search

SciML / NonlinearSolve.jl

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
https://docs.sciml.ai/NonlinearSolve/stable/
MIT License
216 stars 39 forks source link

Implementing ForwardDiff.hessian through NonlinearLeastSquaresProblem #445

Open IJ05 opened 1 month ago

IJ05 commented 1 month ago

I wanted to find the partial double and mixed derivatives of the variables c1_length, c2_length, c3_length with respect to the variables px and py. The first order derivatives of the same, obtained using ForwardDiff.gradient or ForwardDiff.jacobian are working fine, but ForwardDiff.hessian returns a method error.

Below is a MWE of the concerned functions: Minimum working example

using NonlinearSolve, ForwardDiff, SciMLSensitivity

function objfn(F,init,params)
    th1,th2 = init
    px,py,l1,l2 = params
    F[1] = l1*cos(th1)+l2*cos(th1+th2)-px
    F[2] = l1*sin(th1)+l2*sin(th1+th2)-py
    return F
end
function solve_nlprob(pxpy)
    px,py = pxpy
theta1 = pi/4;
theta2 = pi/4
initial_guess = [theta1;theta2];
l1 = 60; l2 = 60;
p = [px.value;py.value;l1;l2];
prob = NonlinearLeastSquaresProblem(NonlinearFunction(objfn, resid_prototype = zeros(2)), initial_guess,p)
resu = solve(prob,reltol = 1e-12, abstol = 1e-12);
th1,th2 = resu.u
cable1_base = [-90;0;0];
cable2_base = [-150;0;0];
cable3_base = [150;0;0];
cable1_top = [l1*cos(th1)/2;l1*sin(th1)/2;0];
cable23_top = [l1*cos(th1)+l2*cos(th1+th2)/2;l1*sin(th1)+l2*sin(th1+th2)/2;0];
c1_length=sqrt((cable1_top[1]-cable1_base[1])^2 + (cable1_top[2]-cable1_base[2])^2)
c2_length=sqrt((cable23_top[1]-cable2_base[1])^2 + (cable23_top[2]-cable2_base[2])^2)
c3_length=sqrt((cable23_top[1]-cable3_base[1])^2 + (cable23_top[2]-cable3_base[2])^2)
    return c1_length
end

The output for grad1 = ForwardDiff.gradient(solve_nlprob,[34.0,87.0]) is

2-element Vector{Float64}:
 0.0
 0.0

The output error for hess1 = ForwardDiff.hessian(solve_nlprob,[34.0,87.0]) is a method error which is:

Error and Stacktrace

MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2})

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:207
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:792
  (::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number}
   @ Base char.jl:50
  ...

