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#' Prediction conciliation by projection.
#'
#' Uses a simple L2 projection to reconciliate hierarchical time
#' series forecasts.
#'
#' @param preds_indiv : K-length vector with predictions ybar_1,...,ybar_K for individual regions
#' @param pred_total : number with prediction ybar_* for the total consumption
#' @param weights_indiv : K-length vector with weights a_1,...,a_K for individual regions
#' @param weight_total : number with weight a_* for the total consumption
#' @return A vector with the reconciliated predictions for the
#' individuals and the total.
#' @examples
#' K <- 5
#' proj(preds_indiv = rep(0, K), 1,
#' weights_indiv = rep(1, K),
#' weight_total = 2)
proj <- function(preds_indiv, pred_total,
weights_indiv, weight_total ) {
z <- sum(preds_indiv) - pred_total
suma <- sum(1 / weights_indiv) + 1 / weight_total
s <- z / suma / weights_indiv
return(list(preds = preds_indiv - s))
}
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