R/Fixed_point_method_one_constraint_K_SPOR_DynProg.R

In HSPOR: Hidden Smooth Polynomial Regression for Rupture Detection

.Fixed_point_method_one_constraint_K_SPOR_DynProg <- function(datX,datY,deg,sigma2,constraint,constraint_point,indic = 'beginning',FP_nbIter=20){

  if (indic == 'beginning'){
    X=datX[datX>constraint_point[1]]
    Y=datY[datX>constraint_point[1]]
  } else {
    X=datX[datX<=constraint_point[1]]
    Y=datY[datX<=constraint_point[1]]
  }

  for(p in 1:FP_nbIter){
    #vector 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)
  }

  #Minus_Complete_log_likelihood
  s <- 0
  for(i in 1:(deg+1)){
    s <- s + mat_param[1,i] * X^(deg+1-i)
  }

  pZ = rep(1,length(X))
  wp <-  pZ*((1/sqrt(2*pi*sigma2)) * exp( - ((Y - s)^2)/(2*sigma2)))

  MLL <- -sum(log(wp))
  list(mat_param,sigma2,MLL)
}