R/mc_math_elementary.R

In ADtools: Automatic Differentiation Toolbox

element_wise_derivative <- function(f, df) {
  function(x) {                          # nocov
    px <- x@x
    dx <- x@dx

    x@x <- f(px)
    dx <- diag_v0_times_m0(as.numeric(df(px)), dx)
    x@dx <- dx

    return(x)
  }                                      # nocov
}


#' Element-wise square-root of a dual object
#' @param x A "dual" object.
setMethod(
  "sqrt",
  signature(x = "dual"),
  element_wise_derivative(sqrt, function(x) 0.5 / sqrt(x))
)

#' Element-wise sine of a dual object
#' @param x A "dual" object.
setMethod(
  "sin",
  signature(x = "dual"),
  element_wise_derivative(sin, cos)
)

#' Element-wise cosine of a dual object
#' @param x A "dual" object.
setMethod(
  "cos",
  signature(x = "dual"),
  element_wise_derivative(cos, function(x) -sin(x))
)

#' Element-wise tangent of a dual object
#' @param x A "dual" object.
setMethod(
  "tan",
  signature(x = "dual"),
  element_wise_derivative(tan, function(x) cos(x)^{-2})
)

#' Element-wise exponential of a dual object
#' @param x A "dual" object.
setMethod(
  "exp",
  signature(x = "dual"),
  element_wise_derivative(exp, exp)
)

#' Element-wise logarithm of a dual object
#' @param x A "dual" object.
setMethod(
  "log",
  signature(x = "dual"),
  element_wise_derivative(log, function(x) 1 / x)
)

#' Element-wise gamma of a dual object
#' @param x A "dual" object.
setMethod(
  "gamma",
  signature(x = "dual"),
  element_wise_derivative(gamma, function(x) digamma(x) * gamma(x))
)