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Original file line number | Diff line number | Diff line change |
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@concrete struct GeneralKlement <: AbstractNewtonAlgorithm{false, Nothing} | ||
max_resets::Int | ||
linsolve | ||
precs | ||
linesearch | ||
singular_tolerance | ||
end | ||
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function GeneralKlement(; max_resets::Int = 5, linsolve = nothing, | ||
linesearch = LineSearch(), precs = DEFAULT_PRECS, singular_tolerance = nothing) | ||
linesearch = linesearch isa LineSearch ? linesearch : LineSearch(; method = linesearch) | ||
return GeneralKlement(max_resets, linsolve, precs, linesearch, singular_tolerance) | ||
end | ||
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@concrete mutable struct GeneralKlementCache{iip} <: AbstractNonlinearSolveCache{iip} | ||
f | ||
alg | ||
u | ||
fu | ||
fu2 | ||
du | ||
p | ||
linsolve | ||
J | ||
J_cache | ||
J_cache2 | ||
Jᵀ²du | ||
Jdu | ||
resets | ||
singular_tolerance | ||
force_stop | ||
maxiters::Int | ||
internalnorm | ||
retcode::ReturnCode.T | ||
abstol | ||
prob | ||
stats::NLStats | ||
lscache | ||
end | ||
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get_fu(cache::GeneralKlementCache) = cache.fu | ||
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function SciMLBase.__init(prob::NonlinearProblem{uType, iip}, alg::GeneralKlement, args...; | ||
alias_u0 = false, maxiters = 1000, abstol = 1e-6, internalnorm = DEFAULT_NORM, | ||
linsolve_kwargs = (;), kwargs...) where {uType, iip} | ||
@unpack f, u0, p = prob | ||
u = alias_u0 ? u0 : deepcopy(u0) | ||
fu = evaluate_f(prob, u) | ||
J = __init_identity_jacobian(u, fu) | ||
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if u isa Number | ||
linsolve = nothing | ||
else | ||
weight = similar(u) | ||
recursivefill!(weight, true) | ||
Pl, Pr = wrapprecs(alg.precs(J, nothing, u, p, nothing, nothing, nothing, nothing, | ||
nothing)..., weight) | ||
linprob = LinearProblem(J, _vec(fu); u0 = _vec(fu)) | ||
linsolve = init(linprob, alg.linsolve; alias_A = true, alias_b = true, Pl, Pr, | ||
linsolve_kwargs...) | ||
end | ||
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singular_tolerance = alg.singular_tolerance === nothing ? inv(sqrt(eps(eltype(u)))) : | ||
eltype(u)(alg.singular_tolerance) | ||
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return GeneralKlementCache{iip}(f, alg, u, fu, zero(fu), _mutable_zero(u), p, linsolve, | ||
J, zero(J), zero(J), zero(fu), zero(fu), 0, singular_tolerance, false, | ||
maxiters, internalnorm, ReturnCode.Default, abstol, prob, NLStats(1, 0, 0, 0, 0), | ||
init_linesearch_cache(alg.linesearch, f, u, p, fu, Val(iip))) | ||
end | ||
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function perform_step!(cache::GeneralKlementCache{true}) | ||
@unpack u, fu, f, p, alg, J, linsolve, du = cache | ||
T = eltype(J) | ||
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# FIXME: How can we do this faster? | ||
if cond(J) > cache.singular_tolerance | ||
if cache.resets == alg.max_resets | ||
cache.force_stop = true | ||
cache.retcode = ReturnCode.Unstable | ||
return nothing | ||
end | ||
fill!(J, zero(T)) | ||
J[diagind(J)] .= T(1) | ||
cache.resets += 1 | ||
end | ||
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# u = u - J \ fu | ||
linres = dolinsolve(alg.precs, linsolve; A = J, b = -_vec(fu), linu = _vec(du), | ||
p, reltol = cache.abstol) | ||
cache.linsolve = linres.cache | ||
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# Line Search | ||
α = perform_linesearch!(cache.lscache, u, du) | ||
axpy!(α, du, u) | ||
f(cache.fu2, u, p) | ||
