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# Copyright (c) 2013-2020 Stefan Moeding
# All rights reserved.
#
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# modification, are permitted provided that the following conditions
# are met:
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
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#
# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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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)
}
)
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