R/gradient.R

In usl: Analyze System Scalability with the Universal Scalability Law

# Copyright (c) 2014-2020 Stefan Moeding
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#
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##############################################################################
#' Calculate gradient for the universal scalability function
#'
#' The implementation of this function has been adopted from the generated
#' output of the \code{\link{deriv}} function.
#'
#' @param x The USL object.
#'
#' @return The gradient matrix.
#'
#' @seealso \code{\link{usl}}
#'
#' @keywords internal
#'
gradient.usl <- function(x) {
  alpha = x@coefficients['alpha']
  beta  = x@coefficients['beta']
  gamma = x@coefficients['gamma']
  n = x@frame[, x@regr, drop = TRUE]

  # Based on the output of:
  # deriv(~ (gamma * n) / (1 + (alpha * (n-1)) + (beta * n * (n-1))), # rhs
  #       c('alpha', 'beta', 'gamma'),                                # params
  #       function(alpha, beta, gamma, n){})                          # args

  expr1 <- gamma * n
  expr2 <- n - 1
  expr3 <- 1 + (alpha * expr2) + (beta * n * expr2)
  expr4 <- expr3 ^ 2

  grad.alpha <- -(expr1 * expr2 / expr4)
  grad.beta  <- -(expr1 * (n * expr2) / expr4)
  grad.gamma <- n / expr3

  matrix(c(grad.alpha, grad.beta, grad.gamma),
         nrow = length(n),
         dimnames = list(1:length(n), x@coef.names))
}