Utilitary functions

RecurrenceMicrostatesAnalysis.jl has several utilitary functions to help when using the library. These functions allows to simplify the process to implement recurrence analysis to a project, facilitating the set of a threshold, or the preparation of continuous data to be analysed.

Warning

Some function presented in this section was still in development, so these function can change in future versions.

Preparing a continuous data

When working with continuous data, it is important to do a discretization, changing the time resolution to improve the available information. prepare is an utilitary function to discretize the data, applying a vicinity parameter to change the data time resolution [10].

julia> function lorenz!(du, u, p, t)
           du[1] = 10.0 * (u[2] - u[1])
           du[2] = u[1] * (28.0 - u[3]) - u[2]
           du[3] = u[1] * u[2] - (8 / 3) * u[3]
       endlorenz! (generic function with 1 method)
julia> using DifferentialEquations, RecurrenceMicrostatesAnalysis
julia> u0 = [1.0; 0.0; 0.0];
julia> tspan = (0.0, 1000.0);
julia> prob = ODEProblem(lorenz!, u0, tspan);
julia> sol = solve(prob);
julia> data_prepared = prepare(sol, 0.2)3×4133 Matrix{Float64}:
 1.0   5.46738  12.3621  -5.86995  -8.91899  …   0.493252  5.04799  16.1972
 0.0  11.6854   -4.1674  -8.32987  -9.88552      0.871561  9.8981    8.52887
 0.0   2.49205  44.2997  26.4556   26.5527      10.5164    7.57713  43.8558

Info

It is possible to see the difference between the data solution and the prepareted data when we make a RP. RP without vicinity application and with vicinity

The prepare function can also apply a transient phase to the data, using the kword transient, and define the data length, using the kword K.

julia> data_prepared = prepare(sol, 0.2; transient = 6000, K = 1000)3×1000 Matrix{Float64}:
 -0.89148  -4.24782  -15.1813  -1.40175  …  2.86423  16.7419  -0.439991
 -1.90309  -7.4907   -12.1429   2.02437     5.35815  17.7081  -4.00474
 18.2339   12.3067    38.8897  25.6219      9.20178  37.6122  25.3385

Finding threshold

The threshold is a free parameter that need to be defined by the user when working with RP, RQA, or RMA. Using the principle of maximizing the recurrence entropy, we build a function to estimate a good value for threshold [10]. The find_parameters function returns a Float64 value to be used as threshold and the maximazed entropy. It is important to note that this function can be a little slower, since it needs to compute a recurrence motif distributions for each threshold in some interval.

julia> th, s = find_parameters(data_prepared, 3)(17.07249006479173, 5.418566751884777)