Stacktrace:
  [1] convert(#unused#::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2})
    @ Base .\number.jl:7
  [2] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, i1::Int64)
    @ Base .\array.jl:969
  [3] objfn(F::Vector{Float64}, init::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, params::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}})
    @ Main .\In[3]:4
  [4] NonlinearFunction
    @ C:\Users\user\.julia\packages\SciMLBase\2HZ5m\src\scimlfunctions.jl:2356 [inlined]
  [5] evaluate_f
    @ C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\utils.jl:151 [inlined]
  [6] __init(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, ::GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}; alias_u0::Bool, maxiters::Int64, abstol::Float64, reltol::Float64, termination_condition::Nothing, internalnorm::typeof(DiffEqBase.NONLINEARSOLVE_DEFAULT_NORM), kwargs::Base.Pairs{Symbol, Bool, Tuple{Symbol, Symbol}, NamedTuple{(:default_set, :second_time), Tuple{Bool, Bool}}})
    @ NonlinearSolve C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\gaussnewton.jl:94
  [7] init_call(_prob::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, args::GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:528
  [8] init_up(prob::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, sensealg::Nothing, u0::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, p::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, args::GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}; kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:553
  [9] init(prob::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, args::GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}; sensealg::Nothing, u0::Nothing, p::Nothing, kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:541
 [10] __solve(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, ::GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}; kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ NonlinearSolve C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\NonlinearSolve.jl:134
 [11] macro expansion
    @ C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\default.jl:123 [inlined]
 [12] __solve(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, ::NonlinearSolvePolyAlgorithm{:NLLS, 5, Tuple{GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{Nothing, Nothing, Bool}, Nothing}, TrustRegion{nothing, Nothing, Rational{Int64}, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), Rational{Int64}, Nothing}, GaussNewton{nothing, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), LineSearch{BackTracking{Float64, Int64}, Nothing, Bool}, Nothing}, TrustRegion{nothing, Nothing, Rational{Int64}, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), Rational{Int64}, Nothing}, LevenbergMarquardt{true, Nothing, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), Float64, Float64, Float64, Float64, Float64, Float64, Float64}}}; kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ NonlinearSolve C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\default.jl:115
 [13] __solve(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, ::Nothing; kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:default_set, :second_time, :reltol, :abstol), Tuple{Bool, Bool, Float64, Float64}}})
    @ NonlinearSolve C:\Users\user\.julia\packages\NonlinearSolve\KlGj2\src\default.jl:398
 [14] __solve(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}; default_set::Bool, second_time::Bool, kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol, Symbol}, NamedTuple{(:reltol, :abstol), Tuple{Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:1370
 [15] solve_call(::NonlinearLeastSquaresProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol, Symbol}, NamedTuple{(:reltol, :abstol), Tuple{Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:608
 [16] solve_up(::NonlinearLeastSquaresProblem{Vector{Float64}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, ::Nothing, ::Vector{Float64}, ::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}; kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol, Symbol}, NamedTuple{(:reltol, :abstol), Tuple{Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:1049
 [17] solve(::NonlinearLeastSquaresProblem{Vector{Float64}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, NonlinearFunction{true, SciMLBase.FullSpecialize, typeof(objfn), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, SymbolicIndexingInterface.SymbolCache{Nothing, Nothing, Nothing}, Vector{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{true}, kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol, Symbol}, NamedTuple{(:reltol, :abstol), Tuple{Float64, Float64}}})
    @ DiffEqBase C:\Users\user\.julia\packages\DiffEqBase\eTCPy\src\solve.jl:980
 [18] solve_nlprob(pxpy::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2}})
    @ Main .\In[43]:9
 [19] vector_mode_dual_eval!
    @ C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\apiutils.jl:24 [inlined]
 [20] vector_mode_gradient(f::typeof(solve_nlprob), x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2}}})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\gradient.jl:89
 [21] gradient
    @ C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\gradient.jl:19 [inlined]
 [22] #99
    @ C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\hessian.jl:16 [inlined]
 [23] vector_mode_dual_eval!
    @ C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\apiutils.jl:24 [inlined]
 [24] vector_mode_jacobian(f::ForwardDiff.var"#99#100"{typeof(solve_nlprob), ForwardDiff.HessianConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}}}, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\jacobian.jl:125
 [25] jacobian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}}, ::Val{false})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\jacobian.jl:21
 [26] hessian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.HessianConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}}, ::Val{true})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\hessian.jl:17
 [27] hessian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.HessianConfig{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(solve_nlprob), Float64}, Float64, 2}}})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\hessian.jl:15
 [28] hessian(f::Function, x::Vector{Float64})
    @ ForwardDiff C:\Users\user\.julia\packages\ForwardDiff\PcZ48\src\hessian.jl:15
 [29] top-level scope
    @ In[48]:1

