diff --git a/src/OrdinaryDiffEq.jl b/src/OrdinaryDiffEq.jl index f51aa640ee..092e76d0ef 100644 --- a/src/OrdinaryDiffEq.jl +++ b/src/OrdinaryDiffEq.jl @@ -66,6 +66,7 @@ module OrdinaryDiffEq include("caches/adams_bashforth_moulton_caches.jl") include("caches/nordsieck_caches.jl") include("caches/bdf_caches.jl") + include("caches/rkc_caches.jl") include("caches/euler_imex_caches.jl") include("alg_utils.jl") @@ -78,6 +79,7 @@ module OrdinaryDiffEq include("tableaus/rosenbrock_tableaus.jl") include("tableaus/sdirk_tableaus.jl") include("tableaus/rkn_tableaus.jl") + include("tableaus/rkc_tableaus.jl") include("integrators/type.jl") include("integrators/integrator_utils.jl") @@ -105,6 +107,7 @@ module OrdinaryDiffEq include("perform_step/adams_bashforth_moulton_perform_step.jl") include("perform_step/nordsieck_perform_step.jl") include("perform_step/bdf_perform_step.jl") + include("perform_step/rkc_perform_step.jl") include("perform_step/euler_imex_perform_step.jl") include("dense/generic_dense.jl") @@ -121,6 +124,7 @@ module OrdinaryDiffEq include("adams_utils.jl") include("bdf_utils.jl") include("exponential_utils.jl") + include("rkc_utils.jl") include("derivative_wrappers.jl") include("iterator_interface.jl") include("constants.jl") @@ -176,6 +180,8 @@ module OrdinaryDiffEq export Nystrom4, Nystrom4VelocityIndependent, Nystrom5VelocityIndependent, IRKN3, IRKN4, DPRKN6, DPRKN8, DPRKN12, ERKN4, ERKN5 + export ROCK2 + export AB3, AB4, AB5, ABM32, ABM43, ABM54 export VCAB3, VCAB4, VCAB5, VCABM3, VCABM4, VCABM5 diff --git a/src/alg_utils.jl b/src/alg_utils.jl index 070d83cc91..9e778e5c31 100644 --- a/src/alg_utils.jl +++ b/src/alg_utils.jl @@ -246,6 +246,8 @@ alg_order(alg::JVODE) = 1 #dummy value alg_order(alg::ABDF2) = 2 alg_order(alg::QNDF1) = 1 +alg_order(alg::ROCK2) = 2 + alg_maximum_order(alg) = alg_order(alg) alg_maximum_order(alg::CompositeAlgorithm) = maximum(alg_order(x) for x in alg.algs) diff --git a/src/algorithms.jl b/src/algorithms.jl index bbed581342..48a838ddd9 100644 --- a/src/algorithms.jl +++ b/src/algorithms.jl @@ -287,6 +287,9 @@ Base.@pure JVODE(algorithm=:Adams;bias1=6, bias2=6,bias3=10, addon=1//10^6) = JVODE(algorithm,bias1,bias2,bias3,addon) Base.@pure JVODE_Adams(;kwargs...) = JVODE(:Adams;kwargs...) +# ROCK methods +struct ROCK2 <: OrdinaryDiffEqAdaptiveAlgorithm end + ################################################################################ # Generic implicit methods diff --git a/src/caches/rkc_caches.jl b/src/caches/rkc_caches.jl new file mode 100644 index 0000000000..4504039ea9 --- /dev/null +++ b/src/caches/rkc_caches.jl @@ -0,0 +1,40 @@ +mutable struct ROCK2ConstantCache{T,T2,zType} <: OrdinaryDiffEqConstantCache + ms::SVector{46, Int} + fp1::SVector{46, T} + fp2::SVector{46, T} + recf::Vector{T2} + zprev::zType + mdegprev::Int + mdeg::Int + recind::Int +end +struct ROCK2Cache{uType,rateType,uEltypeNoUnits} <: OrdinaryDiffEqMutableCache # WIP + u::uType + uprev::uType + gprev::uType + gprev2::uType + tmp::uType + atmp::uEltypeNoUnits + fsalfirst::rateType + k::rateType + k2::rateType + constantcache::ROCK2ConstantCache +end +u_cache(c::ROCK2Cache) = (c.atmp,) +du_cache(c::ROCK2Cache) = (c.fsalfirst,c.k,c.k2) + +function