# Chaostools tangent\_integrator stiff solvers
**URL:** https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464
**Category:** Modelling & Simulations
**Created:** [July 17, 2019, 2:11pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464 "2019-07-17T14:11:14Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 2:11pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/1 "2019-07-17T14:11:14Z")
Hi,
I want to use the `tangent_integrator` function from the `ChaosTools` package with solvers for stiff problems:
```julia
integ = tangent_integrator(cds, w0; alg=Rodas5(), abstol=1e-9, reltol=1e-9)
step!(integ, 1.0)
```
but this gives me:
> MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{DiffEqDiffTools.UJacobianWrapper{ODEFunction{true,getfield(DynamicalSystemsBase, Symbol(“##21#22”)){6,typeof(f),typeof(jac)},LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Array{Float64,1}},Float64},Float64,11})
> Closest candidates are:
> Float64(::Real, !Matched::RoundingMode) where T\<:AbstractFloat at rounding.jl:194
> Float64(::T\<:Number) where T\<:Number at boot.jl:741
> Float64(!Matched::Int8) at float.jl:60
> …
I had this problem before when calling radau-fortran solver, see [https://discourse.julialang.org/t/lyapunov-exponents-using-chaostools-and-fortran-radau-solver/26007](https://discourse.julialang.org/t/lyapunov-exponents-using-chaostools-and-fortran-radau-solver/26007).
I also tried, as suggested in the documentation, to chose a solver by `alg_hint` keyword, but I had a look into the implementation of `tangent_integrator` and this is not making use of the hint-keyword. How can I use e.g. `Rodas5()` with the `tangent:integratorfunction` ?
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 2:20pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/2 "2019-07-17T14:20:09Z")
Hey there.
1. The `alg_hint` is not used by `tangent_integrator`, it is DifferentialEquations.jl exclusive, sorry.
2. To be able to reproduce your problem, it is useful to provide a MinimalWorkingExample, some runnable code that leads to the same error.
3. Depending on your dynamical system, it may just be the case that `Rodas5` does not support the state type that the tangent integrator uses, since this can vary from matrix to vector-of-vectors.
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 2:22pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/3 "2019-07-17T14:22:27Z")
@Datseris I will try to make up a minimal example quickly.
What is the “state type”?
Do you mean by state type: in-place or out-of-place versions of the functions?
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 2:28pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/4 "2019-07-17T14:28:27Z")
The “state type” is simple `typeof(integ.u)` , i.e. what is the
Julia structure that represents the state of the integrator. This
is of course affected by whether the integrator is in-place or
not, but there are other factors as well.
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 2:31pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/5 "2019-07-17T14:31:12Z")
So I made a working example with the Lorenz system:
```julia
function lorenz_iip(du,u,p,t)
sigma = p[1]
rho = p[2]
beta = p[3]
# f
du[1] = sigma*(u[2]-u[1])
du[2] = u[1]*(rho-u[3])-u[2]
du[3] = u[1]*u[2]-beta*u[3]
end
function lorenz_jac_iip(J,u,p,t)
sigma = p[1]
rho = p[2]
beta = p[3]
J[1,1] = -sigma
J[1,2] = sigma
J[1,3] = 0
J[2,1] = rho-u[3]
J[2,2] = -1
J[2,3] = -u[1]
J[3,1] = u[2]
J[3,2] = u[1]
J[3,3] = -beta
end
Random.seed!(42)
N=10000
tol = 1e-12
w0 = Matrix(LinearAlgebra.qr(Random.rand(3,3)).Q)
param = [16.,45.92,4.]
x_start = [19.,20.,50.]
cds = ContinuousDynamicalSystem(lorenz_iip,x_start,param,lorenz_jac_iip)
integ_rodas = tangent_integrator(cds; alg=Rodas5(), abstol=tol, reltol=tol)
integ = tangent_integrator(cds; abstol=tol, reltol=tol)
```
and when I call `step!(integ)` this works but calling `step!(integ_rodas)` gives me the above error message:
> MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{DiffEqDiffTools.UJacobianWrapper{ODEFunction{true,getfield(DynamicalSystemsBase, Symbol(“##21#22”)){3,typeof(lorenz\_iip),typeof(lorenz\_jac\_iip)},LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},Float64,Array{Float64,1}},Float64},Float64,12})
> Closest candidates are:
> Float64(::Real, !Matched::RoundingMode) where T\<:AbstractFloat at rounding.jl:194
> Float64(::T\<:Number) where T\<:Number at boot.jl:741
> Float64(!Matched::Int8) at float.jl:60
> …
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 2:33pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/6 "2019-07-17T14:33:18Z")
I checked the states:
`typeof(integ.u)` and `typeof(integ_rodas.u)` both give
> Array{Float64,2}
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 2:41pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/7 "2019-07-17T14:41:21Z")
Okay, a first question to ask before trying anything else is: @ChrisRackauckas , does `Rodas5` work with `Matrix` states?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 17, 2019, 2:54pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/8 "2019-07-17T14:54:48Z")
Yes
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 17, 2019, 3:01pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/9 "2019-07-17T15:01:14Z")
Are you creating any cache variables? If you are, are they dual cached?
