#*******************************************************************************
# Source file name "BR.r"

# Function returns the fishing mortality vector (by age) 
# when the target condition is met
# Function takes the following arguments:
# - v the variance of the estimated mean
# - mu is the estimated mean stock size
# - f is the fishing mortality
# - A_vec is an age vector fishing mortalities
# - m is natural mortality
# - pred_abund is predator abundance
# - N is actual total population
# - type_ is target type (N or F)
# - target is target value
#*******************************************************************************

A_error <- 0.21    # Expressed as coefficent of variance (CV)
A_bias <- 0.2      # Expressed as a proportion of A

get_F_BQ <- function(v,mu,m,pred_abund,N,type_,target){                       
  # error_lim_F/N is the allowed error 
  error_lim_F <- target/10000
  error_lim_N <- target/10000  
  A <- 1 # Fishing mortality multiplier. Used for a whole year it gives F       
  A_vec <- rep(A,nofageclasses) * selectivity       
  A_hat <- rnorm(1,mean=A*(1+A_bias), sd=A_error*(A*(1+A_bias)))  
  # Error expressed as CV
  alpha <- 1 + (m/A_hat)
  betha <- function(t1){ return ((1-(exp(-(m+A_hat)*t1)))/(1-(exp(-A_hat*t1))))}
  # Get the catch from OPMOD with t1 effort
  g_ <- function(t1) { return (get_hypo_catch_N(t1,A_vec,pred_abund)) }        
  # Here we use the actual A_vec to generate catch. 
  r <- function(t1){ return ((mu-betha(t1)*g_(t1)*(1-(v/mu)))                   
                              /((exp(alpha*A_hat*t1)-1)*(v/mu)+1)) }            
  # Whereas here an estimated A (A_hat) is used.
  if(type_ == "NMSY"){
    # Initial test if fishing should occur
    t1 <- 1e-4
    # Remove the natural mortality that occurs after fishing to the end of year
    assessed_target <- r(t1)*exp((t1-1)*m)  
    if(assessed_target < target) return(A_vec*0)
    # Test if target can be obtained within one year
    t1 <- 1
    assessed_target <- r(t1)*exp((t1-1)*m)
    if(assessed_target > target){ return (A_vec*t1) } 
    # Find t
    t1 <- timestep <- 1  
    # Initial value of assessed_target prepared for the first step in the loop                                                       
    assessed_target <- target + 4*error_lim_N  
    while(abs(target - assessed_target) > error_lim_N){                 
      assessed_target <- r(t1)*exp((t1-1)*m)
      if(assessed_target == target){ return (A_vec*t1) } # Returns the actual F
      if(assessed_target > target){ t1 <- t1 + timestep/2 }
      if(assessed_target < target){ t1 <- t1 - timestep/2 }
      timestep <- timestep/2   
    }
  }
  if(type_ == "FMSY"){
    # Modify target to match non-yearly F
    target <- 1-exp(-target)
    # If target cannot be obtained within one year
    t1 <- 1
    assessed_target <- g_(t1)/(alpha*g_(t1)+r(t1))
    if(assessed_target < target){ return (A_vec*t1) }
    # Find t
    t1 <- timestep <- 1
    # Initial value of assessed_target prepared for the first step in the loop
    assessed_target <- target + 4*error_lim_F  
    while(abs(target - assessed_target) > error_lim_F){
      assessed_target <- g_(t1)/(alpha*g_(t1)+r(t1))   
      if(assessed_target == target){ return (A_vec*t1) } # Returns the actual F
      if(assessed_target > target){ t1 <- t1 - timestep/2 }
      if(assessed_target < target){ t1 <- t1 + timestep/2 } 
      timestep <- timestep/2
    }
  }
  if(type_ == "0"){
    print(paste("mu",mu,sep=" "))
    print(paste("assessed target",assessed_target,sep=" "))
    print(paste("target",target,sep=" "))                       
  }
  return(A_vec*t1)
}
#*******************************************************************************