#This function solves a linear system in order to find the minimizer of -loglikelood
##over a cone generated by a few active vertices.


CalculateOptMLE <- function(valfbar,S,K,X,Vec0,Mat0){
	
	
	m <- length(S)
	n <- length(X)
	nm <- Vec0[1:m]
	#rep(n,m)
	valfbar <- as.vector(valfbar)
	valfbar.inv <- 1/valfbar 
	Dfbar <- diag(valfbar.inv)
	MatY <- EvaluateMatf(S=S,K=K,X=X,Mat0)
	MatV <- t(Dfbar%*%MatY)%*%(Dfbar%*%MatY)
	B <- 2*(t(MatY)%*%valfbar.inv)-nm
	#Alpha <- solve.Matrix(MatV,B,tol=rcond.V*0.1)
	#Alpha <- solve.Hermitian(MatV,B,tol=0)
	rcond.V <-  rcond.svd.Matrix(svd.Matrix(MatV))
	cat("rcond=", rcond.V, "\n")
	Alpha <- solve.svd.Matrix(svd.Matrix(MatV),B,rcond.V*0.1)

	
	Alpha
	
	
	
}