},false},ResettableStacks.ResettableStack{Tuple{Float64,Float64,Flo
at64},false},RSWM{Float64},Nothing,RandomNumbers.Xorshifts.Xoroshiro128Plus
},SDEProblem{Float64,Tuple{Float64,Float64},false,DiffEqBase.NullParameters
,NoiseProcess{Float64,1,Float64,Float64,Float64,Array{Float64,1},typeof(Dif
fEqNoiseProcess.WHITE_NOISE_DIST),typeof(DiffEqNoiseProcess.WHITE_NOISE_BRI
DGE),false,ResettableStacks.ResettableStack{Tuple{Float64,Float64,Float64},
false},ResettableStacks.ResettableStack{Tuple{Float64,Float64,Float64},fals
e},RSWM{Float64},Nothing,RandomNumbers.Xorshifts.Xoroshiro128Plus},SDEFunct
ion{false,typeof(DiffEqProblemLibrary.SDEProblemLibrary.f_linear),typeof(Di
ffEqProblemLibrary.SDEProblemLibrary.σ_linear),LinearAlgebra.UniformScaling
{Bool},typeof(DiffEqProblemLibrary.SDEProblemLibrary.linear_analytic),Nothi
ng,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,
Nothing,Nothing},typeof(DiffEqProblemLibrary.SDEProblemLibrary.σ_linear),Ba
se.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},Nothing}
,SRIW1,StochasticDiffEq.LinearInterpolationData{Array{Float64,1},Array{Floa
t64,1}},DiffEqBase.DEStats},1})
Closest candidates are:
  append!(!Matched::BitArray{1}, ::Any) at bitarray.jl:766
  append!(!Matched::Plots.Series, ::Any...) at /builds/JuliaGPU/DiffEqBench
marks.jl/.julia/packages/Plots/3INZP/src/utils.jl:839
  append!(!Matched::Array{T,1} where T, ::AbstractArray{T,1} where T) at ar
ray.jl:953
  ...

gr(fmt=:svg)
lw=3
leg=String["RSwM1","RSwM2","RSwM3"]

titleFontSize = 16
guideFontSize = 14
legendFontSize= 14
tickFontSize  = 12

for k in 1:size(probs,1)
  global probs, Ns, fullMeans, fullMedians, fullElapsed, fullTols
  p1[k] = Plots.plot(fullTols[k],fullMeans[k],xscale=:log10,yscale=:log10,  xguide="Absolute Tolerance",yguide="Mean Final Error",title="Example $k"  ,linewidth=lw,grid=false,lab=leg,titlefont=font(titleFontSize),legendfont=font(legendFontSize),tickfont=font(tickFontSize),guidefont=font(guideFontSize))
  p2[k] = Plots.plot(fullTols[k],fullMedians[k],xscale=:log10,yscale=:log10,xguide="Absolute Tolerance",yguide="Median Final Error",title="Example $k",linewidth=lw,grid=false,lab=leg,titlefont=font(titleFontSize),legendfont=font(legendFontSize),tickfont=font(tickFontSize),guidefont=font(guideFontSize))
  p3[k] = Plots.plot(fullTols[k],fullElapsed[k],xscale=:log10,yscale=:log10,xguide="Absolute Tolerance",yguide="Elapsed Time",title="Example $k"      ,linewidth=lw,grid=false,lab=leg,titlefont=font(titleFontSize),legendfont=font(legendFontSize),tickfont=font(tickFontSize),guidefont=font(guideFontSize))
end
Error: UndefRefError: access to undefined reference

Plots.plot!(p1[1])
Error: UndefRefError: access to undefined reference

Plots.plot(p1[1],p1[2],p1[3],layout=(3,1),size=(1000,800))
Error: UndefRefError: access to undefined reference

#savefig("meanvstol.png")
#savefig("meanvstol.pdf")
plot(p3[1],p3[2],p3[3],layout=(3,1),size=(1000,800))
Error: UndefRefError: access to undefined reference

#savefig("timevstol.png")
#savefig("timevstol.pdf")
plot(p1[1],p3[1],p1[2],p3[2],p1[3],p3[3],layout=(3,2),size=(1000,800))
Error: UndefRefError: access to undefined reference

using DiffEqBenchmarks
DiffEqBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])

Appendix

These benchmarks are a part of the DiffEqBenchmarks.jl repository, found at: https://github.com/JuliaDiffEq/DiffEqBenchmarks.jl

To locally run this tutorial, do the following commands:

using DiffEqBenchmarks
DiffEqBenchmarks.weave_file("AdaptiveSDE","AdaptiveEfficiencyTests.jmd")

Computer Information:

Julia Version 1.4.2
Commit 44fa15b150* (2020-05-23 18:35 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)
Environment:
  JULIA_DEPOT_PATH = /builds/JuliaGPU/DiffEqBenchmarks.jl/.julia
  JULIA_CUDA_MEMORY_LIMIT = 2147483648
  JULIA_PROJECT = @.
  JULIA_NUM_THREADS = 8

Package Information:

Status: `/builds/JuliaGPU/DiffEqBenchmarks.jl/benchmarks/AdaptiveSDE/Project.toml`
[78ddff82-25fc-5f2b-89aa-309469cbf16f] DiffEqMonteCarlo 0.15.1
[77a26b50-5914-5dd7-bc55-306e6241c503] DiffEqNoiseProcess 5.0.2
[a077e3f3-b75c-5d7f-a0c6-6bc4c8ec64a9] DiffEqProblemLibrary 4.8.0
[2dcacdae-9679-587a-88bb-8b444fb7085b] ParallelDataTransfer 0.5.0
[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.5.3
[789caeaf-c7a9-5a7d-9973-96adeb23e2a0] StochasticDiffEq 6.24.0
[8ba89e20-285c-5b6f-9357-94700520ee1b] Distributed 
[9a3f8284-a2c9-5f02-9a11-845980a1fd5c] Random