#'@rdname CST_Analogs
#'@title Downscaling using Analogs based on large scale fields.
#' 
#'@author Carmen Alvarez-Castro, \email{carmen.alvarez-castro@cmcc.it}
#'@author Nuria Perez-Zanon \email{nuria.perez@bsc.es}
#'        
#'@description This function perform a downscaling using Analogs. To compute 
#'the analogs, the function search for days with similar large scale conditions
#'to downscaled fields in the local scale. 
#'The large scale and the local scale regions are defined by the user.
#'The large scale is usually given by atmospheric circulation as sea level 
#'pressure or geopotential height (Yiou et al, 2013) but the function gives the
#' possibility to use another field. The local scale will be usually given by 
#' precipitation or Temperature, but might be another variable. 
#' The analogs function will find the best analogs based in three criterias:
#' (1) Minimal distance in the large scale pattern (i.e. SLP)
#' (2) Minimal distance in the large scale pattern (i.e. SLP) and minimal 
#' distance in the local scale pattern (i.e. SLP). 
#' (3) Minimal distance in the large scale pattern (i.e. SLP), minimal 
#' distance in the local scale pattern (i.e. SLP) and maxima correlation in the 
#' local variable to downscale (i.e Precipitation).
#' The search of analogs must be done in the longest dataset posible. This is 
#' important since it is necessary to have a good representation of the 
#' possible states of the field in the past, and therefore, to get better 
#' analogs. Once the search of the analogs is complete, and in order to used the 
#' three criterias the user can select a number of analogs nAnalogs to restrict 
#' the selection of the best analogs in a short number of posibilities, the best
#' ones. By default this parameter will be 1.
#' This function has not constrains of specific regions, variables to downscale,
#' or data to be used (seasonal forecast data, climate projections data, 
#' reanalyses data). 
#' The regrid into a finner scale is done interpolating with CST_Load. 
#' Then, this interpolation is corrected selecting the analogs in the large 
#' and local scale in based of the observations. 
#' The function is an adapted version of the method of Yiou et al 2013.       
#'@references Yiou, P., T. Salameh, P. Drobinski, L. Menut, R. Vautard,
#' and M. Vrac, 2013 : Ensemble reconstruction of the atmospheric column 
#' from surface pressure using analogues.  Clim. Dyn., 41, 1419-1437. 
#' \email{pascal.yiou@lsce.ipsl.fr}
#'@param criteria different criteria to be used for the selection of analogs
#'if criteria = "Large_dist"
#'if criteria ="Local_dist"
#'if criteria ="Local_cor"
#'@param expL      variable for the Large scale in the model (same variable 
#'might be used in the local scale for criteria 2)
#'@param obsL      variable for the large scale in the observations
#'@param expVar    variable for the local scale in the model usually different
#'to the variable in expL
#'@param obsVar    variable for the local scale in the observations usually 
#'different to the variable in obsL
#'@param lon_local longitude in the local scale
#'@param lat_local latitude in the local scale
#'@param region  region for the local scale
#'@param nAnalogs  number of Analogs to be selected to apply the criterias (this
#'is not the necessary the number of analogs that the user can get)
#'@param return_list TRUE if you want to get a list with the best analogs FALSE 
#'if not. 
#'@param mAnalogs months for searching the analogs
#'@import multiapply
#'@import ClimProjDiags
#'@import s2dverification
#'@return list  list with the best analogs (time, distance) 
#'@return values values of a certain variable 
#'@example
#'
#'@export
CST_Analogs <- function()
 
  
  
  
  
