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| 1 | +module ForwardDiffStaticArraysExt |
| 2 | + |
| 3 | +using ForwardDiff, StaticArrays |
| 4 | +using ForwardDiff.LinearAlgebra |
| 5 | +using ForwardDiff.DiffResults |
| 6 | +using ForwardDiff: Dual, partials, GradientConfig, JacobianConfig, HessianConfig, Tag, Chunk, |
| 7 | + gradient, hessian, jacobian, gradient!, hessian!, jacobian!, |
| 8 | + extract_gradient!, extract_jacobian!, extract_value!, |
| 9 | + vector_mode_gradient, vector_mode_gradient!, |
| 10 | + vector_mode_jacobian, vector_mode_jacobian!, valtype, value, _lyap_div! |
| 11 | +using DiffResults: DiffResult, ImmutableDiffResult, MutableDiffResult |
| 12 | + |
| 13 | +@generated function dualize(::Type{T}, x::StaticArray) where T |
| 14 | + N = length(x) |
| 15 | + dx = Expr(:tuple, [:(Dual{T}(x[$i], chunk, Val{$i}())) for i in 1:N]...) |
| 16 | + V = StaticArrays.similar_type(x, Dual{T,eltype(x),N}) |
| 17 | + return quote |
| 18 | + chunk = Chunk{$N}() |
| 19 | + $(Expr(:meta, :inline)) |
| 20 | + return $V($(dx)) |
| 21 | + end |
| 22 | +end |
| 23 | + |
| 24 | +@inline static_dual_eval(::Type{T}, f, x::StaticArray) where T = f(dualize(T, x)) |
| 25 | + |
| 26 | +function LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N} |
| 27 | + λ,Q = eigen(Symmetric(value.(parent(A)))) |
| 28 | + parts = ntuple(j -> diag(Q' * getindex.(partials.(A), j) * Q), N) |
| 29 | + Dual{Tg}.(λ, tuple.(parts...)) |
| 30 | +end |
| 31 | + |
| 32 | +function LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N} |
| 33 | + λ = eigvals(A) |
| 34 | + _,Q = eigen(Symmetric(value.(parent(A)))) |
| 35 | + parts = ntuple(j -> Q*_lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N) |
| 36 | + Eigen(λ,Dual{Tg}.(Q, tuple.(parts...))) |
| 37 | +end |
| 38 | + |
| 39 | +# Gradient |
| 40 | +@inline ForwardDiff.gradient(f, x::StaticArray) = vector_mode_gradient(f, x) |
| 41 | +@inline ForwardDiff.gradient(f, x::StaticArray, cfg::GradientConfig) = gradient(f, x) |
| 42 | +@inline ForwardDiff.gradient(f, x::StaticArray, cfg::GradientConfig, ::Val) = gradient(f, x) |
| 43 | + |
| 44 | +@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray) = vector_mode_gradient!(result, f, x) |
| 45 | +@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::GradientConfig) = gradient!(result, f, x) |
| 46 | +@inline ForwardDiff.gradient!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::GradientConfig, ::Val) = gradient!(result, f, x) |
| 47 | + |
| 48 | +@generated function extract_gradient(::Type{T}, y::Real, x::S) where {T,S<:StaticArray} |
| 49 | + result = Expr(:tuple, [:(partials(T, y, $i)) for i in 1:length(x)]...) |
| 50 | + return quote |
| 51 | + $(Expr(:meta, :inline)) |
| 52 | + V = StaticArrays.similar_type(S, valtype($y)) |
| 53 | + return V($result) |
| 54 | + end |
| 55 | +end |
| 56 | + |
| 57 | +@inline function ForwardDiff.vector_mode_gradient(f, x::StaticArray) |
| 58 | + T = typeof(Tag(f, eltype(x))) |
| 59 | + return extract_gradient(T, static_dual_eval(T, f, x), x) |
| 60 | +end |
| 61 | + |
| 62 | +@inline function ForwardDiff.vector_mode_gradient!(result, f, x::StaticArray) |
| 63 | + T = typeof(Tag(f, eltype(x))) |
| 64 | + return extract_gradient!(T, result, static_dual_eval(T, f, x)) |
| 65 | +end |
| 66 | + |
| 67 | +# Jacobian |
| 68 | +@inline ForwardDiff.jacobian(f, x::StaticArray) = vector_mode_jacobian(f, x) |
| 69 | +@inline ForwardDiff.jacobian(f, x::StaticArray, cfg::JacobianConfig) = jacobian(f, x) |
| 70 | +@inline ForwardDiff.jacobian(f, x::StaticArray, cfg::JacobianConfig, ::Val) = jacobian(f, x) |
