#' @export
directions <- function(dr, k) {
    UseMethod("directions")
}

#' Computes projected training data \code{X} for given dimension `k`.
#'
#' Projects the dimensional design matrix \eqn{X} on the columnspace of the
#' cve-estimate for given dimension \eqn{k}.
#'
#' @param dr Instance of \code{'cve'} as returned by \code{\link{cve}}.
#' @param k SDR dimension to use for projection.
#'
#' @return the \eqn{n\times k}{n x k} dimensional matrix \eqn{X B} where \eqn{B}
#'  is the  cve-estimate for dimension \eqn{k}.
#'
#' @examples
#' # create B for simulation (k = 1)
#' B <- rep(1, 5) / sqrt(5)
#' set.seed(21)
#' # creat predictor data x ~ N(0, I_p)
#' x <- matrix(rnorm(500), 100, 5)
#' # simulate response variable
#' #    y = f(B'x) + err
#' # with f(x1) = x1 and err ~ N(0, 0.25^2)
#' y <- x %*% B + 0.25 * rnorm(100)
#' # calculate cve with method 'simple' for k = 1
#' set.seed(21)
#' cve.obj.simple <- cve(y ~ x, k = 1, method = 'simple')
#' # get projected data for k = 1
#' x.proj <- directions(cve.obj.simple, k = 1)
#' # plot y against projected data
#' plot(x.proj, y)
#'
#' @method directions cve
#' @aliases directions directions.cve
#' @export
directions.cve <- function(dr, k) {
    if (!(k %in% names(dr$res))) {
        stop("SDR directions for requested dimension `k` not computed.")
    }
    return(dr$X %*% dr$res[[as.character(k)]]$B)
}