#'@rdname Analogs
#'@title Search for analogs based on large scale fields.
#' 
#'@author Carmen Alvarez-Castro, \email{carmen.alvarez-castro@cmcc.it}
#'@author Nuria Perez-Zanon \email{nuria.perez@bsc.es}
#'        
#'@description This function search for days with similar large scale 
#'conditions or similar large and local scale conditions. 
#'
#'The large scale and the local scale regions are defined by the user.
#'The large scale is usually given by atmospheric circulation as sea level 
#'pressure or geopotential height (Yiou et al, 2013) but the function gives the
#' possibility to use another field. For the local scale the user can select 
#' any variable. 
#' The analogs function will find the best analogs based in three criterias:
#' (1) Minimal distance in the large scale pattern (i.e. SLP)
#' (2) Minimal distance in the large scale pattern (i.e. SLP) and minimal 
#' distance in the local scale pattern (i.e. SLP). 
#' (3) Minimal distance in the large scale pattern (i.e. SLP), minimal 
#' distance in the local scale pattern (i.e. SLP) and maxima correlation in the 
#' local variable to find the analog (i.e Precipitation).
#' Once the search of the analogs is complete, and in order to used the 
#' three criterias the user can select a number of analogs nAnalogs to restrict 
#' the selection of the best analogs in a short number of posibilities, the best
#' ones. By default this parameter will be 1.
#' This function has not constrains of specific regions, variables to find the
#' analogs, or data to be used (seasonal forecast data, climate projections 
#' data, reanalyses data). 
#' The input data might be interpolated or not. 
#' The function is an adapted version of the method of Yiou et al 2013.       
#'@references Yiou, P., T. Salameh, P. Drobinski, L. Menut, R. Vautard,
#' and M. Vrac, 2013 : Ensemble reconstruction of the atmospheric column 
#' from surface pressure using analogues.  Clim. Dyn., 41, 1419-1437. 
#' \email{pascal.yiou@lsce.ipsl.fr}
#'@param criteria different criteria to be used for the selection of analogs
#'if criteria = "Large_dist"
#'if criteria ="Local_dist"
#'if criteria ="Local_cor"
#'@param expL      variable for the Large scale in the model (same variable 
#'might be used in the local scale for criteria 2)
#'@param obsL      variable for the large scale in the observations
#'@param expVar    variable for the local scale in the model usually different
#'to the variable in expL
#'@param obsVar    variable for the local scale in the observations usually 
#'different to the variable in obsL
#'@param lon_local longitude in the local scale
#'@param lat_local latitude in the local scale
#'@param region  region for the local scale
#'@param nAnalogs  number of Analogs to be selected to apply the criterias (this
#'is not the necessary the number of analogs that the user can get)
#'@param return_list TRUE if you want to get a list with the best analogs FALSE 
#'if not. 
#'@import multiapply
#'@import ClimProjDiags
#'@import s2dverification
#'@return list  list with the best analogs (time, distance) 
#'@return values values of a certain variable 
#'@example
#'
#'@export  
# Analogs <- 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)
#   }
#   
#   Analogs <- Apply(data = list(var_obs = obs, var_exp = exp),
#                       target_dims = list(target_dims_obs, c('member', 'sdate')),
#                       fun = .select)$output1
#   
#   return(Analogs)
# }

time_obsL <- as.Date(c("2005-01-01", "2005-02-01", "2005-03-01",
                       "2005-04-01", "2005-05-01"))
Analogs <- function(expL, obsL, time_obsL, expVar = NULL, obsVar = NULL, 
                    criteria = "Large_dist",
                    lon_local = NULL, lat_local = NULL, region = NULL, 
                    nAnalogs = 1, return_list = FALSE) {
  # checks
  metric <- Select(expL = expL, obsL = obsL,  expVar = expVar, obsVar = obsVar, 
                   criteria = criteria, lon_local = lon_local, lat_local = lat_local,
                   region = region)
  position_best <- Apply(list(metric), target_dims = 'time', fun = BestAnalog,
                criteria = criteria, return = return_list)
  
