#' @include ShapeForecaster.R
#'
#' @title Neighbors Shape Forecaster
#'
#' @description Predict tomorrow as a weighted combination of "futures of the past" days.
#'   Inherits \code{\link{ShapeForecaster}}
NeighborsShapeForecaster = setRefClass(
	Class = "NeighborsShapeForecaster",
	contains = "ShapeForecaster",

	methods = list(
		initialize = function(...)
		{
			callSuper(...)
		},
		predict = function(today, memory, horizon, ...)
		{
			# (re)initialize computed parameters
			params <<- list("weights"=NA, "indices"=NA, "window"=NA)

			first_day = max(today - memory, 1)
			# The first day is generally not complete:
			if (length(data$getCenteredSerie(1)) < length(data$getCenteredSerie(2)))
				first_day = 2

			# Predict only on non-NAs days (TODO:)
			if (any(is.na(data$getSerie(today))))
				return (NA)

			# Determine indices of no-NAs days followed by no-NAs tomorrows
			fdays_indices = c()
			for (i in first_day:(today-1))
			{
				if ( !any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))) )
					fdays_indices = c(fdays_indices, i)
			}

			#GET OPTIONAL PARAMS
			# Similarity computed with exogenous variables ? endogenous ? both ? ("exo","endo","mix")
			simtype = ifelse(hasArg("simtype"), list(...)$simtype, "exo")
			simthresh = ifelse(hasArg("simthresh"), list(...)$simthresh, 0.)
			kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss")
			mix_strategy = ifelse(hasArg("mix_strategy"), list(...)$mix_strategy, "neighb") #or "mult"
			same_season = ifelse(hasArg("same_season"), list(...)$same_season, TRUE)
			if (hasArg(h_window))
				return (.predictAux(fdays_indices, today, horizon, list(...)$h_window, kernel, simtype,
					simthresh, mix_strategy, FALSE))
			#END GET

			# Indices for cross-validation; TODO: 45 = magic number
			indices = getSimilarDaysIndices(today, limit=45, same_season=same_season)
			#indices = (end_index-45):(end_index-1)

			# Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
			errorOnLastNdays = function(h, kernel, simtype)
			{
				error = 0
				nb_jours = 0
				for (i in indices)
				{
					# NOTE: predict only on non-NAs days followed by non-NAs (TODO:)
					if (!any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))))
					{
						nb_jours = nb_jours + 1
						# mix_strategy is never used here (simtype != "mix"), therefore left blank
						prediction = .predictAux(fdays_indices, i, horizon, h, kernel, simtype, simthresh,
							"", FALSE)
						if (!is.na(prediction[1]))
							error = error + mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
					}
				}
				return (error / nb_jours)
			}

			h_best_exo = 1.
			if (simtype != "endo" && !(simtype=="mix" && mix_strategy=="neighb"))
			{
				h_best_exo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel,
					simtype="exo")$minimum
			}
			if (simtype != "exo")
			{
				h_best_endo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel,
					simtype="endo")$minimum
			}

			if (simtype == "endo")
			{
				return (.predictAux(fdays_indices, today, horizon, h_best_endo, kernel, "endo",
					simthresh, "", TRUE))
			}
			if (simtype == "exo")
			{
				return (.predictAux(fdays_indices, today, horizon, h_best_exo, kernel, "exo",
					simthresh, "", TRUE))
			}
			if (simtype == "mix")
			{
				return (.predictAux(fdays_indices, today, horizon, c(h_best_endo,h_best_exo), kernel,
					"mix", simthresh, mix_strategy, TRUE))
			}
		},
		# Precondition: "today" is full (no NAs)
		.predictAux = function(fdays_indices, today, horizon, h, kernel, simtype, simthresh,
			mix_strategy, final_call)
		{
			dat = data$data #HACK: faster this way...

