#'Compute the Mean Bias
#'
#'The Mean Bias or Mean Error (Wilks, 2011) is defined as the mean difference 
#'between the ensemble mean forecast and the observations. It is a deterministic
#'metric. Positive values indicate that the forecasts are on average too high
#'and negative values indicate that the forecasts are on average too low; however,
#'it gives no information about the typical magnitude of individual forecast errors.
#'
#'@param exp A named numerical array of the forecast with at least time 
#'  dimension.  
#'@param obs A named numerical array of the observation with at least time 
#'  dimension. The dimensions must be the same as 'exp' except 'memb_dim' and 
#'  'dat_dim'.
#'@param time_dim A character string indicating the name of the time dimension.
#'  The default value is 'sdate'.
#'@param memb_dim A character string indicating the name of the member dimension
#'  to compute the ensemble mean; it should be set to NULL if the parameter 'exp'
#'  is already the ensemble mean. The default value is NULL.
#'@param na.rm A logical value indicating if NAs should be removed (TRUE) or
#'  kept (FALSE) for computation. The default value is FALSE.
#'@param ncores An integer indicating the number of cores to use for parallel 
#'  computation. The default value is NULL.
#'
#'@return
#'A numerical array of Bias with dimensions the dimensions of
#''exp' except 'time_dim' and 'memb_dim' dimensions.
#'
#'@references 
#'Wilks, 2011; https://doi.org/10.1016/B978-0-12-385022-5.00008-7
#'
#'@examples
#'exp <- array(rnorm(1000), dim = c(dat = 1, lat = 3, lon = 5, member = 10, year = 50))
#'obs <- array(rnorm(1000), dim = c(dat = 1, lat = 3, lon = 5, year = 50))
#'bias <- Bias(exp = exp, obs = obs, time_dim = 'year', memb_dim = 'member', na.rm = FALSE, ncores = 1)
#'
#'@import multiApply
#'@export
Bias <- function(exp, obs, time_dim = 'sdate', memb_dim = NULL, na.rm = FALSE, ncores = NULL) {
  
  # Check inputs
  ## exp and obs (1)
  if (!is.array(exp) | !is.numeric(exp))
    stop('Parameter "exp" must be a numeric array.')
  if (!is.array(obs) | !is.numeric(obs))
    stop('Parameter "obs" must be a numeric array.')
  if(any(is.null(names(dim(exp))))| any(nchar(names(dim(exp))) == 0) |
     any(is.null(names(dim(obs))))| any(nchar(names(dim(obs))) == 0)) {
    stop("Parameter 'exp' and 'obs' must have dimension names.")
  }
  ## time_dim
  if (!is.character(time_dim) | length(time_dim) != 1)
    stop('Parameter "time_dim" must be a character string.')
  if (!time_dim %in% names(dim(exp)) | !time_dim %in% names(dim(obs))) {
    stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
  }
  ## memb_dim
  if (!is.character(memb_dim) | length(memb_dim) > 1) {
    stop("Parameter 'memb_dim' must be a character string.")
  }
  if (!memb_dim %in% names(dim(exp))) {
    stop("Parameter 'memb_dim' is not found in 'exp' dimension.")
  }
  ## dat_dim
  # if (!is.null(dat_dim)) {
  #   if (!is.character(dat_dim) | length(dat_dim) > 1) {
  #     stop("Parameter 'dat_dim' must be a character string.")
  #   }
  #   if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
  #     stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.",
  #          " Set it as NULL if there is no dataset dimension.")
  #   }
  # }
  ## exp and obs (2)
  name_exp <- sort(names(dim(exp)))
  name_obs <- sort(names(dim(obs)))
  name_exp <- name_exp[-which(name_exp == memb_dim)]
  if (memb_dim %in% name_obs) {
    name_obs <- name_obs[-which(name_obs == memb_dim)]
  }
  # if (!is.null(dat_dim)) {
  #   name_exp <- name_exp[-which(name_exp == dat_dim)]
  #   name_obs <- name_obs[-which(name_obs == dat_dim)]
  # }
  if (!identical(length(name_exp), length(name_obs)) |
      !identical(dim(exp)[name_exp], dim(obs)[name_obs])) {
    stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
                "all dimensions except 'memb_dim'")) # and 'dat_dim'."))
  }
  ## na.rm
  if (!is.logical(na.rm) | length(na.rm) > 1) {
    stop("Parameter 'na.rm' must be one logical value.")
  }
  ## ncores
  if (!is.null(ncores)) {
    if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 |
        length(ncores) > 1) {
      stop("Parameter 'ncores' must be either NULL or a positive integer.")
    }
  }
  
  ## Ensemble mean
  if (!is.null(memb_dim)) {
    exp <- MeanDims(exp, memb_dim, na.rm = na.rm)
  }
  
  ## Mean bias
  bias <- multiApply::Apply(data = list(exp, obs),
                            target_dims = time_dim,
                            fun = .Bias,
                            ncores = ncores)$output1
  ## Return the mean bias
  bias <- MeanDims(bias, time_dim, na.rm = na.rm)
  
  return(bias)
}

.Bias <- function(exp, obs) {
  bias <- exp - obs
  return(bias)
}