alg_cache(alg::ROCK2,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits,uprev,uprev2,f,t,dt,reltol,p,calck,::Type{Val{true}}) + constantcache = ROCK2ConstantCache(uEltypeNoUnits, uEltypeNoUnits, u) # WIP: not sure about what type to use in here + gprev = similar(u) + gprev2 = similar(u) + tmp = similar(u) + atmp = similar(u,uEltypeNoUnits,axes(u)) + fsalfirst = zero(rate_prototype) + k = zero(rate_prototype) + k2 = zero(rate_prototype) + ROCK2Cache(u, uprev, gprev, gprev2, tmp, atmp, fsalfirst, k, k2, constantcache) +end + +function alg_cache(alg::ROCK2,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits,uprev,uprev2,f,t,dt,reltol,p,calck,::Type{Val{false}}) + ROCK2ConstantCache(uEltypeNoUnits, uEltypeNoUnits, u) # WIP: not sure about what type to use in here +end diff --git a/src/perform_step/rkc_perform_step.jl b/src/perform_step/rkc_perform_step.jl new file mode 100644 index 0000000000..f78af38cae --- /dev/null +++ b/src/perform_step/rkc_perform_step.jl @@ -0,0 +1,121 @@ +function initialize!(integrator, cache::ROCK2ConstantCache) + integrator.kshortsize = 2 + integrator.k = typeof(integrator.k)(undef, integrator.kshortsize) + integrator.fsalfirst = integrator.f(integrator.uprev, integrator.p, integrator.t) # Pre-start fsal + + # Avoid undefined entries if k is an array of arrays + integrator.fsallast = zero(integrator.fsalfirst) + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast +end + +@muladd function perform_step!(integrator, cache::ROCK2ConstantCache, repeat_step=false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack ms, fp1, fp2, recf = cache + # The number of stage. + mdeg = Int(floor(sqrt((1.5 + dt * integrator.eigen_est)/0.811) + 1)) + if mdeg >= 200 + mdeg = 200 + end + cache.mdeg = max(mdeg, 3) - 2 + cache.mdeg != cache.mdegprev && choosedeg!(cache) + # recurrence + # for the first stage + temp1 = dt * recf[cache.recind] + ci1 = t + temp1 + ci2 = t + temp1 + ci3 = t + gprev2 = copy(uprev) + gprev = uprev + temp1 * fsalfirst + ms[cache.mdeg] < 2 && ( u = gprev ) + # for the second to the ms[cache.mdeg] th stages + for i in 2:ms[cache.mdeg] + temp1 = dt * recf[cache.recind + 2 * (i - 2) + 1] + temp3 = -recf[cache.recind + 2 * (i - 2) + 2] + temp2 = 1 - temp3 + ci1 = temp1 + temp2 * ci2 + temp3 * ci3 + u = temp1 * u + temp2 * gprev + temp3 * gprev2 + i < ms[cache.mdeg] && (gprev2 = gprev; gprev = u) + ci3 = ci2 + ci2 = ci1 + end # end if + # two-stage finishing procedure. + temp1 = dt * fp1[cache.mdeg] + temp2 = dt * fp2[cache.mdeg] + gprev2 = f(u, p, ci1) + gprev = u + temp1 * gprev2 + ci1 += temp1 + u = f(gprev, p, ci1) + temp3 = temp2 * (u - gprev2) + u = gprev + temp1 * u + temp3 + # error estimate + if integrator.opts.adaptive + atmp = calculate_residuals(temp3, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm) + integrator.EEst = integrator.opts.internalnorm(atmp) + end + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast = f(u, p, t+dt) + integrator.u = u +end + +function initialize!(integrator, cache::ROCK2Cache) + integrator.kshortsize = 2 + resize!(integrator.k, integrator.kshortsize) + integrator.fsalfirst = cache.fsalfirst # done by pointers, no copying + integrator.fsallast = cache.k + integrator.k[1] = integrator.fsalfirst + integrator.k[2] = integrator.fsallast + integrator.f(integrator.fsalfirst, integrator.uprev, integrator.p, integrator.t) # Pre-start fsal +end + +@muladd function perform_step!