R/Pwr.R

In nnR: Neural Networks Made Algebraic

source("R/Prd.R")
source("R/Aff.R")
source("R/stacking.R")
source("R/Tun.R")
source("R/aux_fun.R")

#' @title Pwr
#' @description
#' A function that returns the \eqn{\mathsf{Pwr}} neural networks.
#'
#'
#' @param exponent The power to which we will raise. Computation
#' time increases as exponent increases
#' @param q a real number in \eqn{(2,\infty)}. Accuracy as well as computation
#' time increases as \eqn{q} gets closer to \eqn{2} increases
#' @param eps a real number in \eqn{(0,\infty)}. ccuracy as well as computation
#' time increases as \eqn{\varepsilon} gets closer to \eqn{0} increases
#'
#' @return A neural network that approximates raising a number to exponent, when
#' given appropriate \eqn{q,\varepsilon} and exponent when instantiated
#' under ReLU activation at \eqn{x}.
#'
#' @examples
#' Pwr(2.1, 0.1, 2) |> inst(ReLU, 3) # This may take some time, please only click once.
#'
#' @export


Pwr <- function(q, eps, exponent) {
  if (q <= 2) {
    stop("Too small q, q must be > 2")
  } else if (eps <= 0) {
    stop("Too small eps, eps must be > 0")
  } else if (exponent %% 1 != 0 || exponent < 0) {
    stop("Exponent must be a non-negative integer")
  } else {
    if (exponent == 0) {
      Aff(0, 1) -> return_network
      return(return_network)
    } else if (exponent >= 1) {
      Cpy(2, 1) -> first_third
      Pwr(q, eps, exponent - 1) |> stk(Pwr(q, eps, exponent - 1) |> dep() |> Tun()) -> mid_third
      Prd(q, eps) -> last_third
      last_third |>
        comp(mid_third) |>
        comp(first_third) -> return_network
    } else {
      return("Invalid exponent, must be non-negative integer")
    }
    return(return_network)
  }
}

Vectorize(Pwr) -> Pwr