Environment

  1. Output of using Pkg Pkg.status() is: 
    Status `C:\Users\user\OneDrive\Desktop\Isaac John\julia_env\Project.toml`
[824d6782] Bonito v3.1.1
[f6369f11] ForwardDiff v0.10.36
[e9467ef8] GLMakie v0.10.1
[7073ff75] IJulia v1.24.2
⌅ [8913a72c] NonlinearSolve v3.4.0
⌅ [1ed8b502] SciMLSensitivity v7.51.0
[276b4fcb] WGLMakie v0.10.1
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
  2. Output of Pkg.status(; mode = PKGMODE_MANIFEST) is 
    Status `C:\Users\user\OneDrive\Desktop\Isaac John\julia_env\Manifest.toml`
⌅ [47edcb42] ADTypes v0.2.7
[621f4979] AbstractFFTs v1.5.0
[1520ce14] AbstractTrees v0.4.5
⌅ [79e6a3ab] Adapt v3.7.2
[66dad0bd] AliasTables v1.1.3
[27a7e980] Animations v0.4.1
[ec485272] ArnoldiMethod v0.4.0
⌅ [4fba245c] ArrayInterface v7.7.1
⌃ [4c555306] ArrayLayouts v1.9.2
[a9b6321e] Atomix v0.1.0
[67c07d97] Automa v1.0.3
[13072b0f] AxisAlgorithms v1.1.0
[39de3d68] AxisArrays v0.4.7
[d1d4a3ce] BitFlags v0.1.8
[62783981] BitTwiddlingConvenienceFunctions v0.1.5
[824d6782] Bonito v3.1.1
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.5
[49dc2e85] Calculus v0.5.1
[7057c7e9] Cassette v0.3.13
[082447d4] ChainRules v1.66.0
[d360d2e6] ChainRulesCore v1.23.0
[fb6a15b2] CloseOpenIntervals v0.1.12
[944b1d66] CodecZlib v0.7.4
[a2cac450] ColorBrewer v0.4.0
[35d6a980] ColorSchemes v3.25.0
[3da002f7] ColorTypes v0.11.5
[c3611d14] ColorVectorSpace v0.10.0
[5ae59095] Colors v0.12.11
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.0
[34da2185] Compat v4.15.0
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.4.1
[8f4d0f93] Conda v1.10.0
[187b0558] ConstructionBase v1.5.5
[d38c429a] Contour v0.6.3
[adafc99b] CpuId v0.3.1
[9a962f9c] DataAPI v1.16.0
[864edb3b] DataStructures v0.18.20
[e2d170a0] DataValueInterfaces v1.0.0
[927a84f5] DelaunayTriangulation v1.0.3
⌃ [2b5f629d] DiffEqBase v6.145.6
⌅ [459566f4] DiffEqCallbacks v2.36.1
[77a26b50] DiffEqNoiseProcess v5.21.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[b4f34e82] Distances v0.10.11
[31c24e10] Distributions v0.25.108
[ffbed154] DocStringExtensions v0.9.3
[fa6b7ba4] DualNumbers v0.6.8
[da5c29d0] EllipsisNotation v1.8.0
[4e289a0a] EnumX v1.0.4
⌅ [7da242da] Enzyme v0.11.20
⌅ [f151be2c] EnzymeCore v0.6.6
[429591f6] ExactPredicates v2.2.8
[460bff9d] ExceptionUnwrapping v0.1.10
⌅ [d4d017d3] ExponentialUtilities v1.25.0
[e2ba6199] ExprTools v0.1.10
[411431e0] Extents v0.1.2
[7a1cc6ca] FFTW v1.8.0
[7034ab61] FastBroadcast v0.2.8
[9aa1b823] FastClosures v0.3.2
[29a986be] FastLapackInterface v2.0.3
[5789e2e9] FileIO v1.16.3
[8fc22ac5] FilePaths v0.8.3
[48062228] FilePathsBase v0.9.21
[1a297f60] FillArrays v1.11.0
⌅ [6a86dc24] FiniteDiff v2.22.0
[53c48c17] FixedPointNumbers v0.8.5
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v0.10.36
[b38be410] FreeType v4.1.1
[663a7486] FreeTypeAbstraction v0.10.3
⌅ [f62d2435] FunctionProperties v0.1.1
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[d9f16b24] Functors v0.4.10