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:02pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/10 "2019-07-17T15:02:40Z")
I tested some more algorithms, and so far none of `Kvaerno5`, `KenCarp4, Rodas4P worked.
```julia
cds = ContinuousDynamicalSystem(lorenz_iip,x_start,param)
```
- leaving out the Jacobian (I assume its auto diffed then), does not work either.
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:03pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/11 "2019-07-17T15:03:20Z")
I am just running the code above in a Jupyter notebook. What do you mean by cached/dual cached in this context?
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 3:03pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/12 "2019-07-17T15:03:25Z")
To the best of my understanding, `tangent_integrator` propagates everything to `__init` and `ODEProblem`. See here: [https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/continuous.jl#L50-L68](https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/continuous.jl#L50-L68) :
```julia
function tangent_integrator(ds::CDS{IIP}, Q0::AbstractMatrix;
u0 = ds.u0, diffeq...) where {IIP}
t0 = ds.t0
Q = safe_matrix_type(Val{IIP}(), Q0)
u = safe_state_type(Val{IIP}(), u0)
k = size(Q)[2]
k > dimension(ds) && throw(ArgumentError(
"It is not possible to evolve more tangent vectors than the system's dimension!"
))
tangentf = create_tangent(ds.f, ds.jacobian, ds.J, Val{IIP}(), Val{k}())
tanprob = ODEProblem{IIP}(tangentf, hcat(u, Q), (t0, typeof(t0)(Inf)), ds.p)
solver = _get_solver(diffeq)
return __init(tanprob, solver; DEFAULT_DIFFEQ_KWARGS..., internalnorm = _tannorm,
save_everystep = false, diffeq...)
end
```
(also, since the problem comes from using different integration algorithms, it cannot stem from **DynamicalSystems.jl** since the `step!` functionality is beyond our control; we only initialize the states and functions and give everything to `init`)
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:09pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/13 "2019-07-17T15:09:19Z")
Can you point to the implementation of `create_tangent`? How do you tie together the “f” and “jacobian”? Could this be something, the stiff solvers do not like?
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 3:11pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/14 "2019-07-17T15:11:00Z")
The tangent space function is created generally in this part of the code: [https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/dynamicalsystem.jl#L342](https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/dynamicalsystem.jl#L342)
e.g. for the case of in-place system with provided jacobian function one has ([https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/dynamicalsystem.jl#L343-L355](https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/dynamicalsystem.jl#L343-L355) )
```julia
function create_tangent(@nospecialize(f::F), @nospecialize(jacobian::JAC), J::JM,
::Val{true}, ::Val{k}) where {F, JAC, JM, k}
J = deepcopy(J)
tangentf = (du, u, p, t) -> begin
uv = @view u[:, 1]
f(view(du, :, 1), uv, p, t)
jacobian(J, uv, p, t)
mul!((@view du[:, 2:(k+1)]), J, (@view u[:, 2:(k+1)]))
nothing
end
return tangentf
end
```
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:11pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/15 "2019-07-17T15:11:22Z")
I can not post the whole stack trace here, as it is too long (over 32000 characters). I can post it somewhere else, if someone is interested 🙂
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:19pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/16 "2019-07-17T15:19:54Z")
@Datseris So if i switch to `Rodas5(autodiff=false)` this works. So it seems that differentiating `tangentf` fails for some reason.
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 3:21pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/17 "2019-07-17T15:21:40Z")
Hm, nice that you found the root of the problem. I’ve cited above how the tangent function is created, but I don’t really have a clue of what Rodas does (or what it is in general), so I can’t really help on why this fails.
Maybe Chris has some ideas?
---
### Author:  [@jamblejoe](https://discourse.julialang.org/u/jamblejoe)
#### Post date: [July 17, 2019, 3:39pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/18 "2019-07-17T15:39:27Z")
Hmm, I do know way too little to track down this error further. Are the non stiff algorithms not using `ForwardDiff` ? Because they work flawlessly here. Maybe @ChrisRackauckas can help?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 17, 2019, 4:50pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/19 "2019-07-17T16:50:49Z")
> [@Datseris](#):
>
> J = deepcopy(J)
Yup, you’re creating cache variables which aren’t dual cached which violates the assumptions of autodiff.
[http://docs.juliadiffeq.org/latest/basics/faq.html#I-get-Dual-number-errors-when-I-solve-my-ODE-with-Rosenbrock-or-SDIRK-methods](http://docs.juliadiffeq.org/latest/basics/faq.html#I-get-Dual-number-errors-when-I-solve-my-ODE-with-Rosenbrock-or-SDIRK-methods)…?-1
---
### Author:  [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [July 17, 2019, 4:58pm UTC](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464/20 "2019-07-17T16:58:05Z")
Ah cool, this seems like something that can be fixed!
@jamblejoe if you want to open a PR for this on DynamicalSystemsBase you are welcomed! (I won’t have time to fix it myself)
[Next page](https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464.md?page=2)