# n = number of cells; k = total number of subjects
# multichoose creates all combinations
multichoose=  function(n, k) 
{
  
  if(k < 0 || n <= 0)
    return(NULL);
  
  if(k == 0) {
    return(list(numeric(n)))
  }
  
  if(n == 1) {
    return(list(k));
  }
  
  arr = multichoose(n - 1, k);
  arr2 = multichoose(n, k - 1);
  
  out = list();
  
  for(i in 1:(length(arr)) ) {
    arr[[i]]= c(0, arr[[i]])
    out= c(out, arr[i]);
  }
  for(i in 1:(length(arr2))  ) {
    arr2[[i]][1]= arr2[[i]][1]+1
    out=c(out,( arr2[i]))
  }
  return(out);
}



# create matrix
createUnbalancedMatrix12 <- function(times=1) {
  m=as.data.frame(t(matrix(unlist(multichoose(4,12)), nrow=4, ncol=455)))
  colnames(m) = c("00","01","10","11")
  #remove balanced 
  m <- m[ -which(m[,1]==3 & m[,2]==3 & m[,3]==3 & m[,4]==3),]
  # select patterns with all cells > 1
  m2 <- m[ which(m[,1]> 1 & m[,2]>1 & m[,3]>1 & m[,4]>1),]
  m2=m2*times
  rownames(m2) <- 1:nrow(m2)
  #nrow(m2)
  
  n=12*times
  Ai=((m2$"10"+m2$"11")-(m2$"00"+m2$"01"))/n
  Bi=((m2$"01"+m2$"11")-(m2$"00"+m2$"10"))/n
  ABi=(m2$"11"-(m2$"00"+m2$"10"+m2$"01"))/n  # 01 coding
  ABi2=((m2$"00"+m2$"11")-(m2$"10"+m2$"01"))/n # -1+1 coding
  ub=round(cbind(Ai,Bi,ABi,ABi2),3)
  invisible(cbind(m2,ub))
}


#(createUnbalancedMatrix12(10)) #test