GPoM (version 1.0)

autoGPoMoSearch: autoGPoMoSearch : automatic search of polynomial Equations

Description

The algorithm aims to get an ensemble of equations to be tested from a given template of allowed terms. The maximum size of the equation depends on the model dimension nVar, and on the maximum polynomial degree dMax. The algorithm remove polynomial terms one by one, considering that a term is poorly useful when removing it leads to the smaller fitting degradation.

Usage

autoGPoMoSearch(data, dt, nVar = nVar, dMax = dMax, weight = NULL,
  show = 0, underSamp = NULL, filterReg = NULL)

Arguments

data

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

dt

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).

weight

Weighting function of input data series. By default uniform weight is applied. This weighting function can also be used to apply the analysis piecewise using zeros and ones.

show

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

underSamp

Points used for undersampling the data. For undersamp = 1 the complete time series is used. For undersamp = 2, only one data out of two is kept, etc.

filterReg

A vector that specifies the a priori structure of the the function of the output model in canonical form. The organisation of the filter follows the convention defined in poLabs and can be obtained using poLabs(nVar,dMax). Value is 1 if the regressor is available, 0 if it is not.

Value

A list of two matrices:

$filtMemo describes the selected terms (1 if the term is used, 0 if not)

$KMemo provides the correspoing coefficients

Examples

# NOT RUN {
data('RosYco')
filt = autoGPoMoSearch(RosYco[,2], nVar = 3, dMax = 2,
                       dt = 1/125, show = 1)
# As an example, the equations of the fourth line has the following terms:
poLabs(nVar = 3, dMax = 2)[filt$filtMemo[5,] != 0]
# which coefficients correspond to
cbind(filt$KMemo[5,], poLabs(nVar = 3, dMax = 2))[filt$filtMemo[5,] != 0,]

# }