# UndefRefError: access to undefined reference, when I use NLsolve.jl

**URL:** <https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795>\
**Category:** Optimization (Mathematical)\
**Created:** [May 5, 2020, 9:05am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795 "2020-05-05T09:05:39Z")\
**Posts on this page:** 11\
**Page:** 1

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 5, 2020, 9:05am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/1 "2020-05-05T09:05:39Z")

</div>

I am new to Julia and the Julia community. I’d appreciate it if someone can help me with this error. I have also opened an [issue](https://github.com/JuliaNLSolvers/NLsolve.jl/issues/236#issue-612443067) in the package NLsolve.jl.

I tried to use variables and parameters with type Float64 and auto differentiation with`autodiff=: forward`. Because the package ForwardDiff.jl requires variables to be of type Real, see [here](http://www.juliadiff.org/ForwardDiff.jl/stable/user/limitations/), I changed the initial guess to be of type Real, with parameters remain of type Float64. In this case, the function `f!` can be evaluated(as in the MWE), while the `nlsolve` doesn’t work.

Here is the error information.

```julia
ERROR: UndefRefError: access to undefined reference
Stacktrace:
 [1] getindex at ./array.jl:788 [inlined]
 [2] seed! at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/apiutils.jl:59 [inlined]
 [3] seed! at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/apiutils.jl:58 [inlined]
 [4] vector_mode_dual_eval(::var"#1071#1072", ::Array{Real,1}, ::Array{Float64,1}, ::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#1071#1072",Real},Real,1,Tuple{Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1},Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1}}}) at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/apiutils.jl:43
 [5] vector_mode_jacobian!(::DiffResults.MutableDiffResult{1,Array{Real,1},Tuple{Array{Float64,2}}}, ::var"#1071#1072", ::Array{Real,1}, ::Array{Float64,1}, ::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#1071#1072",Real},Real,1,Tuple{Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1},Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1}}}) at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/jacobian.jl:164
 [6] jacobian! at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/jacobian.jl:74 [inlined]
 [7] (::NLSolversBase.var"#fj_forwarddiff!#24"{var"#1071#1072",ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#1071#1072",Real},Real,1,Tuple{Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1},Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#1071#1072",Real},Real,1},1}}},Array{Real,1}})(::Array{Real,1}, ::Array{Float64,2}, ::Array{Float64,1}) at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/objective_types/oncedifferentiable.jl:160
 [8] value_jacobian!!(::OnceDifferentiable{Array{Real,1},Array{Float64,2},Array{Float64,1}}, ::Array{Real,1}, ::Array{Float64,2}, ::Array{Float64,1}) at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/interface.jl:124
 [9] value_jacobian!! at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/interface.jl:122 [inlined]
 [10] newton_(::OnceDifferentiable{Array{Real,1},Array{Float64,2},Array{Float64,1}}, ::Array{Real,1}, ::Int64, ::Float64, ::Int64, ::Bool, ::Bool, ::Bool, ::Static, ::NLsolve.var"#27#29", ::NLsolve.NewtonCache{Array{Float64,1}}) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/solvers/newton.jl:48
 [11] newton(::OnceDifferentiable{Array{Real,1},Array{Float64,2},Array{Float64,1}}, ::Array{Real,1}, ::Int64, ::Float64, ::Int64, ::Bool, ::Bool, ::Bool, ::Static, ::NLsolve.NewtonCache{Array{Float64,1}}; linsolve::Function) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/solvers/newton.jl:134
 [12] nlsolve(::OnceDifferentiable{Array{Real,1},Array{Float64,2},Array{Float64,1}}, ::Array{Real,1}; method::Symbol, xtol::Int64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, linesearch::Static, linsolve::NLsolve.var"#27#29", factor::Int64, autoscale::Bool, m::Int64, beta::Int64, aa_start::Int64, droptol::Float64) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/nlsolve/nlsolve.jl:23
 [13] nlsolve(::Function, ::Array{Real,1}; method::Symbol, autodiff::Symbol, inplace::Bool, kwargs::Base.Iterators.Pairs{Symbol,Real,Tuple{Symbol,Symbol},NamedTuple{(:ftol, :show_trace),Tuple{Float64,Bool}}}) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/nlsolve/nlsolve.jl:52
 [14] top-level scope at none:0

