R/derivative_function.R

In tsiR: An Implementation of the TSIR Model

#' @title derivative
#'
#' @description This function computes an 8 point derivative.
#'
#' @param X The variable to differentiate with respect to.
#' @param Y The function / vector to differentiate.
derivative <- function(X,Y){

  ## compute 9 point derivative
  weights <- c(1/280, -4/105, 1/5, -4/5, 0, 4/5, -1/5, 4/105, -1/280)

  x <- seq(X[1], X[(length(X))], length=1e4)
  y <- approxfun(X, Y)(x)
  y[1] <- 2*y[2] - y[3]

  dx <- diff(x)[1]
  dy <- rep(0,length(y)-8)

  for(i in 5:(length(y)-4)){
    dy[i-4] <- sum(weights * y[(i-4):(i+4)]) / dx
  }

  ## interpolate to match vector length

  dy <- approxfun(seq(X[1], X[length(X)], length=length(dy)), dy)(X)
  #dy <- approx(dy,n=length(X))$y
  return(dy)
}