upstream<-function(A,y,x,m, write.xlsx=TRUE, name="Upstream.xlsx"){
if(class(A)!="matrix") A<-as.matrix(A)
if(class(y)!="numeric") y<-as.numeric(y)
if(class(x)!="numeric") x<-as.numeric(x)
if(class(m)!="numeric") m<-as.numeric(m)
nosect<-dim(A)[1]
A<-(A/y)
w<-y/(y-x+m)
dij<-A*w
d.inv<-solve(diag(nosect)-dij)
u<-cbind(rep(1,nosect))
U<-d.inv%*%u
if(write.xlsx==TRUE)write.xlsx(U, file=name, sheetName="Sheet1", showNA=TRUE)
U
}
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