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#' Print an Engression Model Object
#'
#' This function is a utility that displays a summary of a fitted Engression model object.
#'
#' @param x A trained engression model returned from the engressionfit function.
#' @param ... additional arguments (currently ignored)
#'
#' @return This function does not return anything. It prints a summary of the model,
#' including information about its architecture and training process, and the loss
#' values achieved at several epochs during training.
#'
#' @examples
#' \donttest{
#' n = 1000
#' p = 5
#'
#' X = matrix(rnorm(n*p),ncol=p)
#' Y = (X[,1]+rnorm(n)*0.1)^2 + (X[,2]+rnorm(n)*0.1) + rnorm(n)*0.1
#'
#' ## fit engression object
#' engr = engression(X,Y)
#' print(engr)
#' }
#'
#' @export
print.engression <- function(x, ...){
cat("\n engression object with ")
cat("\n \t noise dimensions: ",x$noise_dim)
cat("\n \t hidden dimensions: ",x$hidden_dim)
cat("\n \t number of layers: ",x$num_layer)
cat("\n \t dropout rate: ",x$dropout)
cat("\n \t batch normalization: ",x$batch_norm)
cat("\n \t number of epochs: ",x$num_epochs)
cat("\n \t learning rate: ",x$lr)
cat("\n \t standardization: ",x$standardize)
m = nrow(x$lossvec)
printat = pmax(1, floor(seq(1,m, length=11)))
pr = cbind(printat, x$lossvec[printat,])
colnames(pr) = c("epoch", colnames(x$lossvec))
cat("\n training loss: \n")
print(pr)
cat("\n prediction-loss E(|Y-Yhat|) and variance-loss E(|Yhat-Yhat'|)should ideally be equally large --\n consider training for more epochs if there is a mismatch \n\n")
}
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