######################################################
#  R function for solving g_1(lambda)=0 in Wu (2005) #
######################################################

#########################################
# R Function for EL Lagrange Multiplier #
#     x is of dimension 2 or higher     #
# Input: u=(x_1,x_2,...,x_n)            #
#        ds=(d_1,d_2,...,d_n)           #
#        (Design Wights: d_i=1/pi_i)    #
#        ds=(1,1,...1) for iid data     #
#        mu: benchmark means for x      #
# Output: lambda=M                      #
#                                       #
# Written by Changbao Wu, March, 2000   #
# Modified by Randy Sitter, June, 2006  #
#########################################

Lag2=function(u,ds,mu){ 
  n=length(ds)
  u=u-rep(1,n)%*%t(mu)
  M=0*mu
  dif=1
  tol=1e-8
  k=0
  while(dif>tol & k<=50){
  D1=t(u)%*%((ds/(1+u%*%M))*rep(1,n))
  DD=-t(u)%*%(c((ds/(1+u%*%M)^2))*u)
  D2=solve(DD,D1,tol=1e-40)
  dif=max(abs(D2))
  rule=1
  while(rule>0){
    rule=0
    if(min(1+t(M-D2)%*%t(u))<=0) rule=rule+1
    if(rule>0) D2=D2/2
               }
    M=M-D2
    k=k+1
                   }
  if(k>=50) M=0*mu
  return(as.vector(M))
          }