			fdays_indices = fdays_indices[fdays_indices < today]
			# TODO: 3 = magic number
			if (length(fdays_indices) < 3)
				return (NA)

			if (simtype != "exo")
			{
				h_endo = ifelse(simtype=="mix", h[1], h)

				# Distances from last observed day to days in the past
				distances2 = rep(NA, length(fdays_indices))
				for (i in seq_along(fdays_indices))
				{
					delta = dat[[today]]$serie - dat[[ fdays_indices[i] ]]$serie
					# Require at least half of non-NA common values to compute the distance
					if (sum(is.na(delta)) <= 0) #length(delta)/2)
						distances2[i] = mean(delta^2) #, na.rm=TRUE)
				}

				sd_dist = sd(distances2)
				simils_endo =
					if (kernel=="Gauss") {
						exp(-distances2/(sd_dist*h_endo^2))
					} else { #Epanechnikov
						u = 1 - distances2/(sd_dist*h_endo^2)
						u[abs(u)>1] = 0.
						u
					}
			}

			if (simtype != "endo")
			{
				h_exo = ifelse(simtype=="mix", h[2], h)

				# TODO: [rnormand] if predict_at == 0h then we should use measures from day minus 1
				M = matrix( nrow=1+length(fdays_indices), ncol=1+length(dat[[today]]$exo_hat) )
				M[1,] = c( dat[[today]]$level, as.double(dat[[today]]$exo_hat) )
				for (i in seq_along(fdays_indices))
				{
					M[i+1,] = c( dat[[ fdays_indices[i] ]]$level,
						as.double(dat[[ fdays_indices[i] ]]$exo_hat) )
				}

				sigma = cov(M) #NOTE: robust covariance is way too slow
				sigma_inv = qr.solve(sigma)

				# Distances from last observed day to days in the past
				distances2 = rep(NA, nrow(M)-1)
				for (i in 2:nrow(M))
				{
					delta = M[1,] - M[i,]
					distances2[i-1] = delta %*% sigma_inv %*% delta
				}

				sd_dist = sd(distances2)
				simils_exo =
					if (kernel=="Gauss") {
						exp(-distances2/(sd_dist*h_exo^2))
					} else { #Epanechnikov
						u = 1 - distances2/(sd_dist*h_exo^2)
						u[abs(u)>1] = 0.
						u
					}
			}

			if (simtype=="mix")
			{
				if (mix_strategy == "neighb")
				{
					#Only (60) most similar days according to exogen variables are kept into consideration
					#TODO: 60 = magic number
					keep_indices = sort(simils_exo, index.return=TRUE)$ix[1:(min(60,length(simils_exo)))]
					simils_endo[-keep_indices] = 0.
				} else #mix_strategy == "mult"
				{
					simils_endo = simils_endo * simils_exo
				}
			}

			similarities =
				if (simtype != "exo") {
					simils_endo
				} else {
					simils_exo
				}

			if (simthresh > 0.)
			{
				max_sim = max(similarities)
				# Set to 0 all similarities s where s / max_sim < simthresh, but keep at least 60
				ordering = sort(similarities / max_sim, index.return=TRUE)
				if (ordering[60] < simthresh)
				{
					similarities[ ordering$ix[ - (1:60) ] ] = 0.
				} else
				{
					limit = 61
					while (limit < length(similarities) && ordering[limit] >= simthresh)
						limit = limit + 1
					similarities[ ordering$ix[ - 1:limit] ] = 0.
				}
			}

			prediction = rep(0, horizon)
			for (i in seq_along(fdays_indices))
				prediction = prediction + similarities[i] * dat[[ fdays_indices[i]+1 ]]$serie[1:horizon]

			prediction = prediction / sum(similarities, na.rm=TRUE)
			if (final_call)
			{
				params$weights <<- similarities
				params$indices <<- fdays_indices
				params$window <<-
					if (simtype=="endo") {
						h_endo
					} else if (simtype=="exo") {
						h_exo
					} else {
						c(h_endo,h_exo)
					}
			}
			return (prediction)
		}
	)
)