  time_obsL[position_best]
  obsL[position_best,,,,]
}
#'@example
#'expL <- 1 : (8*10*2*6*7)
dim(expL) <- c(lat = 8, lon = 10, time = 2, member = 6, sdate = 7)
obsL <- 1 : (8*10*5)
dim(obsL) <- c(lat = 8, lon = 10, time = 5)
#'met <- Select(expL = expL, obsL = obsL)
#'lat_local <- lat <- seq(0, 19, 2.5)
lon_local <- lon <- seq(0, 23, 2.5)
met = Select(expL, obsL, criteria = "Local_dist", lon_local = lon, 
             lat_local = lat,
             region = c(lonmin = 0, lonmax = 5, latmin = 0, latmax = 5))
#'dim(met$metric1)
#'str(met)
expL <- 1 : c(8*10*2)
dim(expL) <- c(lat = 8, lon = 10, time = 2)
obsL <- 1 : (8*10*5)
dim(obsL) <- c(lat = 8, lon = 10, time = 5)
met = Select(expL, obsL, criteria = "Local_dist", lon_local = lon, 
             lat_local = lat,
             region = c(lonmin = 0, lonmax = 5, latmin = 0, latmax = 5))
#'pos <- BestAnalog(met)
#'pos <- BestAnalog(met, return_list = TRUE, nAnalogs = 2)
#'pos
res <- Apply(met, target_dims = 'time', fun = BestAnalog, criteria = 'Local_dist')$output1

BestAnalog <- function(metric, criteria = 'Large_dist', return_list = FALSE, 
                       nAnalogs = 1) {
  print(class(metric))
print(length(metric))
    if (criteria == 'Large_dist') {
      pos1 <- metric$pos1
       if (return_list == FALSE) {
          pos <- pos1[1]
       } else {
           pos <- pos1[1 : nAnalogs]
       }
  } else if (criteria== 'Local_dist') {
    # pos1 <- c(7, 13, 5, 3, 6, 12, 10, 1, 8, 9, 11, 4, 2, 14)
    # pos2 <- c(4, 8, 13, 6, 3, 1, 12, 5, 9, 7, 10, 2, 11, 14)
    pos1 <- metric$pos1[1 : nAnalogs]
    pos2 <- metric$pos2[1 : nAnalogs]
    best <- match(pos1, pos2)
    pos <- pos1[as.logical(best)]
    pos <- pos[which(!is.na(pos))]
       if (return_list == FALSE) {
         pos <- pos[1]
       }
  } else if (criteria == 'Local_cor') {
    pos1 <- metric$pos1[1 : nAnalogs]
    pos2 <- metric$pos2[1 : nAnalogs]
    best <- match(pos1, pos2)
    pos <- pos1[as.logical(best)]
    pos <- pos[which(!is.na(pos))]
    # pos3 <- c(6, 11, 14, 3, 13, 7, 2, 5, 1, 12, 10, 9, 8, 4) 
    pos3 <- metric$pos3[1 : nAnalogs]
    best <- match(pos, pos3)
    pos <- pos[order(best, decreasing = F)]
    pos <- pos[which(!is.na(pos))]
      if (return_list == FALSE) {
          pos[1]
      } 
    return(pos)
  }
}

expL <- (1  + 2): (4 * 3 * 2 + 2)
dim(expL) <- c(lat = 4, lon = 3, time = 2)
obsL <- 1 : c(4 * 3 * 5)
dim(obsL) <- c(lat = 4, lon = 3, time = 5)
res = Select(expL, obsL)
expL <- (1  + 2): (8 * 10 * 2 + 2)
dim(expL) <- c(lat = 8, lon = 10, time = 2)
obsL <- 1 : c(8 * 10 * 5)
dim(obsL) <- c(lat = 8, lon = 10, time = 5)
lat_local <- lat <- seq(0, 19, 2.5)
lon_local <- lon <- seq(0, 23, 2.5)
res = Select(expL, obsL, criteria = "Local_dist", lon_local = lon, 
             lat_local = lat,
             region = c(lonmin = 0, lonmax = 5, latmin = 0, latmax = 5))
# probar mas ejemplos con diferentes criterios, latitudes, longitudes
Select <- function(expL, obsL,  expVar = NULL, obsVar = NULL, criteria = "Large_dist",
                   lon_local = NULL, lat_local = NULL, region = NULL) {
  #check expL
  #check obsL
  #check obsVar
  if (any(names(dim(expL)) == 'time')) {
    names(dim(expL))[which(names(dim(expL)) == 'time')] <- 'time_exp'
  }
  metric1 <- Apply(list(obsL), target_dims = list(c('lat', 'lon')), 
                   fun = .select, expL, metric = "dist")$output1
  dim_time_obs <- which(names(dim(metric1)) == 'time')
  margins <- c(1 : length(dim(metric1)))[-dim_time_obs]
  pos1 <- apply(metric1, margins, order)
  names(dim(pos1))[1] <- 'time'
  metric1 <-  apply(metric1, margins, sort)
  names(dim(metric1))[1] <- 'time'

