#'Forecast Calibration based on the ensemble inflation
#'
#'@author Verónica Torralba, \email{veronica.torralba@bsc.es}
#'@description This function applies a variance inflation technique described in Doblas-Reyes et al. (2005) in leave-one-out cross-validation. This bias adjustment method produces calibrated forecasts with equivalent mean and variance to that of the reference dataset, but at the same time preserve reliability. 
#'
#'@references Doblas-Reyes F.J, Hagedorn R, Palmer T.N. The rationale behind the success of multi-model ensembles in seasonal forecasting—II calibration and combination. Tellus A. 2005;57:234–252. doi:10.1111/j.1600-0870.2005.00104.x
#'
#'@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
#'@import multiApply
#'
#'@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 as output of Load function
from s2dverification package.")
  }

  if (dim(data$obs)[which(names(dim(data$obs)) == 'member')] != 1) {
    stop("The length of the dimension 'member' in label 'obs' of parameter 'data' must be equal to 1.")
  }
  
  Calibrated <- Calibration(data$mod, data$obs)
  dimnames <- names(dim(Calibrated))
  Calibrated <- aperm(Calibrated, c(3, 1, 2, 4, 5, 6))
  names(dim(Calibrated)) <- dimnames[c(3, 1, 2, 4, 5, 6)] 
  data$calibration <- Calibrated
  data$obs <- NULL
  data$mod <- NULL
  data <- data[c("calibration", names(data)[-which(names(data) == "calibration")])]
  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 (any(is.na(exp)))  {
    warning("Parameter 'exp' contains NA values.")
  }
  
  if (any(is.na(obs))) {
    warning("Parameter 'obs' contains NA values.")
  }

  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 <- dim(var_exp)[which(names(dim(var_exp)) == 'sdate')][]
  nmembers <- dim(var_exp)[which(names(dim(var_exp)) == 'member')][]

  if (all(names(dim(var_exp)) != c('member','sdate'))) {
    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[ , -t])
    climPred[t] <- mean(var_exp[ , -t])
  }
  var_obs <- var_obs - climObs
 
  calibrated <- NA * var_exp
  for (t in 1 : ntime) {
    # defining forecast,hindcast and observation in cross-validation
    fcst <- NA * var_exp[ , t]
    hcst <- NA * var_exp[ , -t]
    for (i in 1 : nmembers) {
      fcst[i] <- var_exp[i, t] - climPred[t]
      hcst[i, ] <- var_exp[i, -t]- climPred[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)
}