use LinearSolve.jl

Author: ChrisRackauckas

Project.toml

@@ -7,10 +7,8 @@ version = "0.3.22"
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
-RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
@@ -21,9 +19,7 @@ UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 ArrayInterfaceCore = "0.1.1"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-IterativeSolvers = "0.9"
 RecursiveArrayTools = "2"
-RecursiveFactorization = "0.1, 0.2"
 Reexport = "0.2, 1"
 SciMLBase = "1.32"
 Setfield = "0.7, 0.8, 1"

src/NonlinearSolve.jl

@@ -16,7 +16,7 @@ import RecursiveFactorization
 
 abstract type AbstractNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractNonlinearSolveAlgorithm end
-abstract type AbstractNewtonAlgorithm{CS, AD} <: AbstractNonlinearSolveAlgorithm end
+abstract type AbstractNewtonAlgorithm{CS, AD, FDT, ST, CJ} <: AbstractNonlinearSolveAlgorithm end
 abstract type AbstractImmutableNonlinearSolver <: AbstractNonlinearSolveAlgorithm end
 
 include("utils.jl")

src/raphson.jl

@@ -1,12 +1,14 @@
-struct NewtonRaphson{CS, AD, DT, L} <: AbstractNewtonAlgorithm{CS, AD}
-    diff_type::DT
+struct NewtonRaphson{CS, AD, FDT, L, P, ST, CJ} <: AbstractNewtonAlgorithm{CS, AD, FDT, ST, CJ}
     linsolve::L
+    precs::P
 end
 
-function NewtonRaphson(; autodiff = true, chunk_size = 12, diff_type = Val{:forward},
-                       linsolve = DEFAULT_LINSOLVE)
-    NewtonRaphson{chunk_size, autodiff, typeof(diff_type), typeof(linsolve)}(diff_type,
-                                                                             linsolve)
+function NewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
+    standardtag = Val{true}(), concrete_jac = nothing,
+    diff_type = Val{:forward}, linsolve = nothing, precs = DEFAULT_PRECS)
+    NewtonRaphson{_unwrap_val(chunk_size), _unwrap_val(autodiff), diff_type,
+    typeof(linsolve), typeof(precs), _unwrap_val(standardtag),
+    _unwrap_val(concrete_jac)}(linsolve, precs)
 end
 
 mutable struct NewtonRaphsonCache{ufType, L, jType, uType, JC}
@@ -17,10 +19,64 @@ mutable struct NewtonRaphsonCache{ufType, L, jType, uType, JC}
     jac_config::JC
 end
 
+function dolinsolve(precs::P, linsolve; A = nothing, linu = nothing, b = nothing,
+                    du = nothing, u = nothing, p = nothing, t = nothing,
+                    weight = nothing, solverdata = nothing,
+                    reltol = nothing) where P
+    A !== nothing && (linsolve = LinearSolve.set_A(linsolve, A))
+    b !== nothing && (linsolve = LinearSolve.set_b(linsolve, b))
+    linu !== nothing && (linsolve = LinearSolve.set_u(linsolve, linu))
+
+    Plprev = linsolve.Pl isa LinearSolve.ComposePreconditioner ? linsolve.Pl.outer :
+             linsolve.Pl
+    Prprev = linsolve.Pr isa LinearSolve.ComposePreconditioner ? linsolve.Pr.outer :
+             linsolve.Pr
+
+    _Pl, _Pr = precs(linsolve.A, du, u, p, nothing, A !== nothing, Plprev, Prprev,
+                          solverdata)
+    if (_Pl !== nothing || _Pr !== nothing)
+        _weight = weight === nothing ?
+                  (linsolve.Pr isa Diagonal ? linsolve.Pr.diag : linsolve.Pr.inner.diag) :
+                  weight
+        Pl, Pr = wrapprecs(_Pl, _Pr, _weight)
+        linsolve = LinearSolve.set_prec(linsolve, Pl, Pr)
+    end
+
+    linres = if reltol === nothing
+        solve(linsolve; reltol)
+    else
+        solve(linsolve; reltol)
+    end
+
+    return linres
+end
+
+function wrapprecs(_Pl, _Pr, weight)
+    if _Pl !== nothing
+        Pl = LinearSolve.ComposePreconditioner(LinearSolve.InvPreconditioner(Diagonal(_vec(weight))),
+                                               _Pl)
+    else
+        Pl = LinearSolve.InvPreconditioner(Diagonal(_vec(weight)))
+    end
+
+    if _Pr !== nothing
+        Pr = LinearSolve.ComposePreconditioner(Diagonal(_vec(weight)), _Pr)
+    else
+        Pr = Diagonal(_vec(weight))
+    end
+    Pl, Pr
+end
+
 function alg_cache(alg::NewtonRaphson, f, u, p, ::Val{true})
-    uf = JacobianWrapper(f, p)
-    linsolve = alg.linsolve(Val{:init}, f, u)
+    uf = JacobianWrapper(f,p)
     J = false .* u .* u'
+
+    linprob = LinearProblem(W, _vec(zero(u)); u0 = _vec(zero(u)))
+    Pl, Pr = wrapprecs(alg.precs(W, nothing, u, p, nothing, nothing, nothing, nothing,
+                                 nothing)..., weight)
+    linsolve = init(linprob, alg.linsolve, alias_A = true, alias_b = true,
+                    Pl = Pl, Pr = Pr)
+
     du1 = zero(u)
     tmp = zero(u)
     if alg_autodiff(alg)
@@ -47,9 +103,12 @@ function perform_step(solver::NewtonImmutableSolver, alg::NewtonRaphson, ::Val{t
     @unpack J, linsolve, du1 = cache
     calc_J!(J, solver, cache)
     # u = u - J \ fu
-    linsolve(du1, J, fu, true)
+    linsolve = dolinsolve(alg.precs, solver.linsolve, A = J, b = fu, u = du1, 
+                          p = p, reltol = solver.tol)
+    @set! cache.linsolve = linsolve            
     @. u = u - du1
     f(fu, u, p)
+    
     if solver.internalnorm(solver.fu) < solver.tol
         @set! solver.force_stop = true
     end

