function lyap_taylorinteg can't work

[Grotex]

Greetings.

When using lyap_taylorinteg to work out the Lyapunov spectrum of the Lorenz system, an error was throw out. (with Julia 1.6.1)

julia> using TaylorIntegration, TaylorSeries

julia> function lorenz!(t, x, dx) dx[1] = σ(x[2]-x[1]) dx[2] = x[1](ρ-x[3])-x[2] dx[3] = x[1]x[2]-βx[3] nothing end lorenz! (generic function with 1 method)

julia> const σ = 10.71 10.71

julia> const ρ = 119 119

julia> const β = 8.93 8.93

julia>

julia>

julia> const x0 = [19.0, 20.0, 50.0] 3-element Vector{Float64}: 19.0 20.0 50.0

julia> const t0 = 0.0 0.0

julia> const tmax = 100.0 100.0

julia> @time tv, xv, λv = lyap_taylorinteg(lorenz!, x0, t0, tmax, 28, 1e-20; maxsteps=2000000); ERROR: AssertionError: length(q0) must be equal to number of variables set by TaylorN Stacktrace: [1] lyap_taylorinteg(f!::Function, q0::Vector{Float64}, t0::Float64, tmax::Float64, order::Int64, abstol::Float64, params::Nothing, jacobianfunc!::Nothing; maxsteps::Int64, parse_eqs::Bool) @ TaylorIntegration C:\Users\gsjiang.julia\packages\TaylorIntegration\hUDy9\src\lyapunovspectrum.jl:241 [2] top-level scope @ .\timing.jl:210 [inlined] [3] top-level scope @ .\REPL[9]:0

Why this error occurs?

[Grotex]

ERROR: AssertionError: length(q0) must be equal to number of variables set by TaylorN

this is THE ERROR according to output result

[PerezHz]

Hi @Grotex!

Since lyap_taylorinteg is using TaylorN internally, this requires a call to set_variables before calling lyap_taylorinteg, e.g.:

xi = set_variables("δ", order=1, numvars=length(x0)) # variable name can be anything
# then, call lyap_taylorinteg...

Note that the order kwarg must be 1, and numvars must be equal to length(x0). We are keeping this out of lyap_taylorinteg since set_variables modifies certain global variables defined in TaylorSeries, so in this way this global variable modification is transparent to the user.

There's an example in the docs, which deals precisely with the Lyapunov spectrum for the Lorenz system.

cc: @lbenet

[lbenet]

In addition to the comment of @PerezHz, note that the function lorenz! you defined above does not follow the convention we use, which is the same as in DifferentialEquations. The arguments of that function should be du, u, p, t, where du is the left hand side of the ODEs, u are the dependent variables, p are parameters, and t is the independent variable (time).

[lbenet]

Does the example in the docs clarify this issue? Can we close it?

[Grotex]

Does the example in the docs clarify this issue? Can we close it?

OK, I understand. Close it.