R/Jacobian_Matrix_two_constraints_K_SPOR_DynProg.R

In HSPOR: Hidden Smooth Polynomial Regression for Rupture Detection

.Jacobian_Matrix_two_constraints_K_SPOR_DynProg <- function(X,Y,deg,sigma2,constraint,begin_point,end_point){

  # Models parameters
  m3 <- matrix(0,deg+1,deg+1)
  d1 <- deg
  for(i in 1:(deg+1)){
    d2 <- deg
    for(j in 1:(deg+1)){
      m3[i,j] <- sum(X^(d1 + d2))
      d2 <- d2-1
    }
    d1 <- d1-1
  }

  #Constraints == 1 (continuity)
  if(constraint == 1){
    m1 <- matrix(0,2,(deg+1)+2)
    m2 <- matrix(0,(deg+1),2)

    for(i in 1:(deg+1)){
      m1[1,i] <- begin_point[1]^(deg + 1 - i)
      m1[2,i] <- end_point[1]^(deg + 1 - i)
      m2[i,1] <- (begin_point[1]^(deg + 1 - i))*sigma2
      m2[i,2] <- (end_point[1]^(deg + 1 - i))*sigma2
    }
  }

  #Constraints == 2 (continuity & derivability)
  if(constraint == 2){
    m1 <- matrix(0,4,(deg+1)+4)
    m2 <- matrix(0,(deg+1),4)

    for(i in 1:(deg+1)){
      m1[1,i] <- begin_point[1]^(deg + 1 - i)
      m1[2,i] <- end_point[1]^(deg + 1 - i)
      m1[3,i] <- (deg + 1 - i)*(begin_point[1]^(max(0,deg-i)))
      m1[4,i] <- (deg + 1 - i)*(end_point[1]^(max(0,deg-i)))
      m2[i,1] <- (begin_point[1]^(deg + 1 - i))*sigma2
      m2[i,2] <- (end_point[1]^(deg + 1 - i))*sigma2
      m2[i,3] <- (deg + 1 - i)*(begin_point[1]^(max(0,deg-i)))*sigma2
      m2[i,4] <- (deg + 1 - i)*(end_point[1]^(max(0,deg-i)))*sigma2
    }
  }

  if(constraint == 0){
    matFi <- m3
  } else{
    m4 <- cbind(m3,m2)
    matFi <- rbind(m1,m4)
  }

  return(matFi)

}