findAllSets: Find all possible sets of equation combinations considering an ensemble of possible equation.

Description

For each equation to be retrieved, an ensemble of potential formulation is given. For instance, if three possible formulations are provided for equation (1), one for equation (2) and two for equation (3). In this case, six (i.e. 3*1*2) possible sets of equations can be obtained from these potential formulations. The aim of this program is to formulate all the potential systems from the individual formulations provided of the individual equations.

Usage

findAllSets(allFilt, nS = c(3), nPmin = 1, nPmax = 14)

Value

SetsNp A list of two matrices $Sets A matrix defining all the sets the equation combination (each line provides a combination, for instance, a line with 1,2,2 means the first equation of allFilt$X1, the second one of allFilt$X2 and the second one of allFilt$X3) $Np A matrix providing the number of parameters of all equation combination (each line provides the number of parameter of the selected equations)

Arguments

allFilt: A list with: (1) A matrix allFilt$Xi of possible formulations for each equation (corresponding to variable Xi); And (2) a vector allFilt$Npi providing the number of polynomial terms contained in each formulation.
nS: A vector providing the number of dimensions used for each input variables (see Examples 1 and 2). The dimension of the resulting model will be nVar = sum(nS).
nPmin: Corresponds to the minimum number of parameters (and thus of polynomial term) allowed.
nPmax: Corresponds to the maximum number of parameters (and thus of polynomial) allowed.

Author

Sylvain Mangiarotti

Examples

Run this code

#############
# Example 1 #
#############
# We build an example
allFilt <- list()
# For equation 1 (variable X1)
allFilt$Np1 <- 1         # only one formulation with one single parameter
# For equation 2 (variable X2)
allFilt$Np2 <- c(3, 2)   # two potential formulations, with respectively three and four parameters
# For equation 3 (variable X3)
allFilt$Np3 <- c(4, 2)   # two potential formulations, with respectively two and four parameters
# Formulations for variables Xi:
# For X1:
allFilt$X1 <- t(as.matrix(c(0,0,0,1,0,0,0,0,0,0)))
# For X2:
allFilt$X2 <- t(matrix(c(0,-0.85,0,-0.27,0,0,0,0.46,0,0,
                         0,-0.64,0,0,0,0,0,0.43,0,0),
                       ncol=2, nrow=10))
# For X3:
allFilt$X3 <- t(matrix(c(0, 0.52,  0, -1.22e-05,  0, 0, 0.99, 5.38e-05, 0, 0,
                         0, 0.52, 0, 0, 0, 0, 0.99, 0, 0, 0),
                       ncol=2, nrow=10))
# From these individual we can retrieve all possible formulations
findAllSets(allFilt, nS=c(3), nPmin=1, nPmax=14)
# if only formulations with seven maximum number of terms are expected:
findAllSets(allFilt, nS=c(3), nPmin=1, nPmax=7)