(integrator, cache::ROCK2Cache, repeat_step=false) + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + @unpack k, k2, tmp, gprev2, gprev, atmp = cache + @unpack ms, fp1, fp2, recf = cache.constantcache + ccache = cache.constantcache + # The number of stage. + mdeg = Int(floor(sqrt((1.5 + dt * integrator.eigen_est)/0.811) + 1)) + if mdeg >= 200 + mdeg = 200 + end + ccache.mdeg = max(mdeg, 3) - 2 + ccache.mdeg != ccache.mdegprev && choosedeg!(cache) + # recurrence + # for the first stage + temp1 = dt * recf[ccache.recind] + ci1 = t + temp1 + ci2 = t + temp1 + ci3 = t + @. gprev2 = uprev + @. gprev = uprev + temp1 * fsalfirst + ms[ccache.mdeg] < 2 && ( @. u = gprev ) + # for the second to the ms[ccache.mdeg] th stages + for i in 2:ms[ccache.mdeg] + temp1 = dt * recf[ccache.recind + 2 * (i - 2) + 1] + temp3 = -recf[ccache.recind + 2 * (i - 2) + 2] + temp2 = 1 - temp3 + ci1 = temp1 + temp2 * ci2 + temp3 * ci3 + @. u = temp1 * u + temp2 * gprev + temp3 * gprev2 + i < ms[ccache.mdeg] && (gprev2 .= gprev; gprev .= u) + ci3 = ci2 + ci2 = ci1 + end # end if + # two-stage finishing procedure. + temp1 = dt * fp1[ccache.mdeg] + temp2 = dt * fp2[ccache.mdeg] + f(k, u, p, ci1) + @. gprev = u + temp1 * k + ci1 += temp1 + f(k2, gprev, p, ci1) + @. tmp = temp2 * (k2 - k) + @. u = gprev + temp1 * k2 + tmp + # error estimate + if integrator.opts.adaptive + calculate_residuals!(atmp, tmp, uprev, u, integrator.opts.abstol, integrator.opts.reltol,integrator.opts.internalnorm) + integrator.EEst = integrator.opts.internalnorm(atmp) + end + integrator.k[1] = integrator.fsalfirst + f(integrator.fsallast, u, p, t+dt) + integrator.k[2] = integrator.fsallast + integrator.u = u +end diff --git a/src/rkc_utils.jl b/src/rkc_utils.jl new file mode 100644 index 0000000000..f4bfbf25cf --- /dev/null +++ b/src/rkc_utils.jl @@ -0,0 +1,80 @@ +# This function calculates the largest eigenvalue +# (absolute value wise) by power iteration. + +function maxeig!(integrator, cache::OrdinaryDiffEqConstantCache) + isfirst = integrator.iter == 1 || integrator.u_modified + @unpack t, dt, uprev, u, f, p, fsalfirst = integrator + maxiter = 50 + safe = 1.2 + # Initial guess for eigenvector `z` + if isfirst + fz = fsalfirst + z = f(fz, p, t) + else + z = cache.zprev + end + # Perturbation + u_norm = integrator.opts.internalnorm(uprev) + z_norm = integrator.opts.internalnorm(z) + pert = eps(u_norm) + sqrt_pert = sqrt(pert) + is_u_zero = u_norm == zero(u_norm) + is_z_zero = z_norm == zero(z_norm) + # Normalize `z` such that z-u lie in a circle + if ( !is_u_zero && !is_z_zero ) + dz_u = u_norm * sqrt_pert + quot = dz_u/z_norm + z = uprev + quot*z + elseif !is_u_zero + dz_u = u_norm * sqrt_pert + z = uprev + uprev*dz_u + elseif !is_z_zero + dz_u = pert + quot = dz_u/z_norm + z *= quot + else + dz_u = pert + z = dz_u + end # endif + # Start power iteration + integrator.eigen_est = 0 + for iter in 1:maxiter + fz = f(z, p, t) + tmp = fz - fsalfirst + Δ = integrator.opts.internalnorm(tmp) + eig_prev = integrator.eigen_est + integrator.eigen_est = Δ/dz_u * safe + # Convergence + if iter >= 2 && abs(eig_prev - integrator.eigen_est) < integrator.eigen_est*0.05 + # Store the eigenvector + cache.zprev = z + return true + end + # Next `z` + if Δ != zero(Δ) + quot = dz_u/Δ + z = uprev + quot*tmp + else + # An arbitrary change on `z` + nind = length(uprev) + ind = 1 + iter % nind + z[ind] = uprev[ind] - (z[ind] - uprev[ind]) + end + end + return false +end + +function choosedeg!