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.Fixed_point_smoothing_method_one_constraint_K_SPOR_DynProg <- function(datX,datY,deg,sigma2,constraint,constraint_point,nb_pt_pond,indic = 'beginning',FP_nbIter=20){
if(indic == 'beginning'){
if(nb_pt_pond != 0){
#lissage autour du saut : on prend 5 observations supplémentaires avant l'instant de transition
X <- c(datX[(which(datX == datX[datX>=constraint_point[1]][1])-nb_pt_pond):(which(datX == datX[datX>=constraint_point[1]][1])-1)],datX[datX>=constraint_point[1]])
Y <- c(datY[(which(datX == datX[datX>=constraint_point[1]][1])-nb_pt_pond):(which(datX == datX[datX>=constraint_point[1]][1])-1)],datY[datX>=constraint_point[1]])
obs_weights1 <- 1-(1-((X[1:(2*nb_pt_pond)] - X[1])/(X[2*nb_pt_pond] - X[1]))^2)
obs_weights = c(obs_weights1,rep(1,length(X)-length(obs_weights1)))
}else{
X <- datX[datX>=constraint_point[1]]
Y <- datY[datX>=constraint_point[1]]
obs_weights <- rep(1,length(X))
}
}else {
#ponderation de la vraisemblance
if(nb_pt_pond != 0){
#Si point de debut on prend 5 observations supplementaires après l'instant de transition
X <- c(datX[datX<constraint_point[1]],datX[(which(datX == datX[datX<constraint_point[1]][length(datX[datX<constraint_point[1]])])+1):
(which(datX == datX[datX<constraint_point[1]][length(datX[datX<constraint_point[1]])])+nb_pt_pond)])
Y <- c(datY[datX<constraint_point[1]],datY[(which(datX == datX[datX<constraint_point[1]][length(datX[datX<constraint_point[1]])])+1):
(which(datX == datX[datX<constraint_point[1]][length(datX[datX<constraint_point[1]])])+nb_pt_pond)])
obs_weights1 <- 1-((X[max(1,(length(X)-(2*nb_pt_pond-1))):length(X)] - X[max(1,(length(X)-(2*nb_pt_pond-1)))])/(X[length(X)] - X[max(1,(length(X)-(2*nb_pt_pond-1)))]))^2
obs_weights = c(rep(1,length(X)-length(obs_weights1)),obs_weights1)
}else{
X <- datX[datX<constraint_point[1]]
Y <- datY[datX<constraint_point[1]]
obs_weights <- rep(1,length(X))
}
}
for(p in 1:FP_nbIter){
# parameters estimation
M_mat <- .Jacobian_Matrix_one_constraint_K_SPOR_DynProg(X,Y,deg,sigma2,constraint,constraint_point)
gammaV <- .Vector_solution_one_constraint_K_SPOR_DynProg(X,Y,deg,constraint,constraint_point)
mat_param <- .Parameters_estimation_K_SPOR_DynProg(M_mat,gammaV,deg)
sigma2 <- .Variance_estimation_K_SPOR_DynProg(X,Y,deg,mat_param)
}
#penalized Minus_Complete_log_likelihood
s <- 0
for(i in 1:(deg+1)){
s <- s + mat_param[1,i] * X^(deg+1-i)
}
wp <- obs_weights*((1/sqrt(2*pi*sigma2)) * exp( - ((Y - s)^2)/(2*sigma2)))
if (indic == 'beginning'){
penalised_MLL <- -sum(log(wp[-1]))
}else{
penalised_MLL <- -sum(log(wp[-length(wp)]))
}
list(mat_param,sigma2,penalised_MLL)
}
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