get_ue0.R

#' get_ue0
#'
#' gets initial scaled reserve.
#' Obtains the initial scaled reserve for eggs given the scaled reserve density at birth.
#' Specification of length at birth as third input by-passes its computation, so if you want to specify an initial value for this quantity, you should use get_lb directly.
#'
#' @param p 1 or 3 -vector with parameters g, k_J/ k_M, v_H^b, see get_lb
#' @param eb optional scalar with scaled reserbe density at birth (default: eb = 1)
#' @param lb0 optional scalar with scaled length at birth (default: lb is optained from get_lb)
#'
#' @return [uE0, lb, info] scaled with scaled reserve at t=0: $U_E^0 g^2 k_M^3/ v^2$ with $U_E^0 = M_E^0/ \{J_{EAm}\}$; lb: scalar with scaled length at birth; info: indicator equals 1 if successful, 0 otherwise
#' @export
#'
#' @examples
#' g = 6; k = 6; kap = .8; uHb = .001; vHb = uHb/ (1 - kap);
#' par = c(g, k, vHb);
get_ue0=function(p, eb = 1, lb0 = NA){
  # created at 2007/07/27 by Bas Kooijman; modified 2010/05/02

  ## Syntax
  # [uE0, lb, info] = <../get_ue0.m *get_ue0*>(p, eb, lb0)

  ## Description
  # Obtains the initial scaled reserve given the scaled reserve density at birth.
  # Function get_ue0 does so for eggs, get_ue0_foetus for foetuses.
  # Specification of length at birth as third input by-passes its computation,
  #   so if you want to specify an initial value for this quantity, you should use get_lb directly.
  #
  # Input
  #
  # * p: 1 or 3 -vector with parameters g, k_J/ k_M, v_H^b, see get_lb
  # * eb: optional scalar with scaled reserbe density at birth
  #   (default: eb = 1)
  # * lb0: optional scalar with scaled length at birth
  #   (default: lb is optained from get_lb)
  #
  # Output
  #
  # * uE0: scaled with scaled reserve at t=0: $U_E^0 g^2 k_M^3/ v^2$
    #   with $U_E^0 = M_E^0/ \{J_{EAm}\}$
    # * lb: scalar with scaled length at birth
  # * info: indicator equals 1 if successful, 0 otherwise

  ## Remarks
  # See <get_ue0_foetus.html *get_ue0_foetus*> for foetal development.
  # See <initial_scaled_reserve.html *initial_scaled_reserve*>, for a non-dimensionless scaling.

  ## Example of use
  # see <../mydata_ue0.m *mydata_ue0*>

  # if (!exists('eb')) {
  #   eb = 1 # maximum value as juvenile
  # }

  if (is.na(lb0)){
    if (length(p) < 3) {
      print('not enough input parameters, see get_lb \n');
      uE0 = NA
      lb = NA
      info = 0
    }
  lbinfo = get_lb(p, eb)
  lb=lbinfo[1]
  info=lbinfo[2]
  } else {
    lb = lb0
    info = 1
  }


  # unpack p
  g = p[1]  # energy investment ratio

  xb = g/ (eb + g)
  uE0 = (3 * g/ (3 * g * xb^(1/ 3)/ lb - beta0(0, xb)))^3

  #print(paste("uE0", uE0))

  return(c(uE0 = unname(uE0), lb = unname(lb), info = unname(info)))
}