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lib/NonlinearSolveBase/ext/NonlinearSolveBaseTaylorDiffExt.jl
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,20 @@ | ||
| module NonlinearSolveBaseTaylorDiffExt | ||
| using SciMLBase: NonlinearFunction | ||
| using NonlinearSolveBase: HalleyDescentCache | ||
| import NonlinearSolveBase: evaluate_hvvp | ||
| using TaylorDiff: derivative, derivative! | ||
| using FastClosures: @closure | ||
|
|
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| function evaluate_hvvp( | ||
| hvvp, cache::HalleyDescentCache, f::NonlinearFunction{iip}, p, u, δu) where {iip} | ||
| if iip | ||
| binary_f = @closure (y, x) -> f(y, x, p) | ||
| derivative!(hvvp, binary_f, cache.fu, u, δu, Val(2)) | ||
| else | ||
| unary_f = Base.Fix2(f, p) | ||
| hvvp = derivative(unary_f, u, δu, Val(2)) | ||
| end | ||
| hvvp | ||
| end | ||
|
|
||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,100 @@ | ||
| """ | ||
| HalleyDescent(; linsolve = nothing) | ||
| Improve the NewtonDescent with higher-order terms. First compute the descent direction as ``J a = -fu``. | ||
| Then compute the hessian-vector-vector product and solve for the second-order correction term as ``J b = H a a``. | ||
| Finally, compute the descent direction as ``δu = a * a / (b / 2 - a)``. | ||
| Note that `import TaylorDiff` is required to use this descent algorithm. | ||
| See also [`NewtonDescent`](@ref). | ||
| """ | ||
| @kwdef @concrete struct HalleyDescent <: AbstractDescentDirection | ||
| linsolve = nothing | ||
| end | ||
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| supports_line_search(::HalleyDescent) = true | ||
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| @concrete mutable struct HalleyDescentCache <: AbstractDescentCache | ||
| f | ||
| p | ||
| δu | ||
| δus | ||
| b | ||
| fu | ||
| hvvp | ||
| lincache | ||
| timer | ||
| preinverted_jacobian <: Union{Val{false}, Val{true}} | ||
| end | ||
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| @internal_caches HalleyDescentCache :lincache | ||
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| function InternalAPI.init( | ||
| prob::NonlinearProblem, alg::HalleyDescent, J, fu, u; stats, | ||
| shared = Val(1), pre_inverted::Val = Val(false), | ||
| linsolve_kwargs = (;), abstol = nothing, reltol = nothing, | ||
| timer = get_timer_output(), kwargs...) | ||
| @bb δu = similar(u) | ||
| @bb b = similar(u) | ||
| @bb fu = similar(fu) | ||
| @bb hvvp = similar(fu) | ||
| δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i | ||
| @bb δu_ = similar(u) | ||
| end | ||
| lincache = Utils.unwrap_val(pre_inverted) ? nothing : | ||
| construct_linear_solver( | ||
| alg, alg.linsolve, J, Utils.safe_vec(fu), Utils.safe_vec(u); | ||
| stats, abstol, reltol, linsolve_kwargs... | ||
| ) | ||
| return HalleyDescentCache( | ||
| prob.f, prob.p, δu, δus, b, fu, hvvp, lincache, timer, pre_inverted) | ||
| end | ||
|
|
||
| function InternalAPI.solve!( | ||
| cache::HalleyDescentCache, J, fu, u, idx::Val = Val(1); | ||
| skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...) | ||
| δu = SciMLBase.get_du(cache, idx) | ||
| skip_solve && return DescentResult(; δu) | ||
| if preinverted_jacobian(cache) | ||
| @assert J!==nothing "`J` must be provided when `pre_inverted = Val(true)`." | ||
| @bb δu = J × vec(fu) | ||
| else | ||
| @static_timeit cache.timer "linear solve 1" begin | ||
| linres = cache.lincache(; | ||
| A = J, b = Utils.safe_vec(fu), | ||
| kwargs..., linu = Utils.safe_vec(δu), | ||
| reuse_A_if_factorization = !new_jacobian || (idx !== Val(1))) | ||
| δu = Utils.restructure(SciMLBase.get_du(cache, idx), linres.u) | ||
| if !linres.success | ||
| set_du!(cache, δu, idx) | ||
| return DescentResult(; δu, success = false, linsolve_success = false) | ||
| end | ||
| end | ||
| end | ||
| b = cache.b | ||
| # compute the hessian-vector-vector product | ||
| hvvp = evaluate_hvvp(cache.hvvp, cache, cache.f, cache.p, u, δu) | ||
| # second linear solve, reuse factorization if possible | ||
| if preinverted_jacobian(cache) | ||
| @bb b = J × vec(hvvp) | ||
| else | ||
| @static_timeit cache.timer "linear solve 2" begin | ||
| linres = cache.lincache(; | ||
| A = J, b = Utils.safe_vec(hvvp), | ||
| kwargs..., linu = Utils.safe_vec(b), | ||
| reuse_A_if_factorization = true) | ||
| b = Utils.restructure(cache.b, linres.u) | ||
| if !linres.success | ||
| set_du!(cache, δu, idx) | ||
| return DescentResult(; δu, success = false, linsolve_success = false) | ||
| end | ||
| end | ||
| end | ||
| @bb @. δu = δu * δu / (b / 2 - δu) | ||
| set_du!(cache, δu, idx) | ||
| cache.b = b | ||
| return DescentResult(; δu) | ||
| end | ||
|
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||
| evaluate_hvvp(hvvp, cache, f, p, u, δu) = error("not implemented. please import TaylorDiff") |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,15 @@ | ||
| """ | ||
| Halley(; concrete_jac = nothing, linsolve = nothing, linesearch = missing, | ||
| autodiff = nothing) | ||
| An experimental Halley's method implementation. Improves the convergence rate of Newton's method by using second-order derivative information to correct the descent direction. | ||
| Currently depends on TaylorDiff.jl to handle the correction terms, | ||
| might have more general implementation in the future. | ||
| """ | ||
| function Halley(; concrete_jac = nothing, linsolve = nothing, | ||
| linesearch = missing, autodiff = nothing) | ||
| return GeneralizedFirstOrderAlgorithm(; | ||
| concrete_jac, name = :Halley, linesearch, | ||
| descent = HalleyDescent(; linsolve), autodiff) | ||
| end |
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