我正试图将自动微分(ForwardDiff(应用于包含find_zero(Roots(实例的函数，但遇到一个错误，该错误似乎与find_zer0不接受ForwardDiff.Doual类型有关。
这里有一个(人为的(最小工作示例来说明这个问题：
using Distributions
using Roots
using StatsFuns
using ForwardDiff
function test_fun(θ::AbstractVector{T}) where T
μ,σ,p = θ;
z_star = find_zero(z -> logistic(z) - p, 0.0)
return pdf(Normal(μ,σ),z_star)
end
test_fun([0.0,1.0,0.75])
ForwardDiff.gradient(test_fun,[0.0,1.0,0.75])
这会导致以下错误：
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3})
Closest candidates are:
Float64(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:200
Float64(::T) where T<:Number at boot.jl:716
Float64(::Irrational{:invsqrt2}) at irrationals.jl:189
...
Stacktrace:
[1] convert(::Type{Float64}, ::ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}) at ./number.jl:7
[2] setproperty!(::Roots.UnivariateZeroState{Float64,ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}, ::Symbol, ::ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}) at ./Base.jl:34
[3] update_state(::Roots.Secant, ::Roots.DerivativeFree{Roots.DerivativeFree{var"#5#6"{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}}}, ::Roots.UnivariateZeroState{Float64,ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}, ::Roots.UnivariateZeroOptions{Float64,Float64,ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3},ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}) at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/derivative_free.jl:163
[4] find_zero(::Roots.Secant, ::Roots.AlefeldPotraShi, ::Roots.DerivativeFree{Roots.DerivativeFree{var"#5#6"{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}}}, ::Roots.UnivariateZeroState{Float64,ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}, ::Roots.UnivariateZeroOptions{Float64,Float64,ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3},ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}, ::Roots.NullTracks) at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/find_zero.jl:868
[5] find_zero(::Roots.DerivativeFree{var"#5#6"{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3}}}, ::Float64, ::Roots.Secant, ::Roots.AlefeldPotraShi; tracks::Roots.NullTracks, verbose::Bool, p::Nothing, kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/find_zero.jl:689
[6] #find_zero#36 at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/derivative_free.jl:123 [inlined]
[7] find_zero at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/derivative_free.jl:120 [inlined]
[8] #find_zero#5 at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/find_zero.jl:707 [inlined]
[9] find_zero at /bbkinghome/asharris/.julia/packages/Roots/TZpjF/src/find_zero.jl:707 [inlined]
[10] test_fun at ./REPL[7856]:3 [inlined]
[11] vector_mode_dual_eval at /bbkinghome/asharris/.julia/packages/ForwardDiff/QOqCN/src/apiutils.jl:37 [inlined]
[12] vector_mode_gradient(::typeof(test_fun), ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3},1}}) at /bbkinghome/asharris/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:106
[13] gradient(::Function, ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3},1}}, ::Val{true}) at /bbkinghome/asharris/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:19
[14] gradient(::Function, ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_fun),Float64},Float64,3},1}}) at /bbkinghome/asharris/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:17 (repeats 2 times)
[15] top-level scope at REPL[7858]:1
[16] run_repl(::REPL.AbstractREPL, ::Any) at /builddir/build/BUILD/julia/build/usr/share/julia/stdlib/v1.5/REPL/src/REPL.jl:288
我使用FowardDiff软件包的经验有限，可能误解了Dual类型的工作原理，所以如果有人知道如何解决这个问题，我将不胜感激。非常感谢！
z_star = find_zero(z -> logistic(z) - p, 0.0)
你有一个固定的初始条件，它是非对偶的。把它变成双重的。
z_star = find_zero(z -> logistic(z) - p, zero(eltype(θ))