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```
#' function roundcube
#'
#'
#' This function rounds small counts in a set of hypercubes D produced by the function redcube
#' and searches for a solution with smallest possible deviations from the original hypercube at
#' some aggregated levels.
#'
#' @encoding UTF8
#'
#' @param rc The list of outpts from redcube
#' @param sort An ordered list of variables in hypercubes in D meant for priority sorting of the reduced
#' hypercube B before rounding. Not all variables in D should be included.
#' @param control A list of marginals of the hypercubes in D where deviations of aggregated rounded counts
#' are checked against original counts.
#' @param minit Minimum number of searches to be carried out.
#' @param maxit Maximum number of searches to be carried out.
#' @param maxdiff If maximum difference in "control" is no larger than maxit, the stop search.
#' @param seed Input seed for first systematic random search.
#'
#' @return
#' Ar: The rounded version of A
#' Br: The rounded version of B
#' D: The original hypercube of interest.
#' Dr: The rounded version of D. The final table of interest.
#' maxdiff: The largest absolute difference between cells D and Dr among cells in the control list.
#' nmaxdiff: The number of occurences if Maxdiff
#'
#' @keywords internal
#'
#' @importFrom stats runif
#'
#' @author Johan Heldal, January 2018
#'
roundcube <- function(rc,sort,control,minit,maxit,maxdiff,seed) {
A <- rc[[1]] # The hypercube dataframe with all cells and variables..
B <- rc[[2]] # The reduced dataframe.
C <- rc[[3]] # The rows in A that are not in B.
D <- rc[[4]] # The tables/hypercubes of interest.
Dr <-rc[[5]] # The small counts (<b) in D.
b <- rc[[6]] # The rounding base.
d <- rc[[7]] # The list of variabel vectors defining D.
nin <- rc[[8]] # The count variable.
nrB <- nrow(B)
ncB <- ncol(B)
Avars <- colnames(A[,1:(ncB-1)])
#
# Steplength for systematic sampling.
#
ss <- round(sum(B[,nin])/b)
sumn <- sum(B[,nin])
if (sumn>=b/2) {stp <- sumn/ss}
if (sumn<b/2) {stp <- 0}
#
# Calculate control marginals for the reduced matrix B
#
S <- aggrtab(B,control,FALSE,nin=nin,nout=nin)[[2]]
lS <- length(S)
#
# Initiate iterations
#
draw <- rep(0,nrB)
set.seed(seed,kind="Mersenne-Twister")
mmdiff <- 99999
#
# Start iterations
#
iter <- 0
while ((iter <- iter+1) <= maxit) {
#
# For each iteration,sort the records in B by sort*u, u random.
# Result in Bu
#
u <- runif(nrB)
Bu <- cbind(B,u)
colnames(Bu) <- c(colnames(B),"u")
sortvars <- c(sort,"u") # Names of the sort variables
nvsort <- length(sortvars)
sortvars2 <- paste(rep("Bu$",nvsort),sortvars,sep="",collapse=",")
txt <- paste("order(",sortvars2,")")
Bu <- Bu[eval(parse(text=txt)),] # Sorting is carried out
#
# Round: Draw a systematic pps-sample of cells in Bu with steplength stp.
# Set the selected cell counts to b and the rest to 0.
# Result in Bm.
#
csn <- cumsum(Bu[,ncB])
strt <- runif(1)
draw[1] <- strt*stp
for (j in 1:(nrB-1)) {
draw[j+1] <- draw[j] + stp*(csn[j]>= draw[j])
}
m <- b*(csn>=draw) # Rounded reduced counts, this solution
Bm <- cbind(Bu[,Avars],m) # Rounded reduced cube, this solution
#
# Calculate the control marginals Sm for the rounded reduced cube
#
Sm <- aggrtab(Bm,control,FALSE,nin="m",nout="m")[[2]] # List of
Sk <- as.data.frame(NULL) # "Current" original and rounded control table counts and differences.
Sd <- as.data.frame(NULL) #
k <- 0
#cat("iter = ",iter,"\n")
while((k <- k+1) <= lS) {
#cat("k = ",k,"\n")
mm <- Sm[[k]]$m # Frequencies of rounded reduced control table no. k.