```

Here is the MWE.

```julia
using NLsolve

function f!(res::AbstractArray,guess::AbstractArray,param::Float64)
    x = similar(guess)
    x[1] = guess[1]
    res[1] = x[1]^param-param*x[1]+1
    return res
end

# Initialize initial guess
guess = Array{Real,1}(undef,1)
guess[1] = 5.0
# Parameter
param = 2.0
# First evaluate(this works)
res = similar(guess)
init_f = f!(res,guess,param)
# Solve the problem(this goes with the error)
result = nlsolve((res,guess) -> f!(res,guess,param),
    guess,
    ftol = 1e-6,
    method = :newton,
    autodiff = :forward,
    show_trace = true,
    )

```

Thank you in advance.

---

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 6, 2020, 9:31am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/2 "2020-05-06T09:31:52Z")

</div>

I think the error is in line 49 of **nlsolve.jl**.

df = OnceDifferentiable(f, initial\_x, similar(initial\_x); autodiff=autodiff, inplace=inplace)

If the `initial_x` is of type `Array{Real}` , then `similar(initial_x)` returns an undefined array.

---

<div class="post-metadata">

**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [May 6, 2020, 10:18am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/3 "2020-05-06T10:18:22Z")

</div>

The mistake is on your side. You put type constraint that should not be. First you can remove the `AbstractArray` on the definition of `f!`, it does nothing (very little actually) so why bother?

More importantly, you should change `guess = Array{Real,1}(undef,1)` to `guess = Array{Float64,1}(undef,1)` or better do `guess = [0.5]`.

This is a classic mistake. When you define `guess`, you don’t give it a concrete type and even force it to be very loosely typed over the reals.

Then you get

```julia
julia> # Solve the problem(this goes with the error)
       result = nlsolve((res,guess) -> f!(res,guess,param),
           guess,
           ftol = 1e-9,
           method = :newton,
           autodiff = :forward,
           show_trace = true,
           )
Iter f(x) inf-norm Step 2-norm 
------ -------------- --------------
     0 2.500000e-01 NaN
     1 6.250000e-02 6.250000e-02
     2 1.562500e-02 1.562500e-02
     3 3.906250e-03 3.906250e-03
     4 9.765625e-04 9.765625e-04
     5 2.441406e-04 2.441406e-04
     6 6.103516e-05 6.103516e-05
     7 1.525879e-05 1.525879e-05
     8 3.814697e-06 3.814697e-06
     9 9.536743e-07 9.536743e-07
    10 2.384186e-07 2.384186e-07
    11 5.960464e-08 5.960464e-08
    12 1.490116e-08 1.490116e-08
    13 3.725290e-09 3.725290e-09
    14 9.313226e-10 9.313226e-10
Results of Nonlinear Solver Algorithm
 * Algorithm: Newton with line-search
 * Starting Point: [0.5]
 * Zero: [0.999969482421875]
 * Inf-norm of residuals: 0.000000
 * Iterations: 14
 * Convergence: true
   * |x - x'| < 0.0e+00: false
   * |f(x)| < 1.0e-09: true
 * Function Calls (f): 15
 * Jacobian Calls (df/dx): 14

```

However, I am now super surprised by the bad convergence of this newton run, it does not seem very quadratic too me…

---

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 6, 2020, 11:44am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/4 "2020-05-06T11:44:57Z")

</div>

Thank you for your suggestion.

Actually, I am handling a large scale nonlinear system with 6300 equations. Should I remove the `AbstractArray` as well?

By the way, I know that assigning the guess with a `Float64` directly works in this case, but it does not work in my whole problem. As I have mentioned above, I encountered the problem in ForwardDiff.jl so I tried to use initial guess that of type Real. Or do I misunderstand the tip 3 [here](http://www.juliadiff.org/ForwardDiff.jl/stable/user/limitations/)? If I force the guess to be of type Real, then the error is thrown.