  if (criteria == "Large_dist") {
    return(list(metric1 = metric1, pos1 = pos1))
  }
  if (criteria == "Local_dist" | criteria == "Local_cor") {
    obs <- SelBox(obsL, lon = lon_local, lat = lat_local, region = region)$data
    exp <- SelBox(expL, lon = lon_local, lat = lat_local, region = region)$data
    metric2 <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                     fun = .select, exp, metric = "dist")$output1
    margins <- c(1 : length(dim(metric2)))[-dim_time_obs]
    pos2 <- apply(metric2, margins, order)
    names(dim(pos2))[1] <- 'time'
    metric2 <-  apply(metric2, margins, sort)
    names(dim(metric2))[1] <- 'time'
      if (criteria == "Local_dist") {
        return(list(metric1 = metric1, metric2 = metric2, 
                    pos1 = pos1, pos2 = pos2))
      }   
   }
  if (criteria == "Local_cor") {
    obs <- SelBox(obsVar, lon = lon_local, lat = lat_local, region = region)$data
    exp <- SelBox(expVar, lon = lon_local, lat = lat_local, region = region)$data
    metric3 <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                     fun = .select, exp, metric = "cor")$output1
    margins <- c(1 : length(dim(metric3)))[-dim_time_obs]
    pos3 <- apply(metric3, margins, order, decreasing = TRUE)
    names(dim(pos3))[1] <- 'time'
    metric3 <-  apply(metric3, margins, sort)
    names(dim(metric3))[1] <- 'time'
      return(list(metric1 = metric1, metric2 = metric2, metric3 = metric3, 
                  pos1 = pos1, pos2 = pos2, pos3 = pos3))
    }
  else {
    stop("Parameter 'criteria' must to be one of the: 'Large_dist', ",
         "'Local_dist','Local_cor'.")
  }
}
  
# data <- 1:(20 * 3 * 2 * 4)
# dim(data) <- c(lon = 20, lat = 3, time = 2, model = 4)
# lon <- seq(2, 40, 2)
# lat <- c(1, 5, 10)
# a <- SelBox(data = data, lon = lon, lat = lat, region = c(2, 20, 1, 5),
#             londim = 1, latdim = 2, mask = NULL)
# str(a)
  
