Unknown error from ForwardDiff

Specific Domains Optimization (Mathematical)
1

Need some help debugging an error from ForwardDiff. Let me know what additional information would help!

ERROR: 
Stacktrace:
 [1] ≺(::Nothing, ::Type) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\dual.jl:49
 [2] +(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12}, ::ForwardDiff.Dual{nothing,Float64,12}) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\dual.jl:135
 [3] objective_fxn(::Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}) at .\REPL[50]:16
 [4] vector_mode_gradient!(::DiffResults.MutableDiffResult{1,Float64,Tuple{Array{Float64,1}}}, ::typeof(objective_fxn), ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}}) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\apiutils.jl:37
 [5] gradient! at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\gradient.jl:35 [inlined]
 [6] gradient! at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\gradient.jl:33 [inlined]
 [7] (::getfield(NLSolversBase, Symbol("##14#18")){Float64,typeof(objective_fxn),ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}}})(::Array{Float64,1}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\NLSolversBase\NsXIC\src\objective_types\oncedifferentiable.jl:69
 [8] value_gradient!!(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\NLSolversBase\NsXIC\src\interface.jl:82
 [9] initial_state(::LBFGS{Nothing,InitialStatic{Float64},HagerZhang{Float64,Base.RefValue{Bool}},getfield(Optim, Symbol("##19#21"))}, ::Optim.Options{Float64,Nothing}, ::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\solvers\first_order\l_bfgs.jl:158
 [10] optimize(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}, ::LBFGS{Nothing,InitialStatic{Float64},HagerZhang{Float64,Base.RefValue{Bool}},getfield(Optim, Symbol("##19#21"))}, ::Optim.Options{Float64,Nothing}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\optimize.jl:33
 [11] #optimize#87(::Bool, ::Symbol, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\interface.jl:64
 [12] optimize(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\interface.jl:58
 [13] top-level scope at none:0SYSTEM: show(lasterr) caused an error
ArgumentError("`nothing` should not be printed; use `show`, `repr`, or custom output instead.")

Stacktrace:
 [1] ≺(::Nothing, ::Type) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\dual.jl:49
 [2] +(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12}, ::ForwardDiff.Dual{nothing,Float64,12}) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\dual.jl:135
 [3] objective_fxn(::Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}) at .\REPL[50]:16
 [4] vector_mode_gradient!(::DiffResults.MutableDiffResult{1,Float64,Tuple{Array{Float64,1}}}, ::typeof(objective_fxn), ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}}) at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\apiutils.jl:37
 [5] gradient! at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\gradient.jl:35 [inlined]
 [6] gradient! at C:\Users\bdeon\.julia\packages\ForwardDiff\DVizx\src\gradient.jl:33 [inlined]
 [7] (::getfield(NLSolversBase, Symbol("##14#18")){Float64,typeof(objective_fxn),ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12},1}}})(::Array{Float64,1}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\NLSolversBase\NsXIC\src\objective_types\oncedifferentiable.jl:69
 [8] value_gradient!!(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\NLSolversBase\NsXIC\src\interface.jl:82
 [9] initial_state(::LBFGS{Nothing,InitialStatic{Float64},HagerZhang{Float64,Base.RefValue{Bool}},getfield(Optim, Symbol("##19#21"))}, ::Optim.Options{Float64,Nothing}, ::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\solvers\first_order\l_bfgs.jl:158
 [10] optimize(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}, ::LBFGS{Nothing,InitialStatic{Float64},HagerZhang{Float64,Base.RefValue{Bool}},getfield(Optim, Symbol("##19#21"))}, ::Optim.Options{Float64,Nothing}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\optimize.jl:33
 [11] #optimize#87(::Bool, ::Symbol, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\interface.jl:64
 [12] optimize(::OnceDifferentiable{Float64,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}) at C:\Users\bdeon\.julia\packages\Optim\DKSJU\src\multivariate\optimize\interface.jl:58
 [13] top-level scope at none:0
 [14] eval(::Module, ::Any) at .\boot.jl:328
 [15] eval_user_input(::Any, ::REPL.REPLBackend) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.1\REPL\src\REPL.jl:85
 [16] macro expansion at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.1\REPL\src\REPL.jl:117 [inlined]
 [17] (::getfield(REPL, Symbol("##26#27")){REPL.REPLBackend})() at .\task.jl:259

This is in the context of using Optim with autodiff. The error is occuring in my objective function at the line where log_px_typed[k] is being added to. I’m feeding the following objective function to optim

  n, m = size(X)

  nodes, weights = gausshermite(q)
  z_cache1 = DiffCache(T, (m,q), Val{ForwardDiff.pickchunksize(2*m+2)})
  z_cache2 = DiffCache(T, (q,), Val{ForwardDiff.pickchunksize(2*m+2)})

  function objective_fxn(beta)
    a = @view beta[1:m]
    b = @view beta[(m+1):2m]
    tau = @view beta[(2m+1):end]

    P = get_cache(z_cache1, eltype(beta))
    P_typed = reinterpret(eltype(beta[1]), P)

    log_px = get_cache(z_cache2, eltype(beta))
    log_px_typed = reinterpret(eltype(beta[1]), log_px)

    fill_probs!(P_typed, sqrt(2.0 * tau[2]) .* nodes .+ tau[1], a, b)

    result = zero(eltype(beta))
    for p in 1:n
      log_px_typed .= zero(eltype(beta))
      for k in 1:q
        for i in 1:m
          log_px_typed[k] += X[p,i] * log(P[i,k]) + (1 - X[p,i]) * log(1 - P[i,k])
        end
      end
      result += logsumexp(log_px .+ log.(weights))
    end
    return -result + n*log(sqrt(pi))
  end

Seems to be a problem with the ForwardDiff Tag.

If I try this:

TT=ForwardDiff.Dual{ForwardDiff.Tag{typeof(objective_fxn),Float64},Float64,12}
beta = [ones(TT,m); zeros(TT,m); 0.0; 1.0]
objective_fxn(beta)

I get the error but if I try

TT=ForwardDiff.Dual{nothing,Float64,12}
beta = [ones(TT,m); zeros(TT,m); 0.0; 1.0]
objective_fxn(beta)

There is no error

2

I figured out the problem. I kept using the untyped variables (such as P and log_px) rather than the typed variables (P_typed and log_px_typed).