#' Calibration of a CSTools object based on the ensemble inflation of a forecast following Doblas-Reyes et al. (2005) 
#'
#'@author Verónica Torralba, \email{veronica.torralba@bsc.es}
#'@description This function applies a variance inflation technique described in Doblas-Reyes et al. 2005. The calibrated forecasts have an equivalent variance to that of the reference dataset, but at the same time preserve reliability. 
#'
#'@param data a CSTools object (an s2dverification object as output by the \code{Load} function from the s2dverification package).
#'
#'@return a CSTools object (s2dverification object) with the calibrated forecasts (provided in $mod) with the same dimensions as data$mod.
#'
#'@import s2dverification
#'@examples
#'
#'# Example
#'# Creation of sample s2dverification objects. These are not complete
#'# s2dverification objects though. The Load function returns complete objects.
#'mod1 <- 1 : (1 * 3 * 4 * 5 * 6 * 7)
#'dim(mod1) <- c(dataset = 1, member = 3, sdate = 4, ftime = 5, lat = 6, lon = 7)
#'obs1 <- 1 : (1 * 1 * 4 * 5 * 6 * 7)
#'dim(obs1) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 6, lon = 7)
#'lon <- seq(0, 30, 5)
#'lat <- seq(0, 25, 5)
#'data1 <- list(mod = mod1, obs = obs1, lat = lat, lon = lon)
#'a <- CST_Calibration(data1)
#'str(a)
#'@export

CST_Calibration <- function(data) {
  is_s2dv_object <- function(x) {
    if (all(c('mod', 'obs', 'lon', 'lat') %in% names(x))) { #&& length(x) == 11) {
      TRUE
    } else {
      FALSE
    }
  }
  wrong_input <- FALSE
  if (!is.list(data)) {
    wrong_input <- TRUE
  }
  
  if (!is_s2dv_object(data)) {
    wrong_input <- TRUE
  }
  if (wrong_input) {
    stop("Parameter 'data' must be a list of s2dverification objects as returned by ",
         "the s2dverification::Load function.")
  }

  Calibrated <- Calibration(data$mod, data$obs)
  Calibrated <- aperm(Calibrated, c(3, 1, 2, 4, 5, 6))
  data$mod <- Calibrated
  data$obs <- NULL
  return(data)
}

Calibration <- function(exp, obs) {
  if (!all(c('member', 'sdate') %in% names(dim(exp)))) {
    stop("Parameter 'exp' must have the dimensions 'member' and 'sdate'.")
  }

  if (!all(c('sdate') %in% names(dim(obs)))) {
    stop("Parameter 'obs' must have the dimension 'sdate'.")
  }

  if (length(which(is.na(exp))) > 0) {
    warning('There are NA in exp.')
  }
  
  if (length(which(is.na(obs))) > 0) {
    warning('There are NA in obs.')
  }

  target_dims_obs <- 'sdate'
  if ('member' %in% names(dim(obs))) {
    target_dims_obs <- c('member', target_dims_obs)
  }

  Calibrated <- Apply(data = list(var_obs = obs, var_exp = exp),
                      target_dims = list(target_dims_obs, c('member', 'sdate')),
                      fun = '.cal')$output1

  return(Calibrated)
}

.cal <- function(var_obs, var_exp) {
  ntime <- length(var_obs)
  if (dim(var_exp)[1] != dim(var_exp)[2]) {
    nmembers <- dim(var_exp)[-which(dim(var_exp) == length(var_obs))]
  } else{
    nmembers <- dim(var_exp)[1]
  }
  if (!all(dim(var_exp) == c(nmembers, ntime))) {
    var_exp <- t(var_exp)
  }
  if (!all(dim(var_exp) == c(nmembers, ntime))) {
    var_exp <- t(var_exp)
  }
  climObs <- NA * var_obs
  climPred <- NA * var_obs
  for (t in 1:length(var_obs))
  {
    climObs[t] <- mean(var_obs)
    climPred[t] <- mean(var_exp[,-t])
  }
  var_obs <- var_obs - climObs
  for (i in 1:nmembers) {
    var_exp[i,] <- var_exp[i,] - climPred
  }
  calibrated <- NA * var_exp
  for (t in 1:ntime) {
    # defining forecast,hindcast and observation in cross-validation
    fcst <- var_exp[, t]
    hcst <- var_exp[,-t]
    obs <- var_obs[-t]
    #coefficients
    em_fcst <- mean(fcst)
    em_hcst <- apply(hcst, c(2), mean)
    corr <- cor(em_hcst, obs)
    sd_obs <- sd(obs)
    sd_em_hcst <- sd(em_hcst)
    
    fcst_diff <- fcst - em_fcst
    hcst_diff <- NA * hcst
    for (n in 1:nmembers) {
      hcst_diff[n,] <- hcst[n,] - em_hcst
    }
    sd_hcst_diff <- sd(hcst_diff)
    
    a <- corr * (sd_obs / sd_em_hcst)
    b <- (sd_obs / sd_hcst_diff) * sqrt(1 - (corr ^ 2))
    
    calibrated[, t] <- (a * em_fcst) + (b * fcst_diff) + climObs[t]
  }
  names(dim(calibrated)) <- c('member', 'sdate')
  return(calibrated)
}