#'@example
exp <- (1  + 2): (4 * 3 + 2)
dim(exp) <- c(lat = 4, lon = 3)
obs <- 1 : c(5 * 4 * 3)
dim(obs) <- c(time = 5, lat = 4, lon = 3)
res <- .select(exp, obs)
res
res <- .select(exp, obs, metric = 'cor')
dim(res)
.select <- function(exp, obs, metric = "dist") {
  if (metric == "dist") {
    #metric <- sum((obs - exp) ^ 2)
    #metric <- apply(obs, "time", function(x) {sum((x - exp) ^ 2)})
    result <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                    fun = function(x) {sum((x - exp) ^ 2)})$output1
  } else if (metric == "cor") {
    result <- Apply(list(obs), target_dims = list(c('lat', 'lon')), 
                    fun = function(x) {cor(as.vector(x), as.vector(exp))})$output1
  } 
  result
}
# Add '_exp' label to experiment dimmension if they are not lat and lon but in common with obs:
expL <- 1 : (8*10*2*6*7)
dim(expL) <- c(lat = 8, lon = 10, time = 2, member = 6, sdate = 7)
obsL <- 1 : (8*10*5*3)
dim(obsL) <- c(lat = 8, lon = 10, time = 5, member = 3)
dimnames_exp <- names(dim(expL))
#dimnames_exp <- dimnames_exp[-which(dimnames_exp == 'lat' | dimnames_exp == 'lon')]
dimnames_obs <- names(dim(obsL))
#dimnames_obs <- dimnames_obs[-which(dimnames_obs == 'lat' | dimnames_obs == 'lon')]
which(dimnames_exp == dimnames_obs & dimnames_exp)
dimnames_exp[which(dimnames_exp == dimnames_obs)] <- paste0(dimnames_exp[which(dimnames_exp == dimnames_obs)], "_exp")
names(dim(expL)) <- dimnames_exp

repeat_names <- function(names_exp, names_obs) {
  latlon_dim_exp <- which(names_exp == 'lat' | names_exp == 'lon')
  latlon_dim_obs <- which(names_obs == 'lat' | names_obs == 'lon')
  
  dimnames_obs <- dimnames_obs[-which(dimnames_obs == 'lat' | dimnames_obs == 'lon')]
  
}
#'#This auxiliar function looks for replecated dimension names between two vectors.
#'# The repeated dimensions (different than 'lon' and 'lat') will be replaced in the first 
#'# vector with the same name and extra label '_exp'.
#'# Example for 'time' and member' repeated dim in the same order of names 
#'# dimension for 'expL' and 'obsL'
#'expL <- 1 : (8*10*2*6*7)
#'expL <- 1 :c(8*10*2*6*7)
#'dim(expL) <- c(lat = 8, lon = 10, time = 2, member = 6, sdate = 7)
#'obsL <- 1 : (8*10*5*3)
#'dim(obsL) <- c(lat = 8, time = 5, member = 3, lon = 10)
#'names_exp <- names(dim(expL))
#'names_obs <- names(dim(obsL))
#'replace_repeat_dimnames(names_exp, names_obs)
#'#[1] "lat"        "lon"        "time_exp"   "member_exp" "sdate" 
#'
#' Example for time and memeber repeated with different order
#'dim(obsL) <- c(lon = 10, member = 3, time = 5, lat = 8)
#'names_obs <- names(dim(obsL))
#'replace_repeat_dimnames(names_exp, names_obs)
#'#[1] "lat"        "lon"        "time_exp"   "member_exp" "sdate"     
#'
#'# Example for no repeated names:
#'dim(obsL) <- c(lon = 10, time_obs = 5, member_obs = 3, lat = 8)
#'names_obs <- names(dim(obsL))
#'replace_repeat_dimnames(names_exp, names_obs)
#'#[1] "lat"    "lon"    "time"   "member" "sdate" 
replace_repeat_dimnames <- function(names_exp, names_obs, lat_name = 'lat', lon_name = 'lon') {
  if (!is.character(names_exp)) {
    stop("Parameter 'names_exp' must be a vector of characters.")
  }
  if (!is.character(names_obs)) {
    stop("Parameter 'names_obs' must be a vector of characters.")
  }
  
  latlon_dim_exp <- which(names_exp == lat_name | names_exp == lon_name)
  latlon_dim_obs <- which(names_obs == lat_name | names_obs == lon_name)
  if (any(unlist(lapply(names_exp[-latlon_dim_exp],
                        function(x){x == names_obs[-latlon_dim_obs]})))) {
    original_pos <- lapply(names_exp, function(x) which(x == names_obs[-latlon_dim_obs]))
    original_pos <- lapply(pos,length) > 0
    names_exp[original_pos] <- paste0(names_exp[original_pos], "_exp")
  }
  return(names_exp)
  ## Improvements: other dimensions to avoid replacement for more flexibility.
}