######################################################
#  R function for solving g_2(lambda)=0 in Wu (2005) #
######################################################


#########################################
# R Function for EL Lagrange Multiplier #
#           x is univariate             #
# 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=sum p_i x_i                 #
# Output: lambda=M                      #
#                                       #
# Written by Changbao Wu, June, 1999    #
#########################################

Lag1=function(u,ds,mu){
dif=1
tol=1e-8
if(min(u-mu)>=0 | max(u-mu)<=0){
dif=0
M=0
    }
L=-1/max(u-mu)
R=-1/min(u-mu)
while(dif>tol){
M=(L+R)/2
glam=sum((ds*(u-mu))/(1+M*(u-mu)))
if(glam>0) L=M
if(glam<0) R=M
dif=abs(glam)
              }
return(M)
          }