reindex <- function(u){
  u_square <- as.numeric(u^2)
  result <- list()
  result$u <- as.numeric(u)
  result$s <- c(0:length(u))/length(u)
  result$eta_hat <- rep(0, (length(u) + 1))
  for(i in 2:(length(u) + 1)){
    result$eta_hat[i] <- (sum(u_square[1:floor(result$s[i]*length(u))]) +
                            (result$s[i]*length(u) - floor(result$s[i]*length(u)))*
                            u_square[(floor(result$s[i]*length(u)) + 1)])/sum(u_square)
  }
  result$eta_hat[length(result$eta_hat)] <- 1
  result$eta_hat_inv <- rep(0, (length(u) + 1))
  for(i in 2:(length(u) + 1)){
    s <- i/length(u)
    k <- length(result$eta_hat[result$eta_hat < s])
    result$eta_hat_inv[i] <- (k-1)/length(u) +
      1/(length(u)*(result$eta_hat[k+1] - result$eta_hat[k]))*(s - result$eta_hat[k])
  }
  result$eta_hat_inv[length(result$eta_hat_inv)] <- 1
  result$new_index <- floor(result$eta_hat_inv*length(u))
  return(result)
}