Sk <- cbind(S[[k]],mm) # Combine original and rounded counts in reduced control table no. k
diff <- mm - S[[k]][,nin] # Differences between rounded and original controls no. k
Sk <- cbind(Sk,diff)
ncSk <- ncol(Sk)
vSk <- colnames(Sk)
vSk <- c(vSk[(ncSk-2):ncSk],vSk[1:(ncSk-3)]) # Interchange columns
Sk <- Sk[,vSk] # Put "nin", mm and diff first
dk <- vSk[4:ncSk]
if (k==1) {Sd <- Sk}
if (k>1) {
ncSd <- ncol(Sd)
vSd <- colnames(Sd)
dd <- vSd[4:ncSd]
dd_k <- setdiff(dd,dk) # colnames in dd not in dk
dk_d <- setdiff(dk,dd) # colnames in dk not in dd
Sd_k <- as.data.frame(matrix(NA,nrow=nrow(Sd),ncol=length(dk_d)))
colnames(Sd_k) <- dk_d
Sd <- cbind(Sd,Sd_k)
Sk_d <- as.data.frame(matrix(NA,nrow=nrow(Sk),ncol=length(dd_k)))
colnames(Sk_d) <- dd_k
#cat("Sk_d = ","\n")
#print(Sk_d[1:20,])
Sk <- cbind(Sk,Sk_d)
Sk <- Sk[,colnames(Sd)]
Sd <- rbind(Sd,Sk)
vSd <- colnames(Sd)
}
}
mdiff <- max(abs(Sd$diff)) # Maximum diff this iteration
ndiff <- sum(abs(Sd$diff)==mdiff) # No. of occurences of mdiff,this iteration
#cat("iter = ", iter, "mdiff =", mdiff, "ndiff = ", ndiff, "\n")
if (mdiff<mmdiff) {
mmdiff <- mdiff # Maximum difference of so far best solution
nmdiff <- ndiff # No. of occurences of mmdiff in best soltion
Br <- Bm # Br is best reduced solution "so far"
Sr <- Sd # Control tables of the best solution
cat("iter = ",iter," maxdiff = ",mmdiff," nmaxdiff = ",nmdiff,"\n")
}
if ((mdiff==mmdiff)&(ndiff<nmdiff)) {
nmdiff <- ndiff
Br <- Bm
Sr <- Sd
cat("iter = ",iter,", Maxdiff = ",mmdiff,", nmaxdiff = ",nmdiff,"\n")
}
}
# cat("colnames(C) = ", colnames(C), ", dim(C) = ", dim(C), "\n")
# cat("colnames(Br) = ", colnames(Br), ", dim(Br) = ", dim(Br),"\n")
C <- C[,c(Avars,nin)]
Br <- Br[,c(Avars,"m")]
colnames(C) <- colnames(Br)
C <- rbind(C,Br)
# cat("colnames(C) = ", colnames(C), ", dim(C) = ", dim(C),"\n","Avars = ", Avars, "\n")
Cvars2 <- paste(rep("C$",length(Avars)),Avars,sep="",collapse=",")
Ctxt <- paste("order(",Cvars2,")")
# cat("Cvars2 = ",Cvars2,"\n","Ctxt = ",Ctxt,"\n")
C <- C[eval(parse(text=Ctxt)),] # Sorting is carried out
Avars2 <- paste(rep("A$",length(Avars)),Avars,sep="",collapse=", ")
txt <- paste("order(",Avars2,")")
# cat("Avars2 = ",Avars2,"\n","txt = ",txt,"\n")
A <- A[eval(parse(text=txt)),] # Sorting is carried out
# cat("colnames(C) = ", colnames(C), ", dim(C) = ", dim(C),"\n")
# cat("colnames(Br) = ", colnames(Br), ", dim(Br) = ", dim(Br),"\n")
m <- C$m
# cat("dim(A) = ", dim(A), ", length(m) = ", length(m),"\n")
Ar <- cbind(A,m)
cat("colnames(Ar) = ", colnames(Ar), ", dim(Ar) = ", dim(Ar),"\n")
Dr <- aggrtab(Ar,d,FALSE,nin="m",nout="m")[[2]]
return(list(Ar=Ar,Br=Br,D=D,Dr=Dr,Sm=Sm,Sr=Sr,maxdiff=mmdiff,nMaxdiff=nmdiff))
}
```

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