#' use newtons method to find instantaneous f
#' \code{getft} approximates f using newtons method based on catch, life history, and selectivity
#'
#' @author s.j.d. martell
#' @param ct catch
#' @param m natural mortality
#' @param sa selectivity at age
#' @param wa weight at age
#' @param na abundance at age
#'
#' @return instantaneous fishing mortality rate f
#' @export
getFt <- function(ct,m,sa,wa,na)
{ #use newtons root finding method to get ft
ft <- ct/(sum(na*exp(-m/2)*wa*sa))
for(iter in 1:10)
{
t1 <- wa*na
t2 <- exp(-m-ft*sa)
t3 <- (1-t2)
t4 <- m+ft*sa
c1 <- sum(ft*sa*t1*t3/t4)
c2 <- sum(sa*t1*t3/t4 - ft*sa^2*t1*t3/t4^2 + ft*sa^2*t1*t2/t4)
ft <- ft - (c1-ct)/c2 #newton step.
}
return (ft)
}
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