---

<div class="post-metadata">

**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [May 6, 2020, 11:55am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/5 "2020-05-06T11:55:55Z")

</div>

I guess you misunderstand. It is fine to put type constraint in function definitions but they should be loose enough for AD to work. In your case I would remove all type constraint in `f!`. This is what your link is referring too. If you force `f!` to accept only real-valued inputs for example, it would error Forwarddiff because it wants to use `Dual`.

The second mistake is that `x::Array{Real, 1}` is “harmful” because it forces the compiler not to use a concrete type (like `Array{Float64, 1}`), and as said in the [docs](https://docs.julialang.org/en/v1/base/numbers/) `Real` is an **abstract** supertype. It is (or I ) mostly used for dispatch by putting type constraint in the arguments of functions.

---

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 6, 2020, 12:27pm UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/6 "2020-05-06T12:27:54Z")

</div>

I am sorry about the imprecision before.

Previously, I simply fed guess that of type `Float64`. This was my type constraint in the function definition and it seems like no restrictions have been put. I have also tried to get rid of all constraints but the error goes the same.

```julia
function dynamic_problem!(
    res_dynamic::AbstractArray, # residual 
    guess_dynamic::AbstractArray, # guess
    init_dynamic::NamedTuple, # initial conditions
    exos_dynamic::NamedTuple, # exogenous variables
    params_dynamic::NamedTuple, # parameters
    )

```

The error goes:

```julia
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12})
Closest candidates are:
  Float64(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:200
  Float64(::T) where T<:Number at boot.jl:715
  Float64(::Int8) at float.jl:60
  ...
Stacktrace:
 [1] convert(::Type{Float64}, ::ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12}) at ./number.jl:7
 [2] setindex! at ./array.jl:828 [inlined]
 [3] macro expansion at ./multidimensional.jl:786 [inlined]
 [4] macro expansion at ./cartesian.jl:64 [inlined]
 [5] macro expansion at ./multidimensional.jl:781 [inlined]
 [6] _unsafe_setindex!(::IndexLinear, ::Array{Float64,3}, ::Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},2}, ::UnitRange{Int64}, ::UnitRange{Int64}, ::Int64) at ./multidimensional.jl:774
 [7] _setindex! at ./multidimensional.jl:769 [inlined]
 [8] setindex! at ./abstractarray.jl:1073 [inlined]
 [9] dynamic_problem!(::Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}, ::Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}, ::NamedTuple{(:π₁, :Y₁, :Xᶠ₁, :wL₁, :rK₁),Tuple{Array{Float64,3},Array{Float64,2},Array{Float64,2},Array{Float64,1},Array{Float64,2}}}, ::NamedTuple{(:Dᴿ, :L̂, :d̂, :T̂),Tuple{Array{Float64,2},Array{Float64,2},Array{Float64,4},Array{Float64,3}}}, ::NamedTuple{(:T, :NC, :NS, :NK, :β̃ᴸ, :β̃ᴷ, :ψ, :θ, :β̃ᴹ, :ρ, :δ, :α),Tuple{Int64,Int64,Int64,Int64,Array{Float64,2},Array{Float64,3},Array{Float64,2},Int64,Array{Float64,3},Float64,Array{Float64,2},Array{Float64,2}}}) at /Users/pearson/research/gitrepo/replication_exercise_EKNR2016AER/Full_Model/baseline/src/Full_Baseline_Functions.jl:244
 [10] (::var"#32#33")(::Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}, ::Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}) at ./none:2
 [11] chunk_mode_jacobian!(::DiffResults.MutableDiffResult{1,Array{Float64,3},Tuple{Array{Float64,2}}}, ::var"#32#33", ::Array{Float64,3}, ::Array{Float64,3}, ::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#32#33",Float64},Float64,12,Tuple{Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3},Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}}}) at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/jacobian.jl:213
 [12] jacobian! at /Users/pearson/.julia/packages/ForwardDiff/cXTw0/src/jacobian.jl:76 [inlined]
 [13] (::NLSolversBase.var"#fj_forwarddiff!#24"{var"#32#33",ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#32#33",Float64},Float64,12,Tuple{Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3},Array{ForwardDiff.Dual{ForwardDiff.Tag{var"#32#33",Float64},Float64,12},3}}},Array{Float64,3}})(::Array{Float64,3}, ::Array{Float64,2}, ::Array{Float64,3}) at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/objective_types/oncedifferentiable.jl:160
 [14] value_jacobian!!(::OnceDifferentiable{Array{Float64,3},Array{Float64,2},Array{Float64,3}}, ::Array{Float64,3}, ::Array{Float64,2}, ::Array{Float64,3}) at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/interface.jl:124
 [15] value_jacobian!! at /Users/pearson/.julia/packages/NLSolversBase/mGaJg/src/interface.jl:122 [inlined]
 [16] newton_(::OnceDifferentiable{Array{Float64,3},Array{Float64,2},Array{Float64,3}}, ::Array{Float64,3}, ::Float64, ::Float64, ::Int64, ::Bool, ::Bool, ::Bool, ::Static, ::NLsolve.var"#27#29", ::NLsolve.NewtonCache{Array{Float64,3}}) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/solvers/newton.jl:48
 [17] #newton#7 at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/solvers/newton.jl:134 [inlined]
 [18] nlsolve(::OnceDifferentiable{Array{Float64,3},Array{Float64,2},Array{Float64,3}}, ::Array{Float64,3}; method::Symbol, xtol::Float64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, linesearch::Static, linsolve::NLsolve.var"#27#29", factor::Float64, autoscale::Bool, m::Int64, beta::Int64, aa_start::Int64, droptol::Float64) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/nlsolve/nlsolve.jl:23
 [19] nlsolve(::Function, ::Array{Float64,3}; method::Symbol, autodiff::Symbol, inplace::Bool, kwargs::Base.Iterators.Pairs{Symbol,Real,Tuple{Symbol,Symbol},NamedTuple{(:ftol, :show_trace),Tuple{Float64,Bool}}}) at /Users/pearson/.julia/packages/NLsolve/ZBTu4/src/nlsolve/nlsolve.jl:52
 [20] top-level scope at none:0