src/utils.jl

@@ -100,91 +100,6 @@ function num_types_in_tuple(sig::UnionAll)
     length(Base.unwrap_unionall(sig).parameters)
 end
 
-### Default Linsolve
-
-# Try to be as smart as possible
-# lu! if Matrix
-# lu if sparse
-# gmres if operator
-
-mutable struct DefaultLinSolve
-    A::Any
-    iterable::Any
-end
-DefaultLinSolve() = DefaultLinSolve(nothing, nothing)
-
-function (p::DefaultLinSolve)(x, A, b, update_matrix = false; tol = nothing, kwargs...)
-    if p.iterable isa Vector && eltype(p.iterable) <: LinearAlgebra.BlasInt # `iterable` here is the pivoting vector
-        F = LU{eltype(A)}(A, p.iterable, zero(LinearAlgebra.BlasInt))
-        ldiv!(x, F, b)
-        return nothing
-    end
-    if update_matrix
-        if typeof(A) <: Matrix
-            blasvendor = BLAS.vendor()
-            # if the user doesn't use OpenBLAS, we assume that is a better BLAS
-            # implementation like MKL
-            #
-            # RecursiveFactorization seems to be consistantly winning below 100
-            # https://discourse.julialang.org/t/ann-recursivefactorization-jl/39213
-            if ArrayInterfaceCore.can_setindex(x) && (size(A, 1) <= 100 ||
-                ((blasvendor === :openblas || blasvendor === :openblas64) &&
-                 size(A, 1) <= 500))
-                p.A = RecursiveFactorization.lu!(A)
-            else
-                p.A = lu!(A)
-            end
-        elseif typeof(A) <: Tridiagonal
-            p.A = lu!(A)
-        elseif typeof(A) <: Union{SymTridiagonal}
-            p.A = ldlt!(A)
-        elseif typeof(A) <: Union{Symmetric, Hermitian}
-            p.A = bunchkaufman!(A)
-        elseif typeof(A) <: SparseMatrixCSC
-            p.A = lu(A)
-        elseif ArrayInterfaceCore.isstructured(A)
-            p.A = factorize(A)
-        elseif !(typeof(A) <: AbstractDiffEqOperator)
-            # Most likely QR is the one that is overloaded
-            # Works on things like CuArrays
-            p.A = qr(A)
-        end
-    end
-
-    if typeof(A) <: Union{Matrix, SymTridiagonal, Tridiagonal, Symmetric, Hermitian} # No 2-arg form for SparseArrays!
-        x .= b
-        ldiv!(p.A, x)
-        # Missing a little bit of efficiency in a rare case
-        #elseif typeof(A) <: DiffEqArrayOperator
-        #  ldiv!(x,p.A,b)
-    elseif ArrayInterfaceCore.isstructured(A) || A isa SparseMatrixCSC
-        ldiv!(x, p.A, b)
-    elseif typeof(A) <: AbstractDiffEqOperator
-        # No good starting guess, so guess zero
-        if p.iterable === nothing
-            p.iterable = IterativeSolvers.gmres_iterable!(x, A, b; initially_zero = true,
-                                                          restart = 5, maxiter = 5,
-                                                          tol = 1e-16, kwargs...)
-            p.iterable.reltol = tol
-        end
-        x .= false
-        iter = p.iterable
-        purge_history!(iter, x, b)
-
-        for residual in iter
-        end
-    else
-        ldiv!(x, p.A, b)
-    end
-    return nothing
-end
-
-function (p::DefaultLinSolve)(::Type{Val{:init}}, f, u0_prototype)
-    DefaultLinSolve()
-end
-
-const DEFAULT_LINSOLVE = DefaultLinSolve()
-
 @inline UNITLESS_ABS2(x) = real(abs2(x))
 @inline DEFAULT_NORM(u::Union{AbstractFloat, Complex}) = @fastmath abs(u)
 @inline function DEFAULT_NORM(u::Array{T}) where {T <: Union{AbstractFloat, Complex}}