R/predict.R

In usl: Analyze System Scalability with the Universal Scalability Law

# Copyright (c) 2013-2020 Stefan Moeding
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##############################################################################
#' Predict method for Universal Scalability Law models
#'
#' \code{predict} is a function for predictions of the scalability of a system
#' modeled with the Universal Scalability Law. It evaluates the regression
#' function in the frame \code{newdata} (which defaults to
#' \code{model.frame(object)}). Setting \code{interval} to "\code{confidence}"
#' requests the computation of confidence intervals at the specified
#' \code{level}.
#'
#' The parameters \code{alpha} or \code{beta} are useful to do a what-if
#' analysis. Setting these parameters override the model parameters and show
#' how the system would behave with a different contention or coherency delay
#' parameter.
#'
#' \code{predict} internally uses the function returned by
#' \code{\link{scalability,USL-method}} to calculate the result.
#'
#' @param object A USL model object for which prediction is desired.
#' @param newdata An optional data frame in which to look for variables
#'   with which to predict. If omitted, the fitted values are used.
#' @param alpha Optional parameter to be used for evaluation instead of the
#'   parameter computed for the model.
#' @param beta Optional parameter to be used for evaluation instead of the
#'   parameter computed for the model.
#' @param interval Type of interval calculation. Default is to calculate no
#'   confidence interval.
#' @param level Confidence level. Default is 0.95.
#'
#' @return \code{predict} produces a vector of predictions or a matrix of
#'   predictions and bounds with column names \code{fit}, \code{lwr}, and
#'   \code{upr} if \code{interval} is set to "\code{confidence}".
#'
#' @seealso \code{\link{usl}}, \code{\link{scalability,USL-method}},
#'   \code{\link{USL-class}}
#'
#' @references Neil J. Gunther. Guerrilla Capacity Planning: A Tactical
#'   Approach to Planning for Highly Scalable Applications and Services.
#'   Springer, Heidelberg, Germany, 1st edition, 2007.
#'
#' @examples
#' require(usl)
#'
#' data(raytracer)
#'
#' ## Print predicted result from USL model for demo dataset
#' predict(usl(throughput ~ processors, raytracer))
#'
#' ## The same prediction with confidence intervals at the 99% level
#' predict(usl(throughput ~ processors, raytracer),
#'         interval = "confidence", level = 0.99)
#'
#' @export
#'
setMethod(
  f = "predict",
  signature = "USL",
  definition = function(object, newdata, alpha, beta,
                        interval = c("none", "confidence"),
                        level = 0.95) {
    # Predict for the initial data used to create the model
    # if no data frame 'newdata' is given as parameter
    if (missing(newdata)) newdata <- object@frame

    if (missing(alpha)) alpha <- coef(object)[['alpha']]
    if (missing(beta)) beta <- coef(object)[['beta']]

    if (missing(interval)) interval <- "none"

    # Extract regressor variable from data frame
    x <- newdata[, object@regr, drop=TRUE]

    # Calculate values (ignore NA)
    y <- scalability(object, alpha, beta)(x)

    fit <- structure(y, names=row.names(newdata))

    # Return just the vector if the confidence interval is not required
    if (interval != "confidence") return(fit)

    # The following calculation is taken from
    # http://perfdynamics.blogspot.de/2010/09/confidence-bands-for-universal.html
    dof <- length(object@frame[[object@resp]]) - 1L

    y.se  <- sqrt(sum(object@residuals ^ 2) / dof)
    y.ci  <- y.se * qt(level, dof)

    # Create matrix with fitted value and lower/upper confidence interval
    mat <- matrix(c(fit, fit - y.ci, fit + y.ci),
                  nrow = length(fit),
                  dimnames = list(seq(fit), c("fit", "lwr", "upr")))

    return(mat)
  }
)