```

Due to this `MethodError`, I switched to initialize the guess of type `Real`, then the `UndefRefError` rises.

---

<div class="post-metadata">

**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [May 6, 2020, 12:35pm UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/7 "2020-05-06T12:35:52Z")

</div>

> [@PearsonCHEN](#):
>
> function f!(res::AbstractArray,guess::AbstractArray,param::Float64)

can you try with `function f!(res,guess,param)`?

---

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 6, 2020, 12:43pm UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/8 "2020-05-06T12:43:08Z")

</div>

This works fine with a `Float64` guess, while doesn’t work with a `Real` guess(`UndefRefError` arises). However, I still can not tell why the `MethodError` exists in my whole problem with `Float64` guess.

---

<div class="post-metadata">

**Author:** ![pkofod](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pkofod/32/2179_2.png) [@pkofod](https://discourse.julialang.org/u/pkofod)\
**Post date:** [May 6, 2020, 3:20pm UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/9 "2020-05-06T15:20:39Z")

</div>

> [@rveltz](#):
>
> However, I am now super surprised by the bad convergence of this newton run, it does not seem very quadratic too me…

That’s a pretty good question… It should actually converge in one iteration here…

---

<div class="post-metadata">

**Author:** ![PearsonCHEN](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pearsonchen/32/14590_2.png) [@PearsonCHEN](https://discourse.julialang.org/u/PearsonCHEN)\
**Post date:** [May 7, 2020, 12:41am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/10 "2020-05-07T00:41:19Z")

</div>

I see…

Different from the MWE, in the whole problem I didn’t preallocate the array for guess with proper type by using `eltype` or `similar`. If I preallocate the array for guess by using `eltype`, the `MethodError` disappears.

Also, thank you for your tips for the type constraint!

---

<div class="post-metadata">

**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [May 7, 2020, 6:05am UTC](https://discourse.julialang.org/t/undefreferror-access-to-undefined-reference-when-i-use-nlsolve-jl/38795/11 "2020-05-07T06:05:27Z")

</div>

nice!