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#' @title For parameter Identification
#'
#' @description Estimate the polynomial coefficients.
#'
#' @param allForK The list of input parameters
#' @param drv The derivative (on the equation left hand)
#' @param weight The weighting series
#'
#' @importFrom stats lsfit
#' @return \code{allForK} The initial list completed with the model parameters.
#'
#' @author Sylvain Mangiarotti
#'
paramId <- function(allForK, drv, weight) {
nRegModif <- dim(allForK$A)[1]
for (i in 1:nRegModif) {
allForK$phi[,i] <- GSproc(allForK, i, weight)
allForK$A[i,1:i] <- lsfit(allForK$Y[,1:i],
allForK$phi[,i],
intercept = F)$coefficients
}
#
cc <- vector("numeric", length = nRegModif)
for (i in 1:nRegModif) {
cc[i] <- wInProd(drv,
allForK$phi[,i],
weight) /
wInProd(allForK$phi[,i],
allForK$phi[,i],
weight)
}
K <- cc
for (i in 1:nRegModif) {
K[i] <- t(cc[i:nRegModif]) %*% as.matrix(allForK$A[i:nRegModif,i])
}
resTot <- sum((weight * drv - weight * allForK$Y %*% as.matrix(K))^2)
# prepare output
allForK$K <- K
allForK$resTot <- resTot
# return
invisible(allForK)
}
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