如何根据 Julia 中的事件实现 ODE 解决方案的终止？为什么我会收到 BoundsError？

Question

我正在尝试使用 Julia 中的 DifferentialEquations 包求解耦合 ODE，并尝试实施连续回调以检查某个变量何时变得足够小，以便我可以终止积分。函数 xdot、ddot 是较早定义的，并且在没有 cb = callback 参数的情况下也能正常工作。

function w(x,d)
    retval = p(x,d)./rho(x,d)
    if isnan(retval)
        return 0.0
    end
    return retval
end

function wsys!(dv,v,p,t)
    x,d = v
    dv[1] = xdot(x,d)
    dv[2] = ddot(x,d)
end

function w_enough(t,v,integrator)
    w(v[1],v[2]) - 0.0001
end

cb = ContinuousCallback(w_enough,terminate!)

init = [xi,di]
tspan = (0,log(1e4))
prob = ODEProblem(wsys!,init,tspan)

sol = solve(prob,callback=cb);

当我运行最后一行时，出现错误：

BoundsError

Stacktrace:
 [1] getindex at .\number.jl:78 [inlined]
 [2] w_enough(::Array{Float64,1}, ::Float64, ::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,DiffEqBase.NullParameters,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,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(wsys!),LinearAlgebra.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.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}},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 .\In[15]:8
 [3] find_callback_time(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,DiffEqBase.NullParameters,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,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(wsys!),LinearAlgebra.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.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}},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}, ::ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}, ::Int64) at C:\Users\hganj\.julia\packages\DiffEqBase\mDFok\src\callbacks.jl:498
 [4] find_first_continuous_callback at C:\Users\hganj\.julia\packages\DiffEqBase\mDFok\src\callbacks.jl:383 [inlined]
 [5] handle_callbacks!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,DiffEqBase.NullParameters,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,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(wsys!),LinearAlgebra.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.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}},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\hganj\.julia\packages\OrdinaryDiffEqPn99\src\integrators\integrator_utils.jl:247
 [6] _loopfooter!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,DiffEqBase.NullParameters,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,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(wsys!),LinearAlgebra.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.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}},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\hganj\.julia\packages\OrdinaryDiffEqPn99\src\integrators\integrator_utils.jl:202
 [7] loopfooter! at C:\Users\hganj\.julia\packages\OrdinaryDiffEqPn99\src\integrators\integrator_utils.jl:166 [inlined]
 [8] solve!(::OrdinaryDiffEq.ODEIntegrator{CompositeAlgorithm{Tuple{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},true,Array{Float64,1},Float64,DiffEqBase.NullParameters,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,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.CompositeInterpolationData{ODEFunction{true,typeof(wsys!),LinearAlgebra.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.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}},DiffEqBase.DEStats},ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},OrdinaryDiffEq.CompositeCache{Tuple{OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.Rosenbrock23Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.Rosenbrock23Tableau{Float64},DiffEqBase.TimeGradientWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Array{Float64,1},DiffEqBase.NullParameters},DiffEqBase.UJacobianWrapper{ODEFunction{true,typeof(wsys!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,DiffEqBase.NullParameters},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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,typeof(DiffEqBase.ODE_DEFAULT_NORM),typeof(LinearAlgebra.opnorm),CallbackSet{Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}},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\hganj\.julia\packages\OrdinaryDiffEqPn99\src\solve.jl:403
 [9] #__solve#328(::Base.Iterators.Pairs{Symbol,Any,Tuple{Symbol,Symbol,Symbol},NamedTuple{(:default_set, :second_time, :callback),Tuple{Bool,Bool,ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}}}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at C:\Users\hganj\.julia\packages\OrdinaryDiffEqPn99\src\solve.jl:5
 [10] (::DiffEqBase.var"#kw##__solve")(::NamedTuple{(:default_set, :second_time, :callback),Tuple{Bool,Bool,ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType}},AutoSwitch{Tsit5,Rosenbrock23{0,false,DefaultLinSolve,DataType},Rational{Int64},Int64}}) at .\none:0
 [11] #__solve#1(::Bool, ::Base.Iterators.Pairs{Symbol,Any,Tuple{Symbol,Symbol},NamedTuple{(:second_time, :callback),Tuple{Bool,ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}}}}, ::typeof(DiffEqBase.__solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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\hganj\.julia\packages\DifferentialEquations\hc2aQ\src\default_solve.jl:7
 [12] #__solve at .\none:0 [inlined]
 [13] #__solve#448 at C:\Users\hganj\.julia\packages\DiffEqBase\mDFok\src\solve.jl:185 [inlined]
 [14] #__solve at .\none:0 [inlined]
 [15] #solve_call#443(::Bool, ::Base.Iterators.Pairs{Symbol,ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing},Tuple{Symbol},NamedTuple{(:callback,),Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}}}}, ::typeof(DiffEqBase.solve_call), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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\hganj\.julia\packages\DiffEqBase\mDFok\src\solve.jl:44
 [16] #solve_call at .\none:0 [inlined]
 [17] #solve#444 at C:\Users\hganj\.julia\packages\DiffEqBase\mDFok\src\solve.jl:67 [inlined]
 [18] (::DiffEqBase.var"#kw##solve")(::NamedTuple{(:callback,),Tuple{ContinuousCallback{typeof(w_enough),typeof(affect!),typeof(affect!),typeof(DiffEqBase.INITIALIZE_DEFAULT),Float64,Int64,Nothing}}}, ::typeof(solve), ::ODEProblem{Array{Float64,1},Tuple{Float64,Float64},true,DiffEqBase.NullParameters,ODEFunction{true,typeof(wsys!),LinearAlgebra.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
 [19] top-level scope at In[21]:1

在此事件中终止对这段代码很重要，我是 Julia 的新手。如果有任何帮助，我将不胜感激！

Answer 1

function w_enough(t,v,integrator)
    w(v[1],v[2]) - 0.0001
end

是错误的参数顺序，函数as documented应该是：

function w_enough(v,t,integrator)
    w(v[1],v[2]) - 0.0001
end

如何根据 Julia 中的事件实现 ODE 解决方案的终止？为什么我会收到 BoundsError？

How do I implement the termination of an ODE solution based on an event in Julia? Why am I getting a BoundsError?

event-handling

julia

differential-equations

differentialequations.jl