R/elliptic_Z.R

In Carlson: Carlson Elliptic Integrals and Incomplete Elliptic Integrals

#' Jacobi zeta function
#' @description Evaluate the Jacobi zeta function.
#'
#' @param phi amplitude, real or complex number/vector
#' @param m parameter, real or complex number/vector
#' @param minerror bound on relative error passed to \code{\link{elliptic_E}}
#'   and \code{\link{elliptic_F}}
#'
#' @return A complex number or vector, the value(s) of the Jacobi zeta function
#'   \ifelse{html}{\out{Z(φ,m)}}{\eqn{Z(\phi,m)}{Z(phi,m)}}.
#' @export
elliptic_Z <- function(phi, m, minerror = 1e-15) {
  phi <- as.complex(phi)
  m   <- as.complex(m)
  if(length(phi) == 1L) {
    phi <- rep(phi, length(m))
  } else if(length(m) == 1L) {
    m <- rep(m, length(phi))
  } else if(length(phi) != length(m)) {
    stop("Incompatible lengths of `phi` and `m`.")
  }
  ellZcpp(phi, m, minerror)
  # if(is.infinite(Re(m)) && Im(m) == 0){
  #   NaN
  # }else if(m == 1){
  #   if(abs(Re(phi)) <= pi/2){
  #     sin(as.complex(phi))
  #   }else if(Re(phi) > pi/2){
  #     k <- ceiling(Re(phi)/pi - 0.5)
  #     phi <- phi - k*pi
  #     sin(as.complex(phi))
  #   }else{
  #     k <- -floor(0.5 - Re(phi)/pi)
  #     phi <- phi - k*pi
  #     sin(as.complex(phi))
  #   }
  # }else{
  #   elliptic_E(phi, m, minerror) -
  #     elliptic_E(pi/2, m, minerror)/elliptic_F(pi/2, m, minerror) *
  #     elliptic_F(phi, m, minerror)
  # }
}