#Fourth version of objective function - this one uses the normal cdf.
#This is the first ladder 

#---------------------initial values---------------------------------------------------
acc<-10^(-100)		                #Bound on size of objective function
nC<-3			                #Number of Candidates
nV<-dim(anes.2000b)[1]			#Number of Voters
nI<-dim(anes.2000b)[2]			#Number of Issues
Delta<-.1		                #The variance of E
Voter<- anes.2000b[1:nV,]		#array(0,c(nV,nI));
Cand<-array(0,c(nC,nI))
Cand[1,]<-c(1,2,3,4,1,2,3,4,1,2)	#Cavg	#Candidate 1 Starting Placement on Issues-
Cand[2,]<-c(2,4,3,3,3,4,3,1,1,2)	#Candidate 2 Placement on Issues - Gore
Cand[3,]<-c(6,4,4,5,3,2,3,3,1,3)	#Candidate 2 Placement on Issues - Bush
Cavg<-apply(Voter,2,mean)		#mean of voters


#-----------------Initial values for Iterations----------------------------------
nsim<-500;Cmove<-array(0,c(nsim,nI));CObj<-array(0,c(nsim,1))
lastclass<-Cand[1,]
steps<-1;bot<-.1;top<-.25;


#-----------------Iterations-----------------------------------------------------
OBold<-ObjFun3(Voter,Cand,Delta)
for(i in 1:nsim)  {
    Cold<-Cand[1,]
    Next<-Ladder2(Voter,Cand,Delta,lastclass,OBold,steps,bot,top)
    Cand[1,]<-Next$last;test<-Next$obj;OBtest<-Next$obnew
    if(runif(1)<min(1,test)) {OBold<-OBtest} 
    else {Cand[1,]<-Cold;OBtest<-OBold}
    Cmove[i,]<-Cand[1,];CObj[i]<-OBtest
    if(OBtest>acc){lastclass<-Cmove[i,]} else {lastclass<-Cavg}
}


#--------------------------------------------------------------------------------------------
#ObjFun3(Voter,Cand,Delta)
#--------------------------------------------------------------------------------------------
#The Objective Function 3
#v=voter matrix, each row a voter
#c=candidate matrix, each row a candidate
#h=cutoff vector, y=exponential rvs, d=variance

ObjFun3 <-function(v,c,d)  {
    #v<-Voter;c<-Cand;d<-Delta
    nv<-dim(v)[1];nc<-dim(c)[1];h<-array(0,c(nv,(nc-1)));d2<-sqrt(d);
    for(i in 1:nv){for(j in 2:nc){h[i,j-1]<--sum((v[i,]-c[1,])^2)+sum((v[i,]-c[j,])^2)}}
    temp1<-0
    for(i in 1:nv)  {
        temp2<-1
        for(j in 1:(nc-1))  {
            temp2<-temp2*(pnorm(h[i,j],sd=d2))
        }
        temp1<-temp1+temp2
    }
    return(temp1)
}


#--------------------------------------------------------------------------------------------
#The Ladder
#The steps are a normal random walk 
#bot to top in steps

Ladder2 <-function(v,c,d,startclass,obold,steps,bot,top)  {
    #steps<-4;bot<-.25;top<-3;startclass<-lastclass;obold<-OBold
    #v<-Voter;c<-Cand;d<-Delta
    ni<-dim(v)[2];c[1,]<-startclass;obj<-1
    for(i in 1:(steps+1))  {
        c[1,]<-c[1,]+(bot+(i-1)*((top-bot))/steps)*rnorm(ni)		#Up
        obnew<-ObjFun3(v,c,d);obj<-obj*exp(obnew-obold);obold<-obnew
    }	
    for(i in 1:steps)  {
        c[1,]<-c[1,]+(top-i*((top-bot)/steps))*rnorm(ni)			#Down
        obnew<-ObjFun3(v,c,d);obj<-obj*exp(obnew-obold);obold<-obnew
    }		
    last<-c[1,]
    return(last,obj,obnew)
}