GPoM (version 1.0)

autoGPoMoTest: autoGPoMoTest: Test models numerical integrability & classify the attractor reached at the convergence (from chosen initial conditions)

Description

Test the numerical integrability of models (of polynomial structure) possibly obtained with function autoGPoMoSearch, and classify these models as divergent, Fixed Points, Periodic or not classificable (potentially chaotic).

Usage

autoGPoMoTest(data, tin = NULL, dt = NULL, nVar = nVar, dMax = dMax,
  show = 1, verbose = 1, allKL = allKL, IstepMin = 10,
  IstepMax = 10000, tooFarThreshold = 4, LimCyclThreshold = 0,
  fixedPtThreshold = 1e-08, method = "lsoda")

Arguments

data

Input Time series: Each column corresponds to one input variable.

tin

Input date vector which length should correspond to the variables of the input data (same number of lines).

dt

The time sampling of the input series.

nVar

The model dimension expected. This parameter will be deduced from the input data (series) if series is a matrix. If series is a vector, the expected dimension nVar should be provided.

dMax

Maximum degree of the polynomial functions allowed in the model (see poLabs).

show

Indicates (2) or not (0-1) the algorithm progress

verbose

Gives information (if set to 1) about the algorithm progress and keeps silent if set to 0

allKL

A list of the all the models $mToTest1, $mToTest2, etc. to be tested. Each model is provided as a matrix.

IstepMin

Minimum step of integration at the beginning of the analysis (by default IstepMin=10).

IstepMax

Maximum step of integration before stopping the analysis, with the interface this value can be changed during the analysis

tooFarThreshold

Divergence threshold, maximum times number that the model can be greater than the data standard deviation, without being removed from the analysis

LimCyclThreshold

Limit cycle threshold. Minimum neighbors distance between two integration steps, without being removed from the analysis

fixedPtThreshold

Limit cycle threshold. Minimum neighbors distance between two integration steps, without being removed from the analysis

method

The integration technique used for the numerical integration. Default is 'lsoda'. Others such as 'rk4' or 'ode45' may also be used. See package deSolve for details.

Value

A list containing:

$okMod A vector classifying the models: diverging models (0), periodic models of period-1 (-1), unclassified models (1).

$coeff A matrix with the coefficients of one selected model

$models A list of all the models to be tested $mToTest1, $mToTest2, etc. and all selected models $model1, $model2, etc.

$tout The time vector of the output time series (vector length corresponding to the longest numerical integration duration)

$stockoutreg A list of matrices with the integrated trajectories (variable X1 in column 1, X2 in 2, etc.) of all the models $model1, $model2, etc.

Examples

# NOT RUN {
#Examples
data('RosYco')
# Structure choice
data('allToTest')
outGPT <- autoGPoMoTest(RosYco, nVar= 3, dMax = 2, dt = 1/125, show=1,
                        allKL = allToTest, IstepMax = 60)

# }