I am having the following inexplicable error when I try to solve an ode. Can you help me interpret the error message.
julia> include("t.jl");
ERROR: LoadError: UndefVarError: hasproperty not defined
Stacktrace:
[1] check_error(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},Float64,Float64,Float64,Array{Array{Float64,1},1},OrdinaryDiffEq.ODECompositeSolution{Float64,2,Array{Array{Float64,1},1},Nothing,Nothing,Array{Float64,1},Array{Array{Array{Float64,1},1},1},ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Vern7Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Vern7Tableau{Float64,Float64}},OrdinaryDiffEq.Rodas4Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.RodasTableau{Float64,Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DefaultLinSolve,FiniteDiff.JacobianCache{Array{Float64,1},Array{Float64,1},Array{Float64,1},UnitRange{Int64},Nothing,Val{:forward},Float64},FiniteDiff.GradientCache{Nothing,Array{Float64,1},Array{Float64,1},Val{:forward},Float64,Val{true}}}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Vern7Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Vern7Tableau{Float64,Float64}},OrdinaryDiffEq.Rodas4Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.RodasTableau{Float64,Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DefaultLinSolve,FiniteDiff.JacobianCache{Array{Float64,1},Array{Float64,1},Array{Float64,1},UnitRange{Int64},Nothing,Val{:forward},Float64},FiniteDiff.GradientCache{Nothing,Array{Float64,1},Array{Float64,1},Val{:forward},Float64,Val{true}}}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(opnorm),CallbackSet{Tuple{},Tuple{}},typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN),typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE),typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK),DataStructures.BinaryHeap{Float64,DataStructures.LessThan},DataStructures.BinaryHeap{Float64,DataStructures.LessThan},Nothing,Nothing,Int64,Array{Float64,1},Array{Float64,1},Array{Float64,1}},Array{Float64,1},Float64,Nothing}) at C:\Users\iamsu\.julia\packages\DiffEqBase\gQwlE\src\integrator_interface.jl:327
[2] check_error! at C:\Users\iamsu\.julia\packages\DiffEqBase\gQwlE\src\integrator_interface.jl:361 [inlined]
[3] solve!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},Float64,Float64,Float64,Array{Array{Float64,1},1},OrdinaryDiffEq.ODECompositeSolution{Float64,2,Array{Array{Float64,1},1},Nothing,Nothing,Array{Float64,1},Array{Array{Array{Float64,1},1},1},ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Vern7Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Vern7Tableau{Float64,Float64}},OrdinaryDiffEq.Rodas4Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.RodasTableau{Float64,Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DefaultLinSolve,FiniteDiff.JacobianCache{Array{Float64,1},Array{Float64,1},Array{Float64,1},UnitRange{Int64},Nothing,Val{:forward},Float64},FiniteDiff.GradientCache{Nothing,Array{Float64,1},Array{Float64,1},Val{:forward},Float64,Val{true}}}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Vern7Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Vern7Tableau{Float64,Float64}},OrdinaryDiffEq.Rodas4Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.RodasTableau{Float64,Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64}},DefaultLinSolve,FiniteDiff.JacobianCache{Array{Float64,1},Array{Float64,1},Array{Float64,1},UnitRange{Int64},Nothing,Val{:forward},Float64},FiniteDiff.GradientCache{Nothing,Array{Float64,1},Array{Float64,1},Val{:forward},Float64,Val{true}}}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(opnorm),CallbackSet{Tuple{},Tuple{}},typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN),typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE),typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK),DataStructures.BinaryHeap{Float64,DataStructures.LessThan},DataStructures.BinaryHeap{Float64,DataStructures.LessThan},Nothing,Nothing,Int64,Array{Float64,1},Array{Float64,1},Array{Float64,1}},Array{Float64,1},Float64,Nothing}) at C:\Users\iamsu\.julia\packages\OrdinaryDiffEq\8Pn99\src\solve.jl:399
