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picm.ft=function(psi,m,z.obs,zk,k, dN2, Y2, dNsum, Delta, eps,maxiter, shape){
#picm
iter=0
d.e=1
while(d.e>=eps){
iter=iter+1
if(iter>maxiter) break
#picm
den=colSums(Y2*exp(psi))
index.zero=which(den>0) #0/0=0
weight=c()
for(s in 1:m)
weight[s]=sum( (Y2[s,]*dNsum/den)[index.zero] )
if(sum(is.na(weight))+sum(is.infinite(weight))>=1)
break;
if(min(weight)==0) #For trt only: Y2[,s] can be zero due to x*beta is zero
break;
if(shape=='increasing'){
exp.psi.new=pava(Delta/weight, weight)
}else if(shape=='decreasing'){
exp.psi.new=-pava(-Delta/weight, weight)
}
psi.new=log(exp.psi.new)
#distance
d.e=sum(abs(exp(psi.new)-exp(psi)))
psi=psi.new
}
#impose the anchor
psi.new=psi.new-psi.new[k] #psi is the same as psi.new;
conv=0
if(d.e<eps) conv=1
return(list(psi.new=psi.new, conv=conv))
}
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