refactor!: split out preparation

Project.toml

@@ -1,12 +1,11 @@
 name = "ImplicitDifferentiation"
 uuid = "57b37032-215b-411a-8a7c-41a003a55207"
 authors = ["Guillaume Dalle", "Mohamed Tarek"]
-version = "0.8.1"
+version = "0.9.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
-IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"
@@ -33,11 +32,10 @@ Documenter = "1.12.0"
 ExplicitImports = "1"
 FiniteDiff = "2.27.0"
 ForwardDiff = "0.10.36, 1"
-IterativeSolvers = "0.9.4"
 JET = "0.9, 0.10"
 JuliaFormatter = "2.1.2"
 Krylov = "0.9.6, 0.10"
-LinearAlgebra = "1.10"
+LinearAlgebra = "1"
 LinearMaps = "3.11.4"
 LinearOperators = "2.8.0"
 NLsolve = "4.5.1"
@@ -65,6 +63,7 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
 JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -76,4 +75,27 @@ TestItems = "1c621080-faea-4a02-84b6-bbd5e436b8fe"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["ADTypes", "Aqua", "ChainRulesCore", "ChainRulesTestUtils", "ComponentArrays", "DifferentiationInterface", "Documenter", "ExplicitImports", "FiniteDiff", "ForwardDiff", "JET", "JuliaFormatter", "NLsolve", "Optim", "Random", "SparseArrays", "StaticArrays", "Test", "TestItems", "TestItemRunner", "Zygote"]
+test = [
+    "ADTypes",
+    "Aqua",
+    "ChainRulesCore",
+    "ChainRulesTestUtils",
+    "ComponentArrays",
+    "DifferentiationInterface",
+    "Documenter",
+    "ExplicitImports",
+    "FiniteDiff",
+    "ForwardDiff",
+    "JET",
+    "JuliaFormatter",
+    "LinearAlgebra",
+    "NLsolve",
+    "Optim",
+    "Random",
+    "SparseArrays",
+    "StaticArrays",
+    "Test",
+    "TestItems",
+    "TestItemRunner",
+    "Zygote",
+]