[4] #__solve#328(::Base.Iterators.Pairs{Symbol,Real,NTuple{4,Symbol},NamedTuple{(:default_set, :second_time, :save_everystep, :reltol),Tuple{Bool,Bool,Bool,Float64}}}, ::Function, ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at C:\Users\iamsu\.julia\packages\OrdinaryDiffEq\8Pn99\src\solve.jl:5
[5] (::getfield(DiffEqBase, Symbol("#kw##__solve")))(::NamedTuple{(:default_set, :second_time, :save_everystep, :reltol),Tuple{Bool,Bool,Bool,Float64}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}, ::CompositeAlgorithm{Tuple{Vern7,Rodas4{0,false,DefaultLinSolve,DataType}},AutoSwitch{Vern7,Rodas4{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at .\none:0
[6] #__solve#1(::Bool, ::Base.Iterators.Pairs{Symbol,Real,Tuple{Symbol,Symbol,Symbol},NamedTuple{(:second_time, :save_everystep, :reltol),Tuple{Bool,Bool,Float64}}}, ::Function, ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}, ::Nothing) at C:\Users\iamsu\.julia\packages\DifferentialEquations\9ez1L\src\default_solve.jl:7
[7] (::getfield(DiffEqBase, Symbol("#kw##__solve")))(::NamedTuple{(:save_everystep, :reltol),Tuple{Bool,Float64}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}) at .\none:0
[8] (::getfield(DiffEqBase, Symbol("##448#449")){ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},Tuple{}})() at C:\Users\iamsu\.julia\packages\DiffEqBase\gQwlE\src\solve.jl:49
[9] maybe_with_logger(::getfield(DiffEqBase, Symbol("##448#449")){ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem},Tuple{}}, ::Nothing) at C:\Users\iamsu\.julia\packages\DiffEqBase\gQwlE\src\utils.jl:259
[10] #solve_call#447(::Bool, ::Base.Iterators.Pairs{Symbol,Real,Tuple{Symbol,Symbol},NamedTuple{(:reltol, :save_everystep),Tuple{Float64,Bool}}}, ::Function, ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}) at C:\Users\iamsu\.julia\packages\DiffEqBase\gQwlE\src\solve.jl:48
[11] (::getfield(DiffEqBase, Symbol("#kw##solve")))(::NamedTuple{(:reltol, :save_everystep),Tuple{Float64,Bool}}, ::typeof(DiffEqBase.solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Tuple{Array{Complex{Float64},1},Array{Complex{Float64},1},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Complex{Float64},2},Array{Float64,2},Array{Complex{Float64},1},Array{Complex{Float64},1},Int64,Float64},ODEFunction{true,typeof(Vector_S1_mfold_R2!),UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},DiffEqBase.StandardODEProblem}) at .\none:0
[12] top-level scope at none:0
[13] include at .\boot.jl:326 [inlined]
[14] include_relative(::Module, ::String) at .\loading.jl:1038
[15] include(::Module, ::String) at .\sysimg.jl:29
[16] include(::String) at .\client.jl:403
[17] top-level scope at none:0
in expression starting at C:\ShobKichhu\Julia\t.jl:21
I am appending the code for the sake of completion,
using DelimitedFiles;
using Serialization;
using DifferentialEquations;
include("SuperParameterization/VectorField_S1.jl");
include("Data/Landmark.jl");
L=2; m=5;
learn_rate=0.05;
twidth = 100;
kappa=4; v_half = Get_skewIII_GaussianCos_Fourier(100, kappa/2.0); normalize!(v_half);
F_half = Get_isometric_S1R2_embedding_Fourier();
tspan = (0.0, 0.0+twidth);
param = Get_Vector_S1_mfold_R2_parameter(v_half, F_half, L, m, learn_rate);
S0 = rand(Float64, m); S0.*= (2*pi);
u0 = zeros(Float64, 2m);
Threads.@threads for i in 1:m
u0[2i-1] = cos(S0[i]);
u0[2i] = sin(S0[i]);
end
prob = ODEProblem( Vector_S1_mfold_R2!, u0, tspan, param );
sol = DifferentialEquations.solve( prob, reltol=1e-6, save_everystep=false );