(cache::T) where T + isconst = T <: OrdinaryDiffEqConstantCache + isconst || ( cache = cache.constantcache ) + @unpack ms, fp1, fp2, recf, zprev = cache + recind = 0 + @inbounds for i in 1:46 + recind += ms[i]*2 + if ms[i] > cache.mdeg + cache.mdeg = i + cache.recind = recind + return nothing + end # end if + end # end for +end diff --git a/src/tableaus/rkc_tableaus.jl b/src/tableaus/rkc_tableaus.jl new file mode 100644 index 0000000000..c98776f4a8 --- /dev/null +++ b/src/tableaus/rkc_tableaus.jl @@ -0,0 +1,1585 @@ +Base.@pure function ROCK2ConstantCache(::Type{T}, ::Type{T2}, zprev) where {T, T2} + ms = SVector{46, Int}(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, + 22,24,26,28,30,33,36,39,43,47,51,56,61,66,72,78,85,93, + 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recfi, zprev, 1, 1, 1) +end diff --git a/test/ode/ode_convergence_tests.jl b/test/ode/ode_convergence_tests.jl index cc4a210a20..4c47f1cf22 100644 --- a/test/ode/ode_convergence_tests.jl +++ b/test/ode/ode_convergence_tests.jl @@ -1,5 +1,5 @@ # This definitely needs cleaning -using OrdinaryDiffEq, Test, Random +using OrdinaryDiffEq, DiffEqDevTools, Test, Random using DiffEqProblemLibrary.ODEProblemLibrary: importodeproblems; importodeproblems() import DiffEqProblemLibrary.ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear probArr = Vector{ODEProblem}(undef, 2) diff --git a/test/ode/rkc_tests.jl b/test/ode/rkc_tests.jl new file mode 100644 index 0000000000..b791c1897b --- /dev/null +++ b/test/ode/rkc_tests.jl @@ -0,0 +1,30 @@ +using OrdinaryDiffEq, DiffEqDevTools, Test, LinearAlgebra, Random +using DiffEqProblemLibrary.ODEProblemLibrary: importodeproblems; importodeproblems() +using OrdinaryDiffEq: maxeig! +import DiffEqProblemLibrary.ODEProblemLibrary: prob_ode_linear, prob_ode_2Dlinear +probArr = Vector{ODEProblem}(undef, 2) +probArr[1] = prob_ode_linear +probArr[2] = prob_ode_2Dlinear + +srand(123) +@testset "Power Iteration of Runge-Kutta-Chebyshev Tests" begin + for i in 1:10 + A = rand(200,200) + test_f(u,p,t) = A*u + prob = ODEProblem(test_f, rand(200), (0,1.)) + integrator = init(prob, ROCK2()) + eigm = maximum(abs.(eigvals(A))) + maxeig!(integrator, integrator.cache) + eigest = integrator.eigen_est + @test eigest ≈ eigm atol=0.22eigm + end +end + +@testset "Runge-Kutta-Chebyshev Convergence Tests" begin + dts = 1 .//2 .^(8:-1:4) + testTol = 0.1 + for prob in probArr + sim2 = test_convergence(dts,prob,ROCK2()) + @test abs(sim2.𝒪est[:l∞]-2) < testTol + end +end diff --git a/test/runtests.jl b/test/runtests.jl index b5fbf0f978..c6b191b3ff 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -68,6 +68,7 @@ if !is_APPVEYOR && ( group == "All" || group == "AlgConvergence_I" ) @time @testset "SSPRK Tests" begin include("ode/ode_ssprk_tests.jl") end # ~ 25 s @time @testset "OwrenZen Tests" begin include("owrenzen_tests.jl") end + @time @testset "Runge-Kutta-Chebyshev Tests" begin include("ode/rkc_tests.jl") end end if !is_APPVEYOR && ( group == "All" || group == "AlgConvergence_II" )