docs/src/api.md

@@ -22,6 +22,8 @@ ImplicitFunction
 MatrixRepresentation
 OperatorRepresentation
 IterativeLinearSolver
+DirectLinearSolver
+prepare_implicit
 ```
 
 ## Internals

docs/src/faq.md

@@ -18,8 +18,7 @@ However, this can be switched to any other "inner" backend compatible with [Diff
 ### Arrays
 
 Functions that eat or spit out arbitrary arrays are supported, as long as the forward mapping _and_ conditions return arrays of the same size.
-
-If you deal with small arrays (say, less than 100 elements), consider using [StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl) for increased performance.
+The array types involved should be mutable.
 
 ### Scalars
 

examples/3_tricks.jl

@@ -38,7 +38,7 @@ end
 
 function conditions_components(x::ComponentVector, y::ComponentVector, _z)
     c_d, c_e = conditions_components_aux(x.a, x.b, x.m, y.d, y.e)
-    c = ComponentVector(; c_d=c_d, c_e=c_e)
+    c = ComponentVector(; d=c_d, e=c_e)
     return c
 end;
 
@@ -50,7 +50,7 @@ implicit_components = ImplicitFunction(forward_components, conditions_components
 
 a, b, m = [1.0, 2.0], [3.0, 4.0, 5.0], 6.0
 x = ComponentVector(; a=a, b=b, m=m)
-implicit_components(x)
+y, z = implicit_components(x)
 
 # And it works with both ForwardDiff.jl and Zygote.jl
 

ext/ImplicitDifferentiationChainRulesCoreExt.jl

@@ -6,6 +6,7 @@ using ChainRulesCore: unthunk, @not_implemented
 using ImplicitDifferentiation:
     ImplicitDifferentiation,
     ImplicitFunction,
+    ImplicitFunctionPreparation,
     build_Aᵀ,
     build_Bᵀ,
     chainrules_suggested_backend
@@ -14,28 +15,33 @@ using ImplicitDifferentiation:
 ImplicitDifferentiation.chainrules_suggested_backend(rc::RuleConfig) = AutoChainRules(rc)
 
 function ChainRulesCore.rrule(
-    rc::RuleConfig, implicit::ImplicitFunction, x::AbstractArray, args::Vararg{Any,N};
+    rc::RuleConfig,
+    implicit::ImplicitFunction,
+    prep::ImplicitFunctionPreparation,
+    x::AbstractArray,
+    args::Vararg{Any,N};
 ) where {N}
     y, z = implicit(x, args...)
     c = implicit.conditions(x, y, z, args...)
 
     suggested_backend = chainrules_suggested_backend(rc)
-    Aᵀ = build_Aᵀ(implicit, x, y, z, c, args...; suggested_backend)
-    Bᵀ = build_Bᵀ(implicit, x, y, z, c, args...; suggested_backend)
+    Aᵀ = build_Aᵀ(implicit, prep, x, y, z, c, args...; suggested_backend)
+    Bᵀ = build_Bᵀ(implicit, prep, x, y, z, c, args...; suggested_backend)
     project_x = ProjectTo(x)
 
-    function implicit_pullback((dy, dz))
+    function implicit_pullback_prepared((dy, dz))
         dy = unthunk(dy)
         dy_vec = vec(dy)
         dc_vec = implicit.linear_solver(Aᵀ, -dy_vec)
         dx_vec = Bᵀ(dc_vec)
         dx = reshape(dx_vec, size(x))
         df = NoTangent()
+        dprep = @not_implemented("Tangents for mutable arguments are not defined")
         dargs = ntuple(unimplemented_tangent, N)
-        return (df, project_x(dx), dargs...)
+        return (df, dprep, project_x(dx), dargs...)
     end
 
-    return (y, z), implicit_pullback
+    return (y, z), implicit_pullback_prepared
 end
 
 function unimplemented_tangent(_)

ext/ImplicitDifferentiationForwardDiffExt.jl

@@ -2,31 +2,36 @@ module ImplicitDifferentiationForwardDiffExt
 
 using ADTypes: AutoForwardDiff
 using ForwardDiff: Dual, Partials, partials, value
-using ImplicitDifferentiation: ImplicitFunction, build_A, build_B
+using ImplicitDifferentiation:
+    ImplicitFunction, ImplicitFunctionPreparation, build_A, build_B
 
 function (implicit::ImplicitFunction)(
-    x_and_dx::AbstractArray{Dual{T,R,N}}, args...
+    prep::ImplicitFunctionPreparation, x_and_dx::AbstractArray{Dual{T,R,N}}, args...
 ) where {T,R,N}
     x = value.(x_and_dx)
     y, z = implicit(x, args...)
     c = implicit.conditions(x, y, z, args...)
 
     suggested_backend = AutoForwardDiff()
-    A = build_A(implicit, x, y, z, c, args...; suggested_backend)
-    B = build_B(implicit, x, y, z, c, args...; suggested_backend)
+    A = build_A(implicit, prep, x, y, z, c, args...; suggested_backend)
+    B = build_B(implicit, prep, x, y, z, c, args...; suggested_backend)
 
     dX = ntuple(Val(N)) do k
         partials.(x_and_dx, k)
     end
-    dC_mat = mapreduce(hcat, dX) do dₖx
+    dC_vec = map(dX) do dₖx
         dₖx_vec = vec(dₖx)
         dₖc_vec = B(dₖx_vec)
         return dₖc_vec
     end
-    dY_mat = implicit.linear_solver(A, -dC_mat)
+    dY = map(dC_vec) do dₖc_vec
+        dₖy_vec = implicit.linear_solver(A, -dₖc_vec)
+        dₖy = reshape(dₖy_vec, size(y))
+        return dₖy
+    end
 
     y_and_dy = map(y, LinearIndices(y)) do yi, i
-        Dual{T}(yi, Partials(ntuple(k -> dY_mat[i, k], Val(N))))
+        Dual{T}(yi, Partials(ntuple(k -> dY[k][i], Val(N))))
     end
 
     return y_and_dy, z

src/ImplicitDifferentiation.jl

@@ -21,20 +21,21 @@ using DifferentiationInterface:
     pullback,
     pushforward!,
     pushforward
-using Krylov: Krylov
-using IterativeSolvers: IterativeSolvers
+using Krylov: Krylov, krylov_workspace, krylov_solve!, solution
 using LinearOperators: LinearOperator
 using LinearMaps: FunctionMap
 using LinearAlgebra: factorize
 
 include("utils.jl")
 include("settings.jl")
-include("preparation.jl")
 include("implicit_function.jl")
+include("preparation.jl")
 include("execution.jl")
+include("callable.jl")
 
 export MatrixRepresentation, OperatorRepresentation
-export IterativeLinearSolver
+export IterativeLinearSolver, DirectLinearSolver
 export ImplicitFunction
+export prepare_implicit
 
 end

src/callable.jl

@@ -0,0 +1,9 @@
+function (implicit::ImplicitFunction)(x::AbstractArray, args::Vararg{Any,N}) where {N}
+    return implicit(ImplicitFunctionPreparation(), x, args...)
+end
+
+function (implicit::ImplicitFunction)(
+    ::ImplicitFunctionPreparation, x::AbstractArray, args::Vararg{Any,N}
+) where {N}
+    return implicit.solver(x, args...)
+end