[f7f18e0c] GLFW v3.4.1
[e9467ef8] GLMakie v0.10.1
⌃ [0c68f7d7] GPUArrays v9.1.0
⌅ [46192b85] GPUArraysCore v0.1.5
⌅ [61eb1bfa] GPUCompiler v0.25.0
[c145ed77] GenericSchur v0.5.4
[cf35fbd7] GeoInterface v1.3.4
[5c1252a2] GeometryBasics v0.4.11
[86223c79] Graphs v1.11.0
[3955a311] GridLayoutBase v0.11.0
[42e2da0e] Grisu v1.0.2
[cd3eb016] HTTP v1.10.8
[3e5b6fbb] HostCPUFeatures v0.1.16
[34004b35] HypergeometricFunctions v0.3.23
[47d2ed2b] Hyperscript v0.0.5
[7073ff75] IJulia v1.24.2
[7869d1d1] IRTools v0.4.14
[615f187c] IfElse v0.1.1
[2803e5a7] ImageAxes v0.6.11
[c817782e] ImageBase v0.1.7
[a09fc81d] ImageCore v0.10.2
[82e4d734] ImageIO v0.6.8
[bc367c6b] ImageMetadata v0.9.9
[9b13fd28] IndirectArrays v1.0.0
[d25df0c9] Inflate v0.1.4
[a98d9a8b] Interpolations v0.15.1
[d1acc4aa] IntervalArithmetic v0.22.12
[8197267c] IntervalSets v0.7.10
[92d709cd] IrrationalConstants v0.2.2
[f1662d9f] Isoband v0.1.1
[c8e1da08] IterTools v1.10.0
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.5.0
[682c06a0] JSON v0.21.4
[b835a17e] JpegTurbo v0.1.5
⌅ [ccbc3e58] JumpProcesses v9.10.1
⌅ [ef3ab10e] KLU v0.4.1
⌃ [63c18a36] KernelAbstractions v0.9.18
[5ab0869b] KernelDensity v0.6.9
[ba0b0d4f] Krylov v0.9.6
⌅ [929cbde3] LLVM v6.6.3
[b964fa9f] LaTeXStrings v1.3.1
[10f19ff3] LayoutPointers v0.1.15
[50d2b5c4] Lazy v0.15.1
⌅ [5078a376] LazyArrays v1.10.0
[8cdb02fc] LazyModules v0.3.1
[2d8b4e74] LevyArea v1.0.0
[d3d80556] LineSearches v7.2.0
⌅ [7ed4a6bd] LinearSolve v2.22.1
[2ab3a3ac] LogExpFunctions v0.3.27
[e6f89c97] LoggingExtras v1.0.3
[bdcacae8] LoopVectorization v0.12.170
[1914dd2f] MacroTools v0.5.13
[ee78f7c6] Makie v0.21.1
[20f20a25] MakieCore v0.8.1
[d125e4d3] ManualMemory v0.1.8
[dbb5928d] MappedArrays v0.4.2
[0a4f8689] MathTeXEngine v0.6.0
⌅ [a3b82374] MatrixFactorizations v2.2.0
[bb5d69b7] MaybeInplace v0.1.2
[739be429] MbedTLS v1.1.9
[7269a6da] MeshIO v0.4.11
[e1d29d7a] Missings v1.2.0
[66fc600b] ModernGL v1.1.7
[e94cdb99] MosaicViews v0.3.4
[99f44e22] MsgPack v1.2.1
[46d2c3a1] MuladdMacro v0.2.4
[d41bc354] NLSolversBase v7.8.3
[2774e3e8] NLsolve v4.5.1
⌃ [872c559c] NNlib v0.9.16
[77ba4419] NaNMath v1.0.2
[f09324ee] Netpbm v1.1.1
⌅ [8913a72c] NonlinearSolve v3.4.0
[d8793406] ObjectFile v0.4.1
[510215fc] Observables v0.5.5
[6fe1bfb0] OffsetArrays v1.14.0
[52e1d378] OpenEXR v0.3.2
[4d8831e6] OpenSSL v1.4.3
[429524aa] Optim v1.9.4
[3bd65402] Optimisers v0.3.3
[bac558e1] OrderedCollections v1.6.3
⌅ [1dea7af3] OrdinaryDiffEq v6.66.0
[90014a1f] PDMats v0.11.31
[f57f5aa1] PNGFiles v0.4.3
[65ce6f38] PackageExtensionCompat v1.0.2
[19eb6ba3] Packing v0.5.0
[5432bcbf] PaddedViews v0.5.12
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.8.1
[eebad327] PkgVersion v0.3.3
[995b91a9] PlotUtils v1.4.1
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.14
[1d0040c9] PolyesterWeave v0.2.1
[647866c9] PolygonOps v0.1.2
[85a6dd25] PositiveFactorizations v0.2.4
⌅ [d236fae5] PreallocationTools v0.4.13
[aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[92933f4c] ProgressMeter v1.10.0
[43287f4e] PtrArrays v1.1.0
[4b34888f] QOI v1.0.0
[1fd47b50] QuadGK v2.9.4
[74087812] Random123 v1.7.0
[e6cf234a] RandomNumbers v1.5.3
[b3c3ace0] RangeArrays v0.3.2
[c84ed2f1] Ratios v0.4.5
[c1ae055f] RealDot v0.1.0
[3cdcf5f2] RecipesBase v1.3.4
⌅ [731186ca] RecursiveArrayTools v3.3.3
⌅ [f2c3362d] RecursiveFactorization v0.2.22
[189a3867] Reexport v1.2.2
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.0
[ae5879a3] ResettableStacks v1.1.1
[37e2e3b7] ReverseDiff v1.15.3
[79098fc4] Rmath v0.7.1
[5eaf0fd0] RoundingEmulator v0.2.1
⌅ [7e49a35a] RuntimeGeneratedFunctions v0.5.12
[fdea26ae] SIMD v3.5.0
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.42
⌅ [0bca4576] SciMLBase v2.15.2
⌅ [c0aeaf25] SciMLOperators v0.3.7
⌅ [1ed8b502] SciMLSensitivity v7.51.0
[6c6a2e73] Scratch v1.2.1
[efcf1570] Setfield v1.1.1
[65257c39] ShaderAbstractions v0.4.1
[992d4aef] Showoff v1.0.3
[73760f76] SignedDistanceFields v0.4.0
[777ac1f9] SimpleBufferStream v1.1.0
⌅ [727e6d20] SimpleNonlinearSolve v1.4.0
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[45858cf5] Sixel v0.1.3
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.2.1
⌅ [47a9eef4] SparseDiffTools v2.18.0
[dc90abb0] SparseInverseSubset v0.1.2
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.4.0
[cae243ae] StackViews v0.1.1
⌅ [aedffcd0] Static v0.8.9
[0d7ed370] StaticArrayInterface v1.5.0
[90137ffa] StaticArrays v1.9.4
[1e83bf80] StaticArraysCore v1.4.2
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.3
[4c63d2b9] StatsFuns v1.3.1
[789caeaf] StochasticDiffEq v6.65.1
[7792a7ef] StrideArraysCore v0.5.6
[09ab397b] StructArrays v0.6.18
[53d494c1] StructIO v0.3.0
⌅ [2efcf032] SymbolicIndexingInterface v0.3.1
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.11.1
[62fd8b95] TensorCore v0.1.1
[b189fb0b] ThreadPools v2.1.1
[8290d209] ThreadingUtilities v0.5.2
[731e570b] TiffImages v0.10.0
[a759f4b9] TimerOutputs v0.5.24
[9f7883ad] Tracker v0.2.34
[3bb67fe8] TranscodingStreams v0.10.8
⌅ [d5829a12] TriangularSolve v0.1.20
[410a4b4d] Tricks v0.1.8
[981d1d27] TriplotBase v0.1.0
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.20.0
[013be700] UnsafeAtomics v0.2.1
⌃ [d80eeb9a] UnsafeAtomicsLLVM v0.1.3
[3d5dd08c] VectorizationBase v0.21.67
[81def892] VersionParsing v1.3.0
[19fa3120] VertexSafeGraphs v0.2.0
[276b4fcb] WGLMakie v0.10.1
[eead4739] WidgetsBase v0.1.4
[efce3f68] WoodburyMatrices v1.0.0
[c2297ded] ZMQ v1.2.3
[e88e6eb3] Zygote v0.6.70
[700de1a5] ZygoteRules v0.2.5
[6e34b625] Bzip2_jll v1.0.8+1
[4e9b3aee] CRlibm_jll v1.0.1+0
[83423d85] Cairo_jll v1.18.0+2
[04572ae6] Deno_jll v1.33.4+0
[5ae413db] EarCut_jll v2.2.4+0
⌅ [7cc45869] Enzyme_jll v0.0.102+0
[2e619515] Expat_jll v2.6.2+0
[b22a6f82] FFMPEG_jll v6.1.1+0
[f5851436] FFTW_jll v3.3.10+0
[a3f928ae] Fontconfig_jll v2.13.96+0
[d7e528f0] FreeType2_jll v2.13.2+0