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cache.internalnorm(cache.fu2) < cache.abstol && (cache.force_stop = true) | ||
cache.stats.nf += 1 | ||
cache.stats.nsolve += 1 | ||
cache.stats.nfactors += 1 | ||
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cache.force_stop && return nothing | ||
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# Update the Jacobian | ||
cache.J_cache .= cache.J' .^ 2 | ||
cache.Jdu .= _vec(du) .^ 2 | ||
mul!(cache.Jᵀ²du, cache.J_cache, cache.Jdu) | ||
mul!(cache.Jdu, J, _vec(du)) | ||
cache.fu .= cache.fu2 .- cache.fu | ||
cache.fu .= (cache.fu .- _restructure(cache.fu, cache.Jdu)) ./ max.(cache.Jᵀ²du, eps(T)) | ||
mul!(cache.J_cache, _vec(cache.fu), _vec(du)') | ||
cache.J_cache .*= J | ||
mul!(cache.J_cache2, cache.J_cache, J) | ||
J .+= cache.J_cache2 | ||
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cache.fu .= cache.fu2 | ||
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return nothing | ||
end | ||
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function perform_step!(cache::GeneralKlementCache{false}) | ||
@unpack fu, f, p, alg, J, linsolve = cache | ||
T = eltype(J) | ||
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# FIXME: How can we do this faster? | ||
if cond(J) > cache.singular_tolerance | ||
if cache.resets == alg.max_resets | ||
cache.force_stop = true | ||
cache.retcode = ReturnCode.Unstable | ||
return nothing | ||
end | ||
cache.J = __init_identity_jacobian(u, fu) | ||
cache.resets += 1 | ||
end | ||
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# u = u - J \ fu | ||
if linsolve === nothing | ||
cache.du = -fu / cache.J | ||
else | ||
linres = dolinsolve(alg.precs, linsolve; A = J, b = -_vec(fu), | ||
linu = _vec(cache.du), p, reltol = cache.abstol) | ||
cache.linsolve = linres.cache | ||
end | ||
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# Line Search | ||
α = perform_linesearch!(cache.lscache, cache.u, cache.du) | ||
cache.u = @. cache.u + α * cache.du # `u` might not support mutation | ||
cache.fu2 = f(cache.u, p) | ||
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cache.internalnorm(cache.fu2) < cache.abstol && (cache.force_stop = true) | ||
cache.stats.nf += 1 | ||
cache.stats.nsolve += 1 | ||
cache.stats.nfactors += 1 | ||
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cache.force_stop && return nothing | ||
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# Update the Jacobian | ||
cache.J_cache = cache.J' .^ 2 | ||
cache.Jdu = _vec(cache.du) .^ 2 | ||
cache.Jᵀ²du = cache.J_cache * cache.Jdu | ||
cache.Jdu = J * _vec(cache.du) | ||
cache.fu = cache.fu2 .- cache.fu | ||
cache.fu = (cache.fu .- _restructure(cache.fu, cache.Jdu)) ./ max.(cache.Jᵀ²du, eps(T)) | ||
cache.J_cache = ((_vec(cache.fu) * _vec(cache.du)') .* J) * J | ||
cache.J = J .+ cache.J_cache | ||
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cache.fu = cache.fu2 | ||
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return nothing | ||
end | ||
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function SciMLBase.reinit!(cache::GeneralKlementCache{iip}, u0 = cache.u; p = cache.p, | ||
abstol = cache.abstol, maxiters = cache.maxiters) where {iip} | ||
cache.p = p | ||
if iip | ||
recursivecopy!(cache.u, u0) | ||
cache.f(cache.fu, cache.u, p) | ||
else | ||
# don't have alias_u0 but cache.u is never mutated for OOP problems so it doesn't matter | ||
cache.u = u0 | ||
cache.fu = cache.f(cache.u, p) | ||
end | ||
cache.abstol = abstol | ||
cache.maxiters = maxiters | ||
cache.stats.nf = 1 | ||
cache.stats.nsteps = 1 | ||
cache.force_stop = false | ||
cache.retcode = ReturnCode.Default | ||
return cache | ||
end |
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