| 71 | + |
| 72 | +@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray) = vector_mode_jacobian!(result, f, x) |
| 73 | +@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::JacobianConfig) = jacobian!(result, f, x) |
| 74 | +@inline ForwardDiff.jacobian!(result::Union{AbstractArray,DiffResult}, f, x::StaticArray, cfg::JacobianConfig, ::Val) = jacobian!(result, f, x) |
| 75 | + |
| 76 | +@generated function extract_jacobian(::Type{T}, ydual::StaticArray, x::S) where {T,S<:StaticArray} |
| 77 | + M, N = length(ydual), length(x) |
| 78 | + result = Expr(:tuple, [:(partials(T, ydual[$i], $j)) for i in 1:M, j in 1:N]...) |
| 79 | + return quote |
| 80 | + $(Expr(:meta, :inline)) |
| 81 | + V = StaticArrays.similar_type(S, valtype(eltype($ydual)), Size($M, $N)) |
| 82 | + return V($result) |
| 83 | + end |
| 84 | +end |
| 85 | + |
| 86 | +@inline function ForwardDiff.vector_mode_jacobian(f, x::StaticArray) |
| 87 | + T = typeof(Tag(f, eltype(x))) |
| 88 | + return extract_jacobian(T, static_dual_eval(T, f, x), x) |
| 89 | +end |
| 90 | + |
| 91 | +function extract_jacobian(::Type{T}, ydual::AbstractArray, x::StaticArray) where T |
| 92 | + result = similar(ydual, valtype(eltype(ydual)), length(ydual), length(x)) |
| 93 | + return extract_jacobian!(T, result, ydual, length(x)) |
| 94 | +end |
| 95 | + |
| 96 | +@inline function ForwardDiff.vector_mode_jacobian!(result, f, x::StaticArray) |
| 97 | + T = typeof(Tag(f, eltype(x))) |
| 98 | + ydual = static_dual_eval(T, f, x) |
| 99 | + result = extract_jacobian!(T, result, ydual, length(x)) |
| 100 | + result = extract_value!(T, result, ydual) |
| 101 | + return result |
| 102 | +end |
| 103 | + |
| 104 | +@inline function ForwardDiff.vector_mode_jacobian!(result::ImmutableDiffResult, f, x::StaticArray) |
| 105 | + T = typeof(Tag(f, eltype(x))) |
| 106 | + ydual = static_dual_eval(T, f, x) |
| 107 | + result = DiffResults.jacobian!(result, extract_jacobian(T, ydual, x)) |
| 108 | + result = DiffResults.value!(d -> value(T,d), result, ydual) |
| 109 | + return result |
| 110 | +end |
| 111 | + |
| 112 | +# Hessian |
| 113 | +ForwardDiff.hessian(f, x::StaticArray) = jacobian(y -> gradient(f, y), x) |
| 114 | +ForwardDiff.hessian(f, x::StaticArray, cfg::HessianConfig) = hessian(f, x) |
| 115 | +ForwardDiff.hessian(f, x::StaticArray, cfg::HessianConfig, ::Val) = hessian(f, x) |
| 116 | + |
| 117 | +ForwardDiff.hessian!(result::AbstractArray, f, x::StaticArray) = jacobian!(result, y -> gradient(f, y), x) |
| 118 | + |
| 119 | +ForwardDiff.hessian!(result::MutableDiffResult, f, x::StaticArray) = hessian!(result, f, x, HessianConfig(f, result, x)) |
| 120 | + |
| 121 | +ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray, cfg::HessianConfig) = hessian!(result, f, x) |
| 122 | +ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray, cfg::HessianConfig, ::Val) = hessian!(result, f, x) |
| 123 | + |
| 124 | +function ForwardDiff.hessian!(result::ImmutableDiffResult, f, x::StaticArray) |
| 125 | + T = typeof(Tag(f, eltype(x))) |
| 126 | + d1 = dualize(T, x) |
| 127 | + d2 = dualize(T, d1) |
| 128 | + fd2 = f(d2) |
| 129 | + val = value(T,value(T,fd2)) |
| 130 | + grad = extract_gradient(T,value(T,fd2), x) |
| 131 | + hess = extract_jacobian(T,partials(T,fd2), x) |
| 132 | + result = DiffResults.hessian!(result, hess) |
| 133 | + result = DiffResults.gradient!(result, grad) |
| 134 | + result = DiffResults.value!(result, val) |
| 135 | + return result |
| 136 | +end |
| 137 | + |
| 138 | +end |
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