#This function calculates the directional derivative for the LS criterion.
# X is an i.i.d. sample of size n generated from a K-monotone density.
# Theta is the set of knots theta_1,...,theta_m.
# C is the vector of the weights C_1,...,C_m corresponding to f_{theta1},...f_{theta2}
DirecDer <- function(theta,X,S,C,K){

Out <- NULL
J <- 0
for(i in 1:length(S)){
J <- J + C[i]*J.Func(theta,S[i],K)
}

Out <- (1/theta^{K-1/2})*(J-Integr.Fn(theta=theta,K=K,X=X))

Out	
	
}