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#Function for construction of sequential A-optimal block design using array exchange algorithm
seqAoptbrcd.maeA<-function(trt.N,blk.N,theta,nrep,strt,sary,des0,dtype) {
cmat<-cmatbrcd.mae(trt.N,blk.N,theta,des0,dtype)
Ascore0=sum(diag(ginv(cmat)))
#New parametric combinations
blk.N=blk.N+sary
trt.N=trt.N+strt
#Candidate arrays
arrays={}
if(strt==sary){
for(i in 1:strt){
arrays0<-cbind(1:(trt.N-strt+i-1),trt.N-strt+i)
arrays<-as.matrix(rbind(arrays,arrays0))
}
} else {arrays<-t(combn(trt.N,2))}
if(dtype=="rcd") {arrays<-rbind(arrays,t(rbind(arrays[,2],arrays[,1])))}
na=dim(arrays)[1]
#House keeping
del.1<-matrix(1000,na,3)
desbest.1<-matrix(0,nrep*2,blk.N)
aoptbest.1<-matrix(0,nrep,2)
#Start iteration for search of optimal sequential design given initial design
for(irep in 1:nrep){
#select connected initial sequential design
Con.egv.check=0.00000001
while(Con.egv.check<0.000001){
All.trt.check=trt.N-1
while(All.trt.check <trt.N){
sqarray=matrix(0,strt,2);
if(strt>0) {
for(i in 1:strt){
sqary=cbind(1:(trt.N-strt+i-1),trt.N-strt+i)
if(dtype=="rcd") {sqary=rbind(sqary,t(rbind(sqary[,2],sqary[,1])))}
sqarray0<-sqary[sample(1:(length(sqary)/2),1),]
sqarray[i,]=sqarray0
}
}
if((sary-strt)>0) {
adary0<-if((sary-strt)>na) {c(1:na, sample(1:na,(sary-strt-na),replace=TRUE))} else {
sample(1:na,(sary-strt),replace=FALSE)}
sqarray<-rbind(sqarray,arrays[adary0,])}
des=t(rbind(t(des0),sqarray))
trtin<-contrasts(as.factor(des),contrasts=FALSE)[as.factor(des),]
R.trt<-t(trtin)%*%trtin
All.trt.check<-rankMatrix(R.trt)
}
cmato=cmatbrcd.mae(trt.N,blk.N, 0,des, dtype)
egv<-sort(eigen(cmato)$values)
Con.egv.check<-egv[2]
}
cmat<-cmatbrcd.mae(trt.N, blk.N, theta, des, dtype)
aopt=sum(diag(ginv(cmat)))
acold=aopt
descold=t(des)
cdel=100
for(i in (blk.N-sary+1):blk.N){
for(j in 1:na){
temp=descold[i,]
if(all(descold[i,]==arrays[j,])) {aopt=acold; del.1[j,]<-c(j,(acold-aopt),aopt); next}
descold[i,]=arrays[j,]
trtin<-contrasts(as.factor(t(descold)),contrasts=FALSE)[as.factor(t(descold)),]
R.trt<-t(trtin)%*%trtin
if (rankMatrix(R.trt)[1]<trt.N) {aopt=1000; del.1[j,]<-c(j,(acold-aopt),aopt); next}
cmato=cmatbrcd.mae(trt.N,blk.N, 0,t(descold), dtype)
egv<-sort(eigen(cmato)$values)
if(egv[2]<0.000001) {aopt=1000; del.1[j,]<-c(j,(acold-aopt),aopt); next}
cmat=cmatbrcd.mae(trt.N,blk.N,theta,t(descold), dtype)
aopt=sum(diag(ginv(cmat)))
del.n<-del.1[j,]<-c(j,(acold-aopt),aopt)
descold[i,]=temp
}
del.1<-del.1[order(del.1[,3]),]
delbest=t(del.1[1,])
descold[i,]=arrays[delbest[1],]
acold=delbest[3]
cdel=delbest[2]
}
if (irep==1) {desbest.1=t(descold)} else {desbest.1=rbind(desbest.1,t(descold))}
aoptbest.1[irep,]=c(irep,acold)
}
if(nrep==1){nb=aoptbest.1[1]; Ascore=aoptbest.1[2]}else{
best=aoptbest.1[order(aoptbest.1[,2]),]
nb=best[1,1]
Ascore<-best[1,2]
}
Aoptde<- desbest.1[c((nb-1)*2+1,nb*2),]
tkmessageBox(title="Search completed",message=paste("Search completed",sep=""))
cnames=paste0("Ary",1:blk.N)
dimnames(Aoptde)=list(if(dtype=="rcd"){c("Dye 1:", "Dye 2:")} else {NULL},cnames)
dimnames(des0)=list(if(dtype=="rcd"){c("Dye 1:", "Dye 2:")} else {NULL},paste0("Ary",1:(blk.N-sary)))
Aopt_sum2<-list("v"=trt.N,"b"=blk.N,theta=theta,nrep=nrep, strt=strt, sary=sary, dtype=dtype, "optdes0"=des0,"optcrtsv0" =Ascore0,"soptdesF"=Aoptde,"soptcrtsv" =Ascore)
return(Aopt_sum2)
}#End of SeqAoptbrcd.maeA function: construction of sequential A-optimal block design using array exchange algorithm
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