[559328eb] FriBidi_jll v1.0.14+0
[0656b61e] GLFW_jll v3.3.9+0
[78b55507] Gettext_jll v0.21.0+0
[7746bdde] Glib_jll v2.80.2+0
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[905a6f67] Imath_jll v3.1.11+0
[1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
[aacddb02] JpegTurbo_jll v3.0.3+0
[c1c5ebd0] LAME_jll v3.100.2+0
[dad2f222] LLVMExtra_jll v0.0.29+0
[1d63c593] LLVMOpenMP_jll v15.0.7+0
[dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.11+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.49.0+0
[94ce4f54] Libiconv_jll v1.17.0+0
[4b2f31a3] Libmount_jll v2.40.1+0
[38a345b3] Libuuid_jll v2.40.1+0
[856f044c] MKL_jll v2024.1.0+0
[e7412a2a] Ogg_jll v1.3.5+1
[18a262bb] OpenEXR_jll v3.2.4+0
[458c3c95] OpenSSL_jll v3.0.13+1
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[30392449] Pixman_jll v0.43.4+0
[f50d1b31] Rmath_jll v0.4.2+0
[02c8fc9c] XML2_jll v2.12.7+0
[aed1982a] XSLT_jll v1.1.34+0
[4f6342f7] Xorg_libX11_jll v1.8.6+0
[0c0b7dd1] Xorg_libXau_jll v1.0.11+0
[935fb764] Xorg_libXcursor_jll v1.2.0+4
[a3789734] Xorg_libXdmcp_jll v1.1.4+0
[1082639a] Xorg_libXext_jll v1.3.6+0
[d091e8ba] Xorg_libXfixes_jll v5.0.3+4
[a51aa0fd] Xorg_libXi_jll v1.7.10+4
[d1454406] Xorg_libXinerama_jll v1.1.4+4
[ec84b674] Xorg_libXrandr_jll v1.5.2+4
[ea2f1a96] Xorg_libXrender_jll v0.9.11+0
[14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
[c7cfdc94] Xorg_libxcb_jll v1.15.0+0
[c5fb5394] Xorg_xtrans_jll v1.5.0+0
[8f1865be] ZeroMQ_jll v4.3.5+0
[9a68df92] isoband_jll v0.2.3+0
[a4ae2306] libaom_jll v3.9.0+0
[0ac62f75] libass_jll v0.15.1+0
[f638f0a6] libfdk_aac_jll v2.0.2+0
[b53b4c65] libpng_jll v1.6.43+1
[075b6546] libsixel_jll v1.10.3+0
[a9144af2] libsodium_jll v1.0.20+0
[f27f6e37] libvorbis_jll v1.3.7+1
[1317d2d5] oneTBB_jll v2021.12.0+0
[1270edf5] x264_jll v2021.5.5+0
[dfaa095f] x265_jll v3.5.0+0
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[8bf52ea8] CRC32c
[ade2ca70] Dates
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.3
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.9.2
[de0858da] Printf
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics v1.9.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.0.5+0
[deac9b47] LibCURL_jll v7.84.0+0
[29816b5a] LibSSH2_jll v1.10.2+0
[c8ffd9c3] MbedTLS_jll v2.28.2+0
[14a3606d] MozillaCACerts_jll v2022.10.11
[4536629a] OpenBLAS_jll v0.3.21+4
[05823500] OpenLibm_jll v0.8.1+0
[efcefdf7] PCRE2_jll v10.42.0+0
[bea87d4a] SuiteSparse_jll v5.10.1+6
[83775a58] Zlib_jll v1.2.13+0
[8e850b90] libblastrampoline_jll v5.8.0+0
[8e850ede] nghttp2_jll v1.48.0+0
[3f19e933] p7zip_jll v17.4.0+0
Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
  3. Output of versioninfo() is 
    
Julia Version 1.9.3
Commit bed2cd540a (2023-08-24 14:43 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: 16 × AMD Ryzen 7 4700G with Radeon Graphics         
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-14.0.6 (ORCJIT, znver2)
Threads: 2 on 16 virtual cores